diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index d82da9b8..7e104227 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.7","generation_timestamp":"2024-12-22T12:37:04","documenter_version":"1.8.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.7","generation_timestamp":"2024-12-22T18:40:09","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/dev/base/arrays/index.html b/dev/base/arrays/index.html index 256104c7..2efce327 100644 --- a/dev/base/arrays/index.html +++ b/dev/base/arrays/index.html @@ -1760,4 +1760,4 @@ 4 3 2 - 1source
reverse!(A; dims=:)

Like reverse, but operates in-place in A.

Julia 1.6

Multidimensional reverse! requires Julia 1.6.

source
+ 1source
reverse!(A; dims=:)

Like reverse, but operates in-place in A.

Julia 1.6

Multidimensional reverse! requires Julia 1.6.

source
diff --git a/dev/base/base/index.html b/dev/base/base/index.html index 170995b7..9d40b813 100644 --- a/dev/base/base/index.html +++ b/dev/base/base/index.html @@ -1868,4 +1868,4 @@ (true, false)source
Base.isunaryoperator — Function
isunaryoperator(s::Symbol)

Return true if the symbol can be used as a unary (prefix) operator, false otherwise.

Examples

julia> Meta.isunaryoperator(:-), Meta.isunaryoperator(:√), Meta.isunaryoperator(:f)
 (true, true, false)
source
Base.isbinaryoperator — Function
isbinaryoperator(s::Symbol)

Return true if the symbol can be used as a binary (infix) operator, false otherwise.

Examples

julia> Meta.isbinaryoperator(:-), Meta.isbinaryoperator(:√), Meta.isbinaryoperator(:f)
 (true, false, false)
source
Base.Meta.show_sexpr — Function
Meta.show_sexpr([io::IO,], ex)

Show expression ex as a lisp style S-expression.

Examples

julia> Meta.show_sexpr(:(f(x, g(y,z))))
-(:call, :f, :x, (:call, :g, :y, :z))
source
+(:call, :f, :x, (:call, :g, :y, :z))source diff --git a/dev/base/c/index.html b/dev/base/c/index.html index 92093aed..753b12ca 100644 --- a/dev/base/c/index.html +++ b/dev/base/c/index.html @@ -105,4 +105,4 @@ julia> isassigned(Ref{Int}()) truesource
Base.Cchar — Type
Cchar

Equivalent to the native char c-type.

source
Base.Cuchar — Type
Cuchar

Equivalent to the native unsigned char c-type (UInt8).

source
Base.Cshort — Type
Cshort

Equivalent to the native signed short c-type (Int16).

source
Base.Cstring — Type
Cstring

A C-style string composed of the native character type Cchars. Cstrings are NUL-terminated. For C-style strings composed of the native wide character type, see Cwstring. For more information about string interoperability with C, see the manual.

source
Base.Cushort — Type
Cushort

Equivalent to the native unsigned short c-type (UInt16).

source
Base.Cint — Type
Cint

Equivalent to the native signed int c-type (Int32).

source
Base.Cuint — Type
Cuint

Equivalent to the native unsigned int c-type (UInt32).

source
Base.Clong — Type
Clong

Equivalent to the native signed long c-type.

source
Base.Culong — Type
Culong

Equivalent to the native unsigned long c-type.

source
Base.Clonglong — Type
Clonglong

Equivalent to the native signed long long c-type (Int64).

source
Base.Culonglong — Type
Culonglong

Equivalent to the native unsigned long long c-type (UInt64).

source
Base.Cintmax_t — Type
Cintmax_t

Equivalent to the native intmax_t c-type (Int64).

source
Base.Cuintmax_t — Type
Cuintmax_t

Equivalent to the native uintmax_t c-type (UInt64).

source
Base.Csize_t — Type
Csize_t

Equivalent to the native size_t c-type (UInt).

source
Base.Cssize_t — Type
Cssize_t

Equivalent to the native ssize_t c-type.

source
Base.Cptrdiff_t — Type
Cptrdiff_t

Equivalent to the native ptrdiff_t c-type (Int).

source
Base.Cwchar_t — Type
Cwchar_t

Equivalent to the native wchar_t c-type (Int32).

source
Base.Cwstring — Type
Cwstring

A C-style string composed of the native wide character type Cwchar_ts. Cwstrings are NUL-terminated. For C-style strings composed of the native character type, see Cstring. For more information about string interoperability with C, see the manual.

source
Base.Cfloat — Type
Cfloat

Equivalent to the native float c-type (Float32).

source
Base.Cdouble — Type
Cdouble

Equivalent to the native double c-type (Float64).

source

LLVM 接口

Core.Intrinsics.llvmcall — Function
llvmcall(fun_ir::String, returntype, Tuple{argtype1, ...}, argvalue1, ...)
 llvmcall((mod_ir::String, entry_fn::String), returntype, Tuple{argtype1, ...}, argvalue1, ...)
-llvmcall((mod_bc::Vector{UInt8}, entry_fn::String), returntype, Tuple{argtype1, ...}, argvalue1, ...)

Call the LLVM code provided in the first argument. There are several ways to specify this first argument:

  • as a literal string, representing function-level IR (similar to an LLVM define block), with arguments are available as consecutive unnamed SSA variables (%0, %1, etc.);
  • as a 2-element tuple, containing a string of module IR and a string representing the name of the entry-point function to call;
  • as a 2-element tuple, but with the module provided as an Vector{UInt8} with bitcode.

Note that contrary to ccall, the argument types must be specified as a tuple type, and not a tuple of types. All types, as well as the LLVM code, should be specified as literals, and not as variables or expressions (it may be necessary to use @eval to generate these literals).

See test/llvmcall.jl for usage examples.

source
+llvmcall((mod_bc::Vector{UInt8}, entry_fn::String), returntype, Tuple{argtype1, ...}, argvalue1, ...)

Call the LLVM code provided in the first argument. There are several ways to specify this first argument:

Note that contrary to ccall, the argument types must be specified as a tuple type, and not a tuple of types. All types, as well as the LLVM code, should be specified as literals, and not as variables or expressions (it may be necessary to use @eval to generate these literals).

See test/llvmcall.jl for usage examples.

source diff --git a/dev/base/collections/index.html b/dev/base/collections/index.html index 7404c62e..4847a308 100644 --- a/dev/base/collections/index.html +++ b/dev/base/collections/index.html @@ -1633,4 +1633,4 @@ julia> replace.(["xops", "oxps"], "x" => "o") 2-element Vector{String}: "oops" - "oops"source
Base.Pairs — Type
Iterators.Pairs(values, keys) <: AbstractDict{eltype(keys), eltype(values)}

Transforms an indexable container into a Dictionary-view of the same data. Modifying the key-space of the underlying data may invalidate this object.

source
+ "oops"source
Base.Pairs — Type
Iterators.Pairs(values, keys) <: AbstractDict{eltype(keys), eltype(values)}

Transforms an indexable container into a Dictionary-view of the same data. Modifying the key-space of the underlying data may invalidate this object.

source
diff --git a/dev/base/constants/index.html b/dev/base/constants/index.html index bfebe171..c0f5f347 100644 --- a/dev/base/constants/index.html +++ b/dev/base/constants/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

常量

Base.PROGRAM_FILE — Constant
PROGRAM_FILE

A string containing the script name passed to Julia from the command line. Note that the script name remains unchanged from within included files. Alternatively see @__FILE__.

source
Base.ARGS — Constant
ARGS

An array of the command line arguments passed to Julia, as strings.

source
Base.C_NULL — Constant
C_NULL

The C null pointer constant, sometimes used when calling external code.

source
Base.DEPOT_PATH — Constant
DEPOT_PATH

A stack of "depot" locations where the package manager, as well as Julia's code loading mechanisms, look for package registries, installed packages, named environments, repo clones, cached compiled package images, and configuration files. By default it includes:

  1. ~/.julia where ~ is the user home as appropriate on the system;
  2. an architecture-specific shared system directory, e.g. /usr/local/share/julia;
  3. an architecture-independent shared system directory, e.g. /usr/share/julia.

So DEPOT_PATH might be:

[joinpath(homedir(), ".julia"), "/usr/local/share/julia", "/usr/share/julia"]

The first entry is the "user depot" and should be writable by and owned by the current user. The user depot is where: registries are cloned, new package versions are installed, named environments are created and updated, package repos are cloned, newly compiled package image files are saved, log files are written, development packages are checked out by default, and global configuration data is saved. Later entries in the depot path are treated as read-only and are appropriate for registries, packages, etc. installed and managed by system administrators.

DEPOT_PATH is populated based on the JULIA_DEPOT_PATH environment variable if set.

DEPOT_PATH contents

Each entry in DEPOT_PATH is a path to a directory which contains subdirectories used by Julia for various purposes. Here is an overview of some of the subdirectories that may exist in a depot:

  • artifacts: Contains content that packages use for which Pkg manages the installation of.
  • clones: Contains full clones of package repos. Maintained by Pkg.jl and used as a cache.
  • config: Contains julia-level configuration such as a startup.jl
  • compiled: Contains precompiled *.ji files for packages. Maintained by Julia.
  • dev: Default directory for Pkg.develop. Maintained by Pkg.jl and the user.
  • environments: Default package environments. For instance the global environment for a specific julia version. Maintained by Pkg.jl.
  • logs: Contains logs of Pkg and REPL operations. Maintained by Pkg.jl and Julia.
  • packages: Contains packages, some of which were explicitly installed and some which are implicit dependencies. Maintained by Pkg.jl.
  • registries: Contains package registries. By default only General. Maintained by Pkg.jl.
  • scratchspaces: Contains content that a package itself installs via the Scratch.jl package. Pkg.gc() will delete content that is known to be unused.
Note

Packages that want to store content should use the scratchspaces subdirectory via Scratch.jl instead of creating new subdirectories in the depot root.

See also JULIA_DEPOT_PATH, and Code Loading.

source
Base.LOAD_PATH — Constant
LOAD_PATH

An array of paths for using and import statements to consider as project environments or package directories when loading code. It is populated based on the JULIA_LOAD_PATH environment variable if set; otherwise it defaults to ["@", "@v#.#", "@stdlib"]. Entries starting with @ have special meanings:

  • @ refers to the "current active environment", the initial value of which is initially determined by the JULIA_PROJECT environment variable or the --project command-line option.

  • @stdlib expands to the absolute path of the current Julia installation's standard library directory.

  • @name refers to a named environment, which are stored in depots (see JULIA_DEPOT_PATH) under the environments subdirectory. The user's named environments are stored in ~/.julia/environments so @name would refer to the environment in ~/.julia/environments/name if it exists and contains a Project.toml file. If name contains # characters, then they are replaced with the major, minor and patch components of the Julia version number. For example, if you are running Julia 1.2 then @v#.# expands to @v1.2 and will look for an environment by that name, typically at ~/.julia/environments/v1.2.

The fully expanded value of LOAD_PATH that is searched for projects and packages can be seen by calling the Base.load_path() function.

See also JULIA_LOAD_PATH, JULIA_PROJECT, JULIA_DEPOT_PATH, and Code Loading.

source
Base.Sys.BINDIR — Constant
Sys.BINDIR::String

A string containing the full path to the directory containing the julia executable.

source
Base.Sys.CPU_THREADS — Constant
Sys.CPU_THREADS::Int

The number of logical CPU cores available in the system, i.e. the number of threads that the CPU can run concurrently. Note that this is not necessarily the number of CPU cores, for example, in the presence of hyper-threading.

See Hwloc.jl or CpuId.jl for extended information, including number of physical cores.

source
Base.Sys.KERNEL — Constant
Sys.KERNEL::Symbol

A symbol representing the name of the operating system, as returned by uname of the build configuration.

source
Base.Sys.ARCH — Constant
Sys.ARCH::Symbol

A symbol representing the architecture of the build configuration.

source

参见：

+
Repository

常量

Base.PROGRAM_FILE — Constant
PROGRAM_FILE

A string containing the script name passed to Julia from the command line. Note that the script name remains unchanged from within included files. Alternatively see @__FILE__.

source
Base.ARGS — Constant
ARGS

An array of the command line arguments passed to Julia, as strings.

source
Base.C_NULL — Constant
C_NULL

The C null pointer constant, sometimes used when calling external code.

source
Base.DEPOT_PATH — Constant
DEPOT_PATH

A stack of "depot" locations where the package manager, as well as Julia's code loading mechanisms, look for package registries, installed packages, named environments, repo clones, cached compiled package images, and configuration files. By default it includes:

  1. ~/.julia where ~ is the user home as appropriate on the system;
  2. an architecture-specific shared system directory, e.g. /usr/local/share/julia;
  3. an architecture-independent shared system directory, e.g. /usr/share/julia.

So DEPOT_PATH might be:

[joinpath(homedir(), ".julia"), "/usr/local/share/julia", "/usr/share/julia"]

The first entry is the "user depot" and should be writable by and owned by the current user. The user depot is where: registries are cloned, new package versions are installed, named environments are created and updated, package repos are cloned, newly compiled package image files are saved, log files are written, development packages are checked out by default, and global configuration data is saved. Later entries in the depot path are treated as read-only and are appropriate for registries, packages, etc. installed and managed by system administrators.

DEPOT_PATH is populated based on the JULIA_DEPOT_PATH environment variable if set.

DEPOT_PATH contents

Each entry in DEPOT_PATH is a path to a directory which contains subdirectories used by Julia for various purposes. Here is an overview of some of the subdirectories that may exist in a depot:

  • artifacts: Contains content that packages use for which Pkg manages the installation of.
  • clones: Contains full clones of package repos. Maintained by Pkg.jl and used as a cache.
  • config: Contains julia-level configuration such as a startup.jl
  • compiled: Contains precompiled *.ji files for packages. Maintained by Julia.
  • dev: Default directory for Pkg.develop. Maintained by Pkg.jl and the user.
  • environments: Default package environments. For instance the global environment for a specific julia version. Maintained by Pkg.jl.
  • logs: Contains logs of Pkg and REPL operations. Maintained by Pkg.jl and Julia.
  • packages: Contains packages, some of which were explicitly installed and some which are implicit dependencies. Maintained by Pkg.jl.
  • registries: Contains package registries. By default only General. Maintained by Pkg.jl.
  • scratchspaces: Contains content that a package itself installs via the Scratch.jl package. Pkg.gc() will delete content that is known to be unused.
Note

Packages that want to store content should use the scratchspaces subdirectory via Scratch.jl instead of creating new subdirectories in the depot root.

See also JULIA_DEPOT_PATH, and Code Loading.

source
Base.LOAD_PATH — Constant
LOAD_PATH

An array of paths for using and import statements to consider as project environments or package directories when loading code. It is populated based on the JULIA_LOAD_PATH environment variable if set; otherwise it defaults to ["@", "@v#.#", "@stdlib"]. Entries starting with @ have special meanings:

  • @ refers to the "current active environment", the initial value of which is initially determined by the JULIA_PROJECT environment variable or the --project command-line option.

  • @stdlib expands to the absolute path of the current Julia installation's standard library directory.

  • @name refers to a named environment, which are stored in depots (see JULIA_DEPOT_PATH) under the environments subdirectory. The user's named environments are stored in ~/.julia/environments so @name would refer to the environment in ~/.julia/environments/name if it exists and contains a Project.toml file. If name contains # characters, then they are replaced with the major, minor and patch components of the Julia version number. For example, if you are running Julia 1.2 then @v#.# expands to @v1.2 and will look for an environment by that name, typically at ~/.julia/environments/v1.2.

The fully expanded value of LOAD_PATH that is searched for projects and packages can be seen by calling the Base.load_path() function.

See also JULIA_LOAD_PATH, JULIA_PROJECT, JULIA_DEPOT_PATH, and Code Loading.

source
Base.Sys.BINDIR — Constant
Sys.BINDIR::String

A string containing the full path to the directory containing the julia executable.

source
Base.Sys.CPU_THREADS — Constant
Sys.CPU_THREADS::Int

The number of logical CPU cores available in the system, i.e. the number of threads that the CPU can run concurrently. Note that this is not necessarily the number of CPU cores, for example, in the presence of hyper-threading.

See Hwloc.jl or CpuId.jl for extended information, including number of physical cores.

source
Base.Sys.KERNEL — Constant
Sys.KERNEL::Symbol

A symbol representing the name of the operating system, as returned by uname of the build configuration.

source
Base.Sys.ARCH — Constant
Sys.ARCH::Symbol

A symbol representing the architecture of the build configuration.

source

参见：

diff --git a/dev/base/file/index.html b/dev/base/file/index.html index e5d0333d..8f6f437d 100644 --- a/dev/base/file/index.html +++ b/dev/base/file/index.html @@ -232,4 +232,4 @@ "/" "home" "myuser" - "example.jl"source + "example.jl"source diff --git a/dev/base/io-network/index.html b/dev/base/io-network/index.html index fc5811b1..b2b174e1 100644 --- a/dev/base/io-network/index.html +++ b/dev/base/io-network/index.html @@ -461,4 +461,4 @@ falsesource

网络 I/O

Base.bytesavailable — Function
bytesavailable(io)

Return the number of bytes available for reading before a read from this stream or buffer will block.

Examples

julia> io = IOBuffer("JuliaLang is a GitHub organization");
 
 julia> bytesavailable(io)
-34
source
Base.ntoh — Function
ntoh(x)

Convert the endianness of a value from Network byte order (big-endian) to that used by the Host.

source
Base.hton — Function
hton(x)

Convert the endianness of a value from that used by the Host to Network byte order (big-endian).

source
Base.ltoh — Function
ltoh(x)

Convert the endianness of a value from Little-endian to that used by the Host.

source
Base.htol — Function
htol(x)

Convert the endianness of a value from that used by the Host to Little-endian.

source
Base.ENDIAN_BOM — Constant
ENDIAN_BOM

The 32-bit byte-order-mark indicates the native byte order of the host machine. Little-endian machines will contain the value 0x04030201. Big-endian machines will contain the value 0x01020304.

source
+34source
Base.ntoh — Function
ntoh(x)

Convert the endianness of a value from Network byte order (big-endian) to that used by the Host.

source
Base.hton — Function
hton(x)

Convert the endianness of a value from that used by the Host to Network byte order (big-endian).

source
Base.ltoh — Function
ltoh(x)

Convert the endianness of a value from Little-endian to that used by the Host.

source
Base.htol — Function
htol(x)

Convert the endianness of a value from that used by the Host to Little-endian.

source
Base.ENDIAN_BOM — Constant
ENDIAN_BOM

The 32-bit byte-order-mark indicates the native byte order of the host machine. Little-endian machines will contain the value 0x04030201. Big-endian machines will contain the value 0x01020304.

source
diff --git a/dev/base/iterators/index.html b/dev/base/iterators/index.html index 086a5014..10b45eed 100644 --- a/dev/base/iterators/index.html +++ b/dev/base/iterators/index.html @@ -252,4 +252,4 @@ julia> collect(rest) 2-element Vector{Char}: 'b': ASCII/Unicode U+0062 (category Ll: Letter, lowercase) - 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)source + 'c': ASCII/Unicode U+0063 (category Ll: Letter, lowercase)source diff --git a/dev/base/libc/index.html b/dev/base/libc/index.html index acc37f31..5eabd674 100644 --- a/dev/base/libc/index.html +++ b/dev/base/libc/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

C 标准库

Base.Libc.malloc — Function
malloc(size::Integer) -> Ptr{Cvoid}

Call malloc from the C standard library.

source
Base.Libc.calloc — Function
calloc(num::Integer, size::Integer) -> Ptr{Cvoid}

Call calloc from the C standard library.

source
Base.Libc.realloc — Function
realloc(addr::Ptr, size::Integer) -> Ptr{Cvoid}

Call realloc from the C standard library.

See warning in the documentation for free regarding only using this on memory originally obtained from malloc.

source
Base.memcpy — Function
memcpy(dst::Ptr, src::Ptr, n::Integer) -> Ptr{Cvoid}

Call memcpy from the C standard library.

Julia 1.10

Support for memcpy requires at least Julia 1.10.

source
Base.memmove — Function
memmove(dst::Ptr, src::Ptr, n::Integer) -> Ptr{Cvoid}

Call memmove from the C standard library.

Julia 1.10

Support for memmove requires at least Julia 1.10.

source
Base.memset — Function
memset(dst::Ptr, val, n::Integer) -> Ptr{Cvoid}

Call memset from the C standard library.

Julia 1.10

Support for memset requires at least Julia 1.10.

source
Base.memcmp — Function
memcmp(a::Ptr, b::Ptr, n::Integer) -> Int

Call memcmp from the C standard library.

Julia 1.10

Support for memcmp requires at least Julia 1.9.

source
Base.Libc.free — Function
free(addr::Ptr)

Call free from the C standard library. Only use this on memory obtained from malloc, not on pointers retrieved from other C libraries. Ptr objects obtained from C libraries should be freed by the free functions defined in that library, to avoid assertion failures if multiple libc libraries exist on the system.

source
Base.Libc.errno — Function
errno([code])

Get the value of the C library's errno. If an argument is specified, it is used to set the value of errno.

The value of errno is only valid immediately after a ccall to a C library routine that sets it. Specifically, you cannot call errno at the next prompt in a REPL, because lots of code is executed between prompts.

source
Base.Libc.FormatMessage — Function
FormatMessage(n=GetLastError())

Convert a Win32 system call error code to a descriptive string [only available on Windows].

source
Base.Libc.time — Method
time(t::TmStruct) -> Float64

Converts a TmStruct struct to a number of seconds since the epoch.

source
Base.Libc.strftime — Function
strftime([format], time)

Convert time, given as a number of seconds since the epoch or a TmStruct, to a formatted string using the given format. Supported formats are the same as those in the standard C library.

source
Base.Libc.strptime — Function
strptime([format], timestr)

Parse a formatted time string into a TmStruct giving the seconds, minute, hour, date, etc. Supported formats are the same as those in the standard C library. On some platforms, timezones will not be parsed correctly. If the result of this function will be passed to time to convert it to seconds since the epoch, the isdst field should be filled in manually. Setting it to -1 will tell the C library to use the current system settings to determine the timezone.

source
Base.Libc.TmStruct — Type
TmStruct([seconds])

Convert a number of seconds since the epoch to broken-down format, with fields sec, min, hour, mday, month, year, wday, yday, and isdst.

source
Base.Libc.flush_cstdio — Function
flush_cstdio()

Flushes the C stdout and stderr streams (which may have been written to by external C code).

source
Base.Libc.systemsleep — Function
systemsleep(s::Real)

Suspends execution for s seconds. This function does not yield to Julia's scheduler and therefore blocks the Julia thread that it is running on for the duration of the sleep time.

See also sleep.

source
+
Repository

C 标准库

Base.Libc.malloc — Function
malloc(size::Integer) -> Ptr{Cvoid}

Call malloc from the C standard library.

source
Base.Libc.calloc — Function
calloc(num::Integer, size::Integer) -> Ptr{Cvoid}

Call calloc from the C standard library.

source
Base.Libc.realloc — Function
realloc(addr::Ptr, size::Integer) -> Ptr{Cvoid}

Call realloc from the C standard library.

See warning in the documentation for free regarding only using this on memory originally obtained from malloc.

source
Base.memcpy — Function
memcpy(dst::Ptr, src::Ptr, n::Integer) -> Ptr{Cvoid}

Call memcpy from the C standard library.

Julia 1.10

Support for memcpy requires at least Julia 1.10.

source
Base.memmove — Function
memmove(dst::Ptr, src::Ptr, n::Integer) -> Ptr{Cvoid}

Call memmove from the C standard library.

Julia 1.10

Support for memmove requires at least Julia 1.10.

source
Base.memset — Function
memset(dst::Ptr, val, n::Integer) -> Ptr{Cvoid}

Call memset from the C standard library.

Julia 1.10

Support for memset requires at least Julia 1.10.

source
Base.memcmp — Function
memcmp(a::Ptr, b::Ptr, n::Integer) -> Int

Call memcmp from the C standard library.

Julia 1.10

Support for memcmp requires at least Julia 1.9.

source
Base.Libc.free — Function
free(addr::Ptr)

Call free from the C standard library. Only use this on memory obtained from malloc, not on pointers retrieved from other C libraries. Ptr objects obtained from C libraries should be freed by the free functions defined in that library, to avoid assertion failures if multiple libc libraries exist on the system.

source
Base.Libc.errno — Function
errno([code])

Get the value of the C library's errno. If an argument is specified, it is used to set the value of errno.

The value of errno is only valid immediately after a ccall to a C library routine that sets it. Specifically, you cannot call errno at the next prompt in a REPL, because lots of code is executed between prompts.

source
Base.Libc.FormatMessage — Function
FormatMessage(n=GetLastError())

Convert a Win32 system call error code to a descriptive string [only available on Windows].

source
Base.Libc.time — Method
time(t::TmStruct) -> Float64

Converts a TmStruct struct to a number of seconds since the epoch.

source
Base.Libc.strftime — Function
strftime([format], time)

Convert time, given as a number of seconds since the epoch or a TmStruct, to a formatted string using the given format. Supported formats are the same as those in the standard C library.

source
Base.Libc.strptime — Function
strptime([format], timestr)

Parse a formatted time string into a TmStruct giving the seconds, minute, hour, date, etc. Supported formats are the same as those in the standard C library. On some platforms, timezones will not be parsed correctly. If the result of this function will be passed to time to convert it to seconds since the epoch, the isdst field should be filled in manually. Setting it to -1 will tell the C library to use the current system settings to determine the timezone.

source
Base.Libc.TmStruct — Type
TmStruct([seconds])

Convert a number of seconds since the epoch to broken-down format, with fields sec, min, hour, mday, month, year, wday, yday, and isdst.

source
Base.Libc.flush_cstdio — Function
flush_cstdio()

Flushes the C stdout and stderr streams (which may have been written to by external C code).

source
Base.Libc.systemsleep — Function
systemsleep(s::Real)

Suspends execution for s seconds. This function does not yield to Julia's scheduler and therefore blocks the Julia thread that it is running on for the duration of the sleep time.

See also sleep.

source
diff --git a/dev/base/math/index.html b/dev/base/math/index.html index d783e571..e57d8a26 100644 --- a/dev/base/math/index.html +++ b/dev/base/math/index.html @@ -1080,4 +1080,4 @@ 3 julia> @fastmath(sin(3)) -0.1411200080598672source

自定义二元运算符

某些 unicode 字符可用于定义新的支持中缀表示法的二元运算符。 例如， ⊗(x,y) = kron(x,y) 定义 ⊗ (otimes) 为 Kronecker 积， 并且可以通过中缀语法将它作为一个二元运算符调用： C = A ⊗ B 也可以使用常用的前缀语法 C = ⊗(A,B)。

其他支持这种扩展的字符包括 \odot ⊙ 和 \oplus ⊕

The complete list is in the parser code: https://github.com/JuliaLang/julia/blob/master/src/julia-parser.scm

像 * 一样解析的包括（按优先级排列） * / ÷ % & ⋅ ∘ × |\\| ∩ ∧ ⊗ ⊘ ⊙ ⊚ ⊛ ⊠ ⊡ ⊓ ∗ ∙ ∤ ⅋ ≀ ⊼ ⋄ ⋆ ⋇ ⋉ ⋊ ⋋ ⋌ ⋏ ⋒ ⟑ ⦸ ⦼ ⦾ ⦿ ⧶ ⧷ ⨇ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⨻ ⨼ ⨽ ⩀ ⩃ ⩄ ⩋ ⩍ ⩎ ⩑ ⩓ ⩕ ⩘ ⩚ ⩜ ⩞ ⩟ ⩠ ⫛ ⊍ ▷ ⨝ ⟕ ⟖ ⟗ 像 + 一样解析的包括 + - |\|| ⊕ ⊖ ⊞ ⊟ |++| ∪ ∨ ⊔ ± ∓ ∔ ∸ ≏ ⊎ ⊻ ⊽ ⋎ ⋓ ⟇ ⧺ ⧻ ⨈ ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨩ ⨪ ⨫ ⨬ ⨭ ⨮ ⨹ ⨺ ⩁ ⩂ ⩅ ⩊ ⩌ ⩏ ⩐ ⩒ ⩔ ⩖ ⩗ ⩛ ⩝ ⩡ ⩢ ⩣ 还有许多其他的与箭头、比较和幂相关的符号。

+0.1411200080598672source

自定义二元运算符

某些 unicode 字符可用于定义新的支持中缀表示法的二元运算符。 例如， ⊗(x,y) = kron(x,y) 定义 ⊗ (otimes) 为 Kronecker 积， 并且可以通过中缀语法将它作为一个二元运算符调用： C = A ⊗ B 也可以使用常用的前缀语法 C = ⊗(A,B)。

其他支持这种扩展的字符包括 \odot ⊙ 和 \oplus ⊕

The complete list is in the parser code: https://github.com/JuliaLang/julia/blob/master/src/julia-parser.scm

像 * 一样解析的包括（按优先级排列） * / ÷ % & ⋅ ∘ × |\\| ∩ ∧ ⊗ ⊘ ⊙ ⊚ ⊛ ⊠ ⊡ ⊓ ∗ ∙ ∤ ⅋ ≀ ⊼ ⋄ ⋆ ⋇ ⋉ ⋊ ⋋ ⋌ ⋏ ⋒ ⟑ ⦸ ⦼ ⦾ ⦿ ⧶ ⧷ ⨇ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⨻ ⨼ ⨽ ⩀ ⩃ ⩄ ⩋ ⩍ ⩎ ⩑ ⩓ ⩕ ⩘ ⩚ ⩜ ⩞ ⩟ ⩠ ⫛ ⊍ ▷ ⨝ ⟕ ⟖ ⟗ 像 + 一样解析的包括 + - |\|| ⊕ ⊖ ⊞ ⊟ |++| ∪ ∨ ⊔ ± ∓ ∔ ∸ ≏ ⊎ ⊻ ⊽ ⋎ ⋓ ⟇ ⧺ ⧻ ⨈ ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨩ ⨪ ⨫ ⨬ ⨭ ⨮ ⨹ ⨺ ⩁ ⩂ ⩅ ⩊ ⩌ ⩏ ⩐ ⩒ ⩔ ⩖ ⩗ ⩛ ⩝ ⩡ ⩢ ⩣ 还有许多其他的与箭头、比较和幂相关的符号。

diff --git a/dev/base/multi-threading/index.html b/dev/base/multi-threading/index.html index e1a84c31..966aa4ed 100644 --- a/dev/base/multi-threading/index.html +++ b/dev/base/multi-threading/index.html @@ -200,4 +200,4 @@ 7 julia> x[] -5source
Base.Threads.atomic_fence — Function
Threads.atomic_fence()

Insert a sequential-consistency memory fence

Inserts a memory fence with sequentially-consistent ordering semantics. There are algorithms where this is needed, i.e. where an acquire/release ordering is insufficient.

This is likely a very expensive operation. Given that all other atomic operations in Julia already have acquire/release semantics, explicit fences should not be necessary in most cases.

For further details, see LLVM's fence instruction.

source

ccall using a libuv threadpool (Experimental)

Base.@threadcall — Macro
@threadcall((cfunc, clib), rettype, (argtypes...), argvals...)

The @threadcall macro is called in the same way as ccall but does the work in a different thread. This is useful when you want to call a blocking C function without causing the current julia thread to become blocked. Concurrency is limited by size of the libuv thread pool, which defaults to 4 threads but can be increased by setting the UV_THREADPOOL_SIZE environment variable and restarting the julia process.

Note that the called function should never call back into Julia.

source

Low-level synchronization primitives

These building blocks are used to create the regular synchronization objects.

Base.Threads.SpinLock — Type
SpinLock()

Create a non-reentrant, test-and-test-and-set spin lock. Recursive use will result in a deadlock. This kind of lock should only be used around code that takes little time to execute and does not block (e.g. perform I/O). In general, ReentrantLock should be used instead.

Each lock must be matched with an unlock. If !islocked(lck::SpinLock) holds, trylock(lck) succeeds unless there are other tasks attempting to hold the lock "at the same time."

Test-and-test-and-set spin locks are quickest up to about 30ish contending threads. If you have more contention than that, different synchronization approaches should be considered.

source
+5source
Base.Threads.atomic_fence — Function
Threads.atomic_fence()

Insert a sequential-consistency memory fence

Inserts a memory fence with sequentially-consistent ordering semantics. There are algorithms where this is needed, i.e. where an acquire/release ordering is insufficient.

This is likely a very expensive operation. Given that all other atomic operations in Julia already have acquire/release semantics, explicit fences should not be necessary in most cases.

For further details, see LLVM's fence instruction.

source

ccall using a libuv threadpool (Experimental)

Base.@threadcall — Macro
@threadcall((cfunc, clib), rettype, (argtypes...), argvals...)

The @threadcall macro is called in the same way as ccall but does the work in a different thread. This is useful when you want to call a blocking C function without causing the current julia thread to become blocked. Concurrency is limited by size of the libuv thread pool, which defaults to 4 threads but can be increased by setting the UV_THREADPOOL_SIZE environment variable and restarting the julia process.

Note that the called function should never call back into Julia.

source

Low-level synchronization primitives

These building blocks are used to create the regular synchronization objects.

Base.Threads.SpinLock — Type
SpinLock()

Create a non-reentrant, test-and-test-and-set spin lock. Recursive use will result in a deadlock. This kind of lock should only be used around code that takes little time to execute and does not block (e.g. perform I/O). In general, ReentrantLock should be used instead.

Each lock must be matched with an unlock. If !islocked(lck::SpinLock) holds, trylock(lck) succeeds unless there are other tasks attempting to hold the lock "at the same time."

Test-and-test-and-set spin locks are quickest up to about 30ish contending threads. If you have more contention than that, different synchronization approaches should be considered.

source
diff --git a/dev/base/numbers/index.html b/dev/base/numbers/index.html index 1021586e..d0ea15d4 100644 --- a/dev/base/numbers/index.html +++ b/dev/base/numbers/index.html @@ -363,4 +363,4 @@ julia> big"_" ERROR: ArgumentError: invalid number format _ for BigInt or BigFloat -[...]source +[...]source diff --git a/dev/base/parallel/index.html b/dev/base/parallel/index.html index f7ad2a7c..f78b09e3 100644 --- a/dev/base/parallel/index.html +++ b/dev/base/parallel/index.html @@ -313,4 +313,4 @@ # output notifying... -done

OneWayEvent lets one task to wait for another task's notify. It is a limited communication interface since wait can only be used once from a single task (note the non-atomic assignment of ev.task)

In this example, notify(ev::OneWayEvent) is allowed to call schedule(ev.task) if and only if it modifies the state from OWE_WAITING to OWE_NOTIFYING. This lets us know that the task executing wait(ev::OneWayEvent) is now in the ok branch and that there cannot be other tasks that tries to schedule(ev.task) since their @atomicreplace(ev.state, state => OWE_NOTIFYING) will fail.

+done

OneWayEvent lets one task to wait for another task's notify. It is a limited communication interface since wait can only be used once from a single task (note the non-atomic assignment of ev.task)

In this example, notify(ev::OneWayEvent) is allowed to call schedule(ev.task) if and only if it modifies the state from OWE_WAITING to OWE_NOTIFYING. This lets us know that the task executing wait(ev::OneWayEvent) is now in the ok branch and that there cannot be other tasks that tries to schedule(ev.task) since their @atomicreplace(ev.state, state => OWE_NOTIFYING) will fail.

diff --git a/dev/base/punctuation/index.html b/dev/base/punctuation/index.html index 7a8aeca6..356f010e 100644 --- a/dev/base/punctuation/index.html +++ b/dev/base/punctuation/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

运算符与记号

数学符号与函数的扩展文档在 这里.

符号含义
@the at-sign marks a macro invocation; optionally followed by an argument list
!感叹号是一个表示逻辑否定的前缀算符
a!function names that end with an exclamation mark modify one or more of their arguments by convention
#the number sign (or hash or pound) character begins single line comments
#=when followed by an equals sign, it begins a multi-line comment (these are nestable)
=#end a multi-line comment by immediately preceding the number sign with an equals sign
$the dollar sign is used for string and expression interpolation
%the percent symbol is the remainder operator
^the caret is the exponentiation operator
&single ampersand is bitwise and
&&double ampersands is short-circuiting boolean and
|single pipe character is bitwise or
||double pipe characters is short-circuiting boolean or
⊻the unicode xor character is bitwise exclusive or
~the tilde is an operator for bitwise not
'a trailing apostrophe is the adjoint (that is, the complex transpose) operator Aᴴ
*the asterisk is used for multiplication, including matrix multiplication and string concatenation
/forward slash divides the argument on its left by the one on its right
\backslash operator divides the argument on its right by the one on its left, commonly used to solve matrix equations
()parentheses with no arguments constructs an empty Tuple
(a,...)parentheses with comma-separated arguments constructs a tuple containing its arguments
(a=1,...)parentheses with comma-separated assignments constructs a NamedTuple
(x;y)parentheses can also be used to group one or more semicolon separated expressions
a[]array indexing (calling getindex or setindex!)
[,]vector literal constructor (calling vect)
[;]vertical concatenation (calling vcat or hvcat)
[ ]with space-separated expressions, horizontal concatenation (calling hcat or hvcat)
T{ }curly braces following a type list that type's parameters
{}curly braces can also be used to group multiple where expressions in function declarations
;semicolons separate statements, begin a list of keyword arguments in function declarations or calls, or are used to separate array literals for vertical concatenation
,commas separate function arguments or tuple or array components
?the question mark delimits the ternary conditional operator (used like: conditional ? if_true : if_false)
" "the single double-quote character delimits String literals
""" """three double-quote characters delimits string literals that may contain " and ignore leading indentation
' 'the single-quote character delimits Char (that is, character) literals
` `the backtick character delimits external process (Cmd) literals
A...triple periods are a postfix operator that "splat" their arguments' contents into many arguments of a function call or declare a varargs function that "slurps" up many arguments into a single tuple
a.bsingle periods access named fields in objects/modules (calling getproperty or setproperty!)
f.()periods may also prefix parentheses (like f.(...)) or infix operators (like .+) to perform the function element-wise (calling broadcast)
a:bcolons (:) used as a binary infix operator construct a range from a to b (inclusive) with fixed step size 1
a:s:bcolons (:) used as a ternary infix operator construct a range from a to b (inclusive) with step size s
:when used by themselves, Colons represent all indices within a dimension, frequently combined with indexing
::double-colons represent a type annotation or typeassert, depending on context, frequently used when declaring function arguments
:( )quoted expression
:aSymbol a
<:子类型运算符
>:supertype operator (reverse of subtype operator)
=single equals sign is assignment
==double equals sign is value equality comparison
===triple equals sign is programmatically identical equality comparison
=>right arrow using an equals sign defines a Pair typically used to populate dictionaries
->right arrow using a hyphen defines an anonymous function on a single line
|>pipe operator passes output from the left argument to input of the right argument, usually a function
∘function composition operator (typed with \circ{tab}) combines two functions as though they are a single larger function
_underscores may be assigned values which will not be saved, often used to ignore multiple return values or create repetitive comprehensions
+
Repository

运算符与记号

数学符号与函数的扩展文档在 这里.

符号含义
@the at-sign marks a macro invocation; optionally followed by an argument list
!感叹号是一个表示逻辑否定的前缀算符
a!function names that end with an exclamation mark modify one or more of their arguments by convention
#the number sign (or hash or pound) character begins single line comments
#=when followed by an equals sign, it begins a multi-line comment (these are nestable)
=#end a multi-line comment by immediately preceding the number sign with an equals sign
$the dollar sign is used for string and expression interpolation
%the percent symbol is the remainder operator
^the caret is the exponentiation operator
&single ampersand is bitwise and
&&double ampersands is short-circuiting boolean and
|single pipe character is bitwise or
||double pipe characters is short-circuiting boolean or
⊻the unicode xor character is bitwise exclusive or
~the tilde is an operator for bitwise not
'a trailing apostrophe is the adjoint (that is, the complex transpose) operator Aᴴ
*the asterisk is used for multiplication, including matrix multiplication and string concatenation
/forward slash divides the argument on its left by the one on its right
\backslash operator divides the argument on its right by the one on its left, commonly used to solve matrix equations
()parentheses with no arguments constructs an empty Tuple
(a,...)parentheses with comma-separated arguments constructs a tuple containing its arguments
(a=1,...)parentheses with comma-separated assignments constructs a NamedTuple
(x;y)parentheses can also be used to group one or more semicolon separated expressions
a[]array indexing (calling getindex or setindex!)
[,]vector literal constructor (calling vect)
[;]vertical concatenation (calling vcat or hvcat)
[ ]with space-separated expressions, horizontal concatenation (calling hcat or hvcat)
T{ }curly braces following a type list that type's parameters
{}curly braces can also be used to group multiple where expressions in function declarations
;semicolons separate statements, begin a list of keyword arguments in function declarations or calls, or are used to separate array literals for vertical concatenation
,commas separate function arguments or tuple or array components
?the question mark delimits the ternary conditional operator (used like: conditional ? if_true : if_false)
" "the single double-quote character delimits String literals
""" """three double-quote characters delimits string literals that may contain " and ignore leading indentation
' 'the single-quote character delimits Char (that is, character) literals
` `the backtick character delimits external process (Cmd) literals
A...triple periods are a postfix operator that "splat" their arguments' contents into many arguments of a function call or declare a varargs function that "slurps" up many arguments into a single tuple
a.bsingle periods access named fields in objects/modules (calling getproperty or setproperty!)
f.()periods may also prefix parentheses (like f.(...)) or infix operators (like .+) to perform the function element-wise (calling broadcast)
a:bcolons (:) used as a binary infix operator construct a range from a to b (inclusive) with fixed step size 1
a:s:bcolons (:) used as a ternary infix operator construct a range from a to b (inclusive) with step size s
:when used by themselves, Colons represent all indices within a dimension, frequently combined with indexing
::double-colons represent a type annotation or typeassert, depending on context, frequently used when declaring function arguments
:( )quoted expression
:aSymbol a
<:子类型运算符
>:supertype operator (reverse of subtype operator)
=single equals sign is assignment
==double equals sign is value equality comparison
===triple equals sign is programmatically identical equality comparison
=>right arrow using an equals sign defines a Pair typically used to populate dictionaries
->right arrow using a hyphen defines an anonymous function on a single line
|>pipe operator passes output from the left argument to input of the right argument, usually a function
∘function composition operator (typed with \circ{tab}) combines two functions as though they are a single larger function
_underscores may be assigned values which will not be saved, often used to ignore multiple return values or create repetitive comprehensions
diff --git a/dev/base/reflection/index.html b/dev/base/reflection/index.html index e9e45120..7a51559a 100644 --- a/dev/base/reflection/index.html +++ b/dev/base/reflection/index.html @@ -36,4 +36,4 @@ @ int.jl:53 within `+' 1 ─ %1 = Base.add_int(x, y)::Int64 └── return %1 -) => Int64

Possible values for debuginfo are: :none, :source, and :default. Per default debug information is not printed, but that can be changed by setting Base.IRShow.default_debuginfo[] = :source.

+) => Int64

Possible values for debuginfo are: :none, :source, and :default. Per default debug information is not printed, but that can be changed by setting Base.IRShow.default_debuginfo[] = :source.

diff --git a/dev/base/simd-types/index.html b/dev/base/simd-types/index.html index c1fb2a87..5ea90b8a 100644 --- a/dev/base/simd-types/index.html +++ b/dev/base/simd-types/index.html @@ -16,4 +16,4 @@ triple(c::m128) = add(add(c,c),c) -code_native(triple,(m128,))

然而，因为无法依靠自动向量化，以后将主要通过使用基于 llvmcall 的库来提供 SIMD 支持。

+code_native(triple,(m128,))

然而，因为无法依靠自动向量化，以后将主要通过使用基于 llvmcall 的库来提供 SIMD 支持。

diff --git a/dev/base/sort/index.html b/dev/base/sort/index.html index ac9dbc16..2f18f1c2 100644 --- a/dev/base/sort/index.html +++ b/dev/base/sort/index.html @@ -428,4 +428,4 @@ julia> partialsortperm!(ix, v, 2:3) 2-element view(::Vector{Int64}, 2:3) with eltype Int64: 4 - 3
source

排序算法

目前，Julia Base 中有四种可用的排序算法：

By default, the sort family of functions uses stable sorting algorithms that are fast on most inputs. The exact algorithm choice is an implementation detail to allow for future performance improvements. Currently, a hybrid of RadixSort, ScratchQuickSort, InsertionSort, and CountingSort is used based on input type, size, and composition. Implementation details are subject to change but currently available in the extended help of ??Base.DEFAULT_STABLE and the docstrings of internal sorting algorithms listed there.

You can explicitly specify your preferred algorithm with the alg keyword (e.g. sort!(v, alg=PartialQuickSort(10:20))) or reconfigure the default sorting algorithm for custom types by adding a specialized method to the Base.Sort.defalg function. For example, InlineStrings.jl defines the following method:

Base.Sort.defalg(::AbstractArray{<:Union{SmallInlineStrings, Missing}}) = InlineStringSort
Julia 1.9

The default sorting algorithm (returned by Base.Sort.defalg) is guaranteed to be stable since Julia 1.9. Previous versions had unstable edge cases when sorting numeric arrays.

Alternate Orderings

By default, sort, searchsorted, and related functions use isless to compare two elements in order to determine which should come first. The Base.Order.Ordering abstract type provides a mechanism for defining alternate orderings on the same set of elements: when calling a sorting function like sort!, an instance of Ordering can be provided with the keyword argument order.

Instances of Ordering define an order through the Base.Order.lt function, which works as a generalization of isless. This function's behavior on custom Orderings must satisfy all the conditions of a strict weak order. See sort! for details and examples of valid and invalid lt functions.

Base.Order.Ordering — Type
Base.Order.Ordering

Abstract type which represents a total order on some set of elements.

Use Base.Order.lt to compare two elements according to the ordering.

source
Base.Order.lt — Function
lt(o::Ordering, a, b)

Test whether a is less than b according to the ordering o.

source
Base.Order.ord — Function
ord(lt, by, rev::Union{Bool, Nothing}, order::Ordering=Forward)

Construct an Ordering object from the same arguments used by sort!. Elements are first transformed by the function by (which may be identity) and are then compared according to either the function lt or an existing ordering order. lt should be isless or a function that obeys the same rules as the lt parameter of sort!. Finally, the resulting order is reversed if rev=true.

Passing an lt other than isless along with an order other than Base.Order.Forward or Base.Order.Reverse is not permitted, otherwise all options are independent and can be used together in all possible combinations.

source
Base.Order.Forward — Constant
Base.Order.Forward

Default ordering according to isless.

source
Base.Order.ReverseOrdering — Type
ReverseOrdering(fwd::Ordering=Forward)

A wrapper which reverses an ordering.

For a given Ordering o, the following holds for all a, b:

lt(ReverseOrdering(o), a, b) == lt(o, b, a)
source
Base.Order.Reverse — Constant
Base.Order.Reverse

Reverse ordering according to isless.

source
Base.Order.By — Type
By(by, order::Ordering=Forward)

Ordering which applies order to elements after they have been transformed by the function by.

source
Base.Order.Lt — Type
Lt(lt)

Ordering that calls lt(a, b) to compare elements. lt must obey the same rules as the lt parameter of sort!.

source
Base.Order.Perm — Type
Perm(order::Ordering, data::AbstractVector)

Ordering on the indices of data where i is less than j if data[i] is less than data[j] according to order. In the case that data[i] and data[j] are equal, i and j are compared by numeric value.

source
+ 3
source

排序算法

目前，Julia Base 中有四种可用的排序算法：

By default, the sort family of functions uses stable sorting algorithms that are fast on most inputs. The exact algorithm choice is an implementation detail to allow for future performance improvements. Currently, a hybrid of RadixSort, ScratchQuickSort, InsertionSort, and CountingSort is used based on input type, size, and composition. Implementation details are subject to change but currently available in the extended help of ??Base.DEFAULT_STABLE and the docstrings of internal sorting algorithms listed there.

You can explicitly specify your preferred algorithm with the alg keyword (e.g. sort!(v, alg=PartialQuickSort(10:20))) or reconfigure the default sorting algorithm for custom types by adding a specialized method to the Base.Sort.defalg function. For example, InlineStrings.jl defines the following method:

Base.Sort.defalg(::AbstractArray{<:Union{SmallInlineStrings, Missing}}) = InlineStringSort
Julia 1.9

The default sorting algorithm (returned by Base.Sort.defalg) is guaranteed to be stable since Julia 1.9. Previous versions had unstable edge cases when sorting numeric arrays.

Alternate Orderings

By default, sort, searchsorted, and related functions use isless to compare two elements in order to determine which should come first. The Base.Order.Ordering abstract type provides a mechanism for defining alternate orderings on the same set of elements: when calling a sorting function like sort!, an instance of Ordering can be provided with the keyword argument order.

Instances of Ordering define an order through the Base.Order.lt function, which works as a generalization of isless. This function's behavior on custom Orderings must satisfy all the conditions of a strict weak order. See sort! for details and examples of valid and invalid lt functions.

Base.Order.Ordering — Type
Base.Order.Ordering

Abstract type which represents a total order on some set of elements.

Use Base.Order.lt to compare two elements according to the ordering.

source
Base.Order.lt — Function
lt(o::Ordering, a, b)

Test whether a is less than b according to the ordering o.

source
Base.Order.ord — Function
ord(lt, by, rev::Union{Bool, Nothing}, order::Ordering=Forward)

Construct an Ordering object from the same arguments used by sort!. Elements are first transformed by the function by (which may be identity) and are then compared according to either the function lt or an existing ordering order. lt should be isless or a function that obeys the same rules as the lt parameter of sort!. Finally, the resulting order is reversed if rev=true.

Passing an lt other than isless along with an order other than Base.Order.Forward or Base.Order.Reverse is not permitted, otherwise all options are independent and can be used together in all possible combinations.

source
Base.Order.Forward — Constant
Base.Order.Forward

Default ordering according to isless.

source
Base.Order.ReverseOrdering — Type
ReverseOrdering(fwd::Ordering=Forward)

A wrapper which reverses an ordering.

For a given Ordering o, the following holds for all a, b:

lt(ReverseOrdering(o), a, b) == lt(o, b, a)
source
Base.Order.Reverse — Constant
Base.Order.Reverse

Reverse ordering according to isless.

source
Base.Order.By — Type
By(by, order::Ordering=Forward)

Ordering which applies order to elements after they have been transformed by the function by.

source
Base.Order.Lt — Type
Lt(lt)

Ordering that calls lt(a, b) to compare elements. lt must obey the same rules as the lt parameter of sort!.

source
Base.Order.Perm — Type
Perm(order::Ordering, data::AbstractVector)

Ordering on the indices of data where i is less than j if data[i] is less than data[j] according to order. In the case that data[i] and data[j] are equal, i and j are compared by numeric value.

source
diff --git a/dev/base/stacktraces/index.html b/dev/base/stacktraces/index.html index cde8ccd6..984fc590 100644 --- a/dev/base/stacktraces/index.html +++ b/dev/base/stacktraces/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

堆栈跟踪

Base.StackTraces.StackFrame — Type
StackFrame

Stack information representing execution context, with the following fields:

  • func::Symbol

    The name of the function containing the execution context.

  • linfo::Union{Core.MethodInstance, Method, Module, Core.CodeInfo, Nothing}

    The MethodInstance or CodeInfo containing the execution context (if it could be found), or Module (for macro expansions)"

  • file::Symbol

    The path to the file containing the execution context.

  • line::Int

    The line number in the file containing the execution context.

  • from_c::Bool

    True if the code is from C.

  • inlined::Bool

    True if the code is from an inlined frame.

  • pointer::UInt64

    Representation of the pointer to the execution context as returned by backtrace.

source
Base.StackTraces.stacktrace — Function
stacktrace([trace::Vector{Ptr{Cvoid}},] [c_funcs::Bool=false]) -> StackTrace

Return a stack trace in the form of a vector of StackFrames. (By default stacktrace doesn't return C functions, but this can be enabled.) When called without specifying a trace, stacktrace first calls backtrace.

source

Base.StackTraces 中以下方法和类型不会被导出，需要显式调用，例如 StackTraces.lookup(ptr)。

Base.StackTraces.lookup — Function
lookup(pointer::Ptr{Cvoid}) -> Vector{StackFrame}

Given a pointer to an execution context (usually generated by a call to backtrace), looks up stack frame context information. Returns an array of frame information for all functions inlined at that point, innermost function first.

source
Base.StackTraces.remove_frames! — Function
remove_frames!(stack::StackTrace, name::Symbol)

Takes a StackTrace (a vector of StackFrames) and a function name (a Symbol) and removes the StackFrame specified by the function name from the StackTrace (also removing all frames above the specified function). Primarily used to remove StackTraces functions from the StackTrace prior to returning it.

source
remove_frames!(stack::StackTrace, m::Module)

Return the StackTrace with all StackFrames from the provided Module removed.

source
+
Repository

堆栈跟踪

Base.StackTraces.StackFrame — Type
StackFrame

Stack information representing execution context, with the following fields:

  • func::Symbol

    The name of the function containing the execution context.

  • linfo::Union{Core.MethodInstance, Method, Module, Core.CodeInfo, Nothing}

    The MethodInstance or CodeInfo containing the execution context (if it could be found), or Module (for macro expansions)"

  • file::Symbol

    The path to the file containing the execution context.

  • line::Int

    The line number in the file containing the execution context.

  • from_c::Bool

    True if the code is from C.

  • inlined::Bool

    True if the code is from an inlined frame.

  • pointer::UInt64

    Representation of the pointer to the execution context as returned by backtrace.

source
Base.StackTraces.stacktrace — Function
stacktrace([trace::Vector{Ptr{Cvoid}},] [c_funcs::Bool=false]) -> StackTrace

Return a stack trace in the form of a vector of StackFrames. (By default stacktrace doesn't return C functions, but this can be enabled.) When called without specifying a trace, stacktrace first calls backtrace.

source

Base.StackTraces 中以下方法和类型不会被导出，需要显式调用，例如 StackTraces.lookup(ptr)。

Base.StackTraces.lookup — Function
lookup(pointer::Ptr{Cvoid}) -> Vector{StackFrame}

Given a pointer to an execution context (usually generated by a call to backtrace), looks up stack frame context information. Returns an array of frame information for all functions inlined at that point, innermost function first.

source
Base.StackTraces.remove_frames! — Function
remove_frames!(stack::StackTrace, name::Symbol)

Takes a StackTrace (a vector of StackFrames) and a function name (a Symbol) and removes the StackFrame specified by the function name from the StackTrace (also removing all frames above the specified function). Primarily used to remove StackTraces functions from the StackTrace prior to returning it.

source
remove_frames!(stack::StackTrace, m::Module)

Return the StackTrace with all StackFrames from the provided Module removed.

source
diff --git a/dev/base/strings/index.html b/dev/base/strings/index.html index 7ceaf182..623ddef7 100644 --- a/dev/base/strings/index.html +++ b/dev/base/strings/index.html @@ -579,4 +579,4 @@ "A" julia> unescape_string("aaa \\g \\n", ['g']) # using `keep` argument -"aaa \\g \n"source +"aaa \\g \n"source diff --git a/dev/devdocs/EscapeAnalysis/index.html b/dev/devdocs/EscapeAnalysis/index.html index ea1bd7e4..51649e36 100644 --- a/dev/devdocs/EscapeAnalysis/index.html +++ b/dev/devdocs/EscapeAnalysis/index.html @@ -245,4 +245,4 @@ ◌ 13 ─ Main.throw(%18)::Union{} ◌ └─── unreachable ◌ 14 ─ return %21

Analysis Usage

analyze_escapes is the entry point to analyze escape information of SSA-IR elements.

Most optimizations like SROA (sroa_pass!) are more effective when applied to an optimized source that the inlining pass (ssa_inlining_pass!) has simplified by resolving inter-procedural calls and expanding callee sources. Accordingly, analyze_escapes is also able to analyze post-inlining IR and collect escape information that is useful for certain memory-related optimizations.

However, since certain optimization passes like inlining can change control flows and eliminate dead code, they can break the inter-procedural validity of escape information. In particularity, in order to collect inter-procedurally valid escape information, we need to analyze a pre-inlining IR.

Because of this reason, analyze_escapes can analyze IRCode at any Julia-level optimization stage, and especially, it is supposed to be used at the following two stages:

Escape information derived by IPO EA is transformed to the ArgEscapeCache data structure and cached globally. By passing an appropriate get_escape_cache callback to analyze_escapes, the escape analysis can improve analysis accuracy by utilizing cached inter-procedural information of non-inlined callees that has been derived by previous IPO EA. More interestingly, it is also valid to use IPO EA escape information for type inference, e.g., inference accuracy can be improved by forming Const/PartialStruct/MustAlias of mutable object.

Since the computational cost of analyze_escapes is not that cheap, both IPO EA and Local EA are better to run only when there is any profitability. Currently EscapeAnalysis provides the is_ipo_profitable heuristic to check a profitability of IPO EA.

Core.Compiler.EscapeAnalysis.analyze_escapes — Function
analyze_escapes(ir::IRCode, nargs::Int, call_resolved::Bool, get_escape_cache::Callable)
-    -> estate::EscapeState

Analyzes escape information in ir:

  • nargs: the number of actual arguments of the analyzed call
  • call_resolved: if interprocedural calls are already resolved by ssa_inlining_pass!
  • get_escape_cache(::Union{InferenceResult,MethodInstance}) -> Union{Nothing,ArgEscapeCache}: retrieves cached argument escape information
source
Core.Compiler.EscapeAnalysis.EscapeState — Type
estate::EscapeState

Extended lattice that maps arguments and SSA values to escape information represented as EscapeInfo. Escape information imposed on SSA IR element x can be retrieved by estate[x].

source
Core.Compiler.EscapeAnalysis.EscapeInfo — Type
x::EscapeInfo

A lattice for escape information, which holds the following properties:

  • x.Analyzed::Bool: not formally part of the lattice, only indicates x has not been analyzed or not
  • x.ReturnEscape::Bool: indicates x can escape to the caller via return
  • x.ThrownEscape::BitSet: records SSA statement numbers where x can be thrown as exception:
    • isempty(x.ThrownEscape): x will never be thrown in this call frame (the bottom)
    • pc ∈ x.ThrownEscape: x may be thrown at the SSA statement at pc
    • -1 ∈ x.ThrownEscape: x may be thrown at arbitrary points of this call frame (the top)
    This information will be used by escape_exception! to propagate potential escapes via exception.
  • x.AliasInfo::Union{Bool,IndexableFields,IndexableElements,Unindexable}: maintains all possible values that can be aliased to fields or array elements of x:
    • x.AliasInfo === false indicates the fields/elements of x aren't analyzed yet
    • x.AliasInfo === true indicates the fields/elements of x can't be analyzed, e.g. the type of x is not known or is not concrete and thus its fields/elements can't be known precisely
    • x.AliasInfo::IndexableFields records all the possible values that can be aliased to fields of object x with precise index information
    • x.AliasInfo::IndexableElements records all the possible values that can be aliased to elements of array x with precise index information
    • x.AliasInfo::Unindexable records all the possible values that can be aliased to fields/elements of x without precise index information
  • x.Liveness::BitSet: records SSA statement numbers where x should be live, e.g. to be used as a call argument, to be returned to a caller, or preserved for :foreigncall:
    • isempty(x.Liveness): x is never be used in this call frame (the bottom)
    • 0 ∈ x.Liveness also has the special meaning that it's a call argument of the currently analyzed call frame (and thus it's visible from the caller immediately).
    • pc ∈ x.Liveness: x may be used at the SSA statement at pc
    • -1 ∈ x.Liveness: x may be used at arbitrary points of this call frame (the top)

There are utility constructors to create common EscapeInfos, e.g.,

  • NoEscape(): the bottom(-like) element of this lattice, meaning it won't escape to anywhere
  • AllEscape(): the topmost element of this lattice, meaning it will escape to everywhere

analyze_escapes will transition these elements from the bottom to the top, in the same direction as Julia's native type inference routine. An abstract state will be initialized with the bottom(-like) elements:

  • the call arguments are initialized as ArgEscape(), whose Liveness property includes 0 to indicate that it is passed as a call argument and visible from a caller immediately
  • the other states are initialized as NotAnalyzed(), which is a special lattice element that is slightly lower than NoEscape, but at the same time doesn't represent any meaning other than it's not analyzed yet (thus it's not formally part of the lattice)
source
Core.Compiler.EscapeAnalysis.is_ipo_profitable — Function
is_ipo_profitable(ir::IRCode, nargs::Int) -> Bool

Heuristically checks if there is any profitability to run the escape analysis on ir and generate IPO escape information cache. Specifically, this function examines if any call argument is "interesting" in terms of their escapability.

source
+ -> estate::EscapeState

Analyzes escape information in ir:

source
Core.Compiler.EscapeAnalysis.EscapeState — Type
estate::EscapeState

Extended lattice that maps arguments and SSA values to escape information represented as EscapeInfo. Escape information imposed on SSA IR element x can be retrieved by estate[x].

source
Core.Compiler.EscapeAnalysis.EscapeInfo — Type
x::EscapeInfo

A lattice for escape information, which holds the following properties:

  • x.Analyzed::Bool: not formally part of the lattice, only indicates x has not been analyzed or not
  • x.ReturnEscape::Bool: indicates x can escape to the caller via return
  • x.ThrownEscape::BitSet: records SSA statement numbers where x can be thrown as exception:
    • isempty(x.ThrownEscape): x will never be thrown in this call frame (the bottom)
    • pc ∈ x.ThrownEscape: x may be thrown at the SSA statement at pc
    • -1 ∈ x.ThrownEscape: x may be thrown at arbitrary points of this call frame (the top)
    This information will be used by escape_exception! to propagate potential escapes via exception.
  • x.AliasInfo::Union{Bool,IndexableFields,IndexableElements,Unindexable}: maintains all possible values that can be aliased to fields or array elements of x:
    • x.AliasInfo === false indicates the fields/elements of x aren't analyzed yet
    • x.AliasInfo === true indicates the fields/elements of x can't be analyzed, e.g. the type of x is not known or is not concrete and thus its fields/elements can't be known precisely
    • x.AliasInfo::IndexableFields records all the possible values that can be aliased to fields of object x with precise index information
    • x.AliasInfo::IndexableElements records all the possible values that can be aliased to elements of array x with precise index information
    • x.AliasInfo::Unindexable records all the possible values that can be aliased to fields/elements of x without precise index information
  • x.Liveness::BitSet: records SSA statement numbers where x should be live, e.g. to be used as a call argument, to be returned to a caller, or preserved for :foreigncall:
    • isempty(x.Liveness): x is never be used in this call frame (the bottom)
    • 0 ∈ x.Liveness also has the special meaning that it's a call argument of the currently analyzed call frame (and thus it's visible from the caller immediately).
    • pc ∈ x.Liveness: x may be used at the SSA statement at pc
    • -1 ∈ x.Liveness: x may be used at arbitrary points of this call frame (the top)

There are utility constructors to create common EscapeInfos, e.g.,

  • NoEscape(): the bottom(-like) element of this lattice, meaning it won't escape to anywhere
  • AllEscape(): the topmost element of this lattice, meaning it will escape to everywhere

analyze_escapes will transition these elements from the bottom to the top, in the same direction as Julia's native type inference routine. An abstract state will be initialized with the bottom(-like) elements:

  • the call arguments are initialized as ArgEscape(), whose Liveness property includes 0 to indicate that it is passed as a call argument and visible from a caller immediately
  • the other states are initialized as NotAnalyzed(), which is a special lattice element that is slightly lower than NoEscape, but at the same time doesn't represent any meaning other than it's not analyzed yet (thus it's not formally part of the lattice)
source
Core.Compiler.EscapeAnalysis.is_ipo_profitable — Function
is_ipo_profitable(ir::IRCode, nargs::Int) -> Bool

Heuristically checks if there is any profitability to run the escape analysis on ir and generate IPO escape information cache. Specifically, this function examines if any call argument is "interesting" in terms of their escapability.

source
diff --git a/dev/devdocs/ast/index.html b/dev/devdocs/ast/index.html index 23af5fcb..f27840ad 100644 --- a/dev/devdocs/ast/index.html +++ b/dev/devdocs/ast/index.html @@ -22,4 +22,4 @@ (block (line 2) (return (call + x 1))))

Type definition:

mutable struct Foo{T<:S}
     x::T
 end

parses as:

(struct true (curly Foo (<: T S))
-        (block (line 2) (:: x T)))

The first argument is a boolean telling whether the type is mutable.

try blocks parse as (try try_block var catch_block finally_block). If no variable is present after catch, var is #f. If there is no finally clause, then the last argument is not present.

Quote expressions

Julia source syntax forms for code quoting (quote and :( )) support interpolation with $. In Lisp terminology, this means they are actually "backquote" or "quasiquote" forms. Internally, there is also a need for code quoting without interpolation. In Julia's scheme code, non-interpolating quote is represented with the expression head inert.

inert expressions are converted to Julia QuoteNode objects. These objects wrap a single value of any type, and when evaluated simply return that value.

A quote expression whose argument is an atom also gets converted to a QuoteNode.

Line numbers

Source location information is represented as (line line_num file_name) where the third component is optional (and omitted when the current line number, but not file name, changes).

These expressions are represented as LineNumberNodes in Julia.

Macros

Macro hygiene is represented through the expression head pair escape and hygienic-scope. The result of a macro expansion is automatically wrapped in (hygienic-scope block module), to represent the result of the new scope. The user can insert (escape block) inside to interpolate code from the caller.

Lowered form

Lowered form (IR) is more important to the compiler, since it is used for type inference, optimizations like inlining, and code generation. It is also less obvious to the human, since it results from a significant rearrangement of the input syntax.

In addition to Symbols and some number types, the following data types exist in lowered form:

Expr types

These symbols appear in the head field of Exprs in lowered form.

Method

A unique'd container describing the shared metadata for a single method.

MethodInstance

A unique'd container describing a single callable signature for a Method. See especially Proper maintenance and care of multi-threading locks for important details on how to modify these fields safely.

CodeInstance

CodeInfo

A (usually temporary) container for holding lowered source code.

Optional Fields:

Boolean properties:

UInt8 settings:

+ (block (line 2) (:: x T)))

The first argument is a boolean telling whether the type is mutable.

try blocks parse as (try try_block var catch_block finally_block). If no variable is present after catch, var is #f. If there is no finally clause, then the last argument is not present.

Quote expressions

Julia source syntax forms for code quoting (quote and :( )) support interpolation with $. In Lisp terminology, this means they are actually "backquote" or "quasiquote" forms. Internally, there is also a need for code quoting without interpolation. In Julia's scheme code, non-interpolating quote is represented with the expression head inert.

inert expressions are converted to Julia QuoteNode objects. These objects wrap a single value of any type, and when evaluated simply return that value.

A quote expression whose argument is an atom also gets converted to a QuoteNode.

Line numbers

Source location information is represented as (line line_num file_name) where the third component is optional (and omitted when the current line number, but not file name, changes).

These expressions are represented as LineNumberNodes in Julia.

Macros

Macro hygiene is represented through the expression head pair escape and hygienic-scope. The result of a macro expansion is automatically wrapped in (hygienic-scope block module), to represent the result of the new scope. The user can insert (escape block) inside to interpolate code from the caller.

Lowered form

Lowered form (IR) is more important to the compiler, since it is used for type inference, optimizations like inlining, and code generation. It is also less obvious to the human, since it results from a significant rearrangement of the input syntax.

In addition to Symbols and some number types, the following data types exist in lowered form:

Expr types

These symbols appear in the head field of Exprs in lowered form.

Method

A unique'd container describing the shared metadata for a single method.

MethodInstance

A unique'd container describing a single callable signature for a Method. See especially Proper maintenance and care of multi-threading locks for important details on how to modify these fields safely.

CodeInstance

CodeInfo

A (usually temporary) container for holding lowered source code.

Optional Fields:

Boolean properties:

UInt8 settings:

diff --git a/dev/devdocs/backtraces/index.html b/dev/devdocs/backtraces/index.html index 67955273..07b39242 100644 --- a/dev/devdocs/backtraces/index.html +++ b/dev/devdocs/backtraces/index.html @@ -21,4 +21,4 @@ Starting program: /home/sabae/src/julia/usr/bin/julia-debug ./test.jl ... (gdb) bt

Create a gist with the backtrace, the version info, and any other pertinent information you can think of and open a new issue on Github with a link to the gist.

Errors during Julia startup

Occasionally errors occur during Julia's startup process (especially when using binary distributions, as opposed to compiling from source) such as the following:

$ julia
-exec: error -5

These errors typically indicate something is not getting loaded properly very early on in the bootup phase, and our best bet in determining what's going wrong is to use external tools to audit the disk activity of the julia process:

Create a gist with the strace/ dtruss output, the version info, and any other pertinent information and open a new issue on Github with a link to the gist.

Other generic segfaults or unreachables reached

As mentioned elsewhere, julia has good integration with rr for generating traces; this includes, on Linux, the ability to automatically run julia under rr and share the trace after a crash. This can be immensely helpful when debugging such crashes and is strongly encouraged when reporting crash issues to the JuliaLang/julia repo. To run julia under rr automatically, do:

julia --bug-report=rr

To generate the rr trace locally, but not share, you can do:

julia --bug-report=rr-local

Note that this is only works on Linux. The blog post on Time Travelling Bug Reporting has many more details.

Glossary

A few terms have been used as shorthand in this guide:

+exec: error -5

These errors typically indicate something is not getting loaded properly very early on in the bootup phase, and our best bet in determining what's going wrong is to use external tools to audit the disk activity of the julia process:

Create a gist with the strace/ dtruss output, the version info, and any other pertinent information and open a new issue on Github with a link to the gist.

Other generic segfaults or unreachables reached

As mentioned elsewhere, julia has good integration with rr for generating traces; this includes, on Linux, the ability to automatically run julia under rr and share the trace after a crash. This can be immensely helpful when debugging such crashes and is strongly encouraged when reporting crash issues to the JuliaLang/julia repo. To run julia under rr automatically, do:

julia --bug-report=rr

To generate the rr trace locally, but not share, you can do:

julia --bug-report=rr-local

Note that this is only works on Linux. The blog post on Time Travelling Bug Reporting has many more details.

Glossary

A few terms have been used as shorthand in this guide:

diff --git a/dev/devdocs/boundscheck/index.html b/dev/devdocs/boundscheck/index.html index 7700df1e..c70aeccf 100644 --- a/dev/devdocs/boundscheck/index.html +++ b/dev/devdocs/boundscheck/index.html @@ -19,4 +19,4 @@ julia> sum(OffsetArray([1, 2, 3], -10)) 9164911648 # inconsistent results or segfault

While the original source of the error here is 1:length(A), the use of @inbounds increases the consequences from a bounds error to a less easily caught and debugged unsafe memory access. It is often difficult or impossible to prove that a method which uses @inbounds is safe, so one must weigh the benefits of performance improvements against the risk of segfaults and silent misbehavior, especially in public facing APIs.

Propagating inbounds

There may be certain scenarios where for code-organization reasons you want more than one layer between the @inbounds and @boundscheck declarations. For instance, the default getindex methods have the chain getindex(A::AbstractArray, i::Real) calls getindex(IndexStyle(A), A, i) calls _getindex(::IndexLinear, A, i).

To override the "one layer of inlining" rule, a function may be marked with Base.@propagate_inbounds to propagate an inbounds context (or out of bounds context) through one additional layer of inlining.

The bounds checking call hierarchy

The overall hierarchy is:

Here A is the array, and I contains the "requested" indices. axes(A) returns a tuple of "permitted" indices of A.

checkbounds(A, I...) throws an error if the indices are invalid, whereas checkbounds(Bool, A, I...) returns false in that circumstance. checkbounds_indices discards any information about the array other than its axes tuple, and performs a pure indices-vs-indices comparison: this allows relatively few compiled methods to serve a huge variety of array types. Indices are specified as tuples, and are usually compared in a 1-1 fashion with individual dimensions handled by calling another important function, checkindex: typically,

checkbounds_indices(Bool, (IA1, IA...), (I1, I...)) = checkindex(Bool, IA1, I1) &
-                                                      checkbounds_indices(Bool, IA, I)

so checkindex checks a single dimension. All of these functions, including the unexported checkbounds_indices have docstrings accessible with ? .

If you have to customize bounds checking for a specific array type, you should specialize checkbounds(Bool, A, I...). However, in most cases you should be able to rely on checkbounds_indices as long as you supply useful axes for your array type.

If you have novel index types, first consider specializing checkindex, which handles a single index for a particular dimension of an array. If you have a custom multidimensional index type (similar to CartesianIndex), then you may have to consider specializing checkbounds_indices.

Note this hierarchy has been designed to reduce the likelihood of method ambiguities. We try to make checkbounds the place to specialize on array type, and try to avoid specializations on index types; conversely, checkindex is intended to be specialized only on index type (especially, the last argument).

Emit bounds checks

Julia can be launched with --check-bounds={yes|no|auto} to emit bounds checks always, never, or respect @inbounds declarations.

+ checkbounds_indices(Bool, IA, I)

so checkindex checks a single dimension. All of these functions, including the unexported checkbounds_indices have docstrings accessible with ? .

If you have to customize bounds checking for a specific array type, you should specialize checkbounds(Bool, A, I...). However, in most cases you should be able to rely on checkbounds_indices as long as you supply useful axes for your array type.

If you have novel index types, first consider specializing checkindex, which handles a single index for a particular dimension of an array. If you have a custom multidimensional index type (similar to CartesianIndex), then you may have to consider specializing checkbounds_indices.

Note this hierarchy has been designed to reduce the likelihood of method ambiguities. We try to make checkbounds the place to specialize on array type, and try to avoid specializations on index types; conversely, checkindex is intended to be specialized only on index type (especially, the last argument).

Emit bounds checks

Julia can be launched with --check-bounds={yes|no|auto} to emit bounds checks always, never, or respect @inbounds declarations.

diff --git a/dev/devdocs/build/arm/index.html b/dev/devdocs/build/arm/index.html index 3a27ab94..bc53f8ff 100644 --- a/dev/devdocs/build/arm/index.html +++ b/dev/devdocs/build/arm/index.html @@ -4,4 +4,4 @@ gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash});
Repository

ARM (Linux)

Julia fully supports ARMv8 (AArch64) processors, and supports ARMv7 and ARMv6 (AArch32) with some caveats. This file provides general guidelines for compilation, in addition to instructions for specific devices.

A list of known issues for ARM is available. If you encounter difficulties, please create an issue including the output from cat /proc/cpuinfo.

32-bit (ARMv6, ARMv7)

Julia has been successfully compiled on several variants of the following ARMv6 & ARMv7 devices:

  • ARMv7 / Cortex A15 Samsung Chromebooks running Ubuntu Linux under Crouton;
  • Raspberry Pi.
  • Odroid.

Julia requires at least the armv6 and vfpv2 instruction sets. It's recommended to use armv7-a. armv5 or soft float are not supported.

Raspberry Pi 1 / Raspberry Pi Zero

If the type of ARM CPU used in the Raspberry Pi is not detected by LLVM, then explicitly set the CPU target by adding the following to Make.user:

JULIA_CPU_TARGET=arm1176jzf-s

To complete the build, you may need to increase the swap file size. To do so, edit /etc/dphys-swapfile, changing the line:

CONF_SWAPSIZE=100

to:

CONF_SWAPSIZE=512

before restarting the swapfile service:

sudo /etc/init.d/dphys-swapfile stop
-sudo /etc/init.d/dphys-swapfile start

Raspberry Pi 2

The type of ARM CPU used in the Raspberry Pi 2 is not detected by LLVM. Explicitly set the CPU target by adding the following to Make.user:

JULIA_CPU_TARGET=cortex-a7

Depending on the exact compiler and distribution, there might be a build failure due to unsupported inline assembly. In that case, add MCPU=armv7-a to Make.user.

AArch64 (ARMv8)

Julia is expected to work and build on ARMv8 cpus. One should follow the general build instructions. Julia expects to have around 8GB of ram or swap enabled to build itself.

Known issues

Starting from Julia v1.10, JITLink is automatically enabled on this architecture for all operating systems when linking to LLVM 15 or later versions. Due to a bug in LLVM memory manager, non-trivial workloads may generate too many memory mappings that on Linux can exceed the limit of memory mappings (mmap) set in the file /proc/sys/vm/max_map_count, resulting in an error like

JIT session error: Cannot allocate memory

Should this happen, ask your system administrator to increase the limit of memory mappings for example with the command

sysctl -w vm.max_map_count=262144
+sudo /etc/init.d/dphys-swapfile start

Raspberry Pi 2

The type of ARM CPU used in the Raspberry Pi 2 is not detected by LLVM. Explicitly set the CPU target by adding the following to Make.user:

JULIA_CPU_TARGET=cortex-a7

Depending on the exact compiler and distribution, there might be a build failure due to unsupported inline assembly. In that case, add MCPU=armv7-a to Make.user.

AArch64 (ARMv8)

Julia is expected to work and build on ARMv8 cpus. One should follow the general build instructions. Julia expects to have around 8GB of ram or swap enabled to build itself.

Known issues

Starting from Julia v1.10, JITLink is automatically enabled on this architecture for all operating systems when linking to LLVM 15 or later versions. Due to a bug in LLVM memory manager, non-trivial workloads may generate too many memory mappings that on Linux can exceed the limit of memory mappings (mmap) set in the file /proc/sys/vm/max_map_count, resulting in an error like

JIT session error: Cannot allocate memory

Should this happen, ask your system administrator to increase the limit of memory mappings for example with the command

sysctl -w vm.max_map_count=262144
diff --git a/dev/devdocs/build/build/index.html b/dev/devdocs/build/build/index.html index ac57e130..7b4d98da 100644 --- a/dev/devdocs/build/build/index.html +++ b/dev/devdocs/build/build/index.html @@ -42,4 +42,4 @@ Patches: - [ ] `deps/$(libname).mk` -- [ ] `deps/patches/$(libname)-*.patch`

Note:

Example: OpenLibm

  1. Update Version numbers in deps/openlibm.version
  2. Update Version number in stdlib/OpenLibm_jll/Project.toml
  3. Update checksums in deps/checksums/openlibm
  4. Check if the patch files deps/patches/openlibm-*.patch exist
+- [ ] `deps/patches/$(libname)-*.patch`

Note:

Example: OpenLibm

  1. Update Version numbers in deps/openlibm.version
  2. Update Version number in stdlib/OpenLibm_jll/Project.toml
  3. Update checksums in deps/checksums/openlibm
  4. Check if the patch files deps/patches/openlibm-*.patch exist
diff --git a/dev/devdocs/build/distributing/index.html b/dev/devdocs/build/distributing/index.html index f48c3dba..c9e5084d 100644 --- a/dev/devdocs/build/distributing/index.html +++ b/dev/devdocs/build/distributing/index.html @@ -47,4 +47,4 @@ signtool sign /f julia-windows-code-sign_2017.p12 /p "PASSWORD" ^ /t http://timestamp.verisign.com/scripts/timstamp.dll ^ /v julia-x.y.z-win32.exe

Note that ^ is a line continuation character in Windows CMD and PASSWORD is a placeholder for the password for this certificate. As usual, contact Elliot or Alex for passwords. If there are no errors, we're all good!

Uploading binaries

Now that everything is signed, we need to upload the binaries to AWS. You can use a program like Cyberduck or the aws command line utility. The binaries should go in the julialang2 bucket in the appropriate folders. For example, Linux x86-64 goes in julialang2/bin/linux/x.y. Be sure to delete the current julia-x.y-latest-linux-<arch>.tar.gz file and replace it with a duplicate of julia-x.y.z-linux-<arch>.tar.gz.

We also need to upload the checksums for everything we've built, including the source tarballs and all release binaries. This is simple:

shasum -a 256 julia-x.y.z* | grep -v -e sha256 -e md5 -e asc > julia-x.y.z.sha256
-md5sum julia-x.y.z* | grep -v -e sha256 -e md5 -e asc > julia-x.y.z.md5

Note that if you're running those commands on macOS, you'll get very slightly different output, which can be reformatted by looking at an existing file. Mac users will also need to use md5 -r instead of md5sum. Upload the .md5 and .sha256 files to julialang2/bin/checksums on AWS.

Ensure that the permissions on AWS for all uploaded files are set to "Everyone: READ."

For each file we've uploaded, we need to purge the Fastly cache so that the links on the website point to the updated files. As an example:

curl -X PURGE https://julialang-s3.julialang.org/bin/checksums/julia-x.y.z.sha256

Sometimes this isn't necessary but it's good to do anyway.

+md5sum julia-x.y.z* | grep -v -e sha256 -e md5 -e asc > julia-x.y.z.md5

Note that if you're running those commands on macOS, you'll get very slightly different output, which can be reformatted by looking at an existing file. Mac users will also need to use md5 -r instead of md5sum. Upload the .md5 and .sha256 files to julialang2/bin/checksums on AWS.

Ensure that the permissions on AWS for all uploaded files are set to "Everyone: READ."

For each file we've uploaded, we need to purge the Fastly cache so that the links on the website point to the updated files. As an example:

curl -X PURGE https://julialang-s3.julialang.org/bin/checksums/julia-x.y.z.sha256

Sometimes this isn't necessary but it's good to do anyway.

diff --git a/dev/devdocs/build/freebsd/index.html b/dev/devdocs/build/freebsd/index.html index 3079d821..e17a37ba 100644 --- a/dev/devdocs/build/freebsd/index.html +++ b/dev/devdocs/build/freebsd/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

FreeBSD

Clang is the default compiler on FreeBSD 11.0-RELEASE and above. The remaining build tools are available from the Ports Collection, and can be installed using pkg install git gcc gmake cmake pkgconf. To build Julia, simply run gmake. (Note that gmake must be used rather than make, since make on FreeBSD corresponds to the incompatible BSD Make rather than GNU Make.)

As mentioned above, it is important to note that the USE_SYSTEM_* flags should be used with caution on FreeBSD. This is because many system libraries, and even libraries from the Ports Collection, link to the system's libgcc_s.so.1, or to another library which links to the system libgcc_s. This library declares its GCC version to be 4.6, which is too old to build Julia, and conflicts with other libraries when linking. Thus it is highly recommended to simply allow Julia to build all of its dependencies. If you do choose to use the USE_SYSTEM_* flags, note that /usr/local is not on the compiler path by default, so you may need to add LDFLAGS=-L/usr/local/lib and CPPFLAGS=-I/usr/local/include to your Make.user, though doing so may interfere with other dependencies.

Note that the x86 architecture does not support threading due to lack of compiler runtime library support, so you may need to set JULIA_THREADS=0 in your Make.user if you're on a 32-bit system.

+
Repository

FreeBSD

Clang is the default compiler on FreeBSD 11.0-RELEASE and above. The remaining build tools are available from the Ports Collection, and can be installed using pkg install git gcc gmake cmake pkgconf. To build Julia, simply run gmake. (Note that gmake must be used rather than make, since make on FreeBSD corresponds to the incompatible BSD Make rather than GNU Make.)

As mentioned above, it is important to note that the USE_SYSTEM_* flags should be used with caution on FreeBSD. This is because many system libraries, and even libraries from the Ports Collection, link to the system's libgcc_s.so.1, or to another library which links to the system libgcc_s. This library declares its GCC version to be 4.6, which is too old to build Julia, and conflicts with other libraries when linking. Thus it is highly recommended to simply allow Julia to build all of its dependencies. If you do choose to use the USE_SYSTEM_* flags, note that /usr/local is not on the compiler path by default, so you may need to add LDFLAGS=-L/usr/local/lib and CPPFLAGS=-I/usr/local/include to your Make.user, though doing so may interfere with other dependencies.

Note that the x86 architecture does not support threading due to lack of compiler runtime library support, so you may need to set JULIA_THREADS=0 in your Make.user if you're on a 32-bit system.

diff --git a/dev/devdocs/build/linux/index.html b/dev/devdocs/build/linux/index.html index a8dc6cf1..c2effe04 100644 --- a/dev/devdocs/build/linux/index.html +++ b/dev/devdocs/build/linux/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

Linux

  • GCC version 4.7 or later is required to build Julia.
  • To use external shared libraries not in the system library search path, set USE_SYSTEM_XXX=1 and LDFLAGS=-Wl,-rpath,/path/to/dir/contains/libXXX.so in Make.user.
  • Instead of setting LDFLAGS, putting the library directory into the environment variable LD_LIBRARY_PATH (at both compile and run time) also works.
  • The USE_SYSTEM_* flags should be used with caution. These are meant only for troubleshooting, porting, and packaging, where package maintainers work closely with the Julia developers to make sure that Julia is built correctly. Production use cases should use the officially provided binaries. Issues arising from the use of these flags will generally not be accepted.
  • See also the external dependencies.

Architecture Customization

Julia can be built for a non-generic architecture by configuring the ARCH Makefile variable in a Make.user file. See the appropriate section of Make.inc for additional customization options, such as MARCH and JULIA_CPU_TARGET.

For example, to build for Pentium 4, set MARCH=pentium4 and install the necessary system libraries for linking. On Ubuntu, these may include lib32gfortran-6-dev, lib32gcc1, and lib32stdc++6, among others.

You can also set MARCH=native in Make.user for a maximum-performance build customized for the current machine CPU.

Linux Build Troubleshooting

ProblemPossible Solution
OpenBLAS build failureSet one of the following build options in Make.user and build again: <ul><li> OPENBLAS_TARGET_ARCH=BARCELONA (AMD CPUs) or OPENBLAS_TARGET_ARCH=NEHALEM (Intel CPUs)<ul>Set OPENBLAS_DYNAMIC_ARCH = 0 to disable compiling multiple architectures in a single binary.</ul></li><li> OPENBLAS_NO_AVX2 = 1 disables AVX2 instructions, allowing OpenBLAS to compile with OPENBLAS_DYNAMIC_ARCH = 1 using old versions of binutils </li><li> USE_SYSTEM_BLAS=1 uses the system provided libblas <ul><li>Set LIBBLAS=-lopenblas and LIBBLASNAME=libopenblas to force the use of the system provided OpenBLAS when multiple BLAS versions are installed. </li></ul></li></ul><p> If you get an error that looks like ../kernel/x86_64/dgemm_kernel_4x4_haswell.S:1709: Error: no such instruction: `vpermpd $ 0xb1,%ymm0,%ymm0', then you need to set OPENBLAS_DYNAMIC_ARCH = 0 or OPENBLAS_NO_AVX2 = 1, or you need a newer version of binutils (2.18 or newer). (Issue #7653)</p><p> If the linker cannot find gfortran and you get an error like julia /usr/bin/x86_64-linux-gnu-ld: cannot find -lgfortran, check the path with gfortran -print-file-name=libgfortran.so and use the output to export something similar to this: export LDFLAGS=-L/usr/lib/gcc/x86_64-linux-gnu/8/. See Issue #6150.</p>
Illegal Instruction errorCheck if your CPU supports AVX while your OS does not (e.g. through virtualization, as described in this issue).
+
Repository

Linux

  • GCC version 4.7 or later is required to build Julia.
  • To use external shared libraries not in the system library search path, set USE_SYSTEM_XXX=1 and LDFLAGS=-Wl,-rpath,/path/to/dir/contains/libXXX.so in Make.user.
  • Instead of setting LDFLAGS, putting the library directory into the environment variable LD_LIBRARY_PATH (at both compile and run time) also works.
  • The USE_SYSTEM_* flags should be used with caution. These are meant only for troubleshooting, porting, and packaging, where package maintainers work closely with the Julia developers to make sure that Julia is built correctly. Production use cases should use the officially provided binaries. Issues arising from the use of these flags will generally not be accepted.
  • See also the external dependencies.

Architecture Customization

Julia can be built for a non-generic architecture by configuring the ARCH Makefile variable in a Make.user file. See the appropriate section of Make.inc for additional customization options, such as MARCH and JULIA_CPU_TARGET.

For example, to build for Pentium 4, set MARCH=pentium4 and install the necessary system libraries for linking. On Ubuntu, these may include lib32gfortran-6-dev, lib32gcc1, and lib32stdc++6, among others.

You can also set MARCH=native in Make.user for a maximum-performance build customized for the current machine CPU.

Linux Build Troubleshooting

ProblemPossible Solution
OpenBLAS build failureSet one of the following build options in Make.user and build again: <ul><li> OPENBLAS_TARGET_ARCH=BARCELONA (AMD CPUs) or OPENBLAS_TARGET_ARCH=NEHALEM (Intel CPUs)<ul>Set OPENBLAS_DYNAMIC_ARCH = 0 to disable compiling multiple architectures in a single binary.</ul></li><li> OPENBLAS_NO_AVX2 = 1 disables AVX2 instructions, allowing OpenBLAS to compile with OPENBLAS_DYNAMIC_ARCH = 1 using old versions of binutils </li><li> USE_SYSTEM_BLAS=1 uses the system provided libblas <ul><li>Set LIBBLAS=-lopenblas and LIBBLASNAME=libopenblas to force the use of the system provided OpenBLAS when multiple BLAS versions are installed. </li></ul></li></ul><p> If you get an error that looks like ../kernel/x86_64/dgemm_kernel_4x4_haswell.S:1709: Error: no such instruction: `vpermpd $ 0xb1,%ymm0,%ymm0', then you need to set OPENBLAS_DYNAMIC_ARCH = 0 or OPENBLAS_NO_AVX2 = 1, or you need a newer version of binutils (2.18 or newer). (Issue #7653)</p><p> If the linker cannot find gfortran and you get an error like julia /usr/bin/x86_64-linux-gnu-ld: cannot find -lgfortran, check the path with gfortran -print-file-name=libgfortran.so and use the output to export something similar to this: export LDFLAGS=-L/usr/lib/gcc/x86_64-linux-gnu/8/. See Issue #6150.</p>
Illegal Instruction errorCheck if your CPU supports AVX while your OS does not (e.g. through virtualization, as described in this issue).
diff --git a/dev/devdocs/build/macos/index.html b/dev/devdocs/build/macos/index.html index f899b463..1a5725f8 100644 --- a/dev/devdocs/build/macos/index.html +++ b/dev/devdocs/build/macos/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

macOS

You need to have the current Xcode command line utilities installed: run xcode-select --install in the terminal. You will need to rerun this terminal command after each macOS update, otherwise you may run into errors involving missing libraries or headers.

The dependent libraries are now built with BinaryBuilder and will be automatically downloaded. This is the preferred way to build Julia source. In case you want to build them all on your own, you will need a 64-bit gfortran to compile Julia dependencies.

brew install gcc

If you have set LD_LIBRARY_PATH or DYLD_LIBRARY_PATH in your .bashrc or equivalent, Julia may be unable to find various libraries that come bundled with it. These environment variables need to be unset for Julia to work.

+
Repository

macOS

You need to have the current Xcode command line utilities installed: run xcode-select --install in the terminal. You will need to rerun this terminal command after each macOS update, otherwise you may run into errors involving missing libraries or headers.

The dependent libraries are now built with BinaryBuilder and will be automatically downloaded. This is the preferred way to build Julia source. In case you want to build them all on your own, you will need a 64-bit gfortran to compile Julia dependencies.

brew install gcc

If you have set LD_LIBRARY_PATH or DYLD_LIBRARY_PATH in your .bashrc or equivalent, Julia may be unable to find various libraries that come bundled with it. These environment variables need to be unset for Julia to work.

diff --git a/dev/devdocs/build/windows/index.html b/dev/devdocs/build/windows/index.html index dfe9cc60..e5f70562 100644 --- a/dev/devdocs/build/windows/index.html +++ b/dev/devdocs/build/windows/index.html @@ -31,4 +31,4 @@ make -C julia-mingw-w64

Cross-compiling from Unix (Linux/Mac/WSL)

You can also use MinGW-w64 cross compilers to build a Windows version of Julia from Linux, Mac, or the Windows Subsystem for Linux (WSL).

First, you will need to ensure your system has the required dependencies. We need wine (>=1.7.5), a system compiler, and some downloaders. Note: a cygwin install might interfere with this method if using WSL.

On Ubuntu (on other Linux systems the dependency names are likely to be similar):

apt-get install wine-stable gcc wget p7zip-full winbind mingw-w64 gfortran-mingw-w64
 dpkg --add-architecture i386 && apt-get update && apt-get install wine32 # add sudo to each if needed
 # switch all of the following to their "-posix" variants (interactively):
-for pkg in i686-w64-mingw32-g++ i686-w64-mingw32-gcc i686-w64-mingw32-gfortran x86_64-w64-mingw32-g++ x86_64-w64-mingw32-gcc x86_64-w64-mingw32-gfortran; do sudo update-alternatives --config $pkg; done

On Mac: Install XCode, XCode command line tools, X11 (now XQuartz), and MacPorts or Homebrew. Then run port install wine wget mingw-w64, or brew install wine wget mingw-w64, as appropriate.

Then run the build:

  1. git clone https://github.com/JuliaLang/julia.git julia-win32
  2. cd julia-win32
  3. echo override XC_HOST = i686-w64-mingw32 >> Make.user
  4. make
  5. make win-extras (Necessary before running make binary-dist)
  6. make binary-dist then make exe to create the Windows installer.
  7. move the julia-*.exe installer to the target machine

If you are building for 64-bit windows, the steps are essentially the same. Just replace i686 in XC_HOST with x86_64. (note: on Mac, wine only runs in 32-bit mode).

Debugging a cross-compiled build under wine

The most effective way to debug a cross-compiled version of Julia on the cross-compilation host is to install a windows version of gdb and run it under wine as usual. The pre-built packages available as part of the MSYS2 project are known to work. Apart from the GDB package you may also need the python and termcap packages. Finally, GDB's prompt may not work when launch from the command line. This can be worked around by prepending wineconsole to the regular GDB invocation.

After compiling

Compiling using one of the options above creates a basic Julia build, but not some extra components that are included if you run the full Julia binary installer. If you need these components, the easiest way to get them is to build the installer yourself using make win-extras followed by make binary-dist and make exe. Then running the resulting installer.

Windows Build Debugging

GDB hangs with cygwin mintty

GDB not attaching to the right process

GDB not showing the right backtrace

Build process is slow/eats memory/hangs my computer

+for pkg in i686-w64-mingw32-g++ i686-w64-mingw32-gcc i686-w64-mingw32-gfortran x86_64-w64-mingw32-g++ x86_64-w64-mingw32-gcc x86_64-w64-mingw32-gfortran; do sudo update-alternatives --config $pkg; done

On Mac: Install XCode, XCode command line tools, X11 (now XQuartz), and MacPorts or Homebrew. Then run port install wine wget mingw-w64, or brew install wine wget mingw-w64, as appropriate.

Then run the build:

  1. git clone https://github.com/JuliaLang/julia.git julia-win32
  2. cd julia-win32
  3. echo override XC_HOST = i686-w64-mingw32 >> Make.user
  4. make
  5. make win-extras (Necessary before running make binary-dist)
  6. make binary-dist then make exe to create the Windows installer.
  7. move the julia-*.exe installer to the target machine

If you are building for 64-bit windows, the steps are essentially the same. Just replace i686 in XC_HOST with x86_64. (note: on Mac, wine only runs in 32-bit mode).

Debugging a cross-compiled build under wine

The most effective way to debug a cross-compiled version of Julia on the cross-compilation host is to install a windows version of gdb and run it under wine as usual. The pre-built packages available as part of the MSYS2 project are known to work. Apart from the GDB package you may also need the python and termcap packages. Finally, GDB's prompt may not work when launch from the command line. This can be worked around by prepending wineconsole to the regular GDB invocation.

After compiling

Compiling using one of the options above creates a basic Julia build, but not some extra components that are included if you run the full Julia binary installer. If you need these components, the easiest way to get them is to build the installer yourself using make win-extras followed by make binary-dist and make exe. Then running the resulting installer.

Windows Build Debugging

GDB hangs with cygwin mintty

GDB not attaching to the right process

GDB not showing the right backtrace

Build process is slow/eats memory/hangs my computer

diff --git a/dev/devdocs/callconv/index.html b/dev/devdocs/callconv/index.html index ba5d5a22..17581cb4 100644 --- a/dev/devdocs/callconv/index.html +++ b/dev/devdocs/callconv/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

Calling Conventions

Julia uses three calling conventions for four distinct purposes:

NamePrefixPurpose
Nativejulia_Speed via specialized signatures
JL Calljlcall_Wrapper for generic calls
JL Calljl_Builtins
C ABIjlcapi_Wrapper callable from C

Julia Native Calling Convention

The native calling convention is designed for fast non-generic calls. It usually uses a specialized signature.

  • LLVM ghosts (zero-length types) are omitted.
  • LLVM scalars and vectors are passed by value.
  • LLVM aggregates (arrays and structs) are passed by reference.

A small return values is returned as LLVM return values. A large return values is returned via the "structure return" (sret) convention, where the caller provides a pointer to a return slot.

An argument or return values that is a homogeneous tuple is sometimes represented as an LLVM vector instead of an LLVM array.

JL Call Convention

The JL Call convention is for builtins and generic dispatch. Hand-written functions using this convention are declared via the macro JL_CALLABLE. The convention uses exactly 3 parameters:

  • F - Julia representation of function that is being applied
  • args - pointer to array of pointers to boxes
  • nargs - length of the array

The return value is a pointer to a box.

C ABI

C ABI wrappers enable calling Julia from C. The wrapper calls a function using the native calling convention.

Tuples are always represented as C arrays.

+
Repository

Calling Conventions

Julia uses three calling conventions for four distinct purposes:

NamePrefixPurpose
Nativejulia_Speed via specialized signatures
JL Calljlcall_Wrapper for generic calls
JL Calljl_Builtins
C ABIjlcapi_Wrapper callable from C

Julia Native Calling Convention

The native calling convention is designed for fast non-generic calls. It usually uses a specialized signature.

  • LLVM ghosts (zero-length types) are omitted.
  • LLVM scalars and vectors are passed by value.
  • LLVM aggregates (arrays and structs) are passed by reference.

A small return values is returned as LLVM return values. A large return values is returned via the "structure return" (sret) convention, where the caller provides a pointer to a return slot.

An argument or return values that is a homogeneous tuple is sometimes represented as an LLVM vector instead of an LLVM array.

JL Call Convention

The JL Call convention is for builtins and generic dispatch. Hand-written functions using this convention are declared via the macro JL_CALLABLE. The convention uses exactly 3 parameters:

  • F - Julia representation of function that is being applied
  • args - pointer to array of pointers to boxes
  • nargs - length of the array

The return value is a pointer to a box.

C ABI

C ABI wrappers enable calling Julia from C. The wrapper calls a function using the native calling convention.

Tuples are always represented as C arrays.

diff --git a/dev/devdocs/cartesian/index.html b/dev/devdocs/cartesian/index.html index aa293bf8..c636deb5 100644 --- a/dev/devdocs/cartesian/index.html +++ b/dev/devdocs/cartesian/index.html @@ -52,4 +52,4 @@ error("Dimension ", 2, " too big") else println("All OK") -endsource +endsource diff --git a/dev/devdocs/compiler/index.html b/dev/devdocs/compiler/index.html index ed26bf26..3fe6e21f 100644 --- a/dev/devdocs/compiler/index.html +++ b/dev/devdocs/compiler/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

本机代码生成过程的高级概述

指针的表示

When emitting code to an object file, pointers will be emitted as relocations. The deserialization code will ensure any object that pointed to one of these constants gets recreated and contains the right runtime pointer.

Otherwise, they will be emitted as literal constants.

To emit one of these objects, call literal_pointer_val. It'll handle tracking the Julia value and the LLVM global, ensuring they are valid both for the current runtime and after deserialization.

When emitted into the object file, these globals are stored as references in a large gvals table. This allows the deserializer to reference them by index, and implement a custom manual mechanism similar to a Global Offset Table (GOT) to restore them.

Function pointers are handled similarly. They are stored as values in a large fvals table. Like globals, this allows the deserializer to reference them by index.

Note that extern functions are handled separately, with names, via the usual symbol resolution mechanism in the linker.

Note too that ccall functions are also handled separately, via a manual GOT and Procedure Linkage Table (PLT).

Representation of Intermediate Values

Values are passed around in a jl_cgval_t struct. This represents an R-value, and includes enough information to determine how to assign or pass it somewhere.

They are created via one of the helper constructors, usually: mark_julia_type (for immediate values) and mark_julia_slot (for pointers to values).

The function convert_julia_type can transform between any two types. It returns an R-value with cgval.typ set to typ. It'll cast the object to the requested representation, making heap boxes, allocating stack copies, and computing tagged unions as needed to change the representation.

By contrast update_julia_type will change cgval.typ to typ, only if it can be done at zero-cost (i.e. without emitting any code).

Union representation

Inferred union types may be stack allocated via a tagged type representation.

The primitive routines that need to be able to handle tagged unions are:

  • mark-type
  • load-local
  • store-local
  • isa
  • is
  • emit_typeof
  • emit_sizeof
  • boxed
  • unbox
  • specialized cc-ret

Everything else should be possible to handle in inference by using these primitives to implement union-splitting.

The representation of the tagged-union is as a pair of < void* union, byte selector >. The selector is fixed-size as byte & 0x7f, and will union-tag the first 126 isbits. It records the one-based depth-first count into the type-union of the isbits objects inside. An index of zero indicates that the union* is actually a tagged heap-allocated jl_value_t*, and needs to be treated as normal for a boxed object rather than as a tagged union.

The high bit of the selector (byte & 0x80) can be tested to determine if the void* is actually a heap-allocated (jl_value_t*) box, thus avoiding the cost of re-allocating a box, while maintaining the ability to efficiently handle union-splitting based on the low bits.

It is guaranteed that byte & 0x7f is an exact test for the type, if the value can be represented by a tag – it will never be marked byte = 0x80. It is not necessary to also test the type-tag when testing isa.

The union* memory region may be allocated at any size. The only constraint is that it is big enough to contain the data currently specified by selector. It might not be big enough to contain the union of all types that could be stored there according to the associated Union type field. Use appropriate care when copying.

Specialized Calling Convention Signature Representation

A jl_returninfo_t object describes the calling convention details of any callable.

If any of the arguments or return type of a method can be represented unboxed, and the method is not varargs, it'll be given an optimized calling convention signature based on its specTypes and rettype fields.

The general principles are that:

  • Primitive types get passed in int/float registers.
  • Tuples of VecElement types get passed in vector registers.
  • Structs get passed on the stack.
  • Return values are handle similarly to arguments, with a size-cutoff at which they will instead be returned via a hidden sret argument.

The total logic for this is implemented by get_specsig_function and deserves_sret.

Additionally, if the return type is a union, it may be returned as a pair of values (a pointer and a tag). If the union values can be stack-allocated, then sufficient space to store them will also be passed as a hidden first argument. It is up to the callee whether the returned pointer will point to this space, a boxed object, or even other constant memory.

+
Repository

本机代码生成过程的高级概述

指针的表示

When emitting code to an object file, pointers will be emitted as relocations. The deserialization code will ensure any object that pointed to one of these constants gets recreated and contains the right runtime pointer.

Otherwise, they will be emitted as literal constants.

To emit one of these objects, call literal_pointer_val. It'll handle tracking the Julia value and the LLVM global, ensuring they are valid both for the current runtime and after deserialization.

When emitted into the object file, these globals are stored as references in a large gvals table. This allows the deserializer to reference them by index, and implement a custom manual mechanism similar to a Global Offset Table (GOT) to restore them.

Function pointers are handled similarly. They are stored as values in a large fvals table. Like globals, this allows the deserializer to reference them by index.

Note that extern functions are handled separately, with names, via the usual symbol resolution mechanism in the linker.

Note too that ccall functions are also handled separately, via a manual GOT and Procedure Linkage Table (PLT).

Representation of Intermediate Values

Values are passed around in a jl_cgval_t struct. This represents an R-value, and includes enough information to determine how to assign or pass it somewhere.

They are created via one of the helper constructors, usually: mark_julia_type (for immediate values) and mark_julia_slot (for pointers to values).

The function convert_julia_type can transform between any two types. It returns an R-value with cgval.typ set to typ. It'll cast the object to the requested representation, making heap boxes, allocating stack copies, and computing tagged unions as needed to change the representation.

By contrast update_julia_type will change cgval.typ to typ, only if it can be done at zero-cost (i.e. without emitting any code).

Union representation

Inferred union types may be stack allocated via a tagged type representation.

The primitive routines that need to be able to handle tagged unions are:

  • mark-type
  • load-local
  • store-local
  • isa
  • is
  • emit_typeof
  • emit_sizeof
  • boxed
  • unbox
  • specialized cc-ret

Everything else should be possible to handle in inference by using these primitives to implement union-splitting.

The representation of the tagged-union is as a pair of < void* union, byte selector >. The selector is fixed-size as byte & 0x7f, and will union-tag the first 126 isbits. It records the one-based depth-first count into the type-union of the isbits objects inside. An index of zero indicates that the union* is actually a tagged heap-allocated jl_value_t*, and needs to be treated as normal for a boxed object rather than as a tagged union.

The high bit of the selector (byte & 0x80) can be tested to determine if the void* is actually a heap-allocated (jl_value_t*) box, thus avoiding the cost of re-allocating a box, while maintaining the ability to efficiently handle union-splitting based on the low bits.

It is guaranteed that byte & 0x7f is an exact test for the type, if the value can be represented by a tag – it will never be marked byte = 0x80. It is not necessary to also test the type-tag when testing isa.

The union* memory region may be allocated at any size. The only constraint is that it is big enough to contain the data currently specified by selector. It might not be big enough to contain the union of all types that could be stored there according to the associated Union type field. Use appropriate care when copying.

Specialized Calling Convention Signature Representation

A jl_returninfo_t object describes the calling convention details of any callable.

If any of the arguments or return type of a method can be represented unboxed, and the method is not varargs, it'll be given an optimized calling convention signature based on its specTypes and rettype fields.

The general principles are that:

  • Primitive types get passed in int/float registers.
  • Tuples of VecElement types get passed in vector registers.
  • Structs get passed on the stack.
  • Return values are handle similarly to arguments, with a size-cutoff at which they will instead be returned via a hidden sret argument.

The total logic for this is implemented by get_specsig_function and deserves_sret.

Additionally, if the return type is a union, it may be returned as a pair of values (a pointer and a tag). If the union values can be stack-allocated, then sufficient space to store them will also be passed as a hidden first argument. It is up to the callee whether the returned pointer will point to this space, a boxed object, or even other constant memory.

diff --git a/dev/devdocs/debuggingtips/index.html b/dev/devdocs/debuggingtips/index.html index 7128156e..541df2d1 100644 --- a/dev/devdocs/debuggingtips/index.html +++ b/dev/devdocs/debuggingtips/index.html @@ -29,4 +29,4 @@ Expr(:return, Expr(:call, :box, :Float32, Expr(:call, :fptrunc, :Float32, :x)::Any)::Any)::Any)::Any)::Any

Finally, and perhaps most usefully, we can force the function to be recompiled in order to step through the codegen process. To do this, clear the cached functionObject from the jl_lamdbda_info_t*:

(gdb) p f->linfo->functionObject
 $8 = (void *) 0x1289d070
 (gdb) set f->linfo->functionObject = NULL

Then, set a breakpoint somewhere useful (e.g. emit_function, emit_expr, emit_call, etc.), and run codegen:

(gdb) p jl_compile(f)
-... # your breakpoint here

Debugging precompilation errors

Module precompilation spawns a separate Julia process to precompile each module. Setting a breakpoint or catching failures in a precompile worker requires attaching a debugger to the worker. The easiest approach is to set the debugger watch for new process launches matching a given name. For example:

(gdb) attach -w -n julia-debug

or:

(lldb) process attach -w -n julia-debug

Then run a script/command to start precompilation. As described earlier, use conditional breakpoints in the parent process to catch specific file-loading events and narrow the debugging window. (some operating systems may require alternative approaches, such as following each fork from the parent process)

Mozilla's Record and Replay Framework (rr)

Julia now works out of the box with rr, the lightweight recording and deterministic debugging framework from Mozilla. This allows you to replay the trace of an execution deterministically. The replayed execution's address spaces, register contents, syscall data etc are exactly the same in every run.

A recent version of rr (3.1.0 or higher) is required.

Reproducing concurrency bugs with rr

rr simulates a single-threaded machine by default. In order to debug concurrent code you can use rr record --chaos which will cause rr to simulate between one to eight cores, chosen randomly. You might therefore want to set JULIA_NUM_THREADS=8 and rerun your code under rr until you have caught your bug.

+... # your breakpoint here

Debugging precompilation errors

Module precompilation spawns a separate Julia process to precompile each module. Setting a breakpoint or catching failures in a precompile worker requires attaching a debugger to the worker. The easiest approach is to set the debugger watch for new process launches matching a given name. For example:

(gdb) attach -w -n julia-debug

or:

(lldb) process attach -w -n julia-debug

Then run a script/command to start precompilation. As described earlier, use conditional breakpoints in the parent process to catch specific file-loading events and narrow the debugging window. (some operating systems may require alternative approaches, such as following each fork from the parent process)

Mozilla's Record and Replay Framework (rr)

Julia now works out of the box with rr, the lightweight recording and deterministic debugging framework from Mozilla. This allows you to replay the trace of an execution deterministically. The replayed execution's address spaces, register contents, syscall data etc are exactly the same in every run.

A recent version of rr (3.1.0 or higher) is required.

Reproducing concurrency bugs with rr

rr simulates a single-threaded machine by default. In order to debug concurrent code you can use rr record --chaos which will cause rr to simulate between one to eight cores, chosen randomly. You might therefore want to set JULIA_NUM_THREADS=8 and rerun your code under rr until you have caught your bug.

diff --git a/dev/devdocs/eval/index.html b/dev/devdocs/eval/index.html index e2ef58e9..7bcf3b8b 100644 --- a/dev/devdocs/eval/index.html +++ b/dev/devdocs/eval/index.html @@ -6,4 +6,4 @@
Repository

Julia 代码的 eval

学习 Julia 语言如何运行代码的最难的一部分是 学习如何让所有的小部分工作协同工作来执行一段代码。

每个代码块通常会通过许多步骤来执行，在转变为期望的结果之前（但愿如此）。并且你可能不熟悉它们的名称，例如（非特定顺序）： flisp，AST，C++，LLVM，eval，typeinf，macroexpand，sysimg（或 system image），启动，变异，解析，执行，即时编译器，解释器解释，装箱，拆箱，内部函数，原始函数

Definitions

  • REPL

    REPL 表示 读取-求值-输出-循环（Read-Eval-Print Loop）。 我们管这个命令行环境的简称就叫REPL。

  • AST

    抽象语法树（Abstract Syntax Tree）是代码结构的数据表现。在这种表现形式下代码被符号化，因此更加方便操作和执行。

Diagram of the compiler flow

Julia Execution

整个进程的千里之行如下：

  1. 用户打开了 julia。
  2. The C function main() from cli/loader_exe.c gets called. This function processes the command line arguments, filling in the jl_options struct and setting the variable ARGS. It then initializes Julia (by calling julia_init in init.c, which may load a previously compiled sysimg). Finally, it passes off control to Julia by calling Base._start().
  3. When _start() takes over control, the subsequent sequence of commands depends on the command line arguments given. For example, if a filename was supplied, it will proceed to execute that file. Otherwise, it will start an interactive REPL.
  4. Skipping the details about how the REPL interacts with the user, let's just say the program ends up with a block of code that it wants to run.
  5. If the block of code to run is in a file, jl_load(char *filename) gets invoked to load the file and parse it. Each fragment of code is then passed to eval to execute.
  6. Each fragment of code (or AST), is handed off to eval() to turn into results.
  7. eval() takes each code fragment and tries to run it in jl_toplevel_eval_flex().
  8. jl_toplevel_eval_flex() decides whether the code is a "toplevel" action (such as using or module), which would be invalid inside a function. If so, it passes off the code to the toplevel interpreter.
  9. jl_toplevel_eval_flex() then expands the code to eliminate any macros and to "lower" the AST to make it simpler to execute.
  10. jl_toplevel_eval_flex() then uses some simple heuristics to decide whether to JIT compile the AST or to interpret it directly.
  11. The bulk of the work to interpret code is handled by eval in interpreter.c.
  12. If instead, the code is compiled, the bulk of the work is handled by codegen.cpp. Whenever a Julia function is called for the first time with a given set of argument types, type inference will be run on that function. This information is used by the codegen step to generate faster code.
  13. Eventually, the user quits the REPL, or the end of the program is reached, and the _start() method returns.
  14. Just before exiting, main() calls jl_atexit_hook(exit_code). This calls Base._atexit() (which calls any functions registered to atexit() inside Julia). Then it calls jl_gc_run_all_finalizers(). Finally, it gracefully cleans up all libuv handles and waits for them to flush and close.

Parsing

The Julia parser is a small lisp program written in femtolisp, the source-code for which is distributed inside Julia in src/flisp.

The interface functions for this are primarily defined in jlfrontend.scm. The code in ast.c handles this handoff on the Julia side.

The other relevant files at this stage are julia-parser.scm, which handles tokenizing Julia code and turning it into an AST, and julia-syntax.scm, which handles transforming complex AST representations into simpler, "lowered" AST representations which are more suitable for analysis and execution.

If you want to test the parser without re-building Julia in its entirety, you can run the frontend on its own as follows:

$ cd src
 $ flisp/flisp
 > (load "jlfrontend.scm")
-> (jl-parse-file "<filename>")

Macro Expansion

When eval() encounters a macro, it expands that AST node before attempting to evaluate the expression. Macro expansion involves a handoff from eval() (in Julia), to the parser function jl_macroexpand() (written in flisp) to the Julia macro itself (written in - what else - Julia) via fl_invoke_julia_macro(), and back.

Typically, macro expansion is invoked as a first step during a call to Meta.lower()/jl_expand(), although it can also be invoked directly by a call to macroexpand()/jl_macroexpand().

Type Inference

Type inference is implemented in Julia by typeinf() in compiler/typeinfer.jl. Type inference is the process of examining a Julia function and determining bounds for the types of each of its variables, as well as bounds on the type of the return value from the function. This enables many future optimizations, such as unboxing of known immutable values, and compile-time hoisting of various run-time operations such as computing field offsets and function pointers. Type inference may also include other steps such as constant propagation and inlining.

More Definitions

  • JIT

    Just-In-Time Compilation The process of generating native-machine code into memory right when it is needed.

  • LLVM

    Low-Level Virtual Machine (a compiler) The Julia JIT compiler is a program/library called libLLVM. Codegen in Julia refers both to the process of taking a Julia AST and turning it into LLVM instructions, and the process of LLVM optimizing that and turning it into native assembly instructions.

  • C++

    The programming language that LLVM is implemented in, which means that codegen is also implemented in this language. The rest of Julia's library is implemented in C, in part because its smaller feature set makes it more usable as a cross-language interface layer.

  • box

    This term is used to describe the process of taking a value and allocating a wrapper around the data that is tracked by the garbage collector (gc) and is tagged with the object's type.

  • unbox

    The reverse of boxing a value. This operation enables more efficient manipulation of data when the type of that data is fully known at compile-time (through type inference).

  • generic function

    A Julia function composed of multiple "methods" that are selected for dynamic dispatch based on the argument type-signature

  • anonymous function or "method"

    A Julia function without a name and without type-dispatch capabilities

  • primitive function

    A function implemented in C but exposed in Julia as a named function "method" (albeit without generic function dispatch capabilities, similar to a anonymous function)

  • intrinsic function

    A low-level operation exposed as a function in Julia. These pseudo-functions implement operations on raw bits such as add and sign extend that cannot be expressed directly in any other way. Since they operate on bits directly, they must be compiled into a function and surrounded by a call to Core.Intrinsics.box(T, ...) to reassign type information to the value.

JIT Code Generation

Codegen is the process of turning a Julia AST into native machine code.

The JIT environment is initialized by an early call to jl_init_codegen in codegen.cpp.

On demand, a Julia method is converted into a native function by the function emit_function(jl_method_instance_t*). (note, when using the MCJIT (in LLVM v3.4+), each function must be JIT into a new module.) This function recursively calls emit_expr() until the entire function has been emitted.

Much of the remaining bulk of this file is devoted to various manual optimizations of specific code patterns. For example, emit_known_call() knows how to inline many of the primitive functions (defined in builtins.c) for various combinations of argument types.

Other parts of codegen are handled by various helper files:

  • debuginfo.cpp

    Handles backtraces for JIT functions

  • ccall.cpp

    Handles the ccall and llvmcall FFI, along with various abi_*.cpp files

  • intrinsics.cpp

    Handles the emission of various low-level intrinsic functions

Bootstrapping

The process of creating a new system image is called "bootstrapping".

The etymology of this word comes from the phrase "pulling oneself up by the bootstraps", and refers to the idea of starting from a very limited set of available functions and definitions and ending with the creation of a full-featured environment.

System Image

The system image is a precompiled archive of a set of Julia files. The sys.ji file distributed with Julia is one such system image, generated by executing the file sysimg.jl, and serializing the resulting environment (including Types, Functions, Modules, and all other defined values) into a file. Therefore, it contains a frozen version of the Main, Core, and Base modules (and whatever else was in the environment at the end of bootstrapping). This serializer/deserializer is implemented by jl_save_system_image/jl_restore_system_image in staticdata.c.

If there is no sysimg file (jl_options.image_file == NULL), this also implies that --build was given on the command line, so the final result should be a new sysimg file. During Julia initialization, minimal Core and Main modules are created. Then a file named boot.jl is evaluated from the current directory. Julia then evaluates any file given as a command line argument until it reaches the end. Finally, it saves the resulting environment to a "sysimg" file for use as a starting point for a future Julia run.

+> (jl-parse-file "<filename>")

Macro Expansion

When eval() encounters a macro, it expands that AST node before attempting to evaluate the expression. Macro expansion involves a handoff from eval() (in Julia), to the parser function jl_macroexpand() (written in flisp) to the Julia macro itself (written in - what else - Julia) via fl_invoke_julia_macro(), and back.

Typically, macro expansion is invoked as a first step during a call to Meta.lower()/jl_expand(), although it can also be invoked directly by a call to macroexpand()/jl_macroexpand().

Type Inference

Type inference is implemented in Julia by typeinf() in compiler/typeinfer.jl. Type inference is the process of examining a Julia function and determining bounds for the types of each of its variables, as well as bounds on the type of the return value from the function. This enables many future optimizations, such as unboxing of known immutable values, and compile-time hoisting of various run-time operations such as computing field offsets and function pointers. Type inference may also include other steps such as constant propagation and inlining.

More Definitions

JIT Code Generation

Codegen is the process of turning a Julia AST into native machine code.

The JIT environment is initialized by an early call to jl_init_codegen in codegen.cpp.

On demand, a Julia method is converted into a native function by the function emit_function(jl_method_instance_t*). (note, when using the MCJIT (in LLVM v3.4+), each function must be JIT into a new module.) This function recursively calls emit_expr() until the entire function has been emitted.

Much of the remaining bulk of this file is devoted to various manual optimizations of specific code patterns. For example, emit_known_call() knows how to inline many of the primitive functions (defined in builtins.c) for various combinations of argument types.

Other parts of codegen are handled by various helper files:

Bootstrapping

The process of creating a new system image is called "bootstrapping".

The etymology of this word comes from the phrase "pulling oneself up by the bootstraps", and refers to the idea of starting from a very limited set of available functions and definitions and ending with the creation of a full-featured environment.

System Image

The system image is a precompiled archive of a set of Julia files. The sys.ji file distributed with Julia is one such system image, generated by executing the file sysimg.jl, and serializing the resulting environment (including Types, Functions, Modules, and all other defined values) into a file. Therefore, it contains a frozen version of the Main, Core, and Base modules (and whatever else was in the environment at the end of bootstrapping). This serializer/deserializer is implemented by jl_save_system_image/jl_restore_system_image in staticdata.c.

If there is no sysimg file (jl_options.image_file == NULL), this also implies that --build was given on the command line, so the final result should be a new sysimg file. During Julia initialization, minimal Core and Main modules are created. Then a file named boot.jl is evaluated from the current directory. Julia then evaluates any file given as a command line argument until it reaches the end. Finally, it saves the resulting environment to a "sysimg" file for use as a starting point for a future Julia run.

diff --git a/dev/devdocs/external_profilers/index.html b/dev/devdocs/external_profilers/index.html index 6d51f512..4f830e30 100644 --- a/dev/devdocs/external_profilers/index.html +++ b/dev/devdocs/external_profilers/index.html @@ -8,4 +8,4 @@ Base.compilecache(pkg) end

Here, we use a custom port for tracy which makes it easier to find the correct client in the Tracy UI to connect to.

Adding metadata to zones

The various jl_timing_show_* and jl_timing_printf functions can be used to attach a string (or strings) to a zone. For example, the trace zone for inference shows the method instance that is being inferred.

The TracyCZoneColor function can be used to set the color of a certain zone. Search through the codebase to see how it is used.

Viewing Tracy files in your browser

Visit https://topolarity.github.io/trace-viewer/ for an (experimental) web viewer for Tracy traces.

You can open a local .tracy file or provide a URL from the web (e.g. a file in a Github repo). If you load a trace file from the web, you can also share the page URL directly with others, enabling them to view the same trace.

Enabling stack trace samples

To enable call stack sampling in Tracy, build Julia with these options in your Make.user file:

WITH_TRACY := 1
 WITH_TRACY_CALLSTACKS := 1
-USE_BINARYBUILDER_LIBTRACYCLIENT := 0

You may also need to run make -C deps clean-libtracyclient to force a re-build of Tracy.

This feature has a significant impact on trace size and profiling overhead, so it is recommended to leave call stack sampling off when possible, especially if you intend to share your trace files online.

Note that the Julia JIT runtime does not yet have integration for Tracy's symbolification, so Julia functions will typically be unknown in these stack traces.

Intel VTune (ITTAPI) Profiler

This section is yet to be written.

+USE_BINARYBUILDER_LIBTRACYCLIENT := 0

You may also need to run make -C deps clean-libtracyclient to force a re-build of Tracy.

This feature has a significant impact on trace size and profiling overhead, so it is recommended to leave call stack sampling off when possible, especially if you intend to share your trace files online.

Note that the Julia JIT runtime does not yet have integration for Tracy's symbolification, so Julia functions will typically be unknown in these stack traces.

Intel VTune (ITTAPI) Profiler

This section is yet to be written.

diff --git a/dev/devdocs/functions/index.html b/dev/devdocs/functions/index.html index 4c7ca976..15faa79c 100644 --- a/dev/devdocs/functions/index.html +++ b/dev/devdocs/functions/index.html @@ -40,4 +40,4 @@ # unless `options` is empty #circle#1(color, fill, pairs(options), circle, center, radius) -end

函数 Core.kwftype(t) 创建字段 t.name.mt.kwsorter（如果它未被创建），并返回该函数的类型。

此设计的特点是不使用关键字参数的调用点不需要特殊处理；这一切的工作方式好像它们根本不是语言的一部分。不使用关键字参数的调用点直接派发到被调用函数的 kwsorter。例如，调用：

circle((0,0), 1.0, color = red; other...)

降低为：

kwcall(merge((color = red,), other), circle, (0,0), 1.0)

kwcall (also inCore) denotes a kwcall signature and dispatch. The keyword splatting operation (written as other...) calls the named tuple merge function. This function further unpacks each element of other, expecting each one to contain two values (a symbol and a value). Naturally, a more efficient implementation is available if all splatted arguments are named tuples. Notice that the original circle function is passed through, to handle closures.

Compiler efficiency issues

为每个函数生成新类型在与 Julia 的「默认专门化所有参数」这一设计理念结合使用时，可能对编译器资源的使用产生严重后果。实际上，此设计的初始实现经历了更长的测试和构造时间、高内存占用以及比基线大近乎 2 倍的系统镜像。在一个幼稚的实现中，该问题非常严重，以至于系统几乎无法使用。需要进行几项重要的优化才能使设计变得可行。

第一个问题是函数值参数的不同值导致函数的过度专门化。许多函数只是将参数「传递」到其它地方，例如，到另一个函数或存储位置。这种函数不需要为每个可能传入的闭包专门化。幸运的是，这种情况很容易区分，只需考虑函数是否调用它的某个参数（即，参数出现在某处的「头部位置」）。性能关键的高阶函数，如 map，肯定会直接调用它们的参数函数，因此仍然会按预期进行专门化。此优化通过在前端记录 analyze-variables 传递期间所调用的参数来实现。当 cache_method 看到某个在 Function 类型层次结构的参数传递到声明为 Any 或 Function 的槽时，它的行为就好像应用了 @nospecialize 注释一样。这种启发式方法在实践中似乎非常有效。

下一个问题涉及方法缓存哈希表的结构。经验研究表明，绝大多数动态分派调用只涉及一个或两个元素。反过来看，只考虑第一个元素便可解决许多这些情况。（旁白：单派发的支持者根本不会对此感到惊讶。但是，这个观点意味着「多重派发在实践中很容易优化」，因此我们应该使用它，而不是「我们应该使用单派发」！）因此，方法缓存使用第一个参数作为其主键。但请注意，这对应于函数调用的元组类型的第二个元素（第一个元素是函数本身的类型）。通常，头部位置的类型非常少变化——实际上，大多数函数属于没有参数的单态类型。但是，构造函数不是这种情况，一个方法表便保存了所有类型的构造函数。因此，Type 方法表是特殊的，使用元组类型的第一个元素而不是第二个。

前端为所有闭包生成类型声明。起初，这通过生成通常的类型声明来实现。但是，这产生了大量的构造函数，这些构造函数全都很简单（只是将所有参数传递给 new）。因为方法是部分排序的，所以插入所有这些方法是 O(n^2)，此外要保留的方法实在太多了。这可通过直接生成 struct_type 表达式（绕过默认的构造函数生成）并直接使用 new 来创建闭包的实例来优化。这事并不漂亮，但你需要做你该做的。

下个问题是 @test 宏，它为每个测试用例生成一个 0 参数闭包。这不是必需的，因为每个用例只需运行一次。因此，@test 被改写以展开到一个 try-catch 块中，该块记录测试结果（true、false 或所引发的异常）并对它调用测试套件处理程序。

+end

函数 Core.kwftype(t) 创建字段 t.name.mt.kwsorter（如果它未被创建），并返回该函数的类型。

此设计的特点是不使用关键字参数的调用点不需要特殊处理；这一切的工作方式好像它们根本不是语言的一部分。不使用关键字参数的调用点直接派发到被调用函数的 kwsorter。例如，调用：

circle((0,0), 1.0, color = red; other...)

降低为：

kwcall(merge((color = red,), other), circle, (0,0), 1.0)

kwcall (also inCore) denotes a kwcall signature and dispatch. The keyword splatting operation (written as other...) calls the named tuple merge function. This function further unpacks each element of other, expecting each one to contain two values (a symbol and a value). Naturally, a more efficient implementation is available if all splatted arguments are named tuples. Notice that the original circle function is passed through, to handle closures.

Compiler efficiency issues

为每个函数生成新类型在与 Julia 的「默认专门化所有参数」这一设计理念结合使用时，可能对编译器资源的使用产生严重后果。实际上，此设计的初始实现经历了更长的测试和构造时间、高内存占用以及比基线大近乎 2 倍的系统镜像。在一个幼稚的实现中，该问题非常严重，以至于系统几乎无法使用。需要进行几项重要的优化才能使设计变得可行。

第一个问题是函数值参数的不同值导致函数的过度专门化。许多函数只是将参数「传递」到其它地方，例如，到另一个函数或存储位置。这种函数不需要为每个可能传入的闭包专门化。幸运的是，这种情况很容易区分，只需考虑函数是否调用它的某个参数（即，参数出现在某处的「头部位置」）。性能关键的高阶函数，如 map，肯定会直接调用它们的参数函数，因此仍然会按预期进行专门化。此优化通过在前端记录 analyze-variables 传递期间所调用的参数来实现。当 cache_method 看到某个在 Function 类型层次结构的参数传递到声明为 Any 或 Function 的槽时，它的行为就好像应用了 @nospecialize 注释一样。这种启发式方法在实践中似乎非常有效。

下一个问题涉及方法缓存哈希表的结构。经验研究表明，绝大多数动态分派调用只涉及一个或两个元素。反过来看，只考虑第一个元素便可解决许多这些情况。（旁白：单派发的支持者根本不会对此感到惊讶。但是，这个观点意味着「多重派发在实践中很容易优化」，因此我们应该使用它，而不是「我们应该使用单派发」！）因此，方法缓存使用第一个参数作为其主键。但请注意，这对应于函数调用的元组类型的第二个元素（第一个元素是函数本身的类型）。通常，头部位置的类型非常少变化——实际上，大多数函数属于没有参数的单态类型。但是，构造函数不是这种情况，一个方法表便保存了所有类型的构造函数。因此，Type 方法表是特殊的，使用元组类型的第一个元素而不是第二个。

前端为所有闭包生成类型声明。起初，这通过生成通常的类型声明来实现。但是，这产生了大量的构造函数，这些构造函数全都很简单（只是将所有参数传递给 new）。因为方法是部分排序的，所以插入所有这些方法是 O(n^2)，此外要保留的方法实在太多了。这可通过直接生成 struct_type 表达式（绕过默认的构造函数生成）并直接使用 new 来创建闭包的实例来优化。这事并不漂亮，但你需要做你该做的。

下个问题是 @test 宏，它为每个测试用例生成一个 0 参数闭包。这不是必需的，因为每个用例只需运行一次。因此，@test 被改写以展开到一个 try-catch 块中，该块记录测试结果（true、false 或所引发的异常）并对它调用测试套件处理程序。

diff --git a/dev/devdocs/gc-sa/index.html b/dev/devdocs/gc-sa/index.html index 65f7276f..a5d0c27a 100644 --- a/dev/devdocs/gc-sa/index.html +++ b/dev/devdocs/gc-sa/index.html @@ -72,4 +72,4 @@ // that val is rooted under these conditions JL_GC_PROMISE_ROOTED(val); } -}

Completeness of analysis

The analyzer only looks at local information. In particular, e.g. in the PROPAGATES_ROOT case above, it assumes that such memory is only modified in ways it can see, not in any called functions (unless it happens to decide to consider them in its analysis) and not in any concurrently running threads. As such, it may miss a few problematic cases, though in practice such concurrent modification is fairly rare. Improving the analyzer to handle more such cases may be an interesting topic for future work.

+}

Completeness of analysis

The analyzer only looks at local information. In particular, e.g. in the PROPAGATES_ROOT case above, it assumes that such memory is only modified in ways it can see, not in any called functions (unless it happens to decide to consider them in its analysis) and not in any concurrently running threads. As such, it may miss a few problematic cases, though in practice such concurrent modification is fairly rare. Improving the analyzer to handle more such cases may be an interesting topic for future work.

diff --git a/dev/devdocs/gc/index.html b/dev/devdocs/gc/index.html index 48c0dd6c..ca6f5425 100644 --- a/dev/devdocs/gc/index.html +++ b/dev/devdocs/gc/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

Garbage Collection in Julia

Introduction

Julia has a non-moving, partially concurrent, parallel, generational and mostly precise mark-sweep collector (an interface for conservative stack scanning is provided as an option for users who wish to call Julia from C).

Allocation

Julia uses two types of allocators, the size of the allocation request determining which one is used. Objects up to 2k bytes are allocated on a per-thread free-list pool allocator, while objects larger than 2k bytes are allocated through libc malloc.

Julia’s pool allocator partitions objects on different size classes, so that a memory page managed by the pool allocator (which spans 4 operating system pages on 64bit platforms) only contains objects of the same size class. Each memory page from the pool allocator is paired with some page metadata stored on per-thread lock-free lists. The page metadata contains information such as whether the page has live objects at all, number of free slots, and offsets to the first and last objects in the free-list contained in that page. These metadata are used to optimize the collection phase: a page which has no live objects at all may be returned to the operating system without any need of scanning it, for example.

While a page that has no objects may be returned to the operating system, its associated metadata is permanently allocated and may outlive the given page. As mentioned above, metadata for allocated pages are stored on per-thread lock-free lists. Metadata for free pages, however, may be stored into three separate lock-free lists depending on whether the page has been mapped but never accessed (page_pool_clean), or whether the page has been lazily sweeped and it's waiting to be madvised by a background GC thread (page_pool_lazily_freed), or whether the page has been madvised (page_pool_freed).

Julia's pool allocator follows a "tiered" allocation discipline. When requesting a memory page for the pool allocator, Julia will:

  • Try to claim a page from page_pool_lazily_freed, which contains pages which were empty on the last stop-the-world phase, but not yet madivsed by a concurrent sweeper GC thread.

  • If it failed claiming a page from page_pool_lazily_freed, it will try to claim a page from the page_pool_clean, which contains pages which were mmaped on a previous page allocation request but never accessed.

  • If it failed claiming a page from pool_page_clean and from page_pool_lazily_freed, it will try to claim a page from page_pool_freed, which contains pages which have already been madvised by a concurrent sweeper GC thread and whose underlying virtual address can be recycled.

  • If it failed in all of the attempts mentioned above, it will mmap a batch of pages, claim one page for itself, and insert the remaining pages into page_pool_clean.

Diagram of tiered pool allocation

Marking and Generational Collection

Julia’s mark phase is implemented through a parallel iterative depth-first-search over the object graph. Julia’s collector is non-moving, so object age information can’t be determined through the memory region in which the object resides alone, but has to be somehow encoded in the object header or on a side table. The lowest two bits of an object’s header are used to store, respectively, a mark bit that is set when an object is scanned during the mark phase and an age bit for the generational collection.

Generational collection is implemented through sticky bits: objects are only pushed to the mark-stack, and therefore traced, if their mark-bits are not set. When objects reach the oldest generation, their mark-bits are not reset during the so-called "quick-sweep", which leads to these objects not being traced in a subsequent mark phase. A "full-sweep", however, causes the mark-bits of all objects to be reset, leading to all objects being traced in a subsequent mark phase. Objects are promoted to the next generation during every sweep phase they survive. On the mutator side, field writes are intercepted through a write barrier that pushes an object’s address into a per-thread remembered set if the object is in the last generation, and if the object at the field being written is not. Objects in this remembered set are then traced during the mark phase.

Sweeping

Sweeping of object pools for Julia may fall into two categories: if a given page managed by the pool allocator contains at least one live object, then a free-list must be threaded through its dead objects; if a given page contains no live objects at all, then its underlying physical memory may be returned to the operating system through, for instance, the use of madvise system calls on Linux.

The first category of sweeping is currently serial and performed in the stop-the-world phase. For the second category of sweeping, if concurrent page sweeping is enabled through the flag --gcthreads=X,1 we perform the madvise system calls in a background sweeper thread, concurrently with the mutator threads. During the stop-the-world phase of the collector, pool allocated pages which contain no live objects are initially pushed into the pool_page_lazily_freed. The background sweeping thread is then woken up and is responsible for removing pages from pool_page_lazily_freed, calling madvise on them, and inserting them into pool_page_freed. As described above, pool_page_lazily_freed is also shared with mutator threads. This implies that on allocation-heavy multithreaded workloads, mutator threads would often avoid a page fault on allocation (coming from accessing a fresh mmaped page or accessing a madvised page) by directly allocating from a page in pool_page_lazily_freed, while the background sweeper thread needs to madvise a reduce number of pages given some of them were already claimed by the mutators.

Heuristics

GC heuristics tune the GC by changing the size of the allocation interval between garbage collections. If a GC was unproductive, then we increase the size of the allocation interval to allow objects more time to die. If a GC returns a lot of space we can shrink the interval. The goal is to find a steady state where we are allocating just about the same amount as we are collecting.

+
Repository

Garbage Collection in Julia

Introduction

Julia has a non-moving, partially concurrent, parallel, generational and mostly precise mark-sweep collector (an interface for conservative stack scanning is provided as an option for users who wish to call Julia from C).

Allocation

Julia uses two types of allocators, the size of the allocation request determining which one is used. Objects up to 2k bytes are allocated on a per-thread free-list pool allocator, while objects larger than 2k bytes are allocated through libc malloc.

Julia’s pool allocator partitions objects on different size classes, so that a memory page managed by the pool allocator (which spans 4 operating system pages on 64bit platforms) only contains objects of the same size class. Each memory page from the pool allocator is paired with some page metadata stored on per-thread lock-free lists. The page metadata contains information such as whether the page has live objects at all, number of free slots, and offsets to the first and last objects in the free-list contained in that page. These metadata are used to optimize the collection phase: a page which has no live objects at all may be returned to the operating system without any need of scanning it, for example.

While a page that has no objects may be returned to the operating system, its associated metadata is permanently allocated and may outlive the given page. As mentioned above, metadata for allocated pages are stored on per-thread lock-free lists. Metadata for free pages, however, may be stored into three separate lock-free lists depending on whether the page has been mapped but never accessed (page_pool_clean), or whether the page has been lazily sweeped and it's waiting to be madvised by a background GC thread (page_pool_lazily_freed), or whether the page has been madvised (page_pool_freed).

Julia's pool allocator follows a "tiered" allocation discipline. When requesting a memory page for the pool allocator, Julia will:

  • Try to claim a page from page_pool_lazily_freed, which contains pages which were empty on the last stop-the-world phase, but not yet madivsed by a concurrent sweeper GC thread.

  • If it failed claiming a page from page_pool_lazily_freed, it will try to claim a page from the page_pool_clean, which contains pages which were mmaped on a previous page allocation request but never accessed.

  • If it failed claiming a page from pool_page_clean and from page_pool_lazily_freed, it will try to claim a page from page_pool_freed, which contains pages which have already been madvised by a concurrent sweeper GC thread and whose underlying virtual address can be recycled.

  • If it failed in all of the attempts mentioned above, it will mmap a batch of pages, claim one page for itself, and insert the remaining pages into page_pool_clean.

Diagram of tiered pool allocation

Marking and Generational Collection

Julia’s mark phase is implemented through a parallel iterative depth-first-search over the object graph. Julia’s collector is non-moving, so object age information can’t be determined through the memory region in which the object resides alone, but has to be somehow encoded in the object header or on a side table. The lowest two bits of an object’s header are used to store, respectively, a mark bit that is set when an object is scanned during the mark phase and an age bit for the generational collection.

Generational collection is implemented through sticky bits: objects are only pushed to the mark-stack, and therefore traced, if their mark-bits are not set. When objects reach the oldest generation, their mark-bits are not reset during the so-called "quick-sweep", which leads to these objects not being traced in a subsequent mark phase. A "full-sweep", however, causes the mark-bits of all objects to be reset, leading to all objects being traced in a subsequent mark phase. Objects are promoted to the next generation during every sweep phase they survive. On the mutator side, field writes are intercepted through a write barrier that pushes an object’s address into a per-thread remembered set if the object is in the last generation, and if the object at the field being written is not. Objects in this remembered set are then traced during the mark phase.

Sweeping

Sweeping of object pools for Julia may fall into two categories: if a given page managed by the pool allocator contains at least one live object, then a free-list must be threaded through its dead objects; if a given page contains no live objects at all, then its underlying physical memory may be returned to the operating system through, for instance, the use of madvise system calls on Linux.

The first category of sweeping is currently serial and performed in the stop-the-world phase. For the second category of sweeping, if concurrent page sweeping is enabled through the flag --gcthreads=X,1 we perform the madvise system calls in a background sweeper thread, concurrently with the mutator threads. During the stop-the-world phase of the collector, pool allocated pages which contain no live objects are initially pushed into the pool_page_lazily_freed. The background sweeping thread is then woken up and is responsible for removing pages from pool_page_lazily_freed, calling madvise on them, and inserting them into pool_page_freed. As described above, pool_page_lazily_freed is also shared with mutator threads. This implies that on allocation-heavy multithreaded workloads, mutator threads would often avoid a page fault on allocation (coming from accessing a fresh mmaped page or accessing a madvised page) by directly allocating from a page in pool_page_lazily_freed, while the background sweeper thread needs to madvise a reduce number of pages given some of them were already claimed by the mutators.

Heuristics

GC heuristics tune the GC by changing the size of the allocation interval between garbage collections. If a GC was unproductive, then we increase the size of the allocation interval to allow objects more time to die. If a GC returns a lot of space we can shrink the interval. The goal is to find a steady state where we are allocating just about the same amount as we are collecting.

diff --git a/dev/devdocs/inference/index.html b/dev/devdocs/inference/index.html index 35bfe15b..46880966 100644 --- a/dev/devdocs/inference/index.html +++ b/dev/devdocs/inference/index.html @@ -26,4 +26,4 @@ 0 └── goto #4 0 4 ─ goto #5 0 5 ─ %10 = Core.tuple(%7)::Tuple{Float64} - 0 └── return %10

The line costs are in the left column. This includes the consequences of inlining and other forms of optimization.

+ 0 └── return %10

The line costs are in the left column. This includes the consequences of inlining and other forms of optimization.

diff --git a/dev/devdocs/init/index.html b/dev/devdocs/init/index.html index eb814a39..d8a66342 100644 --- a/dev/devdocs/init/index.html +++ b/dev/devdocs/init/index.html @@ -12,4 +12,4 @@ jl_any_type, jl_emptysvec, 32);

jl_init_tasks() creates the jl_datatype_t* jl_task_type object; initializes the global jl_root_task struct; and sets jl_current_task to the root task.

jl_init_codegen() initializes the LLVM library.

jl_init_serializer() initializes 8-bit serialization tags for builtin jl_value_t values.

If there is no sysimg file (!jl_options.image_file) then the Core and Main modules are created and boot.jl is evaluated:

jl_core_module = jl_new_module(jl_symbol("Core")) creates the Julia Core module.

jl_init_intrinsic_functions() creates a new Julia module Intrinsics containing constant jl_intrinsic_type symbols. These define an integer code for each intrinsic function. emit_intrinsic() translates these symbols into LLVM instructions during code generation.

jl_init_primitives() hooks C functions up to Julia function symbols. e.g. the symbol Core.:(===)() is bound to C function pointer jl_f_is() by calling add_builtin_func("===", jl_f_is).

jl_new_main_module() creates the global "Main" module and sets jl_current_task->current_module = jl_main_module.

Note: _julia_init() then sets jl_root_task->current_module = jl_core_module. jl_root_task is an alias of jl_current_task at this point, so the current_module set by jl_new_main_module() above is overwritten.

jl_load("boot.jl", sizeof("boot.jl")) calls jl_parse_eval_all which repeatedly calls jl_toplevel_eval_flex() to execute boot.jl. <!– TODO – drill down into eval? –>

jl_get_builtin_hooks() initializes global C pointers to Julia globals defined in boot.jl.

jl_init_box_caches() pre-allocates global boxed integer value objects for values up to 1024. This speeds up allocation of boxed ints later on. e.g.:

jl_value_t *jl_box_uint8(uint32_t x)
 {
     return boxed_uint8_cache[(uint8_t)x];
-}

_julia_init() iterates over the jl_core_module->bindings.table looking for jl_datatype_t values and sets the type name's module prefix to jl_core_module.

jl_add_standard_imports(jl_main_module) does "using Base" in the "Main" module.

Note: _julia_init() now reverts to jl_root_task->current_module = jl_main_module as it was before being set to jl_core_module above.

Platform specific signal handlers are initialized for SIGSEGV (OSX, Linux), and SIGFPE (Windows).

Other signals (SIGINFO, SIGBUS, SIGILL, SIGTERM, SIGABRT, SIGQUIT, SIGSYS and SIGPIPE) are hooked up to sigdie_handler() which prints a backtrace.

jl_init_restored_module() calls jl_module_run_initializer() for each deserialized module to run the __init__() function.

Finally sigint_handler() is hooked up to SIGINT and calls jl_throw(jl_interrupt_exception).

_julia_init() then returns back to main() in cli/loader_exe.c and main() calls repl_entrypoint(argc, (char**)argv).

sysimg

If there is a sysimg file, it contains a pre-cooked image of the Core and Main modules (and whatever else is created by boot.jl). See Building the Julia system image.

jl_restore_system_image() deserializes the saved sysimg into the current Julia runtime environment and initialization continues after jl_init_box_caches() below...

Note: jl_restore_system_image() (and staticdata.c in general) uses the Legacy ios.c library.

repl_entrypoint()

repl_entrypoint() loads the contents of argv[] into Base.ARGS.

If a .jl "program" file was supplied on the command line, then exec_program() calls jl_load(program,len) which calls jl_parse_eval_all which repeatedly calls jl_toplevel_eval_flex() to execute the program.

However, in our example (julia -e 'println("Hello World!")'), jl_get_global(jl_base_module, jl_symbol("_start")) looks up Base._start and jl_apply() executes it.

Base._start

Base._start calls Base.exec_options which calls jl_parse_input_line("println("Hello World!")") to create an expression object and Core.eval(Main, ex) to execute the parsed expression ex in the module context of Main.

Core.eval

Core.eval(Main, ex) calls jl_toplevel_eval_in(m, ex), which calls jl_toplevel_eval_flex. jl_toplevel_eval_flex implements a simple heuristic to decide whether to compile a given code thunk or run it by interpreter. When given println("Hello World!"), it would usually decide to run the code by interpreter, in which case it calls jl_interpret_toplevel_thunk, which then calls eval_body.

The stack dump below shows how the interpreter works its way through various methods of Base.println() and Base.print() before arriving at write(s::IO, a::Array{T}) where T which does ccall(jl_uv_write()).

jl_uv_write() calls uv_write() to write "Hello World!" to JL_STDOUT. See Libuv wrappers for stdio.:

Hello World!
Stack frameSource codeNotes
jl_uv_write()jl_uv.ccalled though ccall
julia_write_282942stream.jlfunction write!(s::IO, a::Array{T}) where T
julia_print_284639ascii.jlprint(io::IO, s::String) = (write(io, s); nothing)
jlcall_print_284639
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.print(Base.TTY, String)
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.print(Base.TTY, String, Char, Char...)
jl_apply()julia.h
jl_f_apply()builtins.c
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.println(Base.TTY, String, String...)
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.println(String,)
jl_apply()julia.h
do_call()interpreter.c
eval_body()interpreter.c
jl_interpret_toplevel_thunkinterpreter.c
jl_toplevel_eval_flextoplevel.c
jl_toplevel_eval_intoplevel.c
Core.evalboot.jl

Since our example has just one function call, which has done its job of printing "Hello World!", the stack now rapidly unwinds back to main().

jl_atexit_hook()

main() calls jl_atexit_hook(). This calls Base._atexit, then calls jl_gc_run_all_finalizers() and cleans up libuv handles.

julia_save()

Finally, main() calls julia_save(), which if requested on the command line, saves the runtime state to a new system image. See jl_compile_all() and jl_save_system_image().

+}

_julia_init() iterates over the jl_core_module->bindings.table looking for jl_datatype_t values and sets the type name's module prefix to jl_core_module.

jl_add_standard_imports(jl_main_module) does "using Base" in the "Main" module.

Note: _julia_init() now reverts to jl_root_task->current_module = jl_main_module as it was before being set to jl_core_module above.

Platform specific signal handlers are initialized for SIGSEGV (OSX, Linux), and SIGFPE (Windows).

Other signals (SIGINFO, SIGBUS, SIGILL, SIGTERM, SIGABRT, SIGQUIT, SIGSYS and SIGPIPE) are hooked up to sigdie_handler() which prints a backtrace.

jl_init_restored_module() calls jl_module_run_initializer() for each deserialized module to run the __init__() function.

Finally sigint_handler() is hooked up to SIGINT and calls jl_throw(jl_interrupt_exception).

_julia_init() then returns back to main() in cli/loader_exe.c and main() calls repl_entrypoint(argc, (char**)argv).

sysimg

If there is a sysimg file, it contains a pre-cooked image of the Core and Main modules (and whatever else is created by boot.jl). See Building the Julia system image.

jl_restore_system_image() deserializes the saved sysimg into the current Julia runtime environment and initialization continues after jl_init_box_caches() below...

Note: jl_restore_system_image() (and staticdata.c in general) uses the Legacy ios.c library.

repl_entrypoint()

repl_entrypoint() loads the contents of argv[] into Base.ARGS.

If a .jl "program" file was supplied on the command line, then exec_program() calls jl_load(program,len) which calls jl_parse_eval_all which repeatedly calls jl_toplevel_eval_flex() to execute the program.

However, in our example (julia -e 'println("Hello World!")'), jl_get_global(jl_base_module, jl_symbol("_start")) looks up Base._start and jl_apply() executes it.

Base._start

Base._start calls Base.exec_options which calls jl_parse_input_line("println("Hello World!")") to create an expression object and Core.eval(Main, ex) to execute the parsed expression ex in the module context of Main.

Core.eval

Core.eval(Main, ex) calls jl_toplevel_eval_in(m, ex), which calls jl_toplevel_eval_flex. jl_toplevel_eval_flex implements a simple heuristic to decide whether to compile a given code thunk or run it by interpreter. When given println("Hello World!"), it would usually decide to run the code by interpreter, in which case it calls jl_interpret_toplevel_thunk, which then calls eval_body.

The stack dump below shows how the interpreter works its way through various methods of Base.println() and Base.print() before arriving at write(s::IO, a::Array{T}) where T which does ccall(jl_uv_write()).

jl_uv_write() calls uv_write() to write "Hello World!" to JL_STDOUT. See Libuv wrappers for stdio.:

Hello World!
Stack frameSource codeNotes
jl_uv_write()jl_uv.ccalled though ccall
julia_write_282942stream.jlfunction write!(s::IO, a::Array{T}) where T
julia_print_284639ascii.jlprint(io::IO, s::String) = (write(io, s); nothing)
jlcall_print_284639
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.print(Base.TTY, String)
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.print(Base.TTY, String, Char, Char...)
jl_apply()julia.h
jl_f_apply()builtins.c
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.println(Base.TTY, String, String...)
jl_apply()julia.h
jl_trampoline()builtins.c
jl_apply()julia.h
jl_apply_generic()gf.cBase.println(String,)
jl_apply()julia.h
do_call()interpreter.c
eval_body()interpreter.c
jl_interpret_toplevel_thunkinterpreter.c
jl_toplevel_eval_flextoplevel.c
jl_toplevel_eval_intoplevel.c
Core.evalboot.jl

Since our example has just one function call, which has done its job of printing "Hello World!", the stack now rapidly unwinds back to main().

jl_atexit_hook()

main() calls jl_atexit_hook(). This calls Base._atexit, then calls jl_gc_run_all_finalizers() and cleans up libuv handles.

julia_save()

Finally, main() calls julia_save(), which if requested on the command line, saves the runtime state to a new system image. See jl_compile_all() and jl_save_system_image().

diff --git a/dev/devdocs/isbitsunionarrays/index.html b/dev/devdocs/isbitsunionarrays/index.html index 7e54d826..55c60c1d 100644 --- a/dev/devdocs/isbitsunionarrays/index.html +++ b/dev/devdocs/isbitsunionarrays/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

isbits Union Optimizations

In Julia, the Array type holds both "bits" values as well as heap-allocated "boxed" values. The distinction is whether the value itself is stored inline (in the direct allocated memory of the array), or if the memory of the array is simply a collection of pointers to objects allocated elsewhere. In terms of performance, accessing values inline is clearly an advantage over having to follow a pointer to the actual value. The definition of "isbits" generally means any Julia type with a fixed, determinate size, meaning no "pointer" fields, see ?isbitstype.

Julia also supports Union types, quite literally the union of a set of types. Custom Union type definitions can be extremely handy for applications wishing to "cut across" the nominal type system (i.e. explicit subtype relationships) and define methods or functionality on these, otherwise unrelated, set of types. A compiler challenge, however, is in determining how to treat these Union types. The naive approach (and indeed, what Julia itself did pre-0.7), is to simply make a "box" and then a pointer in the box to the actual value, similar to the previously mentioned "boxed" values. This is unfortunate, however, because of the number of small, primitive "bits" types (think UInt8, Int32, Float64, etc.) that would easily fit themselves inline in this "box" without needing any indirection for value access. There are two main ways Julia can take advantage of this optimization as of 0.7: isbits Union fields in types, and isbits Union Arrays.

isbits Union Structs

Julia now includes an optimization wherein "isbits Union" fields in types (mutable struct, struct, etc.) will be stored inline. This is accomplished by determining the "inline size" of the Union type (e.g. Union{UInt8, Int16} will have a size of two bytes, which represents the size needed of the largest Union type Int16), and in addition, allocating an extra "type tag byte" (UInt8), whose value signals the type of the actual value stored inline of the "Union bytes". The type tag byte value is the index of the actual value's type in the Union type's order of types. For example, a type tag value of 0x02 for a field with type Union{Nothing, UInt8, Int16} would indicate that an Int16 value is stored in the 16 bits of the field in the structure's memory; a 0x01 value would indicate that a UInt8 value was stored in the first 8 bits of the 16 bits of the field's memory. Lastly, a value of 0x00 signals that the nothing value will be returned for this field, even though, as a singleton type with a single type instance, it technically has a size of 0. The type tag byte for a type's Union field is stored directly after the field's computed Union memory.

isbits Union Arrays

Julia can now also store "isbits Union" values inline in an Array, as opposed to requiring an indirection box. The optimization is accomplished by storing an extra "type tag array" of bytes, one byte per array element, alongside the bytes of the actual array data. This type tag array serves the same function as the type field case: its value signals the type of the actual stored Union value in the array. In terms of layout, a Julia Array can include extra "buffer" space before and after its actual data values, which are tracked in the a->offset and a->maxsize fields of the jl_array_t* type. The "type tag array" is treated exactly as another jl_array_t*, but which shares the same a->offset, a->maxsize, and a->len fields. So the formula to access an isbits Union Array's type tag bytes is a->data + (a->maxsize - a->offset) * a->elsize + a->offset; i.e. the Array's a->data pointer is already shifted by a->offset, so correcting for that, we follow the data all the way to the max of what it can hold a->maxsize, then adjust by a->offset more bytes to account for any present "front buffering" the array might be doing. This layout in particular allows for very efficient resizing operations as the type tag data only ever has to move when the actual array's data has to move.

+
Repository

isbits Union Optimizations

In Julia, the Array type holds both "bits" values as well as heap-allocated "boxed" values. The distinction is whether the value itself is stored inline (in the direct allocated memory of the array), or if the memory of the array is simply a collection of pointers to objects allocated elsewhere. In terms of performance, accessing values inline is clearly an advantage over having to follow a pointer to the actual value. The definition of "isbits" generally means any Julia type with a fixed, determinate size, meaning no "pointer" fields, see ?isbitstype.

Julia also supports Union types, quite literally the union of a set of types. Custom Union type definitions can be extremely handy for applications wishing to "cut across" the nominal type system (i.e. explicit subtype relationships) and define methods or functionality on these, otherwise unrelated, set of types. A compiler challenge, however, is in determining how to treat these Union types. The naive approach (and indeed, what Julia itself did pre-0.7), is to simply make a "box" and then a pointer in the box to the actual value, similar to the previously mentioned "boxed" values. This is unfortunate, however, because of the number of small, primitive "bits" types (think UInt8, Int32, Float64, etc.) that would easily fit themselves inline in this "box" without needing any indirection for value access. There are two main ways Julia can take advantage of this optimization as of 0.7: isbits Union fields in types, and isbits Union Arrays.

isbits Union Structs

Julia now includes an optimization wherein "isbits Union" fields in types (mutable struct, struct, etc.) will be stored inline. This is accomplished by determining the "inline size" of the Union type (e.g. Union{UInt8, Int16} will have a size of two bytes, which represents the size needed of the largest Union type Int16), and in addition, allocating an extra "type tag byte" (UInt8), whose value signals the type of the actual value stored inline of the "Union bytes". The type tag byte value is the index of the actual value's type in the Union type's order of types. For example, a type tag value of 0x02 for a field with type Union{Nothing, UInt8, Int16} would indicate that an Int16 value is stored in the 16 bits of the field in the structure's memory; a 0x01 value would indicate that a UInt8 value was stored in the first 8 bits of the 16 bits of the field's memory. Lastly, a value of 0x00 signals that the nothing value will be returned for this field, even though, as a singleton type with a single type instance, it technically has a size of 0. The type tag byte for a type's Union field is stored directly after the field's computed Union memory.

isbits Union Arrays

Julia can now also store "isbits Union" values inline in an Array, as opposed to requiring an indirection box. The optimization is accomplished by storing an extra "type tag array" of bytes, one byte per array element, alongside the bytes of the actual array data. This type tag array serves the same function as the type field case: its value signals the type of the actual stored Union value in the array. In terms of layout, a Julia Array can include extra "buffer" space before and after its actual data values, which are tracked in the a->offset and a->maxsize fields of the jl_array_t* type. The "type tag array" is treated exactly as another jl_array_t*, but which shares the same a->offset, a->maxsize, and a->len fields. So the formula to access an isbits Union Array's type tag bytes is a->data + (a->maxsize - a->offset) * a->elsize + a->offset; i.e. the Array's a->data pointer is already shifted by a->offset, so correcting for that, we follow the data all the way to the max of what it can hold a->maxsize, then adjust by a->offset more bytes to account for any present "front buffering" the array might be doing. This layout in particular allows for very efficient resizing operations as the type tag data only ever has to move when the actual array's data has to move.

diff --git a/dev/devdocs/jit/index.html b/dev/devdocs/jit/index.html index 76feacd7..b041bbdf 100644 --- a/dev/devdocs/jit/index.html +++ b/dev/devdocs/jit/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

JIT Design and Implementation

This document explains the design and implementation of Julia's JIT, after codegen has finished and unoptimized LLVM IR has been produced. The JIT is responsible for optimizing and compiling this IR to machine code, and for linking it into the current process and making the code available for execution.

Introduction

The JIT is responsible for managing compilation resources, looking up previously compiled code, and compiling new code. It is primarily built on LLVM's On-Request-Compilation (ORCv2) technology, which provides support for a number of useful features such as concurrent compilation, lazy compilation, and the ability to compile code in a separate process. Though LLVM provides a basic JIT compiler in the form of LLJIT, Julia uses many ORCv2 APIs directly to create its own custom JIT compiler.

Overview

Diagram of the compiler flow

Codegen produces an LLVM module containing IR for one or more Julia functions from the original Julia SSA IR produced by type inference (labeled as translate on the compiler diagram above). It also produces a mapping of code-instance to LLVM function name. However, though some optimizations have been applied by the Julia-based compiler on Julia IR, the LLVM IR produced by codegen still contains many opportunities for optimization. Thus, the first step the JIT takes is to run a target-independent optimization pipeline[tdp] on the LLVM module. Then, the JIT runs a target-dependent optimization pipeline, which includes target-specific optimizations and code generation, and outputs an object file. Finally, the JIT links the resulting object file into the current process and makes the code available for execution. All of this is controlled by code in src/jitlayers.cpp.

Currently, only one thread at a time is permitted to enter the optimize-compile-link pipeline at a time, due to restrictions imposed by one of our linkers (RuntimeDyld). However, the JIT is designed to support concurrent optimization and compilation, and the linker restriction is expected to be lifted in the future when RuntimeDyld has been fully superseded on all platforms.

Optimization Pipeline

The optimization pipeline is based off LLVM's new pass manager, but the pipeline is customized for Julia's needs. The pipeline is defined in src/pipeline.cpp, and broadly proceeds through a number of stages as detailed below.

  1. Early Simplification
    1. These passes are mainly used to simplify the IR and canonicalize patterns so that later passes can identify those patterns more easily. Additionally, various intrinsic calls such as branch prediction hints and annotations are lowered into other metadata or other IR features. SimplifyCFG (simplify control flow graph), DCE (dead code elimination), and SROA (scalar replacement of aggregates) are some of the key players here.
  2. Early Optimization
    1. These passes are typically cheap and are primarily focused around reducing the number of instructions in the IR and propagating knowledge to other instructions. For example, EarlyCSE is used to perform common subexpression elimination, and InstCombine and InstSimplify perform a number of small peephole optimizations to make operations less expensive.
  3. Loop Optimization
    1. These passes canonicalize and simplify loops. Loops are often hot code, which makes loop optimization extremely important for performance. Key players here include LoopRotate, LICM, and LoopFullUnroll. Some bounds check elimination also happens here, as a result of the IRCE pass which can prove certain bounds are never exceeded.
  4. Scalar Optimization
    1. The scalar optimization pipeline contains a number of more expensive, but more powerful passes such as GVN (global value numbering), SCCP (sparse conditional constant propagation), and another round of bounds check elimination. These passes are expensive, but they can often remove large amounts of code and make vectorization much more successful and effective. Several other simplification and optimization passes intersperse the more expensive ones to reduce the amount of work they have to do.
  5. Vectorization
    1. Automatic vectorization is an extremely powerful transformation for CPU-intensive code. Briefly, vectorization allows execution of a single instruction on multiple data (SIMD), e.g. performing 8 addition operations at the same time. However, proving code to be both capable of vectorization and profitable to vectorize is difficult, and this relies heavily on the prior optimization passes to massage the IR into a state where vectorization is worth it.
  6. Intrinsic Lowering
    1. Julia inserts a number of custom intrinsics, for reasons such as object allocation, garbage collection, and exception handling. These intrinsics were originally placed to make optimization opportunities more obvious, but they are now lowered into LLVM IR to enable the IR to be emitted as machine code.
  7. Cleanup
    1. These passes are last-chance optimizations, and perform small optimizations such as fused multiply-add propagation and division-remainder simplification. Additionally, targets that do not support half-precision floating point numbers will have their half-precision instructions lowered into single-precision instructions here, and passes are added to provide sanitizer support.

Target-Dependent Optimization and Code Generation

LLVM provides target-dependent optimization and machine code generation in the same pipeline, located in the TargetMachine for a given platform. These passes include instruction selection, instruction scheduling, register allocation, and machine code emission. The LLVM documentation provides a good overview of the process, and the LLVM source code is the best place to look for details on the pipeline and passes.

Linking

Currently, Julia is transitioning between two linkers: the older RuntimeDyld linker, and the newer JITLink linker. JITLink contains a number of features that RuntimeDyld does not have, such as concurrent and reentrant linking, but currently lacks good support for profiling integrations and does not yet support all of the platforms that RuntimeDyld supports. Over time, JITLink is expected to replace RuntimeDyld entirely. Further details on JITLink can be found in the LLVM documentation.

Execution

Once the code has been linked into the current process, it is available for execution. This fact is made known to the generating codeinst by updating the invoke, specsigflags, and specptr fields appropriately. Codeinsts support upgrading invoke, specsigflags, and specptr fields, so long as every combination of these fields that exists at any given point in time is valid to be called. This allows the JIT to update these fields without invalidating existing codeinsts, supporting a potential future concurrent JIT. Specifically, the following states may be valid:

  1. invoke is NULL, specsigflags is 0b00, specptr is NULL
    1. This is the initial state of a codeinst, and indicates that the codeinst has not yet been compiled.
  2. invoke is non-null, specsigflags is 0b00, specptr is NULL
    1. This indicates that the codeinst was not compiled with any specialization, and that the codeinst should be invoked directly. Note that in this instance, invoke does not read either the specsigflags or specptr fields, and therefore they may be modified without invalidating the invoke pointer.
  3. invoke is non-null, specsigflags is 0b10, specptr is non-null
    1. This indicates that the codeinst was compiled, but a specialized function signature was deemed unnecessary by codegen.
  4. invoke is non-null, specsigflags is 0b11, specptr is non-null
    1. This indicates that the codeinst was compiled, and a specialized function signature was deemed necessary by codegen. The specptr field contains a pointer to the specialized function signature. The invoke pointer is permitted to read both specsigflags and specptr fields.

In addition, there are a number of different transitional states that occur during the update process. To account for these potential situations, the following write and read patterns should be used when dealing with these codeinst fields.

  1. When writing invoke, specsigflags, and specptr:
    1. Perform an atomic compare-exchange operation of specptr assuming the old value was NULL. This compare-exchange operation should have at least acquire-release ordering, to provide ordering guarantees of the remaining memory operations in the write.
    2. If specptr was non-null, cease the write operation and wait for bit 0b10 of specsigflags to be written.
    3. Write the new low bit of specsigflags to its final value. This may be a relaxed write.
    4. Write the new invoke pointer to its final value. This must have at least a release memory ordering to synchronize with reads of invoke.
    5. Set the second bit of specsigflags to 1. This must be at least a release memory ordering to synchronize with reads of specsigflags. This step completes the write operation and announces to all other threads that all fields have been set.
  2. When reading all of invoke, specsigflags, and specptr:
    1. Read the invoke field with at least an acquire memory ordering. This load will be referred to as initial_invoke.
    2. If initial_invoke is NULL, the codeinst is not yet executable. invoke is NULL, specsigflags may be treated as 0b00, specptr may be treated as NULL.
    3. Read the specptr field with at least an acquire memory ordering.
    4. If specptr is NULL, then the initial_invoke pointer must not be relying on specptr to guarantee correct execution. Therefore, invoke is non-null, specsigflags may be treated as 0b00, specptr may be treated as NULL.
    5. If specptr is non-null, then initial_invoke might not be the final invoke field that uses specptr. This can occur if specptr has been written, but invoke has not yet been written. Therefore, spin on the second bit of specsigflags until it is set to 1 with at least acquire memory ordering.
    6. Re-read the invoke field with at least an acquire memory ordering. This load will be referred to as final_invoke.
    7. Read the specsigflags field with any memory ordering.
    8. invoke is final_invoke, specsigflags is the value read in step 7, specptr is the value read in step 3.
  3. When updating a specptr to a different but equivalent function pointer:
    1. Perform a release store of the new function pointer to specptr. Races here must be benign, as the old function pointer is required to still be valid, and any new ones are also required to be valid as well. Once a pointer has been written to specptr, it must always be callable whether or not it is later overwritten.

Although these write, read, and update steps are complicated, they ensure that the JIT can update codeinsts without invalidating existing codeinsts, and that the JIT can update codeinsts without invalidating existing invoke pointers. This allows the JIT to potentially reoptimize functions at higher optimization levels in the future, and also will allow the JIT to support concurrent compilation of functions in the future.

  • tdpThis is not a totally-target independent pipeline, as transformations such as vectorization rely upon target information such as vector register width and cost modeling. Additionally, codegen itself makes a few target-dependent assumptions, and the optimization pipeline will take advantage of that knowledge.
+
Repository

JIT Design and Implementation

This document explains the design and implementation of Julia's JIT, after codegen has finished and unoptimized LLVM IR has been produced. The JIT is responsible for optimizing and compiling this IR to machine code, and for linking it into the current process and making the code available for execution.

Introduction

The JIT is responsible for managing compilation resources, looking up previously compiled code, and compiling new code. It is primarily built on LLVM's On-Request-Compilation (ORCv2) technology, which provides support for a number of useful features such as concurrent compilation, lazy compilation, and the ability to compile code in a separate process. Though LLVM provides a basic JIT compiler in the form of LLJIT, Julia uses many ORCv2 APIs directly to create its own custom JIT compiler.

Overview

Diagram of the compiler flow

Codegen produces an LLVM module containing IR for one or more Julia functions from the original Julia SSA IR produced by type inference (labeled as translate on the compiler diagram above). It also produces a mapping of code-instance to LLVM function name. However, though some optimizations have been applied by the Julia-based compiler on Julia IR, the LLVM IR produced by codegen still contains many opportunities for optimization. Thus, the first step the JIT takes is to run a target-independent optimization pipeline[tdp] on the LLVM module. Then, the JIT runs a target-dependent optimization pipeline, which includes target-specific optimizations and code generation, and outputs an object file. Finally, the JIT links the resulting object file into the current process and makes the code available for execution. All of this is controlled by code in src/jitlayers.cpp.

Currently, only one thread at a time is permitted to enter the optimize-compile-link pipeline at a time, due to restrictions imposed by one of our linkers (RuntimeDyld). However, the JIT is designed to support concurrent optimization and compilation, and the linker restriction is expected to be lifted in the future when RuntimeDyld has been fully superseded on all platforms.

Optimization Pipeline

The optimization pipeline is based off LLVM's new pass manager, but the pipeline is customized for Julia's needs. The pipeline is defined in src/pipeline.cpp, and broadly proceeds through a number of stages as detailed below.

  1. Early Simplification
    1. These passes are mainly used to simplify the IR and canonicalize patterns so that later passes can identify those patterns more easily. Additionally, various intrinsic calls such as branch prediction hints and annotations are lowered into other metadata or other IR features. SimplifyCFG (simplify control flow graph), DCE (dead code elimination), and SROA (scalar replacement of aggregates) are some of the key players here.
  2. Early Optimization
    1. These passes are typically cheap and are primarily focused around reducing the number of instructions in the IR and propagating knowledge to other instructions. For example, EarlyCSE is used to perform common subexpression elimination, and InstCombine and InstSimplify perform a number of small peephole optimizations to make operations less expensive.
  3. Loop Optimization
    1. These passes canonicalize and simplify loops. Loops are often hot code, which makes loop optimization extremely important for performance. Key players here include LoopRotate, LICM, and LoopFullUnroll. Some bounds check elimination also happens here, as a result of the IRCE pass which can prove certain bounds are never exceeded.
  4. Scalar Optimization
    1. The scalar optimization pipeline contains a number of more expensive, but more powerful passes such as GVN (global value numbering), SCCP (sparse conditional constant propagation), and another round of bounds check elimination. These passes are expensive, but they can often remove large amounts of code and make vectorization much more successful and effective. Several other simplification and optimization passes intersperse the more expensive ones to reduce the amount of work they have to do.
  5. Vectorization
    1. Automatic vectorization is an extremely powerful transformation for CPU-intensive code. Briefly, vectorization allows execution of a single instruction on multiple data (SIMD), e.g. performing 8 addition operations at the same time. However, proving code to be both capable of vectorization and profitable to vectorize is difficult, and this relies heavily on the prior optimization passes to massage the IR into a state where vectorization is worth it.
  6. Intrinsic Lowering
    1. Julia inserts a number of custom intrinsics, for reasons such as object allocation, garbage collection, and exception handling. These intrinsics were originally placed to make optimization opportunities more obvious, but they are now lowered into LLVM IR to enable the IR to be emitted as machine code.
  7. Cleanup
    1. These passes are last-chance optimizations, and perform small optimizations such as fused multiply-add propagation and division-remainder simplification. Additionally, targets that do not support half-precision floating point numbers will have their half-precision instructions lowered into single-precision instructions here, and passes are added to provide sanitizer support.

Target-Dependent Optimization and Code Generation

LLVM provides target-dependent optimization and machine code generation in the same pipeline, located in the TargetMachine for a given platform. These passes include instruction selection, instruction scheduling, register allocation, and machine code emission. The LLVM documentation provides a good overview of the process, and the LLVM source code is the best place to look for details on the pipeline and passes.

Linking

Currently, Julia is transitioning between two linkers: the older RuntimeDyld linker, and the newer JITLink linker. JITLink contains a number of features that RuntimeDyld does not have, such as concurrent and reentrant linking, but currently lacks good support for profiling integrations and does not yet support all of the platforms that RuntimeDyld supports. Over time, JITLink is expected to replace RuntimeDyld entirely. Further details on JITLink can be found in the LLVM documentation.

Execution

Once the code has been linked into the current process, it is available for execution. This fact is made known to the generating codeinst by updating the invoke, specsigflags, and specptr fields appropriately. Codeinsts support upgrading invoke, specsigflags, and specptr fields, so long as every combination of these fields that exists at any given point in time is valid to be called. This allows the JIT to update these fields without invalidating existing codeinsts, supporting a potential future concurrent JIT. Specifically, the following states may be valid:

  1. invoke is NULL, specsigflags is 0b00, specptr is NULL
    1. This is the initial state of a codeinst, and indicates that the codeinst has not yet been compiled.
  2. invoke is non-null, specsigflags is 0b00, specptr is NULL
    1. This indicates that the codeinst was not compiled with any specialization, and that the codeinst should be invoked directly. Note that in this instance, invoke does not read either the specsigflags or specptr fields, and therefore they may be modified without invalidating the invoke pointer.
  3. invoke is non-null, specsigflags is 0b10, specptr is non-null
    1. This indicates that the codeinst was compiled, but a specialized function signature was deemed unnecessary by codegen.
  4. invoke is non-null, specsigflags is 0b11, specptr is non-null
    1. This indicates that the codeinst was compiled, and a specialized function signature was deemed necessary by codegen. The specptr field contains a pointer to the specialized function signature. The invoke pointer is permitted to read both specsigflags and specptr fields.

In addition, there are a number of different transitional states that occur during the update process. To account for these potential situations, the following write and read patterns should be used when dealing with these codeinst fields.

  1. When writing invoke, specsigflags, and specptr:
    1. Perform an atomic compare-exchange operation of specptr assuming the old value was NULL. This compare-exchange operation should have at least acquire-release ordering, to provide ordering guarantees of the remaining memory operations in the write.
    2. If specptr was non-null, cease the write operation and wait for bit 0b10 of specsigflags to be written.
    3. Write the new low bit of specsigflags to its final value. This may be a relaxed write.
    4. Write the new invoke pointer to its final value. This must have at least a release memory ordering to synchronize with reads of invoke.
    5. Set the second bit of specsigflags to 1. This must be at least a release memory ordering to synchronize with reads of specsigflags. This step completes the write operation and announces to all other threads that all fields have been set.
  2. When reading all of invoke, specsigflags, and specptr:
    1. Read the invoke field with at least an acquire memory ordering. This load will be referred to as initial_invoke.
    2. If initial_invoke is NULL, the codeinst is not yet executable. invoke is NULL, specsigflags may be treated as 0b00, specptr may be treated as NULL.
    3. Read the specptr field with at least an acquire memory ordering.
    4. If specptr is NULL, then the initial_invoke pointer must not be relying on specptr to guarantee correct execution. Therefore, invoke is non-null, specsigflags may be treated as 0b00, specptr may be treated as NULL.
    5. If specptr is non-null, then initial_invoke might not be the final invoke field that uses specptr. This can occur if specptr has been written, but invoke has not yet been written. Therefore, spin on the second bit of specsigflags until it is set to 1 with at least acquire memory ordering.
    6. Re-read the invoke field with at least an acquire memory ordering. This load will be referred to as final_invoke.
    7. Read the specsigflags field with any memory ordering.
    8. invoke is final_invoke, specsigflags is the value read in step 7, specptr is the value read in step 3.
  3. When updating a specptr to a different but equivalent function pointer:
    1. Perform a release store of the new function pointer to specptr. Races here must be benign, as the old function pointer is required to still be valid, and any new ones are also required to be valid as well. Once a pointer has been written to specptr, it must always be callable whether or not it is later overwritten.

Although these write, read, and update steps are complicated, they ensure that the JIT can update codeinsts without invalidating existing codeinsts, and that the JIT can update codeinsts without invalidating existing invoke pointers. This allows the JIT to potentially reoptimize functions at higher optimization levels in the future, and also will allow the JIT to support concurrent compilation of functions in the future.

  • tdpThis is not a totally-target independent pipeline, as transformations such as vectorization rely upon target information such as vector register width and cost modeling. Additionally, codegen itself makes a few target-dependent assumptions, and the optimization pipeline will take advantage of that knowledge.
diff --git a/dev/devdocs/llvm/index.html b/dev/devdocs/llvm/index.html index f4121023..6082ee94 100644 --- a/dev/devdocs/llvm/index.html +++ b/dev/devdocs/llvm/index.html @@ -16,4 +16,4 @@ error("An error occurred") end

During constant folding, LLVM may discover that the condition is always false, and can remove the basic block. However, if GC root lowering is done early, the GC root slots used in the deleted block, as well as any values kept alive in those slots only because they were used in the error path, would be kept alive by LLVM. By doing GC root lowering late, we give LLVM the license to do any of its usual optimizations (constant folding, dead code elimination, etc.), without having to worry (too much) about which values may or may not be GC tracked.

However, in order to be able to do late GC root placement, we need to be able to identify a) which pointers are GC tracked and b) all uses of such pointers. The goal of the GC placement pass is thus simple:

Minimize the number of needed GC roots/stores to them subject to the constraint that at every safepoint, any live GC-tracked pointer (i.e. for which there is a path after this point that contains a use of this pointer) is in some GC slot.

Representation

The primary difficulty is thus choosing an IR representation that allows us to identify GC-tracked pointers and their uses, even after the program has been run through the optimizer. Our design makes use of three LLVM features to achieve this:

Custom address spaces allow us to tag every point with an integer that needs to be preserved through optimizations. The compiler may not insert casts between address spaces that did not exist in the original program and it must never change the address space of a pointer on a load/store/etc operation. This allows us to annotate which pointers are GC-tracked in an optimizer-resistant way. Note that metadata would not be able to achieve the same purpose. Metadata is supposed to always be discardable without altering the semantics of the program. However, failing to identify a GC-tracked pointer alters the resulting program behavior dramatically - it'll probably crash or return wrong results. We currently use three different address spaces (their numbers are defined in src/codegen_shared.cpp):

Invariants

The GC root placement pass makes use of several invariants, which need to be observed by the frontend and are preserved by the optimizer.

First, only the following address space casts are allowed:

Now let us consider what constitutes a use:

We explicitly allow load/stores and simple calls in address spaces Tracked/Derived. Elements of jlcall argument arrays must always be in address space Tracked (it is required by the ABI that they are valid jl_value_t* pointers). The same is true for return instructions (though note that struct return arguments are allowed to have any of the address spaces). The only allowable use of an address space CalleeRooted pointer is to pass it to a call (which must have an appropriately typed operand).

Further, we disallow getelementptr in addrspace Tracked. This is because unless the operation is a noop, the resulting pointer will not be validly storable to a GC slot and may thus not be in this address space. If such a pointer is required, it should be decayed to addrspace Derived first.

Lastly, we disallow inttoptr/ptrtoint instructions in these address spaces. Having these instructions would mean that some i64 values are really GC tracked. This is problematic, because it breaks that stated requirement that we're able to identify GC-relevant pointers. This invariant is accomplished using the LLVM "non-integral pointers" feature, which is new in LLVM 5.0. It prohibits the optimizer from making optimizations that would introduce these operations. Note we can still insert static constants at JIT time by using inttoptr in address space 0 and then decaying to the appropriate address space afterwards.

Supporting ccall

One important aspect missing from the discussion so far is the handling of ccall. ccall has the peculiar feature that the location and scope of a use do not coincide. As an example consider:

A = randn(1024)
 ccall(:foo, Cvoid, (Ptr{Float64},), A)

In lowering, the compiler will insert a conversion from the array to the pointer which drops the reference to the array value. However, we of course need to make sure that the array does stay alive while we're doing the ccall. To understand how this is done, first recall the lowering of the above code:

return $(Expr(:foreigncall, :(:foo), Cvoid, svec(Ptr{Float64}), 0, :(:ccall), Expr(:foreigncall, :(:jl_array_ptr), Ptr{Float64}, svec(Any), 0, :(:ccall), :(A)), :(A)))

The last :(A), is an extra argument list inserted during lowering that informs the code generator which Julia level values need to be kept alive for the duration of this ccall. We then take this information and represent it in an "operand bundle" at the IR level. An operand bundle is essentially a fake use that is attached to the call site. At the IR level, this looks like so:

call void inttoptr (i64 ... to void (double*)*)(double* %5) [ "jl_roots"(%jl_value_t addrspace(10)* %A) ]

The GC root placement pass will treat the jl_roots operand bundle as if it were a regular operand. However, as a final step, after the GC roots are inserted, it will drop the operand bundle to avoid confusing instruction selection.

Supporting pointer_from_objref

pointer_from_objref is special because it requires the user to take explicit control of GC rooting. By our above invariants, this function is illegal, because it performs an address space cast from 10 to 0. However, it can be useful, in certain situations, so we provide a special intrinsic:

declared %jl_value_t *julia.pointer_from_objref(%jl_value_t addrspace(10)*)

which is lowered to the corresponding address space cast after GC root lowering. Do note however that by using this intrinsic, the caller assumes all responsibility for making sure that the value in question is rooted. Further this intrinsic is not considered a use, so the GC root placement pass will not provide a GC root for the function. As a result, the external rooting must be arranged while the value is still tracked by the system. I.e. it is not valid to attempt to use the result of this operation to establish a global root - the optimizer may have already dropped the value.

Keeping values alive in the absence of uses

In certain cases it is necessary to keep an object alive, even though there is no compiler-visible use of said object. This may be case for low level code that operates on the memory-representation of an object directly or code that needs to interface with C code. In order to allow this, we provide the following intrinsics at the LLVM level:

token @llvm.julia.gc_preserve_begin(...)
-void @llvm.julia.gc_preserve_end(token)

(The llvm. in the name is required in order to be able to use the token type). The semantics of these intrinsics are as follows: At any safepoint that is dominated by a gc_preserve_begin call, but that is not not dominated by a corresponding gc_preserve_end call (i.e. a call whose argument is the token returned by a gc_preserve_begin call), the values passed as arguments to that gc_preserve_begin will be kept live. Note that the gc_preserve_begin still counts as a regular use of those values, so the standard lifetime semantics will ensure that the values will be kept alive before entering the preserve region.

+void @llvm.julia.gc_preserve_end(token)

(The llvm. in the name is required in order to be able to use the token type). The semantics of these intrinsics are as follows: At any safepoint that is dominated by a gc_preserve_begin call, but that is not not dominated by a corresponding gc_preserve_end call (i.e. a call whose argument is the token returned by a gc_preserve_begin call), the values passed as arguments to that gc_preserve_begin will be kept live. Note that the gc_preserve_begin still counts as a regular use of those values, so the standard lifetime semantics will ensure that the values will be kept alive before entering the preserve region.

diff --git a/dev/devdocs/locks/index.html b/dev/devdocs/locks/index.html index 272a392d..fa1622c6 100644 --- a/dev/devdocs/locks/index.html +++ b/dev/devdocs/locks/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

Proper maintenance and care of multi-threading locks

The following strategies are used to ensure that the code is dead-lock free (generally by addressing the 4th Coffman condition: circular wait).

  1. structure code such that only one lock will need to be acquired at a time
  2. always acquire shared locks in the same order, as given by the table below
  3. avoid constructs that expect to need unrestricted recursion

Locks

Below are all of the locks that exist in the system and the mechanisms for using them that avoid the potential for deadlocks (no Ostrich algorithm allowed here):

The following are definitely leaf locks (level 1), and must not try to acquire any other lock:

  • safepoint

    Note that this lock is acquired implicitly by JL_LOCK and JL_UNLOCK. use the _NOGC variants to avoid that for level 1 locks.

    While holding this lock, the code must not do any allocation or hit any safepoints. Note that there are safepoints when doing allocation, enabling / disabling GC, entering / restoring exception frames, and taking / releasing locks.

  • shared_map

  • finalizers

  • pagealloc

  • gcpermlock

  • flisp

  • jlinstackwalk (Win32)

  • ResourcePool<?>::mutex

  • RLST_mutex

  • jllockedstream::mutex

  • debuginfo_asyncsafe

  • inferencetimingmutex

  • ExecutionEngine::SessionLock

    flisp itself is already threadsafe, this lock only protects the jl_ast_context_list_t pool likewise, the ResourcePool<?>::mutexes just protect the associated resource pool

The following is a leaf lock (level 2), and only acquires level 1 locks (safepoint) internally:

  • typecache
  • Module->lock
  • JLDebuginfoPlugin::PluginMutex
  • newlyinferredmutex

The following is a level 3 lock, which can only acquire level 1 or level 2 locks internally:

  • Method->writelock

The following is a level 4 lock, which can only recurse to acquire level 1, 2, or 3 locks:

  • MethodTable->writelock

No Julia code may be called while holding a lock above this point.

orc::ThreadSafeContext (TSCtx) locks occupy a special spot in the locking hierarchy. They are used to protect LLVM's global non-threadsafe state, but there may be an arbitrary number of them. By default, all of these locks may be treated as level 5 locks for the purposes of comparing with the rest of the hierarchy. Acquiring a TSCtx should only be done from the JIT's pool of TSCtx's, and all locks on that TSCtx should be released prior to returning it to the pool. If multiple TSCtx locks must be acquired at the same time (due to recursive compilation), then locks should be acquired in the order that the TSCtxs were borrowed from the pool.

The following is a level 5 lock

  • JuliaOJIT::EmissionMutex

The following are a level 6 lock, which can only recurse to acquire locks at lower levels:

  • codegen
  • jlmodulesmutex

The following is an almost root lock (level end-1), meaning only the root look may be held when trying to acquire it:

  • typeinf

    this one is perhaps one of the most tricky ones, since type-inference can be invoked from many points

    currently the lock is merged with the codegen lock, since they call each other recursively

The following lock synchronizes IO operation. Be aware that doing any I/O (for example, printing warning messages or debug information) while holding any other lock listed above may result in pernicious and hard-to-find deadlocks. BE VERY CAREFUL!

  • iolock

  • Individual ThreadSynchronizers locks

    this may continue to be held after releasing the iolock, or acquired without it, but be very careful to never attempt to acquire the iolock while holding it

The following is the root lock, meaning no other lock shall be held when trying to acquire it:

  • toplevel

    this should be held while attempting a top-level action (such as making a new type or defining a new method): trying to obtain this lock inside a staged function will cause a deadlock condition!

    additionally, it's unclear if any code can safely run in parallel with an arbitrary toplevel expression, so it may require all threads to get to a safepoint first

Broken Locks

The following locks are broken:

  • toplevel

    doesn't exist right now

    fix: create it

  • Module->lock

    This is vulnerable to deadlocks since it can't be certain it is acquired in sequence. Some operations (such as import_module) are missing a lock.

    fix: replace with jl_modules_mutex?

  • loading.jl: require and register_root_module

    This file potentially has numerous problems.

    fix: needs locks

Shared Global Data Structures

These data structures each need locks due to being shared mutable global state. It is the inverse list for the above lock priority list. This list does not include level 1 leaf resources due to their simplicity.

MethodTable modifications (def, cache) : MethodTable->writelock

Type declarations : toplevel lock

Type application : typecache lock

Global variable tables : Module->lock

Module serializer : toplevel lock

JIT & type-inference : codegen lock

MethodInstance/CodeInstance updates : Method->writelock, codegen lock

  • These are set at construction and immutable:
    • specTypes
    • sparam_vals
    • def
  • These are set by jl_type_infer (while holding codegen lock):
    • cache
    • rettype
    • inferred
    * valid ages
  • inInference flag:
    • optimization to quickly avoid recurring into jl_type_infer while it is already running
    • actual state (of setting inferred, then fptr) is protected by codegen lock

  • Function pointers:

    • these transition once, from NULL to a value, while the codegen lock is held

  • Code-generator cache (the contents of functionObjectsDecls):

    • these can transition multiple times, but only while the codegen lock is held
    • it is valid to use old version of this, or block for new versions of this, so races are benign, as long as the code is careful not to reference other data in the method instance (such as rettype) and assume it is coordinated, unless also holding the codegen lock

LLVMContext : codegen lock

Method : Method->writelock

  • roots array (serializer and codegen)
  • invoke / specializations / tfunc modifications
+
Repository

Proper maintenance and care of multi-threading locks

The following strategies are used to ensure that the code is dead-lock free (generally by addressing the 4th Coffman condition: circular wait).

  1. structure code such that only one lock will need to be acquired at a time
  2. always acquire shared locks in the same order, as given by the table below
  3. avoid constructs that expect to need unrestricted recursion

Locks

Below are all of the locks that exist in the system and the mechanisms for using them that avoid the potential for deadlocks (no Ostrich algorithm allowed here):

The following are definitely leaf locks (level 1), and must not try to acquire any other lock:

  • safepoint

    Note that this lock is acquired implicitly by JL_LOCK and JL_UNLOCK. use the _NOGC variants to avoid that for level 1 locks.

    While holding this lock, the code must not do any allocation or hit any safepoints. Note that there are safepoints when doing allocation, enabling / disabling GC, entering / restoring exception frames, and taking / releasing locks.

  • shared_map

  • finalizers

  • pagealloc

  • gcpermlock

  • flisp

  • jlinstackwalk (Win32)

  • ResourcePool<?>::mutex

  • RLST_mutex

  • jllockedstream::mutex

  • debuginfo_asyncsafe

  • inferencetimingmutex

  • ExecutionEngine::SessionLock

    flisp itself is already threadsafe, this lock only protects the jl_ast_context_list_t pool likewise, the ResourcePool<?>::mutexes just protect the associated resource pool

The following is a leaf lock (level 2), and only acquires level 1 locks (safepoint) internally:

  • typecache
  • Module->lock
  • JLDebuginfoPlugin::PluginMutex
  • newlyinferredmutex

The following is a level 3 lock, which can only acquire level 1 or level 2 locks internally:

  • Method->writelock

The following is a level 4 lock, which can only recurse to acquire level 1, 2, or 3 locks:

  • MethodTable->writelock

No Julia code may be called while holding a lock above this point.

orc::ThreadSafeContext (TSCtx) locks occupy a special spot in the locking hierarchy. They are used to protect LLVM's global non-threadsafe state, but there may be an arbitrary number of them. By default, all of these locks may be treated as level 5 locks for the purposes of comparing with the rest of the hierarchy. Acquiring a TSCtx should only be done from the JIT's pool of TSCtx's, and all locks on that TSCtx should be released prior to returning it to the pool. If multiple TSCtx locks must be acquired at the same time (due to recursive compilation), then locks should be acquired in the order that the TSCtxs were borrowed from the pool.

The following is a level 5 lock

  • JuliaOJIT::EmissionMutex

The following are a level 6 lock, which can only recurse to acquire locks at lower levels:

  • codegen
  • jlmodulesmutex

The following is an almost root lock (level end-1), meaning only the root look may be held when trying to acquire it:

  • typeinf

    this one is perhaps one of the most tricky ones, since type-inference can be invoked from many points

    currently the lock is merged with the codegen lock, since they call each other recursively

The following lock synchronizes IO operation. Be aware that doing any I/O (for example, printing warning messages or debug information) while holding any other lock listed above may result in pernicious and hard-to-find deadlocks. BE VERY CAREFUL!

  • iolock

  • Individual ThreadSynchronizers locks

    this may continue to be held after releasing the iolock, or acquired without it, but be very careful to never attempt to acquire the iolock while holding it

The following is the root lock, meaning no other lock shall be held when trying to acquire it:

  • toplevel

    this should be held while attempting a top-level action (such as making a new type or defining a new method): trying to obtain this lock inside a staged function will cause a deadlock condition!

    additionally, it's unclear if any code can safely run in parallel with an arbitrary toplevel expression, so it may require all threads to get to a safepoint first

Broken Locks

The following locks are broken:

  • toplevel

    doesn't exist right now

    fix: create it

  • Module->lock

    This is vulnerable to deadlocks since it can't be certain it is acquired in sequence. Some operations (such as import_module) are missing a lock.

    fix: replace with jl_modules_mutex?

  • loading.jl: require and register_root_module

    This file potentially has numerous problems.

    fix: needs locks

Shared Global Data Structures

These data structures each need locks due to being shared mutable global state. It is the inverse list for the above lock priority list. This list does not include level 1 leaf resources due to their simplicity.

MethodTable modifications (def, cache) : MethodTable->writelock

Type declarations : toplevel lock

Type application : typecache lock

Global variable tables : Module->lock

Module serializer : toplevel lock

JIT & type-inference : codegen lock

MethodInstance/CodeInstance updates : Method->writelock, codegen lock

  • These are set at construction and immutable:
    • specTypes
    • sparam_vals
    • def
  • These are set by jl_type_infer (while holding codegen lock):
    • cache
    • rettype
    • inferred
    * valid ages
  • inInference flag:
    • optimization to quickly avoid recurring into jl_type_infer while it is already running
    • actual state (of setting inferred, then fptr) is protected by codegen lock

  • Function pointers:

    • these transition once, from NULL to a value, while the codegen lock is held

  • Code-generator cache (the contents of functionObjectsDecls):

    • these can transition multiple times, but only while the codegen lock is held
    • it is valid to use old version of this, or block for new versions of this, so races are benign, as long as the code is careful not to reference other data in the method instance (such as rettype) and assume it is coordinated, unless also holding the codegen lock

LLVMContext : codegen lock

Method : Method->writelock

  • roots array (serializer and codegen)
  • invoke / specializations / tfunc modifications
diff --git a/dev/devdocs/meta/index.html b/dev/devdocs/meta/index.html index a8963fd1..62ca2480 100644 --- a/dev/devdocs/meta/index.html +++ b/dev/devdocs/meta/index.html @@ -12,4 +12,4 @@ Expr(:meta, :inline) x*(x+3) end -end

Base.pushmeta!(ex, :symbol, args...) appends :symbol to the end of the :meta expression, creating a new :meta expression if necessary. If args is specified, a nested expression containing :symbol and these arguments is appended instead, which can be used to specify additional information.

To use the metadata, you have to parse these :meta expressions. If your implementation can be performed within Julia, Base.popmeta! is very handy: Base.popmeta!(body, :symbol) will scan a function body expression (one without the function signature) for the first :meta expression containing :symbol, extract any arguments, and return a tuple (found::Bool, args::Array{Any}). If the metadata did not have any arguments, or :symbol was not found, the args array will be empty.

Not yet provided is a convenient infrastructure for parsing :meta expressions from C++.

+end

Base.pushmeta!(ex, :symbol, args...) appends :symbol to the end of the :meta expression, creating a new :meta expression if necessary. If args is specified, a nested expression containing :symbol and these arguments is appended instead, which can be used to specify additional information.

To use the metadata, you have to parse these :meta expressions. If your implementation can be performed within Julia, Base.popmeta! is very handy: Base.popmeta!(body, :symbol) will scan a function body expression (one without the function signature) for the first :meta expression containing :symbol, extract any arguments, and return a tuple (found::Bool, args::Array{Any}). If the metadata did not have any arguments, or :symbol was not found, the args array will be empty.

Not yet provided is a convenient infrastructure for parsing :meta expressions from C++.

diff --git a/dev/devdocs/object/index.html b/dev/devdocs/object/index.html index 4f512c4c..eff5c127 100644 --- a/dev/devdocs/object/index.html +++ b/dev/devdocs/object/index.html @@ -27,4 +27,4 @@ jl_array_t *jl_alloc_array_3d(jl_value_t *atype, size_t nr, size_t nc, size_t z); jl_array_t *jl_alloc_vec_any(size_t n);

Note that many of these have alternative allocation functions for various special-purposes. The list here reflects the more common usages, but a more complete list can be found by reading the julia.h header file.

Internal to Julia, storage is typically allocated by newstruct() (or newobj() for the special types):

jl_value_t *newstruct(jl_value_t *type);
 jl_value_t *newobj(jl_value_t *type, size_t nfields);

And at the lowest level, memory is getting allocated by a call to the garbage collector (in gc.c), then tagged with its type:

jl_value_t *jl_gc_allocobj(size_t nbytes);
-void jl_set_typeof(jl_value_t *v, jl_datatype_t *type);
Out of date Warning

The documentation and usage for the function jl_gc_allocobj may be out of date

Note that all objects are allocated in multiples of 4 bytes and aligned to the platform pointer size. Memory is allocated from a pool for smaller objects, or directly with malloc() for large objects.

Singleton Types

Singleton types have only one instance and no data fields. Singleton instances have a size of 0 bytes, and consist only of their metadata. e.g. nothing::Nothing.

See Singleton Types and Nothingness and missing values

+void jl_set_typeof(jl_value_t *v, jl_datatype_t *type);
Out of date Warning

The documentation and usage for the function jl_gc_allocobj may be out of date

Note that all objects are allocated in multiples of 4 bytes and aligned to the platform pointer size. Memory is allocated from a pool for smaller objects, or directly with malloc() for large objects.

Singleton Types

Singleton types have only one instance and no data fields. Singleton instances have a size of 0 bytes, and consist only of their metadata. e.g. nothing::Nothing.

See Singleton Types and Nothingness and missing values

diff --git a/dev/devdocs/offset-arrays/index.html b/dev/devdocs/offset-arrays/index.html index 3e802144..7b6bb43e 100644 --- a/dev/devdocs/offset-arrays/index.html +++ b/dev/devdocs/offset-arrays/index.html @@ -23,4 +23,4 @@ function Base.similar(f::Union{Function,DataType}, shape::Tuple{ZeroRange,Vararg{ZeroRange}}) # body -end

Both of these should allocate your custom array type.

Specializing reshape

Optionally, define a method

Base.reshape(A::AbstractArray, shape::Tuple{ZeroRange,Vararg{ZeroRange}}) = ...

and you can reshape an array so that the result has custom indices.

For objects that mimic AbstractArray but are not subtypes

has_offset_axes depends on having axes defined for the objects you call it on. If there is some reason you don't have an axes method defined for your object, consider defining a method

Base.has_offset_axes(obj::MyNon1IndexedArraylikeObject) = true

This will allow code that assumes 1-based indexing to detect a problem and throw a helpful error, rather than returning incorrect results or segfaulting julia.

Catching errors

If your new array type triggers errors in other code, one helpful debugging step can be to comment out @boundscheck in your getindex and setindex! implementation. This will ensure that every element access checks bounds. Or, restart julia with --check-bounds=yes.

In some cases it may also be helpful to temporarily disable size and length for your new array type, since code that makes incorrect assumptions frequently uses these functions.

+end

Both of these should allocate your custom array type.

Specializing reshape

Optionally, define a method

Base.reshape(A::AbstractArray, shape::Tuple{ZeroRange,Vararg{ZeroRange}}) = ...

and you can reshape an array so that the result has custom indices.

For objects that mimic AbstractArray but are not subtypes

has_offset_axes depends on having axes defined for the objects you call it on. If there is some reason you don't have an axes method defined for your object, consider defining a method

Base.has_offset_axes(obj::MyNon1IndexedArraylikeObject) = true

This will allow code that assumes 1-based indexing to detect a problem and throw a helpful error, rather than returning incorrect results or segfaulting julia.

Catching errors

If your new array type triggers errors in other code, one helpful debugging step can be to comment out @boundscheck in your getindex and setindex! implementation. This will ensure that every element access checks bounds. Or, restart julia with --check-bounds=yes.

In some cases it may also be helpful to temporarily disable size and length for your new array type, since code that makes incorrect assumptions frequently uses these functions.

diff --git a/dev/devdocs/pkgimg/index.html b/dev/devdocs/pkgimg/index.html index baf01e0c..840b6ccd 100644 --- a/dev/devdocs/pkgimg/index.html +++ b/dev/devdocs/pkgimg/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
Repository

Package Images

Julia package images provide object (native code) caches for Julia packages. They are similar to Julia's system image and support many of the same features. In fact the underlying serialization format is the same, and the system image is the base image that the package images are build against.

High-level overview

Package images are shared libraries that contain both code and data. Like .ji cache files, they are generated per package. The data section contains both global data (global variables in the package) as well as the necessary metadata about what methods and types are defined by the package. The code section contains native objects that cache the final output of Julia's LLVM-based compiler.

The command line option --pkgimages=no can be used to turn off object caching for this session. Note that this means that cache files have to likely be regenerated. See JULIA_MAX_NUM_PRECOMPILE_FILES for the upper limit of variants Julia caches per default.

Note

While the package images present themselves as native shared libraries, they are only an approximation thereof. You will not be able to link against them from a native program and they must be loaded from Julia.

Linking

Since the package images contain native code, we must run a linker over them before we can use them. You can set the environment variable JULIA_VERBOSE_LINKING to true to make the package image linking process verbose.

Furthermore, we cannot assume that the user has a working system linker installed. Therefore, Julia ships with LLD, the LLVM linker, to provide a working out of the box experience. In base/linking.jl, we implement a limited interface to be able to link package images on all supported platforms.

Quirks

Despite LLD being a multi-platform linker, it does not provide a consistent interface across platforms. Furthermore, it is meant to be used from clang or another compiler driver, we therefore reimplement some of the logic from llvm-project/clang/lib/Driver/ToolChains. Thankfully one can use lld -flavor to set lld to the right platform

Windows

To avoid having to deal with link.exe we use -flavor gnu, effectively turning lld into a cross-linker from a mingw32 environment. Windows DLLs are required to contain a _DllMainCRTStartup function and to minimize our dependence on mingw32 libraries, we inject a stub definition ourselves.

MacOS

Dynamic libraries on macOS need to link against -lSystem. On recent macOS versions, -lSystem is only available for linking when Xcode is available. To that effect we link with -undefined dynamic_lookup.

Package images optimized for multiple microarchitectures

Similar to multi-versioning for system images, package images support multi-versioning. If you are in a heterogenous environment, with a unified cache, you can set the environment variable JULIA_CPU_TARGET=generic to multi-version the object caches.

Flags that impact package image creation and selection

These are the Julia command line flags that impact cache selection. Package images that were created with different flags will be rejected.

  • -g, --debug-info: Exact match required since it changes code generation.
  • --check-bounds: Exact match required since it changes code generation.
  • --inline: Exact match required since it changes code generation.
  • --pkgimages: To allow running without object caching enabled.
  • -O, --optimize: Reject package images generated for a lower optimization level, but allow for higher optimization levels to be loaded.
+
Repository

Package Images

Julia package images provide object (native code) caches for Julia packages. They are similar to Julia's system image and support many of the same features. In fact the underlying serialization format is the same, and the system image is the base image that the package images are build against.

High-level overview

Package images are shared libraries that contain both code and data. Like .ji cache files, they are generated per package. The data section contains both global data (global variables in the package) as well as the necessary metadata about what methods and types are defined by the package. The code section contains native objects that cache the final output of Julia's LLVM-based compiler.

The command line option --pkgimages=no can be used to turn off object caching for this session. Note that this means that cache files have to likely be regenerated. See JULIA_MAX_NUM_PRECOMPILE_FILES for the upper limit of variants Julia caches per default.

Note

While the package images present themselves as native shared libraries, they are only an approximation thereof. You will not be able to link against them from a native program and they must be loaded from Julia.

Linking

Since the package images contain native code, we must run a linker over them before we can use them. You can set the environment variable JULIA_VERBOSE_LINKING to true to make the package image linking process verbose.

Furthermore, we cannot assume that the user has a working system linker installed. Therefore, Julia ships with LLD, the LLVM linker, to provide a working out of the box experience. In base/linking.jl, we implement a limited interface to be able to link package images on all supported platforms.

Quirks

Despite LLD being a multi-platform linker, it does not provide a consistent interface across platforms. Furthermore, it is meant to be used from clang or another compiler driver, we therefore reimplement some of the logic from llvm-project/clang/lib/Driver/ToolChains. Thankfully one can use lld -flavor to set lld to the right platform

Windows

To avoid having to deal with link.exe we use -flavor gnu, effectively turning lld into a cross-linker from a mingw32 environment. Windows DLLs are required to contain a _DllMainCRTStartup function and to minimize our dependence on mingw32 libraries, we inject a stub definition ourselves.

MacOS

Dynamic libraries on macOS need to link against -lSystem. On recent macOS versions, -lSystem is only available for linking when Xcode is available. To that effect we link with -undefined dynamic_lookup.

Package images optimized for multiple microarchitectures

Similar to multi-versioning for system images, package images support multi-versioning. If you are in a heterogenous environment, with a unified cache, you can set the environment variable JULIA_CPU_TARGET=generic to multi-version the object caches.

Flags that impact package image creation and selection

These are the Julia command line flags that impact cache selection. Package images that were created with different flags will be rejected.

  • -g, --debug-info: Exact match required since it changes code generation.
  • --check-bounds: Exact match required since it changes code generation.
  • --inline: Exact match required since it changes code generation.
  • --pkgimages: To allow running without object caching enabled.
  • -O, --optimize: Reject package images generated for a lower optimization level, but allow for higher optimization levels to be loaded.
diff --git a/dev/devdocs/precompile_hang/index.html b/dev/devdocs/precompile_hang/index.html index a6a5ea3a..4e1de3c3 100644 --- a/dev/devdocs/precompile_hang/index.html +++ b/dev/devdocs/precompile_hang/index.html @@ -14,4 +14,4 @@ MWE\Project.toml MWE\src\MWE.jl

where the source code of MWE.jl is

module MWE
 using ThePackageYouThinkIsCausingTheProblem
-end

and you've added ThePackageYouThinkIsCausingTheProblem to MWE's dependencies.

If that MWE reproduces the hang, you've found your culprit: ThePackageYouThinkIsCausingTheProblem.__init__ must be creating the Timer object. If the timer object can be safely closed, that's a good option. Otherwise, the most common solution is to avoid creating the timer while any package is being precompiled: add

ccall(:jl_generating_output, Cint, ()) == 1 && return nothing

as the first line of ThePackageYouThinkIsCausingTheProblem.__init__, and it will avoid doing any initialization in any Julia process whose purpose is to precompile packages.

Fixing package code to avoid hangs

Search your package for suggestive words (here like "Timer") and see if you can identify where the problem is being created. Note that a method definition like

maketimer() = Timer(timer -> println("hi"), 0; interval=1)

is not problematic in and of itself: it can cause this problem only if maketimer gets called while the module is being defined. This might be happening from a top-level statement such as

const GLOBAL_TIMER = maketimer()

or it might conceivably occur in a precompile workload.

If you struggle to identify the causative lines, then consider doing a binary search: comment out sections of your package (or include lines to omit entire files) until you've reduced the problem in scope.

+end

and you've added ThePackageYouThinkIsCausingTheProblem to MWE's dependencies.

If that MWE reproduces the hang, you've found your culprit: ThePackageYouThinkIsCausingTheProblem.__init__ must be creating the Timer object. If the timer object can be safely closed, that's a good option. Otherwise, the most common solution is to avoid creating the timer while any package is being precompiled: add

ccall(:jl_generating_output, Cint, ()) == 1 && return nothing

as the first line of ThePackageYouThinkIsCausingTheProblem.__init__, and it will avoid doing any initialization in any Julia process whose purpose is to precompile packages.

Fixing package code to avoid hangs

Search your package for suggestive words (here like "Timer") and see if you can identify where the problem is being created. Note that a method definition like

maketimer() = Timer(timer -> println("hi"), 0; interval=1)

is not problematic in and of itself: it can cause this problem only if maketimer gets called while the module is being defined. This might be happening from a top-level statement such as

const GLOBAL_TIMER = maketimer()

or it might conceivably occur in a precompile workload.

If you struggle to identify the causative lines, then consider doing a binary search: comment out sections of your package (or include lines to omit entire files) until you've reduced the problem in scope.

diff --git a/dev/devdocs/probes/index.html b/dev/devdocs/probes/index.html index d7c4a62c..fb6a9b32 100644 --- a/dev/devdocs/probes/index.html +++ b/dev/devdocs/probes/index.html @@ -108,4 +108,4 @@ Thread wake up! 3e312190

Even though we only spawned a single task (which only one thread could process at a time), we woke up all of our other threads! In the future, a smarter task runtime might only wake up a single thread (or none at all; the spawning thread could execute this task!), and we should see this behavior go away.

Task Monitor with BPFnative.jl

BPFnative.jl is able to attach to USDT probe points just like bpftrace. There is a demo available for monitoring the task runtime, GC, and thread sleep/wake transitions here.

Notes on using bpftrace

An example probe in the bpftrace format looks like:

usdt:usr/lib/libjulia-internal.so:julia:gc__begin
 {
   @start[pid] = nsecs;
-}

The probe declaration takes the kind usdt, then either the path to the library or the PID, the provider name julia and the probe name gc__begin. Note that I am using a relative path to the libjulia-internal.so, but this might need to be an absolute path on a production system.

Useful references:

+}

The probe declaration takes the kind usdt, then either the path to the library or the PID, the provider name julia and the probe name gc__begin. Note that I am using a relative path to the libjulia-internal.so, but this might need to be an absolute path on a production system.

Useful references:

diff --git a/dev/devdocs/require/index.html b/dev/devdocs/require/index.html index d6fc8d4f..4eb04fc0 100644 --- a/dev/devdocs/require/index.html +++ b/dev/devdocs/require/index.html @@ -9,4 +9,4 @@ function module_fqn(name::Symbol) fqn = fullname(Base.root_module(name)) return join(fqn, '.') -end +end diff --git a/dev/devdocs/sanitizers/index.html b/dev/devdocs/sanitizers/index.html index 3c567c4a..c6ac8663 100644 --- a/dev/devdocs/sanitizers/index.html +++ b/dev/devdocs/sanitizers/index.html @@ -38,4 +38,4 @@ # tell libblastrampoline to not use RTLD_DEEPBIND export LBT_USE_RTLD_DEEPBIND=0

Run:

cd $BUILD_WORKTREE
-make debug

to build julia-debug with ASAN.

Memory Sanitizer (MSAN)

For detecting use of uninitialized memory, you can use Clang's memory sanitizer (MSAN) by compiling with SANITIZE_MEMORY=1.

Thread Sanitizer (TSAN)

For debugging data-races and other threading related issues you can use Clang's thread sanitizer (TSAN) by compiling with SANITIZE_THREAD=1.

+make debug

to build julia-debug with ASAN.

Memory Sanitizer (MSAN)

For detecting use of uninitialized memory, you can use Clang's memory sanitizer (MSAN) by compiling with SANITIZE_MEMORY=1.

Thread Sanitizer (TSAN)

For debugging data-races and other threading related issues you can use Clang's thread sanitizer (TSAN) by compiling with SANITIZE_THREAD=1.

diff --git a/dev/devdocs/ssair/index.html b/dev/devdocs/ssair/index.html index d7ce37c5..5882ad5f 100644 --- a/dev/devdocs/ssair/index.html +++ b/dev/devdocs/ssair/index.html @@ -55,4 +55,4 @@ 5 ─ $(Expr(:pop_exception, :(%2)))::Any │ $(Expr(:throw_undef_if_not, :y, :(%13)))::Any │ %19 = Core.tuple(%15, %14) -└── return %19

Note in particular that every value live into the critical region gets an upsilon node at the top of the critical region. This is because catch blocks are considered to have an invisible control flow edge from outside the function. As a result, no SSA value dominates the catch blocks, and all incoming values have to come through a φᶜ node.

Main SSA data structure

The main SSAIR data structure is worthy of discussion. It draws inspiration from LLVM and Webkit's B3 IR. The core of the data structure is a flat vector of statements. Each statement is implicitly assigned an SSA value based on its position in the vector (i.e. the result of the statement at idx 1 can be accessed using SSAValue(1) etc). For each SSA value, we additionally maintain its type. Since, SSA values are definitionally assigned only once, this type is also the result type of the expression at the corresponding index. However, while this representation is rather efficient (since the assignments don't need to be explicitly encoded), it of course carries the drawback that order is semantically significant, so reorderings and insertions change statement numbers. Additionally, we do not keep use lists (i.e. it is impossible to walk from a def to all its uses without explicitly computing this map–def lists however are trivial since you can look up the corresponding statement from the index), so the LLVM-style RAUW (replace-all-uses-with) operation is unavailable.

Instead, we do the following:

There is a compact! function that compacts the above data structure by performing the insertion of nodes in the appropriate place, trivial copy propagation, and renaming of uses to any changed SSA values. However, the clever part of this scheme is that this compaction can be done lazily as part of the subsequent pass. Most optimization passes need to walk over the entire list of statements, performing analysis or modifications along the way. We provide an IncrementalCompact iterator that can be used to iterate over the statement list. It will perform any necessary compaction and return the new index of the node, as well as the node itself. It is legal at this point to walk def-use chains, as well as make any modifications or deletions to the IR (insertions are disallowed however).

The idea behind this arrangement is that, since the optimization passes need to touch the corresponding memory anyway and incur the corresponding memory access penalty, performing the extra housekeeping should have comparatively little overhead (and save the overhead of maintaining these data structures during IR modification).

+└── return %19

Note in particular that every value live into the critical region gets an upsilon node at the top of the critical region. This is because catch blocks are considered to have an invisible control flow edge from outside the function. As a result, no SSA value dominates the catch blocks, and all incoming values have to come through a φᶜ node.

Main SSA data structure

The main SSAIR data structure is worthy of discussion. It draws inspiration from LLVM and Webkit's B3 IR. The core of the data structure is a flat vector of statements. Each statement is implicitly assigned an SSA value based on its position in the vector (i.e. the result of the statement at idx 1 can be accessed using SSAValue(1) etc). For each SSA value, we additionally maintain its type. Since, SSA values are definitionally assigned only once, this type is also the result type of the expression at the corresponding index. However, while this representation is rather efficient (since the assignments don't need to be explicitly encoded), it of course carries the drawback that order is semantically significant, so reorderings and insertions change statement numbers. Additionally, we do not keep use lists (i.e. it is impossible to walk from a def to all its uses without explicitly computing this map–def lists however are trivial since you can look up the corresponding statement from the index), so the LLVM-style RAUW (replace-all-uses-with) operation is unavailable.

Instead, we do the following:

There is a compact! function that compacts the above data structure by performing the insertion of nodes in the appropriate place, trivial copy propagation, and renaming of uses to any changed SSA values. However, the clever part of this scheme is that this compaction can be done lazily as part of the subsequent pass. Most optimization passes need to walk over the entire list of statements, performing analysis or modifications along the way. We provide an IncrementalCompact iterator that can be used to iterate over the statement list. It will perform any necessary compaction and return the new index of the node, as well as the node itself. It is legal at this point to walk def-use chains, as well as make any modifications or deletions to the IR (insertions are disallowed however).

The idea behind this arrangement is that, since the optimization passes need to touch the corresponding memory anyway and incur the corresponding memory access penalty, performing the extra housekeeping should have comparatively little overhead (and save the overhead of maintaining these data structures during IR modification).

diff --git a/dev/devdocs/stdio/index.html b/dev/devdocs/stdio/index.html index ae41cd6f..4ef060cd 100644 --- a/dev/devdocs/stdio/index.html +++ b/dev/devdocs/stdio/index.html @@ -18,4 +18,4 @@ jl_uv.c: -> int jl_uv_write(uv_stream_t *stream, ...) -> uv_write(uvw, stream, buf, ...)

printf() during initialization

The libuv streams relied upon by jl_printf() etc., are not available until midway through initialization of the runtime (see init.c, init_stdio()). Error messages or warnings that need to be printed before this are routed to the standard C library fwrite() function by the following mechanism:

In sys.c, the JL_STD* stream pointers are statically initialized to integer constants: STD*_FILENO (0, 1 and 2). In jl_uv.c the jl_uv_puts() function checks its uv_stream_t* stream argument and calls fwrite() if stream is set to STDOUT_FILENO or STDERR_FILENO.

This allows for uniform use of jl_printf() throughout the runtime regardless of whether or not any particular piece of code is reachable before initialization is complete.

Legacy ios.c library

The src/support/ios.c library is inherited from femtolisp. It provides cross-platform buffered file IO and in-memory temporary buffers.

ios.c is still used by:

Use of ios.c in these modules is mostly self-contained and separated from the libuv I/O system. However, there is one place where femtolisp calls through to jl_printf() with a legacy ios_t stream.

There is a hack in ios.h that makes the ios_t.bm field line up with the uv_stream_t.type and ensures that the values used for ios_t.bm to not overlap with valid UV_HANDLE_TYPE values. This allows uv_stream_t pointers to point to ios_t streams.

This is needed because jl_printf() caller jl_static_show() is passed an ios_t stream by femtolisp's fl_print() function. Julia's jl_uv_puts() function has special handling for this:

if (stream->type > UV_HANDLE_TYPE_MAX) {
     return ios_write((ios_t*)stream, str, n);
-}
+} diff --git a/dev/devdocs/subarrays/index.html b/dev/devdocs/subarrays/index.html index e782cb34..68882cd8 100644 --- a/dev/devdocs/subarrays/index.html +++ b/dev/devdocs/subarrays/index.html @@ -66,4 +66,4 @@ 3 2

then A[2:2:4,:] does not have uniform stride, so we cannot guarantee efficient linear indexing. Since we have to base this decision based purely on types encoded in the parameters of the SubArray, S = view(A, 2:2:4, :) cannot implement efficient linear indexing.

A few details

+S = view(A, :, :, 1:1) # Appending extra indices is supported

Naively, you'd think you could just set S.parent = A and S.indices = (:,:,1:1), but supporting this dramatically complicates the reindexing process, especially for views of views. Not only do you need to dispatch on the types of the stored indices, but you need to examine whether a given index is the final one and "merge" any remaining stored indices together. This is not an easy task, and even worse: it's slow since it implicitly depends upon linear indexing.

Fortunately, this is precisely the computation that ReshapedArray performs, and it does so linearly if possible. Consequently, view ensures that the parent array is the appropriate dimensionality for the given indices by reshaping it if needed. The inner SubArray constructor ensures that this invariant is satisfied.

  • CartesianIndex and arrays thereof throw a nasty wrench into the reindex scheme. Recall that reindex simply dispatches on the type of the stored indices in order to determine how many passed indices should be used and where they should go. But with CartesianIndex, there's no longer a one-to-one correspondence between the number of passed arguments and the number of dimensions that they index into. If we return to the above example of Base.reindex(S1, S1.indices, (i, j)), you can see that the expansion is incorrect for i, j = CartesianIndex(), CartesianIndex(2,1). It should skip the CartesianIndex() entirely and return:

    (CartesianIndex(2,1)[1], S1.indices[2], S1.indices[3][CartesianIndex(2,1)[2]])

    Instead, though, we get:

    (CartesianIndex(), S1.indices[2], S1.indices[3][CartesianIndex(2,1)])

    Doing this correctly would require combined dispatch on both the stored and passed indices across all combinations of dimensionalities in an intractable manner. As such, reindex must never be called with CartesianIndex indices. Fortunately, the scalar case is easily handled by first flattening the CartesianIndex arguments to plain integers. Arrays of CartesianIndex, however, cannot be split apart into orthogonal pieces so easily. Before attempting to use reindex, view must ensure that there are no arrays of CartesianIndex in the argument list. If there are, it can simply "punt" by avoiding the reindex calculation entirely, constructing a nested SubArray with two levels of indirection instead.

    • diff --git a/dev/devdocs/sysimg/index.html b/dev/devdocs/sysimg/index.html index d756b534..560b541e 100644 --- a/dev/devdocs/sysimg/index.html +++ b/dev/devdocs/sysimg/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    System Image Building

    Building the Julia system image

    Julia ships with a preparsed system image containing the contents of the Base module, named sys.ji. This file is also precompiled into a shared library called sys.{so,dll,dylib} on as many platforms as possible, so as to give vastly improved startup times. On systems that do not ship with a precompiled system image file, one can be generated from the source files shipped in Julia's DATAROOTDIR/julia/base folder.

    Julia will by default generate its system image on half of the available system threads. This may be controlled by the JULIA_IMAGE_THREADS environment variable.

    This operation is useful for multiple reasons. A user may:

    • Build a precompiled shared library system image on a platform that did not ship with one, thereby improving startup times.
    • Modify Base, rebuild the system image and use the new Base next time Julia is started.
    • Include a userimg.jl file that includes packages into the system image, thereby creating a system image that has packages embedded into the startup environment.

    The PackageCompiler.jl package contains convenient wrapper functions to automate this process.

    System image optimized for multiple microarchitectures

    The system image can be compiled simultaneously for multiple CPU microarchitectures under the same instruction set architecture (ISA). Multiple versions of the same function may be created with minimum dispatch point inserted into shared functions in order to take advantage of different ISA extensions or other microarchitecture features. The version that offers the best performance will be selected automatically at runtime based on available CPU features.

    Specifying multiple system image targets

    A multi-microarchitecture system image can be enabled by passing multiple targets during system image compilation. This can be done either with the JULIA_CPU_TARGET make option or with the -C command line option when running the compilation command manually. Multiple targets are separated by ; in the option string. The syntax for each target is a CPU name followed by multiple features separated by ,. All features supported by LLVM are supported and a feature can be disabled with a - prefix. (+ prefix is also allowed and ignored to be consistent with LLVM syntax). Additionally, a few special features are supported to control the function cloning behavior.

    Note

    It is good practice to specify either clone_all or base(<n>) for every target apart from the first one. This makes it explicit which targets have all functions cloned, and which targets are based on other targets. If this is not done, the default behavior is to not clone every function, and to use the first target's function definition as the fallback when not cloning a function.

    1. clone_all

      By default, only functions that are the most likely to benefit from the microarchitecture features will be cloned. When clone_all is specified for a target, however, all functions in the system image will be cloned for the target. The negative form -clone_all can be used to prevent the built-in heuristic from cloning all functions.

    2. base(<n>)

      Where <n> is a placeholder for a non-negative number (e.g. base(0), base(1)). By default, a partially cloned (i.e. not clone_all) target will use functions from the default target (first one specified) if a function is not cloned. This behavior can be changed by specifying a different base with the base(<n>) option. The nth target (0-based) will be used as the base target instead of the default (0th) one. The base target has to be either 0 or another clone_all target. Specifying a non-clone_all target as the base target will cause an error.

    3. opt_size

      This causes the function for the target to be optimized for size when there isn't a significant runtime performance impact. This corresponds to -Os GCC and Clang option.

    4. min_size

      This causes the function for the target to be optimized for size that might have a significant runtime performance impact. This corresponds to -Oz Clang option.

    As an example, at the time of this writing, the following string is used in the creation of the official x86_64 Julia binaries downloadable from julialang.org:

    generic;sandybridge,-xsaveopt,clone_all;haswell,-rdrnd,base(1)

    This creates a system image with three separate targets; one for a generic x86_64 processor, one with a sandybridge ISA (explicitly excluding xsaveopt) that explicitly clones all functions, and one targeting the haswell ISA, based off of the sandybridge sysimg version, and also excluding rdrnd. When a Julia implementation loads the generated sysimg, it will check the host processor for matching CPU capability flags, enabling the highest ISA level possible. Note that the base level (generic) requires the cx16 instruction, which is disabled in some virtualization software and must be enabled for the generic target to be loaded. Alternatively, a sysimg could be generated with the target generic,-cx16 for greater compatibility, however note that this may cause performance and stability problems in some code.

    Implementation overview

    This is a brief overview of different part involved in the implementation. See code comments for each components for more implementation details.

    1. System image compilation

      The parsing and cloning decision are done in src/processor*. We currently support cloning of function based on the present of loops, simd instructions, or other math operations (e.g. fastmath, fma, muladd). This information is passed on to src/llvm-multiversioning.cpp which does the actual cloning. In addition to doing the cloning and insert dispatch slots (see comments in MultiVersioning::runOnModule for how this is done), the pass also generates metadata so that the runtime can load and initialize the system image correctly. A detailed description of the metadata is available in src/processor.h.

    2. System image loading

      The loading and initialization of the system image is done in src/processor* by parsing the metadata saved during system image generation. Host feature detection and selection decision are done in src/processor_*.cpp depending on the ISA. The target selection will prefer exact CPU name match, larger vector register size, and larger number of features. An overview of this process is in src/processor.cpp.

    +
    Repository

    System Image Building

    Building the Julia system image

    Julia ships with a preparsed system image containing the contents of the Base module, named sys.ji. This file is also precompiled into a shared library called sys.{so,dll,dylib} on as many platforms as possible, so as to give vastly improved startup times. On systems that do not ship with a precompiled system image file, one can be generated from the source files shipped in Julia's DATAROOTDIR/julia/base folder.

    Julia will by default generate its system image on half of the available system threads. This may be controlled by the JULIA_IMAGE_THREADS environment variable.

    This operation is useful for multiple reasons. A user may:

    • Build a precompiled shared library system image on a platform that did not ship with one, thereby improving startup times.
    • Modify Base, rebuild the system image and use the new Base next time Julia is started.
    • Include a userimg.jl file that includes packages into the system image, thereby creating a system image that has packages embedded into the startup environment.

    The PackageCompiler.jl package contains convenient wrapper functions to automate this process.

    System image optimized for multiple microarchitectures

    The system image can be compiled simultaneously for multiple CPU microarchitectures under the same instruction set architecture (ISA). Multiple versions of the same function may be created with minimum dispatch point inserted into shared functions in order to take advantage of different ISA extensions or other microarchitecture features. The version that offers the best performance will be selected automatically at runtime based on available CPU features.

    Specifying multiple system image targets

    A multi-microarchitecture system image can be enabled by passing multiple targets during system image compilation. This can be done either with the JULIA_CPU_TARGET make option or with the -C command line option when running the compilation command manually. Multiple targets are separated by ; in the option string. The syntax for each target is a CPU name followed by multiple features separated by ,. All features supported by LLVM are supported and a feature can be disabled with a - prefix. (+ prefix is also allowed and ignored to be consistent with LLVM syntax). Additionally, a few special features are supported to control the function cloning behavior.

    Note

    It is good practice to specify either clone_all or base(<n>) for every target apart from the first one. This makes it explicit which targets have all functions cloned, and which targets are based on other targets. If this is not done, the default behavior is to not clone every function, and to use the first target's function definition as the fallback when not cloning a function.

    1. clone_all

      By default, only functions that are the most likely to benefit from the microarchitecture features will be cloned. When clone_all is specified for a target, however, all functions in the system image will be cloned for the target. The negative form -clone_all can be used to prevent the built-in heuristic from cloning all functions.

    2. base(<n>)

      Where <n> is a placeholder for a non-negative number (e.g. base(0), base(1)). By default, a partially cloned (i.e. not clone_all) target will use functions from the default target (first one specified) if a function is not cloned. This behavior can be changed by specifying a different base with the base(<n>) option. The nth target (0-based) will be used as the base target instead of the default (0th) one. The base target has to be either 0 or another clone_all target. Specifying a non-clone_all target as the base target will cause an error.

    3. opt_size

      This causes the function for the target to be optimized for size when there isn't a significant runtime performance impact. This corresponds to -Os GCC and Clang option.

    4. min_size

      This causes the function for the target to be optimized for size that might have a significant runtime performance impact. This corresponds to -Oz Clang option.

    As an example, at the time of this writing, the following string is used in the creation of the official x86_64 Julia binaries downloadable from julialang.org:

    generic;sandybridge,-xsaveopt,clone_all;haswell,-rdrnd,base(1)

    This creates a system image with three separate targets; one for a generic x86_64 processor, one with a sandybridge ISA (explicitly excluding xsaveopt) that explicitly clones all functions, and one targeting the haswell ISA, based off of the sandybridge sysimg version, and also excluding rdrnd. When a Julia implementation loads the generated sysimg, it will check the host processor for matching CPU capability flags, enabling the highest ISA level possible. Note that the base level (generic) requires the cx16 instruction, which is disabled in some virtualization software and must be enabled for the generic target to be loaded. Alternatively, a sysimg could be generated with the target generic,-cx16 for greater compatibility, however note that this may cause performance and stability problems in some code.

    Implementation overview

    This is a brief overview of different part involved in the implementation. See code comments for each components for more implementation details.

    1. System image compilation

      The parsing and cloning decision are done in src/processor*. We currently support cloning of function based on the present of loops, simd instructions, or other math operations (e.g. fastmath, fma, muladd). This information is passed on to src/llvm-multiversioning.cpp which does the actual cloning. In addition to doing the cloning and insert dispatch slots (see comments in MultiVersioning::runOnModule for how this is done), the pass also generates metadata so that the runtime can load and initialize the system image correctly. A detailed description of the metadata is available in src/processor.h.

    2. System image loading

      The loading and initialization of the system image is done in src/processor* by parsing the metadata saved during system image generation. Host feature detection and selection decision are done in src/processor_*.cpp depending on the ISA. The target selection will prefer exact CPU name match, larger vector register size, and larger number of features. An overview of this process is in src/processor.cpp.

    diff --git a/dev/devdocs/types/index.html b/dev/devdocs/types/index.html index 6fc19b08..ebb2095a 100644 --- a/dev/devdocs/types/index.html +++ b/dev/devdocs/types/index.html @@ -135,4 +135,4 @@ f(nothing, 2.0)

    上述例子告诉我们：当 x 的类型是空集 nothing::Nothing 时，y 的类型就没有任何限制了。此时方法标签中字段 y 可以是任何类型，即 y::Any。确实，下面两个类型是等价的：

    (Tuple{Union{Nothing,T},T} where T) == Union{Tuple{Nothing,Any}, Tuple{T,T} where T}

    一般的规则是：如果出现在共变位置的一个具体变量只被子类型算法（subtyping algorithm）使用一次，则该具体变量的行为就会像一个抽象变量。上例中，当 x 类型为空时 Nothing，集合 Union{Nothing,T} 中的类型 T 不起作用，即 T 只在第二个槽中被用到。此时，无论把 Tuple{T} where T 中的 T 限制为具体类型还是不限制，该类型都等价于 Tuple{Any}。

    当变量出现在非共变 位置时，无论是否被使用，该变量都不再是具体变量。否则类型的行为就会因为比较对象类型的不同而不同，从而违反传递律（transitive）。例如，

    Tuple{Int,Int8,Vector{Integer}} <: Tuple{T,T,Vector{Union{Integer,T}}} where T

    如果忽略掉合集 Union 内部的 T，则 T 就是具体的，且上述判断结果是 “否”，因为左侧元组前两个成分的类型是不同的。这两个类型不相同。再看下例：

    Tuple{Int,Int8,Vector{Any}} <: Tuple{T,T,Vector{Union{Integer,T}}} where T

    此处合集 Union 内的 T 是不能被忽略的，因为 T 必须等于 Any，即 T == Any。所以 T 不能是具体的，且判断结果为“真”。所以，类型 T 的具体还是抽象是受制于其他类型特征的。这是不被接受的，因为类型的含义必须是清晰和自洽的。所以，向量 Vector 之内的 T 需要同时考虑这两种情况。

    对角变量的子类型

    对角变量的子系统算法（substyping algorithm）有两个成分：（1）确定变量出现次数；（2）确保对角变量只包含具体类型。

    第一个任务由两个计数器完成。环境中的每个自由变量都有两个计数器 occurs_inv 和 occurs_cov (在文件 src/subtype.c 中)，分别用于追踪不变和共变的出现次数。如果 occurs_inv == 0 && occurs_cov > 1 则这个变量就是对角的。

    Most operations for dealing with types are found in the files jltypes.c and subtype.c. A good way to start is to watch subtyping in action. Build Julia with make debug and fire up Julia within a debugger. gdb debugging tips has some tips which may be useful.

    julia> function mysubtype(a,b)
            ccall(:jl_breakpoint, Cvoid, (Any,), nothing)
            a <: b
-       end

    一旦该断点被触发，你就可以在其他函数中设定断点了。

    作为热身，试一下下面代码

    mysubtype(Tuple{Int, Float64}, Tuple{Integer, Real})

    你也可以用一个更复杂的例子让其变得更有趣：

    mysubtype(Tuple{Array{Int,2}, Int8}, Tuple{Array{T}, T} where T)

    子类型和方法排序

    函数 type_morespecific 可用来对函数的方法列表从最具特异行到最不具特异性进行部分排序（partial order）。特异性是严格的：如果 a 比 b 更特异，则 b 就不比 a 更特异。

    如果 a 是 b 的严格子类型（strict subtype），那么 a 就自动的比 b 更特异。接下来，函数 type_morespecific 还引进了一些不太形式化的规则。例如，子类型 subtype 对参数的数量敏感，而函数 type_morespecific 则不敏感。特别的，Tuple{Int,AbstractFloat} 比 Tuple{Integer} 更特异，虽然前者不是后者的子类型。此外， Tuple{Int,AbstractFloat} 和 Tuple{Integer,Float64} 不存在特异性关系。类似的，Tuple{Int,Vararg{Int}} 不是 Tuple{Integer} 的子类型，但前者比后者更特异。但是，长度确实也影响特异性关系morespecific，如 Tuple{Int,Int} 比 Tuple{Int,Vararg{Int}} 更特异。

    要调试方法的排序，定义下面的函数很方便：

    type_morespecific(a, b) = ccall(:jl_type_morespecific, Cint, (Any,Any), a, b)

    它可以被用来测试元组 a 是否比元组 b 更特异。

    + end

    一旦该断点被触发，你就可以在其他函数中设定断点了。

    作为热身，试一下下面代码

    mysubtype(Tuple{Int, Float64}, Tuple{Integer, Real})

    你也可以用一个更复杂的例子让其变得更有趣：

    mysubtype(Tuple{Array{Int,2}, Int8}, Tuple{Array{T}, T} where T)

    子类型和方法排序

    函数 type_morespecific 可用来对函数的方法列表从最具特异行到最不具特异性进行部分排序（partial order）。特异性是严格的：如果 a 比 b 更特异，则 b 就不比 a 更特异。

    如果 a 是 b 的严格子类型（strict subtype），那么 a 就自动的比 b 更特异。接下来，函数 type_morespecific 还引进了一些不太形式化的规则。例如，子类型 subtype 对参数的数量敏感，而函数 type_morespecific 则不敏感。特别的，Tuple{Int,AbstractFloat} 比 Tuple{Integer} 更特异，虽然前者不是后者的子类型。此外， Tuple{Int,AbstractFloat} 和 Tuple{Integer,Float64} 不存在特异性关系。类似的，Tuple{Int,Vararg{Int}} 不是 Tuple{Integer} 的子类型，但前者比后者更特异。但是，长度确实也影响特异性关系morespecific，如 Tuple{Int,Int} 比 Tuple{Int,Vararg{Int}} 更特异。

    要调试方法的排序，定义下面的函数很方便：

    type_morespecific(a, b) = ccall(:jl_type_morespecific, Cint, (Any,Any), a, b)

    它可以被用来测试元组 a 是否比元组 b 更特异。

    diff --git a/dev/devdocs/valgrind/index.html b/dev/devdocs/valgrind/index.html index 93fc691a..8962f221 100644 --- a/dev/devdocs/valgrind/index.html +++ b/dev/devdocs/valgrind/index.html @@ -7,4 +7,4 @@ --xxxxxx-- You may be able to write your own handler. --xxxxxx-- Read the file README_MISSING_SYSCALL_OR_IOCTL. --xxxxxx-- Nevertheless we consider this a bug. Please report ---xxxxxx-- it at http://valgrind.org/support/bug_reports.html.

    This issue has been reported to the Valgrind developers as they have requested.

    Caveats

    Valgrind currently does not support multiple rounding modes, so code that adjusts the rounding mode will behave differently when run under Valgrind.

    In general, if after setting --smc-check=all-non-file you find that your program behaves differently when run under Valgrind, it may help to pass --tool=none to valgrind as you investigate further. This will enable the minimal Valgrind machinery but will also run much faster than when the full memory checker is enabled.

    +--xxxxxx-- it at http://valgrind.org/support/bug_reports.html.

    This issue has been reported to the Valgrind developers as they have requested.

    Caveats

    Valgrind currently does not support multiple rounding modes, so code that adjusts the rounding mode will behave differently when run under Valgrind.

    In general, if after setting --smc-check=all-non-file you find that your program behaves differently when run under Valgrind, it may help to pass --tool=none to valgrind as you investigate further. This will enable the minimal Valgrind machinery but will also run much faster than when the full memory checker is enabled.

    diff --git a/dev/index.html b/dev/index.html index 053b3390..c1ff7ffc 100644 --- a/dev/index.html +++ b/dev/index.html @@ -7,4 +7,4 @@ 集智俱乐部 -

    特别感谢集智俱乐部对Julia中文文档和Julia中文论坛相关服务器资源的赞助！

    ❤❤❤如果您或您所属的组织有意资助Julia中文社区的发展，欢迎前往论坛的社区板块发帖咨询。❤❤❤

    其它中文资料

    通用教程类：

    专题类：

    简介

    科学计算对性能一直有着最高的需求，但目前各领域的专家却大量使用较慢的动态语言来开展他们的日常工作。 偏爱动态语言有很多很好的理由，因此我们不会舍弃动态的特性。 幸运的是，现代编程语言设计与编译器技术可以大大消除性能折衷（trade-off），并提供有足够生产力的单一环境进行原型设计，而且能高效地部署性能密集型应用程序。 Julia 语言在这其中扮演了这样一个角色：它是一门灵活的动态语言，适合用于科学计算和数值计算，并且性能可与传统的静态类型语言媲美。

    由于 Julia 的编译器和其它语言比如 Python 或 R 的解释器有所不同，一开始你可能发现 Julia 的性能并不是很突出。 如果你觉得速度有点慢，我们强烈建议在尝试其他功能前，先读一读文档中的提高性能的窍门。 在理解了 Julia 的运作方式后，写出和 C 一样快的代码对你而言就是小菜一碟。

    Julia 与其他语言的比较

    Julia 拥有可选类型标注和多重派发这两个特性，同时还拥有很棒的性能。 这些都得归功于使用 LLVM 实现的类型推导和即时编译（JIT）技术 (和 可选的提前编译（AOT）)。 Julia 是一门支持过程式、函数式和面向对象的多范式语言。 它像 R、MATLAB 和 Python 一样简单，在高级数值计算方面有丰富的表现力，并且支持通用编程。 为了实现这个目标，Julia 以数学编程语言（mathematical programming languages）为基础，同时也参考了不少流行的动态语言，例如 Lisp、Perl、Python、Lua、和 Ruby。

    Julia 与传统动态语言最重要的区别是：

    尽管人们有时会说动态语言是“无类型的”，但实际上绝对不是这样的：每一个对象都有一个类型，无论它是基础的类型（primitive）还是用户自定义的类型。 大多数的动态语言都缺乏类型声明，这意味着程序员无法告诉编译器值的类型，也就无法显式地讨论类型。 另一方面，在静态语言中，往往必须标注对象的类型。但类型只在编译期才存在，而无法在运行时进行操作和表达。 而在 Julia 中，类型本身是运行时的对象，并可用于向编译器传达信息。

    是什么让 Julia 成为 Julia？

    类型系统和多重派发是 Julia 语言最主要的特征，但一般不需要显式地手动标注或使用：函数通过函数名称和不同类型参数的组合进行定义，在调用时会派发到最接近（most specific）的定义上去。这样的编程模型非常适合数学化的编程，尤其是在传统的面向对象派发中，一些函数的第一个变量理论上并不“拥有”这样一个操作时。 在 Julia 中运算符只是函数的一个特殊标记——例如，为用户定义的新类型添加加法运算，你只要为 + 函数定义一个新的方法就可以了。 已有的代码就可以无缝接入这个新的类型。

    Julia 在设计之初就非常看重性能，再加上它的动态类型推导（可以被可选的类型标注增强），使得 Julia 的计算性能超过了其它的动态语言，甚至能够与静态编译语言竞争。对于大型数值问题，速度一直都是，也一直会是一个重要的关注点：在过去的几十年里，需要处理的数据量很容易与摩尔定律保持同步。

    Julia 的优势

    Julia 的目标是创建一个前所未有的集易用、强大、高效于一体的语言。除此之外，Julia 还拥有以下优势：

    +

    特别感谢集智俱乐部对Julia中文文档和Julia中文论坛相关服务器资源的赞助！

    ❤❤❤如果您或您所属的组织有意资助Julia中文社区的发展，欢迎前往论坛的社区板块发帖咨询。❤❤❤

    其它中文资料

    通用教程类：

    专题类：

    简介

    科学计算对性能一直有着最高的需求，但目前各领域的专家却大量使用较慢的动态语言来开展他们的日常工作。 偏爱动态语言有很多很好的理由，因此我们不会舍弃动态的特性。 幸运的是，现代编程语言设计与编译器技术可以大大消除性能折衷（trade-off），并提供有足够生产力的单一环境进行原型设计，而且能高效地部署性能密集型应用程序。 Julia 语言在这其中扮演了这样一个角色：它是一门灵活的动态语言，适合用于科学计算和数值计算，并且性能可与传统的静态类型语言媲美。

    由于 Julia 的编译器和其它语言比如 Python 或 R 的解释器有所不同，一开始你可能发现 Julia 的性能并不是很突出。 如果你觉得速度有点慢，我们强烈建议在尝试其他功能前，先读一读文档中的提高性能的窍门。 在理解了 Julia 的运作方式后，写出和 C 一样快的代码对你而言就是小菜一碟。

    Julia 与其他语言的比较

    Julia 拥有可选类型标注和多重派发这两个特性，同时还拥有很棒的性能。 这些都得归功于使用 LLVM 实现的类型推导和即时编译（JIT）技术 (和 可选的提前编译（AOT）)。 Julia 是一门支持过程式、函数式和面向对象的多范式语言。 它像 R、MATLAB 和 Python 一样简单，在高级数值计算方面有丰富的表现力，并且支持通用编程。 为了实现这个目标，Julia 以数学编程语言（mathematical programming languages）为基础，同时也参考了不少流行的动态语言，例如 Lisp、Perl、Python、Lua、和 Ruby。

    Julia 与传统动态语言最重要的区别是：

    尽管人们有时会说动态语言是“无类型的”，但实际上绝对不是这样的：每一个对象都有一个类型，无论它是基础的类型（primitive）还是用户自定义的类型。 大多数的动态语言都缺乏类型声明，这意味着程序员无法告诉编译器值的类型，也就无法显式地讨论类型。 另一方面，在静态语言中，往往必须标注对象的类型。但类型只在编译期才存在，而无法在运行时进行操作和表达。 而在 Julia 中，类型本身是运行时的对象，并可用于向编译器传达信息。

    是什么让 Julia 成为 Julia？

    类型系统和多重派发是 Julia 语言最主要的特征，但一般不需要显式地手动标注或使用：函数通过函数名称和不同类型参数的组合进行定义，在调用时会派发到最接近（most specific）的定义上去。这样的编程模型非常适合数学化的编程，尤其是在传统的面向对象派发中，一些函数的第一个变量理论上并不“拥有”这样一个操作时。 在 Julia 中运算符只是函数的一个特殊标记——例如，为用户定义的新类型添加加法运算，你只要为 + 函数定义一个新的方法就可以了。 已有的代码就可以无缝接入这个新的类型。

    Julia 在设计之初就非常看重性能，再加上它的动态类型推导（可以被可选的类型标注增强），使得 Julia 的计算性能超过了其它的动态语言，甚至能够与静态编译语言竞争。对于大型数值问题，速度一直都是，也一直会是一个重要的关注点：在过去的几十年里，需要处理的数据量很容易与摩尔定律保持同步。

    Julia 的优势

    Julia 的目标是创建一个前所未有的集易用、强大、高效于一体的语言。除此之外，Julia 还拥有以下优势：

    diff --git a/dev/manual/arrays/index.html b/dev/manual/arrays/index.html index 9c91a48c..e6374236 100644 --- a/dev/manual/arrays/index.html +++ b/dev/manual/arrays/index.html @@ -541,4 +541,4 @@ julia> stride(V, 1) 3

    这个视图类似于从我们原来的A中每隔一列选择一列——因此当在第二维的索引之间移动时，它需要跳过相当于两个五元素列的内容：

    julia> stride(V, 2)
 10

    第三维很有趣因为它的顺序颠倒了! 因此从第一 "页" 到第二页它必须在内存中到 backwards，所以它在这一维的 strides 是负的!

    julia> stride(V, 3)
--35

    这意味着V 的pointer 实际上指向A 的内存块的中间，并且它在内存中指向元素是同时向后和向前的。 有关定义你自己的跨距数组的更多详细信息，请参阅 等步长数组的接口指南。 StridedVector 和 StridedMatrix 被认为是等步长数组的内置数组类型的方便别名，允许它们仅使用指针和步幅，来分派选择调用调整和优化后的 BLAS 和 LAPACK 函数。

    需要强调的是 strides 是关于内存而不是索引中的偏移。如果你在找在线性（单索引）索引和笛卡尔（多索引）索引间切换的方法，见 LinearIndices 和 CartesianIndices.

    +-35

    这意味着V 的pointer 实际上指向A 的内存块的中间，并且它在内存中指向元素是同时向后和向前的。 有关定义你自己的跨距数组的更多详细信息，请参阅 等步长数组的接口指南。 StridedVector 和 StridedMatrix 被认为是等步长数组的内置数组类型的方便别名，允许它们仅使用指针和步幅，来分派选择调用调整和优化后的 BLAS 和 LAPACK 函数。

    需要强调的是 strides 是关于内存而不是索引中的偏移。如果你在找在线性（单索引）索引和笛卡尔（多索引）索引间切换的方法，见 LinearIndices 和 CartesianIndices.

    diff --git a/dev/manual/asynchronous-programming/index.html b/dev/manual/asynchronous-programming/index.html index 526b7cf5..6e6c1d86 100644 --- a/dev/manual/asynchronous-programming/index.html +++ b/dev/manual/asynchronous-programming/index.html @@ -127,4 +127,4 @@ 10 finished in 0.64 seconds 12 finished in 0.5 seconds 11 finished in 0.97 seconds -0.029772311

    不用 errormonitor(t)，一个更稳健的解决方案是使用 bind(results, t)，这不仅会记录任何意外故障，还会强制相关资源关闭并向上抛出错误。

    更多任务操作

    任务操作建立在称为 yieldto 的底层原始运算上。 yieldto(task, value) 挂起当前 task，然后切换到指定的 task，并使该任务的最后一个 yieldto 调用返回指定的 value。 请注意，yieldto 是使用任务式流程控制所需的唯一操作；我们总是切换到不同的任务，而不是调用和返回。 这就是为什么这个特性也被称为“对称协程”； 每个任务都使用相同的机制来回切换。

    yieldto 功能强大，但大多数 Task 的使用都不会直接调用它。思考为什么会这样。如果你切换当前 Task，你很可能会在某个时候想切换回来。但知道什么时候切换回来和那个 Task 负责切换回来需要大量的协调。例如，put! 和 take! 是阻塞操作，当在渠道环境中使用时，维持状态以记住消费者是谁。不需要人为地记录消费 Task，正是使得 put! 比底层 yieldto 易用的原因。

    除了 yieldto 之外，也需要一些其它的基本函数来更高效地使用 Task。

    Task 和事件

    多数 Task 切换是在等待如 I/O 请求的事件，由 Julia Base 里的调度器执行。调度器维持一个可运行 Task 的队列，并执行一个事件循环，来根据例如收到消息等外部事件来重启 Task。

    等待一个事件的基本函数是 wait。很多对象都实现了 wait 函数；例如，给定一个 Process 对象，wait 将等待它退出。wait 通常是隐式的，例如，wait 可能发生在调用 read 时等待数据可用。

    在所有这些情况下，wait 最终会操作一个 Condition 对象，由它负责排队和重启 Task。当 Task 在一个 Condition 上调用 wait 时，该 Task 就被标记为不可执行，加到条件的队列中，并切回调度器。调度器将选择另一个 Task 来运行，或者阻止外部事件的等待。如果所有运行良好，最终一个事件处理器将在这个条件下调用 notify，使得等待该条件的 Task 又变成可运行。

    通过调用 Task 显式创建的任务，一开始并不被调度器知道。这允许你根据需要使用 yieldto 手动管理任务。 但是，当此类任务等待事件时，它仍会在事件发生时自动重新启动，正如你所期望。

    +0.029772311

    不用 errormonitor(t)，一个更稳健的解决方案是使用 bind(results, t)，这不仅会记录任何意外故障，还会强制相关资源关闭并向上抛出错误。

    更多任务操作

    任务操作建立在称为 yieldto 的底层原始运算上。 yieldto(task, value) 挂起当前 task，然后切换到指定的 task，并使该任务的最后一个 yieldto 调用返回指定的 value。 请注意，yieldto 是使用任务式流程控制所需的唯一操作；我们总是切换到不同的任务，而不是调用和返回。 这就是为什么这个特性也被称为“对称协程”； 每个任务都使用相同的机制来回切换。

    yieldto 功能强大，但大多数 Task 的使用都不会直接调用它。思考为什么会这样。如果你切换当前 Task，你很可能会在某个时候想切换回来。但知道什么时候切换回来和那个 Task 负责切换回来需要大量的协调。例如，put! 和 take! 是阻塞操作，当在渠道环境中使用时，维持状态以记住消费者是谁。不需要人为地记录消费 Task，正是使得 put! 比底层 yieldto 易用的原因。

    除了 yieldto 之外，也需要一些其它的基本函数来更高效地使用 Task。

    Task 和事件

    多数 Task 切换是在等待如 I/O 请求的事件，由 Julia Base 里的调度器执行。调度器维持一个可运行 Task 的队列，并执行一个事件循环，来根据例如收到消息等外部事件来重启 Task。

    等待一个事件的基本函数是 wait。很多对象都实现了 wait 函数；例如，给定一个 Process 对象，wait 将等待它退出。wait 通常是隐式的，例如，wait 可能发生在调用 read 时等待数据可用。

    在所有这些情况下，wait 最终会操作一个 Condition 对象，由它负责排队和重启 Task。当 Task 在一个 Condition 上调用 wait 时，该 Task 就被标记为不可执行，加到条件的队列中，并切回调度器。调度器将选择另一个 Task 来运行，或者阻止外部事件的等待。如果所有运行良好，最终一个事件处理器将在这个条件下调用 notify，使得等待该条件的 Task 又变成可运行。

    通过调用 Task 显式创建的任务，一开始并不被调度器知道。这允许你根据需要使用 yieldto 手动管理任务。 但是，当此类任务等待事件时，它仍会在事件发生时自动重新启动，正如你所期望。

    diff --git a/dev/manual/calling-c-and-fortran-code/index.html b/dev/manual/calling-c-and-fortran-code/index.html index 0fdf25ad..b74ce81f 100644 --- a/dev/manual/calling-c-and-fortran-code/index.html +++ b/dev/manual/calling-c-and-fortran-code/index.html @@ -156,4 +156,4 @@ 8

    ccall interface

    There is another alternative interface to @ccall. This interface is slightly less convenient but it does allow one to specify a calling convention.

    The arguments to ccall are:

    1. A (:function, "library") pair (most common),

      OR

      a :function name symbol or "function" name string (for symbols in the current process or libc),

      OR

      a function pointer (for example, from dlsym).

    2. The function's return type

    3. A tuple of input types, corresponding to the function signature. One common mistake is forgetting that a 1-tuple of argument types must be written with a trailing comma.

    4. The actual argument values to be passed to the function, if any; each is a separate parameter.

    Note

    The (:function, "library") pair, return type, and input types must be literal constants (i.e., they can't be variables, but see Non-constant Function Specifications).

    The remaining parameters are evaluated at compile-time, when the containing method is defined.

    A table of translations between the macro and function interfaces is given below.

    @ccallccall
    @ccall clock()::Int32ccall(:clock, Int32, ())
    @ccall f(a::Cint)::Cintccall(:a, Cint, (Cint,), a)
    @ccall "mylib".f(a::Cint, b::Cdouble)::Cvoidccall((:f, "mylib"), Cvoid, (Cint, Cdouble), (a, b))
    @ccall $fptr.f()::Cvoidccall(fptr, f, Cvoid, ())
    @ccall printf("%s = %d\n"::Cstring ; "foo"::Cstring, foo::Cint)::Cint<unavailable>
    @ccall printf("%s = %d\n"::Cstring ; "2 + 2"::Cstring, "5"::Cstring)::Cintccall(:printf, Cint, (Cstring, Cstring...), "%s = %s\n", "2 + 2", "5")
    <unavailable>ccall(:gethostname, stdcall, Int32, (Ptr{UInt8}, UInt32), hn, length(hn))

    Calling Convention

    The second argument to ccall (immediately preceding return type) can optionally be a calling convention specifier (the @ccall macro currently does not support giving a calling convention). Without any specifier, the platform-default C calling convention is used. Other supported conventions are: stdcall, cdecl, fastcall, and thiscall (no-op on 64-bit Windows). For example (from base/libc.jl) we see the same gethostnameccall as above, but with the correct signature for Windows:

    hn = Vector{UInt8}(undef, 256)
 err = ccall(:gethostname, stdcall, Int32, (Ptr{UInt8}, UInt32), hn, length(hn))

    请参阅 LLVM Language Reference 来获得更多信息。

    还有一个额外的特殊调用约定 llvmcall，它允许直接插入对 LLVM 内部函数的调用。 这在针对不常见的平台（例如 GPGPU）时特别有用。 例如，对于CUDA，我们需要能够读取线程索引：

    ccall("llvm.nvvm.read.ptx.sreg.tid.x", llvmcall, Int32, ())

    与任何 ccall 一样，参数签名必须完全正确。另外，请注意，与Core.Intrinsics开放的等效Julia函数不同，没有兼容层级可以确保内在函数有意义并在当前目标上工作。

    访问全局变量

    可以使用 cglobal 函数按名称访问本地库导出的全局变量。 cglobal 的参数与 ccall 使用相同的符号规范，以及描述存储在变量中的值的类型：

    julia> cglobal((:errno, :libc), Int32)
 Ptr{Int32} @0x00007f418d0816b8

    结果是一个给出值地址的指针。 可以使用 unsafe_load 和 unsafe_store! 通过这个指针来操作该值。

    Note

    在名为“libc”的库中可能找不到此 errno 符号，因为这是系统编译器的实现细节。 通常标准库符号应该只通过名称访问，允许编译器填写正确的符号。 然而，这个例子中显示的 errno 符号在大多数编译器中都是特殊的，所以这里看到的值可能不是你所期望或想要的。 在任何支持多线程的系统上用 C 编译等效代码通常实际上会调用不同的函数（通过宏预处理器重载），并且可能给出与此处打印的遗留值不同的结果。

    通过指针来访问数据

    以下方法被描述为“不安全”，因为错误的指针或类型声明会导致 Julia 突然终止。

    给定一个 Ptr{T}，通常可以使用 unsafe_load(ptr, [index]) 将 T 类型的内容从引用的内存复制到 Julia 对象中。 index 参数是可选的（默认为 1），并遵循基于 1 的索引的 Julia 惯例。 此函数类似于 getindex 和 setindex! 的行为（例如[] 访问语法）。

    返回值将是一个初始化为包含引用内存内容副本的新对象。 引用的内存可以安全地释放或释放。

    如果 T 是 Any，则假定内存包含对 Julia 对象的引用（jl_value_t*），结果将是对该对象的引用，并且不会复制该对象。 在这种情况下，你必须小心确保对象始终对垃圾收集器可见（指针不计数，但新引用计数）以确保内存不会过早释放。 请注意，如果对象最初不是由 Julia 分配的，则新对象将永远不会被 Julia 的垃圾收集器终结。 如果 Ptr 本身实际上是一个 jl_value_t*，它可以通过 unsafe_pointer_to_objref(ptr) 转换回 Julia 对象引用。 （Julia 值 v 可以通过调用 pointer_from_objref(v) 转换为 jl_value_t* 指针，如 Ptr{Cvoid}。）

    可以使用 unsafe_store!(ptr, value, [index]) 执行反向操作（将数据写入 Ptr{T}）。 目前，这仅支持原始类型或其他无指针（isbits）不可变结构类型。

    任何引发错误的操作目前可能尚未实现，应作为错误发布，以便解决。

    如果感兴趣的指针是纯数据数组（原始类型或不可变结构），则函数 unsafe_wrap(Array, ptr,dims, own = false) 可能更有用。 如果 Julia 应该“获得”底层缓冲区的所有权并在返回的 Array 对象最终确定时调用 free(ptr)，则最后一个参数应该为 true。 如果省略了 own 参数或为 false，则调用者必须确保缓冲区一直存在，直到所有访问完成。

    Julia 中 Ptr 类型的算术（例如使用 +）与 C 的指针算术的行为不同。 将整数添加到 Julia 中的 Ptr 总是将指针移动一定数量的 bytes，而不是元素。 这样，通过指针运算获得的地址值不依赖于指针的元素类型。

    线程安全

    一些 C 库从不同的线程执行它们的回调，并且由于 Julia 不是线程安全的，因此你需要采取一些额外的预防措施。 特别是，你需要设置一个两层系统：C 回调应该只 安排（通过 Julia 的事件循环）执行“真实”回调。 为此，创建一个 AsyncCondition 对象并在其上创建 wait：

    cond = Base.AsyncCondition()
-wait(cond)

    传递给 C 的回调应该只通过 ccall 将 cond.handle 作为参数传递给 :uv_async_send 并调用，注意避免任何内存分配操作或与 Julia 运行时的其他交互。

    注意，事件可能会合并，因此对 uv_async_send 的多个调用可能会导致对该条件的单个唤醒通知。

    关于 Callbacks 的更多内容

    关于如何传递 callback 到 C 库的更多细节，请参考此博客。

    C++

    如需封装C++库的工具，即用C++写封装/胶水代码，请参考CxxWrap。

    +wait(cond)

    传递给 C 的回调应该只通过 ccall 将 cond.handle 作为参数传递给 :uv_async_send 并调用，注意避免任何内存分配操作或与 Julia 运行时的其他交互。

    注意，事件可能会合并，因此对 uv_async_send 的多个调用可能会导致对该条件的单个唤醒通知。

    关于 Callbacks 的更多内容

    关于如何传递 callback 到 C 库的更多细节，请参考此博客。

    C++

    如需封装C++库的工具，即用C++写封装/胶水代码，请参考CxxWrap。

    diff --git a/dev/manual/code-loading/index.html b/dev/manual/code-loading/index.html index 415e2a14..87c784ab 100644 --- a/dev/manual/code-loading/index.html +++ b/dev/manual/code-loading/index.html @@ -144,4 +144,4 @@ # Extend functionality in main package with types from the extension dependencies MyPackage.func(x::ExtDep.SomeStruct) = ... -end

    When a package with extensions is added to an environment, the weakdeps and extensions sections are stored in the manifest file in the section for that package. The dependency lookup rules for a package are the same as for its "parent" except that the listed extension dependencies are also considered as dependencies.

    Package/Environment Preferences

    Preferences are dictionaries of metadata that influence package behavior within an environment. The preferences system supports reading preferences at compile-time, which means that at code-loading time, we must ensure that the precompilation files selected by Julia were built with the same preferences as the current environment before loading them. The public API for modifying Preferences is contained within the Preferences.jl package. Preferences are stored as TOML dictionaries within a (Julia)LocalPreferences.toml file next to the currently-active project. If a preference is "exported", it is instead stored within the (Julia)Project.toml instead. The intention is to allow shared projects to contain shared preferences, while allowing for users themselves to override those preferences with their own settings in the LocalPreferences.toml file, which should be .gitignored as the name implies.

    Preferences that are accessed during compilation are automatically marked as compile-time preferences, and any change recorded to these preferences will cause the Julia compiler to recompile any cached precompilation file(s) (.ji and corresponding .so, .dll, or .dylib files) for that module. This is done by serializing the hash of all compile-time preferences during compilation, then checking that hash against the current environment when searching for the proper file(s) to load.

    Preferences can be set with depot-wide defaults; if package Foo is installed within your global environment and it has preferences set, these preferences will apply as long as your global environment is part of your LOAD_PATH. Preferences in environments higher up in the environment stack get overridden by the more proximal entries in the load path, ending with the currently active project. This allows depot-wide preference defaults to exist, with active projects able to merge or even completely overwrite these inherited preferences. See the docstring for Preferences.set_preferences!() for the full details of how to set preferences to allow or disallow merging.

    总结

    在软件包系统中，联邦软件包管理和精确的软件可复制性是困难但有价值的目标。结合起来，这些目标导致了一个比大多数动态语言更加复杂的包加载机制，但它也产生了通常与静态语言相关的可伸缩性和可复制性。通常，Julia用户应该能够使用内置的包管理器来管理他们的项目，而无需精确理解这些交互细节。通过调用Pkg.add("X")添加X包到对应的项目，并清晰显示相关文件，选择Pkg.activate("Y")后, 可调用import X 即可加载X包，而无需作过多考虑。

    +end

    When a package with extensions is added to an environment, the weakdeps and extensions sections are stored in the manifest file in the section for that package. The dependency lookup rules for a package are the same as for its "parent" except that the listed extension dependencies are also considered as dependencies.

    Package/Environment Preferences

    Preferences are dictionaries of metadata that influence package behavior within an environment. The preferences system supports reading preferences at compile-time, which means that at code-loading time, we must ensure that the precompilation files selected by Julia were built with the same preferences as the current environment before loading them. The public API for modifying Preferences is contained within the Preferences.jl package. Preferences are stored as TOML dictionaries within a (Julia)LocalPreferences.toml file next to the currently-active project. If a preference is "exported", it is instead stored within the (Julia)Project.toml instead. The intention is to allow shared projects to contain shared preferences, while allowing for users themselves to override those preferences with their own settings in the LocalPreferences.toml file, which should be .gitignored as the name implies.

    Preferences that are accessed during compilation are automatically marked as compile-time preferences, and any change recorded to these preferences will cause the Julia compiler to recompile any cached precompilation file(s) (.ji and corresponding .so, .dll, or .dylib files) for that module. This is done by serializing the hash of all compile-time preferences during compilation, then checking that hash against the current environment when searching for the proper file(s) to load.

    Preferences can be set with depot-wide defaults; if package Foo is installed within your global environment and it has preferences set, these preferences will apply as long as your global environment is part of your LOAD_PATH. Preferences in environments higher up in the environment stack get overridden by the more proximal entries in the load path, ending with the currently active project. This allows depot-wide preference defaults to exist, with active projects able to merge or even completely overwrite these inherited preferences. See the docstring for Preferences.set_preferences!() for the full details of how to set preferences to allow or disallow merging.

    总结

    在软件包系统中，联邦软件包管理和精确的软件可复制性是困难但有价值的目标。结合起来，这些目标导致了一个比大多数动态语言更加复杂的包加载机制，但它也产生了通常与静态语言相关的可伸缩性和可复制性。通常，Julia用户应该能够使用内置的包管理器来管理他们的项目，而无需精确理解这些交互细节。通过调用Pkg.add("X")添加X包到对应的项目，并清晰显示相关文件，选择Pkg.activate("Y")后, 可调用import X 即可加载X包，而无需作过多考虑。

    diff --git a/dev/manual/command-line-interface/index.html b/dev/manual/command-line-interface/index.html index f1fb82c9..20132558 100644 --- a/dev/manual/command-line-interface/index.html +++ b/dev/manual/command-line-interface/index.html @@ -16,4 +16,4 @@ ...

    Note that although you should have a ~/.julia directory once you've run Julia for the first time, you may need to create the ~/.julia/config folder and the ~/.julia/config/startup.jl file if you use it.

    To have startup code run only in The Julia REPL (and not when julia is e.g. run on a script), use atreplinit in startup.jl:

    atreplinit() do repl
     # ...
-end

    Command-line switches for Julia

    There are various ways to run Julia code and provide options, similar to those available for the perl and ruby programs:

    julia [switches] -- [programfile] [args...]

    The following is a complete list of command-line switches available when launching julia (a '*' marks the default value, if applicable; settings marked '($)' may trigger package precompilation):

    SwitchDescription
    -v, --versionDisplay version information
    -h, --helpPrint command-line options (this message).
    --help-hiddenUncommon options not shown by -h
    --project[={<dir>|@.}]Set <dir> as the home project/environment. The default @. option will search through parent directories until a Project.toml or JuliaProject.toml file is found.
    -J, --sysimage <file>Start up with the given system image file
    -H, --home <dir>Set location of julia executable
    --startup-file={yes*|no}Load JULIA_DEPOT_PATH/config/startup.jl; if JULIA_DEPOT_PATH environment variable is unset, load ~/.julia/config/startup.jl
    --handle-signals={yes*|no}Enable or disable Julia's default signal handlers
    --sysimage-native-code={yes*|no}Use native code from system image if available
    --compiled-modules={yes*|no}Enable or disable incremental precompilation of modules
    --pkgimages={yes*|no}Enable or disable usage of native code caching in the form of pkgimages
    -e, --eval <expr>Evaluate <expr>
    -E, --print <expr>Evaluate <expr> and display the result
    -L, --load <file>Load <file> immediately on all processors
    -t, --threads {N|auto}Enable N threads; auto tries to infer a useful default number of threads to use but the exact behavior might change in the future. Currently, auto uses the number of CPUs assigned to this julia process based on the OS-specific affinity assignment interface, if supported (Linux and Windows). If this is not supported (macOS) or process affinity is not configured, it uses the number of CPU threads.
    --gcthreads=N[,M]Use N threads for the mark phase of GC and M (0 or 1) threads for the concurrent sweeping phase of GC. N is set to half of the number of compute threads and M is set to 0 if unspecified.
    -p, --procs {N|auto}Integer value N launches N additional local worker processes; auto launches as many workers as the number of local CPU threads (logical cores)
    --machine-file <file>Run processes on hosts listed in <file>
    -iInteractive mode; REPL runs and isinteractive() is true
    -q, --quietQuiet startup: no banner, suppress REPL warnings
    --banner={yes|no|auto*}Enable or disable startup banner
    --color={yes|no|auto*}Enable or disable color text
    --history-file={yes*|no}Load or save history
    --depwarn={yes|no*|error}Enable or disable syntax and method deprecation warnings (error turns warnings into errors)
    --warn-overwrite={yes|no*}Enable or disable method overwrite warnings
    --warn-scope={yes*|no}Enable or disable warning for ambiguous top-level scope
    -C, --cpu-target <target>Limit usage of CPU features up to <target>; set to help to see the available options
    -O, --optimize={0,1,2*,3}Set the optimization level (level is 3 if -O is used without a level) ($)
    --min-optlevel={0*,1,2,3}Set the lower bound on per-module optimization
    -g, --debug-info={0,1*,2}Set the level of debug info generation (level is 2 if -g is used without a level) ($)
    --inline={yes|no}Control whether inlining is permitted, including overriding @inline declarations
    --check-bounds={yes|no|auto*}Emit bounds checks always, never, or respect @inbounds declarations ($)
    --math-mode={ieee,fast}Disallow or enable unsafe floating point optimizations (overrides @fastmath declaration)
    --code-coverage[={none*|user|all}]Count executions of source lines (omitting setting is equivalent to user)
    --code-coverage=@<path>Count executions but only in files that fall under the given file path/directory. The @ prefix is required to select this option. A @ with no path will track the current directory.
    --code-coverage=tracefile.infoAppend coverage information to the LCOV tracefile (filename supports format tokens).
    --track-allocation[={none*|user|all}]Count bytes allocated by each source line (omitting setting is equivalent to "user")
    --track-allocation=@<path>Count bytes but only in files that fall under the given file path/directory. The @ prefix is required to select this option. A @ with no path will track the current directory.
    --bug-report=KINDLaunch a bug report session. It can be used to start a REPL, run a script, or evaluate expressions. It first tries to use BugReporting.jl installed in current environment and falls back to the latest compatible BugReporting.jl if not. For more information, see --bug-report=help.
    --compile={yes*|no|all|min}Enable or disable JIT compiler, or request exhaustive or minimal compilation
    --output-o <name>Generate an object file (including system image data)
    --output-ji <name>Generate a system image data file (.ji)
    --strip-metadataRemove docstrings and source location info from system image
    --strip-irRemove IR (intermediate representation) of compiled functions
    --output-unopt-bc <name>Generate unoptimized LLVM bitcode (.bc)
    --output-bc <name>Generate LLVM bitcode (.bc)
    --output-asm <name>Generate an assembly file (.s)
    --output-incremental={yes|no*}Generate an incremental output file (rather than complete)
    --trace-compile={stderr,name}Print precompile statements for methods compiled during execution or save to a path
    --image-codegenForce generate code in imaging mode
    --heap-size-hint=<size>Forces garbage collection if memory usage is higher than that value. The memory hint might be specified in megabytes (e.g., 500M) or gigabytes (e.g., 1G)
    Julia 1.1

    In Julia 1.0, the default --project=@. option did not search up from the root directory of a Git repository for the Project.toml file. From Julia 1.1 forward, it does.

    +end

    Command-line switches for Julia

    There are various ways to run Julia code and provide options, similar to those available for the perl and ruby programs:

    julia [switches] -- [programfile] [args...]

    The following is a complete list of command-line switches available when launching julia (a '*' marks the default value, if applicable; settings marked '($)' may trigger package precompilation):

    SwitchDescription
    -v, --versionDisplay version information
    -h, --helpPrint command-line options (this message).
    --help-hiddenUncommon options not shown by -h
    --project[={<dir>|@.}]Set <dir> as the home project/environment. The default @. option will search through parent directories until a Project.toml or JuliaProject.toml file is found.
    -J, --sysimage <file>Start up with the given system image file
    -H, --home <dir>Set location of julia executable
    --startup-file={yes*|no}Load JULIA_DEPOT_PATH/config/startup.jl; if JULIA_DEPOT_PATH environment variable is unset, load ~/.julia/config/startup.jl
    --handle-signals={yes*|no}Enable or disable Julia's default signal handlers
    --sysimage-native-code={yes*|no}Use native code from system image if available
    --compiled-modules={yes*|no}Enable or disable incremental precompilation of modules
    --pkgimages={yes*|no}Enable or disable usage of native code caching in the form of pkgimages
    -e, --eval <expr>Evaluate <expr>
    -E, --print <expr>Evaluate <expr> and display the result
    -L, --load <file>Load <file> immediately on all processors
    -t, --threads {N|auto}Enable N threads; auto tries to infer a useful default number of threads to use but the exact behavior might change in the future. Currently, auto uses the number of CPUs assigned to this julia process based on the OS-specific affinity assignment interface, if supported (Linux and Windows). If this is not supported (macOS) or process affinity is not configured, it uses the number of CPU threads.
    --gcthreads=N[,M]Use N threads for the mark phase of GC and M (0 or 1) threads for the concurrent sweeping phase of GC. N is set to half of the number of compute threads and M is set to 0 if unspecified.
    -p, --procs {N|auto}Integer value N launches N additional local worker processes; auto launches as many workers as the number of local CPU threads (logical cores)
    --machine-file <file>Run processes on hosts listed in <file>
    -iInteractive mode; REPL runs and isinteractive() is true
    -q, --quietQuiet startup: no banner, suppress REPL warnings
    --banner={yes|no|auto*}Enable or disable startup banner
    --color={yes|no|auto*}Enable or disable color text
    --history-file={yes*|no}Load or save history
    --depwarn={yes|no*|error}Enable or disable syntax and method deprecation warnings (error turns warnings into errors)
    --warn-overwrite={yes|no*}Enable or disable method overwrite warnings
    --warn-scope={yes*|no}Enable or disable warning for ambiguous top-level scope
    -C, --cpu-target <target>Limit usage of CPU features up to <target>; set to help to see the available options
    -O, --optimize={0,1,2*,3}Set the optimization level (level is 3 if -O is used without a level) ($)
    --min-optlevel={0*,1,2,3}Set the lower bound on per-module optimization
    -g, --debug-info={0,1*,2}Set the level of debug info generation (level is 2 if -g is used without a level) ($)
    --inline={yes|no}Control whether inlining is permitted, including overriding @inline declarations
    --check-bounds={yes|no|auto*}Emit bounds checks always, never, or respect @inbounds declarations ($)
    --math-mode={ieee,fast}Disallow or enable unsafe floating point optimizations (overrides @fastmath declaration)
    --code-coverage[={none*|user|all}]Count executions of source lines (omitting setting is equivalent to user)
    --code-coverage=@<path>Count executions but only in files that fall under the given file path/directory. The @ prefix is required to select this option. A @ with no path will track the current directory.
    --code-coverage=tracefile.infoAppend coverage information to the LCOV tracefile (filename supports format tokens).
    --track-allocation[={none*|user|all}]Count bytes allocated by each source line (omitting setting is equivalent to "user")
    --track-allocation=@<path>Count bytes but only in files that fall under the given file path/directory. The @ prefix is required to select this option. A @ with no path will track the current directory.
    --bug-report=KINDLaunch a bug report session. It can be used to start a REPL, run a script, or evaluate expressions. It first tries to use BugReporting.jl installed in current environment and falls back to the latest compatible BugReporting.jl if not. For more information, see --bug-report=help.
    --compile={yes*|no|all|min}Enable or disable JIT compiler, or request exhaustive or minimal compilation
    --output-o <name>Generate an object file (including system image data)
    --output-ji <name>Generate a system image data file (.ji)
    --strip-metadataRemove docstrings and source location info from system image
    --strip-irRemove IR (intermediate representation) of compiled functions
    --output-unopt-bc <name>Generate unoptimized LLVM bitcode (.bc)
    --output-bc <name>Generate LLVM bitcode (.bc)
    --output-asm <name>Generate an assembly file (.s)
    --output-incremental={yes|no*}Generate an incremental output file (rather than complete)
    --trace-compile={stderr,name}Print precompile statements for methods compiled during execution or save to a path
    --image-codegenForce generate code in imaging mode
    --heap-size-hint=<size>Forces garbage collection if memory usage is higher than that value. The memory hint might be specified in megabytes (e.g., 500M) or gigabytes (e.g., 1G)
    Julia 1.1

    In Julia 1.0, the default --project=@. option did not search up from the root directory of a Git repository for the Project.toml file. From Julia 1.1 forward, it does.

    diff --git a/dev/manual/command-line-options/index.html b/dev/manual/command-line-options/index.html index b724391a..e24a8a24 100644 --- a/dev/manual/command-line-options/index.html +++ b/dev/manual/command-line-options/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    命令行选项

    以下是启动 julia 时可用的命令行选项的完整列表：

    选项描述
    -v, --version显示版本信息
    -h, --help显示命令行参数
    --project[={<dir>|@.}]将 <dir> 设置为主项目/环境。默认的 @. 选项将搜索父目录，直至找到 Project.toml 或 JuliaProject.toml 文件。
    -J, --sysimage <file>用指定的系统镜像文件（system image file）启动
    -H, --home <dir>设置 julia 可执行文件的路径
    --startup-file={yes|no}是否载入 ~/.julia/config/startup.jl
    --handle-signals={yes|no}开启或关闭 Julia 默认的 signal handlers
    --sysimage-native-code={yes|no}在可能的情况下，使用系统镜像里的原生代码
    --compiled-modules={yes|no}开启或关闭 module 的增量预编译功能
    -e, --eval <expr>执行 <expr>
    -E, --print <expr>执行 <expr> 并显示结果
    -L, --load <file>立即在所有进程中载入 <file>
    -t, --threads {N|auto}开启 N 个线程：auto 将 N 设置为当前 CPU 线程数，但这个行为可能在以后版本有所变动。
    -p, --procs {N|auto}这里的整数 N 表示启动 N 个额外的工作进程；auto 表示启动与 CPU 线程数目（logical cores）一样多的进程
    --machine-file <file>在 <file> 中列出的主机上运行进程
    -i交互式模式；REPL 运行且 isinteractive() 为 true
    -q, --quiet安静的启动；REPL 启动时无横幅，不显示警告
    --banner={yes|no|auto}开启或关闭 REPL 横幅
    --color={yes|no|auto}开启或关闭文字颜色
    --history-file={yes|no}载入或导出历史记录
    --depwarn={yes|no|error}开启或关闭语法弃用警告，error 表示将弃用警告转换为错误。
    --warn-overwrite={yes|no}开启或关闭“method overwrite”警告
    -C, --cpu-target <target>设置 <target> 来限制使用 CPU 的某些特性；设置为 help 可以查看可用的选项
    -O, --optimize={0,1,2,3}设置编译器优化级别(若未配置此选项，则默认等级为2；若配置了此选项却没指定具体级别，则默认级别为3)。
    --min-optlevel={0,1,2,3}设置每个模块加载的优化下限（默认为 0）
    -g, -g <level>开启或设置 debug 信息的生成等级。若未配置此选项，则默认 debug 信息的级别为 1；若配置了此选项却没指定具体级别，则默认级别为 2。
    --inline={yes|no}控制是否允许函数内联，此选项会覆盖源文件中的 @inline 声明
    --check-bounds={yes|no|auto}是否进行边界检查：总是、从不、或依照宏 @inbounds 声明
    --math-mode={ieee,fast}开启或关闭非安全的浮点数代数计算优化，此选项会覆盖源文件中的 @fastmath 声明
    --code-coverage={none|user|all}对源文件中每行代码执行的次数计数
    --code-coverage等价于 --code-coverage=user
    --track-allocation={none|user|all}对源文件中每行代码的内存分配计数，单位 byte
    --track-allocation等价于 --track-allocation=user
    Julia 1.1

    在 Julia 1.0 中，默认的 --project=@. 选项不会在 Git 仓库的根目录中寻找 Project.toml 文件。从 Julia 1.1 开始，此选项会在其中寻找该文件。

    +
    Repository

    命令行选项

    以下是启动 julia 时可用的命令行选项的完整列表：

    选项描述
    -v, --version显示版本信息
    -h, --help显示命令行参数
    --project[={<dir>|@.}]将 <dir> 设置为主项目/环境。默认的 @. 选项将搜索父目录，直至找到 Project.toml 或 JuliaProject.toml 文件。
    -J, --sysimage <file>用指定的系统镜像文件（system image file）启动
    -H, --home <dir>设置 julia 可执行文件的路径
    --startup-file={yes|no}是否载入 ~/.julia/config/startup.jl
    --handle-signals={yes|no}开启或关闭 Julia 默认的 signal handlers
    --sysimage-native-code={yes|no}在可能的情况下，使用系统镜像里的原生代码
    --compiled-modules={yes|no}开启或关闭 module 的增量预编译功能
    -e, --eval <expr>执行 <expr>
    -E, --print <expr>执行 <expr> 并显示结果
    -L, --load <file>立即在所有进程中载入 <file>
    -t, --threads {N|auto}开启 N 个线程：auto 将 N 设置为当前 CPU 线程数，但这个行为可能在以后版本有所变动。
    -p, --procs {N|auto}这里的整数 N 表示启动 N 个额外的工作进程；auto 表示启动与 CPU 线程数目（logical cores）一样多的进程
    --machine-file <file>在 <file> 中列出的主机上运行进程
    -i交互式模式；REPL 运行且 isinteractive() 为 true
    -q, --quiet安静的启动；REPL 启动时无横幅，不显示警告
    --banner={yes|no|auto}开启或关闭 REPL 横幅
    --color={yes|no|auto}开启或关闭文字颜色
    --history-file={yes|no}载入或导出历史记录
    --depwarn={yes|no|error}开启或关闭语法弃用警告，error 表示将弃用警告转换为错误。
    --warn-overwrite={yes|no}开启或关闭“method overwrite”警告
    -C, --cpu-target <target>设置 <target> 来限制使用 CPU 的某些特性；设置为 help 可以查看可用的选项
    -O, --optimize={0,1,2,3}设置编译器优化级别(若未配置此选项，则默认等级为2；若配置了此选项却没指定具体级别，则默认级别为3)。
    --min-optlevel={0,1,2,3}设置每个模块加载的优化下限（默认为 0）
    -g, -g <level>开启或设置 debug 信息的生成等级。若未配置此选项，则默认 debug 信息的级别为 1；若配置了此选项却没指定具体级别，则默认级别为 2。
    --inline={yes|no}控制是否允许函数内联，此选项会覆盖源文件中的 @inline 声明
    --check-bounds={yes|no|auto}是否进行边界检查：总是、从不、或依照宏 @inbounds 声明
    --math-mode={ieee,fast}开启或关闭非安全的浮点数代数计算优化，此选项会覆盖源文件中的 @fastmath 声明
    --code-coverage={none|user|all}对源文件中每行代码执行的次数计数
    --code-coverage等价于 --code-coverage=user
    --track-allocation={none|user|all}对源文件中每行代码的内存分配计数，单位 byte
    --track-allocation等价于 --track-allocation=user
    Julia 1.1

    在 Julia 1.0 中，默认的 --project=@. 选项不会在 Git 仓库的根目录中寻找 Project.toml 文件。从 Julia 1.1 开始，此选项会在其中寻找该文件。

    diff --git a/dev/manual/complex-and-rational-numbers/index.html b/dev/manual/complex-and-rational-numbers/index.html index 49b25f95..07ee6e07 100644 --- a/dev/manual/complex-and-rational-numbers/index.html +++ b/dev/manual/complex-and-rational-numbers/index.html @@ -184,4 +184,4 @@ true julia> 1//3 - 0.33 -0.0033333333333332993 +0.0033333333333332993 diff --git a/dev/manual/constructors/index.html b/dev/manual/constructors/index.html index fa43f3e8..1059e1df 100644 --- a/dev/manual/constructors/index.html +++ b/dev/manual/constructors/index.html @@ -217,4 +217,4 @@ @ Main none:4 Stacktrace: -[...]

    此构造函数将会被 SummedArray(a) 这种写法触发。new{T,S} 的这种写法允许指定待构建类型的参数，也就是说调用它会返回一个 SummedArray{T,S} 的实例。new{T,S} 也可以用于其它构造函数的定义中，但为了方便，Julia 会根据正在构造的类型自动推导出 new{} 花括号里的参数（如果可行的话）。

    +[...]

    此构造函数将会被 SummedArray(a) 这种写法触发。new{T,S} 的这种写法允许指定待构建类型的参数，也就是说调用它会返回一个 SummedArray{T,S} 的实例。new{T,S} 也可以用于其它构造函数的定义中，但为了方便，Julia 会根据正在构造的类型自动推导出 new{} 花括号里的参数（如果可行的话）。

    diff --git a/dev/manual/control-flow/index.html b/dev/manual/control-flow/index.html index 0c075f7d..4ff9a710 100644 --- a/dev/manual/control-flow/index.html +++ b/dev/manual/control-flow/index.html @@ -374,4 +374,4 @@ # operate on file f finally close(f) -end

    当控制流离开 try 代码块（例如，遇到 return，或者正常结束），close(f) 就会被执行。如果 try 代码块由于异常退出，这个异常会继续传递。catch 代码块可以和 try 还有 finally 配合使用。这时 finally 代码块会在 catch 处理错误之后才运行。

    Tasks 任务（或协程）

    Task 是一种允许计算以更灵活的方式被中断或者恢复的流程控制特性。 我们提及它只是为了说明的完整性；详细的介绍参见：异步编程。

    +end

    当控制流离开 try 代码块（例如，遇到 return，或者正常结束），close(f) 就会被执行。如果 try 代码块由于异常退出，这个异常会继续传递。catch 代码块可以和 try 还有 finally 配合使用。这时 finally 代码块会在 catch 处理错误之后才运行。

    Tasks 任务（或协程）

    Task 是一种允许计算以更灵活的方式被中断或者恢复的流程控制特性。 我们提及它只是为了说明的完整性；详细的介绍参见：异步编程。

    diff --git a/dev/manual/conversion-and-promotion/index.html b/dev/manual/conversion-and-promotion/index.html index b065794c..085316de 100644 --- a/dev/manual/conversion-and-promotion/index.html +++ b/dev/manual/conversion-and-promotion/index.html @@ -58,4 +58,4 @@ promote_rule(::Type{BigInt}, ::Type{Int8}) = BigInt

    在后一种情况下，输出类型是 BigInt，因为 BigInt 是唯一一个足以容纳任意精度整数运算结果的类型。还要注意，不需要同时定义 promote_rule(::Type{A}, ::Type{B}) 和 promote_rule(::Type{B}, ::Type{A})——对称性隐含在类型提升过程中使用 promote_rule 的方式。

    以 promote_rule 函数为基础定义了 promote_type 函数，在给定任意数量的类型对象时，它返回这些值作为 promote 的参数应被提升的通用类型。因此，如果想知道在没有实际值情况下，具有确定类型的一些值会被类型提升为什么类型，可以使用 promote_type：

    julia> promote_type(Int8, Int64)
 Int64

    Note that we do not overload promote_type directly: we overload promote_rule instead. promote_type uses promote_rule, and adds the symmetry. Overloading it directly can cause ambiguity errors. We overload promote_rule to define how things should be promoted, and we use promote_type to query that.

    在内部，promote_type 在 promote 中用于确定参数值应被转换为什么类型以便进行类型提升。 好奇的读者可以阅读 promotion.jl，该文件用大概 35 行定义了完整的类型提升规则。

    Internally, promote_type is used inside of promote to determine what type argument values should be converted to for promotion. The curious reader can read the code in promotion.jl, which defines the complete promotion mechanism in about 35 lines.

    案例研究：有理数的类型提升

    最后，我们来完成关于 Julia 的有理数类型的案例研究，该案例通过以下类型提升规则相对复杂地使用了类型提升机制：

    promote_rule(::Type{Rational{T}}, ::Type{S}) where {T<:Integer,S<:Integer} = Rational{promote_type(T,S)}
 promote_rule(::Type{Rational{T}}, ::Type{Rational{S}}) where {T<:Integer,S<:Integer} = Rational{promote_type(T,S)}
-promote_rule(::Type{Rational{T}}, ::Type{S}) where {T<:Integer,S<:AbstractFloat} = promote_type(T,S)

    第一条规则说，使用其它整数类型类型提升有理数类型会得到个有理数类型，其分子/分母类型是使用其它整数类型提升该有理数分子/分母类型的结果。第二条规则将相同的逻辑应用于两种不同的有理数类型，它们进行类型提升会得到有理数类型，其分子/分母类型是它们各自的分子/分母类型进行提升的结果。第三个也是最后一个规则规定，使用浮点数类型提升有理数类型与使用该浮点数类型提升其分子/分母类型会产生相同的类型。

    这一小部分的类型提升规则，连同该类型的构造函数和数字的默认 convert 方法，便足以使有理数与 Julia 的其它数值类型——整数、浮点数和复数——完全自然地互操作。通过以相同的方式提供类型转换方法和类型提升规则，任何用户定义的数值类型都可像 Julia 的预定义数值类型一样自然地进行互操作。

    +promote_rule(::Type{Rational{T}}, ::Type{S}) where {T<:Integer,S<:AbstractFloat} = promote_type(T,S)

    第一条规则说，使用其它整数类型类型提升有理数类型会得到个有理数类型，其分子/分母类型是使用其它整数类型提升该有理数分子/分母类型的结果。第二条规则将相同的逻辑应用于两种不同的有理数类型，它们进行类型提升会得到有理数类型，其分子/分母类型是它们各自的分子/分母类型进行提升的结果。第三个也是最后一个规则规定，使用浮点数类型提升有理数类型与使用该浮点数类型提升其分子/分母类型会产生相同的类型。

    这一小部分的类型提升规则，连同该类型的构造函数和数字的默认 convert 方法，便足以使有理数与 Julia 的其它数值类型——整数、浮点数和复数——完全自然地互操作。通过以相同的方式提供类型转换方法和类型提升规则，任何用户定义的数值类型都可像 Julia 的预定义数值类型一样自然地进行互操作。

    diff --git a/dev/manual/distributed-computing/index.html b/dev/manual/distributed-computing/index.html index c51f0a5a..87740dfb 100644 --- a/dev/manual/distributed-computing/index.html +++ b/dev/manual/distributed-computing/index.html @@ -438,4 +438,4 @@ @printf("sum of ranks: %s\n", sr) end -MPI.Finalize()
    mpirun -np 4 ./julia example.jl
    +MPI.Finalize()
    mpirun -np 4 ./julia example.jl
    diff --git a/dev/manual/documentation/index.html b/dev/manual/documentation/index.html index ea162b20..88ec6156 100644 --- a/dev/manual/documentation/index.html +++ b/dev/manual/documentation/index.html @@ -187,4 +187,4 @@ @__doc__ $(f)(x) = 1 $(f)(x, y) = 2 end |> esc -end

    @__doc__ has no effect when a macro that uses it is not documented.

    source +end

    @__doc__ has no effect when a macro that uses it is not documented.

    source diff --git a/dev/manual/embedding/index.html b/dev/manual/embedding/index.html index f4254f91..6a9e422d 100644 --- a/dev/manual/embedding/index.html +++ b/dev/manual/embedding/index.html @@ -236,4 +236,4 @@ [J 2] i = 4 -> 2.0 [C 23938640] i = 5 [J 1] i = 3 -> 1.7320508075688772 -[J 2] i = 5 -> 2.23606797749979

    As can be seen, Julia thread 1 corresponds to pthread ID 3bfd9c00, and Julia thread 2 corresponds to ID 23938640, showing that indeed multiple threads are used at the C level, and that we can safely call Julia C API routines from those threads.

    +[J 2] i = 5 -> 2.23606797749979

    As can be seen, Julia thread 1 corresponds to pthread ID 3bfd9c00, and Julia thread 2 corresponds to ID 23938640, showing that indeed multiple threads are used at the C level, and that we can safely call Julia C API routines from those threads.

    diff --git a/dev/manual/environment-variables/index.html b/dev/manual/environment-variables/index.html index a60da2d3..c9c1133a 100644 --- a/dev/manual/environment-variables/index.html +++ b/dev/manual/environment-variables/index.html @@ -5,4 +5,4 @@ gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash});
    Repository

    环境变量

    Julia 可以配置许多环境变量，一种常见的方式是直接配置操作系统环境变量，另一种更便携的方式是在 Julia 中配置。假设你要将环境变量 JULIA_EDITOR 设置为 vim，可以直接在 REPL 中输入 ENV["JULIA_EDITOR"] = "vim"（请根据具体情况对此进行修改），也可以将其添加到用户主目录中的配置文件 ~/.julia/config/startup.jl，这样做会使其永久生效。环境变量的当前值是通过执行 ENV["JULIA_EDITOR"] 来确定的。

    Julia 使用的环境变量通常以 JULIA 开头。如果调用 InteractiveUtils.versioninfo 时使用关键字参数 verbose = true，那么输出结果将列出与 Julia 相关的已定义环境变量，即包括那些名称中包含 JULIA 的环境变量。

    Note

    某些变量需要在 Julia 启动之前设置，比如 JULIA_NUM_THREADS 和 JULIA_PROJECT，因为在启动过程中将这些变量添加到 ~/.julia/config/startup.jl 中为时已晚。在 Bash 中，环境变量可以手动设置，这可通过在 Julia 启动前运行诸如 export JULIA_NUM_THREADS=4 的命令，亦可通过向 ~/.bashrc 或 ~/.bash_profile 添加相同命令来在 Bash 每次启动时设置该变量。

    文件位置

    JULIA_BINDIR

    包含 Julia 可执行文件的目录的绝对路径，它会设置全局变量 Sys.BINDIR。$JULIA_BINDIR 如果没有设置，那么 Julia 会在运行时确定 Sys.BINDIR 的值。

    在默认情况下，可执行文件是指：

    $JULIA_BINDIR/julia
 $JULIA_BINDIR/julia-debug

    全局变量 Base.DATAROOTDIR 是一个从 Sys.BINDIR 到 Julia 数据目录的相对路径。

    $JULIA_BINDIR/$DATAROOTDIR/julia/base

    上述路径是 Julia 最初搜索源文件的路径（通过 Base.find_source_file()）。

    同样，全局变量 Base.SYSCONFDIR 是一个到配置文件目录的相对路径。在默认情况下，Julia 会在下列文件中搜索 startup.jl 文件（通过 Base.load_julia_startup()）

    $JULIA_BINDIR/$SYSCONFDIR/julia/startup.jl
-$JULIA_BINDIR/../etc/julia/startup.jl

    例如，在 Linux 下安装的 Julia 可执行文件位于 /bin/julia，DATAROOTDIR 为 ../share，SYSCONFDIR 为 ../etc，JULIA_BINDIR 会被设置为 /bin，会有一个源文件搜索路径：

    /share/julia/base

    和一个全局配置文件搜索路径：

    /etc/julia/startup.jl

    JULIA_PROJECT

    指示哪个项目应该是初始活动项目的目录路径。 设置这个环境变量和指定--project启动选项效果一样，但是--project优先级更高。 如果变量设置为 @. （注意尾随的点），那么 Julia 会尝试从当前目录及其父目录中查找包含 Project.toml 或 JuliaProject.toml 文件的项目目录。 另请参阅有关 代码加载 的章节。

    Note

    JULIA_PROJECT 必须在启动 julia 前定义；于 startup.jl 中定义它对于启动的过程为时已晚。

    JULIA_LOAD_PATH

    JULIA_LOAD_PATH 环境变量用于补充全局的 Julia 变量 LOAD_PATH ，该变量可用于确定通过 import 和 using 可以加载哪些包（请参阅 Code Loading）。

    与 shell 使用的 PATH 变量不同， 在 JULIA_LOAD_PATH 中的空条目将会在填充 LOAD_PATH 时被扩展为 LOAD_PATH 的默认值 ["@", "@v#.#", "@stdlib"] 。这样，无论 JULIA_LOAD_PATH 是否已被设置，均可以使用 shell 脚本轻松地在加载路径前面或后面添加值。例如要将 /foo/bar 添加到 LOAD_PATH 之前，只需要使用下列脚本：

    export JULIA_LOAD_PATH="/foo/bar:$JULIA_LOAD_PATH"

    如果已经设置了 JULIA_LOAD_PATH 环境变量，那么 /foo/bar 将被添加在原有值之前。另一方面，如果 JULIA_LOAD_PATH 尚未设置，那么它会被设置为 /foo/bar: ，而这将使用 LOAD_PATH 的值扩展为 ["/foo/bar", "@", "@v#.#", "@stdlib"] 。如果 JULIA_LOAD_PATH 被设置为空字符串，那么它将被扩展为一个空的 LOAD_PATH 数组。换句话说，这个空字符串数组将被认为是零元素的数组，而非是一个空字符串单元素的数组。使用这样的加载行为是为了可以通过环境变量设置空的加载路径。如果你需要使用默认的加载路径，请不要设置这一环境变量，如果它必须有值，那么可将其设置为字符串 : 。

    Note

    在 Windows 上，路径元素由 ; 字符分隔，就像 Windows 上的大多数路径列表一样。 将上一段中的 : 替换为 ;。

    JULIA_DEPOT_PATH

    JULIA_DEPOT_PATH 环境变量用于填充全局的 Julia 变量 DEPOT_PATH ，该变量用于控制包管理器以及 Juila 代码加载机制在何处查找包注册表、已安装的包、命名环境、克隆的存储库、缓存的预编译包映像、配置文件和 REPL 历史记录文件的默认位置。

    与 shell 使用的 PATH 变量不同，但与 JULIA_LOAD_PATH 类似， 在 JULIA_DEPOT_PATH 中的空条目将会被扩展为 DEPOT_PATH 的默认值。这样，无论 JULIA_DEPOT_PATH 是否已被设置，均可以使用 shell 脚本轻松地在仓库路径前面或后面添加值。例如要将 /foo/bar 添加到 DEPOT_PATH 之前，只需要使用下列脚本：

    export JULIA_DEPOT_PATH="/foo/bar:$JULIA_DEPOT_PATH"

    如果已经设置了 JULIA_DEPOT_PATH 环境变量，那么 /foo/bar 将被添加在原有值之前。另一方面，如果 JULIA_DEPOT_PATH 尚未设置，那么它会被设置为 /foo/bar: ，而这将使 /foo/bar 被添加到默认仓库路径之前。如果 JULIA_DEPOT_PATH 被设置为空字符串，那么它将扩展为一个空的 DEPOT_PATH 数组。换句话说，这个空字符串数组将被认为是零元素的数组，而非是一个空字符串单元素的数组。使用这样的加载行为是为了可以通过环境变量设置空的仓库路径。如果你需要使用默认的仓库路径，请不要设置这一环境变量，如果它必须有值，那么可将其设置为字符串 : 。

    Note

    在 Windows 上，路径元素由 ; 字符分隔，就像 Windows 上的大多数路径列表一样。 将上一段中的 : 替换为 ;。

    Note

    JULIA_DEPOT_PATH must be defined before starting julia; defining it in startup.jl is too late in the startup process; at that point you can instead directly modify the DEPOT_PATH array, which is populated from the environment variable.

    JULIA_HISTORY

    REPL 历史文件中 REPL.find_hist_file() 的绝对路径。如果没有设置 $JULIA_HISTORY，那么 REPL.find_hist_file() 默认为

    $(DEPOT_PATH[1])/logs/repl_history.jl

    JULIA_MAX_NUM_PRECOMPILE_FILES

    Sets the maximum number of different instances of a single package that are to be stored in the precompile cache (default = 10).

    JULIA_VERBOSE_LINKING

    If set to true, linker commands will be displayed during precompilation.

    Pkg.jl

    JULIA_CI

    If set to true, this indicates to the package server that any package operations are part of a continuous integration (CI) system for the purposes of gathering package usage statistics.

    JULIA_NUM_PRECOMPILE_TASKS

    The number of parallel tasks to use when precompiling packages. See Pkg.precompile.

    JULIA_PKG_DEVDIR

    The default directory used by Pkg.develop for downloading packages.

    JULIA_PKG_IGNORE_HASHES

    If set to 1, this will ignore incorrect hashes in artifacts. This should be used carefully, as it disables verification of downloads, but can resolve issues when moving files across different types of file systems. See Pkg.jl issue #2317 for more details.

    Julia 1.6

    This is only supported in Julia 1.6 and above.

    JULIA_PKG_OFFLINE

    If set to true, this will enable offline mode: see Pkg.offline.

    Julia 1.5

    Pkg's offline mode requires Julia 1.5 or later.

    JULIA_PKG_PRECOMPILE_AUTO

    If set to 0, this will disable automatic precompilation by package actions which change the manifest. See Pkg.precompile.

    JULIA_PKG_SERVER

    由Pkg.jl 使用，用于下载软件包和更新注册表。默认情况下，Pkg 使用 https://pkg.julialang.org 来获取 Julia 包。 你可以使用此环境变量来选择不同的服务器。此外，你可以禁用 PkgServer 协议的使用，并通过设置直接从它们的主机（GitHub、GitLab 等）访问包：

    export JULIA_PKG_SERVER=""

    JULIA_PKG_SERVER_REGISTRY_PREFERENCE

    Specifies the preferred registry flavor. Currently supported values are conservative (the default), which will only publish resources that have been processed by the storage server (and thereby have a higher probability of being available from the PkgServers), whereas eager will publish registries whose resources have not necessarily been processed by the storage servers. Users behind restrictive firewalls that do not allow downloading from arbitrary servers should not use the eager flavor.

    Julia 1.7

    This only affects Julia 1.7 and above.

    JULIA_PKG_UNPACK_REGISTRY

    If set to true, this will unpack the registry instead of storing it as a compressed tarball.

    Julia 1.7

    This only affects Julia 1.7 and above. Earlier versions will always unpack the registry.

    JULIA_PKG_USE_CLI_GIT

    If set to true, Pkg operations which use the git protocol will use an external git executable instead of the default libgit2 library.

    Julia 1.7

    Use of the git executable is only supported on Julia 1.7 and above.

    JULIA_PKGRESOLVE_ACCURACY

    The accuracy of the package resolver. This should be a positive integer, the default is 1.

    JULIA_PKG_PRESERVE_TIERED_INSTALLED

    Change the default package installation strategy to Pkg.PRESERVE_TIERED_INSTALLED to let the package manager try to install versions of packages while keeping as many versions of packages already installed as possible.

    Julia 1.9

    This only affects Julia 1.9 and above.

    Network transport

    JULIA_NO_VERIFY_HOSTS / JULIA_SSL_NO_VERIFY_HOSTS / JULIA_SSH_NO_VERIFY_HOSTS / JULIA_ALWAYS_VERIFY_HOSTS

    Specify hosts whose identity should or should not be verified for specific transport layers. See NetworkOptions.verify_host

    JULIA_SSL_CA_ROOTS_PATH

    Specify the file or directory containing the certificate authority roots. See NetworkOptions.ca_roots

    External applications

    JULIA_SHELL

    Julia 用来执行外部命令的 shell 的绝对路径（通过 Base.repl_cmd()）。默认为环境变量 $SHELL，如果 $SHELL 未设置，则为 /bin/sh。

    Note

    在 Windows 上，此环境变量将被忽略，并且外部命令会直接被执行。

    JULIA_EDITOR

    InteractiveUtils.editor() 的返回值–编辑器，例如，InteractiveUtils.edit，会启动偏好编辑器，比如 vim。

    $JULIA_EDITOR 优先于 $VISUAL，而后者优先于 $EDITOR。如果这些环境变量都没有设置，那么在 Windows 和 OS X 上会设置为 open，或者 /etc/alternatives/editor（如果存在的话），否则为 emacs。

    To use Visual Studio Code on Windows, set $JULIA_EDITOR to code.cmd.

    并行

    JULIA_CPU_THREADS

    改写全局变量 Base.Sys.CPU_THREADS，逻辑 CPU 核心数。

    JULIA_WORKER_TIMEOUT

    一个 Float64 值，用来确定 Distributed.worker_timeout() 的值（默认：60.0）。此函数提供 worker 进程在死亡之前等待 master 进程建立连接的秒数。

    JULIA_NUM_THREADS

    一个无符号 64 位整数 (uint64_t)，用于设置 Julia 可用的最大线程数。 如果$JULIA_NUM_THREADS 不为正数或未设置，或者无法通过系统调用确定CPU 线程数，则将线程数设置为1。

    如果$JULIA_NUM_THREADS 设置为auto，则线程数将设置为CPU线程数。

    Note

    JULIA_NUM_THREADS 必须在启动 julia 之前定义； 启动过程中在startup.jl 中定义它是不能奏效的。

    Julia 1.5

    在 Julia 1.5 和更高版本中，也可在启动时使用 -t/--threads 命令行参数指定线程数。

    Julia 1.7

    $JULIA_NUM_THREADS 的 auto 值需要 Julia 1.7 或更高版本。

    Julia 1.7

    The auto value for $JULIA_NUM_THREADS requires Julia 1.7 or above.

    JULIA_THREAD_SLEEP_THRESHOLD

    如果被设置为字符串，并且以大小写敏感的子字符串 "infinite" 开头，那么自旋线程从不睡眠。否则，$JULIA_THREAD_SLEEP_THRESHOLD 被解释为一个无符号 64 位整数（uint64_t），并且提供以纳秒为单位的自旋线程睡眠的时间量。

    JULIA_NUM_GC_THREADS

    Sets the number of threads used by Garbage Collection. If unspecified is set to half of the number of worker threads.

    Julia 1.10

    The environment variable was added in 1.10

    JULIA_IMAGE_THREADS

    An unsigned 32-bit integer that sets the number of threads used by image compilation in this Julia process. The value of this variable may be ignored if the module is a small module. If left unspecified, the smaller of the value of JULIA_CPU_THREADS or half the number of logical CPU cores is used in its place.

    JULIA_IMAGE_TIMINGS

    A boolean value that determines if detailed timing information is printed during during image compilation. Defaults to 0.

    JULIA_EXCLUSIVE

    如果设置为 0 以外的任何值，那么 Julia 的线程策略与在专用计算机上一致：主线程在 proc 0 上且线程间是关联的。否则，Julia 让操作系统处理线程策略。

    REPL 格式化输出

    决定 REPL 应当如何格式化输出的环境变量。通常，这些变量应当被设置为 ANSI 终端转义序列。 Julia 提供了具有相同功能的高级接口；请参阅 Julia REPL 章节。

    JULIA_ERROR_COLOR

    Base.error_color()（默认值：亮红，"\033[91m"），errors 在终端中的格式。

    JULIA_WARN_COLOR

    Base.warn_color()（默认值：黄，"\033[93m"），warnings 在终端中的格式。

    JULIA_INFO_COLOR

    Base.info_color()（默认值：青，"\033[36m"），info 在终端中的格式。

    JULIA_INPUT_COLOR

    Base.input_color()（默认值：标准，"\033[0m"），在终端中，输入应有的格式。

    JULIA_ANSWER_COLOR

    Base.answer_color()（默认值：标准，"\033[0m"），在终端中，输出应有的格式。

    System and Package Image Building

    JULIA_CPU_TARGET

    Modify the target machine architecture for (pre)compiling system and package images. JULIA_CPU_TARGET only affects machine code image generation being output to a disk cache. Unlike the --cpu-target, or -C, command line option, it does not influence just-in-time (JIT) code generation within a Julia session where machine code is only stored in memory.

    Valid values for JULIA_CPU_TARGET can be obtained by executing julia -C help.

    Setting JULIA_CPU_TARGET is important for heterogeneous compute systems where processors of distinct types or features may be present. This is commonly encountered in high performance computing (HPC) clusters since the component nodes may be using distinct processors.

    The CPU target string is a list of strings separated by ; each string starts with a CPU or architecture name and followed by an optional list of features separated by ,. A generic or empty CPU name means the basic required feature set of the target ISA which is at least the architecture the C/C++ runtime is compiled with. Each string is interpreted by LLVM.

    A few special features are supported:

    1. clone_all

      This forces the target to have all functions in sysimg cloned. When used in negative form (i.e. -clone_all), this disables full clone that's enabled by default for certain targets.

    2. base([0-9]*)

      This specifies the (0-based) base target index. The base target is the target that the current target is based on, i.e. the functions that are not being cloned will use the version in the base target. This option causes the base target to be fully cloned (as if clone_all is specified for it) if it is not the default target (0). The index can only be smaller than the current index.

    3. opt_size

      Optimize for size with minimum performance impact. Clang/GCC's -Os.

    4. min_size

      Optimize only for size. Clang's -Oz.

    Debugging and profiling

    JULIA_DEBUG

    Enable debug logging for a file or module, see Logging for more information.

    JULIA_GC_ALLOC_POOL, JULIA_GC_ALLOC_OTHER, JULIA_GC_ALLOC_PRINT

    这些环境变量取值为字符串，可以以字符 ‘r’ 开头，后接一个由三个带符号 64 位整数（int64_t）组成的、以冒号分割的列表的插值字符串。这个整数的三元组 a:b:c 代表算术序列 a, a + b, a + 2*b, ... c。

    • 如果是第 n 次调用 jl_gc_pool_alloc()，并且 n 属于 $JULIA_GC_ALLOC_POOL 代表的算术序列， 那么垃圾回收是强制的。
    • 如果是第 n 次调用 maybe_collect()，并且 n 属于 $JULIA_GC_ALLOC_OTHER 代表的算术序列，那么垃圾 回收是强制的。
    • 如果是第 n 次调用 jl_gc_alloc()，并且 n 属于 $JULIA_GC_ALLOC_PRINT 代表的算术序列，那么 调用 jl_gc_pool_alloc() 和 maybe_collect() 的次数会 被打印。

    如果这些环境变量的值以字符 ‘r' 开头，那么垃圾回收事件间的间隔是随机的。

    Note

    这些环境变量生效要求 Julia 在编译时带有垃圾收集调试支持（也就是，在构建配置中将 WITH_GC_DEBUG_ENV 设置为 1）。

    JULIA_GC_NO_GENERATIONAL

    如果设置为 0 以外的任何值，那么 Julia 的垃圾收集器将从不执行「快速扫描」内存。

    Note

    此环境变量生效要求 Julia 在编译时带有垃圾收集调试支持（也就是，在构建配置中将 WITH_GC_DEBUG_ENV 设置为 1）。

    JULIA_GC_WAIT_FOR_DEBUGGER

    如果设置为 0 以外的任何值，Julia 的垃圾收集器每当出现严重错误时将等待调试器连接而不是中止。

    Note

    此环境变量生效要求 Julia 在编译时带有垃圾收集调试支持（也就是，在构建配置中将 WITH_GC_DEBUG_ENV 设置为 1）。

    ENABLE_JITPROFILING

    如果设置为 0 以外的任何值，那么编译器将为即时（JIT）性能分析创建并注册一个事件监听器。

    Note

    此环境变量仅在使用 JIT 性能分析支持编译 Julia 时有效，使用如下之一：

    • Intel's VTune™ Amplifier(USE_INTEL_JITEVENTS 在配置中设置为1), 或
    • OProfile(USE_OPROFILE_JITEVENTS 在配置中设置为1)。
    • Perf (USE_PERF_JITEVENTS 在构建配置中设置为 1)。 默认情况下启用此集成。

    ENABLE_GDBLISTENER

    如果设置为除0之外的任何内容，则在发布版本上启用 Julia 代码的 GDB 注册。 在 Julia 的调试版本中，这始终处于启用状态。 推荐与 -g 2 一起使用。

    JULIA_LLVM_ARGS

    要传递给 LLVM 后端的参数。

    +$JULIA_BINDIR/../etc/julia/startup.jl

    例如，在 Linux 下安装的 Julia 可执行文件位于 /bin/julia，DATAROOTDIR 为 ../share，SYSCONFDIR 为 ../etc，JULIA_BINDIR 会被设置为 /bin，会有一个源文件搜索路径：

    /share/julia/base

    和一个全局配置文件搜索路径：

    /etc/julia/startup.jl

    JULIA_PROJECT

    指示哪个项目应该是初始活动项目的目录路径。 设置这个环境变量和指定--project启动选项效果一样，但是--project优先级更高。 如果变量设置为 @. （注意尾随的点），那么 Julia 会尝试从当前目录及其父目录中查找包含 Project.toml 或 JuliaProject.toml 文件的项目目录。 另请参阅有关 代码加载 的章节。

    Note

    JULIA_PROJECT 必须在启动 julia 前定义；于 startup.jl 中定义它对于启动的过程为时已晚。

    JULIA_LOAD_PATH

    JULIA_LOAD_PATH 环境变量用于补充全局的 Julia 变量 LOAD_PATH ，该变量可用于确定通过 import 和 using 可以加载哪些包（请参阅 Code Loading）。

    与 shell 使用的 PATH 变量不同， 在 JULIA_LOAD_PATH 中的空条目将会在填充 LOAD_PATH 时被扩展为 LOAD_PATH 的默认值 ["@", "@v#.#", "@stdlib"] 。这样，无论 JULIA_LOAD_PATH 是否已被设置，均可以使用 shell 脚本轻松地在加载路径前面或后面添加值。例如要将 /foo/bar 添加到 LOAD_PATH 之前，只需要使用下列脚本：

    export JULIA_LOAD_PATH="/foo/bar:$JULIA_LOAD_PATH"

    如果已经设置了 JULIA_LOAD_PATH 环境变量，那么 /foo/bar 将被添加在原有值之前。另一方面，如果 JULIA_LOAD_PATH 尚未设置，那么它会被设置为 /foo/bar: ，而这将使用 LOAD_PATH 的值扩展为 ["/foo/bar", "@", "@v#.#", "@stdlib"] 。如果 JULIA_LOAD_PATH 被设置为空字符串，那么它将被扩展为一个空的 LOAD_PATH 数组。换句话说，这个空字符串数组将被认为是零元素的数组，而非是一个空字符串单元素的数组。使用这样的加载行为是为了可以通过环境变量设置空的加载路径。如果你需要使用默认的加载路径，请不要设置这一环境变量，如果它必须有值，那么可将其设置为字符串 : 。

    Note

    在 Windows 上，路径元素由 ; 字符分隔，就像 Windows 上的大多数路径列表一样。 将上一段中的 : 替换为 ;。

    JULIA_DEPOT_PATH

    JULIA_DEPOT_PATH 环境变量用于填充全局的 Julia 变量 DEPOT_PATH ，该变量用于控制包管理器以及 Juila 代码加载机制在何处查找包注册表、已安装的包、命名环境、克隆的存储库、缓存的预编译包映像、配置文件和 REPL 历史记录文件的默认位置。

    与 shell 使用的 PATH 变量不同，但与 JULIA_LOAD_PATH 类似， 在 JULIA_DEPOT_PATH 中的空条目将会被扩展为 DEPOT_PATH 的默认值。这样，无论 JULIA_DEPOT_PATH 是否已被设置，均可以使用 shell 脚本轻松地在仓库路径前面或后面添加值。例如要将 /foo/bar 添加到 DEPOT_PATH 之前，只需要使用下列脚本：

    export JULIA_DEPOT_PATH="/foo/bar:$JULIA_DEPOT_PATH"

    如果已经设置了 JULIA_DEPOT_PATH 环境变量，那么 /foo/bar 将被添加在原有值之前。另一方面，如果 JULIA_DEPOT_PATH 尚未设置，那么它会被设置为 /foo/bar: ，而这将使 /foo/bar 被添加到默认仓库路径之前。如果 JULIA_DEPOT_PATH 被设置为空字符串，那么它将扩展为一个空的 DEPOT_PATH 数组。换句话说，这个空字符串数组将被认为是零元素的数组，而非是一个空字符串单元素的数组。使用这样的加载行为是为了可以通过环境变量设置空的仓库路径。如果你需要使用默认的仓库路径，请不要设置这一环境变量，如果它必须有值，那么可将其设置为字符串 : 。

    Note

    在 Windows 上，路径元素由 ; 字符分隔，就像 Windows 上的大多数路径列表一样。 将上一段中的 : 替换为 ;。

    Note

    JULIA_DEPOT_PATH must be defined before starting julia; defining it in startup.jl is too late in the startup process; at that point you can instead directly modify the DEPOT_PATH array, which is populated from the environment variable.

    JULIA_HISTORY

    REPL 历史文件中 REPL.find_hist_file() 的绝对路径。如果没有设置 $JULIA_HISTORY，那么 REPL.find_hist_file() 默认为

    $(DEPOT_PATH[1])/logs/repl_history.jl

    JULIA_MAX_NUM_PRECOMPILE_FILES

    Sets the maximum number of different instances of a single package that are to be stored in the precompile cache (default = 10).

    JULIA_VERBOSE_LINKING

    If set to true, linker commands will be displayed during precompilation.

    Pkg.jl

    JULIA_CI

    If set to true, this indicates to the package server that any package operations are part of a continuous integration (CI) system for the purposes of gathering package usage statistics.

    JULIA_NUM_PRECOMPILE_TASKS

    The number of parallel tasks to use when precompiling packages. See Pkg.precompile.

    JULIA_PKG_DEVDIR

    The default directory used by Pkg.develop for downloading packages.

    JULIA_PKG_IGNORE_HASHES

    If set to 1, this will ignore incorrect hashes in artifacts. This should be used carefully, as it disables verification of downloads, but can resolve issues when moving files across different types of file systems. See Pkg.jl issue #2317 for more details.

    Julia 1.6

    This is only supported in Julia 1.6 and above.

    JULIA_PKG_OFFLINE

    If set to true, this will enable offline mode: see Pkg.offline.

    Julia 1.5

    Pkg's offline mode requires Julia 1.5 or later.

    JULIA_PKG_PRECOMPILE_AUTO

    If set to 0, this will disable automatic precompilation by package actions which change the manifest. See Pkg.precompile.

    JULIA_PKG_SERVER

    由Pkg.jl 使用，用于下载软件包和更新注册表。默认情况下，Pkg 使用 https://pkg.julialang.org 来获取 Julia 包。 你可以使用此环境变量来选择不同的服务器。此外，你可以禁用 PkgServer 协议的使用，并通过设置直接从它们的主机（GitHub、GitLab 等）访问包：

    export JULIA_PKG_SERVER=""

    JULIA_PKG_SERVER_REGISTRY_PREFERENCE

    Specifies the preferred registry flavor. Currently supported values are conservative (the default), which will only publish resources that have been processed by the storage server (and thereby have a higher probability of being available from the PkgServers), whereas eager will publish registries whose resources have not necessarily been processed by the storage servers. Users behind restrictive firewalls that do not allow downloading from arbitrary servers should not use the eager flavor.

    Julia 1.7

    This only affects Julia 1.7 and above.

    JULIA_PKG_UNPACK_REGISTRY

    If set to true, this will unpack the registry instead of storing it as a compressed tarball.

    Julia 1.7

    This only affects Julia 1.7 and above. Earlier versions will always unpack the registry.

    JULIA_PKG_USE_CLI_GIT

    If set to true, Pkg operations which use the git protocol will use an external git executable instead of the default libgit2 library.

    Julia 1.7

    Use of the git executable is only supported on Julia 1.7 and above.

    JULIA_PKGRESOLVE_ACCURACY

    The accuracy of the package resolver. This should be a positive integer, the default is 1.

    JULIA_PKG_PRESERVE_TIERED_INSTALLED

    Change the default package installation strategy to Pkg.PRESERVE_TIERED_INSTALLED to let the package manager try to install versions of packages while keeping as many versions of packages already installed as possible.

    Julia 1.9

    This only affects Julia 1.9 and above.

    Network transport

    JULIA_NO_VERIFY_HOSTS / JULIA_SSL_NO_VERIFY_HOSTS / JULIA_SSH_NO_VERIFY_HOSTS / JULIA_ALWAYS_VERIFY_HOSTS

    Specify hosts whose identity should or should not be verified for specific transport layers. See NetworkOptions.verify_host

    JULIA_SSL_CA_ROOTS_PATH

    Specify the file or directory containing the certificate authority roots. See NetworkOptions.ca_roots

    External applications

    JULIA_SHELL

    Julia 用来执行外部命令的 shell 的绝对路径（通过 Base.repl_cmd()）。默认为环境变量 $SHELL，如果 $SHELL 未设置，则为 /bin/sh。

    Note

    在 Windows 上，此环境变量将被忽略，并且外部命令会直接被执行。

    JULIA_EDITOR

    InteractiveUtils.editor() 的返回值–编辑器，例如，InteractiveUtils.edit，会启动偏好编辑器，比如 vim。

    $JULIA_EDITOR 优先于 $VISUAL，而后者优先于 $EDITOR。如果这些环境变量都没有设置，那么在 Windows 和 OS X 上会设置为 open，或者 /etc/alternatives/editor（如果存在的话），否则为 emacs。

    To use Visual Studio Code on Windows, set $JULIA_EDITOR to code.cmd.

    并行

    JULIA_CPU_THREADS

    改写全局变量 Base.Sys.CPU_THREADS，逻辑 CPU 核心数。

    JULIA_WORKER_TIMEOUT

    一个 Float64 值，用来确定 Distributed.worker_timeout() 的值（默认：60.0）。此函数提供 worker 进程在死亡之前等待 master 进程建立连接的秒数。

    JULIA_NUM_THREADS

    一个无符号 64 位整数 (uint64_t)，用于设置 Julia 可用的最大线程数。 如果$JULIA_NUM_THREADS 不为正数或未设置，或者无法通过系统调用确定CPU 线程数，则将线程数设置为1。

    如果$JULIA_NUM_THREADS 设置为auto，则线程数将设置为CPU线程数。

    Note

    JULIA_NUM_THREADS 必须在启动 julia 之前定义； 启动过程中在startup.jl 中定义它是不能奏效的。

    Julia 1.5

    在 Julia 1.5 和更高版本中，也可在启动时使用 -t/--threads 命令行参数指定线程数。

    Julia 1.7

    $JULIA_NUM_THREADS 的 auto 值需要 Julia 1.7 或更高版本。

    Julia 1.7

    The auto value for $JULIA_NUM_THREADS requires Julia 1.7 or above.

    JULIA_THREAD_SLEEP_THRESHOLD

    如果被设置为字符串，并且以大小写敏感的子字符串 "infinite" 开头，那么自旋线程从不睡眠。否则，$JULIA_THREAD_SLEEP_THRESHOLD 被解释为一个无符号 64 位整数（uint64_t），并且提供以纳秒为单位的自旋线程睡眠的时间量。

    JULIA_NUM_GC_THREADS

    Sets the number of threads used by Garbage Collection. If unspecified is set to half of the number of worker threads.

    Julia 1.10

    The environment variable was added in 1.10

    JULIA_IMAGE_THREADS

    An unsigned 32-bit integer that sets the number of threads used by image compilation in this Julia process. The value of this variable may be ignored if the module is a small module. If left unspecified, the smaller of the value of JULIA_CPU_THREADS or half the number of logical CPU cores is used in its place.

    JULIA_IMAGE_TIMINGS

    A boolean value that determines if detailed timing information is printed during during image compilation. Defaults to 0.

    JULIA_EXCLUSIVE

    如果设置为 0 以外的任何值，那么 Julia 的线程策略与在专用计算机上一致：主线程在 proc 0 上且线程间是关联的。否则，Julia 让操作系统处理线程策略。

    REPL 格式化输出

    决定 REPL 应当如何格式化输出的环境变量。通常，这些变量应当被设置为 ANSI 终端转义序列。 Julia 提供了具有相同功能的高级接口；请参阅 Julia REPL 章节。

    JULIA_ERROR_COLOR

    Base.error_color()（默认值：亮红，"\033[91m"），errors 在终端中的格式。

    JULIA_WARN_COLOR

    Base.warn_color()（默认值：黄，"\033[93m"），warnings 在终端中的格式。

    JULIA_INFO_COLOR

    Base.info_color()（默认值：青，"\033[36m"），info 在终端中的格式。

    JULIA_INPUT_COLOR

    Base.input_color()（默认值：标准，"\033[0m"），在终端中，输入应有的格式。

    JULIA_ANSWER_COLOR

    Base.answer_color()（默认值：标准，"\033[0m"），在终端中，输出应有的格式。

    System and Package Image Building

    JULIA_CPU_TARGET

    Modify the target machine architecture for (pre)compiling system and package images. JULIA_CPU_TARGET only affects machine code image generation being output to a disk cache. Unlike the --cpu-target, or -C, command line option, it does not influence just-in-time (JIT) code generation within a Julia session where machine code is only stored in memory.

    Valid values for JULIA_CPU_TARGET can be obtained by executing julia -C help.

    Setting JULIA_CPU_TARGET is important for heterogeneous compute systems where processors of distinct types or features may be present. This is commonly encountered in high performance computing (HPC) clusters since the component nodes may be using distinct processors.

    The CPU target string is a list of strings separated by ; each string starts with a CPU or architecture name and followed by an optional list of features separated by ,. A generic or empty CPU name means the basic required feature set of the target ISA which is at least the architecture the C/C++ runtime is compiled with. Each string is interpreted by LLVM.

    A few special features are supported:

    1. clone_all

      This forces the target to have all functions in sysimg cloned. When used in negative form (i.e. -clone_all), this disables full clone that's enabled by default for certain targets.

    2. base([0-9]*)

      This specifies the (0-based) base target index. The base target is the target that the current target is based on, i.e. the functions that are not being cloned will use the version in the base target. This option causes the base target to be fully cloned (as if clone_all is specified for it) if it is not the default target (0). The index can only be smaller than the current index.

    3. opt_size

      Optimize for size with minimum performance impact. Clang/GCC's -Os.

    4. min_size

      Optimize only for size. Clang's -Oz.

    Debugging and profiling

    JULIA_DEBUG

    Enable debug logging for a file or module, see Logging for more information.

    JULIA_GC_ALLOC_POOL, JULIA_GC_ALLOC_OTHER, JULIA_GC_ALLOC_PRINT

    这些环境变量取值为字符串，可以以字符 ‘r’ 开头，后接一个由三个带符号 64 位整数（int64_t）组成的、以冒号分割的列表的插值字符串。这个整数的三元组 a:b:c 代表算术序列 a, a + b, a + 2*b, ... c。

    如果这些环境变量的值以字符 ‘r' 开头，那么垃圾回收事件间的间隔是随机的。

    Note

    这些环境变量生效要求 Julia 在编译时带有垃圾收集调试支持（也就是，在构建配置中将 WITH_GC_DEBUG_ENV 设置为 1）。

    JULIA_GC_NO_GENERATIONAL

    如果设置为 0 以外的任何值，那么 Julia 的垃圾收集器将从不执行「快速扫描」内存。

    Note

    此环境变量生效要求 Julia 在编译时带有垃圾收集调试支持（也就是，在构建配置中将 WITH_GC_DEBUG_ENV 设置为 1）。

    JULIA_GC_WAIT_FOR_DEBUGGER

    如果设置为 0 以外的任何值，Julia 的垃圾收集器每当出现严重错误时将等待调试器连接而不是中止。

    Note

    此环境变量生效要求 Julia 在编译时带有垃圾收集调试支持（也就是，在构建配置中将 WITH_GC_DEBUG_ENV 设置为 1）。

    ENABLE_JITPROFILING

    如果设置为 0 以外的任何值，那么编译器将为即时（JIT）性能分析创建并注册一个事件监听器。

    Note

    此环境变量仅在使用 JIT 性能分析支持编译 Julia 时有效，使用如下之一：

    ENABLE_GDBLISTENER

    如果设置为除0之外的任何内容，则在发布版本上启用 Julia 代码的 GDB 注册。 在 Julia 的调试版本中，这始终处于启用状态。 推荐与 -g 2 一起使用。

    JULIA_LLVM_ARGS

    要传递给 LLVM 后端的参数。

    diff --git a/dev/manual/faq/index.html b/dev/manual/faq/index.html index a56a7bf5..ee2cdca5 100644 --- a/dev/manual/faq/index.html +++ b/dev/manual/faq/index.html @@ -333,4 +333,4 @@ A = randn(1000, 1000) B = randn(1000, 1000) @btime $A \ $B -@btime $A * $B

    也许和其他语言不同比如Matlab或R。

    由于像这样的操作都非常直接地从相关的BLAS函数调用，这样做的原因是，

    1. 在每种语言中使用的BLAS库

    2. 并发线程的数量

    Julia 编译并使用自己的 OpenBLAS 副本，当前线程数上限为 8（或内核数）。

    修改 OpenBLAS 设置或使用不同的 BLAS 库编译 Julia，例如 Intel MKL，可能会提高性能。 你可以使用 MKL.jl，这是一个使 Julia 的线性代数使用英特尔 MKL BLAS 和 LAPACK 而不是 OpenBLAS 的包，或搜索论坛以获取有关如何使用的建议。 请注意，英特尔 MKL 不能与 Julia 捆绑在一起，因为它不是开源的。

    计算集群

    我该如何管理分布式文件系统的预编译缓存？

    When using Julia in high-performance computing (HPC) facilities with shared filesystems, it is recommended to use a shared depot (via the JULIA_DEPOT_PATH environment variable). Since Julia v1.10, multiple Julia processes on functionally similar workers and using the same depot will coordinate via pidfile locks to only spend effort precompiling on one process while the others wait. The precompilation process will indicate when the process is precompiling or waiting for another that is precompiling. If non-interactive the messages are via @debug.

    However, due to caching of binary code, the cache rejection since v1.9 is more strict and users may need to set the JULIA_CPU_TARGET environment variable appropriately to get a single cache that is usable throughout the HPC environment.

    Julia 版本发布

    你希望使用稳定的、长期支持的或是每日构建版本的Julia？

    Julia 的稳定版是最新发布的 Julia 版本，这是大多数人想要运行的版本。 它具有最新的功能，包括改进的性能。 Julia 的稳定版本根据 SemVer 版本化为 v1.x.y。 在作为候选版本进行几周的测试后，大约每 4-5 个月就会发布一个与新稳定版本相对应的新 Julia 次要版本。 与 LTS 版本不同，在 Julia 的另一个稳定版本发布后，稳定版本通常不会收到错误修正。 但是，始终可以升级到下一个稳定版本，因为 Julia v1.x 的每个版本都将继续运行为早期版本编写的代码。

    如果正在寻找非常稳定的代码库，你可能更喜欢 Julia 的 LTS（长期支持）版本。 Julia 当前的 LTS 版本根据 SemVer 版本为 v1.0.x； 此分支将继续接收错误修复，直到选择新的 LTS 分支，此时 v1.0.x 系列将不再收到常规错误修复，建议除最保守的用户之外的所有用户升级到新的 LTS 版本系列。作为软件包开发人员，你可能更喜欢针对 LTS 版本进行开发，以最大限度地增加可以使用你的软件包的用户数量。 根据 SemVer，为 v1.0 编写的代码将继续适用于所有未来的 LTS 和稳定版本。 一般来说，即使针对 LTS，也可以在最新的 Stable 版本中开发和运行代码，以利用改进的性能； 只要避免使用新功能（例如添加的库函数或新方法）。

    如果您想利用该语言的最新更新，您可能更喜欢 Julia 的每日构建版本，并且不介意今天可用的版本是否偶尔无法正常工作。 顾名思义，每日构建版本的发布大约每晚发布一次（取决于构建基础设施的稳定性）。 一般来说，每日构建的发布是相当安全的——你的代码不会着火。 然而，它们可能出现偶尔的版本倒退和问题，直到更彻底的预发布测试才会发现。 你可能希望针对每日构建版本进行测试，以确保在发布之前捕获影响你的用例的版本倒退。

    最后，您也可以考虑为自己从源代码构建 Julia。 此选项主要适用于那些熟悉命令行或对学习感兴趣的人。 如果你是这样的人，你可能也有兴趣阅读我们的 贡献指南。

    可以在https://julialang.org/downloads/的下载页面上找到每种下载类型的链接。 请注意，并非所有版本的Julia都适用于所有平台。

    更新我的 Julia 版本后，如何转移已安装软件包的列表？

    julia 的每个次要版本都有自己的默认 环境。 因此，在安装新的 Julia 次要版本时，默认情况下你使用先前次要版本添加的包将不可用。 给定 julia 版本的环境由文件Project.toml和Manifest.toml定义，文件夹中的文件与.julia/environments/中的版本号匹配，例如.julia/environments/v1.3。

    如果你安装了一个新的 Julia 次要版本，比如 1.4，并且想要在它的默认环境中使用与以前版本（例如 1.3）相同的包，你可以从1.3 文件夹复制文件 Project.toml 的内容到1.4。然后，在新的 Julia 版本的会话中，输入] 键进入“包管理模式”，并运行命令 instantiate。

    此操作将从复制的文件中解析一组与目标 Julia 版本兼容的可行包，并在合适时安装或更新它们。 如果你不仅要重现软件包，还要重现在以前的 Julia 版本中使用的版本，您还应该在运行 Pkg 命令 instantiate 之前复制 Manifest.toml 文件。 但是，请注意，包可能定义了兼容性约束，这些约束可能会受到更改 Julia 版本的影响，因此你在1.3中拥有的确切版本集可能不适用于1.4。

    +@btime $A * $B

    也许和其他语言不同比如Matlab或R。

    由于像这样的操作都非常直接地从相关的BLAS函数调用，这样做的原因是，

    1. 在每种语言中使用的BLAS库

    2. 并发线程的数量

    Julia 编译并使用自己的 OpenBLAS 副本，当前线程数上限为 8（或内核数）。

    修改 OpenBLAS 设置或使用不同的 BLAS 库编译 Julia，例如 Intel MKL，可能会提高性能。 你可以使用 MKL.jl，这是一个使 Julia 的线性代数使用英特尔 MKL BLAS 和 LAPACK 而不是 OpenBLAS 的包，或搜索论坛以获取有关如何使用的建议。 请注意，英特尔 MKL 不能与 Julia 捆绑在一起，因为它不是开源的。

    计算集群

    我该如何管理分布式文件系统的预编译缓存？

    When using Julia in high-performance computing (HPC) facilities with shared filesystems, it is recommended to use a shared depot (via the JULIA_DEPOT_PATH environment variable). Since Julia v1.10, multiple Julia processes on functionally similar workers and using the same depot will coordinate via pidfile locks to only spend effort precompiling on one process while the others wait. The precompilation process will indicate when the process is precompiling or waiting for another that is precompiling. If non-interactive the messages are via @debug.

    However, due to caching of binary code, the cache rejection since v1.9 is more strict and users may need to set the JULIA_CPU_TARGET environment variable appropriately to get a single cache that is usable throughout the HPC environment.

    Julia 版本发布

    你希望使用稳定的、长期支持的或是每日构建版本的Julia？

    Julia 的稳定版是最新发布的 Julia 版本，这是大多数人想要运行的版本。 它具有最新的功能，包括改进的性能。 Julia 的稳定版本根据 SemVer 版本化为 v1.x.y。 在作为候选版本进行几周的测试后，大约每 4-5 个月就会发布一个与新稳定版本相对应的新 Julia 次要版本。 与 LTS 版本不同，在 Julia 的另一个稳定版本发布后，稳定版本通常不会收到错误修正。 但是，始终可以升级到下一个稳定版本，因为 Julia v1.x 的每个版本都将继续运行为早期版本编写的代码。

    如果正在寻找非常稳定的代码库，你可能更喜欢 Julia 的 LTS（长期支持）版本。 Julia 当前的 LTS 版本根据 SemVer 版本为 v1.0.x； 此分支将继续接收错误修复，直到选择新的 LTS 分支，此时 v1.0.x 系列将不再收到常规错误修复，建议除最保守的用户之外的所有用户升级到新的 LTS 版本系列。作为软件包开发人员，你可能更喜欢针对 LTS 版本进行开发，以最大限度地增加可以使用你的软件包的用户数量。 根据 SemVer，为 v1.0 编写的代码将继续适用于所有未来的 LTS 和稳定版本。 一般来说，即使针对 LTS，也可以在最新的 Stable 版本中开发和运行代码，以利用改进的性能； 只要避免使用新功能（例如添加的库函数或新方法）。

    如果您想利用该语言的最新更新，您可能更喜欢 Julia 的每日构建版本，并且不介意今天可用的版本是否偶尔无法正常工作。 顾名思义，每日构建版本的发布大约每晚发布一次（取决于构建基础设施的稳定性）。 一般来说，每日构建的发布是相当安全的——你的代码不会着火。 然而，它们可能出现偶尔的版本倒退和问题，直到更彻底的预发布测试才会发现。 你可能希望针对每日构建版本进行测试，以确保在发布之前捕获影响你的用例的版本倒退。

    最后，您也可以考虑为自己从源代码构建 Julia。 此选项主要适用于那些熟悉命令行或对学习感兴趣的人。 如果你是这样的人，你可能也有兴趣阅读我们的 贡献指南。

    可以在https://julialang.org/downloads/的下载页面上找到每种下载类型的链接。 请注意，并非所有版本的Julia都适用于所有平台。

    更新我的 Julia 版本后，如何转移已安装软件包的列表？

    julia 的每个次要版本都有自己的默认 环境。 因此，在安装新的 Julia 次要版本时，默认情况下你使用先前次要版本添加的包将不可用。 给定 julia 版本的环境由文件Project.toml和Manifest.toml定义，文件夹中的文件与.julia/environments/中的版本号匹配，例如.julia/environments/v1.3。

    如果你安装了一个新的 Julia 次要版本，比如 1.4，并且想要在它的默认环境中使用与以前版本（例如 1.3）相同的包，你可以从1.3 文件夹复制文件 Project.toml 的内容到1.4。然后，在新的 Julia 版本的会话中，输入] 键进入“包管理模式”，并运行命令 instantiate。

    此操作将从复制的文件中解析一组与目标 Julia 版本兼容的可行包，并在合适时安装或更新它们。 如果你不仅要重现软件包，还要重现在以前的 Julia 版本中使用的版本，您还应该在运行 Pkg 命令 instantiate 之前复制 Manifest.toml 文件。 但是，请注意，包可能定义了兼容性约束，这些约束可能会受到更改 Julia 版本的影响，因此你在1.3中拥有的确切版本集可能不适用于1.4。

    diff --git a/dev/manual/functions/index.html b/dev/manual/functions/index.html index 811e69a3..6b7316c7 100644 --- a/dev/manual/functions/index.html +++ b/dev/manual/functions/index.html @@ -454,4 +454,4 @@ 0.5 6 -4 - true

    更多阅读

    我们应该在这里提到，这远不是定义函数的完整图景。Julia 拥有一个复杂的类型系统并且允许对参数类型进行多重分派。这里给出的示例都没有为它们的参数提供任何类型注释，意味着它们可以作用于任何类型的参数。类型系统在类型中描述，而方法则描述了根据运行时参数类型上的多重分派所选择的方法定义函数。

    + true

    更多阅读

    我们应该在这里提到，这远不是定义函数的完整图景。Julia 拥有一个复杂的类型系统并且允许对参数类型进行多重分派。这里给出的示例都没有为它们的参数提供任何类型注释，意味着它们可以作用于任何类型的参数。类型系统在类型中描述，而方法则描述了根据运行时参数类型上的多重分派所选择的方法定义函数。

    diff --git a/dev/manual/getting-started/index.html b/dev/manual/getting-started/index.html index b5e38b15..80e46185 100644 --- a/dev/manual/getting-started/index.html +++ b/dev/manual/getting-started/index.html @@ -24,4 +24,4 @@ begin - begin...end denotes a block of code.

    如果已经对 Julia 有所了解，你可以先看 Performance Tips 和 Workflow Tips。

    + begin...end denotes a block of code.

    如果已经对 Julia 有所了解，你可以先看 Performance Tips 和 Workflow Tips。

    diff --git a/dev/manual/handling-operating-system-variation/index.html b/dev/manual/handling-operating-system-variation/index.html index 33172270..286f77bf 100644 --- a/dev/manual/handling-operating-system-variation/index.html +++ b/dev/manual/handling-operating-system-variation/index.html @@ -11,4 +11,4 @@ apple_specific_thing(a) else generic_thing(a) -end

    在链式嵌套的条件表达式中（包括 if/elseif/end），@static 必须在每一层都调用（括号是可选的，但是为了可读性，建议添加）。

    @static Sys.iswindows() ? :a : (@static Sys.isapple() ? :b : :c)
    +end

    在链式嵌套的条件表达式中（包括 if/elseif/end），@static 必须在每一层都调用（括号是可选的，但是为了可读性，建议添加）。

    @static Sys.iswindows() ? :a : (@static Sys.isapple() ? :b : :c)
    diff --git a/dev/manual/index.html b/dev/manual/index.html index 4a46875f..3df05a4b 100644 --- a/dev/manual/index.html +++ b/dev/manual/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    Julia 1.10 Documentation

    Welcome to the documentation for Julia 1.10.

    请阅读 release notes 以了解自上次发行以来发生了什么变化。

    Note

    The documentation is also available in PDF format: julia-1.10.7.pdf.

    Below is a non-exhasutive list of links that will be useful as you learn and use the Julia programming language.

    简介

    科学计算对性能一直有着最高的需求，但目前各领域的专家却大量使用较慢的动态语言来开展他们的日常工作。 偏爱动态语言有很多很好的理由，因此我们不会舍弃动态的特性。 幸运的是，现代编程语言设计与编译器技术可以大大消除性能折衷（trade-off），并提供有足够生产力的单一环境进行原型设计，而且能高效地部署性能密集型应用程序。 Julia 语言在这其中扮演了这样一个角色：它是一门灵活的动态语言，适合用于科学计算和数值计算，并且性能可与传统的静态类型语言媲美。

    由于 Julia 的编译器和其它语言比如 Python 或 R 的解释器有所不同，一开始你可能发现 Julia 的性能并不是很突出。 如果你觉得速度有点慢，我们强烈建议在尝试其他功能前，先读一读文档中的提高性能的窍门部分。 一旦你理解了 Julia 的运作方式后，写出和 C 一样快的代码就是小菜一碟。

    Julia Compared to Other Languages

    Julia features optional typing, multiple dispatch, and good performance, achieved using type inference and just-in-time (JIT) compilation (and optional ahead-of-time compilation), implemented using LLVM. It is multi-paradigm, combining features of imperative, functional, and object-oriented programming. Julia provides ease and expressiveness for high-level numerical computing, in the same way as languages such as R, MATLAB, and Python, but also supports general programming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp, Perl, Python, Lua, and Ruby.

    Julia 与传统动态语言最重要的区别是：

    • The core language imposes very little; Julia Base and the standard library are written in Julia itself, including primitive operations like integer arithmetic
    • A rich language of types for constructing and describing objects, that can also optionally be used to make type declarations
    • The ability to define function behavior across many combinations of argument types via multiple dispatch
    • Automatic generation of efficient, specialized code for different argument types
    • Good performance, approaching that of statically-compiled languages like C

    Although one sometimes speaks of dynamic languages as being "typeless", they are definitely not. Every object, whether primitive or user-defined, has a type. The lack of type declarations in most dynamic languages, however, means that one cannot instruct the compiler about the types of values, and often cannot explicitly talk about types at all. In static languages, on the other hand, while one can – and usually must – annotate types for the compiler, types exist only at compile time and cannot be manipulated or expressed at run time. In Julia, types are themselves run-time objects, and can also be used to convey information to the compiler.

    What Makes Julia, Julia?

    While the casual programmer need not explicitly use types or multiple dispatch, they are the core unifying features of Julia: functions are defined on different combinations of argument types, and applied by dispatching to the most specific matching definition. This model is a good fit for mathematical programming, where it is unnatural for the first argument to "own" an operation as in traditional object-oriented dispatch. Operators are just functions with special notation – to extend addition to new user-defined data types, you define new methods for the + function. Existing code then seamlessly applies to the new data types.

    Partly because of run-time type inference (augmented by optional type annotations), and partly because of a strong focus on performance from the inception of the project, Julia's computational efficiency exceeds that of other dynamic languages, and even rivals that of statically-compiled languages. For large scale numerical problems, speed always has been, continues to be, and probably always will be crucial: the amount of data being processed has easily kept pace with Moore's Law over the past decades.

    Advantages of Julia

    Julia aims to create an unprecedented combination of ease-of-use, power, and efficiency in a single language. In addition to the above, some advantages of Julia over comparable systems include:

    • Free and open source (MIT licensed)
    • User-defined types are as fast and compact as built-ins
    • No need to vectorize code for performance; devectorized code is fast
    • Designed for parallelism and distributed computation
    • Lightweight "green" threading (coroutines)
    • Unobtrusive yet powerful type system
    • Elegant and extensible conversions and promotions for numeric and other types
    • Efficient support for Unicode, including but not limited to UTF-8
    • Call C functions directly (no wrappers or special APIs needed)
    • Powerful shell-like capabilities for managing other processes
    • Lisp-like macros and other metaprogramming facilities
    +
    Repository

    Julia 1.10 Documentation

    Welcome to the documentation for Julia 1.10.

    请阅读 release notes 以了解自上次发行以来发生了什么变化。

    Note

    The documentation is also available in PDF format: julia-1.10.7.pdf.

    Below is a non-exhasutive list of links that will be useful as you learn and use the Julia programming language.

    简介

    科学计算对性能一直有着最高的需求，但目前各领域的专家却大量使用较慢的动态语言来开展他们的日常工作。 偏爱动态语言有很多很好的理由，因此我们不会舍弃动态的特性。 幸运的是，现代编程语言设计与编译器技术可以大大消除性能折衷（trade-off），并提供有足够生产力的单一环境进行原型设计，而且能高效地部署性能密集型应用程序。 Julia 语言在这其中扮演了这样一个角色：它是一门灵活的动态语言，适合用于科学计算和数值计算，并且性能可与传统的静态类型语言媲美。

    由于 Julia 的编译器和其它语言比如 Python 或 R 的解释器有所不同，一开始你可能发现 Julia 的性能并不是很突出。 如果你觉得速度有点慢，我们强烈建议在尝试其他功能前，先读一读文档中的提高性能的窍门部分。 一旦你理解了 Julia 的运作方式后，写出和 C 一样快的代码就是小菜一碟。

    Julia Compared to Other Languages

    Julia features optional typing, multiple dispatch, and good performance, achieved using type inference and just-in-time (JIT) compilation (and optional ahead-of-time compilation), implemented using LLVM. It is multi-paradigm, combining features of imperative, functional, and object-oriented programming. Julia provides ease and expressiveness for high-level numerical computing, in the same way as languages such as R, MATLAB, and Python, but also supports general programming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp, Perl, Python, Lua, and Ruby.

    Julia 与传统动态语言最重要的区别是：

    • The core language imposes very little; Julia Base and the standard library are written in Julia itself, including primitive operations like integer arithmetic
    • A rich language of types for constructing and describing objects, that can also optionally be used to make type declarations
    • The ability to define function behavior across many combinations of argument types via multiple dispatch
    • Automatic generation of efficient, specialized code for different argument types
    • Good performance, approaching that of statically-compiled languages like C

    Although one sometimes speaks of dynamic languages as being "typeless", they are definitely not. Every object, whether primitive or user-defined, has a type. The lack of type declarations in most dynamic languages, however, means that one cannot instruct the compiler about the types of values, and often cannot explicitly talk about types at all. In static languages, on the other hand, while one can – and usually must – annotate types for the compiler, types exist only at compile time and cannot be manipulated or expressed at run time. In Julia, types are themselves run-time objects, and can also be used to convey information to the compiler.

    What Makes Julia, Julia?

    While the casual programmer need not explicitly use types or multiple dispatch, they are the core unifying features of Julia: functions are defined on different combinations of argument types, and applied by dispatching to the most specific matching definition. This model is a good fit for mathematical programming, where it is unnatural for the first argument to "own" an operation as in traditional object-oriented dispatch. Operators are just functions with special notation – to extend addition to new user-defined data types, you define new methods for the + function. Existing code then seamlessly applies to the new data types.

    Partly because of run-time type inference (augmented by optional type annotations), and partly because of a strong focus on performance from the inception of the project, Julia's computational efficiency exceeds that of other dynamic languages, and even rivals that of statically-compiled languages. For large scale numerical problems, speed always has been, continues to be, and probably always will be crucial: the amount of data being processed has easily kept pace with Moore's Law over the past decades.

    Advantages of Julia

    Julia aims to create an unprecedented combination of ease-of-use, power, and efficiency in a single language. In addition to the above, some advantages of Julia over comparable systems include:

    • Free and open source (MIT licensed)
    • User-defined types are as fast and compact as built-ins
    • No need to vectorize code for performance; devectorized code is fast
    • Designed for parallelism and distributed computation
    • Lightweight "green" threading (coroutines)
    • Unobtrusive yet powerful type system
    • Elegant and extensible conversions and promotions for numeric and other types
    • Efficient support for Unicode, including but not limited to UTF-8
    • Call C functions directly (no wrappers or special APIs needed)
    • Powerful shell-like capabilities for managing other processes
    • Lisp-like macros and other metaprogramming facilities
    diff --git a/dev/manual/integers-and-floating-point-numbers/index.html b/dev/manual/integers-and-floating-point-numbers/index.html index 5f8e6079..07a24b08 100644 --- a/dev/manual/integers-and-floating-point-numbers/index.html +++ b/dev/manual/integers-and-floating-point-numbers/index.html @@ -327,4 +327,4 @@ 1 julia> one(BigFloat) -1.0 +1.0 diff --git a/dev/manual/interfaces/index.html b/dev/manual/interfaces/index.html index 3b99fcdd..37eea01c 100644 --- a/dev/manual/interfaces/index.html +++ b/dev/manual/interfaces/index.html @@ -243,4 +243,4 @@ 4.0 julia> p.r -6.363961030678928

    Finally, it is worth noting that adding instance properties like this is quite rarely done in Julia and should in general only be done if there is a good reason for doing so.

    +6.363961030678928

    Finally, it is worth noting that adding instance properties like this is quite rarely done in Julia and should in general only be done if there is a good reason for doing so.

    diff --git a/dev/manual/mathematical-operations/index.html b/dev/manual/mathematical-operations/index.html index f67e1e04..32f8d7b8 100644 --- a/dev/manual/mathematical-operations/index.html +++ b/dev/manual/mathematical-operations/index.html @@ -179,4 +179,4 @@ asin acos atan acot asec acsc asinh acosh atanh acoth asech acsch sinc cosc

    所有这些函数都是单参数函数，不过 atan 也可以接收两个参数 来表示传统的 atan2 函数。

    另外，sinpi(x) 和 cospi(x) 分别用来对 sin(pi*x) 和 cos(pi*x) 进行更精确的计算。

    要计算角度而非弧度的三角函数，以 d 做后缀。 比如，sind(x) 计算 x 的 sine 值，其中 x 是一个角度值。 下面是角度变量的三角函数完整列表：

    sind   cosd   tand   cotd   secd   cscd
-asind  acosd  atand  acotd  asecd  acscd

    特殊函数

    SpecialFunctions.jl 提供了许多其他的特殊数学函数。

    +asind acosd atand acotd asecd acscd

    特殊函数

    SpecialFunctions.jl 提供了许多其他的特殊数学函数。

    diff --git a/dev/manual/metaprogramming/index.html b/dev/manual/metaprogramming/index.html index 01f2f4e4..7a99cdfe 100644 --- a/dev/manual/metaprogramming/index.html +++ b/dev/manual/metaprogramming/index.html @@ -485,4 +485,4 @@ end return ind + 1 end -end

    在内部，这段代码创建了函数的两个实现：一个生成函数的实现，其使用 if @generated 中的第一个块，一个通常的函数的实现，其使用 else 块。在 if @generated 块的 then 部分中，代码与其它生成函数具有相同的语义：参数名称引用类型，且代码应返回表达式。可能会出现多个 if @generated 块，在这种情况下，生成函数的实现使用所有的 then 块，而替代实现使用所有的 else 块。

    请注意，我们在函数顶部添加了错误检查。此代码对两个版本都是通用的，且是两个版本中的运行时代码（它将被引用并返回为生成函数版本中的表达式）。这意味着局部变量的值和类型在代码生成时不可用——用于代码生成的代码只能看到参数类型。

    在这种定义方式中，代码生成功能本质上只是一种可选的优化。如果方便，编译器将使用它，否则可能选择使用通常的实现。这种方式是首选的，因为它允许编译器做出更多决策和以更多方式编译程序，还因为通常代码比由代码生成的代码更易读。但是，使用哪种实现取决于编译器实现细节，因此，两个实现的行为必须相同。

    +end

    在内部，这段代码创建了函数的两个实现：一个生成函数的实现，其使用 if @generated 中的第一个块，一个通常的函数的实现，其使用 else 块。在 if @generated 块的 then 部分中，代码与其它生成函数具有相同的语义：参数名称引用类型，且代码应返回表达式。可能会出现多个 if @generated 块，在这种情况下，生成函数的实现使用所有的 then 块，而替代实现使用所有的 else 块。

    请注意，我们在函数顶部添加了错误检查。此代码对两个版本都是通用的，且是两个版本中的运行时代码（它将被引用并返回为生成函数版本中的表达式）。这意味着局部变量的值和类型在代码生成时不可用——用于代码生成的代码只能看到参数类型。

    在这种定义方式中，代码生成功能本质上只是一种可选的优化。如果方便，编译器将使用它，否则可能选择使用通常的实现。这种方式是首选的，因为它允许编译器做出更多决策和以更多方式编译程序，还因为通常代码比由代码生成的代码更易读。但是，使用哪种实现取决于编译器实现细节，因此，两个实现的行为必须相同。

    diff --git a/dev/manual/methods/index.html b/dev/manual/methods/index.html index 37eaff07..9fd9ced6 100644 --- a/dev/manual/methods/index.html +++ b/dev/manual/methods/index.html @@ -446,4 +446,4 @@ else x -> x - 1 end -end
    +end
    diff --git a/dev/manual/missing/index.html b/dev/manual/missing/index.html index 8840e43a..9dbbc2f1 100644 --- a/dev/manual/missing/index.html +++ b/dev/manual/missing/index.html @@ -162,4 +162,4 @@ true julia> any([false, missing]) -missing +missing diff --git a/dev/manual/modules/index.html b/dev/manual/modules/index.html index 4f6757fc..ab80bcea 100644 --- a/dev/manual/modules/index.html +++ b/dev/manual/modules/index.html @@ -134,4 +134,4 @@ # instead use accessor functions: getstdout() = Base.stdout #= best option =# # or move the assignment into the runtime: -__init__() = global mystdout = Base.stdout #= also works =#

    此处为预编译中的操作附加了若干限制，以帮助用户避免其他误操作：

    1. 调用 eval 来在另一个模块中引发副作用。当增量预编译被标记时，该操作同时会导致抛出一个警告。
    2. 当 __init__() 已经开始执行后，在局部作用域中声明 global const（见 issue #12010，计划为此情况添加一个错误提示）
    3. 在增量预编译时替换模块是一个运行时错误。

    一些其他需要注意的点：

    1. 在源代码文件本身被修改之后，不会执行代码重载或缓存失效化处理（包括由 Pkg.update 执行的修改，此外在 Pkg.rm 执行后也没有清理操作）
    2. 变形数组的内存共享特性会被预编译忽略（每个数组样貌都会获得一个拷贝）
    3. 文件系统在编译期间和运行期间被假设为不变的，比如使用 @__FILE__/source_path() 在运行期间寻找资源、或使用 BinDeps 宏 @checked_lib。有时这是不可避免的。但是可能的话，在编译期将资源复制到模块里面是个好做法，这样在运行期间，就不需要去寻找它们了。
    4. WeakRef 对象和完成器目前在序列化器中无法被恰当地处理（在接下来的发行版中将修复）。
    5. 通常，最好避免去捕捉内部元数据对象的引用，如 Method、MethodInstance、TypeMapLevel、TypeMapEntry 及这些对象的字段，因为这会迷惑序列化器，且可能会引发你不想要的结果。此操作不足以成为一个错误，但你需做好准备：系统会尝试拷贝一部分，然后创建其余部分的单个独立实例。

    在开发模块时，关闭增量预编译可能会有所帮助。命令行标记 --compiled-modules={yes|no} 可以让你切换预编译的开启和关闭。 当 Julia 附加 --compiled-modules=no 启动，在载入模块和模块依赖时，编译缓存中的序列化模块会被忽略。 More fine-grained control is available with --pkgimages=no, which suppresses only native-code storage during precompilation. Base.compilecache 仍可以被手动调用。 此命令行标记的状态会被传递给 Pkg.build，禁止其在安装、更新、显式构建包时触发自动预编译。

    You can also debug some precompilation failures with environment variables. Setting JULIA_VERBOSE_LINKING=true may help resolve failures in linking shared libraries of compiled native code. See the Developer Documentation part of the Julia manual, where you will find further details in the section documenting Julia's internals under "Package Images".

    +__init__() = global mystdout = Base.stdout #= also works =#

    此处为预编译中的操作附加了若干限制，以帮助用户避免其他误操作：

    1. 调用 eval 来在另一个模块中引发副作用。当增量预编译被标记时，该操作同时会导致抛出一个警告。
    2. 当 __init__() 已经开始执行后，在局部作用域中声明 global const（见 issue #12010，计划为此情况添加一个错误提示）
    3. 在增量预编译时替换模块是一个运行时错误。

    一些其他需要注意的点：

    1. 在源代码文件本身被修改之后，不会执行代码重载或缓存失效化处理（包括由 Pkg.update 执行的修改，此外在 Pkg.rm 执行后也没有清理操作）
    2. 变形数组的内存共享特性会被预编译忽略（每个数组样貌都会获得一个拷贝）
    3. 文件系统在编译期间和运行期间被假设为不变的，比如使用 @__FILE__/source_path() 在运行期间寻找资源、或使用 BinDeps 宏 @checked_lib。有时这是不可避免的。但是可能的话，在编译期将资源复制到模块里面是个好做法，这样在运行期间，就不需要去寻找它们了。
    4. WeakRef 对象和完成器目前在序列化器中无法被恰当地处理（在接下来的发行版中将修复）。
    5. 通常，最好避免去捕捉内部元数据对象的引用，如 Method、MethodInstance、TypeMapLevel、TypeMapEntry 及这些对象的字段，因为这会迷惑序列化器，且可能会引发你不想要的结果。此操作不足以成为一个错误，但你需做好准备：系统会尝试拷贝一部分，然后创建其余部分的单个独立实例。

    在开发模块时，关闭增量预编译可能会有所帮助。命令行标记 --compiled-modules={yes|no} 可以让你切换预编译的开启和关闭。 当 Julia 附加 --compiled-modules=no 启动，在载入模块和模块依赖时，编译缓存中的序列化模块会被忽略。 More fine-grained control is available with --pkgimages=no, which suppresses only native-code storage during precompilation. Base.compilecache 仍可以被手动调用。 此命令行标记的状态会被传递给 Pkg.build，禁止其在安装、更新、显式构建包时触发自动预编译。

    You can also debug some precompilation failures with environment variables. Setting JULIA_VERBOSE_LINKING=true may help resolve failures in linking shared libraries of compiled native code. See the Developer Documentation part of the Julia manual, where you will find further details in the section documenting Julia's internals under "Package Images".

    diff --git a/dev/manual/multi-threading/index.html b/dev/manual/multi-threading/index.html index e27658f2..730c4ce7 100644 --- a/dev/manual/multi-threading/index.html +++ b/dev/manual/multi-threading/index.html @@ -165,4 +165,4 @@ end end nothing -end

  • 相关的第三种策略是使用不需要 yield 的队列。我们目前没有在 Base 中实现无锁队列，但 Base.IntrusiveLinkedListSynchronized{T} 是合适的。 这通常是用于带有事件循环的代码的好策略。例如，这个策略被 Gtk.jl 用来管理生命周期引用计数。 在这种方法中，我们不会在终结器内部做任何显式工作，而是将其添加到队列中以在更安全的时间运行。 事实上，Julia 的任务调度器已经使用了这种方法，因此将终结器定义为 x -> @spawn do_cleanup(x) 就是这种方法的一个示例。 但是请注意，这并不控制 do_cleanup 在哪个线程上运行，因此 do_cleanup 仍需要获取锁。 如果你实现自己的队列，则不必如此，因为你只能明确地从线程中排出该队列。

    • +end

  • 相关的第三种策略是使用不需要 yield 的队列。我们目前没有在 Base 中实现无锁队列，但 Base.IntrusiveLinkedListSynchronized{T} 是合适的。 这通常是用于带有事件循环的代码的好策略。例如，这个策略被 Gtk.jl 用来管理生命周期引用计数。 在这种方法中，我们不会在终结器内部做任何显式工作，而是将其添加到队列中以在更安全的时间运行。 事实上，Julia 的任务调度器已经使用了这种方法，因此将终结器定义为 x -> @spawn do_cleanup(x) 就是这种方法的一个示例。 但是请注意，这并不控制 do_cleanup 在哪个线程上运行，因此 do_cleanup 仍需要获取锁。 如果你实现自己的队列，则不必如此，因为你只能明确地从线程中排出该队列。

    • diff --git a/dev/manual/networking-and-streams/index.html b/dev/manual/networking-and-streams/index.html index 528f3e00..6d16714d 100644 --- a/dev/manual/networking-and-streams/index.html +++ b/dev/manual/networking-and-streams/index.html @@ -147,4 +147,4 @@ group = Sockets.IPv6("ff05::5:6:7") socket = Sockets.UDPSocket() send(socket, group, 6789, "Hello over IPv6") -close(socket) +close(socket) diff --git a/dev/manual/noteworthy-differences/index.html b/dev/manual/noteworthy-differences/index.html index 9f8fe7f1..83ac6dd6 100644 --- a/dev/manual/noteworthy-differences/index.html +++ b/dev/manual/noteworthy-differences/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    与其他语言的显著差异

    与 MATLAB 的显著差异

    虽然 MATLAB 用户可能会发现 Julia 的语法很熟悉，但 Julia 不是 MATLAB 的克隆。 它们之间存在重大的语法和功能差异。 以下是一些可能会使习惯于 MATLAB 的 Julia 用户感到困扰的显著差异：

    • Julia 数组使用方括号 A[i,j] 进行索引。

    • Julia 数组在分配给另一个变量时不会被复制。 在A = B之后，改变B的元素也会改变A的元素。 To avoid this, use A = copy(B).

    • Julia 的值在向函数传递时不发生复制。如果某个函数修改了数组，这一修改对调用者是可见的。

    • Julia 不会在赋值语句中自动增长数组。 而在 MATLAB 中 a(4) = 3.2 可以创建数组 a = [0 0 0 3.2]，而 a(5) = 7 可以将它增长为 a = [0 0 0 3.2 7]。如果 a 的长度小于 5 或者这个语句是第一次使用标识符 a，则相应的 Julia 语句 a[5] = 7 会抛出错误。Julia 使用 push! 和 append! 来增长 Vector，它们比 MATLAB 的 a(end+1) = val 更高效。

    • 虚数单位 sqrt(-1) 在 Julia 中表示为 im，而不是在 MATLAB 中的 i 或 j。

    • 在 Julia 中，不带小数点的字面数字（如 42）创建的是整数而不是浮点数。 因此，如果某些操作的预期结果是浮点数，就会产生域错误；例如，julia> a = -1; 2^a 会产生域错误，因为结果不是整数 （详情请参见常见问题中的域错误）。

    • 在 Julia 中，能返回多个值并将其赋值为元组，例如 (a, b) = (1, 2) 或 a, b = 1, 2。 在 Julia 中不存在 MATLAB 的 nargout，它通常在 MATLAB 中用于根据返回值的数量执行可选工作。取而代之的是，用户可以使用可选参数和关键字参数来实现类似的功能。

    • Julia 拥有真正的一维数组。列向量的大小为 N，而不是 Nx1。例如，rand(N) 创建一个一维数组。

    • 在 Julia 中，[x,y,z] 将始终构造一个包含x、y 和 z 的 3 元数组。

      • 要在第一个维度（「垂直列」）中连接元素，请使用 vcat(x,y,z) 或用分号分隔（[x; y; z]）。
      • 要在第二个维度（「水平行」）中连接元素，请使用 hcat(x,y,z) 或用空格分隔（[x y z]）。
      • 要构造分块矩阵（在前两个维度中连接元素），请使用 hvcat 或组合空格和分号（[a b; c d]）。

    • 在 Julia 中，a:b 和 a:b:c 构造 AbstractRange 对象。使用 collect(a:b) 构造一个类似 MATLAB 中完整的向量。通常，不需要调用 collect。在大多数情况下，AbstractRange 对象将像普通数组一样运行，但效率更高，因为它是懒惰求值。这种创建专用对象而不是完整数组的模式经常被使用，并且也可以在诸如 range 之类的函数中看到，或者在诸如 enumerate 和 zip 之类的迭代器中看到。特殊对象大多可以像正常数组一样使用。

    • The : operator has a different precedence in R and Julia. In particular, in Julia arithmetic operators have higher precedence than the : operator, whereas the reverse is true in R. For example, 1:n-1 in Julia is equivalent to 1:(n-1) in R.

    • Julia 中的函数返回其最后一个表达式或 return 关键字的值而无需在函数定义中列出要返回的变量的名称（有关详细信息，请参阅 return 关键字）。

    • Julia 脚本可以包含任意数量的函数，并且在加载文件时，所有定义都将在外部可见。可以从当前工作目录之外的文件加载函数定义。

    • 在 Julia 中，例如 sum、prod 和 max 的归约操作会作用到数组的每一个元素上，当调用时只有一个函数，例如 sum(A)，即使 A 并不只有一个维度。

    • 在 Julia 中，调用无参数的函数时必须使用小括号，例如 rand()。

    • Julia 不鼓励使用分号来结束语句。语句的结果不会自动打印（除了在 REPL 中），并且代码的一行不必使用分号结尾。println 或者 @printf 能用来打印特定输出。

    • 在 Julia 中，如果 A 和 B 是数组，像 A == B 这样的逻辑比较运算符不会返回布尔值数组。相反地，请使用 A .== B。对于其他的像是 <、> 的布尔运算符同理。

    • 在 Julia 中，运算符&、| 和 ⊻（xor）进行按位操作，分别与MATLAB中的and、or 和 xor 等价，并且优先级与 Python 的按位运算符相似（不像 C）。他们可以对标量运算或者数组中逐元素运算，可以用来合并逻辑数组，但是注意运算顺序的区别：括号可能是必要的（例如，选择 A 中等于 1 或 2 的元素可使用 (A .== 1) .| (A .== 2)）。

    • 在 Julia 中，集合的元素可以使用 splat 运算符 ... 来作为参数传递给函数，如 xs=[1,2]; f(xs...)。

    • Julia 的 svd 将奇异值作为向量而非密集对角矩阵返回。

    • 在 Julia 中，... 不用于延续代码行。不同的是，Julia 中不完整的表达式会自动延续到下一行。

    • 在 Julia 和 MATLAB 中，变量 ans 被设置为交互式会话中提交的最后一个表达式的值。在 Julia 中与 MATLAB 不同的是，当 Julia 代码以非交互式模式运行时并不会设置 ans。

    • Julia 的 struct 不支持在运行时动态地添加字段，这与 MATLAB 的 class 不同。 如需支持，请使用 Dict。Julia 中的字典不是有序的。

    • 在 Julia 中，每个模块有自身的全局作用域/命名空间，而在 MATLAB 中只有一个全局作用域。

    • 在 MATLAB 中，删除不需要的值的惯用方法是使用逻辑索引，如表达式 x(x>3) 或语句 x(x>3) = [] 来 in-place 修改 x。相比之下，Julia 提供了更高阶的函数 filter 和 filter!，允许用户编写 filter(z->z>3, x) 和 filter!(z->z>3, x) 来代替相应直译 x[x.>3] 和 x = x[x.>3]。使用 filter! 可以减少临时数组的使用。

    • 类似于提取（或「解引用」）元胞数组的所有元素的操作，例如 MATLAB 中的 vertcat(A{:})，在 Julia 中是使用 splat 运算符编写的，例如 vcat(A...)。

    • 在 Julia 中，adjoint 函数执行共轭转置；在 MATLAB 中，adjoint 提供了经典伴随，它是余子式的转置。

    • 在 Julia 中，a^b^c 被认为是 a^(b^c) 而在 MATLAB 中它是 (a^b)^c。

    与 R 的显著差异

    Julia 的目标之一是为数据分析和统计编程提供高效的语言。对于从 R 转到 Julia 的用户来说，这是一些显著差异：

    • Julia 的单引号封闭字符，而不是字符串。

    • Julia 可以通过索引字符串来创建子字符串。在 R 中，在创建子字符串之前必须将字符串转换为字符向量。

    • 在 Julia 中，与 Python 相同但与 R 不同的是，字符串可由三重引号 """ ... """ 创建。此语法对于构造包含换行符的字符串很方便。

    • 在 Julia 中，可变参数使用 splat 运算符 ... 指定，该运算符总是跟在具体变量的名称后面，与 R 的不同，R 的 ... 可以单独出现。

    • 在 Julia 中，模数是 mod(a, b)，而不是 a %% b。Julia 中的 % 是余数运算符。

    • Julia constructs vectors using brackets. Julia's [1, 2, 3] is the equivalent of R's c(1, 2, 3).

    • 在 Julia 中，并非所有数据结构都支持逻辑索引。此外，Julia 中的逻辑索引只支持长度等于被索引对象的向量。例如：

      • 在 R 中，c(1, 2, 3, 4)[c(TRUE, FALSE)] 等价于 c(1, 3)。
      • 在 R 中，c(1, 2, 3, 4)[c(TRUE, FALSE, TRUE, FALSE)] 等价于 c(1, 3)。
      • 在 Julia 中，[1, 2, 3, 4][[true, false]] 抛出 BoundsError。
      • 在 Julia 中，[1, 2, 3, 4][[true, false, true, false]] 产生 [1, 3]。

    • 与许多语言一样，Julia 并不总是允许对不同长度的向量进行操作，与 R 不同，R 中的向量只需要共享一个公共的索引范围。例如，c(1, 2, 3, 4) + c(1, 2) 是有效的 R，但等价的 [1, 2, 3, 4] + [1, 2] 在 Julia 中会抛出一个错误。

    • 在逗号不改变代码含义时，Julia 允许使用可选的尾随括号。在索引数组时，这可能在 R 用户间造成混淆。例如，R 中的 x[1,] 将返回矩阵的第一行；但是，在 Julia 中，引号被忽略，于是 x[1,] == x[1]，并且将返回第一个元素。要提取一行，请务必使用 :，如 x[1,:]。

    • Julia 的 map 首先接受函数，然后是该函数的参数，这与 R 中的 lapply(<structure>, function, ...) 不同。类似地，R 中的 apply(X, MARGIN, FUN, ...) 等价于 Julia 的 mapslices，其中函数是第一个参数。

    • R 中的多变量 apply，如 mapply(choose, 11:13, 1:3)，在 Julia 中可以编写成 broadcast(binomial, 11:13, 1:3)。等价地，Julia 提供了更短的点语法来向量化函数 binomial.(11:13, 1:3)。

    • Julia 使用 end 来表示条件块（如 if）、循环块（如 while/for）和函数的结束。为了代替单行 if ( cond ) statement，Julia 允许形式为 if cond; statement; end、cond && statement 和 !cond || statement 的语句。后两种语法中的赋值语句必须显式地包含在括号中，例如 cond && (x = value)，这是因为运算符的优先级。

    • 在 Julia 中，<-, <<- 和 -> 不是赋值运算符。

    • Julia 的 -> 创建一个匿名函数。

    • Julia 使用括号构造向量。Julia 的 [1, 2, 3] 等价于 R 的 c(1, 2, 3)。

    • Julia 的 * 运算符可以执行矩阵乘法，这与 R 不同。如果 A 和 B 都是矩阵，那么 A * B 在 Julia 中表示矩阵乘法，等价于 R 的 A %*% B。在 R 中，相同的符号将执行逐元素（Hadamard）乘积。要在 Julia 中使用逐元素乘法运算，你需要编写 A .* B。

    • Julia 使用 transpose 函数来执行矩阵转置，使用 ' 运算符或 adjoint 函数来执行共轭转置。因此，Julia 的 transpose(A) 等价于 R 的 t(A)。另外，Julia 中的非递归转置由 permutedims 函数提供。

    • Julia 在编写 if 语句或 for/while 循环时不需要括号：请使用 for i in [1, 2, 3] 代替 for (int i=1; i <= 3; i++)，以及 if i == 1 代替 if (i == 1)

    • Julia 不把数字 0 和 1 视为布尔值。在 Julia 中不能编写 if (1)，因为 if 语句只接受布尔值。相反，可以编写 if true、if Bool(1) 或 if 1==1。

    • Julia 不提供 nrow 和 ncol。相反，请使用 size(M, 1) 代替 nrow(M) 以及 size(M, 2) 代替 ncol(M)

    • Julia 仔细区分了标量、向量和矩阵。在 R 中，1 和 c(1) 是相同的。在 Julia 中，它们不能互换地使用。

    • Julia 的 diag 和 diagm 与 R 的不同。

    • Julia 赋值操作的左侧不能为函数调用的结果：你不能编写 diag(M) = fill(1, n)。

    • Julia 不鼓励使用函数填充主命名空间。Julia 的大多数统计功能都可在 JuliaStats 组织的包中找到。例如：

    • Julia 提供了元组和真正的哈希表，但不提供 R 风格的列表。在返回多个项时，通常应使用元组或具名元组：请使用 (1, 2) 或 (a=1, b=2) 代替 list(a = 1, b = 2)。

    • Julia 鼓励用户编写自己的类型，它比 R 中的 S3 或 S4 对象更容易使用。Julia 的多重派发系统意味着 table(x::TypeA) 和 table(x::TypeB) 类似于 R 的 table.TypeA(x) 和 table.TypeB(x)。

    • Julia 的值在向函数传递时不发生复制。如果某个函数修改了数组，这一修改对调用者是可见的。这与 R 非常不同，允许新函数更高效地操作大型数据结构。

    • 在 Julia 中，向量和矩阵使用 hcat、vcat 和 hvcat 拼接，而不是像在 R 中那样使用 c、rbind 和 cbind。

    • 在 Julia 中，像 a:b 这样的 range 不是 R 中的向量简写，而是一个专门的 AbstractRange 对象，该对象用于没有高内存开销地进行迭代。要将 range 转换为 vector，请使用 collect(a:b)。

    • Julia 的 max 和 min 分别等价于 R 中的 pmax 和 pmin，但两者的参数都需要具有相同的维度。虽然 maximum 和 minimum 代替了 R 中的 max 和 min，但它们之间有重大区别。

    • Julia 的 sum、prod、maximum 和 minimum 与它们在 R 中的对应物不同。它们都接受一个可选的关键字参数 dims，它表示执行操作的维度。例如，在 Julia 中令 A = [1 2; 3 4]，在 R 中令 B <- rbind(c(1,2),c(3,4)) 是与之相同的矩阵。然后 sum(A) 得到与 sum(B) 相同的结果，但 sum(A, dims=1) 是一个包含每一列总和的行向量，sum(A, dims=2) 是一个包含每一行总和的列向量。这与 R 的行为形成了对比，在 R 中，单独的 colSums(B) 和 rowSums(B) 提供了这些功能。如果 dims 关键字参数是向量，则它指定执行求和的所有维度，并同时保持待求和数组的维数，例如 sum(A, dims=(1,2)) == hcat(10)。应该注意的是，没有针对第二个参数的错误检查。

    • Julia 具有一些可以改变其参数的函数。例如，它具有 sort 和 sort!。

    • 在 R 中，高性能需要向量化。在 Julia 中，这几乎恰恰相反：性能最高的代码通常通过去向量化的循环来实现。

    • Julia 是立即求值的，不支持 R 风格的惰性求值。对于大多数用户来说，这意味着很少有未引用的表达式或列名。

    • Julia 不支持 NULL 类型。最接近的等价物是 nothing，但它的行为类似于标量值而不是列表。请使用 x === nothing 代替 is.null(x)。

    • 在 Julia 中，缺失值由 missing 表示，而不是由 NA 表示。请使用 ismissing(x)（或者在向量上使用逐元素操作 ismissing.(x)）代替 isna(x)。通常使用 skipmissing 代替 na.rm=TRUE（尽管在某些特定情况下函数接受 skipmissing 参数）。

    • Julia 缺少 R 中的 assign 或 get 的等价物。

    • 在 Julia 中，return 不需要括号。

    • 在 R 中，删除不需要的值的惯用方法是使用逻辑索引，如表达式 x[x>3] 或语句 x = x[x>3] 来 in-place 修改 x。相比之下，Julia 提供了更高阶的函数 filter 和 filter!，允许用户编写 filter(z->z>3, x) 和 filter!(z->z>3, x) 来代替相应直译 x[x.>3] 和 x = x[x.>3]。使用 filter! 可以减少临时数组的使用。

    与 Python 的显著差异

    • Julia 的 for, if, while 等语句块都以 end 关键字结束。代码的缩进不像在 Python 中那样重要。Julia 也没有 pass 关键字。

    • Julia 中的字符串使用双引号构造，如 "text"，也可以使用三引号构造多行字符串。而在 Python 中可以使用单引号（'text'）或者双引号（"text"）。单引号在 Julia 中用来表示单个字符，例如 'c'。

    • 在 Julia 中字符串的拼接使用 *，而不是像 Python 一样使用 +。类似的，字符串重复多次 Julia 使用 ^ 而不是 *。Julia 也不支持隐式的字符串拼接，例如 Python 中的 'ab' 'cd' == 'abcd'。

    • Python 列表——灵活但缓慢——对应于 Julia 的 Vector{Any} 类型或更一般的 Vector{T}，其中 T 是一些非具体元素类型。 “快”的数组，如 NumPy 数组，它们就地存储元素（即，dtype 是 np.float64、[('f1', np.uint64), ('f2', np.int32)]， 等）可以用 Array{T} 表示，其中 T 是一个具体的、不可变的元素类型。 这包括内置类型，如 Float64、Int32、Int64，也包括更复杂的类型，如 Tuple{UInt64,Float64} 和许多用户定义的类型。

    • 在 Julia 中，数组、字符串等的索引从 1 开始，而不是从 0 开始。

    • Julia 里的切片包含最后一个元素。Julia 里的 a[2:3] 等同于 Python 中的 a[1:3]。

    • Unlike Python, Julia allows AbstractArrays with arbitrary indexes. Python's special interpretation of negative indexing, a[-1] and a[-2], should be written a[end] and a[end-1] in Julia.

    • Julia 的索引必须写全。Python 中的 x[1:] 等价于 Julia 中的 x[2:end]。

    • In Julia, : before any object creates a Symbol or quotes an expression; so, x[:5] is same as x[5]. If you want to get the first n elements of an array, then use range indexing.

    • Julia 的范围语法为 x[start:step:stop]，而 Python 的格式为 x[start:(stop+1):step]。

    因此 Python 中的 x[0:10:2] 等价于 Julia 里的 x[1:2:10]。类似的 Python 中的反转数组 x[::-1] 等价于 Julia 中的 x[end:-1:1]。

    • In Julia, ranges can be constructed independently as start:step:stop, the same syntax it uses in array-indexing. The range function is also supported.

    • 在 Julia 中队一个矩阵取索引 X[[1,2], [1,3]] 返回一个子矩阵，它包含了第一和第二行与第一和第三列的交集。 在 Python 中 X[[1,2], [1,3]] 返回一个向量，它包含索引 [1,1] 和 [2,3] 的值。Julia 中的 X[[1,2], [1,3]] 等价于 Python 中的 X[np.ix_([0,1],[0,2])]。Python 中的 X[[1,2], [1,3]] 等价于 Julia 中的 X[[CartesianIndex(1,1), CartesianIndex(2,3)]]。

    • Julia 没有用来续行的语法：如果在行的末尾，到目前为止的输入是一个完整的表达式，则认为其已经结束；否则，认为输入继续。强制表达式继续的一种方式是将其包含在括号中。

    • 默认情况下，Julia 数组是列优先（Fortran 排序），而 NumPy 数组是行优先（C 排序）。为了在循环数组时获得最佳性能，Julia 中的循环顺序应相对于 NumPy 颠倒（请参阅性能提示的相关部分）。

    • Julia 的更新运算符（例如 +=，-=，···）是非原位操作（not in-place），而 Numpy 的是。这意味着 A = [1, 1]; B = A; B += [3, 3] 不会改变 A 中的值，而将名称 B 重新绑定到右侧表达式 B = B + 3 的结果，这是一个新的数组。对于 in-place 操作，使用 B .+= 3（另请参阅 dot operators）、显式的循环或者 InplaceOps.jl。

    • Julia 的函数在调用时，每次都对默认参数重新求值，不像 Python 只在函数定义时对默认参数求一次值。 举例来说：Julia 的函数 f(x=rand()) = x 在无参数调用时（f()），每次都会返回不同的随机数。 另一方面，函数 g(x=[1,2]) = push!(x,3) 无参数调用时 g()，永远返回 [1,2,3]。

    • 在 Julia 中，必须使用关键字来传递关键字参数，这与 Python 中通常可以按位置传递它们不同。尝试按位置传递关键字参数会改变方法签名，从而导致 MethodError 或调用错误的方法。

    • 在 Julia 中，% 是余数运算符，而在 Python 中是模运算符。

    （译注：二者在参数有负数时有区别）

    • 在 Julia 中，常用的整数类型 Int 对应机器的整数类型，Int32 或 Int64。不像 Python 中的整数 int 是任意精度的。这意味着 Julia 中默认的整数类型会溢出，因此 2^64 == 0。如果你要表示一个大数，请选择一个合适的类型。如：Int128、任意精度的 BigInt 或者浮点类型 Flost64。

    • Julia 中虚数单位 sqrt(-1) 是 im，而不是 Python 中的 j。

    • Julia 中指数是 ^，而不是 Python 中的 **。

    • Julia 使用 Nothing 类型的实例 nothing 代表空值（null），而不是 Python 中 NoneType 类的 None。

    • 在 Julia 中，标准的运算符作用在矩阵上就得到矩阵操作，不像 Python 标准运算符默认是逐元素操作。当 A 和 B 都是矩阵时，A * B 在 Julia 中代表着矩阵乘法，而不是 Python 中的逐元素相乘。即：Julia 中的 A * B 等同于 Python 的 A @ B；Python 中的 A * B 等同于 Julia 中的 A .* B。

    • Julia 中的伴随操作符 ' 返回向量的转置（一种行向量的懒惰表示法）。Python 中对向量执行 .T 返回它本身（没有效果）。

    • In Julia, a function may contain multiple concrete implementations (called methods), which are selected via multiple dispatch based on the types of all arguments to the call, as compared to functions in Python, which have a single implementation and no polymorphism (as opposed to Python method calls which use a different syntax and allows dispatch on the receiver of the method).

    • Julia 没有类（class），取而代替的是结构体（structures），可以是可变的或不可变的，它们只包含数据而不包含方法。

    • 在 Python 中调用类实例的方法 (x = MyClass(*args); x.f(y)) 对应于 Julia 中的函数调用，例如 x = MyType(args...); f(x, y)。 总的来说，多重派发比 Python 类系统更灵活和强大。

    • Julia 的结构体有且只能有一个抽象超类型（abstract supertype），而 Python 的类可以纪成一个或多个、抽象或具体的超类（superclasses）。

    • 逻辑 Julia 程序结构（包和模块）独立于文件结构（include 用于附加文件），而 Python 代码结构由目录（包）和文件（模块）定义。

    • Julia 中的三元运算符 x > 0 ? 1 : -1 对应于 Python 中的条件表达式 1 if x > 0 else -1。

    • Julia 中以 @ 开头的符号是宏（macro），而 Python 中是装饰器（decorator）。

    • Julia 的异常处理使用 try — catch — finally，而不是 Python 的 try — except — finally。与 Python 不同的是，因为性能的原因，Julia 不推荐在正常流程中使用异常处理。 (compared with Python, Julia is faster at ordinary control flow but slower at exception-catching).

    • Julia 的循环很快，所以没必要手动向量化（vectorized）。

    • 小心 Julia 中的非常量全局变量，尤其它出现在循环中时。因为你在 Julia 中可以写出贴近硬件的代码，这时使用全局变量的影响非常大（参见性能建议）

    • In Julia, rounding and truncation are explicit. Python's int(3.7) should be floor(Int, 3.7) or Int(floor(3.7)) and is distinguished from round(Int, 3.7). floor(x) and round(x) on their own return an integer value of the same type as x rather than always returning Int.

    • In Julia, parsing is explicit. Python's float("3.7") would be parse(Float64, "3.7") in Julia.

    • Python 中大多数的值都能用在逻辑运算中。例如：if "a" 永真，if "" 恒假。在 Julia 中你只能使用布尔类型的值，或者显示的将其他值转为布尔类型，否则就会抛出异常。例如当你想测试字符串是否为空是，请使用 if !isempty("")。

    • 在 Julia 中大多数代码块都会引入新的本地作用域（local scope）。例如：循环和异常处理的 try — catch — finally。注意：列表推断（comprehensions）与生成器在 Julia 和 Python 中都会引入新的作用域；而 if 分支则都不会引入。

    与 C/C++ 的显著差异

    • Julia 的数组由方括号索引，方括号中可以包含不止一个维度 A[i,j]。这样的语法不仅仅是像 C/C++ 中那样对指针或者地址引用的语法糖，参见关于数组构造的语法的 Julia 文档。

    • 在 Julia 中，数组、字符串等的索引从 1 开始，而不是从 0 开始。

    • Julia 的数组在赋值给另一个变量时不发生复制。执行 A = B 后，改变 B 中元素也会修改 A。像 += 这样的更新运算符不会以 in-place 的方式执行，而是相当于 A = A + B，将左侧绑定到右侧表达式的计算结果上。

    • Julia 的数组是列优先的（Fortran 顺序），而 C/C++ 的数组默认是行优先的。要使数组上的循环性能最优，在 Julia 中循环的顺序应该与 C/C++ 相反（参见 性能建议）。

    • Julia 的值在赋值或向函数传递时不发生复制。如果某个函数修改了数组，这一修改对调用者是可见的。

    • 在 Julia 中，空格是有意义的，这与 C/C++ 不同，所以向 Julia 程序中添加或删除空格时必须谨慎。

    • 在 Julia 中，没有小数点的数值字面量（如 42）生成有符号整数，类型为 Int，但如果字面量太长，超过了机器字长，则会被自动提升为容量更大的类型，例如 Int64（如果 Int 是 Int32）、Int128，或者任意精度的 BigInt 类型。不存在诸如 L, LL, U, UL, ULL 这样的数值字面量后缀指示无符号和/或有符号与无符号。十进制字面量始终是有符号的，十六进制字面量（像 C/C++ 一样由 0x 开头）是无符号的。另外，十六进制字面量与 C/C++/Java 不同，也与 Julia 中的十进制字面量不同，它们的类型取决于字面量的长度，包括开头的 0。例如，0x0 和 0x00 的类型是 UInt8，0x000 和 0x0000 的类型是 UInt16。同理，字面量的长度在 5-8 之间，类型为 UInt32；在 9-16 之间，类型为 UInt64；在 17-32 之间，类型为 UInt128。当定义十六进制掩码时，就需要将这一问题考虑在内，比如 ~0xf == 0xf0 与 ~0x000f == 0xfff0 完全不同。64 位 Float64 和 32 位 Float32 的字面量分别表示为 1.0 和 1.0f0。浮点字面量在无法被精确表示时舍入（且不会提升为 BigFloat 类型）。浮点字面量在行为上与 C/C++ 更接近。八进制（前缀为 0o）和二进制（前缀为 0b）也被视为无符号的。

    • 在 Julia 中，当两个操作数都是整数类型时，除法运算符 / 返回一个浮点数。 要执行整数除法，请使用 div 或 ÷。

    • 使用浮点类型索引数组在 Julia 中通常是错误的。 C 表达式 a[i / 2] 的 Julia 等价写法是 a[i ÷ 2 + 1]，其中 i 是整数类型。

    • 字符串字面量可用 " 或 """ 分隔，用 """ 分隔的字面量可以包含 " 字符而无需像 "\"" 这样来引用它。字符串字面量可以包含插入其中的其他变量或表达式，由 $variablename 或 $(expression) 表示，它在该函数所处的上下文中计算变量名或表达式。

    • // 表示 Rational 数，而非单行注释（其在 Julia 中是 #）

    • #= 表示多行注释的开头，=# 结束之。

    • Julia 中的函数返回其最后一个表达式或 return 关键字的值。可以从函数中返回多个值并将其作为元组赋值，如 (a, b) = myfunction() 或 a, b = myfunction()，而不必像在 C/C++ 中那样必须传递指向值的指针（即 a = myfunction(&b)）。

    • Julia 不要求使用分号来结束语句。表达式的结果不会自动打印（除了在交互式提示符中，即 REPL），且代码行不需要以分号结尾。println 或 @printf 可用于打印特定输出。在 REPL 中，; 可用于抑制输出。; 在 [ ] 中也有不同的含义，需要注意。; 可用于在单行中分隔表达式，但在许多情况下不是绝对必要的，更经常是为了可读性。

    • 在 Julia 中，运算符 ⊻（xor）执行按位 XOR 操作，即 C/C++ 中的 ^。此外，按位运算符不具有与 C/C++ 相同的优先级，所以可能需要括号。

    • Julia 的 ^ 是取幂（pow），而非 C/C++ 中的按位 XOR（在 Julia 中请使用 ⊻ 或 xor）

    • Julia 有两个右移运算符，>> 和 >>>。 >> 执行算术移位，>>> 始终执行逻辑移位，这与 C/C++ 不同，其中 >> 的含义取决于被移位的值的类型。

    • Julia 的 -> 创建一个匿名函数，它并不通过指针访问成员。

    • Julia 在编写 if 语句或 for/while 循环时不需要括号：请使用 for i in [1, 2, 3] 代替 for (int i=1; i <= 3; i++)，以及 if i == 1 代替 if (i == 1)

    • Julia 不把数字 0 和 1 视为布尔值。在 Julia 中不能编写 if (1)，因为 if 语句只接受布尔值。相反，可以编写 if true、if Bool(1) 或 if 1==1。

    • Julia 使用 end 来表示条件块（如 if）、循环块（如 while/for）和函数的结束。为了代替单行 if ( cond ) statement，Julia 允许形式为 if cond; statement; end、cond && statement 和 !cond || statement 的语句。后两种语法中的赋值语句必须显式地包含在括号中，例如 cond && (x = value)，这是因为运算符的优先级。

    • Julia 没有用来续行的语法：如果在行的末尾，到目前为止的输入是一个完整的表达式，则认为其已经结束；否则，认为输入继续。强制表达式继续的一种方式是将其包含在括号中。

    • Julia 宏对已解析的表达式进行操作，而非程序的文本，这允许它们执行复杂的 Julia 代码转换。宏名称以 @ 字符开头，具有类似函数的语法 @mymacro(arg1, arg2, arg3) 和类似语句的语法 @mymacro arg1 arg2 arg3。两种形式的语法可以相互转换；如果宏出现在另一个表达式中，则类似函数的形式尤其有用，并且它通常是最清晰的。类似语句的形式通常用于标注块，如在分布式 for 结构中：@distributed for i in 1:n; #= body =#; end。如果宏结构的结尾不那么清晰，请使用类似函数的形式。

    • Julia 有一个枚举类型，使用宏 @enum(name, value1, value2, ...) 来表示，例如：@enum(Fruit, banana=1, apple, pear)。

    • 按照惯例，修改其参数的函数在名称的末尾有个 !，例如 push!。

    • 在 C++ 中，默认情况下，你具有静态分派，即为了支持动态派发，你需要将函数标注为 virtual 函数。另一方面，Julia 中的每个方法都是「virtual」（尽管它更通用，因为方法是在每个参数类型上派发的，而不仅仅是 this，并且使用的是最具体的声明规则）。

    Julia ⇔ C/C++: Namespaces

    • C/C++ namespaces correspond roughly to Julia modules.
    • There are no private globals or fields in Julia. Everything is publicly accessible through fully qualified paths (or relative paths, if desired).
    • using MyNamespace::myfun (C++) corresponds roughly to import MyModule: myfun (Julia).
    • using namespace MyNamespace (C++) corresponds roughly to using MyModule (Julia)
      • In Julia, only exported symbols are made available to the calling module.
      • In C++, only elements found in the included (public) header files are made available.
    • Caveat: import/using keywords (Julia) also load modules (see below).
    • Caveat: import/using (Julia) works only at the global scope level (modules)
      • In C++, using namespace X works within arbitrary scopes (ex: function scope).

    Julia ⇔ C/C++: Module loading

    • When you think of a C/C++ "library", you are likely looking for a Julia "package".
      • Caveat: C/C++ libraries often house multiple "software modules" whereas Julia "packages" typically house one.
      • Reminder: Julia modules are global scopes (not necessarily "software modules").
    • Instead of build/make scripts, Julia uses "Project Environments" (sometimes called either "Project" or "Environment").
      • Build scripts are only needed for more complex applications (like those needing to compile or download C/C++ executables).
      • To develop application or project in Julia, you can initialize its root directory as a "Project Environment", and house application-specific code/packages there. This provides good control over project dependencies, and future reproducibility.
      • Available packages are added to a "Project Environment" with the Pkg.add() function or Pkg REPL mode. (This does not load said package, however).
      • The list of available packages (direct dependencies) for a "Project Environment" are saved in its Project.toml file.
      • The full dependency information for a "Project Environment" is auto-generated & saved in its Manifest.toml file by Pkg.resolve().
    • Packages ("software modules") available to the "Project Environment" are loaded with import or using.
      • In C/C++, you #include <moduleheader> to get object/function declarations, and link in libraries when you build the executable.
      • In Julia, calling using/import again just brings the existing module into scope, but does not load it again (similar to adding the non-standard #pragma once to C/C++).
    • Directory-based package repositories (Julia) can be made available by adding repository paths to the Base.LOAD_PATH array.
      • Packages from directory-based repositories do not require the Pkg.add() tool prior to being loaded with import or using. They are simply available to the project.
      • Directory-based package repositories are the quickest solution to developping local libraries of "software modules".

    Julia ⇔ C/C++: Assembling modules

    • In C/C++, .c/.cpp files are compiled & added to a library with build/make scripts.
      • In Julia, import [PkgName]/using [PkgName] statements load [PkgName].jl located in a package's [PkgName]/src/ subdirectory.
      • In turn, [PkgName].jl typically loads associated source files with calls to include "[someotherfile].jl".
    • include "./path/to/somefile.jl" (Julia) is very similar to #include "./path/to/somefile.jl" (C/C++).
      • However include "..." (Julia) is not used to include header files (not required).
      • Do not use include "..." (Julia) to load code from other "software modules" (use import/using instead).
      • include "path/to/some/module.jl" (Julia) would instantiate multiple versions of the same code in different modules (creating distinct types (etc.) with the same names).
      • include "somefile.jl" is typically used to assemble multiple files within the same Julia package ("software module"). It is therefore relatively straightforward to ensure file are included only once (No #ifdef confusion).

    Julia ⇔ C/C++: Module interface

    • C++ exposes interfaces using "public" .h/.hpp files whereas Julia modules mark specific symbols that are intended for their users as publicor exported.
      • Often, Julia modules simply add functionality by generating new "methods" to existing functions (ex: Base.push!).
      • Developers of Julia packages therefore cannot rely on header files for interface documentation.
      • Interfaces for Julia packages are typically described using docstrings, README.md, static web pages, ...
    • Some developers choose not to export all symbols required to use their package/module.
      • Users might be expected to access these components by qualifying functions/structs/... with the package/module name (ex: MyModule.run_this_task(...)).

    Julia ⇔ C/C++: Quick reference

    Software ConceptJuliaC/C++
    unnamed scopebegin ... end{ ... }
    function scopefunction x() ... endint x() { ... }
    global scopemodule MyMod ... endnamespace MyNS { ... }
    software moduleA Julia "package".h/.hpp files<br>+compiled somelib.a
    assembling<br>software modulesSomePkg.jl: ...<br>import("subfile1.jl")<br>import("subfile2.jl")<br>...$(AR) *.o &rArr; somelib.a
    import<br>software moduleimport SomePkg#include <somelib><br>+link in somelib.a
    module libraryLOAD_PATH[], *Git repository,<br>**custom package registrymore .h/.hpp files<br>+bigger compiled somebiglib.a

    * The Julia package manager supports registering multiple packages from a single Git repository.<br> * This allows users to house a library of related packages in a single repository.<br> ** Julia registries are primarily designed to provide versioning \& distribution of packages.<br> ** Custom package registries can be used to create a type of module library.

    与 Common Lisp 的显著差异

    • Julia 默认使用 1 开始的数组索引，它也能处理任意的索引顺序。

    • 函数和变量共用一个命名空间（"Lisp-1"）。

    • For performance, Julia prefers that operations have type stability. Where Common Lisp abstracts away from the underlying machine operations, Julia cleaves closer to them. For example:

      • Integer division using / always returns a floating-point result, even if the computation is exact.
        • // always returns a rational result
        • ÷ always returns a (truncated) integer result
      • Bignums are supported, but conversion is not automatic; ordinary integers overflow.
      • Complex numbers are supported, but to get complex results, you need complex inputs.
      • There are multiple Complex and Rational types, with different component types.

    • 典型的使用 Julia 进行原型开发时，也会对镜像进行连续的修改，Revise.jl 包提供了这个功能。

    • 对于性能，Julia 更喜欢操作具有 类型稳定性。 Common Lisp 从底层机器操作中抽象出来，而 Julia 则更接近它们。 例如：

      • 使用 / 的整数除法总是返回浮点结果，即使计算是精确的。
        • // 总是返回一个有理数结果
        • ÷ 总是返回一个（被截断的）整数结果
      • Julia 支持大整数，但不会自动转换。默认的整数类型会溢出。
      • 支持复数，但要获得复数结果，你需要复数输入。
      • 有多种 Complex 和 Rational 类型，具有不同的组成类型。

    • 模块（名称空间）可以是分层的。import 和 using 有着双重角色：他们加载代码并让代码在命名空间中可用。import 用于仅有模块名是可用的情况，大致等价于 ASDF:LOAD-OP。槽名（Slot name）不需要单独导出。全局变量不能从模块的外部赋值，除了 eval(mod, :(var = val)) 这个例外情况。

    • 宏以 @ 开头，并没有像 Common Lisp 那样无缝地集成到语言中；因此在 Julia 中，宏的使用不像在 Common Lisp 中那样广泛。Julia 支持宏的一种卫生（hygiene）形式。因为不同的表层语法，Julia 中没有 COMMON-LISP:&BODY 的等价形式。

    • 所有的函数都是通用的并且使用多重分派。函数的参数列表也无需遵循一样的模板，这让我们有了一个强大的范式：do。可选参数与关键字参数的处理方式不同。方法的歧义没有像在 Common Lisp 对象系统中那样得到解决，因此需要为交集定义更具体的方法。

    • 符号不属于任何包，它本身也不包含任何值。M.var 会对 M 模块里的  var 符号求值。

    • Julia 完全支持函数式编程风格，包括闭包等特性。但这并不是 Julia 的惯用风格。修改捕获变量时需要一些额外的变通以便提高性能。

    +
    Repository

    与其他语言的显著差异

    与 MATLAB 的显著差异

    虽然 MATLAB 用户可能会发现 Julia 的语法很熟悉，但 Julia 不是 MATLAB 的克隆。 它们之间存在重大的语法和功能差异。 以下是一些可能会使习惯于 MATLAB 的 Julia 用户感到困扰的显著差异：

    • Julia 数组使用方括号 A[i,j] 进行索引。

    • Julia 数组在分配给另一个变量时不会被复制。 在A = B之后，改变B的元素也会改变A的元素。 To avoid this, use A = copy(B).

    • Julia 的值在向函数传递时不发生复制。如果某个函数修改了数组，这一修改对调用者是可见的。

    • Julia 不会在赋值语句中自动增长数组。 而在 MATLAB 中 a(4) = 3.2 可以创建数组 a = [0 0 0 3.2]，而 a(5) = 7 可以将它增长为 a = [0 0 0 3.2 7]。如果 a 的长度小于 5 或者这个语句是第一次使用标识符 a，则相应的 Julia 语句 a[5] = 7 会抛出错误。Julia 使用 push! 和 append! 来增长 Vector，它们比 MATLAB 的 a(end+1) = val 更高效。

    • 虚数单位 sqrt(-1) 在 Julia 中表示为 im，而不是在 MATLAB 中的 i 或 j。

    • 在 Julia 中，不带小数点的字面数字（如 42）创建的是整数而不是浮点数。 因此，如果某些操作的预期结果是浮点数，就会产生域错误；例如，julia> a = -1; 2^a 会产生域错误，因为结果不是整数 （详情请参见常见问题中的域错误）。

    • 在 Julia 中，能返回多个值并将其赋值为元组，例如 (a, b) = (1, 2) 或 a, b = 1, 2。 在 Julia 中不存在 MATLAB 的 nargout，它通常在 MATLAB 中用于根据返回值的数量执行可选工作。取而代之的是，用户可以使用可选参数和关键字参数来实现类似的功能。

    • Julia 拥有真正的一维数组。列向量的大小为 N，而不是 Nx1。例如，rand(N) 创建一个一维数组。

    • 在 Julia 中，[x,y,z] 将始终构造一个包含x、y 和 z 的 3 元数组。

      • 要在第一个维度（「垂直列」）中连接元素，请使用 vcat(x,y,z) 或用分号分隔（[x; y; z]）。
      • 要在第二个维度（「水平行」）中连接元素，请使用 hcat(x,y,z) 或用空格分隔（[x y z]）。
      • 要构造分块矩阵（在前两个维度中连接元素），请使用 hvcat 或组合空格和分号（[a b; c d]）。

    • 在 Julia 中，a:b 和 a:b:c 构造 AbstractRange 对象。使用 collect(a:b) 构造一个类似 MATLAB 中完整的向量。通常，不需要调用 collect。在大多数情况下，AbstractRange 对象将像普通数组一样运行，但效率更高，因为它是懒惰求值。这种创建专用对象而不是完整数组的模式经常被使用，并且也可以在诸如 range 之类的函数中看到，或者在诸如 enumerate 和 zip 之类的迭代器中看到。特殊对象大多可以像正常数组一样使用。

    • The : operator has a different precedence in R and Julia. In particular, in Julia arithmetic operators have higher precedence than the : operator, whereas the reverse is true in R. For example, 1:n-1 in Julia is equivalent to 1:(n-1) in R.

    • Julia 中的函数返回其最后一个表达式或 return 关键字的值而无需在函数定义中列出要返回的变量的名称（有关详细信息，请参阅 return 关键字）。

    • Julia 脚本可以包含任意数量的函数，并且在加载文件时，所有定义都将在外部可见。可以从当前工作目录之外的文件加载函数定义。

    • 在 Julia 中，例如 sum、prod 和 max 的归约操作会作用到数组的每一个元素上，当调用时只有一个函数，例如 sum(A)，即使 A 并不只有一个维度。

    • 在 Julia 中，调用无参数的函数时必须使用小括号，例如 rand()。

    • Julia 不鼓励使用分号来结束语句。语句的结果不会自动打印（除了在 REPL 中），并且代码的一行不必使用分号结尾。println 或者 @printf 能用来打印特定输出。

    • 在 Julia 中，如果 A 和 B 是数组，像 A == B 这样的逻辑比较运算符不会返回布尔值数组。相反地，请使用 A .== B。对于其他的像是 <、> 的布尔运算符同理。

    • 在 Julia 中，运算符&、| 和 ⊻（xor）进行按位操作，分别与MATLAB中的and、or 和 xor 等价，并且优先级与 Python 的按位运算符相似（不像 C）。他们可以对标量运算或者数组中逐元素运算，可以用来合并逻辑数组，但是注意运算顺序的区别：括号可能是必要的（例如，选择 A 中等于 1 或 2 的元素可使用 (A .== 1) .| (A .== 2)）。

    • 在 Julia 中，集合的元素可以使用 splat 运算符 ... 来作为参数传递给函数，如 xs=[1,2]; f(xs...)。

    • Julia 的 svd 将奇异值作为向量而非密集对角矩阵返回。

    • 在 Julia 中，... 不用于延续代码行。不同的是，Julia 中不完整的表达式会自动延续到下一行。

    • 在 Julia 和 MATLAB 中，变量 ans 被设置为交互式会话中提交的最后一个表达式的值。在 Julia 中与 MATLAB 不同的是，当 Julia 代码以非交互式模式运行时并不会设置 ans。

    • Julia 的 struct 不支持在运行时动态地添加字段，这与 MATLAB 的 class 不同。 如需支持，请使用 Dict。Julia 中的字典不是有序的。

    • 在 Julia 中，每个模块有自身的全局作用域/命名空间，而在 MATLAB 中只有一个全局作用域。

    • 在 MATLAB 中，删除不需要的值的惯用方法是使用逻辑索引，如表达式 x(x>3) 或语句 x(x>3) = [] 来 in-place 修改 x。相比之下，Julia 提供了更高阶的函数 filter 和 filter!，允许用户编写 filter(z->z>3, x) 和 filter!(z->z>3, x) 来代替相应直译 x[x.>3] 和 x = x[x.>3]。使用 filter! 可以减少临时数组的使用。

    • 类似于提取（或「解引用」）元胞数组的所有元素的操作，例如 MATLAB 中的 vertcat(A{:})，在 Julia 中是使用 splat 运算符编写的，例如 vcat(A...)。

    • 在 Julia 中，adjoint 函数执行共轭转置；在 MATLAB 中，adjoint 提供了经典伴随，它是余子式的转置。

    • 在 Julia 中，a^b^c 被认为是 a^(b^c) 而在 MATLAB 中它是 (a^b)^c。

    与 R 的显著差异

    Julia 的目标之一是为数据分析和统计编程提供高效的语言。对于从 R 转到 Julia 的用户来说，这是一些显著差异：

    • Julia 的单引号封闭字符，而不是字符串。

    • Julia 可以通过索引字符串来创建子字符串。在 R 中，在创建子字符串之前必须将字符串转换为字符向量。

    • 在 Julia 中，与 Python 相同但与 R 不同的是，字符串可由三重引号 """ ... """ 创建。此语法对于构造包含换行符的字符串很方便。

    • 在 Julia 中，可变参数使用 splat 运算符 ... 指定，该运算符总是跟在具体变量的名称后面，与 R 的不同，R 的 ... 可以单独出现。

    • 在 Julia 中，模数是 mod(a, b)，而不是 a %% b。Julia 中的 % 是余数运算符。

    • Julia constructs vectors using brackets. Julia's [1, 2, 3] is the equivalent of R's c(1, 2, 3).

    • 在 Julia 中，并非所有数据结构都支持逻辑索引。此外，Julia 中的逻辑索引只支持长度等于被索引对象的向量。例如：

      • 在 R 中，c(1, 2, 3, 4)[c(TRUE, FALSE)] 等价于 c(1, 3)。
      • 在 R 中，c(1, 2, 3, 4)[c(TRUE, FALSE, TRUE, FALSE)] 等价于 c(1, 3)。
      • 在 Julia 中，[1, 2, 3, 4][[true, false]] 抛出 BoundsError。
      • 在 Julia 中，[1, 2, 3, 4][[true, false, true, false]] 产生 [1, 3]。

    • 与许多语言一样，Julia 并不总是允许对不同长度的向量进行操作，与 R 不同，R 中的向量只需要共享一个公共的索引范围。例如，c(1, 2, 3, 4) + c(1, 2) 是有效的 R，但等价的 [1, 2, 3, 4] + [1, 2] 在 Julia 中会抛出一个错误。

    • 在逗号不改变代码含义时，Julia 允许使用可选的尾随括号。在索引数组时，这可能在 R 用户间造成混淆。例如，R 中的 x[1,] 将返回矩阵的第一行；但是，在 Julia 中，引号被忽略，于是 x[1,] == x[1]，并且将返回第一个元素。要提取一行，请务必使用 :，如 x[1,:]。

    • Julia 的 map 首先接受函数，然后是该函数的参数，这与 R 中的 lapply(<structure>, function, ...) 不同。类似地，R 中的 apply(X, MARGIN, FUN, ...) 等价于 Julia 的 mapslices，其中函数是第一个参数。

    • R 中的多变量 apply，如 mapply(choose, 11:13, 1:3)，在 Julia 中可以编写成 broadcast(binomial, 11:13, 1:3)。等价地，Julia 提供了更短的点语法来向量化函数 binomial.(11:13, 1:3)。

    • Julia 使用 end 来表示条件块（如 if）、循环块（如 while/for）和函数的结束。为了代替单行 if ( cond ) statement，Julia 允许形式为 if cond; statement; end、cond && statement 和 !cond || statement 的语句。后两种语法中的赋值语句必须显式地包含在括号中，例如 cond && (x = value)，这是因为运算符的优先级。

    • 在 Julia 中，<-, <<- 和 -> 不是赋值运算符。

    • Julia 的 -> 创建一个匿名函数。

    • Julia 使用括号构造向量。Julia 的 [1, 2, 3] 等价于 R 的 c(1, 2, 3)。

    • Julia 的 * 运算符可以执行矩阵乘法，这与 R 不同。如果 A 和 B 都是矩阵，那么 A * B 在 Julia 中表示矩阵乘法，等价于 R 的 A %*% B。在 R 中，相同的符号将执行逐元素（Hadamard）乘积。要在 Julia 中使用逐元素乘法运算，你需要编写 A .* B。

    • Julia 使用 transpose 函数来执行矩阵转置，使用 ' 运算符或 adjoint 函数来执行共轭转置。因此，Julia 的 transpose(A) 等价于 R 的 t(A)。另外，Julia 中的非递归转置由 permutedims 函数提供。

    • Julia 在编写 if 语句或 for/while 循环时不需要括号：请使用 for i in [1, 2, 3] 代替 for (int i=1; i <= 3; i++)，以及 if i == 1 代替 if (i == 1)

    • Julia 不把数字 0 和 1 视为布尔值。在 Julia 中不能编写 if (1)，因为 if 语句只接受布尔值。相反，可以编写 if true、if Bool(1) 或 if 1==1。

    • Julia 不提供 nrow 和 ncol。相反，请使用 size(M, 1) 代替 nrow(M) 以及 size(M, 2) 代替 ncol(M)

    • Julia 仔细区分了标量、向量和矩阵。在 R 中，1 和 c(1) 是相同的。在 Julia 中，它们不能互换地使用。

    • Julia 的 diag 和 diagm 与 R 的不同。

    • Julia 赋值操作的左侧不能为函数调用的结果：你不能编写 diag(M) = fill(1, n)。

    • Julia 不鼓励使用函数填充主命名空间。Julia 的大多数统计功能都可在 JuliaStats 组织的包中找到。例如：

    • Julia 提供了元组和真正的哈希表，但不提供 R 风格的列表。在返回多个项时，通常应使用元组或具名元组：请使用 (1, 2) 或 (a=1, b=2) 代替 list(a = 1, b = 2)。

    • Julia 鼓励用户编写自己的类型，它比 R 中的 S3 或 S4 对象更容易使用。Julia 的多重派发系统意味着 table(x::TypeA) 和 table(x::TypeB) 类似于 R 的 table.TypeA(x) 和 table.TypeB(x)。

    • Julia 的值在向函数传递时不发生复制。如果某个函数修改了数组，这一修改对调用者是可见的。这与 R 非常不同，允许新函数更高效地操作大型数据结构。

    • 在 Julia 中，向量和矩阵使用 hcat、vcat 和 hvcat 拼接，而不是像在 R 中那样使用 c、rbind 和 cbind。

    • 在 Julia 中，像 a:b 这样的 range 不是 R 中的向量简写，而是一个专门的 AbstractRange 对象，该对象用于没有高内存开销地进行迭代。要将 range 转换为 vector，请使用 collect(a:b)。

    • Julia 的 max 和 min 分别等价于 R 中的 pmax 和 pmin，但两者的参数都需要具有相同的维度。虽然 maximum 和 minimum 代替了 R 中的 max 和 min，但它们之间有重大区别。

    • Julia 的 sum、prod、maximum 和 minimum 与它们在 R 中的对应物不同。它们都接受一个可选的关键字参数 dims，它表示执行操作的维度。例如，在 Julia 中令 A = [1 2; 3 4]，在 R 中令 B <- rbind(c(1,2),c(3,4)) 是与之相同的矩阵。然后 sum(A) 得到与 sum(B) 相同的结果，但 sum(A, dims=1) 是一个包含每一列总和的行向量，sum(A, dims=2) 是一个包含每一行总和的列向量。这与 R 的行为形成了对比，在 R 中，单独的 colSums(B) 和 rowSums(B) 提供了这些功能。如果 dims 关键字参数是向量，则它指定执行求和的所有维度，并同时保持待求和数组的维数，例如 sum(A, dims=(1,2)) == hcat(10)。应该注意的是，没有针对第二个参数的错误检查。

    • Julia 具有一些可以改变其参数的函数。例如，它具有 sort 和 sort!。

    • 在 R 中，高性能需要向量化。在 Julia 中，这几乎恰恰相反：性能最高的代码通常通过去向量化的循环来实现。

    • Julia 是立即求值的，不支持 R 风格的惰性求值。对于大多数用户来说，这意味着很少有未引用的表达式或列名。

    • Julia 不支持 NULL 类型。最接近的等价物是 nothing，但它的行为类似于标量值而不是列表。请使用 x === nothing 代替 is.null(x)。

    • 在 Julia 中，缺失值由 missing 表示，而不是由 NA 表示。请使用 ismissing(x)（或者在向量上使用逐元素操作 ismissing.(x)）代替 isna(x)。通常使用 skipmissing 代替 na.rm=TRUE（尽管在某些特定情况下函数接受 skipmissing 参数）。

    • Julia 缺少 R 中的 assign 或 get 的等价物。

    • 在 Julia 中，return 不需要括号。

    • 在 R 中，删除不需要的值的惯用方法是使用逻辑索引，如表达式 x[x>3] 或语句 x = x[x>3] 来 in-place 修改 x。相比之下，Julia 提供了更高阶的函数 filter 和 filter!，允许用户编写 filter(z->z>3, x) 和 filter!(z->z>3, x) 来代替相应直译 x[x.>3] 和 x = x[x.>3]。使用 filter! 可以减少临时数组的使用。

    与 Python 的显著差异

    • Julia 的 for, if, while 等语句块都以 end 关键字结束。代码的缩进不像在 Python 中那样重要。Julia 也没有 pass 关键字。

    • Julia 中的字符串使用双引号构造，如 "text"，也可以使用三引号构造多行字符串。而在 Python 中可以使用单引号（'text'）或者双引号（"text"）。单引号在 Julia 中用来表示单个字符，例如 'c'。

    • 在 Julia 中字符串的拼接使用 *，而不是像 Python 一样使用 +。类似的，字符串重复多次 Julia 使用 ^ 而不是 *。Julia 也不支持隐式的字符串拼接，例如 Python 中的 'ab' 'cd' == 'abcd'。

    • Python 列表——灵活但缓慢——对应于 Julia 的 Vector{Any} 类型或更一般的 Vector{T}，其中 T 是一些非具体元素类型。 “快”的数组，如 NumPy 数组，它们就地存储元素（即，dtype 是 np.float64、[('f1', np.uint64), ('f2', np.int32)]， 等）可以用 Array{T} 表示，其中 T 是一个具体的、不可变的元素类型。 这包括内置类型，如 Float64、Int32、Int64，也包括更复杂的类型，如 Tuple{UInt64,Float64} 和许多用户定义的类型。

    • 在 Julia 中，数组、字符串等的索引从 1 开始，而不是从 0 开始。

    • Julia 里的切片包含最后一个元素。Julia 里的 a[2:3] 等同于 Python 中的 a[1:3]。

    • Unlike Python, Julia allows AbstractArrays with arbitrary indexes. Python's special interpretation of negative indexing, a[-1] and a[-2], should be written a[end] and a[end-1] in Julia.

    • Julia 的索引必须写全。Python 中的 x[1:] 等价于 Julia 中的 x[2:end]。

    • In Julia, : before any object creates a Symbol or quotes an expression; so, x[:5] is same as x[5]. If you want to get the first n elements of an array, then use range indexing.

    • Julia 的范围语法为 x[start:step:stop]，而 Python 的格式为 x[start:(stop+1):step]。

    因此 Python 中的 x[0:10:2] 等价于 Julia 里的 x[1:2:10]。类似的 Python 中的反转数组 x[::-1] 等价于 Julia 中的 x[end:-1:1]。

    • In Julia, ranges can be constructed independently as start:step:stop, the same syntax it uses in array-indexing. The range function is also supported.

    • 在 Julia 中队一个矩阵取索引 X[[1,2], [1,3]] 返回一个子矩阵，它包含了第一和第二行与第一和第三列的交集。 在 Python 中 X[[1,2], [1,3]] 返回一个向量，它包含索引 [1,1] 和 [2,3] 的值。Julia 中的 X[[1,2], [1,3]] 等价于 Python 中的 X[np.ix_([0,1],[0,2])]。Python 中的 X[[1,2], [1,3]] 等价于 Julia 中的 X[[CartesianIndex(1,1), CartesianIndex(2,3)]]。

    • Julia 没有用来续行的语法：如果在行的末尾，到目前为止的输入是一个完整的表达式，则认为其已经结束；否则，认为输入继续。强制表达式继续的一种方式是将其包含在括号中。

    • 默认情况下，Julia 数组是列优先（Fortran 排序），而 NumPy 数组是行优先（C 排序）。为了在循环数组时获得最佳性能，Julia 中的循环顺序应相对于 NumPy 颠倒（请参阅性能提示的相关部分）。

    • Julia 的更新运算符（例如 +=，-=，···）是非原位操作（not in-place），而 Numpy 的是。这意味着 A = [1, 1]; B = A; B += [3, 3] 不会改变 A 中的值，而将名称 B 重新绑定到右侧表达式 B = B + 3 的结果，这是一个新的数组。对于 in-place 操作，使用 B .+= 3（另请参阅 dot operators）、显式的循环或者 InplaceOps.jl。

    • Julia 的函数在调用时，每次都对默认参数重新求值，不像 Python 只在函数定义时对默认参数求一次值。 举例来说：Julia 的函数 f(x=rand()) = x 在无参数调用时（f()），每次都会返回不同的随机数。 另一方面，函数 g(x=[1,2]) = push!(x,3) 无参数调用时 g()，永远返回 [1,2,3]。

    • 在 Julia 中，必须使用关键字来传递关键字参数，这与 Python 中通常可以按位置传递它们不同。尝试按位置传递关键字参数会改变方法签名，从而导致 MethodError 或调用错误的方法。

    • 在 Julia 中，% 是余数运算符，而在 Python 中是模运算符。

    （译注：二者在参数有负数时有区别）

    • 在 Julia 中，常用的整数类型 Int 对应机器的整数类型，Int32 或 Int64。不像 Python 中的整数 int 是任意精度的。这意味着 Julia 中默认的整数类型会溢出，因此 2^64 == 0。如果你要表示一个大数，请选择一个合适的类型。如：Int128、任意精度的 BigInt 或者浮点类型 Flost64。

    • Julia 中虚数单位 sqrt(-1) 是 im，而不是 Python 中的 j。

    • Julia 中指数是 ^，而不是 Python 中的 **。

    • Julia 使用 Nothing 类型的实例 nothing 代表空值（null），而不是 Python 中 NoneType 类的 None。

    • 在 Julia 中，标准的运算符作用在矩阵上就得到矩阵操作，不像 Python 标准运算符默认是逐元素操作。当 A 和 B 都是矩阵时，A * B 在 Julia 中代表着矩阵乘法，而不是 Python 中的逐元素相乘。即：Julia 中的 A * B 等同于 Python 的 A @ B；Python 中的 A * B 等同于 Julia 中的 A .* B。

    • Julia 中的伴随操作符 ' 返回向量的转置（一种行向量的懒惰表示法）。Python 中对向量执行 .T 返回它本身（没有效果）。

    • In Julia, a function may contain multiple concrete implementations (called methods), which are selected via multiple dispatch based on the types of all arguments to the call, as compared to functions in Python, which have a single implementation and no polymorphism (as opposed to Python method calls which use a different syntax and allows dispatch on the receiver of the method).

    • Julia 没有类（class），取而代替的是结构体（structures），可以是可变的或不可变的，它们只包含数据而不包含方法。

    • 在 Python 中调用类实例的方法 (x = MyClass(*args); x.f(y)) 对应于 Julia 中的函数调用，例如 x = MyType(args...); f(x, y)。 总的来说，多重派发比 Python 类系统更灵活和强大。

    • Julia 的结构体有且只能有一个抽象超类型（abstract supertype），而 Python 的类可以纪成一个或多个、抽象或具体的超类（superclasses）。

    • 逻辑 Julia 程序结构（包和模块）独立于文件结构（include 用于附加文件），而 Python 代码结构由目录（包）和文件（模块）定义。

    • Julia 中的三元运算符 x > 0 ? 1 : -1 对应于 Python 中的条件表达式 1 if x > 0 else -1。

    • Julia 中以 @ 开头的符号是宏（macro），而 Python 中是装饰器（decorator）。

    • Julia 的异常处理使用 try — catch — finally，而不是 Python 的 try — except — finally。与 Python 不同的是，因为性能的原因，Julia 不推荐在正常流程中使用异常处理。 (compared with Python, Julia is faster at ordinary control flow but slower at exception-catching).

    • Julia 的循环很快，所以没必要手动向量化（vectorized）。

    • 小心 Julia 中的非常量全局变量，尤其它出现在循环中时。因为你在 Julia 中可以写出贴近硬件的代码，这时使用全局变量的影响非常大（参见性能建议）

    • In Julia, rounding and truncation are explicit. Python's int(3.7) should be floor(Int, 3.7) or Int(floor(3.7)) and is distinguished from round(Int, 3.7). floor(x) and round(x) on their own return an integer value of the same type as x rather than always returning Int.

    • In Julia, parsing is explicit. Python's float("3.7") would be parse(Float64, "3.7") in Julia.

    • Python 中大多数的值都能用在逻辑运算中。例如：if "a" 永真，if "" 恒假。在 Julia 中你只能使用布尔类型的值，或者显示的将其他值转为布尔类型，否则就会抛出异常。例如当你想测试字符串是否为空是，请使用 if !isempty("")。

    • 在 Julia 中大多数代码块都会引入新的本地作用域（local scope）。例如：循环和异常处理的 try — catch — finally。注意：列表推断（comprehensions）与生成器在 Julia 和 Python 中都会引入新的作用域；而 if 分支则都不会引入。

    与 C/C++ 的显著差异

    • Julia 的数组由方括号索引，方括号中可以包含不止一个维度 A[i,j]。这样的语法不仅仅是像 C/C++ 中那样对指针或者地址引用的语法糖，参见关于数组构造的语法的 Julia 文档。

    • 在 Julia 中，数组、字符串等的索引从 1 开始，而不是从 0 开始。

    • Julia 的数组在赋值给另一个变量时不发生复制。执行 A = B 后，改变 B 中元素也会修改 A。像 += 这样的更新运算符不会以 in-place 的方式执行，而是相当于 A = A + B，将左侧绑定到右侧表达式的计算结果上。

    • Julia 的数组是列优先的（Fortran 顺序），而 C/C++ 的数组默认是行优先的。要使数组上的循环性能最优，在 Julia 中循环的顺序应该与 C/C++ 相反（参见 性能建议）。

    • Julia 的值在赋值或向函数传递时不发生复制。如果某个函数修改了数组，这一修改对调用者是可见的。

    • 在 Julia 中，空格是有意义的，这与 C/C++ 不同，所以向 Julia 程序中添加或删除空格时必须谨慎。

    • 在 Julia 中，没有小数点的数值字面量（如 42）生成有符号整数，类型为 Int，但如果字面量太长，超过了机器字长，则会被自动提升为容量更大的类型，例如 Int64（如果 Int 是 Int32）、Int128，或者任意精度的 BigInt 类型。不存在诸如 L, LL, U, UL, ULL 这样的数值字面量后缀指示无符号和/或有符号与无符号。十进制字面量始终是有符号的，十六进制字面量（像 C/C++ 一样由 0x 开头）是无符号的。另外，十六进制字面量与 C/C++/Java 不同，也与 Julia 中的十进制字面量不同，它们的类型取决于字面量的长度，包括开头的 0。例如，0x0 和 0x00 的类型是 UInt8，0x000 和 0x0000 的类型是 UInt16。同理，字面量的长度在 5-8 之间，类型为 UInt32；在 9-16 之间，类型为 UInt64；在 17-32 之间，类型为 UInt128。当定义十六进制掩码时，就需要将这一问题考虑在内，比如 ~0xf == 0xf0 与 ~0x000f == 0xfff0 完全不同。64 位 Float64 和 32 位 Float32 的字面量分别表示为 1.0 和 1.0f0。浮点字面量在无法被精确表示时舍入（且不会提升为 BigFloat 类型）。浮点字面量在行为上与 C/C++ 更接近。八进制（前缀为 0o）和二进制（前缀为 0b）也被视为无符号的。

    • 在 Julia 中，当两个操作数都是整数类型时，除法运算符 / 返回一个浮点数。 要执行整数除法，请使用 div 或 ÷。

    • 使用浮点类型索引数组在 Julia 中通常是错误的。 C 表达式 a[i / 2] 的 Julia 等价写法是 a[i ÷ 2 + 1]，其中 i 是整数类型。

    • 字符串字面量可用 " 或 """ 分隔，用 """ 分隔的字面量可以包含 " 字符而无需像 "\"" 这样来引用它。字符串字面量可以包含插入其中的其他变量或表达式，由 $variablename 或 $(expression) 表示，它在该函数所处的上下文中计算变量名或表达式。

    • // 表示 Rational 数，而非单行注释（其在 Julia 中是 #）

    • #= 表示多行注释的开头，=# 结束之。

    • Julia 中的函数返回其最后一个表达式或 return 关键字的值。可以从函数中返回多个值并将其作为元组赋值，如 (a, b) = myfunction() 或 a, b = myfunction()，而不必像在 C/C++ 中那样必须传递指向值的指针（即 a = myfunction(&b)）。

    • Julia 不要求使用分号来结束语句。表达式的结果不会自动打印（除了在交互式提示符中，即 REPL），且代码行不需要以分号结尾。println 或 @printf 可用于打印特定输出。在 REPL 中，; 可用于抑制输出。; 在 [ ] 中也有不同的含义，需要注意。; 可用于在单行中分隔表达式，但在许多情况下不是绝对必要的，更经常是为了可读性。

    • 在 Julia 中，运算符 ⊻（xor）执行按位 XOR 操作，即 C/C++ 中的 ^。此外，按位运算符不具有与 C/C++ 相同的优先级，所以可能需要括号。

    • Julia 的 ^ 是取幂（pow），而非 C/C++ 中的按位 XOR（在 Julia 中请使用 ⊻ 或 xor）

    • Julia 有两个右移运算符，>> 和 >>>。 >> 执行算术移位，>>> 始终执行逻辑移位，这与 C/C++ 不同，其中 >> 的含义取决于被移位的值的类型。

    • Julia 的 -> 创建一个匿名函数，它并不通过指针访问成员。

    • Julia 在编写 if 语句或 for/while 循环时不需要括号：请使用 for i in [1, 2, 3] 代替 for (int i=1; i <= 3; i++)，以及 if i == 1 代替 if (i == 1)

    • Julia 不把数字 0 和 1 视为布尔值。在 Julia 中不能编写 if (1)，因为 if 语句只接受布尔值。相反，可以编写 if true、if Bool(1) 或 if 1==1。

    • Julia 使用 end 来表示条件块（如 if）、循环块（如 while/for）和函数的结束。为了代替单行 if ( cond ) statement，Julia 允许形式为 if cond; statement; end、cond && statement 和 !cond || statement 的语句。后两种语法中的赋值语句必须显式地包含在括号中，例如 cond && (x = value)，这是因为运算符的优先级。

    • Julia 没有用来续行的语法：如果在行的末尾，到目前为止的输入是一个完整的表达式，则认为其已经结束；否则，认为输入继续。强制表达式继续的一种方式是将其包含在括号中。

    • Julia 宏对已解析的表达式进行操作，而非程序的文本，这允许它们执行复杂的 Julia 代码转换。宏名称以 @ 字符开头，具有类似函数的语法 @mymacro(arg1, arg2, arg3) 和类似语句的语法 @mymacro arg1 arg2 arg3。两种形式的语法可以相互转换；如果宏出现在另一个表达式中，则类似函数的形式尤其有用，并且它通常是最清晰的。类似语句的形式通常用于标注块，如在分布式 for 结构中：@distributed for i in 1:n; #= body =#; end。如果宏结构的结尾不那么清晰，请使用类似函数的形式。

    • Julia 有一个枚举类型，使用宏 @enum(name, value1, value2, ...) 来表示，例如：@enum(Fruit, banana=1, apple, pear)。

    • 按照惯例，修改其参数的函数在名称的末尾有个 !，例如 push!。

    • 在 C++ 中，默认情况下，你具有静态分派，即为了支持动态派发，你需要将函数标注为 virtual 函数。另一方面，Julia 中的每个方法都是「virtual」（尽管它更通用，因为方法是在每个参数类型上派发的，而不仅仅是 this，并且使用的是最具体的声明规则）。

    Julia ⇔ C/C++: Namespaces

    • C/C++ namespaces correspond roughly to Julia modules.
    • There are no private globals or fields in Julia. Everything is publicly accessible through fully qualified paths (or relative paths, if desired).
    • using MyNamespace::myfun (C++) corresponds roughly to import MyModule: myfun (Julia).
    • using namespace MyNamespace (C++) corresponds roughly to using MyModule (Julia)
      • In Julia, only exported symbols are made available to the calling module.
      • In C++, only elements found in the included (public) header files are made available.
    • Caveat: import/using keywords (Julia) also load modules (see below).
    • Caveat: import/using (Julia) works only at the global scope level (modules)
      • In C++, using namespace X works within arbitrary scopes (ex: function scope).

    Julia ⇔ C/C++: Module loading

    • When you think of a C/C++ "library", you are likely looking for a Julia "package".
      • Caveat: C/C++ libraries often house multiple "software modules" whereas Julia "packages" typically house one.
      • Reminder: Julia modules are global scopes (not necessarily "software modules").
    • Instead of build/make scripts, Julia uses "Project Environments" (sometimes called either "Project" or "Environment").
      • Build scripts are only needed for more complex applications (like those needing to compile or download C/C++ executables).
      • To develop application or project in Julia, you can initialize its root directory as a "Project Environment", and house application-specific code/packages there. This provides good control over project dependencies, and future reproducibility.
      • Available packages are added to a "Project Environment" with the Pkg.add() function or Pkg REPL mode. (This does not load said package, however).
      • The list of available packages (direct dependencies) for a "Project Environment" are saved in its Project.toml file.
      • The full dependency information for a "Project Environment" is auto-generated & saved in its Manifest.toml file by Pkg.resolve().
    • Packages ("software modules") available to the "Project Environment" are loaded with import or using.
      • In C/C++, you #include <moduleheader> to get object/function declarations, and link in libraries when you build the executable.
      • In Julia, calling using/import again just brings the existing module into scope, but does not load it again (similar to adding the non-standard #pragma once to C/C++).
    • Directory-based package repositories (Julia) can be made available by adding repository paths to the Base.LOAD_PATH array.
      • Packages from directory-based repositories do not require the Pkg.add() tool prior to being loaded with import or using. They are simply available to the project.
      • Directory-based package repositories are the quickest solution to developping local libraries of "software modules".

    Julia ⇔ C/C++: Assembling modules

    • In C/C++, .c/.cpp files are compiled & added to a library with build/make scripts.
      • In Julia, import [PkgName]/using [PkgName] statements load [PkgName].jl located in a package's [PkgName]/src/ subdirectory.
      • In turn, [PkgName].jl typically loads associated source files with calls to include "[someotherfile].jl".
    • include "./path/to/somefile.jl" (Julia) is very similar to #include "./path/to/somefile.jl" (C/C++).
      • However include "..." (Julia) is not used to include header files (not required).
      • Do not use include "..." (Julia) to load code from other "software modules" (use import/using instead).
      • include "path/to/some/module.jl" (Julia) would instantiate multiple versions of the same code in different modules (creating distinct types (etc.) with the same names).
      • include "somefile.jl" is typically used to assemble multiple files within the same Julia package ("software module"). It is therefore relatively straightforward to ensure file are included only once (No #ifdef confusion).

    Julia ⇔ C/C++: Module interface

    • C++ exposes interfaces using "public" .h/.hpp files whereas Julia modules mark specific symbols that are intended for their users as publicor exported.
      • Often, Julia modules simply add functionality by generating new "methods" to existing functions (ex: Base.push!).
      • Developers of Julia packages therefore cannot rely on header files for interface documentation.
      • Interfaces for Julia packages are typically described using docstrings, README.md, static web pages, ...
    • Some developers choose not to export all symbols required to use their package/module.
      • Users might be expected to access these components by qualifying functions/structs/... with the package/module name (ex: MyModule.run_this_task(...)).

    Julia ⇔ C/C++: Quick reference

    Software ConceptJuliaC/C++
    unnamed scopebegin ... end{ ... }
    function scopefunction x() ... endint x() { ... }
    global scopemodule MyMod ... endnamespace MyNS { ... }
    software moduleA Julia "package".h/.hpp files<br>+compiled somelib.a
    assembling<br>software modulesSomePkg.jl: ...<br>import("subfile1.jl")<br>import("subfile2.jl")<br>...$(AR) *.o &rArr; somelib.a
    import<br>software moduleimport SomePkg#include <somelib><br>+link in somelib.a
    module libraryLOAD_PATH[], *Git repository,<br>**custom package registrymore .h/.hpp files<br>+bigger compiled somebiglib.a

    * The Julia package manager supports registering multiple packages from a single Git repository.<br> * This allows users to house a library of related packages in a single repository.<br> ** Julia registries are primarily designed to provide versioning \& distribution of packages.<br> ** Custom package registries can be used to create a type of module library.

    与 Common Lisp 的显著差异

    • Julia 默认使用 1 开始的数组索引，它也能处理任意的索引顺序。

    • 函数和变量共用一个命名空间（"Lisp-1"）。

    • For performance, Julia prefers that operations have type stability. Where Common Lisp abstracts away from the underlying machine operations, Julia cleaves closer to them. For example:

      • Integer division using / always returns a floating-point result, even if the computation is exact.
        • // always returns a rational result
        • ÷ always returns a (truncated) integer result
      • Bignums are supported, but conversion is not automatic; ordinary integers overflow.
      • Complex numbers are supported, but to get complex results, you need complex inputs.
      • There are multiple Complex and Rational types, with different component types.

    • 典型的使用 Julia 进行原型开发时，也会对镜像进行连续的修改，Revise.jl 包提供了这个功能。

    • 对于性能，Julia 更喜欢操作具有 类型稳定性。 Common Lisp 从底层机器操作中抽象出来，而 Julia 则更接近它们。 例如：

      • 使用 / 的整数除法总是返回浮点结果，即使计算是精确的。
        • // 总是返回一个有理数结果
        • ÷ 总是返回一个（被截断的）整数结果
      • Julia 支持大整数，但不会自动转换。默认的整数类型会溢出。
      • 支持复数，但要获得复数结果，你需要复数输入。
      • 有多种 Complex 和 Rational 类型，具有不同的组成类型。

    • 模块（名称空间）可以是分层的。import 和 using 有着双重角色：他们加载代码并让代码在命名空间中可用。import 用于仅有模块名是可用的情况，大致等价于 ASDF:LOAD-OP。槽名（Slot name）不需要单独导出。全局变量不能从模块的外部赋值，除了 eval(mod, :(var = val)) 这个例外情况。

    • 宏以 @ 开头，并没有像 Common Lisp 那样无缝地集成到语言中；因此在 Julia 中，宏的使用不像在 Common Lisp 中那样广泛。Julia 支持宏的一种卫生（hygiene）形式。因为不同的表层语法，Julia 中没有 COMMON-LISP:&BODY 的等价形式。

    • 所有的函数都是通用的并且使用多重分派。函数的参数列表也无需遵循一样的模板，这让我们有了一个强大的范式：do。可选参数与关键字参数的处理方式不同。方法的歧义没有像在 Common Lisp 对象系统中那样得到解决，因此需要为交集定义更具体的方法。

    • 符号不属于任何包，它本身也不包含任何值。M.var 会对 M 模块里的  var 符号求值。

    • Julia 完全支持函数式编程风格，包括闭包等特性。但这并不是 Julia 的惯用风格。修改捕获变量时需要一些额外的变通以便提高性能。

    diff --git a/dev/manual/parallel-computing/index.html b/dev/manual/parallel-computing/index.html index 0651cb0c..0cc9c0cf 100644 --- a/dev/manual/parallel-computing/index.html +++ b/dev/manual/parallel-computing/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    并行计算

    Julia 支持这四类并发和并行编程：

    1. 异步“任务”或协程：

      Julia Tasks 允许暂停和恢复 I/O、事件处理、生产者-消费者进程和类似模式的计算。 Tasks 可以通过 wait 和 fetch 等操作进行同步，并通过 Channel 进行通信。 虽然严格来说不是并行计算，但 Julia 允许在多个线程上调度 Task。

    2. 多线程：

      Julia 的多线程提供了在多个线程、CPU 内核或共享内存上同时调度任务的能力。 这通常是在个人 PC 或单个大型多核服务器上获得并行性的最简单方法。 Julia 的多线程是可组合的。当一个多线程函数调用另一个多线程函数时，Julia 将在可用资源上全局调度所有线程，而不会超额使用。

    3. 分布式计算:

      分布式计算运行多个具有独立内存空间的 Julia 进程。 这些可以在同一台计算机或多台计算机上。 Distributed 标准库提供了远程执行 Julia 函数的能力。 使用这个基本构建块，可以构建许多不同类型的分布式计算抽象。 像 DistributedArrays.jl 这样的包就是这种抽象的一个示例。 另一方面，像 MPI.jl 和 Elemental.jl 这样的包提供对现有 MPI 生态库的访问。

    4. GPU 计算:

      Julia GPU 编译器提供了在 GPU 上本地运行 Julia 代码的能力。 有一个针对 GPU 的丰富的 Julia 软件包生态系统。 JuliaGPU.org 网站提供了功能列表、支持的 GPU、相关包和文档。

    +
    Repository

    并行计算

    Julia 支持这四类并发和并行编程：

    1. 异步“任务”或协程：

      Julia Tasks 允许暂停和恢复 I/O、事件处理、生产者-消费者进程和类似模式的计算。 Tasks 可以通过 wait 和 fetch 等操作进行同步，并通过 Channel 进行通信。 虽然严格来说不是并行计算，但 Julia 允许在多个线程上调度 Task。

    2. 多线程：

      Julia 的多线程提供了在多个线程、CPU 内核或共享内存上同时调度任务的能力。 这通常是在个人 PC 或单个大型多核服务器上获得并行性的最简单方法。 Julia 的多线程是可组合的。当一个多线程函数调用另一个多线程函数时，Julia 将在可用资源上全局调度所有线程，而不会超额使用。

    3. 分布式计算:

      分布式计算运行多个具有独立内存空间的 Julia 进程。 这些可以在同一台计算机或多台计算机上。 Distributed 标准库提供了远程执行 Julia 函数的能力。 使用这个基本构建块，可以构建许多不同类型的分布式计算抽象。 像 DistributedArrays.jl 这样的包就是这种抽象的一个示例。 另一方面，像 MPI.jl 和 Elemental.jl 这样的包提供对现有 MPI 生态库的访问。

    4. GPU 计算:

      Julia GPU 编译器提供了在 GPU 上本地运行 Julia 代码的能力。 有一个针对 GPU 的丰富的 Julia 软件包生态系统。 JuliaGPU.org 网站提供了功能列表、支持的 GPU、相关包和文档。

    diff --git a/dev/manual/performance-tips/index.html b/dev/manual/performance-tips/index.html index 0f6a6962..e1983e0b 100644 --- a/dev/manual/performance-tips/index.html +++ b/dev/manual/performance-tips/index.html @@ -577,4 +577,4 @@ x -> x * r end return f -end

    The let block creates a new variable r whose scope is only the inner function. The second technique recovers full language performance in the presence of captured variables. Note that this is a rapidly evolving aspect of the compiler, and it is likely that future releases will not require this degree of programmer annotation to attain performance. In the mean time, some user-contributed packages like FastClosures automate the insertion of let statements as in abmult3.

    Multithreading and linear algebra

    This section applies to multithreaded Julia code which, in each thread, performs linear algebra operations. Indeed, these linear algebra operations involve BLAS / LAPACK calls, which are themselves multithreaded. In this case, one must ensure that cores aren't oversubscribed due to the two different types of multithreading.

    Julia compiles and uses its own copy of OpenBLAS for linear algebra, whose number of threads is controlled by the environment variable OPENBLAS_NUM_THREADS. It can either be set as a command line option when launching Julia, or modified during the Julia session with BLAS.set_num_threads(N) (the submodule BLAS is exported by using LinearAlgebra). Its current value can be accessed with BLAS.get_num_threads().

    When the user does not specify anything, Julia tries to choose a reasonable value for the number of OpenBLAS threads (e.g. based on the platform, the Julia version, etc.). However, it is generally recommended to check and set the value manually. The OpenBLAS behavior is as follows:

    When you start Julia in multithreaded mode with JULIA_NUM_THREADS=X, it is generally recommended to set OPENBLAS_NUM_THREADS=1. Given the behavior described above, increasing the number of BLAS threads to N>1 can very easily lead to worse performance, in particular when N<<X. However this is just a rule of thumb, and the best way to set each number of threads is to experiment on your specific application.

    Alternative linear algebra backends

    As an alternative to OpenBLAS, there exist several other backends that can help with linear algebra performance. Prominent examples include MKL.jl and AppleAccelerate.jl.

    These are external packages, so we will not discuss them in detail here. Please refer to their respective documentations (especially because they have different behaviors than OpenBLAS with respect to multithreading).

    +end

    The let block creates a new variable r whose scope is only the inner function. The second technique recovers full language performance in the presence of captured variables. Note that this is a rapidly evolving aspect of the compiler, and it is likely that future releases will not require this degree of programmer annotation to attain performance. In the mean time, some user-contributed packages like FastClosures automate the insertion of let statements as in abmult3.

    Multithreading and linear algebra

    This section applies to multithreaded Julia code which, in each thread, performs linear algebra operations. Indeed, these linear algebra operations involve BLAS / LAPACK calls, which are themselves multithreaded. In this case, one must ensure that cores aren't oversubscribed due to the two different types of multithreading.

    Julia compiles and uses its own copy of OpenBLAS for linear algebra, whose number of threads is controlled by the environment variable OPENBLAS_NUM_THREADS. It can either be set as a command line option when launching Julia, or modified during the Julia session with BLAS.set_num_threads(N) (the submodule BLAS is exported by using LinearAlgebra). Its current value can be accessed with BLAS.get_num_threads().

    When the user does not specify anything, Julia tries to choose a reasonable value for the number of OpenBLAS threads (e.g. based on the platform, the Julia version, etc.). However, it is generally recommended to check and set the value manually. The OpenBLAS behavior is as follows:

    When you start Julia in multithreaded mode with JULIA_NUM_THREADS=X, it is generally recommended to set OPENBLAS_NUM_THREADS=1. Given the behavior described above, increasing the number of BLAS threads to N>1 can very easily lead to worse performance, in particular when N<<X. However this is just a rule of thumb, and the best way to set each number of threads is to experiment on your specific application.

    Alternative linear algebra backends

    As an alternative to OpenBLAS, there exist several other backends that can help with linear algebra performance. Prominent examples include MKL.jl and AppleAccelerate.jl.

    These are external packages, so we will not discuss them in detail here. Please refer to their respective documentations (especially because they have different behaviors than OpenBLAS with respect to multithreading).

    diff --git a/dev/manual/profile/index.html b/dev/manual/profile/index.html index b3576da4..ca8daa4a 100644 --- a/dev/manual/profile/index.html +++ b/dev/manual/profile/index.html @@ -70,4 +70,4 @@ Profile.init(n = 10^7, delay = 0.01)

    n 是能够存储的指令指针总数，默认值为 10^6。如果通常的回溯是 20 个指令指针，那么可以收集 50000 次回溯，这意味着统计不确定性少于 1%。这对于大多数应用来说可能已经足够了。

    因此，你更可能需要修改 delay，它以秒为单位，设置在快照之间 Julia 用于执行所请求计算的时长。长时间运行的工作可能不需要经常回溯。默认设置为 delay = 0.001。当然，你可以减少和增加 delay；但是，一旦 delay 接近执行一次回溯所需的时间（在作者的笔记本上约为 30 微妙），性能分析的开销就会增加。

    内存分配分析

    减少内存分配是提高性能的最常用技术之一。 Julia provides several tools measure this:

    @time

    The total amount of allocation can be measured with @time, @allocated and @allocations, and specific lines triggering allocation can often be inferred from profiling via the cost of garbage collection that these lines incur. However, sometimes it is more efficient to directly measure the amount of memory allocated by each line of code.

    GC Logging

    While @time logs high-level stats about memory usage and garbage collection over the course of evaluating an expression, it can be useful to log each garbage collection event, to get an intuitive sense of how often the garbage collector is running, how long it's running each time, and how much garbage it collects each time. This can be enabled with GC.enable_logging(true), which causes Julia to log to stderr every time a garbage collection happens.

    Allocation Profiler

    Julia 1.8

    This functionality requires at least Julia 1.8.

    The allocation profiler records the stack trace, type, and size of each allocation while it is running. It can be invoked with Profile.Allocs.@profile.

    This information about the allocations is returned as an array of Alloc objects, wrapped in an AllocResults object. The best way to visualize these is currently with the PProf.jl and ProfileCanvas.jl packages, which can visualize the call stacks which are making the most allocations.

    The allocation profiler does have significant overhead, so a sample_rate argument can be passed to speed it up by making it skip some allocations. Passing sample_rate=1.0 will make it record everything (which is slow); sample_rate=0.1 will record only 10% of the allocations (faster), etc.

    Note

    The current implementation of the Allocations Profiler does not capture types for all allocations. Allocations for which the profiler could not capture the type are represented as having type Profile.Allocs.UnknownType.

    You can read more about the missing types and the plan to improve this, here: issue #43688.

    Line-by-Line Allocation Tracking

    An alternative way to measure allocations is to start Julia with the --track-allocation=<setting> command-line option, for which you can choose none (the default, do not measure allocation), user (measure memory allocation everywhere except Julia's core code), or all (measure memory allocation at each line of Julia code). Allocation gets measured for each line of compiled code. When you quit Julia, the cumulative results are written to text files with .mem appended after the file name, residing in the same directory as the source file. Each line lists the total number of bytes allocated. The Coverage package contains some elementary analysis tools, for example to sort the lines in order of number of bytes allocated.

    在解释结果时，有一些需要注意的细节。在 user 设定下，直接从 REPL 调用的任何函数的第一行都将会显示内存分配，这是由发生在 REPL 代码本身的事件造成的。更重要的是，JIT 编译也会添加内存分配计数，因为 Julia 的编译器大部分是用 Julia 编写的（并且编译通常需要内存分配）。建议的分析过程是先通过执行待分析的所有命令来强制编译，然后调用 Profile.clear_malloc_data() 来重置所有内存计数器。最后，执行所需的命令并退出 Julia 以触发 .mem 文件的生成。

    Note

    --track-allocation changes code generation to log the allocations, and so the allocations may be different than what happens without the option. We recommend using the allocation profiler instead.

    外部性能分析

    Julia 目前支持的外部性能分析工具有 Intel VTune、OProfile 和 perf。

    根据你所选择的工具，编译时请在 Make.user 中将 USE_INTEL_JITEVENTS、USE_OPROFILE_JITEVENTS 和 USE_PERF_JITEVENTS 设置为 1。多个上述编译标志是支持的。

    在运行 Julia 前，请将环境变量 ENABLE_JITPROFILING 设置为 1。

    现在，你可以通过多种方式使用这些工具！例如，可以使用 OProfile 来尝试做个简单的记录：

    >ENABLE_JITPROFILING=1 sudo operf -Vdebug ./julia test/fastmath.jl
 >opreport -l `which ./julia`

    或与 perf 类似：

    $ ENABLE_JITPROFILING=1 perf record -o /tmp/perf.data --call-graph dwarf -k 1 ./julia /test/fastmath.jl
 $ perf inject --jit --input /tmp/perf.data --output /tmp/perf-jit.data
-$ perf report --call-graph -G -i /tmp/perf-jit.data

    你可以测量关于程序的更多有趣数据，若要获得详尽的列表，请阅读 Linux perf 示例页面。

    请记住，perf 会为每次执行保存一个 perf.data 文件，即使对于小程序，它也可能变得非常大。此外，perf LLVM 模块会将调试对象保存在 ~/.debug/jit 中，记得经常清理该文件夹。

    +$ perf report --call-graph -G -i /tmp/perf-jit.data

    你可以测量关于程序的更多有趣数据，若要获得详尽的列表，请阅读 Linux perf 示例页面。

    请记住，perf 会为每次执行保存一个 perf.data 文件，即使对于小程序，它也可能变得非常大。此外，perf LLVM 模块会将调试对象保存在 ~/.debug/jit 中，记得经常清理该文件夹。

    diff --git a/dev/manual/running-external-programs/index.html b/dev/manual/running-external-programs/index.html index 6241659f..892b85d1 100644 --- a/dev/manual/running-external-programs/index.html +++ b/dev/manual/running-external-programs/index.html @@ -136,4 +136,4 @@ foo ever! julia> run(addenv(`sh -c "echo foo \$HOWLONG"`, "HOWLONG" => "ever!")); -foo ever! +foo ever! diff --git a/dev/manual/stacktraces/index.html b/dev/manual/stacktraces/index.html index d1942fb0..d01b8cfc 100644 --- a/dev/manual/stacktraces/index.html +++ b/dev/manual/stacktraces/index.html @@ -196,4 +196,4 @@ jl_apply_generic at gf.c:2167 julia> println("The top frame is from $(frame[1].func)!") -The top frame is from jl_apply_generic! +The top frame is from jl_apply_generic! diff --git a/dev/manual/strings/index.html b/dev/manual/strings/index.html index dfa9d012..2a2d65ea 100644 --- a/dev/manual/strings/index.html +++ b/dev/manual/strings/index.html @@ -436,4 +436,4 @@ 0xbf

    字符字面量也用到了相同的行为。

    对于小于 \u80 的代码，每个代码的 UTF-8 编码恰好只是由相应 \x 转义产生的单个字节，因此忽略两者的差别无伤大雅。然而，从 x80 到 \xff 的转义比起从 u80 到 \uff 的转义来，就有一个主要的差别：前者都只编码为一个字节，它没有形成任何有效 UTF-8 数据，除非它后面有非常特殊的连接字节；而后者则都代表 2 字节编码的 Unicode 代码。

    如果这些还是太难理解，试着读一下 "每个软件开发人员绝对必须知道的最基础 Unicode 和字符集知识"。它是一个优质的 Unicode 和 UTF-8 指南，或许能帮助解除一些这方面的疑惑。

    版本号字面量

    版本号很容易用 v"..." 形式的非标准字符串字面量表示。版本号字面量生成遵循语义版本规范的 VersionNumber 对象，因此由主、次、补丁号构成，后跟预发行 (pre-release) 和生成阿尔法数注释（build alpha-numeric）。例如，v"0.2.1-rc1+win64" 可分为主版本号 0，次版本号 2，补丁版本号 1，预发行版号 rc1，以及生成版本 win64。输入版本字面量时，除了主版本号以外所有内容都是可选的，因此 v"0.2" 等效于 v"0.2.0"（预发行号和生成注释为空），v"2" 等效于 v"2.0.0"，等等。

    VersionNumber 对象在轻松正确地比较两个（或更多）版本时非常有用。例如，常数 VERSION 把 Julia 的版本号保留为一个 VersionNumber 对象，因此可以像下面这样用简单的声明定义一些特定版本的行为：

    if v"0.2" <= VERSION < v"0.3-"
     # 针对 0.2 发行版系列做些事情
 end

    注意在上例中用到了非标准版本号 v"0.3-"，其中有尾随符 -：这个符号是 Julia 标准的扩展，它可以用来表明低于任何 0.3 发行版的版本，包括所有的预发行版。所以上例中代码只能在稳定版本 0.2 上运行，而不能在 v"0.3.0-rc1" 这样的版本上运行。为了支持非稳定（即预发行）的 0.2 版本，下限检查应像这样应该改为：v"0.2-" <= VERSION。

    另一个非标准版本规范扩展使得能够使用 + 来表示生成版本的上限，例如 VERSION > v"0.2-rc1+" 可以用来表示任意高于 0.2-rc1 和其任意生成版本的版本：它对 v"0.2-rc1+win64" 返回 false 而对 v"0.2-rc2" 返回 true。

    在比较中使用这样的特殊版本是个好办法（特别是，总是应该对高版本使用尾随 -，除非有好理由不这样），但它们不应该被用作任何内容的实际版本，因为它们在语义版本控制方案中无效。

    除了用于定义常数 VERSION，VersionNumber 对象在 Pkg 模块应用广泛，常用于指定软件包的版本及其依赖。

    原始字符串字面量

    无插值和非转义的原始字符串可用 raw"..." 形式的非标准字符串字面量表示。原始字符串字面量生成普通的 String 对象，它无需插值和非转义地包含和输入完全一样的封闭式内容。这对于包含其他语言中使用 " 或 \" 作为特殊字符的代码或标记的字符串很有用。

    例外的是，引号仍必须转义，例如 raw"\"" 等效于 "\""。为了能够表达所有字符串，反斜杠也必须转义，不过只是当它刚好出现在引号前面时。

    julia> println(raw"\\ \\\"")
-\\ \"

    请注意，前两个反斜杠在输出中逐字显示，这是因为它们不是在引号前面。然而，接下来的一个反斜杠字符转义了后面的一个反斜杠；又由于这些反斜杠出现在引号前面，最后一个反斜杠转义了一个引号。

    +\\ \"

    请注意，前两个反斜杠在输出中逐字显示，这是因为它们不是在引号前面。然而，接下来的一个反斜杠字符转义了后面的一个反斜杠；又由于这些反斜杠出现在引号前面，最后一个反斜杠转义了一个引号。

    diff --git a/dev/manual/style-guide/index.html b/dev/manual/style-guide/index.html index e15d1bce..7c5d4620 100644 --- a/dev/manual/style-guide/index.html +++ b/dev/manual/style-guide/index.html @@ -60,4 +60,4 @@ 1.0 julia> h(1) -2//1

    所以，可能时尽量使用 Int 字面量，对非整数字面量使用 Rational{Int}，这样可以让代码变得更容易使用。

    +2//1

    所以，可能时尽量使用 Int 字面量，对非整数字面量使用 Rational{Int}，这样可以让代码变得更容易使用。

    diff --git a/dev/manual/types/index.html b/dev/manual/types/index.html index 78504dff..fa84641d 100644 --- a/dev/manual/types/index.html +++ b/dev/manual/types/index.html @@ -454,4 +454,4 @@ "First" julia> firstlast(Val(false)) -"Last"

    为了保证 Julia 的一致性，调用处应当始终传递 Val 实例 而不是 类型，也就是使用 foo(Val(:bar)) 而不是 foo(Val{:bar})。

    值得注意的是，参数「值」类型非常容易被误用，包括 Val；在不适用的情形下，你很容易使代码性能变得更糟糕。特别是，你可能永远都不会想要写出如上所示的代码。有关 Val 的正确（和不正确）使用的更多信息，请阅读性能建议中更广泛的讨论。

    +"Last"

    为了保证 Julia 的一致性，调用处应当始终传递 Val 实例 而不是 类型，也就是使用 foo(Val(:bar)) 而不是 foo(Val{:bar})。

    值得注意的是，参数「值」类型非常容易被误用，包括 Val；在不适用的情形下，你很容易使代码性能变得更糟糕。特别是，你可能永远都不会想要写出如上所示的代码。有关 Val 的正确（和不正确）使用的更多信息，请阅读性能建议中更广泛的讨论。

    diff --git a/dev/manual/unicode-input/index.html b/dev/manual/unicode-input/index.html index 2f867e33..bf093447 100644 --- a/dev/manual/unicode-input/index.html +++ b/dev/manual/unicode-input/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    Unicode 输入表

    在 Julia REPL 或其它编辑器中，可以像输入 LaTeX 符号一样，用 tab 补全下表列出的 Unicode 字符。在 REPL 中，可以先按 ? 进入帮助模式，然后将 Unicode 字符复制粘贴进去，一般在文档开头就会写输入方式。

    Warning

    此表第二列可能会缺失一些字符，对某些字符的显示效果也可能会与在 Julia REPL 中不一致。如果发生了这种状况，强烈建议用户检查一下浏览器或 REPL 的字体设置，目前已知很多字体都有显示问题。

    Code point(s)Character(s)Tab completion sequence(s)Unicode name(s)
    U+000A1¡\exclamdownInverted Exclamation Mark
    U+000A3£\sterlingPound Sign
    U+000A5¥\yenYen Sign
    U+000A6¦\brokenbarBroken Bar / Broken Vertical Bar
    U+000A7§\SSection Sign
    U+000A9©\copyright, \:copyright:Copyright Sign
    U+000AAª\ordfeminineFeminine Ordinal Indicator
    U+000AC¬\negNot Sign
    U+000AE®\circledR, \:registered:Registered Sign / Registered Trade Mark Sign
    U+000AF¯\highminusMacron / Spacing Macron
    U+000B0°\degreeDegree Sign
    U+000B1±\pmPlus-Minus Sign / Plus-Or-Minus Sign
    U+000B2²\^2Superscript Two / Superscript Digit Two
    U+000B3³\^3Superscript Three / Superscript Digit Three
    U+000B6\PPilcrow Sign / Paragraph Sign
    U+000B7·\cdotpMiddle Dot
    U+000B9¹\^1Superscript One / Superscript Digit One
    U+000BAº\ordmasculineMasculine Ordinal Indicator
    U+000BC¼\1/4Vulgar Fraction One Quarter / Fraction One Quarter
    U+000BD½\1/2Vulgar Fraction One Half / Fraction One Half
    U+000BE¾\3/4Vulgar Fraction Three Quarters / Fraction Three Quarters
    U+000BF¿\questiondownInverted Question Mark
    U+000C5Å\AALatin Capital Letter A With Ring Above / Latin Capital Letter A Ring
    U+000C6Æ\AELatin Capital Letter Ae / Latin Capital Letter A E
    U+000D0Ð\DHLatin Capital Letter Eth
    U+000D7×\timesMultiplication Sign
    U+000D8Ø\OLatin Capital Letter O With Stroke / Latin Capital Letter O Slash
    U+000DEÞ\THLatin Capital Letter Thorn
    U+000DFß\ssLatin Small Letter Sharp S
    U+000E5å\aaLatin Small Letter A With Ring Above / Latin Small Letter A Ring
    U+000E6æ\aeLatin Small Letter Ae / Latin Small Letter A E
    U+000F0ð\eth, \dhLatin Small Letter Eth
    U+000F7÷\divDivision Sign
    U+000F8ø\oLatin Small Letter O With Stroke / Latin Small Letter O Slash
    U+000FEþ\thLatin Small Letter Thorn
    U+00110Đ\DJLatin Capital Letter D With Stroke / Latin Capital Letter D Bar
    U+00111đ\djLatin Small Letter D With Stroke / Latin Small Letter D Bar
    U+00127ħ\hbarLatin Small Letter H With Stroke / Latin Small Letter H Bar
    U+00131ı\imathLatin Small Letter Dotless I
    U+00141Ł\LLatin Capital Letter L With Stroke / Latin Capital Letter L Slash
    U+00142ł\lLatin Small Letter L With Stroke / Latin Small Letter L Slash
    U+0014AŊ\NGLatin Capital Letter Eng
    U+0014Bŋ\ngLatin Small Letter Eng
    U+00152Œ\OELatin Capital Ligature Oe / Latin Capital Letter O E
    U+00153œ\oeLatin Small Ligature Oe / Latin Small Letter O E
    U+00195ƕ\hvligLatin Small Letter Hv / Latin Small Letter H V
    U+0019Eƞ\nrlegLatin Small Letter N With Long Right Leg
    U+001B5Ƶ\ZbarLatin Capital Letter Z With Stroke / Latin Capital Letter Z Bar
    U+001C2ǂ\doublepipeLatin Letter Alveolar Click / Latin Letter Pipe Double Bar
    U+00237ȷ\jmathLatin Small Letter Dotless J
    U+00250ɐ\trnaLatin Small Letter Turned A
    U+00252ɒ\trnsaLatin Small Letter Turned Alpha / Latin Small Letter Turned Script A
    U+00254ɔ\openoLatin Small Letter Open O
    U+00256ɖ\rtldLatin Small Letter D With Tail / Latin Small Letter D Retroflex Hook
    U+00259ə\schwaLatin Small Letter Schwa
    U+00263ɣ\pgammaLatin Small Letter Gamma
    U+00264ɤ\pbgamLatin Small Letter Rams Horn / Latin Small Letter Baby Gamma
    U+00265ɥ\trnhLatin Small Letter Turned H
    U+0026Cɬ\btdlLatin Small Letter L With Belt / Latin Small Letter L Belt
    U+0026Dɭ\rtllLatin Small Letter L With Retroflex Hook / Latin Small Letter L Retroflex Hook
    U+0026Fɯ\trnmLatin Small Letter Turned M
    U+00270ɰ\trnmlrLatin Small Letter Turned M With Long Leg
    U+00271ɱ\ltlmrLatin Small Letter M With Hook / Latin Small Letter M Hook
    U+00272ɲ\ltlnLatin Small Letter N With Left Hook / Latin Small Letter N Hook
    U+00273ɳ\rtlnLatin Small Letter N With Retroflex Hook / Latin Small Letter N Retroflex Hook
    U+00277ɷ\clomegLatin Small Letter Closed Omega
    U+00278ɸ\ltphiLatin Small Letter Phi
    U+00279ɹ\trnrLatin Small Letter Turned R
    U+0027Aɺ\trnrlLatin Small Letter Turned R With Long Leg
    U+0027Bɻ\rttrnrLatin Small Letter Turned R With Hook / Latin Small Letter Turned R Hook
    U+0027Cɼ\rlLatin Small Letter R With Long Leg
    U+0027Dɽ\rtlrLatin Small Letter R With Tail / Latin Small Letter R Hook
    U+0027Eɾ\fhrLatin Small Letter R With Fishhook / Latin Small Letter Fishhook R
    U+00282ʂ\rtlsLatin Small Letter S With Hook / Latin Small Letter S Hook
    U+00283ʃ\eshLatin Small Letter Esh
    U+00287ʇ\trntLatin Small Letter Turned T
    U+00288ʈ\rtltLatin Small Letter T With Retroflex Hook / Latin Small Letter T Retroflex Hook
    U+0028Aʊ\pupsilLatin Small Letter Upsilon
    U+0028Bʋ\pscrvLatin Small Letter V With Hook / Latin Small Letter Script V
    U+0028Cʌ\invvLatin Small Letter Turned V
    U+0028Dʍ\invwLatin Small Letter Turned W
    U+0028Eʎ\trnyLatin Small Letter Turned Y
    U+00290ʐ\rtlzLatin Small Letter Z With Retroflex Hook / Latin Small Letter Z Retroflex Hook
    U+00292ʒ\yoghLatin Small Letter Ezh / Latin Small Letter Yogh
    U+00294ʔ\glstLatin Letter Glottal Stop
    U+00295ʕ\reglstLatin Letter Pharyngeal Voiced Fricative / Latin Letter Reversed Glottal Stop
    U+00296ʖ\inglstLatin Letter Inverted Glottal Stop
    U+0029Eʞ\turnkLatin Small Letter Turned K
    U+002A4ʤ\dyoghLatin Small Letter Dezh Digraph / Latin Small Letter D Yogh
    U+002A7ʧ\teshLatin Small Letter Tesh Digraph / Latin Small Letter T Esh
    U+002B0ʰ\^hModifier Letter Small H
    U+002B2ʲ\^jModifier Letter Small J
    U+002B3ʳ\^rModifier Letter Small R
    U+002B7ʷ\^wModifier Letter Small W
    U+002B8ʸ\^yModifier Letter Small Y
    U+002BCʼ\raspModifier Letter Apostrophe
    U+002C8ˈ\vertsModifier Letter Vertical Line
    U+002CCˌ\vertiModifier Letter Low Vertical Line
    U+002D0ː\lmrkModifier Letter Triangular Colon
    U+002D1ˑ\hlmrkModifier Letter Half Triangular Colon
    U+002D2˒\sbrhrModifier Letter Centred Right Half Ring / Modifier Letter Centered Right Half Ring
    U+002D3˓\sblhrModifier Letter Centred Left Half Ring / Modifier Letter Centered Left Half Ring
    U+002D4˔\raisModifier Letter Up Tack
    U+002D5˕\lowModifier Letter Down Tack
    U+002D8˘\uBreve / Spacing Breve
    U+002DC˜\tildelowSmall Tilde / Spacing Tilde
    U+002E1ˡ\^lModifier Letter Small L
    U+002E2ˢ\^sModifier Letter Small S
    U+002E3ˣ\^xModifier Letter Small X
    U+00300 ̀ \graveCombining Grave Accent / Non-Spacing Grave
    U+00301 ́ \acuteCombining Acute Accent / Non-Spacing Acute
    U+00302 ̂ \hatCombining Circumflex Accent / Non-Spacing Circumflex
    U+00303 ̃ \tildeCombining Tilde / Non-Spacing Tilde
    U+00304 ̄ \barCombining Macron / Non-Spacing Macron
    U+00305 ̅ \overbarCombining Overline / Non-Spacing Overscore
    U+00306 ̆ \breveCombining Breve / Non-Spacing Breve
    U+00307 ̇ \dotCombining Dot Above / Non-Spacing Dot Above
    U+00308 ̈ \ddotCombining Diaeresis / Non-Spacing Diaeresis
    U+00309 ̉ \ovhookCombining Hook Above / Non-Spacing Hook Above
    U+0030A ̊ \ocircCombining Ring Above / Non-Spacing Ring Above
    U+0030B ̋ \HCombining Double Acute Accent / Non-Spacing Double Acute
    U+0030C ̌ \checkCombining Caron / Non-Spacing Hacek
    U+00310 ̐ \candraCombining Candrabindu / Non-Spacing Candrabindu
    U+00312 ̒ \oturnedcommaCombining Turned Comma Above / Non-Spacing Turned Comma Above
    U+00315 ̕ \ocommatoprightCombining Comma Above Right / Non-Spacing Comma Above Right
    U+0031A ̚ \droangCombining Left Angle Above / Non-Spacing Left Angle Above
    U+00321 ̡ \palhCombining Palatalized Hook Below / Non-Spacing Palatalized Hook Below
    U+00322 ̢ \rhCombining Retroflex Hook Below / Non-Spacing Retroflex Hook Below
    U+00327 ̧ \cCombining Cedilla / Non-Spacing Cedilla
    U+00328 ̨ \kCombining Ogonek / Non-Spacing Ogonek
    U+0032A ̪ \sbbrgCombining Bridge Below / Non-Spacing Bridge Below
    U+00330 ̰ \wideutildeCombining Tilde Below / Non-Spacing Tilde Below
    U+00332 ̲ \underbarCombining Low Line / Non-Spacing Underscore
    U+00336 ̶ \strike, \soutCombining Long Stroke Overlay / Non-Spacing Long Bar Overlay
    U+00338 ̸ \notCombining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0034D ͍ \underleftrightarrowCombining Left Right Arrow Below
    U+00391Α\AlphaGreek Capital Letter Alpha
    U+00392Β\BetaGreek Capital Letter Beta
    U+00393Γ\GammaGreek Capital Letter Gamma
    U+00394Δ\DeltaGreek Capital Letter Delta
    U+00395Ε\EpsilonGreek Capital Letter Epsilon
    U+00396Ζ\ZetaGreek Capital Letter Zeta
    U+00397Η\EtaGreek Capital Letter Eta
    U+00398Θ\ThetaGreek Capital Letter Theta
    U+00399Ι\IotaGreek Capital Letter Iota
    U+0039AΚ\KappaGreek Capital Letter Kappa
    U+0039BΛ\LambdaGreek Capital Letter Lamda / Greek Capital Letter Lambda
    U+0039CΜ\upMuGreek Capital Letter Mu
    U+0039DΝ\upNuGreek Capital Letter Nu
    U+0039EΞ\XiGreek Capital Letter Xi
    U+0039FΟ\upOmicronGreek Capital Letter Omicron
    U+003A0Π\PiGreek Capital Letter Pi
    U+003A1Ρ\RhoGreek Capital Letter Rho
    U+003A3Σ\SigmaGreek Capital Letter Sigma
    U+003A4Τ\TauGreek Capital Letter Tau
    U+003A5Υ\UpsilonGreek Capital Letter Upsilon
    U+003A6Φ\PhiGreek Capital Letter Phi
    U+003A7Χ\ChiGreek Capital Letter Chi
    U+003A8Ψ\PsiGreek Capital Letter Psi
    U+003A9Ω\OmegaGreek Capital Letter Omega
    U+003B1α\alphaGreek Small Letter Alpha
    U+003B2β\betaGreek Small Letter Beta
    U+003B3γ\gammaGreek Small Letter Gamma
    U+003B4δ\deltaGreek Small Letter Delta
    U+003B5ε\upepsilon, \varepsilonGreek Small Letter Epsilon
    U+003B6ζ\zetaGreek Small Letter Zeta
    U+003B7η\etaGreek Small Letter Eta
    U+003B8θ\thetaGreek Small Letter Theta
    U+003B9ι\iotaGreek Small Letter Iota
    U+003BAκ\kappaGreek Small Letter Kappa
    U+003BBλ\lambdaGreek Small Letter Lamda / Greek Small Letter Lambda
    U+003BCμ\muGreek Small Letter Mu
    U+003BDν\nuGreek Small Letter Nu
    U+003BEξ\xiGreek Small Letter Xi
    U+003BFο\upomicronGreek Small Letter Omicron
    U+003C0π\piGreek Small Letter Pi
    U+003C1ρ\rhoGreek Small Letter Rho
    U+003C2ς\varsigmaGreek Small Letter Final Sigma
    U+003C3σ\sigmaGreek Small Letter Sigma
    U+003C4τ\tauGreek Small Letter Tau
    U+003C5υ\upsilonGreek Small Letter Upsilon
    U+003C6φ\varphiGreek Small Letter Phi
    U+003C7χ\chiGreek Small Letter Chi
    U+003C8ψ\psiGreek Small Letter Psi
    U+003C9ω\omegaGreek Small Letter Omega
    U+003D0ϐ\upvarbetaGreek Beta Symbol / Greek Small Letter Curled Beta
    U+003D1ϑ\varthetaGreek Theta Symbol / Greek Small Letter Script Theta
    U+003D5ϕ\phiGreek Phi Symbol / Greek Small Letter Script Phi
    U+003D6ϖ\varpiGreek Pi Symbol / Greek Small Letter Omega Pi
    U+003D8Ϙ\upoldKoppaGreek Letter Archaic Koppa
    U+003D9ϙ\upoldkoppaGreek Small Letter Archaic Koppa
    U+003DAϚ\StigmaGreek Letter Stigma / Greek Capital Letter Stigma
    U+003DBϛ\upstigmaGreek Small Letter Stigma
    U+003DCϜ\DigammaGreek Letter Digamma / Greek Capital Letter Digamma
    U+003DDϝ\digammaGreek Small Letter Digamma
    U+003DEϞ\KoppaGreek Letter Koppa / Greek Capital Letter Koppa
    U+003DFϟ\upkoppaGreek Small Letter Koppa
    U+003E0Ϡ\SampiGreek Letter Sampi / Greek Capital Letter Sampi
    U+003E1ϡ\upsampiGreek Small Letter Sampi
    U+003F0ϰ\varkappaGreek Kappa Symbol / Greek Small Letter Script Kappa
    U+003F1ϱ\varrhoGreek Rho Symbol / Greek Small Letter Tailed Rho
    U+003F4ϴ\varThetaGreek Capital Theta Symbol
    U+003F5ϵ\epsilonGreek Lunate Epsilon Symbol
    U+003F6϶\backepsilonGreek Reversed Lunate Epsilon Symbol
    U+01D2Cᴬ\^AModifier Letter Capital A
    U+01D2Eᴮ\^BModifier Letter Capital B
    U+01D30ᴰ\^DModifier Letter Capital D
    U+01D31ᴱ\^EModifier Letter Capital E
    U+01D33ᴳ\^GModifier Letter Capital G
    U+01D34ᴴ\^HModifier Letter Capital H
    U+01D35ᴵ\^IModifier Letter Capital I
    U+01D36ᴶ\^JModifier Letter Capital J
    U+01D37ᴷ\^KModifier Letter Capital K
    U+01D38ᴸ\^LModifier Letter Capital L
    U+01D39ᴹ\^MModifier Letter Capital M
    U+01D3Aᴺ\^NModifier Letter Capital N
    U+01D3Cᴼ\^OModifier Letter Capital O
    U+01D3Eᴾ\^PModifier Letter Capital P
    U+01D3Fᴿ\^RModifier Letter Capital R
    U+01D40ᵀ\^TModifier Letter Capital T
    U+01D41ᵁ\^UModifier Letter Capital U
    U+01D42ᵂ\^WModifier Letter Capital W
    U+01D43ᵃ\^aModifier Letter Small A
    U+01D45ᵅ\^alphaModifier Letter Small Alpha
    U+01D47ᵇ\^bModifier Letter Small B
    U+01D48ᵈ\^dModifier Letter Small D
    U+01D49ᵉ\^eModifier Letter Small E
    U+01D4Bᵋ\^epsilonModifier Letter Small Open E
    U+01D4Dᵍ\^gModifier Letter Small G
    U+01D4Fᵏ\^kModifier Letter Small K
    U+01D50ᵐ\^mModifier Letter Small M
    U+01D52ᵒ\^oModifier Letter Small O
    U+01D56ᵖ\^pModifier Letter Small P
    U+01D57ᵗ\^tModifier Letter Small T
    U+01D58ᵘ\^uModifier Letter Small U
    U+01D5Bᵛ\^vModifier Letter Small V
    U+01D5Dᵝ\^betaModifier Letter Small Beta
    U+01D5Eᵞ\^gammaModifier Letter Small Greek Gamma
    U+01D5Fᵟ\^deltaModifier Letter Small Delta
    U+01D60ᵠ\^phiModifier Letter Small Greek Phi
    U+01D61ᵡ\^chiModifier Letter Small Chi
    U+01D62ᵢ\_iLatin Subscript Small Letter I
    U+01D63ᵣ\_rLatin Subscript Small Letter R
    U+01D64ᵤ\_uLatin Subscript Small Letter U
    U+01D65ᵥ\_vLatin Subscript Small Letter V
    U+01D66ᵦ\_betaGreek Subscript Small Letter Beta
    U+01D67ᵧ\_gammaGreek Subscript Small Letter Gamma
    U+01D68ᵨ\_rhoGreek Subscript Small Letter Rho
    U+01D69ᵩ\_phiGreek Subscript Small Letter Phi
    U+01D6Aᵪ\_chiGreek Subscript Small Letter Chi
    U+01D9Cᶜ\^cModifier Letter Small C
    U+01DA0ᶠ\^fModifier Letter Small F
    U+01DA5ᶥ\^iotaModifier Letter Small Iota
    U+01DB2ᶲ\^ltphiModifier Letter Small Phi
    U+01DBBᶻ\^zModifier Letter Small Z
    U+01DBFᶿ\^thetaModifier Letter Small Theta
    U+02002 \enspaceEn Space
    U+02003 \quadEm Space
    U+02005 \thickspaceFour-Per-Em Space
    U+02009 \thinspaceThin Space
    U+0200A \hspaceHair Space
    U+02013–\endashEn Dash
    U+02014—\emdashEm Dash
    U+02016‖\VertDouble Vertical Line / Double Vertical Bar
    U+02018‘\lqLeft Single Quotation Mark / Single Turned Comma Quotation Mark
    U+02019’\rqRight Single Quotation Mark / Single Comma Quotation Mark
    U+0201B‛\reaposSingle High-Reversed-9 Quotation Mark / Single Reversed Comma Quotation Mark
    U+0201C“\ldqLeft Double Quotation Mark / Double Turned Comma Quotation Mark
    U+0201D”\rdqRight Double Quotation Mark / Double Comma Quotation Mark
    U+02020†\daggerDagger
    U+02021‡\ddaggerDouble Dagger
    U+02022•\bulletBullet
    U+02026…\dots, \ldotsHorizontal Ellipsis
    U+02030‰\perthousandPer Mille Sign
    U+02031‱\pertenthousandPer Ten Thousand Sign
    U+02032′\primePrime
    U+02033″\pprimeDouble Prime
    U+02034‴\ppprimeTriple Prime
    U+02035‵\backprimeReversed Prime
    U+02036‶\backpprimeReversed Double Prime
    U+02037‷\backppprimeReversed Triple Prime
    U+02039‹\guilsinglleftSingle Left-Pointing Angle Quotation Mark / Left Pointing Single Guillemet
    U+0203A›\guilsinglrightSingle Right-Pointing Angle Quotation Mark / Right Pointing Single Guillemet
    U+0203C‼\:bangbang:Double Exclamation Mark
    U+02040⁀\tieconcatCharacter Tie
    U+02049⁉\:interrobang:Exclamation Question Mark
    U+02057⁗\pppprimeQuadruple Prime
    U+0205D⁝\tricolonTricolon
    U+02060⁠\nolinebreakWord Joiner
    U+02070⁰\^0Superscript Zero / Superscript Digit Zero
    U+02071ⁱ\^iSuperscript Latin Small Letter I
    U+02074⁴\^4Superscript Four / Superscript Digit Four
    U+02075⁵\^5Superscript Five / Superscript Digit Five
    U+02076⁶\^6Superscript Six / Superscript Digit Six
    U+02077⁷\^7Superscript Seven / Superscript Digit Seven
    U+02078⁸\^8Superscript Eight / Superscript Digit Eight
    U+02079⁹\^9Superscript Nine / Superscript Digit Nine
    U+0207A⁺\^+Superscript Plus Sign
    U+0207B⁻\^-Superscript Minus / Superscript Hyphen-Minus
    U+0207C⁼\^=Superscript Equals Sign
    U+0207D⁽\^(Superscript Left Parenthesis / Superscript Opening Parenthesis
    U+0207E⁾\^)Superscript Right Parenthesis / Superscript Closing Parenthesis
    U+0207Fⁿ\^nSuperscript Latin Small Letter N
    U+02080₀\_0Subscript Zero / Subscript Digit Zero
    U+02081₁\_1Subscript One / Subscript Digit One
    U+02082₂\_2Subscript Two / Subscript Digit Two
    U+02083₃\_3Subscript Three / Subscript Digit Three
    U+02084₄\_4Subscript Four / Subscript Digit Four
    U+02085₅\_5Subscript Five / Subscript Digit Five
    U+02086₆\_6Subscript Six / Subscript Digit Six
    U+02087₇\_7Subscript Seven / Subscript Digit Seven
    U+02088₈\_8Subscript Eight / Subscript Digit Eight
    U+02089₉\_9Subscript Nine / Subscript Digit Nine
    U+0208A₊\_+Subscript Plus Sign
    U+0208B₋\_-Subscript Minus / Subscript Hyphen-Minus
    U+0208C₌\_=Subscript Equals Sign
    U+0208D₍\_(Subscript Left Parenthesis / Subscript Opening Parenthesis
    U+0208E₎\_)Subscript Right Parenthesis / Subscript Closing Parenthesis
    U+02090ₐ\_aLatin Subscript Small Letter A
    U+02091ₑ\_eLatin Subscript Small Letter E
    U+02092ₒ\_oLatin Subscript Small Letter O
    U+02093ₓ\_xLatin Subscript Small Letter X
    U+02094ₔ\_schwaLatin Subscript Small Letter Schwa
    U+02095ₕ\_hLatin Subscript Small Letter H
    U+02096ₖ\_kLatin Subscript Small Letter K
    U+02097ₗ\_lLatin Subscript Small Letter L
    U+02098ₘ\_mLatin Subscript Small Letter M
    U+02099ₙ\_nLatin Subscript Small Letter N
    U+0209Aₚ\_pLatin Subscript Small Letter P
    U+0209Bₛ\_sLatin Subscript Small Letter S
    U+0209Cₜ\_tLatin Subscript Small Letter T
    U+020A7₧\pesPeseta Sign
    U+020AC€\euroEuro Sign
    U+020D0 ⃐ \leftharpoonaccentCombining Left Harpoon Above / Non-Spacing Left Harpoon Above
    U+020D1 ⃑ \rightharpoonaccentCombining Right Harpoon Above / Non-Spacing Right Harpoon Above
    U+020D2 ⃒ \vertoverlayCombining Long Vertical Line Overlay / Non-Spacing Long Vertical Bar Overlay
    U+020D6 ⃖ \overleftarrowCombining Left Arrow Above / Non-Spacing Left Arrow Above
    U+020D7 ⃗ \vecCombining Right Arrow Above / Non-Spacing Right Arrow Above
    U+020DB ⃛ \dddotCombining Three Dots Above / Non-Spacing Three Dots Above
    U+020DC ⃜ \ddddotCombining Four Dots Above / Non-Spacing Four Dots Above
    U+020DD ⃝ \enclosecircleCombining Enclosing Circle / Enclosing Circle
    U+020DE ⃞ \enclosesquareCombining Enclosing Square / Enclosing Square
    U+020DF ⃟ \enclosediamondCombining Enclosing Diamond / Enclosing Diamond
    U+020E1 ⃡ \overleftrightarrowCombining Left Right Arrow Above / Non-Spacing Left Right Arrow Above
    U+020E4 ⃤ \enclosetriangleCombining Enclosing Upward Pointing Triangle
    U+020E7 ⃧ \annuityCombining Annuity Symbol
    U+020E8 ⃨ \threeunderdotCombining Triple Underdot
    U+020E9 ⃩ \widebridgeaboveCombining Wide Bridge Above
    U+020EC ⃬ \underrightharpoondownCombining Rightwards Harpoon With Barb Downwards
    U+020ED ⃭ \underleftharpoondownCombining Leftwards Harpoon With Barb Downwards
    U+020EE ⃮ \underleftarrowCombining Left Arrow Below
    U+020EF ⃯ \underrightarrowCombining Right Arrow Below
    U+020F0 ⃰ \asteraccentCombining Asterisk Above
    U+02102ℂ\bbCDouble-Struck Capital C / Double-Struck C
    U+02107ℇ\eulermascheroniEuler Constant / Eulers
    U+0210Aℊ\scrgScript Small G
    U+0210Bℋ\scrHScript Capital H / Script H
    U+0210Cℌ\frakHBlack-Letter Capital H / Black-Letter H
    U+0210Dℍ\bbHDouble-Struck Capital H / Double-Struck H
    U+0210Eℎ\ith, \planckPlanck Constant
    U+0210Fℏ\hslashPlanck Constant Over Two Pi / Planck Constant Over 2 Pi
    U+02110ℐ\scrIScript Capital I / Script I
    U+02111ℑ\Im, \frakIBlack-Letter Capital I / Black-Letter I
    U+02112ℒ\scrLScript Capital L / Script L
    U+02113ℓ\ellScript Small L
    U+02115ℕ\bbNDouble-Struck Capital N / Double-Struck N
    U+02116№\numeroNumero Sign / Numero
    U+02118℘\wpScript Capital P / Script P
    U+02119ℙ\bbPDouble-Struck Capital P / Double-Struck P
    U+0211Aℚ\bbQDouble-Struck Capital Q / Double-Struck Q
    U+0211Bℛ\scrRScript Capital R / Script R
    U+0211Cℜ\Re, \frakRBlack-Letter Capital R / Black-Letter R
    U+0211Dℝ\bbRDouble-Struck Capital R / Double-Struck R
    U+0211E℞\xratPrescription Take
    U+02122™\trademark, \:tm:Trade Mark Sign / Trademark
    U+02124ℤ\bbZDouble-Struck Capital Z / Double-Struck Z
    U+02126Ω\ohmOhm Sign / Ohm
    U+02127℧\mhoInverted Ohm Sign / Mho
    U+02128ℨ\frakZBlack-Letter Capital Z / Black-Letter Z
    U+02129℩\turnediotaTurned Greek Small Letter Iota
    U+0212BÅ\AngstromAngstrom Sign / Angstrom Unit
    U+0212Cℬ\scrBScript Capital B / Script B
    U+0212Dℭ\frakCBlack-Letter Capital C / Black-Letter C
    U+0212Fℯ\scre, \eulerScript Small E
    U+02130ℰ\scrEScript Capital E / Script E
    U+02131ℱ\scrFScript Capital F / Script F
    U+02132Ⅎ\FinvTurned Capital F / Turned F
    U+02133ℳ\scrMScript Capital M / Script M
    U+02134ℴ\scroScript Small O
    U+02135ℵ\alephAlef Symbol / First Transfinite Cardinal
    U+02136ℶ\bethBet Symbol / Second Transfinite Cardinal
    U+02137ℷ\gimelGimel Symbol / Third Transfinite Cardinal
    U+02138ℸ\dalethDalet Symbol / Fourth Transfinite Cardinal
    U+02139ℹ\:information_source:Information Source
    U+0213Cℼ\bbpiDouble-Struck Small Pi
    U+0213Dℽ\bbgammaDouble-Struck Small Gamma
    U+0213Eℾ\bbGammaDouble-Struck Capital Gamma
    U+0213Fℿ\bbPiDouble-Struck Capital Pi
    U+02140⅀\bbsumDouble-Struck N-Ary Summation
    U+02141⅁\GameTurned Sans-Serif Capital G
    U+02142⅂\sansLturnedTurned Sans-Serif Capital L
    U+02143⅃\sansLmirroredReversed Sans-Serif Capital L
    U+02144⅄\YupTurned Sans-Serif Capital Y
    U+02145ⅅ\bbiDDouble-Struck Italic Capital D
    U+02146ⅆ\bbidDouble-Struck Italic Small D
    U+02147ⅇ\bbieDouble-Struck Italic Small E
    U+02148ⅈ\bbiiDouble-Struck Italic Small I
    U+02149ⅉ\bbijDouble-Struck Italic Small J
    U+0214A⅊\PropertyLineProperty Line
    U+0214B⅋\upandTurned Ampersand
    U+02150⅐\1/7Vulgar Fraction One Seventh
    U+02151⅑\1/9Vulgar Fraction One Ninth
    U+02152⅒\1/10Vulgar Fraction One Tenth
    U+02153⅓\1/3Vulgar Fraction One Third / Fraction One Third
    U+02154⅔\2/3Vulgar Fraction Two Thirds / Fraction Two Thirds
    U+02155⅕\1/5Vulgar Fraction One Fifth / Fraction One Fifth
    U+02156⅖\2/5Vulgar Fraction Two Fifths / Fraction Two Fifths
    U+02157⅗\3/5Vulgar Fraction Three Fifths / Fraction Three Fifths
    U+02158⅘\4/5Vulgar Fraction Four Fifths / Fraction Four Fifths
    U+02159⅙\1/6Vulgar Fraction One Sixth / Fraction One Sixth
    U+0215A⅚\5/6Vulgar Fraction Five Sixths / Fraction Five Sixths
    U+0215B⅛\1/8Vulgar Fraction One Eighth / Fraction One Eighth
    U+0215C⅜\3/8Vulgar Fraction Three Eighths / Fraction Three Eighths
    U+0215D⅝\5/8Vulgar Fraction Five Eighths / Fraction Five Eighths
    U+0215E⅞\7/8Vulgar Fraction Seven Eighths / Fraction Seven Eighths
    U+0215F⅟\1/Fraction Numerator One
    U+02189↉\0/3Vulgar Fraction Zero Thirds
    U+02190←\leftarrowLeftwards Arrow / Left Arrow
    U+02191↑\uparrowUpwards Arrow / Up Arrow
    U+02192→\to, \rightarrowRightwards Arrow / Right Arrow
    U+02193↓\downarrowDownwards Arrow / Down Arrow
    U+02194↔\leftrightarrow, \:left_right_arrow:Left Right Arrow
    U+02195↕\updownarrow, \:arrow_up_down:Up Down Arrow
    U+02196↖\nwarrow, \:arrow_upper_left:North West Arrow / Upper Left Arrow
    U+02197↗\nearrow, \:arrow_upper_right:North East Arrow / Upper Right Arrow
    U+02198↘\searrow, \:arrow_lower_right:South East Arrow / Lower Right Arrow
    U+02199↙\swarrow, \:arrow_lower_left:South West Arrow / Lower Left Arrow
    U+0219A↚\nleftarrowLeftwards Arrow With Stroke / Left Arrow With Stroke
    U+0219B↛\nrightarrowRightwards Arrow With Stroke / Right Arrow With Stroke
    U+0219C↜\leftwavearrowLeftwards Wave Arrow / Left Wave Arrow
    U+0219D↝\rightwavearrowRightwards Wave Arrow / Right Wave Arrow
    U+0219E↞\twoheadleftarrowLeftwards Two Headed Arrow / Left Two Headed Arrow
    U+0219F↟\twoheaduparrowUpwards Two Headed Arrow / Up Two Headed Arrow
    U+021A0↠\twoheadrightarrowRightwards Two Headed Arrow / Right Two Headed Arrow
    U+021A1↡\twoheaddownarrowDownwards Two Headed Arrow / Down Two Headed Arrow
    U+021A2↢\leftarrowtailLeftwards Arrow With Tail / Left Arrow With Tail
    U+021A3↣\rightarrowtailRightwards Arrow With Tail / Right Arrow With Tail
    U+021A4↤\mapsfromLeftwards Arrow From Bar / Left Arrow From Bar
    U+021A5↥\mapsupUpwards Arrow From Bar / Up Arrow From Bar
    U+021A6↦\mapstoRightwards Arrow From Bar / Right Arrow From Bar
    U+021A7↧\mapsdownDownwards Arrow From Bar / Down Arrow From Bar
    U+021A8↨\updownarrowbarUp Down Arrow With Base
    U+021A9↩\hookleftarrow, \:leftwards_arrow_with_hook:Leftwards Arrow With Hook / Left Arrow With Hook
    U+021AA↪\hookrightarrow, \:arrow_right_hook:Rightwards Arrow With Hook / Right Arrow With Hook
    U+021AB↫\looparrowleftLeftwards Arrow With Loop / Left Arrow With Loop
    U+021AC↬\looparrowrightRightwards Arrow With Loop / Right Arrow With Loop
    U+021AD↭\leftrightsquigarrowLeft Right Wave Arrow
    U+021AE↮\nleftrightarrowLeft Right Arrow With Stroke
    U+021AF↯\downzigzagarrowDownwards Zigzag Arrow / Down Zigzag Arrow
    U+021B0↰\LshUpwards Arrow With Tip Leftwards / Up Arrow With Tip Left
    U+021B1↱\RshUpwards Arrow With Tip Rightwards / Up Arrow With Tip Right
    U+021B2↲\LdshDownwards Arrow With Tip Leftwards / Down Arrow With Tip Left
    U+021B3↳\RdshDownwards Arrow With Tip Rightwards / Down Arrow With Tip Right
    U+021B4↴\linefeedRightwards Arrow With Corner Downwards / Right Arrow With Corner Down
    U+021B5↵\carriagereturnDownwards Arrow With Corner Leftwards / Down Arrow With Corner Left
    U+021B6↶\curvearrowleftAnticlockwise Top Semicircle Arrow
    U+021B7↷\curvearrowrightClockwise Top Semicircle Arrow
    U+021B8↸\barovernorthwestarrowNorth West Arrow To Long Bar / Upper Left Arrow To Long Bar
    U+021B9↹\barleftarrowrightarrowbarLeftwards Arrow To Bar Over Rightwards Arrow To Bar / Left Arrow To Bar Over Right Arrow To Bar
    U+021BA↺\circlearrowleftAnticlockwise Open Circle Arrow
    U+021BB↻\circlearrowrightClockwise Open Circle Arrow
    U+021BC↼\leftharpoonupLeftwards Harpoon With Barb Upwards / Left Harpoon With Barb Up
    U+021BD↽\leftharpoondownLeftwards Harpoon With Barb Downwards / Left Harpoon With Barb Down
    U+021BE↾\upharpoonrightUpwards Harpoon With Barb Rightwards / Up Harpoon With Barb Right
    U+021BF↿\upharpoonleftUpwards Harpoon With Barb Leftwards / Up Harpoon With Barb Left
    U+021C0⇀\rightharpoonupRightwards Harpoon With Barb Upwards / Right Harpoon With Barb Up
    U+021C1⇁\rightharpoondownRightwards Harpoon With Barb Downwards / Right Harpoon With Barb Down
    U+021C2⇂\downharpoonrightDownwards Harpoon With Barb Rightwards / Down Harpoon With Barb Right
    U+021C3⇃\downharpoonleftDownwards Harpoon With Barb Leftwards / Down Harpoon With Barb Left
    U+021C4⇄\rightleftarrowsRightwards Arrow Over Leftwards Arrow / Right Arrow Over Left Arrow
    U+021C5⇅\dblarrowupdownUpwards Arrow Leftwards Of Downwards Arrow / Up Arrow Left Of Down Arrow
    U+021C6⇆\leftrightarrowsLeftwards Arrow Over Rightwards Arrow / Left Arrow Over Right Arrow
    U+021C7⇇\leftleftarrowsLeftwards Paired Arrows / Left Paired Arrows
    U+021C8⇈\upuparrowsUpwards Paired Arrows / Up Paired Arrows
    U+021C9⇉\rightrightarrowsRightwards Paired Arrows / Right Paired Arrows
    U+021CA⇊\downdownarrowsDownwards Paired Arrows / Down Paired Arrows
    U+021CB⇋\leftrightharpoonsLeftwards Harpoon Over Rightwards Harpoon / Left Harpoon Over Right Harpoon
    U+021CC⇌\rightleftharpoonsRightwards Harpoon Over Leftwards Harpoon / Right Harpoon Over Left Harpoon
    U+021CD⇍\nLeftarrowLeftwards Double Arrow With Stroke / Left Double Arrow With Stroke
    U+021CE⇎\nLeftrightarrowLeft Right Double Arrow With Stroke
    U+021CF⇏\nRightarrowRightwards Double Arrow With Stroke / Right Double Arrow With Stroke
    U+021D0⇐\LeftarrowLeftwards Double Arrow / Left Double Arrow
    U+021D1⇑\UparrowUpwards Double Arrow / Up Double Arrow
    U+021D2⇒\RightarrowRightwards Double Arrow / Right Double Arrow
    U+021D3⇓\DownarrowDownwards Double Arrow / Down Double Arrow
    U+021D4⇔\LeftrightarrowLeft Right Double Arrow
    U+021D5⇕\UpdownarrowUp Down Double Arrow
    U+021D6⇖\NwarrowNorth West Double Arrow / Upper Left Double Arrow
    U+021D7⇗\NearrowNorth East Double Arrow / Upper Right Double Arrow
    U+021D8⇘\SearrowSouth East Double Arrow / Lower Right Double Arrow
    U+021D9⇙\SwarrowSouth West Double Arrow / Lower Left Double Arrow
    U+021DA⇚\LleftarrowLeftwards Triple Arrow / Left Triple Arrow
    U+021DB⇛\RrightarrowRightwards Triple Arrow / Right Triple Arrow
    U+021DC⇜\leftsquigarrowLeftwards Squiggle Arrow / Left Squiggle Arrow
    U+021DD⇝\rightsquigarrowRightwards Squiggle Arrow / Right Squiggle Arrow
    U+021DE⇞\nHuparrowUpwards Arrow With Double Stroke / Up Arrow With Double Stroke
    U+021DF⇟\nHdownarrowDownwards Arrow With Double Stroke / Down Arrow With Double Stroke
    U+021E0⇠\leftdasharrowLeftwards Dashed Arrow / Left Dashed Arrow
    U+021E1⇡\updasharrowUpwards Dashed Arrow / Up Dashed Arrow
    U+021E2⇢\rightdasharrowRightwards Dashed Arrow / Right Dashed Arrow
    U+021E3⇣\downdasharrowDownwards Dashed Arrow / Down Dashed Arrow
    U+021E4⇤\barleftarrowLeftwards Arrow To Bar / Left Arrow To Bar
    U+021E5⇥\rightarrowbarRightwards Arrow To Bar / Right Arrow To Bar
    U+021E6⇦\leftwhitearrowLeftwards White Arrow / White Left Arrow
    U+021E7⇧\upwhitearrowUpwards White Arrow / White Up Arrow
    U+021E8⇨\rightwhitearrowRightwards White Arrow / White Right Arrow
    U+021E9⇩\downwhitearrowDownwards White Arrow / White Down Arrow
    U+021EA⇪\whitearrowupfrombarUpwards White Arrow From Bar / White Up Arrow From Bar
    U+021F4⇴\circleonrightarrowRight Arrow With Small Circle
    U+021F5⇵\DownArrowUpArrowDownwards Arrow Leftwards Of Upwards Arrow
    U+021F6⇶\rightthreearrowsThree Rightwards Arrows
    U+021F7⇷\nvleftarrowLeftwards Arrow With Vertical Stroke
    U+021F8⇸\nvrightarrowRightwards Arrow With Vertical Stroke
    U+021F9⇹\nvleftrightarrowLeft Right Arrow With Vertical Stroke
    U+021FA⇺\nVleftarrowLeftwards Arrow With Double Vertical Stroke
    U+021FB⇻\nVrightarrowRightwards Arrow With Double Vertical Stroke
    U+021FC⇼\nVleftrightarrowLeft Right Arrow With Double Vertical Stroke
    U+021FD⇽\leftarrowtriangleLeftwards Open-Headed Arrow
    U+021FE⇾\rightarrowtriangleRightwards Open-Headed Arrow
    U+021FF⇿\leftrightarrowtriangleLeft Right Open-Headed Arrow
    U+02200∀\forallFor All
    U+02201∁\complementComplement
    U+02202∂\partialPartial Differential
    U+02203∃\existsThere Exists
    U+02204∄\nexistsThere Does Not Exist
    U+02205∅\varnothing, \emptysetEmpty Set
    U+02206∆\incrementIncrement
    U+02207∇\del, \nablaNabla
    U+02208∈\inElement Of
    U+02209∉\notinNot An Element Of
    U+0220A∊\smallinSmall Element Of
    U+0220B∋\niContains As Member
    U+0220C∌\nniDoes Not Contain As Member
    U+0220D∍\smallniSmall Contains As Member
    U+0220E∎\QEDEnd Of Proof
    U+0220F∏\prodN-Ary Product
    U+02210∐\coprodN-Ary Coproduct
    U+02211∑\sumN-Ary Summation
    U+02212−\minusMinus Sign
    U+02213∓\mpMinus-Or-Plus Sign
    U+02214∔\dotplusDot Plus
    U+02216∖\setminusSet Minus
    U+02217∗\astAsterisk Operator
    U+02218∘\circRing Operator
    U+02219∙\vysmblkcircleBullet Operator
    U+0221A√\surd, \sqrtSquare Root
    U+0221B∛\cbrtCube Root
    U+0221C∜\fourthrootFourth Root
    U+0221D∝\proptoProportional To
    U+0221E∞\inftyInfinity
    U+0221F∟\rightangleRight Angle
    U+02220∠\angleAngle
    U+02221∡\measuredangleMeasured Angle
    U+02222∢\sphericalangleSpherical Angle
    U+02223∣\midDivides
    U+02224∤\nmidDoes Not Divide
    U+02225∥\parallelParallel To
    U+02226∦\nparallelNot Parallel To
    U+02227∧\wedgeLogical And
    U+02228∨\veeLogical Or
    U+02229∩\capIntersection
    U+0222A∪\cupUnion
    U+0222B∫\intIntegral
    U+0222C∬\iintDouble Integral
    U+0222D∭\iiintTriple Integral
    U+0222E∮\ointContour Integral
    U+0222F∯\oiintSurface Integral
    U+02230∰\oiiintVolume Integral
    U+02231∱\clwintegralClockwise Integral
    U+02232∲\varointclockwiseClockwise Contour Integral
    U+02233∳\ointctrclockwiseAnticlockwise Contour Integral
    U+02234∴\thereforeTherefore
    U+02235∵\becauseBecause
    U+02237∷\ColonProportion
    U+02238∸\dotminusDot Minus
    U+0223A∺\dotsminusdotsGeometric Proportion
    U+0223B∻\kernelcontractionHomothetic
    U+0223C∼\simTilde Operator
    U+0223D∽\backsimReversed Tilde
    U+0223E∾\lazysinvInverted Lazy S
    U+0223F∿\sinewaveSine Wave
    U+02240≀\wrWreath Product
    U+02241≁\nsimNot Tilde
    U+02242≂\eqsimMinus Tilde
    U+02242 + U+00338≂̸\neqsimMinus Tilde + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02243≃\simeqAsymptotically Equal To
    U+02244≄\nsimeNot Asymptotically Equal To
    U+02245≅\congApproximately Equal To
    U+02246≆\approxnotequalApproximately But Not Actually Equal To
    U+02247≇\ncongNeither Approximately Nor Actually Equal To
    U+02248≈\approxAlmost Equal To
    U+02249≉\napproxNot Almost Equal To
    U+0224A≊\approxeqAlmost Equal Or Equal To
    U+0224B≋\tildetrplTriple Tilde
    U+0224C≌\allequalAll Equal To
    U+0224D≍\asympEquivalent To
    U+0224E≎\BumpeqGeometrically Equivalent To
    U+0224E + U+00338≎̸\nBumpeqGeometrically Equivalent To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0224F≏\bumpeqDifference Between
    U+0224F + U+00338≏̸\nbumpeqDifference Between + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02250≐\doteqApproaches The Limit
    U+02251≑\DoteqGeometrically Equal To
    U+02252≒\fallingdotseqApproximately Equal To Or The Image Of
    U+02253≓\risingdotseqImage Of Or Approximately Equal To
    U+02254≔\coloneqColon Equals / Colon Equal
    U+02255≕\eqcolonEquals Colon / Equal Colon
    U+02256≖\eqcircRing In Equal To
    U+02257≗\circeqRing Equal To
    U+02258≘\arceqCorresponds To
    U+02259≙\wedgeqEstimates
    U+0225A≚\veeeqEquiangular To
    U+0225B≛\starequalStar Equals
    U+0225C≜\triangleqDelta Equal To
    U+0225D≝\eqdefEqual To By Definition
    U+0225E≞\measeqMeasured By
    U+0225F≟\questeqQuestioned Equal To
    U+02260≠\ne, \neqNot Equal To
    U+02261≡\equivIdentical To
    U+02262≢\nequivNot Identical To
    U+02263≣\EquivStrictly Equivalent To
    U+02264≤\le, \leqLess-Than Or Equal To / Less Than Or Equal To
    U+02265≥\ge, \geqGreater-Than Or Equal To / Greater Than Or Equal To
    U+02266≦\leqqLess-Than Over Equal To / Less Than Over Equal To
    U+02267≧\geqqGreater-Than Over Equal To / Greater Than Over Equal To
    U+02268≨\lneqqLess-Than But Not Equal To / Less Than But Not Equal To
    U+02268 + U+0FE00≨︀\lvertneqqLess-Than But Not Equal To / Less Than But Not Equal To + Variation Selector-1
    U+02269≩\gneqqGreater-Than But Not Equal To / Greater Than But Not Equal To
    U+02269 + U+0FE00≩︀\gvertneqqGreater-Than But Not Equal To / Greater Than But Not Equal To + Variation Selector-1
    U+0226A≪\llMuch Less-Than / Much Less Than
    U+0226A + U+00338≪̸\NotLessLessMuch Less-Than / Much Less Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0226B≫\ggMuch Greater-Than / Much Greater Than
    U+0226B + U+00338≫̸\NotGreaterGreaterMuch Greater-Than / Much Greater Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0226C≬\betweenBetween
    U+0226D≭\nasympNot Equivalent To
    U+0226E≮\nlessNot Less-Than / Not Less Than
    U+0226F≯\ngtrNot Greater-Than / Not Greater Than
    U+02270≰\nleqNeither Less-Than Nor Equal To / Neither Less Than Nor Equal To
    U+02271≱\ngeqNeither Greater-Than Nor Equal To / Neither Greater Than Nor Equal To
    U+02272≲\lesssimLess-Than Or Equivalent To / Less Than Or Equivalent To
    U+02273≳\gtrsimGreater-Than Or Equivalent To / Greater Than Or Equivalent To
    U+02274≴\nlesssimNeither Less-Than Nor Equivalent To / Neither Less Than Nor Equivalent To
    U+02275≵\ngtrsimNeither Greater-Than Nor Equivalent To / Neither Greater Than Nor Equivalent To
    U+02276≶\lessgtrLess-Than Or Greater-Than / Less Than Or Greater Than
    U+02277≷\gtrlessGreater-Than Or Less-Than / Greater Than Or Less Than
    U+02278≸\notlessgreaterNeither Less-Than Nor Greater-Than / Neither Less Than Nor Greater Than
    U+02279≹\notgreaterlessNeither Greater-Than Nor Less-Than / Neither Greater Than Nor Less Than
    U+0227A≺\precPrecedes
    U+0227B≻\succSucceeds
    U+0227C≼\preccurlyeqPrecedes Or Equal To
    U+0227D≽\succcurlyeqSucceeds Or Equal To
    U+0227E≾\precsimPrecedes Or Equivalent To
    U+0227E + U+00338≾̸\nprecsimPrecedes Or Equivalent To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0227F≿\succsimSucceeds Or Equivalent To
    U+0227F + U+00338≿̸\nsuccsimSucceeds Or Equivalent To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02280⊀\nprecDoes Not Precede
    U+02281⊁\nsuccDoes Not Succeed
    U+02282⊂\subsetSubset Of
    U+02283⊃\supsetSuperset Of
    U+02284⊄\nsubsetNot A Subset Of
    U+02285⊅\nsupsetNot A Superset Of
    U+02286⊆\subseteqSubset Of Or Equal To
    U+02287⊇\supseteqSuperset Of Or Equal To
    U+02288⊈\nsubseteqNeither A Subset Of Nor Equal To
    U+02289⊉\nsupseteqNeither A Superset Of Nor Equal To
    U+0228A⊊\subsetneqSubset Of With Not Equal To / Subset Of Or Not Equal To
    U+0228A + U+0FE00⊊︀\varsubsetneqqSubset Of With Not Equal To / Subset Of Or Not Equal To + Variation Selector-1
    U+0228B⊋\supsetneqSuperset Of With Not Equal To / Superset Of Or Not Equal To
    U+0228B + U+0FE00⊋︀\varsupsetneqSuperset Of With Not Equal To / Superset Of Or Not Equal To + Variation Selector-1
    U+0228D⊍\cupdotMultiset Multiplication
    U+0228E⊎\uplusMultiset Union
    U+0228F⊏\sqsubsetSquare Image Of
    U+0228F + U+00338⊏̸\NotSquareSubsetSquare Image Of + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02290⊐\sqsupsetSquare Original Of
    U+02290 + U+00338⊐̸\NotSquareSupersetSquare Original Of + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02291⊑\sqsubseteqSquare Image Of Or Equal To
    U+02292⊒\sqsupseteqSquare Original Of Or Equal To
    U+02293⊓\sqcapSquare Cap
    U+02294⊔\sqcupSquare Cup
    U+02295⊕\oplusCircled Plus
    U+02296⊖\ominusCircled Minus
    U+02297⊗\otimesCircled Times
    U+02298⊘\oslashCircled Division Slash
    U+02299⊙\odotCircled Dot Operator
    U+0229A⊚\circledcircCircled Ring Operator
    U+0229B⊛\circledastCircled Asterisk Operator
    U+0229C⊜\circledequalCircled Equals
    U+0229D⊝\circleddashCircled Dash
    U+0229E⊞\boxplusSquared Plus
    U+0229F⊟\boxminusSquared Minus
    U+022A0⊠\boxtimesSquared Times
    U+022A1⊡\boxdotSquared Dot Operator
    U+022A2⊢\vdashRight Tack
    U+022A3⊣\dashvLeft Tack
    U+022A4⊤\topDown Tack
    U+022A5⊥\botUp Tack
    U+022A7⊧\modelsModels
    U+022A8⊨\vDashTrue
    U+022A9⊩\VdashForces
    U+022AA⊪\VvdashTriple Vertical Bar Right Turnstile
    U+022AB⊫\VDashDouble Vertical Bar Double Right Turnstile
    U+022AC⊬\nvdashDoes Not Prove
    U+022AD⊭\nvDashNot True
    U+022AE⊮\nVdashDoes Not Force
    U+022AF⊯\nVDashNegated Double Vertical Bar Double Right Turnstile
    U+022B0⊰\prurelPrecedes Under Relation
    U+022B1⊱\scurelSucceeds Under Relation
    U+022B2⊲\vartriangleleftNormal Subgroup Of
    U+022B3⊳\vartrianglerightContains As Normal Subgroup
    U+022B4⊴\trianglelefteqNormal Subgroup Of Or Equal To
    U+022B5⊵\trianglerighteqContains As Normal Subgroup Or Equal To
    U+022B6⊶\originalOriginal Of
    U+022B7⊷\imageImage Of
    U+022B8⊸\multimapMultimap
    U+022B9⊹\hermitconjmatrixHermitian Conjugate Matrix
    U+022BA⊺\intercalIntercalate
    U+022BB⊻\veebar, \xorXor
    U+022BC⊼\barwedge, \nandNand
    U+022BD⊽\barvee, \norNor
    U+022BE⊾\rightanglearcRight Angle With Arc
    U+022BF⊿\varlrtriangleRight Triangle
    U+022C0⋀\bigwedgeN-Ary Logical And
    U+022C1⋁\bigveeN-Ary Logical Or
    U+022C2⋂\bigcapN-Ary Intersection
    U+022C3⋃\bigcupN-Ary Union
    U+022C4⋄\diamondDiamond Operator
    U+022C5⋅\cdotDot Operator
    U+022C6⋆\starStar Operator
    U+022C7⋇\divideontimesDivision Times
    U+022C8⋈\bowtieBowtie
    U+022C9⋉\ltimesLeft Normal Factor Semidirect Product
    U+022CA⋊\rtimesRight Normal Factor Semidirect Product
    U+022CB⋋\leftthreetimesLeft Semidirect Product
    U+022CC⋌\rightthreetimesRight Semidirect Product
    U+022CD⋍\backsimeqReversed Tilde Equals
    U+022CE⋎\curlyveeCurly Logical Or
    U+022CF⋏\curlywedgeCurly Logical And
    U+022D0⋐\SubsetDouble Subset
    U+022D1⋑\SupsetDouble Superset
    U+022D2⋒\CapDouble Intersection
    U+022D3⋓\CupDouble Union
    U+022D4⋔\pitchforkPitchfork
    U+022D5⋕\equalparallelEqual And Parallel To
    U+022D6⋖\lessdotLess-Than With Dot / Less Than With Dot
    U+022D7⋗\gtrdotGreater-Than With Dot / Greater Than With Dot
    U+022D8⋘\verymuchlessVery Much Less-Than / Very Much Less Than
    U+022D9⋙\gggVery Much Greater-Than / Very Much Greater Than
    U+022DA⋚\lesseqgtrLess-Than Equal To Or Greater-Than / Less Than Equal To Or Greater Than
    U+022DB⋛\gtreqlessGreater-Than Equal To Or Less-Than / Greater Than Equal To Or Less Than
    U+022DC⋜\eqlessEqual To Or Less-Than / Equal To Or Less Than
    U+022DD⋝\eqgtrEqual To Or Greater-Than / Equal To Or Greater Than
    U+022DE⋞\curlyeqprecEqual To Or Precedes
    U+022DF⋟\curlyeqsuccEqual To Or Succeeds
    U+022E0⋠\npreccurlyeqDoes Not Precede Or Equal
    U+022E1⋡\nsucccurlyeqDoes Not Succeed Or Equal
    U+022E2⋢\nsqsubseteqNot Square Image Of Or Equal To
    U+022E3⋣\nsqsupseteqNot Square Original Of Or Equal To
    U+022E4⋤\sqsubsetneqSquare Image Of Or Not Equal To
    U+022E5⋥\sqsupsetneqSquare Original Of Or Not Equal To
    U+022E6⋦\lnsimLess-Than But Not Equivalent To / Less Than But Not Equivalent To
    U+022E7⋧\gnsimGreater-Than But Not Equivalent To / Greater Than But Not Equivalent To
    U+022E8⋨\precnsimPrecedes But Not Equivalent To
    U+022E9⋩\succnsimSucceeds But Not Equivalent To
    U+022EA⋪\ntriangleleftNot Normal Subgroup Of
    U+022EB⋫\ntrianglerightDoes Not Contain As Normal Subgroup
    U+022EC⋬\ntrianglelefteqNot Normal Subgroup Of Or Equal To
    U+022ED⋭\ntrianglerighteqDoes Not Contain As Normal Subgroup Or Equal
    U+022EE⋮\vdotsVertical Ellipsis
    U+022EF⋯\cdotsMidline Horizontal Ellipsis
    U+022F0⋰\adotsUp Right Diagonal Ellipsis
    U+022F1⋱\ddotsDown Right Diagonal Ellipsis
    U+022F2⋲\disinElement Of With Long Horizontal Stroke
    U+022F3⋳\varisinsElement Of With Vertical Bar At End Of Horizontal Stroke
    U+022F4⋴\isinsSmall Element Of With Vertical Bar At End Of Horizontal Stroke
    U+022F5⋵\isindotElement Of With Dot Above
    U+022F6⋶\varisinobarElement Of With Overbar
    U+022F7⋷\isinobarSmall Element Of With Overbar
    U+022F8⋸\isinvbElement Of With Underbar
    U+022F9⋹\isinEElement Of With Two Horizontal Strokes
    U+022FA⋺\nisdContains With Long Horizontal Stroke
    U+022FB⋻\varnisContains With Vertical Bar At End Of Horizontal Stroke
    U+022FC⋼\nisSmall Contains With Vertical Bar At End Of Horizontal Stroke
    U+022FD⋽\varniobarContains With Overbar
    U+022FE⋾\niobarSmall Contains With Overbar
    U+022FF⋿\bagmemberZ Notation Bag Membership
    U+02300⌀\diameterDiameter Sign
    U+02302⌂\houseHouse
    U+02305⌅\varbarwedgeProjective
    U+02306⌆\vardoublebarwedgePerspective
    U+02308⌈\lceilLeft Ceiling
    U+02309⌉\rceilRight Ceiling
    U+0230A⌊\lfloorLeft Floor
    U+0230B⌋\rfloorRight Floor
    U+02310⌐\invnotReversed Not Sign
    U+02311⌑\sqlozengeSquare Lozenge
    U+02312⌒\proflineArc
    U+02313⌓\profsurfSegment
    U+02315⌕\recorderTelephone Recorder
    U+02317⌗\viewdataViewdata Square
    U+02319⌙\turnednotTurned Not Sign
    U+0231A⌚\:watch:Watch
    U+0231B⌛\:hourglass:Hourglass
    U+0231C⌜\ulcornerTop Left Corner
    U+0231D⌝\urcornerTop Right Corner
    U+0231E⌞\llcornerBottom Left Corner
    U+0231F⌟\lrcornerBottom Right Corner
    U+02322⌢\frownFrown
    U+02323⌣\smileSmile
    U+0232C⌬\varhexagonlrbondsBenzene Ring
    U+02332⌲\conictaperConical Taper
    U+02336⌶\topbotApl Functional Symbol I-Beam
    U+0233D⌽\obarApl Functional Symbol Circle Stile
    U+0233F⌿\notslashApl Functional Symbol Slash Bar
    U+02340⍀\notbackslashApl Functional Symbol Backslash Bar
    U+02353⍓\boxupcaretApl Functional Symbol Quad Up Caret
    U+02370⍰\boxquestionApl Functional Symbol Quad Question
    U+02394⎔\hexagonSoftware-Function Symbol
    U+023A3⎣\dlcornLeft Square Bracket Lower Corner
    U+023B0⎰\lmoustacheUpper Left Or Lower Right Curly Bracket Section
    U+023B1⎱\rmoustacheUpper Right Or Lower Left Curly Bracket Section
    U+023B4⎴\overbracketTop Square Bracket
    U+023B5⎵\underbracketBottom Square Bracket
    U+023B6⎶\bbrktbrkBottom Square Bracket Over Top Square Bracket
    U+023B7⎷\sqrtbottomRadical Symbol Bottom
    U+023B8⎸\lvboxlineLeft Vertical Box Line
    U+023B9⎹\rvboxlineRight Vertical Box Line
    U+023CE⏎\varcarriagereturnReturn Symbol
    U+023DE⏞\overbraceTop Curly Bracket
    U+023DF⏟\underbraceBottom Curly Bracket
    U+023E2⏢\trapeziumWhite Trapezium
    U+023E3⏣\benzenrBenzene Ring With Circle
    U+023E4⏤\strnsStraightness
    U+023E5⏥\fltnsFlatness
    U+023E6⏦\accurrentAc Current
    U+023E7⏧\elintersElectrical Intersection
    U+023E9⏩\:fast_forward:Black Right-Pointing Double Triangle
    U+023EA⏪\:rewind:Black Left-Pointing Double Triangle
    U+023EB⏫\:arrow_double_up:Black Up-Pointing Double Triangle
    U+023EC⏬\:arrow_double_down:Black Down-Pointing Double Triangle
    U+023F0⏰\:alarm_clock:Alarm Clock
    U+023F3⏳\:hourglass_flowing_sand:Hourglass With Flowing Sand
    U+02422␢\blanksymbolBlank Symbol / Blank
    U+02423␣\visiblespaceOpen Box
    U+024C2Ⓜ\:m:Circled Latin Capital Letter M
    U+024C8Ⓢ\circledSCircled Latin Capital Letter S
    U+02506┆\dshfncBox Drawings Light Triple Dash Vertical / Forms Light Triple Dash Vertical
    U+02519┙\sqfnwBox Drawings Up Light And Left Heavy / Forms Up Light And Left Heavy
    U+02571╱\diagupBox Drawings Light Diagonal Upper Right To Lower Left / Forms Light Diagonal Upper Right To Lower Left
    U+02572╲\diagdownBox Drawings Light Diagonal Upper Left To Lower Right / Forms Light Diagonal Upper Left To Lower Right
    U+02580▀\blockuphalfUpper Half Block
    U+02584▄\blocklowhalfLower Half Block
    U+02588█\blockfullFull Block
    U+0258C▌\blocklefthalfLeft Half Block
    U+02590▐\blockrighthalfRight Half Block
    U+02591░\blockqtrshadedLight Shade
    U+02592▒\blockhalfshadedMedium Shade
    U+02593▓\blockthreeqtrshadedDark Shade
    U+025A0■\blacksquareBlack Square
    U+025A1□\squareWhite Square
    U+025A2▢\squovalWhite Square With Rounded Corners
    U+025A3▣\blackinwhitesquareWhite Square Containing Black Small Square
    U+025A4▤\squarehfillSquare With Horizontal Fill
    U+025A5▥\squarevfillSquare With Vertical Fill
    U+025A6▦\squarehvfillSquare With Orthogonal Crosshatch Fill
    U+025A7▧\squarenwsefillSquare With Upper Left To Lower Right Fill
    U+025A8▨\squareneswfillSquare With Upper Right To Lower Left Fill
    U+025A9▩\squarecrossfillSquare With Diagonal Crosshatch Fill
    U+025AA▪\smblksquare, \:black_small_square:Black Small Square
    U+025AB▫\smwhtsquare, \:white_small_square:White Small Square
    U+025AC▬\hrectangleblackBlack Rectangle
    U+025AD▭\hrectangleWhite Rectangle
    U+025AE▮\vrectangleblackBlack Vertical Rectangle
    U+025AF▯\vrectoWhite Vertical Rectangle
    U+025B0▰\parallelogramblackBlack Parallelogram
    U+025B1▱\parallelogramWhite Parallelogram
    U+025B2▲\bigblacktriangleupBlack Up-Pointing Triangle / Black Up Pointing Triangle
    U+025B3△\bigtriangleupWhite Up-Pointing Triangle / White Up Pointing Triangle
    U+025B4▴\blacktriangleBlack Up-Pointing Small Triangle / Black Up Pointing Small Triangle
    U+025B5▵\vartriangleWhite Up-Pointing Small Triangle / White Up Pointing Small Triangle
    U+025B6▶\blacktriangleright, \:arrow_forward:Black Right-Pointing Triangle / Black Right Pointing Triangle
    U+025B7▷\trianglerightWhite Right-Pointing Triangle / White Right Pointing Triangle
    U+025B8▸\smallblacktrianglerightBlack Right-Pointing Small Triangle / Black Right Pointing Small Triangle
    U+025B9▹\smalltrianglerightWhite Right-Pointing Small Triangle / White Right Pointing Small Triangle
    U+025BA►\blackpointerrightBlack Right-Pointing Pointer / Black Right Pointing Pointer
    U+025BB▻\whitepointerrightWhite Right-Pointing Pointer / White Right Pointing Pointer
    U+025BC▼\bigblacktriangledownBlack Down-Pointing Triangle / Black Down Pointing Triangle
    U+025BD▽\bigtriangledownWhite Down-Pointing Triangle / White Down Pointing Triangle
    U+025BE▾\blacktriangledownBlack Down-Pointing Small Triangle / Black Down Pointing Small Triangle
    U+025BF▿\triangledownWhite Down-Pointing Small Triangle / White Down Pointing Small Triangle
    U+025C0◀\blacktriangleleft, \:arrow_backward:Black Left-Pointing Triangle / Black Left Pointing Triangle
    U+025C1◁\triangleleftWhite Left-Pointing Triangle / White Left Pointing Triangle
    U+025C2◂\smallblacktriangleleftBlack Left-Pointing Small Triangle / Black Left Pointing Small Triangle
    U+025C3◃\smalltriangleleftWhite Left-Pointing Small Triangle / White Left Pointing Small Triangle
    U+025C4◄\blackpointerleftBlack Left-Pointing Pointer / Black Left Pointing Pointer
    U+025C5◅\whitepointerleftWhite Left-Pointing Pointer / White Left Pointing Pointer
    U+025C6◆\mdlgblkdiamondBlack Diamond
    U+025C7◇\mdlgwhtdiamondWhite Diamond
    U+025C8◈\blackinwhitediamondWhite Diamond Containing Black Small Diamond
    U+025C9◉\fisheyeFisheye
    U+025CA◊\lozengeLozenge
    U+025CB○\bigcircWhite Circle
    U+025CC◌\dottedcircleDotted Circle
    U+025CD◍\circlevertfillCircle With Vertical Fill
    U+025CE◎\bullseyeBullseye
    U+025CF●\mdlgblkcircleBlack Circle
    U+025D0◐\cirflCircle With Left Half Black
    U+025D1◑\cirfrCircle With Right Half Black
    U+025D2◒\cirfbCircle With Lower Half Black
    U+025D3◓\circletophalfblackCircle With Upper Half Black
    U+025D4◔\circleurquadblackCircle With Upper Right Quadrant Black
    U+025D5◕\blackcircleulquadwhiteCircle With All But Upper Left Quadrant Black
    U+025D6◖\blacklefthalfcircleLeft Half Black Circle
    U+025D7◗\blackrighthalfcircleRight Half Black Circle
    U+025D8◘\rvbullInverse Bullet
    U+025D9◙\inversewhitecircleInverse White Circle
    U+025DA◚\invwhiteupperhalfcircleUpper Half Inverse White Circle
    U+025DB◛\invwhitelowerhalfcircleLower Half Inverse White Circle
    U+025DC◜\ularcUpper Left Quadrant Circular Arc
    U+025DD◝\urarcUpper Right Quadrant Circular Arc
    U+025DE◞\lrarcLower Right Quadrant Circular Arc
    U+025DF◟\llarcLower Left Quadrant Circular Arc
    U+025E0◠\topsemicircleUpper Half Circle
    U+025E1◡\botsemicircleLower Half Circle
    U+025E2◢\lrblacktriangleBlack Lower Right Triangle
    U+025E3◣\llblacktriangleBlack Lower Left Triangle
    U+025E4◤\ulblacktriangleBlack Upper Left Triangle
    U+025E5◥\urblacktriangleBlack Upper Right Triangle
    U+025E6◦\smwhtcircleWhite Bullet
    U+025E7◧\sqflSquare With Left Half Black
    U+025E8◨\sqfrSquare With Right Half Black
    U+025E9◩\squareulblackSquare With Upper Left Diagonal Half Black
    U+025EA◪\sqfseSquare With Lower Right Diagonal Half Black
    U+025EB◫\boxbarWhite Square With Vertical Bisecting Line
    U+025EC◬\trianglecdotWhite Up-Pointing Triangle With Dot / White Up Pointing Triangle With Dot
    U+025ED◭\triangleleftblackUp-Pointing Triangle With Left Half Black / Up Pointing Triangle With Left Half Black
    U+025EE◮\trianglerightblackUp-Pointing Triangle With Right Half Black / Up Pointing Triangle With Right Half Black
    U+025EF◯\lgwhtcircleLarge Circle
    U+025F0◰\squareulquadWhite Square With Upper Left Quadrant
    U+025F1◱\squarellquadWhite Square With Lower Left Quadrant
    U+025F2◲\squarelrquadWhite Square With Lower Right Quadrant
    U+025F3◳\squareurquadWhite Square With Upper Right Quadrant
    U+025F4◴\circleulquadWhite Circle With Upper Left Quadrant
    U+025F5◵\circlellquadWhite Circle With Lower Left Quadrant
    U+025F6◶\circlelrquadWhite Circle With Lower Right Quadrant
    U+025F7◷\circleurquadWhite Circle With Upper Right Quadrant
    U+025F8◸\ultriangleUpper Left Triangle
    U+025F9◹\urtriangleUpper Right Triangle
    U+025FA◺\lltriangleLower Left Triangle
    U+025FB◻\mdwhtsquare, \:white_medium_square:White Medium Square
    U+025FC◼\mdblksquare, \:black_medium_square:Black Medium Square
    U+025FD◽\mdsmwhtsquare, \:white_medium_small_square:White Medium Small Square
    U+025FE◾\mdsmblksquare, \:black_medium_small_square:Black Medium Small Square
    U+025FF◿\lrtriangleLower Right Triangle
    U+02600☀\:sunny:Black Sun With Rays
    U+02601☁\:cloud:Cloud
    U+02605★\bigstarBlack Star
    U+02606☆\bigwhitestarWhite Star
    U+02609☉\astrosunSun
    U+0260E☎\:phone:Black Telephone
    U+02611☑\:ballot_box_with_check:Ballot Box With Check
    U+02614☔\:umbrella_with_rain_drops:, \:umbrella:Umbrella With Rain Drops
    U+02615☕\:coffee:Hot Beverage
    U+0261D☝\:point_up:White Up Pointing Index
    U+02621☡\dangerCaution Sign
    U+0263A☺\:relaxed:White Smiling Face
    U+0263B☻\blacksmileyBlack Smiling Face
    U+0263C☼\sunWhite Sun With Rays
    U+0263D☽\rightmoonFirst Quarter Moon
    U+0263E☾\leftmoonLast Quarter Moon
    U+0263F☿\mercuryMercury
    U+02640♀\venus, \femaleFemale Sign
    U+02642♂\male, \marsMale Sign
    U+02643♃\jupiterJupiter
    U+02644♄\saturnSaturn
    U+02645♅\uranusUranus
    U+02646♆\neptuneNeptune
    U+02647♇\plutoPluto
    U+02648♈\aries, \:aries:Aries
    U+02649♉\taurus, \:taurus:Taurus
    U+0264A♊\gemini, \:gemini:Gemini
    U+0264B♋\cancer, \:cancer:Cancer
    U+0264C♌\leo, \:leo:Leo
    U+0264D♍\virgo, \:virgo:Virgo
    U+0264E♎\libra, \:libra:Libra
    U+0264F♏\scorpio, \:scorpius:Scorpius
    U+02650♐\sagittarius, \:sagittarius:Sagittarius
    U+02651♑\capricornus, \:capricorn:Capricorn
    U+02652♒\aquarius, \:aquarius:Aquarius
    U+02653♓\pisces, \:pisces:Pisces
    U+02660♠\spadesuit, \:spades:Black Spade Suit
    U+02661♡\heartsuitWhite Heart Suit
    U+02662♢\diamondsuitWhite Diamond Suit
    U+02663♣\clubsuit, \:clubs:Black Club Suit
    U+02664♤\varspadesuitWhite Spade Suit
    U+02665♥\varheartsuit, \:hearts:Black Heart Suit
    U+02666♦\vardiamondsuit, \:diamonds:Black Diamond Suit
    U+02667♧\varclubsuitWhite Club Suit
    U+02668♨\:hotsprings:Hot Springs
    U+02669♩\quarternoteQuarter Note
    U+0266A♪\eighthnoteEighth Note
    U+0266B♫\twonotesBeamed Eighth Notes / Barred Eighth Notes
    U+0266D♭\flatMusic Flat Sign / Flat
    U+0266E♮\naturalMusic Natural Sign / Natural
    U+0266F♯\sharpMusic Sharp Sign / Sharp
    U+0267B♻\:recycle:Black Universal Recycling Symbol
    U+0267E♾\acidfreePermanent Paper Sign
    U+0267F♿\:wheelchair:Wheelchair Symbol
    U+02680⚀\diceiDie Face-1
    U+02681⚁\diceiiDie Face-2
    U+02682⚂\diceiiiDie Face-3
    U+02683⚃\diceivDie Face-4
    U+02684⚄\dicevDie Face-5
    U+02685⚅\diceviDie Face-6
    U+02686⚆\circledrightdotWhite Circle With Dot Right
    U+02687⚇\circledtwodotsWhite Circle With Two Dots
    U+02688⚈\blackcircledrightdotBlack Circle With White Dot Right
    U+02689⚉\blackcircledtwodotsBlack Circle With Two White Dots
    U+02693⚓\:anchor:Anchor
    U+026A0⚠\:warning:Warning Sign
    U+026A1⚡\:zap:High Voltage Sign
    U+026A5⚥\hermaphroditeMale And Female Sign
    U+026AA⚪\mdwhtcircle, \:white_circle:Medium White Circle
    U+026AB⚫\mdblkcircle, \:black_circle:Medium Black Circle
    U+026AC⚬\mdsmwhtcircleMedium Small White Circle
    U+026B2⚲\neuterNeuter
    U+026BD⚽\:soccer:Soccer Ball
    U+026BE⚾\:baseball:Baseball
    U+026C4⛄\:snowman:, \:snowman_without_snow:Snowman Without Snow
    U+026C5⛅\:partly_sunny:Sun Behind Cloud
    U+026CE⛎\:ophiuchus:Ophiuchus
    U+026D4⛔\:no_entry:No Entry
    U+026EA⛪\:church:Church
    U+026F2⛲\:fountain:Fountain
    U+026F3⛳\:golf:Flag In Hole
    U+026F5⛵\:boat:Sailboat
    U+026FA⛺\:tent:Tent
    U+026FD⛽\:fuelpump:Fuel Pump
    U+02702✂\:scissors:Black Scissors
    U+02705✅\:white_check_mark:White Heavy Check Mark
    U+02708✈\:airplane:Airplane
    U+02709✉\:email:Envelope
    U+0270A✊\:fist:Raised Fist
    U+0270B✋\:hand:Raised Hand
    U+0270C✌\:v:Victory Hand
    U+0270F✏\:pencil2:Pencil
    U+02712✒\:black_nib:Black Nib
    U+02713✓\checkmarkCheck Mark
    U+02714✔\:heavy_check_mark:Heavy Check Mark
    U+02716✖\:heavy_multiplication_x:Heavy Multiplication X
    U+02720✠\malteseMaltese Cross
    U+02728✨\:sparkles:Sparkles
    U+0272A✪\circledstarCircled White Star
    U+02733✳\:eight_spoked_asterisk:Eight Spoked Asterisk
    U+02734✴\:eight_pointed_black_star:Eight Pointed Black Star
    U+02736✶\varstarSix Pointed Black Star
    U+0273D✽\dingasteriskHeavy Teardrop-Spoked Asterisk
    U+02744❄\:snowflake:Snowflake
    U+02747❇\:sparkle:Sparkle
    U+0274C❌\:x:Cross Mark
    U+0274E❎\:negative_squared_cross_mark:Negative Squared Cross Mark
    U+02753❓\:question:Black Question Mark Ornament
    U+02754❔\:grey_question:White Question Mark Ornament
    U+02755❕\:grey_exclamation:White Exclamation Mark Ornament
    U+02757❗\:exclamation:Heavy Exclamation Mark Symbol
    U+02764❤\:heart:Heavy Black Heart
    U+02795➕\:heavy_plus_sign:Heavy Plus Sign
    U+02796➖\:heavy_minus_sign:Heavy Minus Sign
    U+02797➗\:heavy_division_sign:Heavy Division Sign
    U+0279B➛\draftingarrowDrafting Point Rightwards Arrow / Drafting Point Right Arrow
    U+027A1➡\:arrow_right:Black Rightwards Arrow / Black Right Arrow
    U+027B0➰\:curly_loop:Curly Loop
    U+027BF➿\:loop:Double Curly Loop
    U+027C0⟀\threedangleThree Dimensional Angle
    U+027C1⟁\whiteinwhitetriangleWhite Triangle Containing Small White Triangle
    U+027C2⟂\perpPerpendicular
    U+027C7⟇\veedotOr With Dot Inside
    U+027C8⟈\bsolhsubReverse Solidus Preceding Subset
    U+027C9⟉\suphsolSuperset Preceding Solidus
    U+027D1⟑\wedgedotAnd With Dot
    U+027D2⟒\upinElement Of Opening Upwards
    U+027D5⟕\leftouterjoinLeft Outer Join
    U+027D6⟖\rightouterjoinRight Outer Join
    U+027D7⟗\fullouterjoinFull Outer Join
    U+027D8⟘\bigbotLarge Up Tack
    U+027D9⟙\bigtopLarge Down Tack
    U+027E6⟦\llbracket, \openbracketleftMathematical Left White Square Bracket
    U+027E7⟧\openbracketright, \rrbracketMathematical Right White Square Bracket
    U+027E8⟨\langleMathematical Left Angle Bracket
    U+027E9⟩\rangleMathematical Right Angle Bracket
    U+027F0⟰\UUparrowUpwards Quadruple Arrow
    U+027F1⟱\DDownarrowDownwards Quadruple Arrow
    U+027F5⟵\longleftarrowLong Leftwards Arrow
    U+027F6⟶\longrightarrowLong Rightwards Arrow
    U+027F7⟷\longleftrightarrowLong Left Right Arrow
    U+027F8⟸\impliedby, \LongleftarrowLong Leftwards Double Arrow
    U+027F9⟹\implies, \LongrightarrowLong Rightwards Double Arrow
    U+027FA⟺\Longleftrightarrow, \iffLong Left Right Double Arrow
    U+027FB⟻\longmapsfromLong Leftwards Arrow From Bar
    U+027FC⟼\longmapstoLong Rightwards Arrow From Bar
    U+027FD⟽\LongmapsfromLong Leftwards Double Arrow From Bar
    U+027FE⟾\LongmapstoLong Rightwards Double Arrow From Bar
    U+027FF⟿\longrightsquigarrowLong Rightwards Squiggle Arrow
    U+02900⤀\nvtwoheadrightarrowRightwards Two-Headed Arrow With Vertical Stroke
    U+02901⤁\nVtwoheadrightarrowRightwards Two-Headed Arrow With Double Vertical Stroke
    U+02902⤂\nvLeftarrowLeftwards Double Arrow With Vertical Stroke
    U+02903⤃\nvRightarrowRightwards Double Arrow With Vertical Stroke
    U+02904⤄\nvLeftrightarrowLeft Right Double Arrow With Vertical Stroke
    U+02905⤅\twoheadmapstoRightwards Two-Headed Arrow From Bar
    U+02906⤆\MapsfromLeftwards Double Arrow From Bar
    U+02907⤇\MapstoRightwards Double Arrow From Bar
    U+02908⤈\downarrowbarredDownwards Arrow With Horizontal Stroke
    U+02909⤉\uparrowbarredUpwards Arrow With Horizontal Stroke
    U+0290A⤊\UuparrowUpwards Triple Arrow
    U+0290B⤋\DdownarrowDownwards Triple Arrow
    U+0290C⤌\leftbkarrowLeftwards Double Dash Arrow
    U+0290D⤍\bkarowRightwards Double Dash Arrow
    U+0290E⤎\leftdbkarrowLeftwards Triple Dash Arrow
    U+0290F⤏\dbkarowRightwards Triple Dash Arrow
    U+02910⤐\drbkarrowRightwards Two-Headed Triple Dash Arrow
    U+02911⤑\rightdotarrowRightwards Arrow With Dotted Stem
    U+02912⤒\UpArrowBarUpwards Arrow To Bar
    U+02913⤓\DownArrowBarDownwards Arrow To Bar
    U+02914⤔\nvrightarrowtailRightwards Arrow With Tail With Vertical Stroke
    U+02915⤕\nVrightarrowtailRightwards Arrow With Tail With Double Vertical Stroke
    U+02916⤖\twoheadrightarrowtailRightwards Two-Headed Arrow With Tail
    U+02917⤗\nvtwoheadrightarrowtailRightwards Two-Headed Arrow With Tail With Vertical Stroke
    U+02918⤘\nVtwoheadrightarrowtailRightwards Two-Headed Arrow With Tail With Double Vertical Stroke
    U+0291D⤝\diamondleftarrowLeftwards Arrow To Black Diamond
    U+0291E⤞\rightarrowdiamondRightwards Arrow To Black Diamond
    U+0291F⤟\diamondleftarrowbarLeftwards Arrow From Bar To Black Diamond
    U+02920⤠\barrightarrowdiamondRightwards Arrow From Bar To Black Diamond
    U+02925⤥\hksearowSouth East Arrow With Hook
    U+02926⤦\hkswarowSouth West Arrow With Hook
    U+02927⤧\tonaNorth West Arrow And North East Arrow
    U+02928⤨\toeaNorth East Arrow And South East Arrow
    U+02929⤩\tosaSouth East Arrow And South West Arrow
    U+0292A⤪\towaSouth West Arrow And North West Arrow
    U+0292B⤫\rdiagovfdiagRising Diagonal Crossing Falling Diagonal
    U+0292C⤬\fdiagovrdiagFalling Diagonal Crossing Rising Diagonal
    U+0292D⤭\seovnearrowSouth East Arrow Crossing North East Arrow
    U+0292E⤮\neovsearrowNorth East Arrow Crossing South East Arrow
    U+0292F⤯\fdiagovnearrowFalling Diagonal Crossing North East Arrow
    U+02930⤰\rdiagovsearrowRising Diagonal Crossing South East Arrow
    U+02931⤱\neovnwarrowNorth East Arrow Crossing North West Arrow
    U+02932⤲\nwovnearrowNorth West Arrow Crossing North East Arrow
    U+02934⤴\:arrow_heading_up:Arrow Pointing Rightwards Then Curving Upwards
    U+02935⤵\:arrow_heading_down:Arrow Pointing Rightwards Then Curving Downwards
    U+02942⥂\RlarrRightwards Arrow Above Short Leftwards Arrow
    U+02944⥄\rLarrShort Rightwards Arrow Above Leftwards Arrow
    U+02945⥅\rightarrowplusRightwards Arrow With Plus Below
    U+02946⥆\leftarrowplusLeftwards Arrow With Plus Below
    U+02947⥇\rarrxRightwards Arrow Through X
    U+02948⥈\leftrightarrowcircleLeft Right Arrow Through Small Circle
    U+02949⥉\twoheaduparrowcircleUpwards Two-Headed Arrow From Small Circle
    U+0294A⥊\leftrightharpoonupdownLeft Barb Up Right Barb Down Harpoon
    U+0294B⥋\leftrightharpoondownupLeft Barb Down Right Barb Up Harpoon
    U+0294C⥌\updownharpoonrightleftUp Barb Right Down Barb Left Harpoon
    U+0294D⥍\updownharpoonleftrightUp Barb Left Down Barb Right Harpoon
    U+0294E⥎\LeftRightVectorLeft Barb Up Right Barb Up Harpoon
    U+0294F⥏\RightUpDownVectorUp Barb Right Down Barb Right Harpoon
    U+02950⥐\DownLeftRightVectorLeft Barb Down Right Barb Down Harpoon
    U+02951⥑\LeftUpDownVectorUp Barb Left Down Barb Left Harpoon
    U+02952⥒\LeftVectorBarLeftwards Harpoon With Barb Up To Bar
    U+02953⥓\RightVectorBarRightwards Harpoon With Barb Up To Bar
    U+02954⥔\RightUpVectorBarUpwards Harpoon With Barb Right To Bar
    U+02955⥕\RightDownVectorBarDownwards Harpoon With Barb Right To Bar
    U+02956⥖\DownLeftVectorBarLeftwards Harpoon With Barb Down To Bar
    U+02957⥗\DownRightVectorBarRightwards Harpoon With Barb Down To Bar
    U+02958⥘\LeftUpVectorBarUpwards Harpoon With Barb Left To Bar
    U+02959⥙\LeftDownVectorBarDownwards Harpoon With Barb Left To Bar
    U+0295A⥚\LeftTeeVectorLeftwards Harpoon With Barb Up From Bar
    U+0295B⥛\RightTeeVectorRightwards Harpoon With Barb Up From Bar
    U+0295C⥜\RightUpTeeVectorUpwards Harpoon With Barb Right From Bar
    U+0295D⥝\RightDownTeeVectorDownwards Harpoon With Barb Right From Bar
    U+0295E⥞\DownLeftTeeVectorLeftwards Harpoon With Barb Down From Bar
    U+0295F⥟\DownRightTeeVectorRightwards Harpoon With Barb Down From Bar
    U+02960⥠\LeftUpTeeVectorUpwards Harpoon With Barb Left From Bar
    U+02961⥡\LeftDownTeeVectorDownwards Harpoon With Barb Left From Bar
    U+02962⥢\leftharpoonsupdownLeftwards Harpoon With Barb Up Above Leftwards Harpoon With Barb Down
    U+02963⥣\upharpoonsleftrightUpwards Harpoon With Barb Left Beside Upwards Harpoon With Barb Right
    U+02964⥤\rightharpoonsupdownRightwards Harpoon With Barb Up Above Rightwards Harpoon With Barb Down
    U+02965⥥\downharpoonsleftrightDownwards Harpoon With Barb Left Beside Downwards Harpoon With Barb Right
    U+02966⥦\leftrightharpoonsupLeftwards Harpoon With Barb Up Above Rightwards Harpoon With Barb Up
    U+02967⥧\leftrightharpoonsdownLeftwards Harpoon With Barb Down Above Rightwards Harpoon With Barb Down
    U+02968⥨\rightleftharpoonsupRightwards Harpoon With Barb Up Above Leftwards Harpoon With Barb Up
    U+02969⥩\rightleftharpoonsdownRightwards Harpoon With Barb Down Above Leftwards Harpoon With Barb Down
    U+0296A⥪\leftharpoonupdashLeftwards Harpoon With Barb Up Above Long Dash
    U+0296B⥫\dashleftharpoondownLeftwards Harpoon With Barb Down Below Long Dash
    U+0296C⥬\rightharpoonupdashRightwards Harpoon With Barb Up Above Long Dash
    U+0296D⥭\dashrightharpoondownRightwards Harpoon With Barb Down Below Long Dash
    U+0296E⥮\UpEquilibriumUpwards Harpoon With Barb Left Beside Downwards Harpoon With Barb Right
    U+0296F⥯\ReverseUpEquilibriumDownwards Harpoon With Barb Left Beside Upwards Harpoon With Barb Right
    U+02970⥰\RoundImpliesRight Double Arrow With Rounded Head
    U+02977⥷\leftarrowlessLeftwards Arrow Through Less-Than
    U+0297A⥺\leftarrowsubsetLeftwards Arrow Through Subset
    U+02980⦀\VvertTriple Vertical Bar Delimiter
    U+02986⦆\ElroangRight White Parenthesis
    U+02999⦙\ddfncDotted Fence
    U+0299B⦛\measuredangleleftMeasured Angle Opening Left
    U+0299C⦜\AngleRight Angle Variant With Square
    U+0299D⦝\rightanglemdotMeasured Right Angle With Dot
    U+0299E⦞\anglesAngle With S Inside
    U+0299F⦟\angdnrAcute Angle
    U+029A0⦠\lpargtSpherical Angle Opening Left
    U+029A1⦡\sphericalangleupSpherical Angle Opening Up
    U+029A2⦢\turnangleTurned Angle
    U+029A3⦣\revangleReversed Angle
    U+029A4⦤\angleubarAngle With Underbar
    U+029A5⦥\revangleubarReversed Angle With Underbar
    U+029A6⦦\wideangledownOblique Angle Opening Up
    U+029A7⦧\wideangleupOblique Angle Opening Down
    U+029A8⦨\measanglerutoneMeasured Angle With Open Arm Ending In Arrow Pointing Up And Right
    U+029A9⦩\measanglelutonwMeasured Angle With Open Arm Ending In Arrow Pointing Up And Left
    U+029AA⦪\measanglerdtoseMeasured Angle With Open Arm Ending In Arrow Pointing Down And Right
    U+029AB⦫\measangleldtoswMeasured Angle With Open Arm Ending In Arrow Pointing Down And Left
    U+029AC⦬\measangleurtoneMeasured Angle With Open Arm Ending In Arrow Pointing Right And Up
    U+029AD⦭\measangleultonwMeasured Angle With Open Arm Ending In Arrow Pointing Left And Up
    U+029AE⦮\measangledrtoseMeasured Angle With Open Arm Ending In Arrow Pointing Right And Down
    U+029AF⦯\measangledltoswMeasured Angle With Open Arm Ending In Arrow Pointing Left And Down
    U+029B0⦰\revemptysetReversed Empty Set
    U+029B1⦱\emptysetobarEmpty Set With Overbar
    U+029B2⦲\emptysetocircEmpty Set With Small Circle Above
    U+029B3⦳\emptysetoarrEmpty Set With Right Arrow Above
    U+029B4⦴\emptysetoarrlEmpty Set With Left Arrow Above
    U+029B7⦷\circledparallelCircled Parallel
    U+029B8⦸\obslashCircled Reverse Solidus
    U+029BC⦼\odotslashdotCircled Anticlockwise-Rotated Division Sign
    U+029BE⦾\circledwhitebulletCircled White Bullet
    U+029BF⦿\circledbulletCircled Bullet
    U+029C0⧀\olessthanCircled Less-Than
    U+029C1⧁\ogreaterthanCircled Greater-Than
    U+029C4⧄\boxdiagSquared Rising Diagonal Slash
    U+029C5⧅\boxbslashSquared Falling Diagonal Slash
    U+029C6⧆\boxastSquared Asterisk
    U+029C7⧇\boxcircleSquared Small Circle
    U+029CA⧊\LapTriangle With Dot Above
    U+029CB⧋\defasTriangle With Underbar
    U+029CF⧏\LeftTriangleBarLeft Triangle Beside Vertical Bar
    U+029CF + U+00338⧏̸\NotLeftTriangleBarLeft Triangle Beside Vertical Bar + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+029D0⧐\RightTriangleBarVertical Bar Beside Right Triangle
    U+029D0 + U+00338⧐̸\NotRightTriangleBarVertical Bar Beside Right Triangle + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+029DF⧟\dualmapDouble-Ended Multimap
    U+029E1⧡\lrtriangleeqIncreases As
    U+029E2⧢\shuffleShuffle Product
    U+029E3⧣\eparslEquals Sign And Slanted Parallel
    U+029E4⧤\smeparslEquals Sign And Slanted Parallel With Tilde Above
    U+029E5⧥\eqvparslIdentical To And Slanted Parallel
    U+029EB⧫\blacklozengeBlack Lozenge
    U+029F4⧴\RuleDelayedRule-Delayed
    U+029F6⧶\dsolSolidus With Overbar
    U+029F7⧷\rsolbarReverse Solidus With Horizontal Stroke
    U+029FA⧺\doubleplusDouble Plus
    U+029FB⧻\tripleplusTriple Plus
    U+02A00⨀\bigodotN-Ary Circled Dot Operator
    U+02A01⨁\bigoplusN-Ary Circled Plus Operator
    U+02A02⨂\bigotimesN-Ary Circled Times Operator
    U+02A03⨃\bigcupdotN-Ary Union Operator With Dot
    U+02A04⨄\biguplusN-Ary Union Operator With Plus
    U+02A05⨅\bigsqcapN-Ary Square Intersection Operator
    U+02A06⨆\bigsqcupN-Ary Square Union Operator
    U+02A07⨇\conjquantTwo Logical And Operator
    U+02A08⨈\disjquantTwo Logical Or Operator
    U+02A09⨉\bigtimesN-Ary Times Operator
    U+02A0A⨊\modtwosumModulo Two Sum
    U+02A0B⨋\sumintSummation With Integral
    U+02A0C⨌\iiiintQuadruple Integral Operator
    U+02A0D⨍\intbarFinite Part Integral
    U+02A0E⨎\intBarIntegral With Double Stroke
    U+02A0F⨏\clockointIntegral Average With Slash
    U+02A10⨐\cirfnintCirculation Function
    U+02A11⨑\awintAnticlockwise Integration
    U+02A12⨒\rppolintLine Integration With Rectangular Path Around Pole
    U+02A13⨓\scpolintLine Integration With Semicircular Path Around Pole
    U+02A14⨔\npolintLine Integration Not Including The Pole
    U+02A15⨕\pointintIntegral Around A Point Operator
    U+02A16⨖\sqrintQuaternion Integral Operator
    U+02A18⨘\intxIntegral With Times Sign
    U+02A19⨙\intcapIntegral With Intersection
    U+02A1A⨚\intcupIntegral With Union
    U+02A1B⨛\upintIntegral With Overbar
    U+02A1C⨜\lowintIntegral With Underbar
    U+02A1D⨝\joinJoin
    U+02A1F⨟\bbsemiZ Notation Schema Composition
    U+02A22⨢\ringplusPlus Sign With Small Circle Above
    U+02A23⨣\plushatPlus Sign With Circumflex Accent Above
    U+02A24⨤\simplusPlus Sign With Tilde Above
    U+02A25⨥\plusdotPlus Sign With Dot Below
    U+02A26⨦\plussimPlus Sign With Tilde Below
    U+02A27⨧\plussubtwoPlus Sign With Subscript Two
    U+02A28⨨\plustrifPlus Sign With Black Triangle
    U+02A29⨩\commaminusMinus Sign With Comma Above
    U+02A2A⨪\minusdotMinus Sign With Dot Below
    U+02A2B⨫\minusfdotsMinus Sign With Falling Dots
    U+02A2C⨬\minusrdotsMinus Sign With Rising Dots
    U+02A2D⨭\opluslhrimPlus Sign In Left Half Circle
    U+02A2E⨮\oplusrhrimPlus Sign In Right Half Circle
    U+02A2F⨯\TimesVector Or Cross Product
    U+02A30⨰\dottimesMultiplication Sign With Dot Above
    U+02A31⨱\timesbarMultiplication Sign With Underbar
    U+02A32⨲\btimesSemidirect Product With Bottom Closed
    U+02A33⨳\smashtimesSmash Product
    U+02A34⨴\otimeslhrimMultiplication Sign In Left Half Circle
    U+02A35⨵\otimesrhrimMultiplication Sign In Right Half Circle
    U+02A36⨶\otimeshatCircled Multiplication Sign With Circumflex Accent
    U+02A37⨷\OtimesMultiplication Sign In Double Circle
    U+02A38⨸\odivCircled Division Sign
    U+02A39⨹\triangleplusPlus Sign In Triangle
    U+02A3A⨺\triangleminusMinus Sign In Triangle
    U+02A3B⨻\triangletimesMultiplication Sign In Triangle
    U+02A3C⨼\intprodInterior Product
    U+02A3D⨽\intprodrRighthand Interior Product
    U+02A3F⨿\amalgAmalgamation Or Coproduct
    U+02A40⩀\capdotIntersection With Dot
    U+02A41⩁\uminusUnion With Minus Sign
    U+02A42⩂\barcupUnion With Overbar
    U+02A43⩃\barcapIntersection With Overbar
    U+02A44⩄\capwedgeIntersection With Logical And
    U+02A45⩅\cupveeUnion With Logical Or
    U+02A4A⩊\twocupsUnion Beside And Joined With Union
    U+02A4B⩋\twocapsIntersection Beside And Joined With Intersection
    U+02A4C⩌\closedvarcupClosed Union With Serifs
    U+02A4D⩍\closedvarcapClosed Intersection With Serifs
    U+02A4E⩎\SqcapDouble Square Intersection
    U+02A4F⩏\SqcupDouble Square Union
    U+02A50⩐\closedvarcupsmashprodClosed Union With Serifs And Smash Product
    U+02A51⩑\wedgeodotLogical And With Dot Above
    U+02A52⩒\veeodotLogical Or With Dot Above
    U+02A53⩓\AndDouble Logical And
    U+02A54⩔\OrDouble Logical Or
    U+02A55⩕\wedgeonwedgeTwo Intersecting Logical And
    U+02A56⩖\ElOrTwo Intersecting Logical Or
    U+02A57⩗\bigslopedveeSloping Large Or
    U+02A58⩘\bigslopedwedgeSloping Large And
    U+02A5A⩚\wedgemidvertLogical And With Middle Stem
    U+02A5B⩛\veemidvertLogical Or With Middle Stem
    U+02A5C⩜\midbarwedgeLogical And With Horizontal Dash
    U+02A5D⩝\midbarveeLogical Or With Horizontal Dash
    U+02A5E⩞\perspcorrespondLogical And With Double Overbar
    U+02A5F⩟\minhatLogical And With Underbar
    U+02A60⩠\wedgedoublebarLogical And With Double Underbar
    U+02A61⩡\varveebarSmall Vee With Underbar
    U+02A62⩢\doublebarveeLogical Or With Double Overbar
    U+02A63⩣\veedoublebarLogical Or With Double Underbar
    U+02A66⩦\eqdotEquals Sign With Dot Below
    U+02A67⩧\dotequivIdentical With Dot Above
    U+02A6A⩪\dotsimTilde Operator With Dot Above
    U+02A6B⩫\simrdotsTilde Operator With Rising Dots
    U+02A6C⩬\simminussimSimilar Minus Similar
    U+02A6D⩭\congdotCongruent With Dot Above
    U+02A6E⩮\asteqEquals With Asterisk
    U+02A6F⩯\hatapproxAlmost Equal To With Circumflex Accent
    U+02A70⩰\approxeqqApproximately Equal Or Equal To
    U+02A71⩱\eqqplusEquals Sign Above Plus Sign
    U+02A72⩲\pluseqqPlus Sign Above Equals Sign
    U+02A73⩳\eqqsimEquals Sign Above Tilde Operator
    U+02A74⩴\ColoneqDouble Colon Equal
    U+02A75⩵\EqualTwo Consecutive Equals Signs
    U+02A76⩶\eqeqeqThree Consecutive Equals Signs
    U+02A77⩷\ddotseqEquals Sign With Two Dots Above And Two Dots Below
    U+02A78⩸\equivDDEquivalent With Four Dots Above
    U+02A79⩹\ltcirLess-Than With Circle Inside
    U+02A7A⩺\gtcirGreater-Than With Circle Inside
    U+02A7B⩻\ltquestLess-Than With Question Mark Above
    U+02A7C⩼\gtquestGreater-Than With Question Mark Above
    U+02A7D⩽\leqslantLess-Than Or Slanted Equal To
    U+02A7D + U+00338⩽̸\nleqslantLess-Than Or Slanted Equal To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02A7E⩾\geqslantGreater-Than Or Slanted Equal To
    U+02A7E + U+00338⩾̸\ngeqslantGreater-Than Or Slanted Equal To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02A7F⩿\lesdotLess-Than Or Slanted Equal To With Dot Inside
    U+02A80⪀\gesdotGreater-Than Or Slanted Equal To With Dot Inside
    U+02A81⪁\lesdotoLess-Than Or Slanted Equal To With Dot Above
    U+02A82⪂\gesdotoGreater-Than Or Slanted Equal To With Dot Above
    U+02A83⪃\lesdotorLess-Than Or Slanted Equal To With Dot Above Right
    U+02A84⪄\gesdotolGreater-Than Or Slanted Equal To With Dot Above Left
    U+02A85⪅\lessapproxLess-Than Or Approximate
    U+02A86⪆\gtrapproxGreater-Than Or Approximate
    U+02A87⪇\lneqLess-Than And Single-Line Not Equal To
    U+02A88⪈\gneqGreater-Than And Single-Line Not Equal To
    U+02A89⪉\lnapproxLess-Than And Not Approximate
    U+02A8A⪊\gnapproxGreater-Than And Not Approximate
    U+02A8B⪋\lesseqqgtrLess-Than Above Double-Line Equal Above Greater-Than
    U+02A8C⪌\gtreqqlessGreater-Than Above Double-Line Equal Above Less-Than
    U+02A8D⪍\lsimeLess-Than Above Similar Or Equal
    U+02A8E⪎\gsimeGreater-Than Above Similar Or Equal
    U+02A8F⪏\lsimgLess-Than Above Similar Above Greater-Than
    U+02A90⪐\gsimlGreater-Than Above Similar Above Less-Than
    U+02A91⪑\lgELess-Than Above Greater-Than Above Double-Line Equal
    U+02A92⪒\glEGreater-Than Above Less-Than Above Double-Line Equal
    U+02A93⪓\lesgesLess-Than Above Slanted Equal Above Greater-Than Above Slanted Equal
    U+02A94⪔\geslesGreater-Than Above Slanted Equal Above Less-Than Above Slanted Equal
    U+02A95⪕\eqslantlessSlanted Equal To Or Less-Than
    U+02A96⪖\eqslantgtrSlanted Equal To Or Greater-Than
    U+02A97⪗\elsdotSlanted Equal To Or Less-Than With Dot Inside
    U+02A98⪘\egsdotSlanted Equal To Or Greater-Than With Dot Inside
    U+02A99⪙\eqqlessDouble-Line Equal To Or Less-Than
    U+02A9A⪚\eqqgtrDouble-Line Equal To Or Greater-Than
    U+02A9B⪛\eqqslantlessDouble-Line Slanted Equal To Or Less-Than
    U+02A9C⪜\eqqslantgtrDouble-Line Slanted Equal To Or Greater-Than
    U+02A9D⪝\simlessSimilar Or Less-Than
    U+02A9E⪞\simgtrSimilar Or Greater-Than
    U+02A9F⪟\simlESimilar Above Less-Than Above Equals Sign
    U+02AA0⪠\simgESimilar Above Greater-Than Above Equals Sign
    U+02AA1⪡\NestedLessLessDouble Nested Less-Than
    U+02AA1 + U+00338⪡̸\NotNestedLessLessDouble Nested Less-Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AA2⪢\NestedGreaterGreaterDouble Nested Greater-Than
    U+02AA2 + U+00338⪢̸\NotNestedGreaterGreaterDouble Nested Greater-Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AA3⪣\partialmeetcontractionDouble Nested Less-Than With Underbar
    U+02AA4⪤\gljGreater-Than Overlapping Less-Than
    U+02AA5⪥\glaGreater-Than Beside Less-Than
    U+02AA6⪦\ltccLess-Than Closed By Curve
    U+02AA7⪧\gtccGreater-Than Closed By Curve
    U+02AA8⪨\lesccLess-Than Closed By Curve Above Slanted Equal
    U+02AA9⪩\gesccGreater-Than Closed By Curve Above Slanted Equal
    U+02AAA⪪\smtSmaller Than
    U+02AAB⪫\latLarger Than
    U+02AAC⪬\smteSmaller Than Or Equal To
    U+02AAD⪭\lateLarger Than Or Equal To
    U+02AAE⪮\bumpeqqEquals Sign With Bumpy Above
    U+02AAF⪯\preceqPrecedes Above Single-Line Equals Sign
    U+02AAF + U+00338⪯̸\npreceqPrecedes Above Single-Line Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AB0⪰\succeqSucceeds Above Single-Line Equals Sign
    U+02AB0 + U+00338⪰̸\nsucceqSucceeds Above Single-Line Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AB1⪱\precneqPrecedes Above Single-Line Not Equal To
    U+02AB2⪲\succneqSucceeds Above Single-Line Not Equal To
    U+02AB3⪳\preceqqPrecedes Above Equals Sign
    U+02AB4⪴\succeqqSucceeds Above Equals Sign
    U+02AB5⪵\precneqqPrecedes Above Not Equal To
    U+02AB6⪶\succneqqSucceeds Above Not Equal To
    U+02AB7⪷\precapproxPrecedes Above Almost Equal To
    U+02AB8⪸\succapproxSucceeds Above Almost Equal To
    U+02AB9⪹\precnapproxPrecedes Above Not Almost Equal To
    U+02ABA⪺\succnapproxSucceeds Above Not Almost Equal To
    U+02ABB⪻\PrecDouble Precedes
    U+02ABC⪼\SuccDouble Succeeds
    U+02ABD⪽\subsetdotSubset With Dot
    U+02ABE⪾\supsetdotSuperset With Dot
    U+02ABF⪿\subsetplusSubset With Plus Sign Below
    U+02AC0⫀\supsetplusSuperset With Plus Sign Below
    U+02AC1⫁\submultSubset With Multiplication Sign Below
    U+02AC2⫂\supmultSuperset With Multiplication Sign Below
    U+02AC3⫃\subedotSubset Of Or Equal To With Dot Above
    U+02AC4⫄\supedotSuperset Of Or Equal To With Dot Above
    U+02AC5⫅\subseteqqSubset Of Above Equals Sign
    U+02AC5 + U+00338⫅̸\nsubseteqqSubset Of Above Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AC6⫆\supseteqqSuperset Of Above Equals Sign
    U+02AC6 + U+00338⫆̸\nsupseteqqSuperset Of Above Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AC7⫇\subsimSubset Of Above Tilde Operator
    U+02AC8⫈\supsimSuperset Of Above Tilde Operator
    U+02AC9⫉\subsetapproxSubset Of Above Almost Equal To
    U+02ACA⫊\supsetapproxSuperset Of Above Almost Equal To
    U+02ACB⫋\subsetneqqSubset Of Above Not Equal To
    U+02ACC⫌\supsetneqqSuperset Of Above Not Equal To
    U+02ACD⫍\lsqhookSquare Left Open Box Operator
    U+02ACE⫎\rsqhookSquare Right Open Box Operator
    U+02ACF⫏\csubClosed Subset
    U+02AD0⫐\csupClosed Superset
    U+02AD1⫑\csubeClosed Subset Or Equal To
    U+02AD2⫒\csupeClosed Superset Or Equal To
    U+02AD3⫓\subsupSubset Above Superset
    U+02AD4⫔\supsubSuperset Above Subset
    U+02AD5⫕\subsubSubset Above Subset
    U+02AD6⫖\supsupSuperset Above Superset
    U+02AD7⫗\suphsubSuperset Beside Subset
    U+02AD8⫘\supdsubSuperset Beside And Joined By Dash With Subset
    U+02AD9⫙\forkvElement Of Opening Downwards
    U+02ADB⫛\mlcpTransversal Intersection
    U+02ADC⫝̸\forksForking
    U+02ADD⫝\forksnotNonforking
    U+02AE3⫣\dashVDouble Vertical Bar Left Turnstile
    U+02AE4⫤\DashvVertical Bar Double Left Turnstile
    U+02AEA⫪\Top, \downvDashDouble Down Tack
    U+02AEB⫫\upvDash, \Bot, \indepDouble Up Tack
    U+02AF4⫴\interleaveTriple Vertical Bar Binary Relation
    U+02AF6⫶\tdcolTriple Colon Operator
    U+02AF7⫷\lllnestTriple Nested Less-Than
    U+02AF8⫸\gggnestTriple Nested Greater-Than
    U+02AF9⫹\leqqslantDouble-Line Slanted Less-Than Or Equal To
    U+02AFA⫺\geqqslantDouble-Line Slanted Greater-Than Or Equal To
    U+02B05⬅\:arrow_left:Leftwards Black Arrow
    U+02B06⬆\:arrow_up:Upwards Black Arrow
    U+02B07⬇\:arrow_down:Downwards Black Arrow
    U+02B12⬒\squaretopblackSquare With Top Half Black
    U+02B13⬓\squarebotblackSquare With Bottom Half Black
    U+02B14⬔\squareurblackSquare With Upper Right Diagonal Half Black
    U+02B15⬕\squarellblackSquare With Lower Left Diagonal Half Black
    U+02B16⬖\diamondleftblackDiamond With Left Half Black
    U+02B17⬗\diamondrightblackDiamond With Right Half Black
    U+02B18⬘\diamondtopblackDiamond With Top Half Black
    U+02B19⬙\diamondbotblackDiamond With Bottom Half Black
    U+02B1A⬚\dottedsquareDotted Square
    U+02B1B⬛\lgblksquare, \:black_large_square:Black Large Square
    U+02B1C⬜\lgwhtsquare, \:white_large_square:White Large Square
    U+02B1D⬝\vysmblksquareBlack Very Small Square
    U+02B1E⬞\vysmwhtsquareWhite Very Small Square
    U+02B1F⬟\pentagonblackBlack Pentagon
    U+02B20⬠\pentagonWhite Pentagon
    U+02B21⬡\varhexagonWhite Hexagon
    U+02B22⬢\varhexagonblackBlack Hexagon
    U+02B23⬣\hexagonblackHorizontal Black Hexagon
    U+02B24⬤\lgblkcircleBlack Large Circle
    U+02B25⬥\mdblkdiamondBlack Medium Diamond
    U+02B26⬦\mdwhtdiamondWhite Medium Diamond
    U+02B27⬧\mdblklozengeBlack Medium Lozenge
    U+02B28⬨\mdwhtlozengeWhite Medium Lozenge
    U+02B29⬩\smblkdiamondBlack Small Diamond
    U+02B2A⬪\smblklozengeBlack Small Lozenge
    U+02B2B⬫\smwhtlozengeWhite Small Lozenge
    U+02B2C⬬\blkhorzovalBlack Horizontal Ellipse
    U+02B2D⬭\whthorzovalWhite Horizontal Ellipse
    U+02B2E⬮\blkvertovalBlack Vertical Ellipse
    U+02B2F⬯\whtvertovalWhite Vertical Ellipse
    U+02B30⬰\circleonleftarrowLeft Arrow With Small Circle
    U+02B31⬱\leftthreearrowsThree Leftwards Arrows
    U+02B32⬲\leftarrowonoplusLeft Arrow With Circled Plus
    U+02B33⬳\longleftsquigarrowLong Leftwards Squiggle Arrow
    U+02B34⬴\nvtwoheadleftarrowLeftwards Two-Headed Arrow With Vertical Stroke
    U+02B35⬵\nVtwoheadleftarrowLeftwards Two-Headed Arrow With Double Vertical Stroke
    U+02B36⬶\twoheadmapsfromLeftwards Two-Headed Arrow From Bar
    U+02B37⬷\twoheadleftdbkarrowLeftwards Two-Headed Triple Dash Arrow
    U+02B38⬸\leftdotarrowLeftwards Arrow With Dotted Stem
    U+02B39⬹\nvleftarrowtailLeftwards Arrow With Tail With Vertical Stroke
    U+02B3A⬺\nVleftarrowtailLeftwards Arrow With Tail With Double Vertical Stroke
    U+02B3B⬻\twoheadleftarrowtailLeftwards Two-Headed Arrow With Tail
    U+02B3C⬼\nvtwoheadleftarrowtailLeftwards Two-Headed Arrow With Tail With Vertical Stroke
    U+02B3D⬽\nVtwoheadleftarrowtailLeftwards Two-Headed Arrow With Tail With Double Vertical Stroke
    U+02B3E⬾\leftarrowxLeftwards Arrow Through X
    U+02B3F⬿\leftcurvedarrowWave Arrow Pointing Directly Left
    U+02B40⭀\equalleftarrowEquals Sign Above Leftwards Arrow
    U+02B41⭁\bsimilarleftarrowReverse Tilde Operator Above Leftwards Arrow
    U+02B42⭂\leftarrowbackapproxLeftwards Arrow Above Reverse Almost Equal To
    U+02B43⭃\rightarrowgtrRightwards Arrow Through Greater-Than
    U+02B44⭄\rightarrowsupsetRightwards Arrow Through Superset
    U+02B45⭅\LLeftarrowLeftwards Quadruple Arrow
    U+02B46⭆\RRightarrowRightwards Quadruple Arrow
    U+02B47⭇\bsimilarrightarrowReverse Tilde Operator Above Rightwards Arrow
    U+02B48⭈\rightarrowbackapproxRightwards Arrow Above Reverse Almost Equal To
    U+02B49⭉\similarleftarrowTilde Operator Above Leftwards Arrow
    U+02B4A⭊\leftarrowapproxLeftwards Arrow Above Almost Equal To
    U+02B4B⭋\leftarrowbsimilarLeftwards Arrow Above Reverse Tilde Operator
    U+02B4C⭌\rightarrowbsimilarRightwards Arrow Above Reverse Tilde Operator
    U+02B50⭐\medwhitestar, \:star:White Medium Star
    U+02B51⭑\medblackstarBlack Small Star
    U+02B52⭒\smwhitestarWhite Small Star
    U+02B53⭓\rightpentagonblackBlack Right-Pointing Pentagon
    U+02B54⭔\rightpentagonWhite Right-Pointing Pentagon
    U+02B55⭕\:o:Heavy Large Circle
    U+02C7Cⱼ\_jLatin Subscript Small Letter J
    U+02C7Dⱽ\^VModifier Letter Capital V
    U+03012〒\postalmarkPostal Mark
    U+03030〰\:wavy_dash:Wavy Dash
    U+0303D〽\:part_alternation_mark:Part Alternation Mark
    U+03297㊗\:congratulations:Circled Ideograph Congratulation
    U+03299㊙\:secret:Circled Ideograph Secret
    U+0A71Bꜛ\^uparrowModifier Letter Raised Up Arrow
    U+0A71Cꜜ\^downarrowModifier Letter Raised Down Arrow
    U+0A71Dꜝ\^!Modifier Letter Raised Exclamation Mark
    U+1D400𝐀\bfAMathematical Bold Capital A
    U+1D401𝐁\bfBMathematical Bold Capital B
    U+1D402𝐂\bfCMathematical Bold Capital C
    U+1D403𝐃\bfDMathematical Bold Capital D
    U+1D404𝐄\bfEMathematical Bold Capital E
    U+1D405𝐅\bfFMathematical Bold Capital F
    U+1D406𝐆\bfGMathematical Bold Capital G
    U+1D407𝐇\bfHMathematical Bold Capital H
    U+1D408𝐈\bfIMathematical Bold Capital I
    U+1D409𝐉\bfJMathematical Bold Capital J
    U+1D40A𝐊\bfKMathematical Bold Capital K
    U+1D40B𝐋\bfLMathematical Bold Capital L
    U+1D40C𝐌\bfMMathematical Bold Capital M
    U+1D40D𝐍\bfNMathematical Bold Capital N
    U+1D40E𝐎\bfOMathematical Bold Capital O
    U+1D40F𝐏\bfPMathematical Bold Capital P
    U+1D410𝐐\bfQMathematical Bold Capital Q
    U+1D411𝐑\bfRMathematical Bold Capital R
    U+1D412𝐒\bfSMathematical Bold Capital S
    U+1D413𝐓\bfTMathematical Bold Capital T
    U+1D414𝐔\bfUMathematical Bold Capital U
    U+1D415𝐕\bfVMathematical Bold Capital V
    U+1D416𝐖\bfWMathematical Bold Capital W
    U+1D417𝐗\bfXMathematical Bold Capital X
    U+1D418𝐘\bfYMathematical Bold Capital Y
    U+1D419𝐙\bfZMathematical Bold Capital Z
    U+1D41A𝐚\bfaMathematical Bold Small A
    U+1D41B𝐛\bfbMathematical Bold Small B
    U+1D41C𝐜\bfcMathematical Bold Small C
    U+1D41D𝐝\bfdMathematical Bold Small D
    U+1D41E𝐞\bfeMathematical Bold Small E
    U+1D41F𝐟\bffMathematical Bold Small F
    U+1D420𝐠\bfgMathematical Bold Small G
    U+1D421𝐡\bfhMathematical Bold Small H
    U+1D422𝐢\bfiMathematical Bold Small I
    U+1D423𝐣\bfjMathematical Bold Small J
    U+1D424𝐤\bfkMathematical Bold Small K
    U+1D425𝐥\bflMathematical Bold Small L
    U+1D426𝐦\bfmMathematical Bold Small M
    U+1D427𝐧\bfnMathematical Bold Small N
    U+1D428𝐨\bfoMathematical Bold Small O
    U+1D429𝐩\bfpMathematical Bold Small P
    U+1D42A𝐪\bfqMathematical Bold Small Q
    U+1D42B𝐫\bfrMathematical Bold Small R
    U+1D42C𝐬\bfsMathematical Bold Small S
    U+1D42D𝐭\bftMathematical Bold Small T
    U+1D42E𝐮\bfuMathematical Bold Small U
    U+1D42F𝐯\bfvMathematical Bold Small V
    U+1D430𝐰\bfwMathematical Bold Small W
    U+1D431𝐱\bfxMathematical Bold Small X
    U+1D432𝐲\bfyMathematical Bold Small Y
    U+1D433𝐳\bfzMathematical Bold Small Z
    U+1D434𝐴\itAMathematical Italic Capital A
    U+1D435𝐵\itBMathematical Italic Capital B
    U+1D436𝐶\itCMathematical Italic Capital C
    U+1D437𝐷\itDMathematical Italic Capital D
    U+1D438𝐸\itEMathematical Italic Capital E
    U+1D439𝐹\itFMathematical Italic Capital F
    U+1D43A𝐺\itGMathematical Italic Capital G
    U+1D43B𝐻\itHMathematical Italic Capital H
    U+1D43C𝐼\itIMathematical Italic Capital I
    U+1D43D𝐽\itJMathematical Italic Capital J
    U+1D43E𝐾\itKMathematical Italic Capital K
    U+1D43F𝐿\itLMathematical Italic Capital L
    U+1D440𝑀\itMMathematical Italic Capital M
    U+1D441𝑁\itNMathematical Italic Capital N
    U+1D442𝑂\itOMathematical Italic Capital O
    U+1D443𝑃\itPMathematical Italic Capital P
    U+1D444𝑄\itQMathematical Italic Capital Q
    U+1D445𝑅\itRMathematical Italic Capital R
    U+1D446𝑆\itSMathematical Italic Capital S
    U+1D447𝑇\itTMathematical Italic Capital T
    U+1D448𝑈\itUMathematical Italic Capital U
    U+1D449𝑉\itVMathematical Italic Capital V
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    U+1D450𝑐\itcMathematical Italic Small C
    U+1D451𝑑\itdMathematical Italic Small D
    U+1D452𝑒\iteMathematical Italic Small E
    U+1D453𝑓\itfMathematical Italic Small F
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    U+1D456𝑖\itiMathematical Italic Small I
    U+1D457𝑗\itjMathematical Italic Small J
    U+1D458𝑘\itkMathematical Italic Small K
    U+1D459𝑙\itlMathematical Italic Small L
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    U+1D45B𝑛\itnMathematical Italic Small N
    U+1D45C𝑜\itoMathematical Italic Small O
    U+1D45D𝑝\itpMathematical Italic Small P
    U+1D45E𝑞\itqMathematical Italic Small Q
    U+1D45F𝑟\itrMathematical Italic Small R
    U+1D460𝑠\itsMathematical Italic Small S
    U+1D461𝑡\ittMathematical Italic Small T
    U+1D462𝑢\ituMathematical Italic Small U
    U+1D463𝑣\itvMathematical Italic Small V
    U+1D464𝑤\itwMathematical Italic Small W
    U+1D465𝑥\itxMathematical Italic Small X
    U+1D466𝑦\ityMathematical Italic Small Y
    U+1D467𝑧\itzMathematical Italic Small Z
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    U+1D46C𝑬\biEMathematical Bold Italic Capital E
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    U+1D46E𝑮\biGMathematical Bold Italic Capital G
    U+1D46F𝑯\biHMathematical Bold Italic Capital H
    U+1D470𝑰\biIMathematical Bold Italic Capital I
    U+1D471𝑱\biJMathematical Bold Italic Capital J
    U+1D472𝑲\biKMathematical Bold Italic Capital K
    U+1D473𝑳\biLMathematical Bold Italic Capital L
    U+1D474𝑴\biMMathematical Bold Italic Capital M
    U+1D475𝑵\biNMathematical Bold Italic Capital N
    U+1D476𝑶\biOMathematical Bold Italic Capital O
    U+1D477𝑷\biPMathematical Bold Italic Capital P
    U+1D478𝑸\biQMathematical Bold Italic Capital Q
    U+1D479𝑹\biRMathematical Bold Italic Capital R
    U+1D47A𝑺\biSMathematical Bold Italic Capital S
    U+1D47B𝑻\biTMathematical Bold Italic Capital T
    U+1D47C𝑼\biUMathematical Bold Italic Capital U
    U+1D47D𝑽\biVMathematical Bold Italic Capital V
    U+1D47E𝑾\biWMathematical Bold Italic Capital W
    U+1D47F𝑿\biXMathematical Bold Italic Capital X
    U+1D480𝒀\biYMathematical Bold Italic Capital Y
    U+1D481𝒁\biZMathematical Bold Italic Capital Z
    U+1D482𝒂\biaMathematical Bold Italic Small A
    U+1D483𝒃\bibMathematical Bold Italic Small B
    U+1D484𝒄\bicMathematical Bold Italic Small C
    U+1D485𝒅\bidMathematical Bold Italic Small D
    U+1D486𝒆\bieMathematical Bold Italic Small E
    U+1D487𝒇\bifMathematical Bold Italic Small F
    U+1D488𝒈\bigMathematical Bold Italic Small G
    U+1D489𝒉\bihMathematical Bold Italic Small H
    U+1D48A𝒊\biiMathematical Bold Italic Small I
    U+1D48B𝒋\bijMathematical Bold Italic Small J
    U+1D48C𝒌\bikMathematical Bold Italic Small K
    U+1D48D𝒍\bilMathematical Bold Italic Small L
    U+1D48E𝒎\bimMathematical Bold Italic Small M
    U+1D48F𝒏\binMathematical Bold Italic Small N
    U+1D490𝒐\bioMathematical Bold Italic Small O
    U+1D491𝒑\bipMathematical Bold Italic Small P
    U+1D492𝒒\biqMathematical Bold Italic Small Q
    U+1D493𝒓\birMathematical Bold Italic Small R
    U+1D494𝒔\bisMathematical Bold Italic Small S
    U+1D495𝒕\bitMathematical Bold Italic Small T
    U+1D496𝒖\biuMathematical Bold Italic Small U
    U+1D497𝒗\bivMathematical Bold Italic Small V
    U+1D498𝒘\biwMathematical Bold Italic Small W
    U+1D499𝒙\bixMathematical Bold Italic Small X
    U+1D49A𝒚\biyMathematical Bold Italic Small Y
    U+1D49B𝒛\bizMathematical Bold Italic Small Z
    U+1D49C𝒜\scrAMathematical Script Capital A
    U+1D49E𝒞\scrCMathematical Script Capital C
    U+1D49F𝒟\scrDMathematical Script Capital D
    U+1D4A2𝒢\scrGMathematical Script Capital G
    U+1D4A5𝒥\scrJMathematical Script Capital J
    U+1D4A6𝒦\scrKMathematical Script Capital K
    U+1D4A9𝒩\scrNMathematical Script Capital N
    U+1D4AA𝒪\scrOMathematical Script Capital O
    U+1D4AB𝒫\scrPMathematical Script Capital P
    U+1D4AC𝒬\scrQMathematical Script Capital Q
    U+1D4AE𝒮\scrSMathematical Script Capital S
    U+1D4AF𝒯\scrTMathematical Script Capital T
    U+1D4B0𝒰\scrUMathematical Script Capital U
    U+1D4B1𝒱\scrVMathematical Script Capital V
    U+1D4B2𝒲\scrWMathematical Script Capital W
    U+1D4B3𝒳\scrXMathematical Script Capital X
    U+1D4B4𝒴\scrYMathematical Script Capital Y
    U+1D4B5𝒵\scrZMathematical Script Capital Z
    U+1D4B6𝒶\scraMathematical Script Small A
    U+1D4B7𝒷\scrbMathematical Script Small B
    U+1D4B8𝒸\scrcMathematical Script Small C
    U+1D4B9𝒹\scrdMathematical Script Small D
    U+1D4BB𝒻\scrfMathematical Script Small F
    U+1D4BD𝒽\scrhMathematical Script Small H
    U+1D4BE𝒾\scriMathematical Script Small I
    U+1D4BF𝒿\scrjMathematical Script Small J
    U+1D4C0𝓀\scrkMathematical Script Small K
    U+1D4C1𝓁\scrlMathematical Script Small L
    U+1D4C2𝓂\scrmMathematical Script Small M
    U+1D4C3𝓃\scrnMathematical Script Small N
    U+1D4C5𝓅\scrpMathematical Script Small P
    U+1D4C6𝓆\scrqMathematical Script Small Q
    U+1D4C7𝓇\scrrMathematical Script Small R
    U+1D4C8𝓈\scrsMathematical Script Small S
    U+1D4C9𝓉\scrtMathematical Script Small T
    U+1D4CA𝓊\scruMathematical Script Small U
    U+1D4CB𝓋\scrvMathematical Script Small V
    U+1D4CC𝓌\scrwMathematical Script Small W
    U+1D4CD𝓍\scrxMathematical Script Small X
    U+1D4CE𝓎\scryMathematical Script Small Y
    U+1D4CF𝓏\scrzMathematical Script Small Z
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    U+1D4D1𝓑\bscrBMathematical Bold Script Capital B
    U+1D4D2𝓒\bscrCMathematical Bold Script Capital C
    U+1D4D3𝓓\bscrDMathematical Bold Script Capital D
    U+1D4D4𝓔\bscrEMathematical Bold Script Capital E
    U+1D4D5𝓕\bscrFMathematical Bold Script Capital F
    U+1D4D6𝓖\bscrGMathematical Bold Script Capital G
    U+1D4D7𝓗\bscrHMathematical Bold Script Capital H
    U+1D4D8𝓘\bscrIMathematical Bold Script Capital I
    U+1D4D9𝓙\bscrJMathematical Bold Script Capital J
    U+1D4DA𝓚\bscrKMathematical Bold Script Capital K
    U+1D4DB𝓛\bscrLMathematical Bold Script Capital L
    U+1D4DC𝓜\bscrMMathematical Bold Script Capital M
    U+1D4DD𝓝\bscrNMathematical Bold Script Capital N
    U+1D4DE𝓞\bscrOMathematical Bold Script Capital O
    U+1D4DF𝓟\bscrPMathematical Bold Script Capital P
    U+1D4E0𝓠\bscrQMathematical Bold Script Capital Q
    U+1D4E1𝓡\bscrRMathematical Bold Script Capital R
    U+1D4E2𝓢\bscrSMathematical Bold Script Capital S
    U+1D4E3𝓣\bscrTMathematical Bold Script Capital T
    U+1D4E4𝓤\bscrUMathematical Bold Script Capital U
    U+1D4E5𝓥\bscrVMathematical Bold Script Capital V
    U+1D4E6𝓦\bscrWMathematical Bold Script Capital W
    U+1D4E7𝓧\bscrXMathematical Bold Script Capital X
    U+1D4E8𝓨\bscrYMathematical Bold Script Capital Y
    U+1D4E9𝓩\bscrZMathematical Bold Script Capital Z
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    U+1D4ED𝓭\bscrdMathematical Bold Script Small D
    U+1D4EE𝓮\bscreMathematical Bold Script Small E
    U+1D4EF𝓯\bscrfMathematical Bold Script Small F
    U+1D4F0𝓰\bscrgMathematical Bold Script Small G
    U+1D4F1𝓱\bscrhMathematical Bold Script Small H
    U+1D4F2𝓲\bscriMathematical Bold Script Small I
    U+1D4F3𝓳\bscrjMathematical Bold Script Small J
    U+1D4F4𝓴\bscrkMathematical Bold Script Small K
    U+1D4F5𝓵\bscrlMathematical Bold Script Small L
    U+1D4F6𝓶\bscrmMathematical Bold Script Small M
    U+1D4F7𝓷\bscrnMathematical Bold Script Small N
    U+1D4F8𝓸\bscroMathematical Bold Script Small O
    U+1D4F9𝓹\bscrpMathematical Bold Script Small P
    U+1D4FA𝓺\bscrqMathematical Bold Script Small Q
    U+1D4FB𝓻\bscrrMathematical Bold Script Small R
    U+1D4FC𝓼\bscrsMathematical Bold Script Small S
    U+1D4FD𝓽\bscrtMathematical Bold Script Small T
    U+1D4FE𝓾\bscruMathematical Bold Script Small U
    U+1D4FF𝓿\bscrvMathematical Bold Script Small V
    U+1D500𝔀\bscrwMathematical Bold Script Small W
    U+1D501𝔁\bscrxMathematical Bold Script Small X
    U+1D502𝔂\bscryMathematical Bold Script Small Y
    U+1D503𝔃\bscrzMathematical Bold Script Small Z
    U+1D504𝔄\frakAMathematical Fraktur Capital A
    U+1D505𝔅\frakBMathematical Fraktur Capital B
    U+1D507𝔇\frakDMathematical Fraktur Capital D
    U+1D508𝔈\frakEMathematical Fraktur Capital E
    U+1D509𝔉\frakFMathematical Fraktur Capital F
    U+1D50A𝔊\frakGMathematical Fraktur Capital G
    U+1D50D𝔍\frakJMathematical Fraktur Capital J
    U+1D50E𝔎\frakKMathematical Fraktur Capital K
    U+1D50F𝔏\frakLMathematical Fraktur Capital L
    U+1D510𝔐\frakMMathematical Fraktur Capital M
    U+1D511𝔑\frakNMathematical Fraktur Capital N
    U+1D512𝔒\frakOMathematical Fraktur Capital O
    U+1D513𝔓\frakPMathematical Fraktur Capital P
    U+1D514𝔔\frakQMathematical Fraktur Capital Q
    U+1D516𝔖\frakSMathematical Fraktur Capital S
    U+1D517𝔗\frakTMathematical Fraktur Capital T
    U+1D518𝔘\frakUMathematical Fraktur Capital U
    U+1D519𝔙\frakVMathematical Fraktur Capital V
    U+1D51A𝔚\frakWMathematical Fraktur Capital W
    U+1D51B𝔛\frakXMathematical Fraktur Capital X
    U+1D51C𝔜\frakYMathematical Fraktur Capital Y
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    U+1D51F𝔟\frakbMathematical Fraktur Small B
    U+1D520𝔠\frakcMathematical Fraktur Small C
    U+1D521𝔡\frakdMathematical Fraktur Small D
    U+1D522𝔢\frakeMathematical Fraktur Small E
    U+1D523𝔣\frakfMathematical Fraktur Small F
    U+1D524𝔤\frakgMathematical Fraktur Small G
    U+1D525𝔥\frakhMathematical Fraktur Small H
    U+1D526𝔦\frakiMathematical Fraktur Small I
    U+1D527𝔧\frakjMathematical Fraktur Small J
    U+1D528𝔨\frakkMathematical Fraktur Small K
    U+1D529𝔩\fraklMathematical Fraktur Small L
    U+1D52A𝔪\frakmMathematical Fraktur Small M
    U+1D52B𝔫\fraknMathematical Fraktur Small N
    U+1D52C𝔬\frakoMathematical Fraktur Small O
    U+1D52D𝔭\frakpMathematical Fraktur Small P
    U+1D52E𝔮\frakqMathematical Fraktur Small Q
    U+1D52F𝔯\frakrMathematical Fraktur Small R
    U+1D530𝔰\fraksMathematical Fraktur Small S
    U+1D531𝔱\fraktMathematical Fraktur Small T
    U+1D532𝔲\frakuMathematical Fraktur Small U
    U+1D533𝔳\frakvMathematical Fraktur Small V
    U+1D534𝔴\frakwMathematical Fraktur Small W
    U+1D535𝔵\frakxMathematical Fraktur Small X
    U+1D536𝔶\frakyMathematical Fraktur Small Y
    U+1D537𝔷\frakzMathematical Fraktur Small Z
    U+1D538𝔸\bbAMathematical Double-Struck Capital A
    U+1D539𝔹\bbBMathematical Double-Struck Capital B
    U+1D53B𝔻\bbDMathematical Double-Struck Capital D
    U+1D53C𝔼\bbEMathematical Double-Struck Capital E
    U+1D53D𝔽\bbFMathematical Double-Struck Capital F
    U+1D53E𝔾\bbGMathematical Double-Struck Capital G
    U+1D540𝕀\bbIMathematical Double-Struck Capital I
    U+1D541𝕁\bbJMathematical Double-Struck Capital J
    U+1D542𝕂\bbKMathematical Double-Struck Capital K
    U+1D543𝕃\bbLMathematical Double-Struck Capital L
    U+1D544𝕄\bbMMathematical Double-Struck Capital M
    U+1D546𝕆\bbOMathematical Double-Struck Capital O
    U+1D54A𝕊\bbSMathematical Double-Struck Capital S
    U+1D54B𝕋\bbTMathematical Double-Struck Capital T
    U+1D54C𝕌\bbUMathematical Double-Struck Capital U
    U+1D54D𝕍\bbVMathematical Double-Struck Capital V
    U+1D54E𝕎\bbWMathematical Double-Struck Capital W
    U+1D54F𝕏\bbXMathematical Double-Struck Capital X
    U+1D550𝕐\bbYMathematical Double-Struck Capital Y
    U+1D552𝕒\bbaMathematical Double-Struck Small A
    U+1D553𝕓\bbbMathematical Double-Struck Small B
    U+1D554𝕔\bbcMathematical Double-Struck Small C
    U+1D555𝕕\bbdMathematical Double-Struck Small D
    U+1D556𝕖\bbeMathematical Double-Struck Small E
    U+1D557𝕗\bbfMathematical Double-Struck Small F
    U+1D558𝕘\bbgMathematical Double-Struck Small G
    U+1D559𝕙\bbhMathematical Double-Struck Small H
    U+1D55A𝕚\bbiMathematical Double-Struck Small I
    U+1D55B𝕛\bbjMathematical Double-Struck Small J
    U+1D55C𝕜\bbkMathematical Double-Struck Small K
    U+1D55D𝕝\bblMathematical Double-Struck Small L
    U+1D55E𝕞\bbmMathematical Double-Struck Small M
    U+1D55F𝕟\bbnMathematical Double-Struck Small N
    U+1D560𝕠\bboMathematical Double-Struck Small O
    U+1D561𝕡\bbpMathematical Double-Struck Small P
    U+1D562𝕢\bbqMathematical Double-Struck Small Q
    U+1D563𝕣\bbrMathematical Double-Struck Small R
    U+1D564𝕤\bbsMathematical Double-Struck Small S
    U+1D565𝕥\bbtMathematical Double-Struck Small T
    U+1D566𝕦\bbuMathematical Double-Struck Small U
    U+1D567𝕧\bbvMathematical Double-Struck Small V
    U+1D568𝕨\bbwMathematical Double-Struck Small W
    U+1D569𝕩\bbxMathematical Double-Struck Small X
    U+1D56A𝕪\bbyMathematical Double-Struck Small Y
    U+1D56B𝕫\bbzMathematical Double-Struck Small Z
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    U+1D570𝕰\bfrakEMathematical Bold Fraktur Capital E
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    U+1D572𝕲\bfrakGMathematical Bold Fraktur Capital G
    U+1D573𝕳\bfrakHMathematical Bold Fraktur Capital H
    U+1D574𝕴\bfrakIMathematical Bold Fraktur Capital I
    U+1D575𝕵\bfrakJMathematical Bold Fraktur Capital J
    U+1D576𝕶\bfrakKMathematical Bold Fraktur Capital K
    U+1D577𝕷\bfrakLMathematical Bold Fraktur Capital L
    U+1D578𝕸\bfrakMMathematical Bold Fraktur Capital M
    U+1D579𝕹\bfrakNMathematical Bold Fraktur Capital N
    U+1D57A𝕺\bfrakOMathematical Bold Fraktur Capital O
    U+1D57B𝕻\bfrakPMathematical Bold Fraktur Capital P
    U+1D57C𝕼\bfrakQMathematical Bold Fraktur Capital Q
    U+1D57D𝕽\bfrakRMathematical Bold Fraktur Capital R
    U+1D57E𝕾\bfrakSMathematical Bold Fraktur Capital S
    U+1D57F𝕿\bfrakTMathematical Bold Fraktur Capital T
    U+1D580𝖀\bfrakUMathematical Bold Fraktur Capital U
    U+1D581𝖁\bfrakVMathematical Bold Fraktur Capital V
    U+1D582𝖂\bfrakWMathematical Bold Fraktur Capital W
    U+1D583𝖃\bfrakXMathematical Bold Fraktur Capital X
    U+1D584𝖄\bfrakYMathematical Bold Fraktur Capital Y
    U+1D585𝖅\bfrakZMathematical Bold Fraktur Capital Z
    U+1D586𝖆\bfrakaMathematical Bold Fraktur Small A
    U+1D587𝖇\bfrakbMathematical Bold Fraktur Small B
    U+1D588𝖈\bfrakcMathematical Bold Fraktur Small C
    U+1D589𝖉\bfrakdMathematical Bold Fraktur Small D
    U+1D58A𝖊\bfrakeMathematical Bold Fraktur Small E
    U+1D58B𝖋\bfrakfMathematical Bold Fraktur Small F
    U+1D58C𝖌\bfrakgMathematical Bold Fraktur Small G
    U+1D58D𝖍\bfrakhMathematical Bold Fraktur Small H
    U+1D58E𝖎\bfrakiMathematical Bold Fraktur Small I
    U+1D58F𝖏\bfrakjMathematical Bold Fraktur Small J
    U+1D590𝖐\bfrakkMathematical Bold Fraktur Small K
    U+1D591𝖑\bfraklMathematical Bold Fraktur Small L
    U+1D592𝖒\bfrakmMathematical Bold Fraktur Small M
    U+1D593𝖓\bfraknMathematical Bold Fraktur Small N
    U+1D594𝖔\bfrakoMathematical Bold Fraktur Small O
    U+1D595𝖕\bfrakpMathematical Bold Fraktur Small P
    U+1D596𝖖\bfrakqMathematical Bold Fraktur Small Q
    U+1D597𝖗\bfrakrMathematical Bold Fraktur Small R
    U+1D598𝖘\bfraksMathematical Bold Fraktur Small S
    U+1D599𝖙\bfraktMathematical Bold Fraktur Small T
    U+1D59A𝖚\bfrakuMathematical Bold Fraktur Small U
    U+1D59B𝖛\bfrakvMathematical Bold Fraktur Small V
    U+1D59C𝖜\bfrakwMathematical Bold Fraktur Small W
    U+1D59D𝖝\bfrakxMathematical Bold Fraktur Small X
    U+1D59E𝖞\bfrakyMathematical Bold Fraktur Small Y
    U+1D59F𝖟\bfrakzMathematical Bold Fraktur Small Z
    U+1D5A0𝖠\sansAMathematical Sans-Serif Capital A
    U+1D5A1𝖡\sansBMathematical Sans-Serif Capital B
    U+1D5A2𝖢\sansCMathematical Sans-Serif Capital C
    U+1D5A3𝖣\sansDMathematical Sans-Serif Capital D
    U+1D5A4𝖤\sansEMathematical Sans-Serif Capital E
    U+1D5A5𝖥\sansFMathematical Sans-Serif Capital F
    U+1D5A6𝖦\sansGMathematical Sans-Serif Capital G
    U+1D5A7𝖧\sansHMathematical Sans-Serif Capital H
    U+1D5A8𝖨\sansIMathematical Sans-Serif Capital I
    U+1D5A9𝖩\sansJMathematical Sans-Serif Capital J
    U+1D5AA𝖪\sansKMathematical Sans-Serif Capital K
    U+1D5AB𝖫\sansLMathematical Sans-Serif Capital L
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    U+1D5AD𝖭\sansNMathematical Sans-Serif Capital N
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    U+1D680𝚀\ttQMathematical Monospace Capital Q
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    U+1D684𝚄\ttUMathematical Monospace Capital U
    U+1D685𝚅\ttVMathematical Monospace Capital V
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    U+1D68D𝚍\ttdMathematical Monospace Small D
    U+1D68E𝚎\tteMathematical Monospace Small E
    U+1D68F𝚏\ttfMathematical Monospace Small F
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    U+1D6AE𝚮\bfEtaMathematical Bold Capital Eta
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    U+1D6C5𝛅\bfdeltaMathematical Bold Small Delta
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    U+1D6CE𝛎\bfnuMathematical Bold Small Nu
    U+1D6CF𝛏\bfxiMathematical Bold Small Xi
    U+1D6D0𝛐\bfomicronMathematical Bold Small Omicron
    U+1D6D1𝛑\bfpiMathematical Bold Small Pi
    U+1D6D2𝛒\bfrhoMathematical Bold Small Rho
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    U+1D6DE𝛞\bfvarkappaMathematical Bold Kappa Symbol
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    U+1D6E3𝛣\itBetaMathematical Italic Capital Beta
    U+1D6E4𝛤\itGammaMathematical Italic Capital Gamma
    U+1D6E5𝛥\itDeltaMathematical Italic Capital Delta
    U+1D6E6𝛦\itEpsilonMathematical Italic Capital Epsilon
    U+1D6E7𝛧\itZetaMathematical Italic Capital Zeta
    U+1D6E8𝛨\itEtaMathematical Italic Capital Eta
    U+1D6E9𝛩\itThetaMathematical Italic Capital Theta
    U+1D6EA𝛪\itIotaMathematical Italic Capital Iota
    U+1D6EB𝛫\itKappaMathematical Italic Capital Kappa
    U+1D6EC𝛬\itLambdaMathematical Italic Capital Lamda
    U+1D6ED𝛭\itMuMathematical Italic Capital Mu
    U+1D6EE𝛮\itNuMathematical Italic Capital Nu
    U+1D6EF𝛯\itXiMathematical Italic Capital Xi
    U+1D6F0𝛰\itOmicronMathematical Italic Capital Omicron
    U+1D6F1𝛱\itPiMathematical Italic Capital Pi
    U+1D6F2𝛲\itRhoMathematical Italic Capital Rho
    U+1D6F3𝛳\itvarThetaMathematical Italic Capital Theta Symbol
    U+1D6F4𝛴\itSigmaMathematical Italic Capital Sigma
    U+1D6F5𝛵\itTauMathematical Italic Capital Tau
    U+1D6F6𝛶\itUpsilonMathematical Italic Capital Upsilon
    U+1D6F7𝛷\itPhiMathematical Italic Capital Phi
    U+1D6F8𝛸\itChiMathematical Italic Capital Chi
    U+1D6F9𝛹\itPsiMathematical Italic Capital Psi
    U+1D6FA𝛺\itOmegaMathematical Italic Capital Omega
    U+1D6FB𝛻\itnablaMathematical Italic Nabla
    U+1D6FC𝛼\italphaMathematical Italic Small Alpha
    U+1D6FD𝛽\itbetaMathematical Italic Small Beta
    U+1D6FE𝛾\itgammaMathematical Italic Small Gamma
    U+1D6FF𝛿\itdeltaMathematical Italic Small Delta
    U+1D700𝜀\itvarepsilonMathematical Italic Small Epsilon
    U+1D701𝜁\itzetaMathematical Italic Small Zeta
    U+1D702𝜂\itetaMathematical Italic Small Eta
    U+1D703𝜃\itthetaMathematical Italic Small Theta
    U+1D704𝜄\itiotaMathematical Italic Small Iota
    U+1D705𝜅\itkappaMathematical Italic Small Kappa
    U+1D706𝜆\itlambdaMathematical Italic Small Lamda
    U+1D707𝜇\itmuMathematical Italic Small Mu
    U+1D708𝜈\itnuMathematical Italic Small Nu
    U+1D709𝜉\itxiMathematical Italic Small Xi
    U+1D70A𝜊\itomicronMathematical Italic Small Omicron
    U+1D70B𝜋\itpiMathematical Italic Small Pi
    U+1D70C𝜌\itrhoMathematical Italic Small Rho
    U+1D70D𝜍\itvarsigmaMathematical Italic Small Final Sigma
    U+1D70E𝜎\itsigmaMathematical Italic Small Sigma
    U+1D70F𝜏\ittauMathematical Italic Small Tau
    U+1D710𝜐\itupsilonMathematical Italic Small Upsilon
    U+1D711𝜑\itvarphiMathematical Italic Small Phi
    U+1D712𝜒\itchiMathematical Italic Small Chi
    U+1D713𝜓\itpsiMathematical Italic Small Psi
    U+1D714𝜔\itomegaMathematical Italic Small Omega
    U+1D715𝜕\itpartialMathematical Italic Partial Differential
    U+1D716𝜖\itepsilonMathematical Italic Epsilon Symbol
    U+1D717𝜗\itvarthetaMathematical Italic Theta Symbol
    U+1D718𝜘\itvarkappaMathematical Italic Kappa Symbol
    U+1D719𝜙\itphiMathematical Italic Phi Symbol
    U+1D71A𝜚\itvarrhoMathematical Italic Rho Symbol
    U+1D71B𝜛\itvarpiMathematical Italic Pi Symbol
    U+1D71C𝜜\biAlphaMathematical Bold Italic Capital Alpha
    U+1D71D𝜝\biBetaMathematical Bold Italic Capital Beta
    U+1D71E𝜞\biGammaMathematical Bold Italic Capital Gamma
    U+1D71F𝜟\biDeltaMathematical Bold Italic Capital Delta
    U+1D720𝜠\biEpsilonMathematical Bold Italic Capital Epsilon
    U+1D721𝜡\biZetaMathematical Bold Italic Capital Zeta
    U+1D722𝜢\biEtaMathematical Bold Italic Capital Eta
    U+1D723𝜣\biThetaMathematical Bold Italic Capital Theta
    U+1D724𝜤\biIotaMathematical Bold Italic Capital Iota
    U+1D725𝜥\biKappaMathematical Bold Italic Capital Kappa
    U+1D726𝜦\biLambdaMathematical Bold Italic Capital Lamda
    U+1D727𝜧\biMuMathematical Bold Italic Capital Mu
    U+1D728𝜨\biNuMathematical Bold Italic Capital Nu
    U+1D729𝜩\biXiMathematical Bold Italic Capital Xi
    U+1D72A𝜪\biOmicronMathematical Bold Italic Capital Omicron
    U+1D72B𝜫\biPiMathematical Bold Italic Capital Pi
    U+1D72C𝜬\biRhoMathematical Bold Italic Capital Rho
    U+1D72D𝜭\bivarThetaMathematical Bold Italic Capital Theta Symbol
    U+1D72E𝜮\biSigmaMathematical Bold Italic Capital Sigma
    U+1D72F𝜯\biTauMathematical Bold Italic Capital Tau
    U+1D730𝜰\biUpsilonMathematical Bold Italic Capital Upsilon
    U+1D731𝜱\biPhiMathematical Bold Italic Capital Phi
    U+1D732𝜲\biChiMathematical Bold Italic Capital Chi
    U+1D733𝜳\biPsiMathematical Bold Italic Capital Psi
    U+1D734𝜴\biOmegaMathematical Bold Italic Capital Omega
    U+1D735𝜵\binablaMathematical Bold Italic Nabla
    U+1D736𝜶\bialphaMathematical Bold Italic Small Alpha
    U+1D737𝜷\bibetaMathematical Bold Italic Small Beta
    U+1D738𝜸\bigammaMathematical Bold Italic Small Gamma
    U+1D739𝜹\bideltaMathematical Bold Italic Small Delta
    U+1D73A𝜺\bivarepsilonMathematical Bold Italic Small Epsilon
    U+1D73B𝜻\bizetaMathematical Bold Italic Small Zeta
    U+1D73C𝜼\bietaMathematical Bold Italic Small Eta
    U+1D73D𝜽\bithetaMathematical Bold Italic Small Theta
    U+1D73E𝜾\biiotaMathematical Bold Italic Small Iota
    U+1D73F𝜿\bikappaMathematical Bold Italic Small Kappa
    U+1D740𝝀\bilambdaMathematical Bold Italic Small Lamda
    U+1D741𝝁\bimuMathematical Bold Italic Small Mu
    U+1D742𝝂\binuMathematical Bold Italic Small Nu
    U+1D743𝝃\bixiMathematical Bold Italic Small Xi
    U+1D744𝝄\biomicronMathematical Bold Italic Small Omicron
    U+1D745𝝅\bipiMathematical Bold Italic Small Pi
    U+1D746𝝆\birhoMathematical Bold Italic Small Rho
    U+1D747𝝇\bivarsigmaMathematical Bold Italic Small Final Sigma
    U+1D748𝝈\bisigmaMathematical Bold Italic Small Sigma
    U+1D749𝝉\bitauMathematical Bold Italic Small Tau
    U+1D74A𝝊\biupsilonMathematical Bold Italic Small Upsilon
    U+1D74B𝝋\bivarphiMathematical Bold Italic Small Phi
    U+1D74C𝝌\bichiMathematical Bold Italic Small Chi
    U+1D74D𝝍\bipsiMathematical Bold Italic Small Psi
    U+1D74E𝝎\biomegaMathematical Bold Italic Small Omega
    U+1D74F𝝏\bipartialMathematical Bold Italic Partial Differential
    U+1D750𝝐\biepsilonMathematical Bold Italic Epsilon Symbol
    U+1D751𝝑\bivarthetaMathematical Bold Italic Theta Symbol
    U+1D752𝝒\bivarkappaMathematical Bold Italic Kappa Symbol
    U+1D753𝝓\biphiMathematical Bold Italic Phi Symbol
    U+1D754𝝔\bivarrhoMathematical Bold Italic Rho Symbol
    U+1D755𝝕\bivarpiMathematical Bold Italic Pi Symbol
    U+1D756𝝖\bsansAlphaMathematical Sans-Serif Bold Capital Alpha
    U+1D757𝝗\bsansBetaMathematical Sans-Serif Bold Capital Beta
    U+1D758𝝘\bsansGammaMathematical Sans-Serif Bold Capital Gamma
    U+1D759𝝙\bsansDeltaMathematical Sans-Serif Bold Capital Delta
    U+1D75A𝝚\bsansEpsilonMathematical Sans-Serif Bold Capital Epsilon
    U+1D75B𝝛\bsansZetaMathematical Sans-Serif Bold Capital Zeta
    U+1D75C𝝜\bsansEtaMathematical Sans-Serif Bold Capital Eta
    U+1D75D𝝝\bsansThetaMathematical Sans-Serif Bold Capital Theta
    U+1D75E𝝞\bsansIotaMathematical Sans-Serif Bold Capital Iota
    U+1D75F𝝟\bsansKappaMathematical Sans-Serif Bold Capital Kappa
    U+1D760𝝠\bsansLambdaMathematical Sans-Serif Bold Capital Lamda
    U+1D761𝝡\bsansMuMathematical Sans-Serif Bold Capital Mu
    U+1D762𝝢\bsansNuMathematical Sans-Serif Bold Capital Nu
    U+1D763𝝣\bsansXiMathematical Sans-Serif Bold Capital Xi
    U+1D764𝝤\bsansOmicronMathematical Sans-Serif Bold Capital Omicron
    U+1D765𝝥\bsansPiMathematical Sans-Serif Bold Capital Pi
    U+1D766𝝦\bsansRhoMathematical Sans-Serif Bold Capital Rho
    U+1D767𝝧\bsansvarThetaMathematical Sans-Serif Bold Capital Theta Symbol
    U+1D768𝝨\bsansSigmaMathematical Sans-Serif Bold Capital Sigma
    U+1D769𝝩\bsansTauMathematical Sans-Serif Bold Capital Tau
    U+1D76A𝝪\bsansUpsilonMathematical Sans-Serif Bold Capital Upsilon
    U+1D76B𝝫\bsansPhiMathematical Sans-Serif Bold Capital Phi
    U+1D76C𝝬\bsansChiMathematical Sans-Serif Bold Capital Chi
    U+1D76D𝝭\bsansPsiMathematical Sans-Serif Bold Capital Psi
    U+1D76E𝝮\bsansOmegaMathematical Sans-Serif Bold Capital Omega
    U+1D76F𝝯\bsansnablaMathematical Sans-Serif Bold Nabla
    U+1D770𝝰\bsansalphaMathematical Sans-Serif Bold Small Alpha
    U+1D771𝝱\bsansbetaMathematical Sans-Serif Bold Small Beta
    U+1D772𝝲\bsansgammaMathematical Sans-Serif Bold Small Gamma
    U+1D773𝝳\bsansdeltaMathematical Sans-Serif Bold Small Delta
    U+1D774𝝴\bsansvarepsilonMathematical Sans-Serif Bold Small Epsilon
    U+1D775𝝵\bsanszetaMathematical Sans-Serif Bold Small Zeta
    U+1D776𝝶\bsansetaMathematical Sans-Serif Bold Small Eta
    U+1D777𝝷\bsansthetaMathematical Sans-Serif Bold Small Theta
    U+1D778𝝸\bsansiotaMathematical Sans-Serif Bold Small Iota
    U+1D779𝝹\bsanskappaMathematical Sans-Serif Bold Small Kappa
    U+1D77A𝝺\bsanslambdaMathematical Sans-Serif Bold Small Lamda
    U+1D77B𝝻\bsansmuMathematical Sans-Serif Bold Small Mu
    U+1D77C𝝼\bsansnuMathematical Sans-Serif Bold Small Nu
    U+1D77D𝝽\bsansxiMathematical Sans-Serif Bold Small Xi
    U+1D77E𝝾\bsansomicronMathematical Sans-Serif Bold Small Omicron
    U+1D77F𝝿\bsanspiMathematical Sans-Serif Bold Small Pi
    U+1D780𝞀\bsansrhoMathematical Sans-Serif Bold Small Rho
    U+1D781𝞁\bsansvarsigmaMathematical Sans-Serif Bold Small Final Sigma
    U+1D782𝞂\bsanssigmaMathematical Sans-Serif Bold Small Sigma
    U+1D783𝞃\bsanstauMathematical Sans-Serif Bold Small Tau
    U+1D784𝞄\bsansupsilonMathematical Sans-Serif Bold Small Upsilon
    U+1D785𝞅\bsansvarphiMathematical Sans-Serif Bold Small Phi
    U+1D786𝞆\bsanschiMathematical Sans-Serif Bold Small Chi
    U+1D787𝞇\bsanspsiMathematical Sans-Serif Bold Small Psi
    U+1D788𝞈\bsansomegaMathematical Sans-Serif Bold Small Omega
    U+1D789𝞉\bsanspartialMathematical Sans-Serif Bold Partial Differential
    U+1D78A𝞊\bsansepsilonMathematical Sans-Serif Bold Epsilon Symbol
    U+1D78B𝞋\bsansvarthetaMathematical Sans-Serif Bold Theta Symbol
    U+1D78C𝞌\bsansvarkappaMathematical Sans-Serif Bold Kappa Symbol
    U+1D78D𝞍\bsansphiMathematical Sans-Serif Bold Phi Symbol
    U+1D78E𝞎\bsansvarrhoMathematical Sans-Serif Bold Rho Symbol
    U+1D78F𝞏\bsansvarpiMathematical Sans-Serif Bold Pi Symbol
    U+1D790𝞐\bisansAlphaMathematical Sans-Serif Bold Italic Capital Alpha
    U+1D791𝞑\bisansBetaMathematical Sans-Serif Bold Italic Capital Beta
    U+1D792𝞒\bisansGammaMathematical Sans-Serif Bold Italic Capital Gamma
    U+1D793𝞓\bisansDeltaMathematical Sans-Serif Bold Italic Capital Delta
    U+1D794𝞔\bisansEpsilonMathematical Sans-Serif Bold Italic Capital Epsilon
    U+1D795𝞕\bisansZetaMathematical Sans-Serif Bold Italic Capital Zeta
    U+1D796𝞖\bisansEtaMathematical Sans-Serif Bold Italic Capital Eta
    U+1D797𝞗\bisansThetaMathematical Sans-Serif Bold Italic Capital Theta
    U+1D798𝞘\bisansIotaMathematical Sans-Serif Bold Italic Capital Iota
    U+1D799𝞙\bisansKappaMathematical Sans-Serif Bold Italic Capital Kappa
    U+1D79A𝞚\bisansLambdaMathematical Sans-Serif Bold Italic Capital Lamda
    U+1D79B𝞛\bisansMuMathematical Sans-Serif Bold Italic Capital Mu
    U+1D79C𝞜\bisansNuMathematical Sans-Serif Bold Italic Capital Nu
    U+1D79D𝞝\bisansXiMathematical Sans-Serif Bold Italic Capital Xi
    U+1D79E𝞞\bisansOmicronMathematical Sans-Serif Bold Italic Capital Omicron
    U+1D79F𝞟\bisansPiMathematical Sans-Serif Bold Italic Capital Pi
    U+1D7A0𝞠\bisansRhoMathematical Sans-Serif Bold Italic Capital Rho
    U+1D7A1𝞡\bisansvarThetaMathematical Sans-Serif Bold Italic Capital Theta Symbol
    U+1D7A2𝞢\bisansSigmaMathematical Sans-Serif Bold Italic Capital Sigma
    U+1D7A3𝞣\bisansTauMathematical Sans-Serif Bold Italic Capital Tau
    U+1D7A4𝞤\bisansUpsilonMathematical Sans-Serif Bold Italic Capital Upsilon
    U+1D7A5𝞥\bisansPhiMathematical Sans-Serif Bold Italic Capital Phi
    U+1D7A6𝞦\bisansChiMathematical Sans-Serif Bold Italic Capital Chi
    U+1D7A7𝞧\bisansPsiMathematical Sans-Serif Bold Italic Capital Psi
    U+1D7A8𝞨\bisansOmegaMathematical Sans-Serif Bold Italic Capital Omega
    U+1D7A9𝞩\bisansnablaMathematical Sans-Serif Bold Italic Nabla
    U+1D7AA𝞪\bisansalphaMathematical Sans-Serif Bold Italic Small Alpha
    U+1D7AB𝞫\bisansbetaMathematical Sans-Serif Bold Italic Small Beta
    U+1D7AC𝞬\bisansgammaMathematical Sans-Serif Bold Italic Small Gamma
    U+1D7AD𝞭\bisansdeltaMathematical Sans-Serif Bold Italic Small Delta
    U+1D7AE𝞮\bisansvarepsilonMathematical Sans-Serif Bold Italic Small Epsilon
    U+1D7AF𝞯\bisanszetaMathematical Sans-Serif Bold Italic Small Zeta
    U+1D7B0𝞰\bisansetaMathematical Sans-Serif Bold Italic Small Eta
    U+1D7B1𝞱\bisansthetaMathematical Sans-Serif Bold Italic Small Theta
    U+1D7B2𝞲\bisansiotaMathematical Sans-Serif Bold Italic Small Iota
    U+1D7B3𝞳\bisanskappaMathematical Sans-Serif Bold Italic Small Kappa
    U+1D7B4𝞴\bisanslambdaMathematical Sans-Serif Bold Italic Small Lamda
    U+1D7B5𝞵\bisansmuMathematical Sans-Serif Bold Italic Small Mu
    U+1D7B6𝞶\bisansnuMathematical Sans-Serif Bold Italic Small Nu
    U+1D7B7𝞷\bisansxiMathematical Sans-Serif Bold Italic Small Xi
    U+1D7B8𝞸\bisansomicronMathematical Sans-Serif Bold Italic Small Omicron
    U+1D7B9𝞹\bisanspiMathematical Sans-Serif Bold Italic Small Pi
    U+1D7BA𝞺\bisansrhoMathematical Sans-Serif Bold Italic Small Rho
    U+1D7BB𝞻\bisansvarsigmaMathematical Sans-Serif Bold Italic Small Final Sigma
    U+1D7BC𝞼\bisanssigmaMathematical Sans-Serif Bold Italic Small Sigma
    U+1D7BD𝞽\bisanstauMathematical Sans-Serif Bold Italic Small Tau
    U+1D7BE𝞾\bisansupsilonMathematical Sans-Serif Bold Italic Small Upsilon
    U+1D7BF𝞿\bisansvarphiMathematical Sans-Serif Bold Italic Small Phi
    U+1D7C0𝟀\bisanschiMathematical Sans-Serif Bold Italic Small Chi
    U+1D7C1𝟁\bisanspsiMathematical Sans-Serif Bold Italic Small Psi
    U+1D7C2𝟂\bisansomegaMathematical Sans-Serif Bold Italic Small Omega
    U+1D7C3𝟃\bisanspartialMathematical Sans-Serif Bold Italic Partial Differential
    U+1D7C4𝟄\bisansepsilonMathematical Sans-Serif Bold Italic Epsilon Symbol
    U+1D7C5𝟅\bisansvarthetaMathematical Sans-Serif Bold Italic Theta Symbol
    U+1D7C6𝟆\bisansvarkappaMathematical Sans-Serif Bold Italic Kappa Symbol
    U+1D7C7𝟇\bisansphiMathematical Sans-Serif Bold Italic Phi Symbol
    U+1D7C8𝟈\bisansvarrhoMathematical Sans-Serif Bold Italic Rho Symbol
    U+1D7C9𝟉\bisansvarpiMathematical Sans-Serif Bold Italic Pi Symbol
    U+1D7CA𝟊\bfDigammaMathematical Bold Capital Digamma
    U+1D7CB𝟋\bfdigammaMathematical Bold Small Digamma
    U+1D7CE𝟎\bfzeroMathematical Bold Digit Zero
    U+1D7CF𝟏\bfoneMathematical Bold Digit One
    U+1D7D0𝟐\bftwoMathematical Bold Digit Two
    U+1D7D1𝟑\bfthreeMathematical Bold Digit Three
    U+1D7D2𝟒\bffourMathematical Bold Digit Four
    U+1D7D3𝟓\bffiveMathematical Bold Digit Five
    U+1D7D4𝟔\bfsixMathematical Bold Digit Six
    U+1D7D5𝟕\bfsevenMathematical Bold Digit Seven
    U+1D7D6𝟖\bfeightMathematical Bold Digit Eight
    U+1D7D7𝟗\bfnineMathematical Bold Digit Nine
    U+1D7D8𝟘\bbzeroMathematical Double-Struck Digit Zero
    U+1D7D9𝟙\bboneMathematical Double-Struck Digit One
    U+1D7DA𝟚\bbtwoMathematical Double-Struck Digit Two
    U+1D7DB𝟛\bbthreeMathematical Double-Struck Digit Three
    U+1D7DC𝟜\bbfourMathematical Double-Struck Digit Four
    U+1D7DD𝟝\bbfiveMathematical Double-Struck Digit Five
    U+1D7DE𝟞\bbsixMathematical Double-Struck Digit Six
    U+1D7DF𝟟\bbsevenMathematical Double-Struck Digit Seven
    U+1D7E0𝟠\bbeightMathematical Double-Struck Digit Eight
    U+1D7E1𝟡\bbnineMathematical Double-Struck Digit Nine
    U+1D7E2𝟢\sanszeroMathematical Sans-Serif Digit Zero
    U+1D7E3𝟣\sansoneMathematical Sans-Serif Digit One
    U+1D7E4𝟤\sanstwoMathematical Sans-Serif Digit Two
    U+1D7E5𝟥\sansthreeMathematical Sans-Serif Digit Three
    U+1D7E6𝟦\sansfourMathematical Sans-Serif Digit Four
    U+1D7E7𝟧\sansfiveMathematical Sans-Serif Digit Five
    U+1D7E8𝟨\sanssixMathematical Sans-Serif Digit Six
    U+1D7E9𝟩\sanssevenMathematical Sans-Serif Digit Seven
    U+1D7EA𝟪\sanseightMathematical Sans-Serif Digit Eight
    U+1D7EB𝟫\sansnineMathematical Sans-Serif Digit Nine
    U+1D7EC𝟬\bsanszeroMathematical Sans-Serif Bold Digit Zero
    U+1D7ED𝟭\bsansoneMathematical Sans-Serif Bold Digit One
    U+1D7EE𝟮\bsanstwoMathematical Sans-Serif Bold Digit Two
    U+1D7EF𝟯\bsansthreeMathematical Sans-Serif Bold Digit Three
    U+1D7F0𝟰\bsansfourMathematical Sans-Serif Bold Digit Four
    U+1D7F1𝟱\bsansfiveMathematical Sans-Serif Bold Digit Five
    U+1D7F2𝟲\bsanssixMathematical Sans-Serif Bold Digit Six
    U+1D7F3𝟳\bsanssevenMathematical Sans-Serif Bold Digit Seven
    U+1D7F4𝟴\bsanseightMathematical Sans-Serif Bold Digit Eight
    U+1D7F5𝟵\bsansnineMathematical Sans-Serif Bold Digit Nine
    U+1D7F6𝟶\ttzeroMathematical Monospace Digit Zero
    U+1D7F7𝟷\ttoneMathematical Monospace Digit One
    U+1D7F8𝟸\tttwoMathematical Monospace Digit Two
    U+1D7F9𝟹\ttthreeMathematical Monospace Digit Three
    U+1D7FA𝟺\ttfourMathematical Monospace Digit Four
    U+1D7FB𝟻\ttfiveMathematical Monospace Digit Five
    U+1D7FC𝟼\ttsixMathematical Monospace Digit Six
    U+1D7FD𝟽\ttsevenMathematical Monospace Digit Seven
    U+1D7FE𝟾\tteightMathematical Monospace Digit Eight
    U+1D7FF𝟿\ttnineMathematical Monospace Digit Nine
    U+1F004🀄\:mahjong:Mahjong Tile Red Dragon
    U+1F0CF🃏\:black_joker:Playing Card Black Joker
    U+1F170🅰\:a:Negative Squared Latin Capital Letter A
    U+1F171🅱\:b:Negative Squared Latin Capital Letter B
    U+1F17E🅾\:o2:Negative Squared Latin Capital Letter O
    U+1F17F🅿\:parking:Negative Squared Latin Capital Letter P
    U+1F18E🆎\:ab:Negative Squared Ab
    U+1F191🆑\:cl:Squared Cl
    U+1F192🆒\:cool:Squared Cool
    U+1F193🆓\:free:Squared Free
    U+1F194🆔\:id:Squared Id
    U+1F195🆕\:new:Squared New
    U+1F196🆖\:ng:Squared Ng
    U+1F197🆗\:ok:Squared Ok
    U+1F198🆘\:sos:Squared Sos
    U+1F199🆙\:up:Squared Up With Exclamation Mark
    U+1F19A🆚\:vs:Squared Vs
    U+1F201🈁\:koko:Squared Katakana Koko
    U+1F202🈂\:sa:Squared Katakana Sa
    U+1F21A🈚\:u7121:Squared Cjk Unified Ideograph-7121
    U+1F22F🈯\:u6307:Squared Cjk Unified Ideograph-6307
    U+1F232🈲\:u7981:Squared Cjk Unified Ideograph-7981
    U+1F233🈳\:u7a7a:Squared Cjk Unified Ideograph-7A7A
    U+1F234🈴\:u5408:Squared Cjk Unified Ideograph-5408
    U+1F235🈵\:u6e80:Squared Cjk Unified Ideograph-6E80
    U+1F236🈶\:u6709:Squared Cjk Unified Ideograph-6709
    U+1F237🈷\:u6708:Squared Cjk Unified Ideograph-6708
    U+1F238🈸\:u7533:Squared Cjk Unified Ideograph-7533
    U+1F239🈹\:u5272:Squared Cjk Unified Ideograph-5272
    U+1F23A🈺\:u55b6:Squared Cjk Unified Ideograph-55B6
    U+1F250🉐\:ideograph_advantage:Circled Ideograph Advantage
    U+1F251🉑\:accept:Circled Ideograph Accept
    U+1F300🌀\:cyclone:Cyclone
    U+1F301🌁\:foggy:Foggy
    U+1F302🌂\:closed_umbrella:Closed Umbrella
    U+1F303🌃\:night_with_stars:Night With Stars
    U+1F304🌄\:sunrise_over_mountains:Sunrise Over Mountains
    U+1F305🌅\:sunrise:Sunrise
    U+1F306🌆\:city_sunset:Cityscape At Dusk
    U+1F307🌇\:city_sunrise:Sunset Over Buildings
    U+1F308🌈\:rainbow:Rainbow
    U+1F309🌉\:bridge_at_night:Bridge At Night
    U+1F30A🌊\:ocean:Water Wave
    U+1F30B🌋\:volcano:Volcano
    U+1F30C🌌\:milky_way:Milky Way
    U+1F30D🌍\:earth_africa:Earth Globe Europe-Africa
    U+1F30E🌎\:earth_americas:Earth Globe Americas
    U+1F30F🌏\:earth_asia:Earth Globe Asia-Australia
    U+1F310🌐\:globe_with_meridians:Globe With Meridians
    U+1F311🌑\:new_moon:New Moon Symbol
    U+1F312🌒\:waxing_crescent_moon:Waxing Crescent Moon Symbol
    U+1F313🌓\:first_quarter_moon:First Quarter Moon Symbol
    U+1F314🌔\:moon:Waxing Gibbous Moon Symbol
    U+1F315🌕\:full_moon:Full Moon Symbol
    U+1F316🌖\:waning_gibbous_moon:Waning Gibbous Moon Symbol
    U+1F317🌗\:last_quarter_moon:Last Quarter Moon Symbol
    U+1F318🌘\:waning_crescent_moon:Waning Crescent Moon Symbol
    U+1F319🌙\:crescent_moon:Crescent Moon
    U+1F31A🌚\:new_moon_with_face:New Moon With Face
    U+1F31B🌛\:first_quarter_moon_with_face:First Quarter Moon With Face
    U+1F31C🌜\:last_quarter_moon_with_face:Last Quarter Moon With Face
    U+1F31D🌝\:full_moon_with_face:Full Moon With Face
    U+1F31E🌞\:sun_with_face:Sun With Face
    U+1F31F🌟\:star2:Glowing Star
    U+1F320🌠\:stars:Shooting Star
    U+1F32D🌭\:hotdog:Hot Dog
    U+1F32E🌮\:taco:Taco
    U+1F32F🌯\:burrito:Burrito
    U+1F330🌰\:chestnut:Chestnut
    U+1F331🌱\:seedling:Seedling
    U+1F332🌲\:evergreen_tree:Evergreen Tree
    U+1F333🌳\:deciduous_tree:Deciduous Tree
    U+1F334🌴\:palm_tree:Palm Tree
    U+1F335🌵\:cactus:Cactus
    U+1F337🌷\:tulip:Tulip
    U+1F338🌸\:cherry_blossom:Cherry Blossom
    U+1F339🌹\:rose:Rose
    U+1F33A🌺\:hibiscus:Hibiscus
    U+1F33B🌻\:sunflower:Sunflower
    U+1F33C🌼\:blossom:Blossom
    U+1F33D🌽\:corn:Ear Of Maize
    U+1F33E🌾\:ear_of_rice:Ear Of Rice
    U+1F33F🌿\:herb:Herb
    U+1F340🍀\:four_leaf_clover:Four Leaf Clover
    U+1F341🍁\:maple_leaf:Maple Leaf
    U+1F342🍂\:fallen_leaf:Fallen Leaf
    U+1F343🍃\:leaves:Leaf Fluttering In Wind
    U+1F344🍄\:mushroom:Mushroom
    U+1F345🍅\:tomato:Tomato
    U+1F346🍆\:eggplant:Aubergine
    U+1F347🍇\:grapes:Grapes
    U+1F348🍈\:melon:Melon
    U+1F349🍉\:watermelon:Watermelon
    U+1F34A🍊\:tangerine:Tangerine
    U+1F34B🍋\:lemon:Lemon
    U+1F34C🍌\:banana:Banana
    U+1F34D🍍\:pineapple:Pineapple
    U+1F34E🍎\:apple:Red Apple
    U+1F34F🍏\:green_apple:Green Apple
    U+1F350🍐\:pear:Pear
    U+1F351🍑\:peach:Peach
    U+1F352🍒\:cherries:Cherries
    U+1F353🍓\:strawberry:Strawberry
    U+1F354🍔\:hamburger:Hamburger
    U+1F355🍕\:pizza:Slice Of Pizza
    U+1F356🍖\:meat_on_bone:Meat On Bone
    U+1F357🍗\:poultry_leg:Poultry Leg
    U+1F358🍘\:rice_cracker:Rice Cracker
    U+1F359🍙\:rice_ball:Rice Ball
    U+1F35A🍚\:rice:Cooked Rice
    U+1F35B🍛\:curry:Curry And Rice
    U+1F35C🍜\:ramen:Steaming Bowl
    U+1F35D🍝\:spaghetti:Spaghetti
    U+1F35E🍞\:bread:Bread
    U+1F35F🍟\:fries:French Fries
    U+1F360🍠\:sweet_potato:Roasted Sweet Potato
    U+1F361🍡\:dango:Dango
    U+1F362🍢\:oden:Oden
    U+1F363🍣\:sushi:Sushi
    U+1F364🍤\:fried_shrimp:Fried Shrimp
    U+1F365🍥\:fish_cake:Fish Cake With Swirl Design
    U+1F366🍦\:icecream:Soft Ice Cream
    U+1F367🍧\:shaved_ice:Shaved Ice
    U+1F368🍨\:ice_cream:Ice Cream
    U+1F369🍩\:doughnut:Doughnut
    U+1F36A🍪\:cookie:Cookie
    U+1F36B🍫\:chocolate_bar:Chocolate Bar
    U+1F36C🍬\:candy:Candy
    U+1F36D🍭\:lollipop:Lollipop
    U+1F36E🍮\:custard:Custard
    U+1F36F🍯\:honey_pot:Honey Pot
    U+1F370🍰\:cake:Shortcake
    U+1F371🍱\:bento:Bento Box
    U+1F372🍲\:stew:Pot Of Food
    U+1F373🍳\:fried_egg:Cooking
    U+1F374🍴\:fork_and_knife:Fork And Knife
    U+1F375🍵\:tea:Teacup Without Handle
    U+1F376🍶\:sake:Sake Bottle And Cup
    U+1F377🍷\:wine_glass:Wine Glass
    U+1F378🍸\:cocktail:Cocktail Glass
    U+1F379🍹\:tropical_drink:Tropical Drink
    U+1F37A🍺\:beer:Beer Mug
    U+1F37B🍻\:beers:Clinking Beer Mugs
    U+1F37C🍼\:baby_bottle:Baby Bottle
    U+1F37E🍾\:champagne:Bottle With Popping Cork
    U+1F37F🍿\:popcorn:Popcorn
    U+1F380🎀\:ribbon:Ribbon
    U+1F381🎁\:gift:Wrapped Present
    U+1F382🎂\:birthday:Birthday Cake
    U+1F383🎃\:jack_o_lantern:Jack-O-Lantern
    U+1F384🎄\:christmas_tree:Christmas Tree
    U+1F385🎅\:santa:Father Christmas
    U+1F386🎆\:fireworks:Fireworks
    U+1F387🎇\:sparkler:Firework Sparkler
    U+1F388🎈\:balloon:Balloon
    U+1F389🎉\:tada:Party Popper
    U+1F38A🎊\:confetti_ball:Confetti Ball
    U+1F38B🎋\:tanabata_tree:Tanabata Tree
    U+1F38C🎌\:crossed_flags:Crossed Flags
    U+1F38D🎍\:bamboo:Pine Decoration
    U+1F38E🎎\:dolls:Japanese Dolls
    U+1F38F🎏\:flags:Carp Streamer
    U+1F390🎐\:wind_chime:Wind Chime
    U+1F391🎑\:rice_scene:Moon Viewing Ceremony
    U+1F392🎒\:school_satchel:School Satchel
    U+1F393🎓\:mortar_board:Graduation Cap
    U+1F3A0🎠\:carousel_horse:Carousel Horse
    U+1F3A1🎡\:ferris_wheel:Ferris Wheel
    U+1F3A2🎢\:roller_coaster:Roller Coaster
    U+1F3A3🎣\:fishing_pole_and_fish:Fishing Pole And Fish
    U+1F3A4🎤\:microphone:Microphone
    U+1F3A5🎥\:movie_camera:Movie Camera
    U+1F3A6🎦\:cinema:Cinema
    U+1F3A7🎧\:headphones:Headphone
    U+1F3A8🎨\:art:Artist Palette
    U+1F3A9🎩\:tophat:Top Hat
    U+1F3AA🎪\:circus_tent:Circus Tent
    U+1F3AB🎫\:ticket:Ticket
    U+1F3AC🎬\:clapper:Clapper Board
    U+1F3AD🎭\:performing_arts:Performing Arts
    U+1F3AE🎮\:video_game:Video Game
    U+1F3AF🎯\:dart:Direct Hit
    U+1F3B0🎰\:slot_machine:Slot Machine
    U+1F3B1🎱\:8ball:Billiards
    U+1F3B2🎲\:game_die:Game Die
    U+1F3B3🎳\:bowling:Bowling
    U+1F3B4🎴\:flower_playing_cards:Flower Playing Cards
    U+1F3B5🎵\:musical_note:Musical Note
    U+1F3B6🎶\:notes:Multiple Musical Notes
    U+1F3B7🎷\:saxophone:Saxophone
    U+1F3B8🎸\:guitar:Guitar
    U+1F3B9🎹\:musical_keyboard:Musical Keyboard
    U+1F3BA🎺\:trumpet:Trumpet
    U+1F3BB🎻\:violin:Violin
    U+1F3BC🎼\:musical_score:Musical Score
    U+1F3BD🎽\:running_shirt_with_sash:Running Shirt With Sash
    U+1F3BE🎾\:tennis:Tennis Racquet And Ball
    U+1F3BF🎿\:ski:Ski And Ski Boot
    U+1F3C0🏀\:basketball:Basketball And Hoop
    U+1F3C1🏁\:checkered_flag:Chequered Flag
    U+1F3C2🏂\:snowboarder:Snowboarder
    U+1F3C3🏃\:runner:Runner
    U+1F3C4🏄\:surfer:Surfer
    U+1F3C5🏅\:sports_medal:Sports Medal
    U+1F3C6🏆\:trophy:Trophy
    U+1F3C7🏇\:horse_racing:Horse Racing
    U+1F3C8🏈\:football:American Football
    U+1F3C9🏉\:rugby_football:Rugby Football
    U+1F3CA🏊\:swimmer:Swimmer
    U+1F3CF🏏\:cricket_bat_and_ball:Cricket Bat And Ball
    U+1F3D0🏐\:volleyball:Volleyball
    U+1F3D1🏑\:field_hockey_stick_and_ball:Field Hockey Stick And Ball
    U+1F3D2🏒\:ice_hockey_stick_and_puck:Ice Hockey Stick And Puck
    U+1F3D3🏓\:table_tennis_paddle_and_ball:Table Tennis Paddle And Ball
    U+1F3E0🏠\:house:House Building
    U+1F3E1🏡\:house_with_garden:House With Garden
    U+1F3E2🏢\:office:Office Building
    U+1F3E3🏣\:post_office:Japanese Post Office
    U+1F3E4🏤\:european_post_office:European Post Office
    U+1F3E5🏥\:hospital:Hospital
    U+1F3E6🏦\:bank:Bank
    U+1F3E7🏧\:atm:Automated Teller Machine
    U+1F3E8🏨\:hotel:Hotel
    U+1F3E9🏩\:love_hotel:Love Hotel
    U+1F3EA🏪\:convenience_store:Convenience Store
    U+1F3EB🏫\:school:School
    U+1F3EC🏬\:department_store:Department Store
    U+1F3ED🏭\:factory:Factory
    U+1F3EE🏮\:izakaya_lantern:Izakaya Lantern
    U+1F3EF🏯\:japanese_castle:Japanese Castle
    U+1F3F0🏰\:european_castle:European Castle
    U+1F3F4🏴\:waving_black_flag:Waving Black Flag
    U+1F3F8🏸\:badminton_racquet_and_shuttlecock:Badminton Racquet And Shuttlecock
    U+1F3F9🏹\:bow_and_arrow:Bow And Arrow
    U+1F3FA🏺\:amphora:Amphora
    U+1F3FB🏻\:skin-tone-2:Emoji Modifier Fitzpatrick Type-1-2
    U+1F3FC🏼\:skin-tone-3:Emoji Modifier Fitzpatrick Type-3
    U+1F3FD🏽\:skin-tone-4:Emoji Modifier Fitzpatrick Type-4
    U+1F3FE🏾\:skin-tone-5:Emoji Modifier Fitzpatrick Type-5
    U+1F3FF🏿\:skin-tone-6:Emoji Modifier Fitzpatrick Type-6
    U+1F400🐀\:rat:Rat
    U+1F401🐁\:mouse2:Mouse
    U+1F402🐂\:ox:Ox
    U+1F403🐃\:water_buffalo:Water Buffalo
    U+1F404🐄\:cow2:Cow
    U+1F405🐅\:tiger2:Tiger
    U+1F406🐆\:leopard:Leopard
    U+1F407🐇\:rabbit2:Rabbit
    U+1F408🐈\:cat2:Cat
    U+1F409🐉\:dragon:Dragon
    U+1F40A🐊\:crocodile:Crocodile
    U+1F40B🐋\:whale2:Whale
    U+1F40C🐌\:snail:Snail
    U+1F40D🐍\:snake:Snake
    U+1F40E🐎\:racehorse:Horse
    U+1F40F🐏\:ram:Ram
    U+1F410🐐\:goat:Goat
    U+1F411🐑\:sheep:Sheep
    U+1F412🐒\:monkey:Monkey
    U+1F413🐓\:rooster:Rooster
    U+1F414🐔\:chicken:Chicken
    U+1F415🐕\:dog2:Dog
    U+1F416🐖\:pig2:Pig
    U+1F417🐗\:boar:Boar
    U+1F418🐘\:elephant:Elephant
    U+1F419🐙\:octopus:Octopus
    U+1F41A🐚\:shell:Spiral Shell
    U+1F41B🐛\:bug:Bug
    U+1F41C🐜\:ant:Ant
    U+1F41D🐝\:bee:Honeybee
    U+1F41E🐞\:ladybug:Lady Beetle
    U+1F41F🐟\:fish:Fish
    U+1F420🐠\:tropical_fish:Tropical Fish
    U+1F421🐡\:blowfish:Blowfish
    U+1F422🐢\:turtle:Turtle
    U+1F423🐣\:hatching_chick:Hatching Chick
    U+1F424🐤\:baby_chick:Baby Chick
    U+1F425🐥\:hatched_chick:Front-Facing Baby Chick
    U+1F426🐦\:bird:Bird
    U+1F427🐧\:penguin:Penguin
    U+1F428🐨\:koala:Koala
    U+1F429🐩\:poodle:Poodle
    U+1F42A🐪\:dromedary_camel:Dromedary Camel
    U+1F42B🐫\:camel:Bactrian Camel
    U+1F42C🐬\:dolphin:Dolphin
    U+1F42D🐭\:mouse:Mouse Face
    U+1F42E🐮\:cow:Cow Face
    U+1F42F🐯\:tiger:Tiger Face
    U+1F430🐰\:rabbit:Rabbit Face
    U+1F431🐱\:cat:Cat Face
    U+1F432🐲\:dragon_face:Dragon Face
    U+1F433🐳\:whale:Spouting Whale
    U+1F434🐴\:horse:Horse Face
    U+1F435🐵\:monkey_face:Monkey Face
    U+1F436🐶\:dog:Dog Face
    U+1F437🐷\:pig:Pig Face
    U+1F438🐸\:frog:Frog Face
    U+1F439🐹\:hamster:Hamster Face
    U+1F43A🐺\:wolf:Wolf Face
    U+1F43B🐻\:bear:Bear Face
    U+1F43C🐼\:panda_face:Panda Face
    U+1F43D🐽\:pig_nose:Pig Nose
    U+1F43E🐾\:feet:Paw Prints
    U+1F440👀\:eyes:Eyes
    U+1F442👂\:ear:Ear
    U+1F443👃\:nose:Nose
    U+1F444👄\:lips:Mouth
    U+1F445👅\:tongue:Tongue
    U+1F446👆\:point_up_2:White Up Pointing Backhand Index
    U+1F447👇\:point_down:White Down Pointing Backhand Index
    U+1F448👈\:point_left:White Left Pointing Backhand Index
    U+1F449👉\:point_right:White Right Pointing Backhand Index
    U+1F44A👊\:facepunch:Fisted Hand Sign
    U+1F44B👋\:wave:Waving Hand Sign
    U+1F44C👌\:ok_hand:Ok Hand Sign
    U+1F44D👍\:+1:Thumbs Up Sign
    U+1F44E👎\:-1:Thumbs Down Sign
    U+1F44F👏\:clap:Clapping Hands Sign
    U+1F450👐\:open_hands:Open Hands Sign
    U+1F451👑\:crown:Crown
    U+1F452👒\:womans_hat:Womans Hat
    U+1F453👓\:eyeglasses:Eyeglasses
    U+1F454👔\:necktie:Necktie
    U+1F455👕\:shirt:T-Shirt
    U+1F456👖\:jeans:Jeans
    U+1F457👗\:dress:Dress
    U+1F458👘\:kimono:Kimono
    U+1F459👙\:bikini:Bikini
    U+1F45A👚\:womans_clothes:Womans Clothes
    U+1F45B👛\:purse:Purse
    U+1F45C👜\:handbag:Handbag
    U+1F45D👝\:pouch:Pouch
    U+1F45E👞\:mans_shoe:Mans Shoe
    U+1F45F👟\:athletic_shoe:Athletic Shoe
    U+1F460👠\:high_heel:High-Heeled Shoe
    U+1F461👡\:sandal:Womans Sandal
    U+1F462👢\:boot:Womans Boots
    U+1F463👣\:footprints:Footprints
    U+1F464👤\:bust_in_silhouette:Bust In Silhouette
    U+1F465👥\:busts_in_silhouette:Busts In Silhouette
    U+1F466👦\:boy:Boy
    U+1F467👧\:girl:Girl
    U+1F468👨\:man:Man
    U+1F469👩\:woman:Woman
    U+1F46A👪\:family:Family
    U+1F46B👫\:couple:, \:man_and_woman_holding_hands:Man And Woman Holding Hands
    U+1F46C👬\:two_men_holding_hands:Two Men Holding Hands
    U+1F46D👭\:two_women_holding_hands:Two Women Holding Hands
    U+1F46E👮\:cop:Police Officer
    U+1F46F👯\:dancers:Woman With Bunny Ears
    U+1F470👰\:bride_with_veil:Bride With Veil
    U+1F471👱\:person_with_blond_hair:Person With Blond Hair
    U+1F472👲\:man_with_gua_pi_mao:Man With Gua Pi Mao
    U+1F473👳\:man_with_turban:Man With Turban
    U+1F474👴\:older_man:Older Man
    U+1F475👵\:older_woman:Older Woman
    U+1F476👶\:baby:Baby
    U+1F477👷\:construction_worker:Construction Worker
    U+1F478👸\:princess:Princess
    U+1F479👹\:japanese_ogre:Japanese Ogre
    U+1F47A👺\:japanese_goblin:Japanese Goblin
    U+1F47B👻\:ghost:Ghost
    U+1F47C👼\:angel:Baby Angel
    U+1F47D👽\:alien:Extraterrestrial Alien
    U+1F47E👾\:space_invader:Alien Monster
    U+1F47F👿\:imp:Imp
    U+1F480💀\:skull:Skull
    U+1F481💁\:information_desk_person:Information Desk Person
    U+1F482💂\:guardsman:Guardsman
    U+1F483💃\:dancer:Dancer
    U+1F484💄\:lipstick:Lipstick
    U+1F485💅\:nail_care:Nail Polish
    U+1F486💆\:massage:Face Massage
    U+1F487💇\:haircut:Haircut
    U+1F488💈\:barber:Barber Pole
    U+1F489💉\:syringe:Syringe
    U+1F48A💊\:pill:Pill
    U+1F48B💋\:kiss:Kiss Mark
    U+1F48C💌\:love_letter:Love Letter
    U+1F48D💍\:ring:Ring
    U+1F48E💎\:gem:Gem Stone
    U+1F48F💏\:couplekiss:Kiss
    U+1F490💐\:bouquet:Bouquet
    U+1F491💑\:couple_with_heart:Couple With Heart
    U+1F492💒\:wedding:Wedding
    U+1F493💓\:heartbeat:Beating Heart
    U+1F494💔\:broken_heart:Broken Heart
    U+1F495💕\:two_hearts:Two Hearts
    U+1F496💖\:sparkling_heart:Sparkling Heart
    U+1F497💗\:heartpulse:Growing Heart
    U+1F498💘\:cupid:Heart With Arrow
    U+1F499💙\:blue_heart:Blue Heart
    U+1F49A💚\:green_heart:Green Heart
    U+1F49B💛\:yellow_heart:Yellow Heart
    U+1F49C💜\:purple_heart:Purple Heart
    U+1F49D💝\:gift_heart:Heart With Ribbon
    U+1F49E💞\:revolving_hearts:Revolving Hearts
    U+1F49F💟\:heart_decoration:Heart Decoration
    U+1F4A0💠\:diamond_shape_with_a_dot_inside:Diamond Shape With A Dot Inside
    U+1F4A1💡\:bulb:Electric Light Bulb
    U+1F4A2💢\:anger:Anger Symbol
    U+1F4A3💣\:bomb:Bomb
    U+1F4A4💤\:zzz:Sleeping Symbol
    U+1F4A5💥\:boom:Collision Symbol
    U+1F4A6💦\:sweat_drops:Splashing Sweat Symbol
    U+1F4A7💧\:droplet:Droplet
    U+1F4A8💨\:dash:Dash Symbol
    U+1F4A9💩\:hankey:Pile Of Poo
    U+1F4AA💪\:muscle:Flexed Biceps
    U+1F4AB💫\:dizzy:Dizzy Symbol
    U+1F4AC💬\:speech_balloon:Speech Balloon
    U+1F4AD💭\:thought_balloon:Thought Balloon
    U+1F4AE💮\:white_flower:White Flower
    U+1F4AF💯\:100:Hundred Points Symbol
    U+1F4B0💰\:moneybag:Money Bag
    U+1F4B1💱\:currency_exchange:Currency Exchange
    U+1F4B2💲\:heavy_dollar_sign:Heavy Dollar Sign
    U+1F4B3💳\:credit_card:Credit Card
    U+1F4B4💴\:yen:Banknote With Yen Sign
    U+1F4B5💵\:dollar:Banknote With Dollar Sign
    U+1F4B6💶\:euro:Banknote With Euro Sign
    U+1F4B7💷\:pound:Banknote With Pound Sign
    U+1F4B8💸\:money_with_wings:Money With Wings
    U+1F4B9💹\:chart:Chart With Upwards Trend And Yen Sign
    U+1F4BA💺\:seat:Seat
    U+1F4BB💻\:computer:Personal Computer
    U+1F4BC💼\:briefcase:Briefcase
    U+1F4BD💽\:minidisc:Minidisc
    U+1F4BE💾\:floppy_disk:Floppy Disk
    U+1F4BF💿\:cd:Optical Disc
    U+1F4C0📀\:dvd:Dvd
    U+1F4C1📁\:file_folder:File Folder
    U+1F4C2📂\:open_file_folder:Open File Folder
    U+1F4C3📃\:page_with_curl:Page With Curl
    U+1F4C4📄\:page_facing_up:Page Facing Up
    U+1F4C5📅\:date:Calendar
    U+1F4C6📆\:calendar:Tear-Off Calendar
    U+1F4C7📇\:card_index:Card Index
    U+1F4C8📈\:chart_with_upwards_trend:Chart With Upwards Trend
    U+1F4C9📉\:chart_with_downwards_trend:Chart With Downwards Trend
    U+1F4CA📊\:bar_chart:Bar Chart
    U+1F4CB📋\:clipboard:Clipboard
    U+1F4CC📌\:pushpin:Pushpin
    U+1F4CD📍\:round_pushpin:Round Pushpin
    U+1F4CE📎\:paperclip:Paperclip
    U+1F4CF📏\:straight_ruler:Straight Ruler
    U+1F4D0📐\:triangular_ruler:Triangular Ruler
    U+1F4D1📑\:bookmark_tabs:Bookmark Tabs
    U+1F4D2📒\:ledger:Ledger
    U+1F4D3📓\:notebook:Notebook
    U+1F4D4📔\:notebook_with_decorative_cover:Notebook With Decorative Cover
    U+1F4D5📕\:closed_book:Closed Book
    U+1F4D6📖\:book:Open Book
    U+1F4D7📗\:green_book:Green Book
    U+1F4D8📘\:blue_book:Blue Book
    U+1F4D9📙\:orange_book:Orange Book
    U+1F4DA📚\:books:Books
    U+1F4DB📛\:name_badge:Name Badge
    U+1F4DC📜\:scroll:Scroll
    U+1F4DD📝\:memo:Memo
    U+1F4DE📞\:telephone_receiver:Telephone Receiver
    U+1F4DF📟\:pager:Pager
    U+1F4E0📠\:fax:Fax Machine
    U+1F4E1📡\:satellite:, \:satellite_antenna:Satellite Antenna
    U+1F4E2📢\:loudspeaker:Public Address Loudspeaker
    U+1F4E3📣\:mega:Cheering Megaphone
    U+1F4E4📤\:outbox_tray:Outbox Tray
    U+1F4E5📥\:inbox_tray:Inbox Tray
    U+1F4E6📦\:package:Package
    U+1F4E7📧\:e-mail:E-Mail Symbol
    U+1F4E8📨\:incoming_envelope:Incoming Envelope
    U+1F4E9📩\:envelope_with_arrow:Envelope With Downwards Arrow Above
    U+1F4EA📪\:mailbox_closed:Closed Mailbox With Lowered Flag
    U+1F4EB📫\:mailbox:Closed Mailbox With Raised Flag
    U+1F4EC📬\:mailbox_with_mail:Open Mailbox With Raised Flag
    U+1F4ED📭\:mailbox_with_no_mail:Open Mailbox With Lowered Flag
    U+1F4EE📮\:postbox:Postbox
    U+1F4EF📯\:postal_horn:Postal Horn
    U+1F4F0📰\:newspaper:Newspaper
    U+1F4F1📱\:iphone:Mobile Phone
    U+1F4F2📲\:calling:Mobile Phone With Rightwards Arrow At Left
    U+1F4F3📳\:vibration_mode:Vibration Mode
    U+1F4F4📴\:mobile_phone_off:Mobile Phone Off
    U+1F4F5📵\:no_mobile_phones:No Mobile Phones
    U+1F4F6📶\:signal_strength:Antenna With Bars
    U+1F4F7📷\:camera:Camera
    U+1F4F8📸\:camera_with_flash:Camera With Flash
    U+1F4F9📹\:video_camera:Video Camera
    U+1F4FA📺\:tv:Television
    U+1F4FB📻\:radio:Radio
    U+1F4FC📼\:vhs:Videocassette
    U+1F4FF📿\:prayer_beads:Prayer Beads
    U+1F500🔀\:twisted_rightwards_arrows:Twisted Rightwards Arrows
    U+1F501🔁\:repeat:Clockwise Rightwards And Leftwards Open Circle Arrows
    U+1F502🔂\:repeat_one:Clockwise Rightwards And Leftwards Open Circle Arrows With Circled One Overlay
    U+1F503🔃\:arrows_clockwise:Clockwise Downwards And Upwards Open Circle Arrows
    U+1F504🔄\:arrows_counterclockwise:Anticlockwise Downwards And Upwards Open Circle Arrows
    U+1F505🔅\:low_brightness:Low Brightness Symbol
    U+1F506🔆\:high_brightness:High Brightness Symbol
    U+1F507🔇\:mute:Speaker With Cancellation Stroke
    U+1F508🔈\:speaker:Speaker
    U+1F509🔉\:sound:Speaker With One Sound Wave
    U+1F50A🔊\:loud_sound:Speaker With Three Sound Waves
    U+1F50B🔋\:battery:Battery
    U+1F50C🔌\:electric_plug:Electric Plug
    U+1F50D🔍\:mag:Left-Pointing Magnifying Glass
    U+1F50E🔎\:mag_right:Right-Pointing Magnifying Glass
    U+1F50F🔏\:lock_with_ink_pen:Lock With Ink Pen
    U+1F510🔐\:closed_lock_with_key:Closed Lock With Key
    U+1F511🔑\:key:Key
    U+1F512🔒\:lock:Lock
    U+1F513🔓\:unlock:Open Lock
    U+1F514🔔\:bell:Bell
    U+1F515🔕\:no_bell:Bell With Cancellation Stroke
    U+1F516🔖\:bookmark:Bookmark
    U+1F517🔗\:link:Link Symbol
    U+1F518🔘\:radio_button:Radio Button
    U+1F519🔙\:back:Back With Leftwards Arrow Above
    U+1F51A🔚\:end:End With Leftwards Arrow Above
    U+1F51B🔛\:on:On With Exclamation Mark With Left Right Arrow Above
    U+1F51C🔜\:soon:Soon With Rightwards Arrow Above
    U+1F51D🔝\:top:Top With Upwards Arrow Above
    U+1F51E🔞\:underage:No One Under Eighteen Symbol
    U+1F51F🔟\:keycap_ten:Keycap Ten
    U+1F520🔠\:capital_abcd:Input Symbol For Latin Capital Letters
    U+1F521🔡\:abcd:Input Symbol For Latin Small Letters
    U+1F522🔢\:1234:Input Symbol For Numbers
    U+1F523🔣\:symbols:Input Symbol For Symbols
    U+1F524🔤\:abc:Input Symbol For Latin Letters
    U+1F525🔥\:fire:Fire
    U+1F526🔦\:flashlight:Electric Torch
    U+1F527🔧\:wrench:Wrench
    U+1F528🔨\:hammer:Hammer
    U+1F529🔩\:nut_and_bolt:Nut And Bolt
    U+1F52A🔪\:hocho:Hocho
    U+1F52B🔫\:gun:Pistol
    U+1F52C🔬\:microscope:Microscope
    U+1F52D🔭\:telescope:Telescope
    U+1F52E🔮\:crystal_ball:Crystal Ball
    U+1F52F🔯\:six_pointed_star:Six Pointed Star With Middle Dot
    U+1F530🔰\:beginner:Japanese Symbol For Beginner
    U+1F531🔱\:trident:Trident Emblem
    U+1F532🔲\:black_square_button:Black Square Button
    U+1F533🔳\:white_square_button:White Square Button
    U+1F534🔴\:red_circle:Large Red Circle
    U+1F535🔵\:large_blue_circle:Large Blue Circle
    U+1F536🔶\:large_orange_diamond:Large Orange Diamond
    U+1F537🔷\:large_blue_diamond:Large Blue Diamond
    U+1F538🔸\:small_orange_diamond:Small Orange Diamond
    U+1F539🔹\:small_blue_diamond:Small Blue Diamond
    U+1F53A🔺\:small_red_triangle:Up-Pointing Red Triangle
    U+1F53B🔻\:small_red_triangle_down:Down-Pointing Red Triangle
    U+1F53C🔼\:arrow_up_small:Up-Pointing Small Red Triangle
    U+1F53D🔽\:arrow_down_small:Down-Pointing Small Red Triangle
    U+1F54B🕋\:kaaba:Kaaba
    U+1F54C🕌\:mosque:Mosque
    U+1F54D🕍\:synagogue:Synagogue
    U+1F54E🕎\:menorah_with_nine_branches:Menorah With Nine Branches
    U+1F550🕐\:clock1:Clock Face One Oclock
    U+1F551🕑\:clock2:Clock Face Two Oclock
    U+1F552🕒\:clock3:Clock Face Three Oclock
    U+1F553🕓\:clock4:Clock Face Four Oclock
    U+1F554🕔\:clock5:Clock Face Five Oclock
    U+1F555🕕\:clock6:Clock Face Six Oclock
    U+1F556🕖\:clock7:Clock Face Seven Oclock
    U+1F557🕗\:clock8:Clock Face Eight Oclock
    U+1F558🕘\:clock9:Clock Face Nine Oclock
    U+1F559🕙\:clock10:Clock Face Ten Oclock
    U+1F55A🕚\:clock11:Clock Face Eleven Oclock
    U+1F55B🕛\:clock12:Clock Face Twelve Oclock
    U+1F55C🕜\:clock130:Clock Face One-Thirty
    U+1F55D🕝\:clock230:Clock Face Two-Thirty
    U+1F55E🕞\:clock330:Clock Face Three-Thirty
    U+1F55F🕟\:clock430:Clock Face Four-Thirty
    U+1F560🕠\:clock530:Clock Face Five-Thirty
    U+1F561🕡\:clock630:Clock Face Six-Thirty
    U+1F562🕢\:clock730:Clock Face Seven-Thirty
    U+1F563🕣\:clock830:Clock Face Eight-Thirty
    U+1F564🕤\:clock930:Clock Face Nine-Thirty
    U+1F565🕥\:clock1030:Clock Face Ten-Thirty
    U+1F566🕦\:clock1130:Clock Face Eleven-Thirty
    U+1F567🕧\:clock1230:Clock Face Twelve-Thirty
    U+1F57A🕺\:man_dancing:Man Dancing
    U+1F595🖕\:middle_finger:Reversed Hand With Middle Finger Extended
    U+1F596🖖\:spock-hand:Raised Hand With Part Between Middle And Ring Fingers
    U+1F5A4🖤\:black_heart:Black Heart
    U+1F5FB🗻\:mount_fuji:Mount Fuji
    U+1F5FC🗼\:tokyo_tower:Tokyo Tower
    U+1F5FD🗽\:statue_of_liberty:Statue Of Liberty
    U+1F5FE🗾\:japan:Silhouette Of Japan
    U+1F5FF🗿\:moyai:Moyai
    U+1F600😀\:grinning:Grinning Face
    U+1F601😁\:grin:Grinning Face With Smiling Eyes
    U+1F602😂\:joy:Face With Tears Of Joy
    U+1F603😃\:smiley:Smiling Face With Open Mouth
    U+1F604😄\:smile:Smiling Face With Open Mouth And Smiling Eyes
    U+1F605😅\:sweat_smile:Smiling Face With Open Mouth And Cold Sweat
    U+1F606😆\:laughing:Smiling Face With Open Mouth And Tightly-Closed Eyes
    U+1F607😇\:innocent:Smiling Face With Halo
    U+1F608😈\:smiling_imp:Smiling Face With Horns
    U+1F609😉\:wink:Winking Face
    U+1F60A😊\:blush:Smiling Face With Smiling Eyes
    U+1F60B😋\:yum:Face Savouring Delicious Food
    U+1F60C😌\:relieved:Relieved Face
    U+1F60D😍\:heart_eyes:Smiling Face With Heart-Shaped Eyes
    U+1F60E😎\:sunglasses:Smiling Face With Sunglasses
    U+1F60F😏\:smirk:Smirking Face
    U+1F610😐\:neutral_face:Neutral Face
    U+1F611😑\:expressionless:Expressionless Face
    U+1F612😒\:unamused:Unamused Face
    U+1F613😓\:sweat:Face With Cold Sweat
    U+1F614😔\:pensive:Pensive Face
    U+1F615😕\:confused:Confused Face
    U+1F616😖\:confounded:Confounded Face
    U+1F617😗\:kissing:Kissing Face
    U+1F618😘\:kissing_heart:Face Throwing A Kiss
    U+1F619😙\:kissing_smiling_eyes:Kissing Face With Smiling Eyes
    U+1F61A😚\:kissing_closed_eyes:Kissing Face With Closed Eyes
    U+1F61B😛\:stuck_out_tongue:Face With Stuck-Out Tongue
    U+1F61C😜\:stuck_out_tongue_winking_eye:Face With Stuck-Out Tongue And Winking Eye
    U+1F61D😝\:stuck_out_tongue_closed_eyes:Face With Stuck-Out Tongue And Tightly-Closed Eyes
    U+1F61E😞\:disappointed:Disappointed Face
    U+1F61F😟\:worried:Worried Face
    U+1F620😠\:angry:Angry Face
    U+1F621😡\:rage:Pouting Face
    U+1F622😢\:cry:Crying Face
    U+1F623😣\:persevere:Persevering Face
    U+1F624😤\:triumph:Face With Look Of Triumph
    U+1F625😥\:disappointed_relieved:Disappointed But Relieved Face
    U+1F626😦\:frowning:Frowning Face With Open Mouth
    U+1F627😧\:anguished:Anguished Face
    U+1F628😨\:fearful:Fearful Face
    U+1F629😩\:weary:Weary Face
    U+1F62A😪\:sleepy:Sleepy Face
    U+1F62B😫\:tired_face:Tired Face
    U+1F62C😬\:grimacing:Grimacing Face
    U+1F62D😭\:sob:Loudly Crying Face
    U+1F62E😮\:open_mouth:Face With Open Mouth
    U+1F62F😯\:hushed:Hushed Face
    U+1F630😰\:cold_sweat:Face With Open Mouth And Cold Sweat
    U+1F631😱\:scream:Face Screaming In Fear
    U+1F632😲\:astonished:Astonished Face
    U+1F633😳\:flushed:Flushed Face
    U+1F634😴\:sleeping:Sleeping Face
    U+1F635😵\:dizzy_face:Dizzy Face
    U+1F636😶\:no_mouth:Face Without Mouth
    U+1F637😷\:mask:Face With Medical Mask
    U+1F638😸\:smile_cat:Grinning Cat Face With Smiling Eyes
    U+1F639😹\:joy_cat:Cat Face With Tears Of Joy
    U+1F63A😺\:smiley_cat:Smiling Cat Face With Open Mouth
    U+1F63B😻\:heart_eyes_cat:Smiling Cat Face With Heart-Shaped Eyes
    U+1F63C😼\:smirk_cat:Cat Face With Wry Smile
    U+1F63D😽\:kissing_cat:Kissing Cat Face With Closed Eyes
    U+1F63E😾\:pouting_cat:Pouting Cat Face
    U+1F63F😿\:crying_cat_face:Crying Cat Face
    U+1F640🙀\:scream_cat:Weary Cat Face
    U+1F641🙁\:slightly_frowning_face:Slightly Frowning Face
    U+1F642🙂\:slightly_smiling_face:Slightly Smiling Face
    U+1F643🙃\:upside_down_face:Upside-Down Face
    U+1F644🙄\:face_with_rolling_eyes:Face With Rolling Eyes
    U+1F645🙅\:no_good:Face With No Good Gesture
    U+1F646🙆\:ok_woman:Face With Ok Gesture
    U+1F647🙇\:bow:Person Bowing Deeply
    U+1F648🙈\:see_no_evil:See-No-Evil Monkey
    U+1F649🙉\:hear_no_evil:Hear-No-Evil Monkey
    U+1F64A🙊\:speak_no_evil:Speak-No-Evil Monkey
    U+1F64B🙋\:raising_hand:Happy Person Raising One Hand
    U+1F64C🙌\:raised_hands:Person Raising Both Hands In Celebration
    U+1F64D🙍\:person_frowning:Person Frowning
    U+1F64E🙎\:person_with_pouting_face:Person With Pouting Face
    U+1F64F🙏\:pray:Person With Folded Hands
    U+1F680🚀\:rocket:Rocket
    U+1F681🚁\:helicopter:Helicopter
    U+1F682🚂\:steam_locomotive:Steam Locomotive
    U+1F683🚃\:railway_car:Railway Car
    U+1F684🚄\:bullettrain_side:High-Speed Train
    U+1F685🚅\:bullettrain_front:High-Speed Train With Bullet Nose
    U+1F686🚆\:train2:Train
    U+1F687🚇\:metro:Metro
    U+1F688🚈\:light_rail:Light Rail
    U+1F689🚉\:station:Station
    U+1F68A🚊\:tram:Tram
    U+1F68B🚋\:train:Tram Car
    U+1F68C🚌\:bus:Bus
    U+1F68D🚍\:oncoming_bus:Oncoming Bus
    U+1F68E🚎\:trolleybus:Trolleybus
    U+1F68F🚏\:busstop:Bus Stop
    U+1F690🚐\:minibus:Minibus
    U+1F691🚑\:ambulance:Ambulance
    U+1F692🚒\:fire_engine:Fire Engine
    U+1F693🚓\:police_car:Police Car
    U+1F694🚔\:oncoming_police_car:Oncoming Police Car
    U+1F695🚕\:taxi:Taxi
    U+1F696🚖\:oncoming_taxi:Oncoming Taxi
    U+1F697🚗\:car:Automobile
    U+1F698🚘\:oncoming_automobile:Oncoming Automobile
    U+1F699🚙\:blue_car:Recreational Vehicle
    U+1F69A🚚\:truck:Delivery Truck
    U+1F69B🚛\:articulated_lorry:Articulated Lorry
    U+1F69C🚜\:tractor:Tractor
    U+1F69D🚝\:monorail:Monorail
    U+1F69E🚞\:mountain_railway:Mountain Railway
    U+1F69F🚟\:suspension_railway:Suspension Railway
    U+1F6A0🚠\:mountain_cableway:Mountain Cableway
    U+1F6A1🚡\:aerial_tramway:Aerial Tramway
    U+1F6A2🚢\:ship:Ship
    U+1F6A3🚣\:rowboat:Rowboat
    U+1F6A4🚤\:speedboat:Speedboat
    U+1F6A5🚥\:traffic_light:Horizontal Traffic Light
    U+1F6A6🚦\:vertical_traffic_light:Vertical Traffic Light
    U+1F6A7🚧\:construction:Construction Sign
    U+1F6A8🚨\:rotating_light:Police Cars Revolving Light
    U+1F6A9🚩\:triangular_flag_on_post:Triangular Flag On Post
    U+1F6AA🚪\:door:Door
    U+1F6AB🚫\:no_entry_sign:No Entry Sign
    U+1F6AC🚬\:smoking:Smoking Symbol
    U+1F6AD🚭\:no_smoking:No Smoking Symbol
    U+1F6AE🚮\:put_litter_in_its_place:Put Litter In Its Place Symbol
    U+1F6AF🚯\:do_not_litter:Do Not Litter Symbol
    U+1F6B0🚰\:potable_water:Potable Water Symbol
    U+1F6B1🚱\:non-potable_water:Non-Potable Water Symbol
    U+1F6B2🚲\:bike:Bicycle
    U+1F6B3🚳\:no_bicycles:No Bicycles
    U+1F6B4🚴\:bicyclist:Bicyclist
    U+1F6B5🚵\:mountain_bicyclist:Mountain Bicyclist
    U+1F6B6🚶\:walking:Pedestrian
    U+1F6B7🚷\:no_pedestrians:No Pedestrians
    U+1F6B8🚸\:children_crossing:Children Crossing
    U+1F6B9🚹\:mens:Mens Symbol
    U+1F6BA🚺\:womens:Womens Symbol
    U+1F6BB🚻\:restroom:Restroom
    U+1F6BC🚼\:baby_symbol:Baby Symbol
    U+1F6BD🚽\:toilet:Toilet
    U+1F6BE🚾\:wc:Water Closet
    U+1F6BF🚿\:shower:Shower
    U+1F6C0🛀\:bath:Bath
    U+1F6C1🛁\:bathtub:Bathtub
    U+1F6C2🛂\:passport_control:Passport Control
    U+1F6C3🛃\:customs:Customs
    U+1F6C4🛄\:baggage_claim:Baggage Claim
    U+1F6C5🛅\:left_luggage:Left Luggage
    U+1F6CC🛌\:sleeping_accommodation:Sleeping Accommodation
    U+1F6D0🛐\:place_of_worship:Place Of Worship
    U+1F6D1🛑\:octagonal_sign:Octagonal Sign
    U+1F6D2🛒\:shopping_trolley:Shopping Trolley
    U+1F6D5🛕\:hindu_temple:Hindu Temple
    U+1F6D6🛖\:hut:Hut
    U+1F6D7🛗\:elevator:Elevator
    U+1F6EB🛫\:airplane_departure:Airplane Departure
    U+1F6EC🛬\:airplane_arriving:Airplane Arriving
    U+1F6F4🛴\:scooter:Scooter
    U+1F6F5🛵\:motor_scooter:Motor Scooter
    U+1F6F6🛶\:canoe:Canoe
    U+1F6F7🛷\:sled:Sled
    U+1F6F8🛸\:flying_saucer:Flying Saucer
    U+1F6F9🛹\:skateboard:Skateboard
    U+1F6FA🛺\:auto_rickshaw:Auto Rickshaw
    U+1F6FB🛻\:pickup_truck:Pickup Truck
    U+1F6FC🛼\:roller_skate:Roller Skate
    U+1F7E0🟠\:large_orange_circle:Large Orange Circle
    U+1F7E1🟡\:large_yellow_circle:Large Yellow Circle
    U+1F7E2🟢\:large_green_circle:Large Green Circle
    U+1F7E3🟣\:large_purple_circle:Large Purple Circle
    U+1F7E4🟤\:large_brown_circle:Large Brown Circle
    U+1F7E5🟥\:large_red_square:Large Red Square
    U+1F7E6🟦\:large_blue_square:Large Blue Square
    U+1F7E7🟧\:large_orange_square:Large Orange Square
    U+1F7E8🟨\:large_yellow_square:Large Yellow Square
    U+1F7E9🟩\:large_green_square:Large Green Square
    U+1F7EA🟪\:large_purple_square:Large Purple Square
    U+1F7EB🟫\:large_brown_square:Large Brown Square
    U+1F90C🤌\:pinched_fingers:Pinched Fingers
    U+1F90D🤍\:white_heart:White Heart
    U+1F90E🤎\:brown_heart:Brown Heart
    U+1F90F🤏\:pinching_hand:Pinching Hand
    U+1F910🤐\:zipper_mouth_face:Zipper-Mouth Face
    U+1F911🤑\:money_mouth_face:Money-Mouth Face
    U+1F912🤒\:face_with_thermometer:Face With Thermometer
    U+1F913🤓\:nerd_face:Nerd Face
    U+1F914🤔\:thinking_face:Thinking Face
    U+1F915🤕\:face_with_head_bandage:Face With Head-Bandage
    U+1F916🤖\:robot_face:Robot Face
    U+1F917🤗\:hugging_face:Hugging Face
    U+1F918🤘\:the_horns:Sign Of The Horns
    U+1F919🤙\:call_me_hand:Call Me Hand
    U+1F91A🤚\:raised_back_of_hand:Raised Back Of Hand
    U+1F91B🤛\:left-facing_fist:Left-Facing Fist
    U+1F91C🤜\:right-facing_fist:Right-Facing Fist
    U+1F91D🤝\:handshake:Handshake
    U+1F91E🤞\:crossed_fingers:Hand With Index And Middle Fingers Crossed
    U+1F91F🤟\:i_love_you_hand_sign:I Love You Hand Sign
    U+1F920🤠\:face_with_cowboy_hat:Face With Cowboy Hat
    U+1F921🤡\:clown_face:Clown Face
    U+1F922🤢\:nauseated_face:Nauseated Face
    U+1F923🤣\:rolling_on_the_floor_laughing:Rolling On The Floor Laughing
    U+1F924🤤\:drooling_face:Drooling Face
    U+1F925🤥\:lying_face:Lying Face
    U+1F926🤦\:face_palm:Face Palm
    U+1F927🤧\:sneezing_face:Sneezing Face
    U+1F928🤨\:face_with_raised_eyebrow:Face With One Eyebrow Raised
    U+1F929🤩\:star-struck:Grinning Face With Star Eyes
    U+1F92A🤪\:zany_face:Grinning Face With One Large And One Small Eye
    U+1F92B🤫\:shushing_face:Face With Finger Covering Closed Lips
    U+1F92C🤬\:face_with_symbols_on_mouth:Serious Face With Symbols Covering Mouth
    U+1F92D🤭\:face_with_hand_over_mouth:Smiling Face With Smiling Eyes And Hand Covering Mouth
    U+1F92E🤮\:face_vomiting:Face With Open Mouth Vomiting
    U+1F92F🤯\:exploding_head:Shocked Face With Exploding Head
    U+1F930🤰\:pregnant_woman:Pregnant Woman
    U+1F931🤱\:breast-feeding:Breast-Feeding
    U+1F932🤲\:palms_up_together:Palms Up Together
    U+1F933🤳\:selfie:Selfie
    U+1F934🤴\:prince:Prince
    U+1F935🤵\:person_in_tuxedo:Man In Tuxedo
    U+1F936🤶\:mrs_claus:Mother Christmas
    U+1F937🤷\:shrug:Shrug
    U+1F938🤸\:person_doing_cartwheel:Person Doing Cartwheel
    U+1F939🤹\:juggling:Juggling
    U+1F93A🤺\:fencer:Fencer
    U+1F93C🤼\:wrestlers:Wrestlers
    U+1F93D🤽\:water_polo:Water Polo
    U+1F93E🤾\:handball:Handball
    U+1F93F🤿\:diving_mask:Diving Mask
    U+1F940🥀\:wilted_flower:Wilted Flower
    U+1F941🥁\:drum_with_drumsticks:Drum With Drumsticks
    U+1F942🥂\:clinking_glasses:Clinking Glasses
    U+1F943🥃\:tumbler_glass:Tumbler Glass
    U+1F944🥄\:spoon:Spoon
    U+1F945🥅\:goal_net:Goal Net
    U+1F947🥇\:first_place_medal:First Place Medal
    U+1F948🥈\:second_place_medal:Second Place Medal
    U+1F949🥉\:third_place_medal:Third Place Medal
    U+1F94A🥊\:boxing_glove:Boxing Glove
    U+1F94B🥋\:martial_arts_uniform:Martial Arts Uniform
    U+1F94C🥌\:curling_stone:Curling Stone
    U+1F94D🥍\:lacrosse:Lacrosse Stick And Ball
    U+1F94E🥎\:softball:Softball
    U+1F94F🥏\:flying_disc:Flying Disc
    U+1F950🥐\:croissant:Croissant
    U+1F951🥑\:avocado:Avocado
    U+1F952🥒\:cucumber:Cucumber
    U+1F953🥓\:bacon:Bacon
    U+1F954🥔\:potato:Potato
    U+1F955🥕\:carrot:Carrot
    U+1F956🥖\:baguette_bread:Baguette Bread
    U+1F957🥗\:green_salad:Green Salad
    U+1F958🥘\:shallow_pan_of_food:Shallow Pan Of Food
    U+1F959🥙\:stuffed_flatbread:Stuffed Flatbread
    U+1F95A🥚\:egg:Egg
    U+1F95B🥛\:glass_of_milk:Glass Of Milk
    U+1F95C🥜\:peanuts:Peanuts
    U+1F95D🥝\:kiwifruit:Kiwifruit
    U+1F95E🥞\:pancakes:Pancakes
    U+1F95F🥟\:dumpling:Dumpling
    U+1F960🥠\:fortune_cookie:Fortune Cookie
    U+1F961🥡\:takeout_box:Takeout Box
    U+1F962🥢\:chopsticks:Chopsticks
    U+1F963🥣\:bowl_with_spoon:Bowl With Spoon
    U+1F964🥤\:cup_with_straw:Cup With Straw
    U+1F965🥥\:coconut:Coconut
    U+1F966🥦\:broccoli:Broccoli
    U+1F967🥧\:pie:Pie
    U+1F968🥨\:pretzel:Pretzel
    U+1F969🥩\:cut_of_meat:Cut Of Meat
    U+1F96A🥪\:sandwich:Sandwich
    U+1F96B🥫\:canned_food:Canned Food
    U+1F96C🥬\:leafy_green:Leafy Green
    U+1F96D🥭\:mango:Mango
    U+1F96E🥮\:moon_cake:Moon Cake
    U+1F96F🥯\:bagel:Bagel
    U+1F970🥰\:smiling_face_with_3_hearts:Smiling Face With Smiling Eyes And Three Hearts
    U+1F971🥱\:yawning_face:Yawning Face
    U+1F972🥲\:smiling_face_with_tear:Smiling Face With Tear
    U+1F973🥳\:partying_face:Face With Party Horn And Party Hat
    U+1F974🥴\:woozy_face:Face With Uneven Eyes And Wavy Mouth
    U+1F975🥵\:hot_face:Overheated Face
    U+1F976🥶\:cold_face:Freezing Face
    U+1F977🥷\:ninja:Ninja
    U+1F978🥸\:disguised_face:Disguised Face
    U+1F97A🥺\:pleading_face:Face With Pleading Eyes
    U+1F97B🥻\:sari:Sari
    U+1F97C🥼\:lab_coat:Lab Coat
    U+1F97D🥽\:goggles:Goggles
    U+1F97E🥾\:hiking_boot:Hiking Boot
    U+1F97F🥿\:womans_flat_shoe:Flat Shoe
    U+1F980🦀\:crab:Crab
    U+1F981🦁\:lion_face:Lion Face
    U+1F982🦂\:scorpion:Scorpion
    U+1F983🦃\:turkey:Turkey
    U+1F984🦄\:unicorn_face:Unicorn Face
    U+1F985🦅\:eagle:Eagle
    U+1F986🦆\:duck:Duck
    U+1F987🦇\:bat:Bat
    U+1F988🦈\:shark:Shark
    U+1F989🦉\:owl:Owl
    U+1F98A🦊\:fox_face:Fox Face
    U+1F98B🦋\:butterfly:Butterfly
    U+1F98C🦌\:deer:Deer
    U+1F98D🦍\:gorilla:Gorilla
    U+1F98E🦎\:lizard:Lizard
    U+1F98F🦏\:rhinoceros:Rhinoceros
    U+1F990🦐\:shrimp:Shrimp
    U+1F991🦑\:squid:Squid
    U+1F992🦒\:giraffe_face:Giraffe Face
    U+1F993🦓\:zebra_face:Zebra Face
    U+1F994🦔\:hedgehog:Hedgehog
    U+1F995🦕\:sauropod:Sauropod
    U+1F996🦖\:t-rex:T-Rex
    U+1F997🦗\:cricket:Cricket
    U+1F998🦘\:kangaroo:Kangaroo
    U+1F999🦙\:llama:Llama
    U+1F99A🦚\:peacock:Peacock
    U+1F99B🦛\:hippopotamus:Hippopotamus
    U+1F99C🦜\:parrot:Parrot
    U+1F99D🦝\:raccoon:Raccoon
    U+1F99E🦞\:lobster:Lobster
    U+1F99F🦟\:mosquito:Mosquito
    U+1F9A0🦠\:microbe:Microbe
    U+1F9A1🦡\:badger:Badger
    U+1F9A2🦢\:swan:Swan
    U+1F9A3🦣\:mammoth:Mammoth
    U+1F9A4🦤\:dodo:Dodo
    U+1F9A5🦥\:sloth:Sloth
    U+1F9A6🦦\:otter:Otter
    U+1F9A7🦧\:orangutan:Orangutan
    U+1F9A8🦨\:skunk:Skunk
    U+1F9A9🦩\:flamingo:Flamingo
    U+1F9AA🦪\:oyster:Oyster
    U+1F9AB🦫\:beaver:Beaver
    U+1F9AC🦬\:bison:Bison
    U+1F9AD🦭\:seal:Seal
    U+1F9AE🦮\:guide_dog:Guide Dog
    U+1F9AF🦯\:probing_cane:Probing Cane
    U+1F9B4🦴\:bone:Bone
    U+1F9B5🦵\:leg:Leg
    U+1F9B6🦶\:foot:Foot
    U+1F9B7🦷\:tooth:Tooth
    U+1F9B8🦸\:superhero:Superhero
    U+1F9B9🦹\:supervillain:Supervillain
    U+1F9BA🦺\:safety_vest:Safety Vest
    U+1F9BB🦻\:ear_with_hearing_aid:Ear With Hearing Aid
    U+1F9BC🦼\:motorized_wheelchair:Motorized Wheelchair
    U+1F9BD🦽\:manual_wheelchair:Manual Wheelchair
    U+1F9BE🦾\:mechanical_arm:Mechanical Arm
    U+1F9BF🦿\:mechanical_leg:Mechanical Leg
    U+1F9C0🧀\:cheese_wedge:Cheese Wedge
    U+1F9C1🧁\:cupcake:Cupcake
    U+1F9C2🧂\:salt:Salt Shaker
    U+1F9C3🧃\:beverage_box:Beverage Box
    U+1F9C4🧄\:garlic:Garlic
    U+1F9C5🧅\:onion:Onion
    U+1F9C6🧆\:falafel:Falafel
    U+1F9C7🧇\:waffle:Waffle
    U+1F9C8🧈\:butter:Butter
    U+1F9C9🧉\:mate_drink:Mate Drink
    U+1F9CA🧊\:ice_cube:Ice Cube
    U+1F9CB🧋\:bubble_tea:Bubble Tea
    U+1F9CD🧍\:standing_person:Standing Person
    U+1F9CE🧎\:kneeling_person:Kneeling Person
    U+1F9CF🧏\:deaf_person:Deaf Person
    U+1F9D0🧐\:face_with_monocle:Face With Monocle
    U+1F9D1🧑\:adult:Adult
    U+1F9D2🧒\:child:Child
    U+1F9D3🧓\:older_adult:Older Adult
    U+1F9D4🧔\:bearded_person:Bearded Person
    U+1F9D5🧕\:person_with_headscarf:Person With Headscarf
    U+1F9D6🧖\:person_in_steamy_room:Person In Steamy Room
    U+1F9D7🧗\:person_climbing:Person Climbing
    U+1F9D8🧘\:person_in_lotus_position:Person In Lotus Position
    U+1F9D9🧙\:mage:Mage
    U+1F9DA🧚\:fairy:Fairy
    U+1F9DB🧛\:vampire:Vampire
    U+1F9DC🧜\:merperson:Merperson
    U+1F9DD🧝\:elf:Elf
    U+1F9DE🧞\:genie:Genie
    U+1F9DF🧟\:zombie:Zombie
    U+1F9E0🧠\:brain:Brain
    U+1F9E1🧡\:orange_heart:Orange Heart
    U+1F9E2🧢\:billed_cap:Billed Cap
    U+1F9E3🧣\:scarf:Scarf
    U+1F9E4🧤\:gloves:Gloves
    U+1F9E5🧥\:coat:Coat
    U+1F9E6🧦\:socks:Socks
    U+1F9E7🧧\:red_envelope:Red Gift Envelope
    U+1F9E8🧨\:firecracker:Firecracker
    U+1F9E9🧩\:jigsaw:Jigsaw Puzzle Piece
    U+1F9EA🧪\:test_tube:Test Tube
    U+1F9EB🧫\:petri_dish:Petri Dish
    U+1F9EC🧬\:dna:Dna Double Helix
    U+1F9ED🧭\:compass:Compass
    U+1F9EE🧮\:abacus:Abacus
    U+1F9EF🧯\:fire_extinguisher:Fire Extinguisher
    U+1F9F0🧰\:toolbox:Toolbox
    U+1F9F1🧱\:bricks:Brick
    U+1F9F2🧲\:magnet:Magnet
    U+1F9F3🧳\:luggage:Luggage
    U+1F9F4🧴\:lotion_bottle:Lotion Bottle
    U+1F9F5🧵\:thread:Spool Of Thread
    U+1F9F6🧶\:yarn:Ball Of Yarn
    U+1F9F7🧷\:safety_pin:Safety Pin
    U+1F9F8🧸\:teddy_bear:Teddy Bear
    U+1F9F9🧹\:broom:Broom
    U+1F9FA🧺\:basket:Basket
    U+1F9FB🧻\:roll_of_paper:Roll Of Paper
    U+1F9FC🧼\:soap:Bar Of Soap
    U+1F9FD🧽\:sponge:Sponge
    U+1F9FE🧾\:receipt:Receipt
    U+1F9FF🧿\:nazar_amulet:Nazar Amulet
    U+1FA70🩰\:ballet_shoes:Ballet Shoes
    U+1FA71🩱\:one-piece_swimsuit:One-Piece Swimsuit
    U+1FA72🩲\:briefs:Briefs
    U+1FA73🩳\:shorts:Shorts
    U+1FA74🩴\:thong_sandal:Thong Sandal
    U+1FA78🩸\:drop_of_blood:Drop Of Blood
    U+1FA79🩹\:adhesive_bandage:Adhesive Bandage
    U+1FA7A🩺\:stethoscope:Stethoscope
    U+1FA80🪀\:yo-yo:Yo-Yo
    U+1FA81🪁\:kite:Kite
    U+1FA82🪂\:parachute:Parachute
    U+1FA83🪃\:boomerang:Boomerang
    U+1FA84🪄\:magic_wand:Magic Wand
    U+1FA85🪅\:pinata:Pinata
    U+1FA86🪆\:nesting_dolls:Nesting Dolls
    U+1FA90🪐\:ringed_planet:Ringed Planet
    U+1FA91🪑\:chair:Chair
    U+1FA92🪒\:razor:Razor
    U+1FA93🪓\:axe:Axe
    U+1FA94🪔\:diya_lamp:Diya Lamp
    U+1FA95🪕\:banjo:Banjo
    U+1FA96🪖\:military_helmet:Military Helmet
    U+1FA97🪗\:accordion:Accordion
    U+1FA98🪘\:long_drum:Long Drum
    U+1FA99🪙\:coin:Coin
    U+1FA9A🪚\:carpentry_saw:Carpentry Saw
    U+1FA9B🪛\:screwdriver:Screwdriver
    U+1FA9C🪜\:ladder:Ladder
    U+1FA9D🪝\:hook:Hook
    U+1FA9E🪞\:mirror:Mirror
    U+1FA9F🪟\:window:Window
    U+1FAA0🪠\:plunger:Plunger
    U+1FAA1🪡\:sewing_needle:Sewing Needle
    U+1FAA2🪢\:knot:Knot
    U+1FAA3🪣\:bucket:Bucket
    U+1FAA4🪤\:mouse_trap:Mouse Trap
    U+1FAA5🪥\:toothbrush:Toothbrush
    U+1FAA6🪦\:headstone:Headstone
    U+1FAA7🪧\:placard:Placard
    U+1FAA8🪨\:rock:Rock
    U+1FAB0🪰\:fly:Fly
    U+1FAB1🪱\:worm:Worm
    U+1FAB2🪲\:beetle:Beetle
    U+1FAB3🪳\:cockroach:Cockroach
    U+1FAB4🪴\:potted_plant:Potted Plant
    U+1FAB5🪵\:wood:Wood
    U+1FAB6🪶\:feather:Feather
    U+1FAC0🫀\:anatomical_heart:Anatomical Heart
    U+1FAC1🫁\:lungs:Lungs
    U+1FAC2🫂\:people_hugging:People Hugging
    U+1FAD0🫐\:blueberries:Blueberries
    U+1FAD1🫑\:bell_pepper:Bell Pepper
    U+1FAD2🫒\:olive:Olive
    U+1FAD3🫓\:flatbread:Flatbread
    U+1FAD4🫔\:tamale:Tamale
    U+1FAD5🫕\:fondue:Fondue
    U+1FAD6🫖\:teapot:Teapot
    +
    Repository

    Unicode 输入表

    在 Julia REPL 或其它编辑器中，可以像输入 LaTeX 符号一样，用 tab 补全下表列出的 Unicode 字符。在 REPL 中，可以先按 ? 进入帮助模式，然后将 Unicode 字符复制粘贴进去，一般在文档开头就会写输入方式。

    Warning

    此表第二列可能会缺失一些字符，对某些字符的显示效果也可能会与在 Julia REPL 中不一致。如果发生了这种状况，强烈建议用户检查一下浏览器或 REPL 的字体设置，目前已知很多字体都有显示问题。

    Code point(s)Character(s)Tab completion sequence(s)Unicode name(s)
    U+000A1¡\exclamdownInverted Exclamation Mark
    U+000A3£\sterlingPound Sign
    U+000A5¥\yenYen Sign
    U+000A6¦\brokenbarBroken Bar / Broken Vertical Bar
    U+000A7§\SSection Sign
    U+000A9©\copyright, \:copyright:Copyright Sign
    U+000AAª\ordfeminineFeminine Ordinal Indicator
    U+000AC¬\negNot Sign
    U+000AE®\circledR, \:registered:Registered Sign / Registered Trade Mark Sign
    U+000AF¯\highminusMacron / Spacing Macron
    U+000B0°\degreeDegree Sign
    U+000B1±\pmPlus-Minus Sign / Plus-Or-Minus Sign
    U+000B2²\^2Superscript Two / Superscript Digit Two
    U+000B3³\^3Superscript Three / Superscript Digit Three
    U+000B6\PPilcrow Sign / Paragraph Sign
    U+000B7·\cdotpMiddle Dot
    U+000B9¹\^1Superscript One / Superscript Digit One
    U+000BAº\ordmasculineMasculine Ordinal Indicator
    U+000BC¼\1/4Vulgar Fraction One Quarter / Fraction One Quarter
    U+000BD½\1/2Vulgar Fraction One Half / Fraction One Half
    U+000BE¾\3/4Vulgar Fraction Three Quarters / Fraction Three Quarters
    U+000BF¿\questiondownInverted Question Mark
    U+000C5Å\AALatin Capital Letter A With Ring Above / Latin Capital Letter A Ring
    U+000C6Æ\AELatin Capital Letter Ae / Latin Capital Letter A E
    U+000D0Ð\DHLatin Capital Letter Eth
    U+000D7×\timesMultiplication Sign
    U+000D8Ø\OLatin Capital Letter O With Stroke / Latin Capital Letter O Slash
    U+000DEÞ\THLatin Capital Letter Thorn
    U+000DFß\ssLatin Small Letter Sharp S
    U+000E5å\aaLatin Small Letter A With Ring Above / Latin Small Letter A Ring
    U+000E6æ\aeLatin Small Letter Ae / Latin Small Letter A E
    U+000F0ð\eth, \dhLatin Small Letter Eth
    U+000F7÷\divDivision Sign
    U+000F8ø\oLatin Small Letter O With Stroke / Latin Small Letter O Slash
    U+000FEþ\thLatin Small Letter Thorn
    U+00110Đ\DJLatin Capital Letter D With Stroke / Latin Capital Letter D Bar
    U+00111đ\djLatin Small Letter D With Stroke / Latin Small Letter D Bar
    U+00127ħ\hbarLatin Small Letter H With Stroke / Latin Small Letter H Bar
    U+00131ı\imathLatin Small Letter Dotless I
    U+00141Ł\LLatin Capital Letter L With Stroke / Latin Capital Letter L Slash
    U+00142ł\lLatin Small Letter L With Stroke / Latin Small Letter L Slash
    U+0014AŊ\NGLatin Capital Letter Eng
    U+0014Bŋ\ngLatin Small Letter Eng
    U+00152Œ\OELatin Capital Ligature Oe / Latin Capital Letter O E
    U+00153œ\oeLatin Small Ligature Oe / Latin Small Letter O E
    U+00195ƕ\hvligLatin Small Letter Hv / Latin Small Letter H V
    U+0019Eƞ\nrlegLatin Small Letter N With Long Right Leg
    U+001B5Ƶ\ZbarLatin Capital Letter Z With Stroke / Latin Capital Letter Z Bar
    U+001C2ǂ\doublepipeLatin Letter Alveolar Click / Latin Letter Pipe Double Bar
    U+00237ȷ\jmathLatin Small Letter Dotless J
    U+00250ɐ\trnaLatin Small Letter Turned A
    U+00252ɒ\trnsaLatin Small Letter Turned Alpha / Latin Small Letter Turned Script A
    U+00254ɔ\openoLatin Small Letter Open O
    U+00256ɖ\rtldLatin Small Letter D With Tail / Latin Small Letter D Retroflex Hook
    U+00259ə\schwaLatin Small Letter Schwa
    U+00263ɣ\pgammaLatin Small Letter Gamma
    U+00264ɤ\pbgamLatin Small Letter Rams Horn / Latin Small Letter Baby Gamma
    U+00265ɥ\trnhLatin Small Letter Turned H
    U+0026Cɬ\btdlLatin Small Letter L With Belt / Latin Small Letter L Belt
    U+0026Dɭ\rtllLatin Small Letter L With Retroflex Hook / Latin Small Letter L Retroflex Hook
    U+0026Fɯ\trnmLatin Small Letter Turned M
    U+00270ɰ\trnmlrLatin Small Letter Turned M With Long Leg
    U+00271ɱ\ltlmrLatin Small Letter M With Hook / Latin Small Letter M Hook
    U+00272ɲ\ltlnLatin Small Letter N With Left Hook / Latin Small Letter N Hook
    U+00273ɳ\rtlnLatin Small Letter N With Retroflex Hook / Latin Small Letter N Retroflex Hook
    U+00277ɷ\clomegLatin Small Letter Closed Omega
    U+00278ɸ\ltphiLatin Small Letter Phi
    U+00279ɹ\trnrLatin Small Letter Turned R
    U+0027Aɺ\trnrlLatin Small Letter Turned R With Long Leg
    U+0027Bɻ\rttrnrLatin Small Letter Turned R With Hook / Latin Small Letter Turned R Hook
    U+0027Cɼ\rlLatin Small Letter R With Long Leg
    U+0027Dɽ\rtlrLatin Small Letter R With Tail / Latin Small Letter R Hook
    U+0027Eɾ\fhrLatin Small Letter R With Fishhook / Latin Small Letter Fishhook R
    U+00282ʂ\rtlsLatin Small Letter S With Hook / Latin Small Letter S Hook
    U+00283ʃ\eshLatin Small Letter Esh
    U+00287ʇ\trntLatin Small Letter Turned T
    U+00288ʈ\rtltLatin Small Letter T With Retroflex Hook / Latin Small Letter T Retroflex Hook
    U+0028Aʊ\pupsilLatin Small Letter Upsilon
    U+0028Bʋ\pscrvLatin Small Letter V With Hook / Latin Small Letter Script V
    U+0028Cʌ\invvLatin Small Letter Turned V
    U+0028Dʍ\invwLatin Small Letter Turned W
    U+0028Eʎ\trnyLatin Small Letter Turned Y
    U+00290ʐ\rtlzLatin Small Letter Z With Retroflex Hook / Latin Small Letter Z Retroflex Hook
    U+00292ʒ\yoghLatin Small Letter Ezh / Latin Small Letter Yogh
    U+00294ʔ\glstLatin Letter Glottal Stop
    U+00295ʕ\reglstLatin Letter Pharyngeal Voiced Fricative / Latin Letter Reversed Glottal Stop
    U+00296ʖ\inglstLatin Letter Inverted Glottal Stop
    U+0029Eʞ\turnkLatin Small Letter Turned K
    U+002A4ʤ\dyoghLatin Small Letter Dezh Digraph / Latin Small Letter D Yogh
    U+002A7ʧ\teshLatin Small Letter Tesh Digraph / Latin Small Letter T Esh
    U+002B0ʰ\^hModifier Letter Small H
    U+002B2ʲ\^jModifier Letter Small J
    U+002B3ʳ\^rModifier Letter Small R
    U+002B7ʷ\^wModifier Letter Small W
    U+002B8ʸ\^yModifier Letter Small Y
    U+002BCʼ\raspModifier Letter Apostrophe
    U+002C8ˈ\vertsModifier Letter Vertical Line
    U+002CCˌ\vertiModifier Letter Low Vertical Line
    U+002D0ː\lmrkModifier Letter Triangular Colon
    U+002D1ˑ\hlmrkModifier Letter Half Triangular Colon
    U+002D2˒\sbrhrModifier Letter Centred Right Half Ring / Modifier Letter Centered Right Half Ring
    U+002D3˓\sblhrModifier Letter Centred Left Half Ring / Modifier Letter Centered Left Half Ring
    U+002D4˔\raisModifier Letter Up Tack
    U+002D5˕\lowModifier Letter Down Tack
    U+002D8˘\uBreve / Spacing Breve
    U+002DC˜\tildelowSmall Tilde / Spacing Tilde
    U+002E1ˡ\^lModifier Letter Small L
    U+002E2ˢ\^sModifier Letter Small S
    U+002E3ˣ\^xModifier Letter Small X
    U+00300 ̀ \graveCombining Grave Accent / Non-Spacing Grave
    U+00301 ́ \acuteCombining Acute Accent / Non-Spacing Acute
    U+00302 ̂ \hatCombining Circumflex Accent / Non-Spacing Circumflex
    U+00303 ̃ \tildeCombining Tilde / Non-Spacing Tilde
    U+00304 ̄ \barCombining Macron / Non-Spacing Macron
    U+00305 ̅ \overbarCombining Overline / Non-Spacing Overscore
    U+00306 ̆ \breveCombining Breve / Non-Spacing Breve
    U+00307 ̇ \dotCombining Dot Above / Non-Spacing Dot Above
    U+00308 ̈ \ddotCombining Diaeresis / Non-Spacing Diaeresis
    U+00309 ̉ \ovhookCombining Hook Above / Non-Spacing Hook Above
    U+0030A ̊ \ocircCombining Ring Above / Non-Spacing Ring Above
    U+0030B ̋ \HCombining Double Acute Accent / Non-Spacing Double Acute
    U+0030C ̌ \checkCombining Caron / Non-Spacing Hacek
    U+00310 ̐ \candraCombining Candrabindu / Non-Spacing Candrabindu
    U+00312 ̒ \oturnedcommaCombining Turned Comma Above / Non-Spacing Turned Comma Above
    U+00315 ̕ \ocommatoprightCombining Comma Above Right / Non-Spacing Comma Above Right
    U+0031A ̚ \droangCombining Left Angle Above / Non-Spacing Left Angle Above
    U+00321 ̡ \palhCombining Palatalized Hook Below / Non-Spacing Palatalized Hook Below
    U+00322 ̢ \rhCombining Retroflex Hook Below / Non-Spacing Retroflex Hook Below
    U+00327 ̧ \cCombining Cedilla / Non-Spacing Cedilla
    U+00328 ̨ \kCombining Ogonek / Non-Spacing Ogonek
    U+0032A ̪ \sbbrgCombining Bridge Below / Non-Spacing Bridge Below
    U+00330 ̰ \wideutildeCombining Tilde Below / Non-Spacing Tilde Below
    U+00332 ̲ \underbarCombining Low Line / Non-Spacing Underscore
    U+00336 ̶ \strike, \soutCombining Long Stroke Overlay / Non-Spacing Long Bar Overlay
    U+00338 ̸ \notCombining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0034D ͍ \underleftrightarrowCombining Left Right Arrow Below
    U+00391Α\AlphaGreek Capital Letter Alpha
    U+00392Β\BetaGreek Capital Letter Beta
    U+00393Γ\GammaGreek Capital Letter Gamma
    U+00394Δ\DeltaGreek Capital Letter Delta
    U+00395Ε\EpsilonGreek Capital Letter Epsilon
    U+00396Ζ\ZetaGreek Capital Letter Zeta
    U+00397Η\EtaGreek Capital Letter Eta
    U+00398Θ\ThetaGreek Capital Letter Theta
    U+00399Ι\IotaGreek Capital Letter Iota
    U+0039AΚ\KappaGreek Capital Letter Kappa
    U+0039BΛ\LambdaGreek Capital Letter Lamda / Greek Capital Letter Lambda
    U+0039CΜ\upMuGreek Capital Letter Mu
    U+0039DΝ\upNuGreek Capital Letter Nu
    U+0039EΞ\XiGreek Capital Letter Xi
    U+0039FΟ\upOmicronGreek Capital Letter Omicron
    U+003A0Π\PiGreek Capital Letter Pi
    U+003A1Ρ\RhoGreek Capital Letter Rho
    U+003A3Σ\SigmaGreek Capital Letter Sigma
    U+003A4Τ\TauGreek Capital Letter Tau
    U+003A5Υ\UpsilonGreek Capital Letter Upsilon
    U+003A6Φ\PhiGreek Capital Letter Phi
    U+003A7Χ\ChiGreek Capital Letter Chi
    U+003A8Ψ\PsiGreek Capital Letter Psi
    U+003A9Ω\OmegaGreek Capital Letter Omega
    U+003B1α\alphaGreek Small Letter Alpha
    U+003B2β\betaGreek Small Letter Beta
    U+003B3γ\gammaGreek Small Letter Gamma
    U+003B4δ\deltaGreek Small Letter Delta
    U+003B5ε\upepsilon, \varepsilonGreek Small Letter Epsilon
    U+003B6ζ\zetaGreek Small Letter Zeta
    U+003B7η\etaGreek Small Letter Eta
    U+003B8θ\thetaGreek Small Letter Theta
    U+003B9ι\iotaGreek Small Letter Iota
    U+003BAκ\kappaGreek Small Letter Kappa
    U+003BBλ\lambdaGreek Small Letter Lamda / Greek Small Letter Lambda
    U+003BCμ\muGreek Small Letter Mu
    U+003BDν\nuGreek Small Letter Nu
    U+003BEξ\xiGreek Small Letter Xi
    U+003BFο\upomicronGreek Small Letter Omicron
    U+003C0π\piGreek Small Letter Pi
    U+003C1ρ\rhoGreek Small Letter Rho
    U+003C2ς\varsigmaGreek Small Letter Final Sigma
    U+003C3σ\sigmaGreek Small Letter Sigma
    U+003C4τ\tauGreek Small Letter Tau
    U+003C5υ\upsilonGreek Small Letter Upsilon
    U+003C6φ\varphiGreek Small Letter Phi
    U+003C7χ\chiGreek Small Letter Chi
    U+003C8ψ\psiGreek Small Letter Psi
    U+003C9ω\omegaGreek Small Letter Omega
    U+003D0ϐ\upvarbetaGreek Beta Symbol / Greek Small Letter Curled Beta
    U+003D1ϑ\varthetaGreek Theta Symbol / Greek Small Letter Script Theta
    U+003D5ϕ\phiGreek Phi Symbol / Greek Small Letter Script Phi
    U+003D6ϖ\varpiGreek Pi Symbol / Greek Small Letter Omega Pi
    U+003D8Ϙ\upoldKoppaGreek Letter Archaic Koppa
    U+003D9ϙ\upoldkoppaGreek Small Letter Archaic Koppa
    U+003DAϚ\StigmaGreek Letter Stigma / Greek Capital Letter Stigma
    U+003DBϛ\upstigmaGreek Small Letter Stigma
    U+003DCϜ\DigammaGreek Letter Digamma / Greek Capital Letter Digamma
    U+003DDϝ\digammaGreek Small Letter Digamma
    U+003DEϞ\KoppaGreek Letter Koppa / Greek Capital Letter Koppa
    U+003DFϟ\upkoppaGreek Small Letter Koppa
    U+003E0Ϡ\SampiGreek Letter Sampi / Greek Capital Letter Sampi
    U+003E1ϡ\upsampiGreek Small Letter Sampi
    U+003F0ϰ\varkappaGreek Kappa Symbol / Greek Small Letter Script Kappa
    U+003F1ϱ\varrhoGreek Rho Symbol / Greek Small Letter Tailed Rho
    U+003F4ϴ\varThetaGreek Capital Theta Symbol
    U+003F5ϵ\epsilonGreek Lunate Epsilon Symbol
    U+003F6϶\backepsilonGreek Reversed Lunate Epsilon Symbol
    U+01D2Cᴬ\^AModifier Letter Capital A
    U+01D2Eᴮ\^BModifier Letter Capital B
    U+01D30ᴰ\^DModifier Letter Capital D
    U+01D31ᴱ\^EModifier Letter Capital E
    U+01D33ᴳ\^GModifier Letter Capital G
    U+01D34ᴴ\^HModifier Letter Capital H
    U+01D35ᴵ\^IModifier Letter Capital I
    U+01D36ᴶ\^JModifier Letter Capital J
    U+01D37ᴷ\^KModifier Letter Capital K
    U+01D38ᴸ\^LModifier Letter Capital L
    U+01D39ᴹ\^MModifier Letter Capital M
    U+01D3Aᴺ\^NModifier Letter Capital N
    U+01D3Cᴼ\^OModifier Letter Capital O
    U+01D3Eᴾ\^PModifier Letter Capital P
    U+01D3Fᴿ\^RModifier Letter Capital R
    U+01D40ᵀ\^TModifier Letter Capital T
    U+01D41ᵁ\^UModifier Letter Capital U
    U+01D42ᵂ\^WModifier Letter Capital W
    U+01D43ᵃ\^aModifier Letter Small A
    U+01D45ᵅ\^alphaModifier Letter Small Alpha
    U+01D47ᵇ\^bModifier Letter Small B
    U+01D48ᵈ\^dModifier Letter Small D
    U+01D49ᵉ\^eModifier Letter Small E
    U+01D4Bᵋ\^epsilonModifier Letter Small Open E
    U+01D4Dᵍ\^gModifier Letter Small G
    U+01D4Fᵏ\^kModifier Letter Small K
    U+01D50ᵐ\^mModifier Letter Small M
    U+01D52ᵒ\^oModifier Letter Small O
    U+01D56ᵖ\^pModifier Letter Small P
    U+01D57ᵗ\^tModifier Letter Small T
    U+01D58ᵘ\^uModifier Letter Small U
    U+01D5Bᵛ\^vModifier Letter Small V
    U+01D5Dᵝ\^betaModifier Letter Small Beta
    U+01D5Eᵞ\^gammaModifier Letter Small Greek Gamma
    U+01D5Fᵟ\^deltaModifier Letter Small Delta
    U+01D60ᵠ\^phiModifier Letter Small Greek Phi
    U+01D61ᵡ\^chiModifier Letter Small Chi
    U+01D62ᵢ\_iLatin Subscript Small Letter I
    U+01D63ᵣ\_rLatin Subscript Small Letter R
    U+01D64ᵤ\_uLatin Subscript Small Letter U
    U+01D65ᵥ\_vLatin Subscript Small Letter V
    U+01D66ᵦ\_betaGreek Subscript Small Letter Beta
    U+01D67ᵧ\_gammaGreek Subscript Small Letter Gamma
    U+01D68ᵨ\_rhoGreek Subscript Small Letter Rho
    U+01D69ᵩ\_phiGreek Subscript Small Letter Phi
    U+01D6Aᵪ\_chiGreek Subscript Small Letter Chi
    U+01D9Cᶜ\^cModifier Letter Small C
    U+01DA0ᶠ\^fModifier Letter Small F
    U+01DA5ᶥ\^iotaModifier Letter Small Iota
    U+01DB2ᶲ\^ltphiModifier Letter Small Phi
    U+01DBBᶻ\^zModifier Letter Small Z
    U+01DBFᶿ\^thetaModifier Letter Small Theta
    U+02002 \enspaceEn Space
    U+02003 \quadEm Space
    U+02005 \thickspaceFour-Per-Em Space
    U+02009 \thinspaceThin Space
    U+0200A \hspaceHair Space
    U+02013–\endashEn Dash
    U+02014—\emdashEm Dash
    U+02016‖\VertDouble Vertical Line / Double Vertical Bar
    U+02018‘\lqLeft Single Quotation Mark / Single Turned Comma Quotation Mark
    U+02019’\rqRight Single Quotation Mark / Single Comma Quotation Mark
    U+0201B‛\reaposSingle High-Reversed-9 Quotation Mark / Single Reversed Comma Quotation Mark
    U+0201C“\ldqLeft Double Quotation Mark / Double Turned Comma Quotation Mark
    U+0201D”\rdqRight Double Quotation Mark / Double Comma Quotation Mark
    U+02020†\daggerDagger
    U+02021‡\ddaggerDouble Dagger
    U+02022•\bulletBullet
    U+02026…\dots, \ldotsHorizontal Ellipsis
    U+02030‰\perthousandPer Mille Sign
    U+02031‱\pertenthousandPer Ten Thousand Sign
    U+02032′\primePrime
    U+02033″\pprimeDouble Prime
    U+02034‴\ppprimeTriple Prime
    U+02035‵\backprimeReversed Prime
    U+02036‶\backpprimeReversed Double Prime
    U+02037‷\backppprimeReversed Triple Prime
    U+02039‹\guilsinglleftSingle Left-Pointing Angle Quotation Mark / Left Pointing Single Guillemet
    U+0203A›\guilsinglrightSingle Right-Pointing Angle Quotation Mark / Right Pointing Single Guillemet
    U+0203C‼\:bangbang:Double Exclamation Mark
    U+02040⁀\tieconcatCharacter Tie
    U+02049⁉\:interrobang:Exclamation Question Mark
    U+02057⁗\pppprimeQuadruple Prime
    U+0205D⁝\tricolonTricolon
    U+02060⁠\nolinebreakWord Joiner
    U+02070⁰\^0Superscript Zero / Superscript Digit Zero
    U+02071ⁱ\^iSuperscript Latin Small Letter I
    U+02074⁴\^4Superscript Four / Superscript Digit Four
    U+02075⁵\^5Superscript Five / Superscript Digit Five
    U+02076⁶\^6Superscript Six / Superscript Digit Six
    U+02077⁷\^7Superscript Seven / Superscript Digit Seven
    U+02078⁸\^8Superscript Eight / Superscript Digit Eight
    U+02079⁹\^9Superscript Nine / Superscript Digit Nine
    U+0207A⁺\^+Superscript Plus Sign
    U+0207B⁻\^-Superscript Minus / Superscript Hyphen-Minus
    U+0207C⁼\^=Superscript Equals Sign
    U+0207D⁽\^(Superscript Left Parenthesis / Superscript Opening Parenthesis
    U+0207E⁾\^)Superscript Right Parenthesis / Superscript Closing Parenthesis
    U+0207Fⁿ\^nSuperscript Latin Small Letter N
    U+02080₀\_0Subscript Zero / Subscript Digit Zero
    U+02081₁\_1Subscript One / Subscript Digit One
    U+02082₂\_2Subscript Two / Subscript Digit Two
    U+02083₃\_3Subscript Three / Subscript Digit Three
    U+02084₄\_4Subscript Four / Subscript Digit Four
    U+02085₅\_5Subscript Five / Subscript Digit Five
    U+02086₆\_6Subscript Six / Subscript Digit Six
    U+02087₇\_7Subscript Seven / Subscript Digit Seven
    U+02088₈\_8Subscript Eight / Subscript Digit Eight
    U+02089₉\_9Subscript Nine / Subscript Digit Nine
    U+0208A₊\_+Subscript Plus Sign
    U+0208B₋\_-Subscript Minus / Subscript Hyphen-Minus
    U+0208C₌\_=Subscript Equals Sign
    U+0208D₍\_(Subscript Left Parenthesis / Subscript Opening Parenthesis
    U+0208E₎\_)Subscript Right Parenthesis / Subscript Closing Parenthesis
    U+02090ₐ\_aLatin Subscript Small Letter A
    U+02091ₑ\_eLatin Subscript Small Letter E
    U+02092ₒ\_oLatin Subscript Small Letter O
    U+02093ₓ\_xLatin Subscript Small Letter X
    U+02094ₔ\_schwaLatin Subscript Small Letter Schwa
    U+02095ₕ\_hLatin Subscript Small Letter H
    U+02096ₖ\_kLatin Subscript Small Letter K
    U+02097ₗ\_lLatin Subscript Small Letter L
    U+02098ₘ\_mLatin Subscript Small Letter M
    U+02099ₙ\_nLatin Subscript Small Letter N
    U+0209Aₚ\_pLatin Subscript Small Letter P
    U+0209Bₛ\_sLatin Subscript Small Letter S
    U+0209Cₜ\_tLatin Subscript Small Letter T
    U+020A7₧\pesPeseta Sign
    U+020AC€\euroEuro Sign
    U+020D0 ⃐ \leftharpoonaccentCombining Left Harpoon Above / Non-Spacing Left Harpoon Above
    U+020D1 ⃑ \rightharpoonaccentCombining Right Harpoon Above / Non-Spacing Right Harpoon Above
    U+020D2 ⃒ \vertoverlayCombining Long Vertical Line Overlay / Non-Spacing Long Vertical Bar Overlay
    U+020D6 ⃖ \overleftarrowCombining Left Arrow Above / Non-Spacing Left Arrow Above
    U+020D7 ⃗ \vecCombining Right Arrow Above / Non-Spacing Right Arrow Above
    U+020DB ⃛ \dddotCombining Three Dots Above / Non-Spacing Three Dots Above
    U+020DC ⃜ \ddddotCombining Four Dots Above / Non-Spacing Four Dots Above
    U+020DD ⃝ \enclosecircleCombining Enclosing Circle / Enclosing Circle
    U+020DE ⃞ \enclosesquareCombining Enclosing Square / Enclosing Square
    U+020DF ⃟ \enclosediamondCombining Enclosing Diamond / Enclosing Diamond
    U+020E1 ⃡ \overleftrightarrowCombining Left Right Arrow Above / Non-Spacing Left Right Arrow Above
    U+020E4 ⃤ \enclosetriangleCombining Enclosing Upward Pointing Triangle
    U+020E7 ⃧ \annuityCombining Annuity Symbol
    U+020E8 ⃨ \threeunderdotCombining Triple Underdot
    U+020E9 ⃩ \widebridgeaboveCombining Wide Bridge Above
    U+020EC ⃬ \underrightharpoondownCombining Rightwards Harpoon With Barb Downwards
    U+020ED ⃭ \underleftharpoondownCombining Leftwards Harpoon With Barb Downwards
    U+020EE ⃮ \underleftarrowCombining Left Arrow Below
    U+020EF ⃯ \underrightarrowCombining Right Arrow Below
    U+020F0 ⃰ \asteraccentCombining Asterisk Above
    U+02102ℂ\bbCDouble-Struck Capital C / Double-Struck C
    U+02107ℇ\eulermascheroniEuler Constant / Eulers
    U+0210Aℊ\scrgScript Small G
    U+0210Bℋ\scrHScript Capital H / Script H
    U+0210Cℌ\frakHBlack-Letter Capital H / Black-Letter H
    U+0210Dℍ\bbHDouble-Struck Capital H / Double-Struck H
    U+0210Eℎ\ith, \planckPlanck Constant
    U+0210Fℏ\hslashPlanck Constant Over Two Pi / Planck Constant Over 2 Pi
    U+02110ℐ\scrIScript Capital I / Script I
    U+02111ℑ\Im, \frakIBlack-Letter Capital I / Black-Letter I
    U+02112ℒ\scrLScript Capital L / Script L
    U+02113ℓ\ellScript Small L
    U+02115ℕ\bbNDouble-Struck Capital N / Double-Struck N
    U+02116№\numeroNumero Sign / Numero
    U+02118℘\wpScript Capital P / Script P
    U+02119ℙ\bbPDouble-Struck Capital P / Double-Struck P
    U+0211Aℚ\bbQDouble-Struck Capital Q / Double-Struck Q
    U+0211Bℛ\scrRScript Capital R / Script R
    U+0211Cℜ\Re, \frakRBlack-Letter Capital R / Black-Letter R
    U+0211Dℝ\bbRDouble-Struck Capital R / Double-Struck R
    U+0211E℞\xratPrescription Take
    U+02122™\trademark, \:tm:Trade Mark Sign / Trademark
    U+02124ℤ\bbZDouble-Struck Capital Z / Double-Struck Z
    U+02126Ω\ohmOhm Sign / Ohm
    U+02127℧\mhoInverted Ohm Sign / Mho
    U+02128ℨ\frakZBlack-Letter Capital Z / Black-Letter Z
    U+02129℩\turnediotaTurned Greek Small Letter Iota
    U+0212BÅ\AngstromAngstrom Sign / Angstrom Unit
    U+0212Cℬ\scrBScript Capital B / Script B
    U+0212Dℭ\frakCBlack-Letter Capital C / Black-Letter C
    U+0212Fℯ\scre, \eulerScript Small E
    U+02130ℰ\scrEScript Capital E / Script E
    U+02131ℱ\scrFScript Capital F / Script F
    U+02132Ⅎ\FinvTurned Capital F / Turned F
    U+02133ℳ\scrMScript Capital M / Script M
    U+02134ℴ\scroScript Small O
    U+02135ℵ\alephAlef Symbol / First Transfinite Cardinal
    U+02136ℶ\bethBet Symbol / Second Transfinite Cardinal
    U+02137ℷ\gimelGimel Symbol / Third Transfinite Cardinal
    U+02138ℸ\dalethDalet Symbol / Fourth Transfinite Cardinal
    U+02139ℹ\:information_source:Information Source
    U+0213Cℼ\bbpiDouble-Struck Small Pi
    U+0213Dℽ\bbgammaDouble-Struck Small Gamma
    U+0213Eℾ\bbGammaDouble-Struck Capital Gamma
    U+0213Fℿ\bbPiDouble-Struck Capital Pi
    U+02140⅀\bbsumDouble-Struck N-Ary Summation
    U+02141⅁\GameTurned Sans-Serif Capital G
    U+02142⅂\sansLturnedTurned Sans-Serif Capital L
    U+02143⅃\sansLmirroredReversed Sans-Serif Capital L
    U+02144⅄\YupTurned Sans-Serif Capital Y
    U+02145ⅅ\bbiDDouble-Struck Italic Capital D
    U+02146ⅆ\bbidDouble-Struck Italic Small D
    U+02147ⅇ\bbieDouble-Struck Italic Small E
    U+02148ⅈ\bbiiDouble-Struck Italic Small I
    U+02149ⅉ\bbijDouble-Struck Italic Small J
    U+0214A⅊\PropertyLineProperty Line
    U+0214B⅋\upandTurned Ampersand
    U+02150⅐\1/7Vulgar Fraction One Seventh
    U+02151⅑\1/9Vulgar Fraction One Ninth
    U+02152⅒\1/10Vulgar Fraction One Tenth
    U+02153⅓\1/3Vulgar Fraction One Third / Fraction One Third
    U+02154⅔\2/3Vulgar Fraction Two Thirds / Fraction Two Thirds
    U+02155⅕\1/5Vulgar Fraction One Fifth / Fraction One Fifth
    U+02156⅖\2/5Vulgar Fraction Two Fifths / Fraction Two Fifths
    U+02157⅗\3/5Vulgar Fraction Three Fifths / Fraction Three Fifths
    U+02158⅘\4/5Vulgar Fraction Four Fifths / Fraction Four Fifths
    U+02159⅙\1/6Vulgar Fraction One Sixth / Fraction One Sixth
    U+0215A⅚\5/6Vulgar Fraction Five Sixths / Fraction Five Sixths
    U+0215B⅛\1/8Vulgar Fraction One Eighth / Fraction One Eighth
    U+0215C⅜\3/8Vulgar Fraction Three Eighths / Fraction Three Eighths
    U+0215D⅝\5/8Vulgar Fraction Five Eighths / Fraction Five Eighths
    U+0215E⅞\7/8Vulgar Fraction Seven Eighths / Fraction Seven Eighths
    U+0215F⅟\1/Fraction Numerator One
    U+02189↉\0/3Vulgar Fraction Zero Thirds
    U+02190←\leftarrowLeftwards Arrow / Left Arrow
    U+02191↑\uparrowUpwards Arrow / Up Arrow
    U+02192→\to, \rightarrowRightwards Arrow / Right Arrow
    U+02193↓\downarrowDownwards Arrow / Down Arrow
    U+02194↔\leftrightarrow, \:left_right_arrow:Left Right Arrow
    U+02195↕\updownarrow, \:arrow_up_down:Up Down Arrow
    U+02196↖\nwarrow, \:arrow_upper_left:North West Arrow / Upper Left Arrow
    U+02197↗\nearrow, \:arrow_upper_right:North East Arrow / Upper Right Arrow
    U+02198↘\searrow, \:arrow_lower_right:South East Arrow / Lower Right Arrow
    U+02199↙\swarrow, \:arrow_lower_left:South West Arrow / Lower Left Arrow
    U+0219A↚\nleftarrowLeftwards Arrow With Stroke / Left Arrow With Stroke
    U+0219B↛\nrightarrowRightwards Arrow With Stroke / Right Arrow With Stroke
    U+0219C↜\leftwavearrowLeftwards Wave Arrow / Left Wave Arrow
    U+0219D↝\rightwavearrowRightwards Wave Arrow / Right Wave Arrow
    U+0219E↞\twoheadleftarrowLeftwards Two Headed Arrow / Left Two Headed Arrow
    U+0219F↟\twoheaduparrowUpwards Two Headed Arrow / Up Two Headed Arrow
    U+021A0↠\twoheadrightarrowRightwards Two Headed Arrow / Right Two Headed Arrow
    U+021A1↡\twoheaddownarrowDownwards Two Headed Arrow / Down Two Headed Arrow
    U+021A2↢\leftarrowtailLeftwards Arrow With Tail / Left Arrow With Tail
    U+021A3↣\rightarrowtailRightwards Arrow With Tail / Right Arrow With Tail
    U+021A4↤\mapsfromLeftwards Arrow From Bar / Left Arrow From Bar
    U+021A5↥\mapsupUpwards Arrow From Bar / Up Arrow From Bar
    U+021A6↦\mapstoRightwards Arrow From Bar / Right Arrow From Bar
    U+021A7↧\mapsdownDownwards Arrow From Bar / Down Arrow From Bar
    U+021A8↨\updownarrowbarUp Down Arrow With Base
    U+021A9↩\hookleftarrow, \:leftwards_arrow_with_hook:Leftwards Arrow With Hook / Left Arrow With Hook
    U+021AA↪\hookrightarrow, \:arrow_right_hook:Rightwards Arrow With Hook / Right Arrow With Hook
    U+021AB↫\looparrowleftLeftwards Arrow With Loop / Left Arrow With Loop
    U+021AC↬\looparrowrightRightwards Arrow With Loop / Right Arrow With Loop
    U+021AD↭\leftrightsquigarrowLeft Right Wave Arrow
    U+021AE↮\nleftrightarrowLeft Right Arrow With Stroke
    U+021AF↯\downzigzagarrowDownwards Zigzag Arrow / Down Zigzag Arrow
    U+021B0↰\LshUpwards Arrow With Tip Leftwards / Up Arrow With Tip Left
    U+021B1↱\RshUpwards Arrow With Tip Rightwards / Up Arrow With Tip Right
    U+021B2↲\LdshDownwards Arrow With Tip Leftwards / Down Arrow With Tip Left
    U+021B3↳\RdshDownwards Arrow With Tip Rightwards / Down Arrow With Tip Right
    U+021B4↴\linefeedRightwards Arrow With Corner Downwards / Right Arrow With Corner Down
    U+021B5↵\carriagereturnDownwards Arrow With Corner Leftwards / Down Arrow With Corner Left
    U+021B6↶\curvearrowleftAnticlockwise Top Semicircle Arrow
    U+021B7↷\curvearrowrightClockwise Top Semicircle Arrow
    U+021B8↸\barovernorthwestarrowNorth West Arrow To Long Bar / Upper Left Arrow To Long Bar
    U+021B9↹\barleftarrowrightarrowbarLeftwards Arrow To Bar Over Rightwards Arrow To Bar / Left Arrow To Bar Over Right Arrow To Bar
    U+021BA↺\circlearrowleftAnticlockwise Open Circle Arrow
    U+021BB↻\circlearrowrightClockwise Open Circle Arrow
    U+021BC↼\leftharpoonupLeftwards Harpoon With Barb Upwards / Left Harpoon With Barb Up
    U+021BD↽\leftharpoondownLeftwards Harpoon With Barb Downwards / Left Harpoon With Barb Down
    U+021BE↾\upharpoonrightUpwards Harpoon With Barb Rightwards / Up Harpoon With Barb Right
    U+021BF↿\upharpoonleftUpwards Harpoon With Barb Leftwards / Up Harpoon With Barb Left
    U+021C0⇀\rightharpoonupRightwards Harpoon With Barb Upwards / Right Harpoon With Barb Up
    U+021C1⇁\rightharpoondownRightwards Harpoon With Barb Downwards / Right Harpoon With Barb Down
    U+021C2⇂\downharpoonrightDownwards Harpoon With Barb Rightwards / Down Harpoon With Barb Right
    U+021C3⇃\downharpoonleftDownwards Harpoon With Barb Leftwards / Down Harpoon With Barb Left
    U+021C4⇄\rightleftarrowsRightwards Arrow Over Leftwards Arrow / Right Arrow Over Left Arrow
    U+021C5⇅\dblarrowupdownUpwards Arrow Leftwards Of Downwards Arrow / Up Arrow Left Of Down Arrow
    U+021C6⇆\leftrightarrowsLeftwards Arrow Over Rightwards Arrow / Left Arrow Over Right Arrow
    U+021C7⇇\leftleftarrowsLeftwards Paired Arrows / Left Paired Arrows
    U+021C8⇈\upuparrowsUpwards Paired Arrows / Up Paired Arrows
    U+021C9⇉\rightrightarrowsRightwards Paired Arrows / Right Paired Arrows
    U+021CA⇊\downdownarrowsDownwards Paired Arrows / Down Paired Arrows
    U+021CB⇋\leftrightharpoonsLeftwards Harpoon Over Rightwards Harpoon / Left Harpoon Over Right Harpoon
    U+021CC⇌\rightleftharpoonsRightwards Harpoon Over Leftwards Harpoon / Right Harpoon Over Left Harpoon
    U+021CD⇍\nLeftarrowLeftwards Double Arrow With Stroke / Left Double Arrow With Stroke
    U+021CE⇎\nLeftrightarrowLeft Right Double Arrow With Stroke
    U+021CF⇏\nRightarrowRightwards Double Arrow With Stroke / Right Double Arrow With Stroke
    U+021D0⇐\LeftarrowLeftwards Double Arrow / Left Double Arrow
    U+021D1⇑\UparrowUpwards Double Arrow / Up Double Arrow
    U+021D2⇒\RightarrowRightwards Double Arrow / Right Double Arrow
    U+021D3⇓\DownarrowDownwards Double Arrow / Down Double Arrow
    U+021D4⇔\LeftrightarrowLeft Right Double Arrow
    U+021D5⇕\UpdownarrowUp Down Double Arrow
    U+021D6⇖\NwarrowNorth West Double Arrow / Upper Left Double Arrow
    U+021D7⇗\NearrowNorth East Double Arrow / Upper Right Double Arrow
    U+021D8⇘\SearrowSouth East Double Arrow / Lower Right Double Arrow
    U+021D9⇙\SwarrowSouth West Double Arrow / Lower Left Double Arrow
    U+021DA⇚\LleftarrowLeftwards Triple Arrow / Left Triple Arrow
    U+021DB⇛\RrightarrowRightwards Triple Arrow / Right Triple Arrow
    U+021DC⇜\leftsquigarrowLeftwards Squiggle Arrow / Left Squiggle Arrow
    U+021DD⇝\rightsquigarrowRightwards Squiggle Arrow / Right Squiggle Arrow
    U+021DE⇞\nHuparrowUpwards Arrow With Double Stroke / Up Arrow With Double Stroke
    U+021DF⇟\nHdownarrowDownwards Arrow With Double Stroke / Down Arrow With Double Stroke
    U+021E0⇠\leftdasharrowLeftwards Dashed Arrow / Left Dashed Arrow
    U+021E1⇡\updasharrowUpwards Dashed Arrow / Up Dashed Arrow
    U+021E2⇢\rightdasharrowRightwards Dashed Arrow / Right Dashed Arrow
    U+021E3⇣\downdasharrowDownwards Dashed Arrow / Down Dashed Arrow
    U+021E4⇤\barleftarrowLeftwards Arrow To Bar / Left Arrow To Bar
    U+021E5⇥\rightarrowbarRightwards Arrow To Bar / Right Arrow To Bar
    U+021E6⇦\leftwhitearrowLeftwards White Arrow / White Left Arrow
    U+021E7⇧\upwhitearrowUpwards White Arrow / White Up Arrow
    U+021E8⇨\rightwhitearrowRightwards White Arrow / White Right Arrow
    U+021E9⇩\downwhitearrowDownwards White Arrow / White Down Arrow
    U+021EA⇪\whitearrowupfrombarUpwards White Arrow From Bar / White Up Arrow From Bar
    U+021F4⇴\circleonrightarrowRight Arrow With Small Circle
    U+021F5⇵\DownArrowUpArrowDownwards Arrow Leftwards Of Upwards Arrow
    U+021F6⇶\rightthreearrowsThree Rightwards Arrows
    U+021F7⇷\nvleftarrowLeftwards Arrow With Vertical Stroke
    U+021F8⇸\nvrightarrowRightwards Arrow With Vertical Stroke
    U+021F9⇹\nvleftrightarrowLeft Right Arrow With Vertical Stroke
    U+021FA⇺\nVleftarrowLeftwards Arrow With Double Vertical Stroke
    U+021FB⇻\nVrightarrowRightwards Arrow With Double Vertical Stroke
    U+021FC⇼\nVleftrightarrowLeft Right Arrow With Double Vertical Stroke
    U+021FD⇽\leftarrowtriangleLeftwards Open-Headed Arrow
    U+021FE⇾\rightarrowtriangleRightwards Open-Headed Arrow
    U+021FF⇿\leftrightarrowtriangleLeft Right Open-Headed Arrow
    U+02200∀\forallFor All
    U+02201∁\complementComplement
    U+02202∂\partialPartial Differential
    U+02203∃\existsThere Exists
    U+02204∄\nexistsThere Does Not Exist
    U+02205∅\varnothing, \emptysetEmpty Set
    U+02206∆\incrementIncrement
    U+02207∇\del, \nablaNabla
    U+02208∈\inElement Of
    U+02209∉\notinNot An Element Of
    U+0220A∊\smallinSmall Element Of
    U+0220B∋\niContains As Member
    U+0220C∌\nniDoes Not Contain As Member
    U+0220D∍\smallniSmall Contains As Member
    U+0220E∎\QEDEnd Of Proof
    U+0220F∏\prodN-Ary Product
    U+02210∐\coprodN-Ary Coproduct
    U+02211∑\sumN-Ary Summation
    U+02212−\minusMinus Sign
    U+02213∓\mpMinus-Or-Plus Sign
    U+02214∔\dotplusDot Plus
    U+02216∖\setminusSet Minus
    U+02217∗\astAsterisk Operator
    U+02218∘\circRing Operator
    U+02219∙\vysmblkcircleBullet Operator
    U+0221A√\surd, \sqrtSquare Root
    U+0221B∛\cbrtCube Root
    U+0221C∜\fourthrootFourth Root
    U+0221D∝\proptoProportional To
    U+0221E∞\inftyInfinity
    U+0221F∟\rightangleRight Angle
    U+02220∠\angleAngle
    U+02221∡\measuredangleMeasured Angle
    U+02222∢\sphericalangleSpherical Angle
    U+02223∣\midDivides
    U+02224∤\nmidDoes Not Divide
    U+02225∥\parallelParallel To
    U+02226∦\nparallelNot Parallel To
    U+02227∧\wedgeLogical And
    U+02228∨\veeLogical Or
    U+02229∩\capIntersection
    U+0222A∪\cupUnion
    U+0222B∫\intIntegral
    U+0222C∬\iintDouble Integral
    U+0222D∭\iiintTriple Integral
    U+0222E∮\ointContour Integral
    U+0222F∯\oiintSurface Integral
    U+02230∰\oiiintVolume Integral
    U+02231∱\clwintegralClockwise Integral
    U+02232∲\varointclockwiseClockwise Contour Integral
    U+02233∳\ointctrclockwiseAnticlockwise Contour Integral
    U+02234∴\thereforeTherefore
    U+02235∵\becauseBecause
    U+02237∷\ColonProportion
    U+02238∸\dotminusDot Minus
    U+0223A∺\dotsminusdotsGeometric Proportion
    U+0223B∻\kernelcontractionHomothetic
    U+0223C∼\simTilde Operator
    U+0223D∽\backsimReversed Tilde
    U+0223E∾\lazysinvInverted Lazy S
    U+0223F∿\sinewaveSine Wave
    U+02240≀\wrWreath Product
    U+02241≁\nsimNot Tilde
    U+02242≂\eqsimMinus Tilde
    U+02242 + U+00338≂̸\neqsimMinus Tilde + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02243≃\simeqAsymptotically Equal To
    U+02244≄\nsimeNot Asymptotically Equal To
    U+02245≅\congApproximately Equal To
    U+02246≆\approxnotequalApproximately But Not Actually Equal To
    U+02247≇\ncongNeither Approximately Nor Actually Equal To
    U+02248≈\approxAlmost Equal To
    U+02249≉\napproxNot Almost Equal To
    U+0224A≊\approxeqAlmost Equal Or Equal To
    U+0224B≋\tildetrplTriple Tilde
    U+0224C≌\allequalAll Equal To
    U+0224D≍\asympEquivalent To
    U+0224E≎\BumpeqGeometrically Equivalent To
    U+0224E + U+00338≎̸\nBumpeqGeometrically Equivalent To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0224F≏\bumpeqDifference Between
    U+0224F + U+00338≏̸\nbumpeqDifference Between + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02250≐\doteqApproaches The Limit
    U+02251≑\DoteqGeometrically Equal To
    U+02252≒\fallingdotseqApproximately Equal To Or The Image Of
    U+02253≓\risingdotseqImage Of Or Approximately Equal To
    U+02254≔\coloneqColon Equals / Colon Equal
    U+02255≕\eqcolonEquals Colon / Equal Colon
    U+02256≖\eqcircRing In Equal To
    U+02257≗\circeqRing Equal To
    U+02258≘\arceqCorresponds To
    U+02259≙\wedgeqEstimates
    U+0225A≚\veeeqEquiangular To
    U+0225B≛\starequalStar Equals
    U+0225C≜\triangleqDelta Equal To
    U+0225D≝\eqdefEqual To By Definition
    U+0225E≞\measeqMeasured By
    U+0225F≟\questeqQuestioned Equal To
    U+02260≠\ne, \neqNot Equal To
    U+02261≡\equivIdentical To
    U+02262≢\nequivNot Identical To
    U+02263≣\EquivStrictly Equivalent To
    U+02264≤\le, \leqLess-Than Or Equal To / Less Than Or Equal To
    U+02265≥\ge, \geqGreater-Than Or Equal To / Greater Than Or Equal To
    U+02266≦\leqqLess-Than Over Equal To / Less Than Over Equal To
    U+02267≧\geqqGreater-Than Over Equal To / Greater Than Over Equal To
    U+02268≨\lneqqLess-Than But Not Equal To / Less Than But Not Equal To
    U+02268 + U+0FE00≨︀\lvertneqqLess-Than But Not Equal To / Less Than But Not Equal To + Variation Selector-1
    U+02269≩\gneqqGreater-Than But Not Equal To / Greater Than But Not Equal To
    U+02269 + U+0FE00≩︀\gvertneqqGreater-Than But Not Equal To / Greater Than But Not Equal To + Variation Selector-1
    U+0226A≪\llMuch Less-Than / Much Less Than
    U+0226A + U+00338≪̸\NotLessLessMuch Less-Than / Much Less Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0226B≫\ggMuch Greater-Than / Much Greater Than
    U+0226B + U+00338≫̸\NotGreaterGreaterMuch Greater-Than / Much Greater Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0226C≬\betweenBetween
    U+0226D≭\nasympNot Equivalent To
    U+0226E≮\nlessNot Less-Than / Not Less Than
    U+0226F≯\ngtrNot Greater-Than / Not Greater Than
    U+02270≰\nleqNeither Less-Than Nor Equal To / Neither Less Than Nor Equal To
    U+02271≱\ngeqNeither Greater-Than Nor Equal To / Neither Greater Than Nor Equal To
    U+02272≲\lesssimLess-Than Or Equivalent To / Less Than Or Equivalent To
    U+02273≳\gtrsimGreater-Than Or Equivalent To / Greater Than Or Equivalent To
    U+02274≴\nlesssimNeither Less-Than Nor Equivalent To / Neither Less Than Nor Equivalent To
    U+02275≵\ngtrsimNeither Greater-Than Nor Equivalent To / Neither Greater Than Nor Equivalent To
    U+02276≶\lessgtrLess-Than Or Greater-Than / Less Than Or Greater Than
    U+02277≷\gtrlessGreater-Than Or Less-Than / Greater Than Or Less Than
    U+02278≸\notlessgreaterNeither Less-Than Nor Greater-Than / Neither Less Than Nor Greater Than
    U+02279≹\notgreaterlessNeither Greater-Than Nor Less-Than / Neither Greater Than Nor Less Than
    U+0227A≺\precPrecedes
    U+0227B≻\succSucceeds
    U+0227C≼\preccurlyeqPrecedes Or Equal To
    U+0227D≽\succcurlyeqSucceeds Or Equal To
    U+0227E≾\precsimPrecedes Or Equivalent To
    U+0227E + U+00338≾̸\nprecsimPrecedes Or Equivalent To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+0227F≿\succsimSucceeds Or Equivalent To
    U+0227F + U+00338≿̸\nsuccsimSucceeds Or Equivalent To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02280⊀\nprecDoes Not Precede
    U+02281⊁\nsuccDoes Not Succeed
    U+02282⊂\subsetSubset Of
    U+02283⊃\supsetSuperset Of
    U+02284⊄\nsubsetNot A Subset Of
    U+02285⊅\nsupsetNot A Superset Of
    U+02286⊆\subseteqSubset Of Or Equal To
    U+02287⊇\supseteqSuperset Of Or Equal To
    U+02288⊈\nsubseteqNeither A Subset Of Nor Equal To
    U+02289⊉\nsupseteqNeither A Superset Of Nor Equal To
    U+0228A⊊\subsetneqSubset Of With Not Equal To / Subset Of Or Not Equal To
    U+0228A + U+0FE00⊊︀\varsubsetneqqSubset Of With Not Equal To / Subset Of Or Not Equal To + Variation Selector-1
    U+0228B⊋\supsetneqSuperset Of With Not Equal To / Superset Of Or Not Equal To
    U+0228B + U+0FE00⊋︀\varsupsetneqSuperset Of With Not Equal To / Superset Of Or Not Equal To + Variation Selector-1
    U+0228D⊍\cupdotMultiset Multiplication
    U+0228E⊎\uplusMultiset Union
    U+0228F⊏\sqsubsetSquare Image Of
    U+0228F + U+00338⊏̸\NotSquareSubsetSquare Image Of + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02290⊐\sqsupsetSquare Original Of
    U+02290 + U+00338⊐̸\NotSquareSupersetSquare Original Of + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02291⊑\sqsubseteqSquare Image Of Or Equal To
    U+02292⊒\sqsupseteqSquare Original Of Or Equal To
    U+02293⊓\sqcapSquare Cap
    U+02294⊔\sqcupSquare Cup
    U+02295⊕\oplusCircled Plus
    U+02296⊖\ominusCircled Minus
    U+02297⊗\otimesCircled Times
    U+02298⊘\oslashCircled Division Slash
    U+02299⊙\odotCircled Dot Operator
    U+0229A⊚\circledcircCircled Ring Operator
    U+0229B⊛\circledastCircled Asterisk Operator
    U+0229C⊜\circledequalCircled Equals
    U+0229D⊝\circleddashCircled Dash
    U+0229E⊞\boxplusSquared Plus
    U+0229F⊟\boxminusSquared Minus
    U+022A0⊠\boxtimesSquared Times
    U+022A1⊡\boxdotSquared Dot Operator
    U+022A2⊢\vdashRight Tack
    U+022A3⊣\dashvLeft Tack
    U+022A4⊤\topDown Tack
    U+022A5⊥\botUp Tack
    U+022A7⊧\modelsModels
    U+022A8⊨\vDashTrue
    U+022A9⊩\VdashForces
    U+022AA⊪\VvdashTriple Vertical Bar Right Turnstile
    U+022AB⊫\VDashDouble Vertical Bar Double Right Turnstile
    U+022AC⊬\nvdashDoes Not Prove
    U+022AD⊭\nvDashNot True
    U+022AE⊮\nVdashDoes Not Force
    U+022AF⊯\nVDashNegated Double Vertical Bar Double Right Turnstile
    U+022B0⊰\prurelPrecedes Under Relation
    U+022B1⊱\scurelSucceeds Under Relation
    U+022B2⊲\vartriangleleftNormal Subgroup Of
    U+022B3⊳\vartrianglerightContains As Normal Subgroup
    U+022B4⊴\trianglelefteqNormal Subgroup Of Or Equal To
    U+022B5⊵\trianglerighteqContains As Normal Subgroup Or Equal To
    U+022B6⊶\originalOriginal Of
    U+022B7⊷\imageImage Of
    U+022B8⊸\multimapMultimap
    U+022B9⊹\hermitconjmatrixHermitian Conjugate Matrix
    U+022BA⊺\intercalIntercalate
    U+022BB⊻\veebar, \xorXor
    U+022BC⊼\barwedge, \nandNand
    U+022BD⊽\barvee, \norNor
    U+022BE⊾\rightanglearcRight Angle With Arc
    U+022BF⊿\varlrtriangleRight Triangle
    U+022C0⋀\bigwedgeN-Ary Logical And
    U+022C1⋁\bigveeN-Ary Logical Or
    U+022C2⋂\bigcapN-Ary Intersection
    U+022C3⋃\bigcupN-Ary Union
    U+022C4⋄\diamondDiamond Operator
    U+022C5⋅\cdotDot Operator
    U+022C6⋆\starStar Operator
    U+022C7⋇\divideontimesDivision Times
    U+022C8⋈\bowtieBowtie
    U+022C9⋉\ltimesLeft Normal Factor Semidirect Product
    U+022CA⋊\rtimesRight Normal Factor Semidirect Product
    U+022CB⋋\leftthreetimesLeft Semidirect Product
    U+022CC⋌\rightthreetimesRight Semidirect Product
    U+022CD⋍\backsimeqReversed Tilde Equals
    U+022CE⋎\curlyveeCurly Logical Or
    U+022CF⋏\curlywedgeCurly Logical And
    U+022D0⋐\SubsetDouble Subset
    U+022D1⋑\SupsetDouble Superset
    U+022D2⋒\CapDouble Intersection
    U+022D3⋓\CupDouble Union
    U+022D4⋔\pitchforkPitchfork
    U+022D5⋕\equalparallelEqual And Parallel To
    U+022D6⋖\lessdotLess-Than With Dot / Less Than With Dot
    U+022D7⋗\gtrdotGreater-Than With Dot / Greater Than With Dot
    U+022D8⋘\verymuchlessVery Much Less-Than / Very Much Less Than
    U+022D9⋙\gggVery Much Greater-Than / Very Much Greater Than
    U+022DA⋚\lesseqgtrLess-Than Equal To Or Greater-Than / Less Than Equal To Or Greater Than
    U+022DB⋛\gtreqlessGreater-Than Equal To Or Less-Than / Greater Than Equal To Or Less Than
    U+022DC⋜\eqlessEqual To Or Less-Than / Equal To Or Less Than
    U+022DD⋝\eqgtrEqual To Or Greater-Than / Equal To Or Greater Than
    U+022DE⋞\curlyeqprecEqual To Or Precedes
    U+022DF⋟\curlyeqsuccEqual To Or Succeeds
    U+022E0⋠\npreccurlyeqDoes Not Precede Or Equal
    U+022E1⋡\nsucccurlyeqDoes Not Succeed Or Equal
    U+022E2⋢\nsqsubseteqNot Square Image Of Or Equal To
    U+022E3⋣\nsqsupseteqNot Square Original Of Or Equal To
    U+022E4⋤\sqsubsetneqSquare Image Of Or Not Equal To
    U+022E5⋥\sqsupsetneqSquare Original Of Or Not Equal To
    U+022E6⋦\lnsimLess-Than But Not Equivalent To / Less Than But Not Equivalent To
    U+022E7⋧\gnsimGreater-Than But Not Equivalent To / Greater Than But Not Equivalent To
    U+022E8⋨\precnsimPrecedes But Not Equivalent To
    U+022E9⋩\succnsimSucceeds But Not Equivalent To
    U+022EA⋪\ntriangleleftNot Normal Subgroup Of
    U+022EB⋫\ntrianglerightDoes Not Contain As Normal Subgroup
    U+022EC⋬\ntrianglelefteqNot Normal Subgroup Of Or Equal To
    U+022ED⋭\ntrianglerighteqDoes Not Contain As Normal Subgroup Or Equal
    U+022EE⋮\vdotsVertical Ellipsis
    U+022EF⋯\cdotsMidline Horizontal Ellipsis
    U+022F0⋰\adotsUp Right Diagonal Ellipsis
    U+022F1⋱\ddotsDown Right Diagonal Ellipsis
    U+022F2⋲\disinElement Of With Long Horizontal Stroke
    U+022F3⋳\varisinsElement Of With Vertical Bar At End Of Horizontal Stroke
    U+022F4⋴\isinsSmall Element Of With Vertical Bar At End Of Horizontal Stroke
    U+022F5⋵\isindotElement Of With Dot Above
    U+022F6⋶\varisinobarElement Of With Overbar
    U+022F7⋷\isinobarSmall Element Of With Overbar
    U+022F8⋸\isinvbElement Of With Underbar
    U+022F9⋹\isinEElement Of With Two Horizontal Strokes
    U+022FA⋺\nisdContains With Long Horizontal Stroke
    U+022FB⋻\varnisContains With Vertical Bar At End Of Horizontal Stroke
    U+022FC⋼\nisSmall Contains With Vertical Bar At End Of Horizontal Stroke
    U+022FD⋽\varniobarContains With Overbar
    U+022FE⋾\niobarSmall Contains With Overbar
    U+022FF⋿\bagmemberZ Notation Bag Membership
    U+02300⌀\diameterDiameter Sign
    U+02302⌂\houseHouse
    U+02305⌅\varbarwedgeProjective
    U+02306⌆\vardoublebarwedgePerspective
    U+02308⌈\lceilLeft Ceiling
    U+02309⌉\rceilRight Ceiling
    U+0230A⌊\lfloorLeft Floor
    U+0230B⌋\rfloorRight Floor
    U+02310⌐\invnotReversed Not Sign
    U+02311⌑\sqlozengeSquare Lozenge
    U+02312⌒\proflineArc
    U+02313⌓\profsurfSegment
    U+02315⌕\recorderTelephone Recorder
    U+02317⌗\viewdataViewdata Square
    U+02319⌙\turnednotTurned Not Sign
    U+0231A⌚\:watch:Watch
    U+0231B⌛\:hourglass:Hourglass
    U+0231C⌜\ulcornerTop Left Corner
    U+0231D⌝\urcornerTop Right Corner
    U+0231E⌞\llcornerBottom Left Corner
    U+0231F⌟\lrcornerBottom Right Corner
    U+02322⌢\frownFrown
    U+02323⌣\smileSmile
    U+0232C⌬\varhexagonlrbondsBenzene Ring
    U+02332⌲\conictaperConical Taper
    U+02336⌶\topbotApl Functional Symbol I-Beam
    U+0233D⌽\obarApl Functional Symbol Circle Stile
    U+0233F⌿\notslashApl Functional Symbol Slash Bar
    U+02340⍀\notbackslashApl Functional Symbol Backslash Bar
    U+02353⍓\boxupcaretApl Functional Symbol Quad Up Caret
    U+02370⍰\boxquestionApl Functional Symbol Quad Question
    U+02394⎔\hexagonSoftware-Function Symbol
    U+023A3⎣\dlcornLeft Square Bracket Lower Corner
    U+023B0⎰\lmoustacheUpper Left Or Lower Right Curly Bracket Section
    U+023B1⎱\rmoustacheUpper Right Or Lower Left Curly Bracket Section
    U+023B4⎴\overbracketTop Square Bracket
    U+023B5⎵\underbracketBottom Square Bracket
    U+023B6⎶\bbrktbrkBottom Square Bracket Over Top Square Bracket
    U+023B7⎷\sqrtbottomRadical Symbol Bottom
    U+023B8⎸\lvboxlineLeft Vertical Box Line
    U+023B9⎹\rvboxlineRight Vertical Box Line
    U+023CE⏎\varcarriagereturnReturn Symbol
    U+023DE⏞\overbraceTop Curly Bracket
    U+023DF⏟\underbraceBottom Curly Bracket
    U+023E2⏢\trapeziumWhite Trapezium
    U+023E3⏣\benzenrBenzene Ring With Circle
    U+023E4⏤\strnsStraightness
    U+023E5⏥\fltnsFlatness
    U+023E6⏦\accurrentAc Current
    U+023E7⏧\elintersElectrical Intersection
    U+023E9⏩\:fast_forward:Black Right-Pointing Double Triangle
    U+023EA⏪\:rewind:Black Left-Pointing Double Triangle
    U+023EB⏫\:arrow_double_up:Black Up-Pointing Double Triangle
    U+023EC⏬\:arrow_double_down:Black Down-Pointing Double Triangle
    U+023F0⏰\:alarm_clock:Alarm Clock
    U+023F3⏳\:hourglass_flowing_sand:Hourglass With Flowing Sand
    U+02422␢\blanksymbolBlank Symbol / Blank
    U+02423␣\visiblespaceOpen Box
    U+024C2Ⓜ\:m:Circled Latin Capital Letter M
    U+024C8Ⓢ\circledSCircled Latin Capital Letter S
    U+02506┆\dshfncBox Drawings Light Triple Dash Vertical / Forms Light Triple Dash Vertical
    U+02519┙\sqfnwBox Drawings Up Light And Left Heavy / Forms Up Light And Left Heavy
    U+02571╱\diagupBox Drawings Light Diagonal Upper Right To Lower Left / Forms Light Diagonal Upper Right To Lower Left
    U+02572╲\diagdownBox Drawings Light Diagonal Upper Left To Lower Right / Forms Light Diagonal Upper Left To Lower Right
    U+02580▀\blockuphalfUpper Half Block
    U+02584▄\blocklowhalfLower Half Block
    U+02588█\blockfullFull Block
    U+0258C▌\blocklefthalfLeft Half Block
    U+02590▐\blockrighthalfRight Half Block
    U+02591░\blockqtrshadedLight Shade
    U+02592▒\blockhalfshadedMedium Shade
    U+02593▓\blockthreeqtrshadedDark Shade
    U+025A0■\blacksquareBlack Square
    U+025A1□\squareWhite Square
    U+025A2▢\squovalWhite Square With Rounded Corners
    U+025A3▣\blackinwhitesquareWhite Square Containing Black Small Square
    U+025A4▤\squarehfillSquare With Horizontal Fill
    U+025A5▥\squarevfillSquare With Vertical Fill
    U+025A6▦\squarehvfillSquare With Orthogonal Crosshatch Fill
    U+025A7▧\squarenwsefillSquare With Upper Left To Lower Right Fill
    U+025A8▨\squareneswfillSquare With Upper Right To Lower Left Fill
    U+025A9▩\squarecrossfillSquare With Diagonal Crosshatch Fill
    U+025AA▪\smblksquare, \:black_small_square:Black Small Square
    U+025AB▫\smwhtsquare, \:white_small_square:White Small Square
    U+025AC▬\hrectangleblackBlack Rectangle
    U+025AD▭\hrectangleWhite Rectangle
    U+025AE▮\vrectangleblackBlack Vertical Rectangle
    U+025AF▯\vrectoWhite Vertical Rectangle
    U+025B0▰\parallelogramblackBlack Parallelogram
    U+025B1▱\parallelogramWhite Parallelogram
    U+025B2▲\bigblacktriangleupBlack Up-Pointing Triangle / Black Up Pointing Triangle
    U+025B3△\bigtriangleupWhite Up-Pointing Triangle / White Up Pointing Triangle
    U+025B4▴\blacktriangleBlack Up-Pointing Small Triangle / Black Up Pointing Small Triangle
    U+025B5▵\vartriangleWhite Up-Pointing Small Triangle / White Up Pointing Small Triangle
    U+025B6▶\blacktriangleright, \:arrow_forward:Black Right-Pointing Triangle / Black Right Pointing Triangle
    U+025B7▷\trianglerightWhite Right-Pointing Triangle / White Right Pointing Triangle
    U+025B8▸\smallblacktrianglerightBlack Right-Pointing Small Triangle / Black Right Pointing Small Triangle
    U+025B9▹\smalltrianglerightWhite Right-Pointing Small Triangle / White Right Pointing Small Triangle
    U+025BA►\blackpointerrightBlack Right-Pointing Pointer / Black Right Pointing Pointer
    U+025BB▻\whitepointerrightWhite Right-Pointing Pointer / White Right Pointing Pointer
    U+025BC▼\bigblacktriangledownBlack Down-Pointing Triangle / Black Down Pointing Triangle
    U+025BD▽\bigtriangledownWhite Down-Pointing Triangle / White Down Pointing Triangle
    U+025BE▾\blacktriangledownBlack Down-Pointing Small Triangle / Black Down Pointing Small Triangle
    U+025BF▿\triangledownWhite Down-Pointing Small Triangle / White Down Pointing Small Triangle
    U+025C0◀\blacktriangleleft, \:arrow_backward:Black Left-Pointing Triangle / Black Left Pointing Triangle
    U+025C1◁\triangleleftWhite Left-Pointing Triangle / White Left Pointing Triangle
    U+025C2◂\smallblacktriangleleftBlack Left-Pointing Small Triangle / Black Left Pointing Small Triangle
    U+025C3◃\smalltriangleleftWhite Left-Pointing Small Triangle / White Left Pointing Small Triangle
    U+025C4◄\blackpointerleftBlack Left-Pointing Pointer / Black Left Pointing Pointer
    U+025C5◅\whitepointerleftWhite Left-Pointing Pointer / White Left Pointing Pointer
    U+025C6◆\mdlgblkdiamondBlack Diamond
    U+025C7◇\mdlgwhtdiamondWhite Diamond
    U+025C8◈\blackinwhitediamondWhite Diamond Containing Black Small Diamond
    U+025C9◉\fisheyeFisheye
    U+025CA◊\lozengeLozenge
    U+025CB○\bigcircWhite Circle
    U+025CC◌\dottedcircleDotted Circle
    U+025CD◍\circlevertfillCircle With Vertical Fill
    U+025CE◎\bullseyeBullseye
    U+025CF●\mdlgblkcircleBlack Circle
    U+025D0◐\cirflCircle With Left Half Black
    U+025D1◑\cirfrCircle With Right Half Black
    U+025D2◒\cirfbCircle With Lower Half Black
    U+025D3◓\circletophalfblackCircle With Upper Half Black
    U+025D4◔\circleurquadblackCircle With Upper Right Quadrant Black
    U+025D5◕\blackcircleulquadwhiteCircle With All But Upper Left Quadrant Black
    U+025D6◖\blacklefthalfcircleLeft Half Black Circle
    U+025D7◗\blackrighthalfcircleRight Half Black Circle
    U+025D8◘\rvbullInverse Bullet
    U+025D9◙\inversewhitecircleInverse White Circle
    U+025DA◚\invwhiteupperhalfcircleUpper Half Inverse White Circle
    U+025DB◛\invwhitelowerhalfcircleLower Half Inverse White Circle
    U+025DC◜\ularcUpper Left Quadrant Circular Arc
    U+025DD◝\urarcUpper Right Quadrant Circular Arc
    U+025DE◞\lrarcLower Right Quadrant Circular Arc
    U+025DF◟\llarcLower Left Quadrant Circular Arc
    U+025E0◠\topsemicircleUpper Half Circle
    U+025E1◡\botsemicircleLower Half Circle
    U+025E2◢\lrblacktriangleBlack Lower Right Triangle
    U+025E3◣\llblacktriangleBlack Lower Left Triangle
    U+025E4◤\ulblacktriangleBlack Upper Left Triangle
    U+025E5◥\urblacktriangleBlack Upper Right Triangle
    U+025E6◦\smwhtcircleWhite Bullet
    U+025E7◧\sqflSquare With Left Half Black
    U+025E8◨\sqfrSquare With Right Half Black
    U+025E9◩\squareulblackSquare With Upper Left Diagonal Half Black
    U+025EA◪\sqfseSquare With Lower Right Diagonal Half Black
    U+025EB◫\boxbarWhite Square With Vertical Bisecting Line
    U+025EC◬\trianglecdotWhite Up-Pointing Triangle With Dot / White Up Pointing Triangle With Dot
    U+025ED◭\triangleleftblackUp-Pointing Triangle With Left Half Black / Up Pointing Triangle With Left Half Black
    U+025EE◮\trianglerightblackUp-Pointing Triangle With Right Half Black / Up Pointing Triangle With Right Half Black
    U+025EF◯\lgwhtcircleLarge Circle
    U+025F0◰\squareulquadWhite Square With Upper Left Quadrant
    U+025F1◱\squarellquadWhite Square With Lower Left Quadrant
    U+025F2◲\squarelrquadWhite Square With Lower Right Quadrant
    U+025F3◳\squareurquadWhite Square With Upper Right Quadrant
    U+025F4◴\circleulquadWhite Circle With Upper Left Quadrant
    U+025F5◵\circlellquadWhite Circle With Lower Left Quadrant
    U+025F6◶\circlelrquadWhite Circle With Lower Right Quadrant
    U+025F7◷\circleurquadWhite Circle With Upper Right Quadrant
    U+025F8◸\ultriangleUpper Left Triangle
    U+025F9◹\urtriangleUpper Right Triangle
    U+025FA◺\lltriangleLower Left Triangle
    U+025FB◻\mdwhtsquare, \:white_medium_square:White Medium Square
    U+025FC◼\mdblksquare, \:black_medium_square:Black Medium Square
    U+025FD◽\mdsmwhtsquare, \:white_medium_small_square:White Medium Small Square
    U+025FE◾\mdsmblksquare, \:black_medium_small_square:Black Medium Small Square
    U+025FF◿\lrtriangleLower Right Triangle
    U+02600☀\:sunny:Black Sun With Rays
    U+02601☁\:cloud:Cloud
    U+02605★\bigstarBlack Star
    U+02606☆\bigwhitestarWhite Star
    U+02609☉\astrosunSun
    U+0260E☎\:phone:Black Telephone
    U+02611☑\:ballot_box_with_check:Ballot Box With Check
    U+02614☔\:umbrella_with_rain_drops:, \:umbrella:Umbrella With Rain Drops
    U+02615☕\:coffee:Hot Beverage
    U+0261D☝\:point_up:White Up Pointing Index
    U+02621☡\dangerCaution Sign
    U+0263A☺\:relaxed:White Smiling Face
    U+0263B☻\blacksmileyBlack Smiling Face
    U+0263C☼\sunWhite Sun With Rays
    U+0263D☽\rightmoonFirst Quarter Moon
    U+0263E☾\leftmoonLast Quarter Moon
    U+0263F☿\mercuryMercury
    U+02640♀\venus, \femaleFemale Sign
    U+02642♂\male, \marsMale Sign
    U+02643♃\jupiterJupiter
    U+02644♄\saturnSaturn
    U+02645♅\uranusUranus
    U+02646♆\neptuneNeptune
    U+02647♇\plutoPluto
    U+02648♈\aries, \:aries:Aries
    U+02649♉\taurus, \:taurus:Taurus
    U+0264A♊\gemini, \:gemini:Gemini
    U+0264B♋\cancer, \:cancer:Cancer
    U+0264C♌\leo, \:leo:Leo
    U+0264D♍\virgo, \:virgo:Virgo
    U+0264E♎\libra, \:libra:Libra
    U+0264F♏\scorpio, \:scorpius:Scorpius
    U+02650♐\sagittarius, \:sagittarius:Sagittarius
    U+02651♑\capricornus, \:capricorn:Capricorn
    U+02652♒\aquarius, \:aquarius:Aquarius
    U+02653♓\pisces, \:pisces:Pisces
    U+02660♠\spadesuit, \:spades:Black Spade Suit
    U+02661♡\heartsuitWhite Heart Suit
    U+02662♢\diamondsuitWhite Diamond Suit
    U+02663♣\clubsuit, \:clubs:Black Club Suit
    U+02664♤\varspadesuitWhite Spade Suit
    U+02665♥\varheartsuit, \:hearts:Black Heart Suit
    U+02666♦\vardiamondsuit, \:diamonds:Black Diamond Suit
    U+02667♧\varclubsuitWhite Club Suit
    U+02668♨\:hotsprings:Hot Springs
    U+02669♩\quarternoteQuarter Note
    U+0266A♪\eighthnoteEighth Note
    U+0266B♫\twonotesBeamed Eighth Notes / Barred Eighth Notes
    U+0266D♭\flatMusic Flat Sign / Flat
    U+0266E♮\naturalMusic Natural Sign / Natural
    U+0266F♯\sharpMusic Sharp Sign / Sharp
    U+0267B♻\:recycle:Black Universal Recycling Symbol
    U+0267E♾\acidfreePermanent Paper Sign
    U+0267F♿\:wheelchair:Wheelchair Symbol
    U+02680⚀\diceiDie Face-1
    U+02681⚁\diceiiDie Face-2
    U+02682⚂\diceiiiDie Face-3
    U+02683⚃\diceivDie Face-4
    U+02684⚄\dicevDie Face-5
    U+02685⚅\diceviDie Face-6
    U+02686⚆\circledrightdotWhite Circle With Dot Right
    U+02687⚇\circledtwodotsWhite Circle With Two Dots
    U+02688⚈\blackcircledrightdotBlack Circle With White Dot Right
    U+02689⚉\blackcircledtwodotsBlack Circle With Two White Dots
    U+02693⚓\:anchor:Anchor
    U+026A0⚠\:warning:Warning Sign
    U+026A1⚡\:zap:High Voltage Sign
    U+026A5⚥\hermaphroditeMale And Female Sign
    U+026AA⚪\mdwhtcircle, \:white_circle:Medium White Circle
    U+026AB⚫\mdblkcircle, \:black_circle:Medium Black Circle
    U+026AC⚬\mdsmwhtcircleMedium Small White Circle
    U+026B2⚲\neuterNeuter
    U+026BD⚽\:soccer:Soccer Ball
    U+026BE⚾\:baseball:Baseball
    U+026C4⛄\:snowman:, \:snowman_without_snow:Snowman Without Snow
    U+026C5⛅\:partly_sunny:Sun Behind Cloud
    U+026CE⛎\:ophiuchus:Ophiuchus
    U+026D4⛔\:no_entry:No Entry
    U+026EA⛪\:church:Church
    U+026F2⛲\:fountain:Fountain
    U+026F3⛳\:golf:Flag In Hole
    U+026F5⛵\:boat:Sailboat
    U+026FA⛺\:tent:Tent
    U+026FD⛽\:fuelpump:Fuel Pump
    U+02702✂\:scissors:Black Scissors
    U+02705✅\:white_check_mark:White Heavy Check Mark
    U+02708✈\:airplane:Airplane
    U+02709✉\:email:Envelope
    U+0270A✊\:fist:Raised Fist
    U+0270B✋\:hand:Raised Hand
    U+0270C✌\:v:Victory Hand
    U+0270F✏\:pencil2:Pencil
    U+02712✒\:black_nib:Black Nib
    U+02713✓\checkmarkCheck Mark
    U+02714✔\:heavy_check_mark:Heavy Check Mark
    U+02716✖\:heavy_multiplication_x:Heavy Multiplication X
    U+02720✠\malteseMaltese Cross
    U+02728✨\:sparkles:Sparkles
    U+0272A✪\circledstarCircled White Star
    U+02733✳\:eight_spoked_asterisk:Eight Spoked Asterisk
    U+02734✴\:eight_pointed_black_star:Eight Pointed Black Star
    U+02736✶\varstarSix Pointed Black Star
    U+0273D✽\dingasteriskHeavy Teardrop-Spoked Asterisk
    U+02744❄\:snowflake:Snowflake
    U+02747❇\:sparkle:Sparkle
    U+0274C❌\:x:Cross Mark
    U+0274E❎\:negative_squared_cross_mark:Negative Squared Cross Mark
    U+02753❓\:question:Black Question Mark Ornament
    U+02754❔\:grey_question:White Question Mark Ornament
    U+02755❕\:grey_exclamation:White Exclamation Mark Ornament
    U+02757❗\:exclamation:Heavy Exclamation Mark Symbol
    U+02764❤\:heart:Heavy Black Heart
    U+02795➕\:heavy_plus_sign:Heavy Plus Sign
    U+02796➖\:heavy_minus_sign:Heavy Minus Sign
    U+02797➗\:heavy_division_sign:Heavy Division Sign
    U+0279B➛\draftingarrowDrafting Point Rightwards Arrow / Drafting Point Right Arrow
    U+027A1➡\:arrow_right:Black Rightwards Arrow / Black Right Arrow
    U+027B0➰\:curly_loop:Curly Loop
    U+027BF➿\:loop:Double Curly Loop
    U+027C0⟀\threedangleThree Dimensional Angle
    U+027C1⟁\whiteinwhitetriangleWhite Triangle Containing Small White Triangle
    U+027C2⟂\perpPerpendicular
    U+027C7⟇\veedotOr With Dot Inside
    U+027C8⟈\bsolhsubReverse Solidus Preceding Subset
    U+027C9⟉\suphsolSuperset Preceding Solidus
    U+027D1⟑\wedgedotAnd With Dot
    U+027D2⟒\upinElement Of Opening Upwards
    U+027D5⟕\leftouterjoinLeft Outer Join
    U+027D6⟖\rightouterjoinRight Outer Join
    U+027D7⟗\fullouterjoinFull Outer Join
    U+027D8⟘\bigbotLarge Up Tack
    U+027D9⟙\bigtopLarge Down Tack
    U+027E6⟦\llbracket, \openbracketleftMathematical Left White Square Bracket
    U+027E7⟧\openbracketright, \rrbracketMathematical Right White Square Bracket
    U+027E8⟨\langleMathematical Left Angle Bracket
    U+027E9⟩\rangleMathematical Right Angle Bracket
    U+027F0⟰\UUparrowUpwards Quadruple Arrow
    U+027F1⟱\DDownarrowDownwards Quadruple Arrow
    U+027F5⟵\longleftarrowLong Leftwards Arrow
    U+027F6⟶\longrightarrowLong Rightwards Arrow
    U+027F7⟷\longleftrightarrowLong Left Right Arrow
    U+027F8⟸\impliedby, \LongleftarrowLong Leftwards Double Arrow
    U+027F9⟹\implies, \LongrightarrowLong Rightwards Double Arrow
    U+027FA⟺\Longleftrightarrow, \iffLong Left Right Double Arrow
    U+027FB⟻\longmapsfromLong Leftwards Arrow From Bar
    U+027FC⟼\longmapstoLong Rightwards Arrow From Bar
    U+027FD⟽\LongmapsfromLong Leftwards Double Arrow From Bar
    U+027FE⟾\LongmapstoLong Rightwards Double Arrow From Bar
    U+027FF⟿\longrightsquigarrowLong Rightwards Squiggle Arrow
    U+02900⤀\nvtwoheadrightarrowRightwards Two-Headed Arrow With Vertical Stroke
    U+02901⤁\nVtwoheadrightarrowRightwards Two-Headed Arrow With Double Vertical Stroke
    U+02902⤂\nvLeftarrowLeftwards Double Arrow With Vertical Stroke
    U+02903⤃\nvRightarrowRightwards Double Arrow With Vertical Stroke
    U+02904⤄\nvLeftrightarrowLeft Right Double Arrow With Vertical Stroke
    U+02905⤅\twoheadmapstoRightwards Two-Headed Arrow From Bar
    U+02906⤆\MapsfromLeftwards Double Arrow From Bar
    U+02907⤇\MapstoRightwards Double Arrow From Bar
    U+02908⤈\downarrowbarredDownwards Arrow With Horizontal Stroke
    U+02909⤉\uparrowbarredUpwards Arrow With Horizontal Stroke
    U+0290A⤊\UuparrowUpwards Triple Arrow
    U+0290B⤋\DdownarrowDownwards Triple Arrow
    U+0290C⤌\leftbkarrowLeftwards Double Dash Arrow
    U+0290D⤍\bkarowRightwards Double Dash Arrow
    U+0290E⤎\leftdbkarrowLeftwards Triple Dash Arrow
    U+0290F⤏\dbkarowRightwards Triple Dash Arrow
    U+02910⤐\drbkarrowRightwards Two-Headed Triple Dash Arrow
    U+02911⤑\rightdotarrowRightwards Arrow With Dotted Stem
    U+02912⤒\UpArrowBarUpwards Arrow To Bar
    U+02913⤓\DownArrowBarDownwards Arrow To Bar
    U+02914⤔\nvrightarrowtailRightwards Arrow With Tail With Vertical Stroke
    U+02915⤕\nVrightarrowtailRightwards Arrow With Tail With Double Vertical Stroke
    U+02916⤖\twoheadrightarrowtailRightwards Two-Headed Arrow With Tail
    U+02917⤗\nvtwoheadrightarrowtailRightwards Two-Headed Arrow With Tail With Vertical Stroke
    U+02918⤘\nVtwoheadrightarrowtailRightwards Two-Headed Arrow With Tail With Double Vertical Stroke
    U+0291D⤝\diamondleftarrowLeftwards Arrow To Black Diamond
    U+0291E⤞\rightarrowdiamondRightwards Arrow To Black Diamond
    U+0291F⤟\diamondleftarrowbarLeftwards Arrow From Bar To Black Diamond
    U+02920⤠\barrightarrowdiamondRightwards Arrow From Bar To Black Diamond
    U+02925⤥\hksearowSouth East Arrow With Hook
    U+02926⤦\hkswarowSouth West Arrow With Hook
    U+02927⤧\tonaNorth West Arrow And North East Arrow
    U+02928⤨\toeaNorth East Arrow And South East Arrow
    U+02929⤩\tosaSouth East Arrow And South West Arrow
    U+0292A⤪\towaSouth West Arrow And North West Arrow
    U+0292B⤫\rdiagovfdiagRising Diagonal Crossing Falling Diagonal
    U+0292C⤬\fdiagovrdiagFalling Diagonal Crossing Rising Diagonal
    U+0292D⤭\seovnearrowSouth East Arrow Crossing North East Arrow
    U+0292E⤮\neovsearrowNorth East Arrow Crossing South East Arrow
    U+0292F⤯\fdiagovnearrowFalling Diagonal Crossing North East Arrow
    U+02930⤰\rdiagovsearrowRising Diagonal Crossing South East Arrow
    U+02931⤱\neovnwarrowNorth East Arrow Crossing North West Arrow
    U+02932⤲\nwovnearrowNorth West Arrow Crossing North East Arrow
    U+02934⤴\:arrow_heading_up:Arrow Pointing Rightwards Then Curving Upwards
    U+02935⤵\:arrow_heading_down:Arrow Pointing Rightwards Then Curving Downwards
    U+02942⥂\RlarrRightwards Arrow Above Short Leftwards Arrow
    U+02944⥄\rLarrShort Rightwards Arrow Above Leftwards Arrow
    U+02945⥅\rightarrowplusRightwards Arrow With Plus Below
    U+02946⥆\leftarrowplusLeftwards Arrow With Plus Below
    U+02947⥇\rarrxRightwards Arrow Through X
    U+02948⥈\leftrightarrowcircleLeft Right Arrow Through Small Circle
    U+02949⥉\twoheaduparrowcircleUpwards Two-Headed Arrow From Small Circle
    U+0294A⥊\leftrightharpoonupdownLeft Barb Up Right Barb Down Harpoon
    U+0294B⥋\leftrightharpoondownupLeft Barb Down Right Barb Up Harpoon
    U+0294C⥌\updownharpoonrightleftUp Barb Right Down Barb Left Harpoon
    U+0294D⥍\updownharpoonleftrightUp Barb Left Down Barb Right Harpoon
    U+0294E⥎\LeftRightVectorLeft Barb Up Right Barb Up Harpoon
    U+0294F⥏\RightUpDownVectorUp Barb Right Down Barb Right Harpoon
    U+02950⥐\DownLeftRightVectorLeft Barb Down Right Barb Down Harpoon
    U+02951⥑\LeftUpDownVectorUp Barb Left Down Barb Left Harpoon
    U+02952⥒\LeftVectorBarLeftwards Harpoon With Barb Up To Bar
    U+02953⥓\RightVectorBarRightwards Harpoon With Barb Up To Bar
    U+02954⥔\RightUpVectorBarUpwards Harpoon With Barb Right To Bar
    U+02955⥕\RightDownVectorBarDownwards Harpoon With Barb Right To Bar
    U+02956⥖\DownLeftVectorBarLeftwards Harpoon With Barb Down To Bar
    U+02957⥗\DownRightVectorBarRightwards Harpoon With Barb Down To Bar
    U+02958⥘\LeftUpVectorBarUpwards Harpoon With Barb Left To Bar
    U+02959⥙\LeftDownVectorBarDownwards Harpoon With Barb Left To Bar
    U+0295A⥚\LeftTeeVectorLeftwards Harpoon With Barb Up From Bar
    U+0295B⥛\RightTeeVectorRightwards Harpoon With Barb Up From Bar
    U+0295C⥜\RightUpTeeVectorUpwards Harpoon With Barb Right From Bar
    U+0295D⥝\RightDownTeeVectorDownwards Harpoon With Barb Right From Bar
    U+0295E⥞\DownLeftTeeVectorLeftwards Harpoon With Barb Down From Bar
    U+0295F⥟\DownRightTeeVectorRightwards Harpoon With Barb Down From Bar
    U+02960⥠\LeftUpTeeVectorUpwards Harpoon With Barb Left From Bar
    U+02961⥡\LeftDownTeeVectorDownwards Harpoon With Barb Left From Bar
    U+02962⥢\leftharpoonsupdownLeftwards Harpoon With Barb Up Above Leftwards Harpoon With Barb Down
    U+02963⥣\upharpoonsleftrightUpwards Harpoon With Barb Left Beside Upwards Harpoon With Barb Right
    U+02964⥤\rightharpoonsupdownRightwards Harpoon With Barb Up Above Rightwards Harpoon With Barb Down
    U+02965⥥\downharpoonsleftrightDownwards Harpoon With Barb Left Beside Downwards Harpoon With Barb Right
    U+02966⥦\leftrightharpoonsupLeftwards Harpoon With Barb Up Above Rightwards Harpoon With Barb Up
    U+02967⥧\leftrightharpoonsdownLeftwards Harpoon With Barb Down Above Rightwards Harpoon With Barb Down
    U+02968⥨\rightleftharpoonsupRightwards Harpoon With Barb Up Above Leftwards Harpoon With Barb Up
    U+02969⥩\rightleftharpoonsdownRightwards Harpoon With Barb Down Above Leftwards Harpoon With Barb Down
    U+0296A⥪\leftharpoonupdashLeftwards Harpoon With Barb Up Above Long Dash
    U+0296B⥫\dashleftharpoondownLeftwards Harpoon With Barb Down Below Long Dash
    U+0296C⥬\rightharpoonupdashRightwards Harpoon With Barb Up Above Long Dash
    U+0296D⥭\dashrightharpoondownRightwards Harpoon With Barb Down Below Long Dash
    U+0296E⥮\UpEquilibriumUpwards Harpoon With Barb Left Beside Downwards Harpoon With Barb Right
    U+0296F⥯\ReverseUpEquilibriumDownwards Harpoon With Barb Left Beside Upwards Harpoon With Barb Right
    U+02970⥰\RoundImpliesRight Double Arrow With Rounded Head
    U+02977⥷\leftarrowlessLeftwards Arrow Through Less-Than
    U+0297A⥺\leftarrowsubsetLeftwards Arrow Through Subset
    U+02980⦀\VvertTriple Vertical Bar Delimiter
    U+02986⦆\ElroangRight White Parenthesis
    U+02999⦙\ddfncDotted Fence
    U+0299B⦛\measuredangleleftMeasured Angle Opening Left
    U+0299C⦜\AngleRight Angle Variant With Square
    U+0299D⦝\rightanglemdotMeasured Right Angle With Dot
    U+0299E⦞\anglesAngle With S Inside
    U+0299F⦟\angdnrAcute Angle
    U+029A0⦠\lpargtSpherical Angle Opening Left
    U+029A1⦡\sphericalangleupSpherical Angle Opening Up
    U+029A2⦢\turnangleTurned Angle
    U+029A3⦣\revangleReversed Angle
    U+029A4⦤\angleubarAngle With Underbar
    U+029A5⦥\revangleubarReversed Angle With Underbar
    U+029A6⦦\wideangledownOblique Angle Opening Up
    U+029A7⦧\wideangleupOblique Angle Opening Down
    U+029A8⦨\measanglerutoneMeasured Angle With Open Arm Ending In Arrow Pointing Up And Right
    U+029A9⦩\measanglelutonwMeasured Angle With Open Arm Ending In Arrow Pointing Up And Left
    U+029AA⦪\measanglerdtoseMeasured Angle With Open Arm Ending In Arrow Pointing Down And Right
    U+029AB⦫\measangleldtoswMeasured Angle With Open Arm Ending In Arrow Pointing Down And Left
    U+029AC⦬\measangleurtoneMeasured Angle With Open Arm Ending In Arrow Pointing Right And Up
    U+029AD⦭\measangleultonwMeasured Angle With Open Arm Ending In Arrow Pointing Left And Up
    U+029AE⦮\measangledrtoseMeasured Angle With Open Arm Ending In Arrow Pointing Right And Down
    U+029AF⦯\measangledltoswMeasured Angle With Open Arm Ending In Arrow Pointing Left And Down
    U+029B0⦰\revemptysetReversed Empty Set
    U+029B1⦱\emptysetobarEmpty Set With Overbar
    U+029B2⦲\emptysetocircEmpty Set With Small Circle Above
    U+029B3⦳\emptysetoarrEmpty Set With Right Arrow Above
    U+029B4⦴\emptysetoarrlEmpty Set With Left Arrow Above
    U+029B7⦷\circledparallelCircled Parallel
    U+029B8⦸\obslashCircled Reverse Solidus
    U+029BC⦼\odotslashdotCircled Anticlockwise-Rotated Division Sign
    U+029BE⦾\circledwhitebulletCircled White Bullet
    U+029BF⦿\circledbulletCircled Bullet
    U+029C0⧀\olessthanCircled Less-Than
    U+029C1⧁\ogreaterthanCircled Greater-Than
    U+029C4⧄\boxdiagSquared Rising Diagonal Slash
    U+029C5⧅\boxbslashSquared Falling Diagonal Slash
    U+029C6⧆\boxastSquared Asterisk
    U+029C7⧇\boxcircleSquared Small Circle
    U+029CA⧊\LapTriangle With Dot Above
    U+029CB⧋\defasTriangle With Underbar
    U+029CF⧏\LeftTriangleBarLeft Triangle Beside Vertical Bar
    U+029CF + U+00338⧏̸\NotLeftTriangleBarLeft Triangle Beside Vertical Bar + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+029D0⧐\RightTriangleBarVertical Bar Beside Right Triangle
    U+029D0 + U+00338⧐̸\NotRightTriangleBarVertical Bar Beside Right Triangle + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+029DF⧟\dualmapDouble-Ended Multimap
    U+029E1⧡\lrtriangleeqIncreases As
    U+029E2⧢\shuffleShuffle Product
    U+029E3⧣\eparslEquals Sign And Slanted Parallel
    U+029E4⧤\smeparslEquals Sign And Slanted Parallel With Tilde Above
    U+029E5⧥\eqvparslIdentical To And Slanted Parallel
    U+029EB⧫\blacklozengeBlack Lozenge
    U+029F4⧴\RuleDelayedRule-Delayed
    U+029F6⧶\dsolSolidus With Overbar
    U+029F7⧷\rsolbarReverse Solidus With Horizontal Stroke
    U+029FA⧺\doubleplusDouble Plus
    U+029FB⧻\tripleplusTriple Plus
    U+02A00⨀\bigodotN-Ary Circled Dot Operator
    U+02A01⨁\bigoplusN-Ary Circled Plus Operator
    U+02A02⨂\bigotimesN-Ary Circled Times Operator
    U+02A03⨃\bigcupdotN-Ary Union Operator With Dot
    U+02A04⨄\biguplusN-Ary Union Operator With Plus
    U+02A05⨅\bigsqcapN-Ary Square Intersection Operator
    U+02A06⨆\bigsqcupN-Ary Square Union Operator
    U+02A07⨇\conjquantTwo Logical And Operator
    U+02A08⨈\disjquantTwo Logical Or Operator
    U+02A09⨉\bigtimesN-Ary Times Operator
    U+02A0A⨊\modtwosumModulo Two Sum
    U+02A0B⨋\sumintSummation With Integral
    U+02A0C⨌\iiiintQuadruple Integral Operator
    U+02A0D⨍\intbarFinite Part Integral
    U+02A0E⨎\intBarIntegral With Double Stroke
    U+02A0F⨏\clockointIntegral Average With Slash
    U+02A10⨐\cirfnintCirculation Function
    U+02A11⨑\awintAnticlockwise Integration
    U+02A12⨒\rppolintLine Integration With Rectangular Path Around Pole
    U+02A13⨓\scpolintLine Integration With Semicircular Path Around Pole
    U+02A14⨔\npolintLine Integration Not Including The Pole
    U+02A15⨕\pointintIntegral Around A Point Operator
    U+02A16⨖\sqrintQuaternion Integral Operator
    U+02A18⨘\intxIntegral With Times Sign
    U+02A19⨙\intcapIntegral With Intersection
    U+02A1A⨚\intcupIntegral With Union
    U+02A1B⨛\upintIntegral With Overbar
    U+02A1C⨜\lowintIntegral With Underbar
    U+02A1D⨝\joinJoin
    U+02A1F⨟\bbsemiZ Notation Schema Composition
    U+02A22⨢\ringplusPlus Sign With Small Circle Above
    U+02A23⨣\plushatPlus Sign With Circumflex Accent Above
    U+02A24⨤\simplusPlus Sign With Tilde Above
    U+02A25⨥\plusdotPlus Sign With Dot Below
    U+02A26⨦\plussimPlus Sign With Tilde Below
    U+02A27⨧\plussubtwoPlus Sign With Subscript Two
    U+02A28⨨\plustrifPlus Sign With Black Triangle
    U+02A29⨩\commaminusMinus Sign With Comma Above
    U+02A2A⨪\minusdotMinus Sign With Dot Below
    U+02A2B⨫\minusfdotsMinus Sign With Falling Dots
    U+02A2C⨬\minusrdotsMinus Sign With Rising Dots
    U+02A2D⨭\opluslhrimPlus Sign In Left Half Circle
    U+02A2E⨮\oplusrhrimPlus Sign In Right Half Circle
    U+02A2F⨯\TimesVector Or Cross Product
    U+02A30⨰\dottimesMultiplication Sign With Dot Above
    U+02A31⨱\timesbarMultiplication Sign With Underbar
    U+02A32⨲\btimesSemidirect Product With Bottom Closed
    U+02A33⨳\smashtimesSmash Product
    U+02A34⨴\otimeslhrimMultiplication Sign In Left Half Circle
    U+02A35⨵\otimesrhrimMultiplication Sign In Right Half Circle
    U+02A36⨶\otimeshatCircled Multiplication Sign With Circumflex Accent
    U+02A37⨷\OtimesMultiplication Sign In Double Circle
    U+02A38⨸\odivCircled Division Sign
    U+02A39⨹\triangleplusPlus Sign In Triangle
    U+02A3A⨺\triangleminusMinus Sign In Triangle
    U+02A3B⨻\triangletimesMultiplication Sign In Triangle
    U+02A3C⨼\intprodInterior Product
    U+02A3D⨽\intprodrRighthand Interior Product
    U+02A3F⨿\amalgAmalgamation Or Coproduct
    U+02A40⩀\capdotIntersection With Dot
    U+02A41⩁\uminusUnion With Minus Sign
    U+02A42⩂\barcupUnion With Overbar
    U+02A43⩃\barcapIntersection With Overbar
    U+02A44⩄\capwedgeIntersection With Logical And
    U+02A45⩅\cupveeUnion With Logical Or
    U+02A4A⩊\twocupsUnion Beside And Joined With Union
    U+02A4B⩋\twocapsIntersection Beside And Joined With Intersection
    U+02A4C⩌\closedvarcupClosed Union With Serifs
    U+02A4D⩍\closedvarcapClosed Intersection With Serifs
    U+02A4E⩎\SqcapDouble Square Intersection
    U+02A4F⩏\SqcupDouble Square Union
    U+02A50⩐\closedvarcupsmashprodClosed Union With Serifs And Smash Product
    U+02A51⩑\wedgeodotLogical And With Dot Above
    U+02A52⩒\veeodotLogical Or With Dot Above
    U+02A53⩓\AndDouble Logical And
    U+02A54⩔\OrDouble Logical Or
    U+02A55⩕\wedgeonwedgeTwo Intersecting Logical And
    U+02A56⩖\ElOrTwo Intersecting Logical Or
    U+02A57⩗\bigslopedveeSloping Large Or
    U+02A58⩘\bigslopedwedgeSloping Large And
    U+02A5A⩚\wedgemidvertLogical And With Middle Stem
    U+02A5B⩛\veemidvertLogical Or With Middle Stem
    U+02A5C⩜\midbarwedgeLogical And With Horizontal Dash
    U+02A5D⩝\midbarveeLogical Or With Horizontal Dash
    U+02A5E⩞\perspcorrespondLogical And With Double Overbar
    U+02A5F⩟\minhatLogical And With Underbar
    U+02A60⩠\wedgedoublebarLogical And With Double Underbar
    U+02A61⩡\varveebarSmall Vee With Underbar
    U+02A62⩢\doublebarveeLogical Or With Double Overbar
    U+02A63⩣\veedoublebarLogical Or With Double Underbar
    U+02A66⩦\eqdotEquals Sign With Dot Below
    U+02A67⩧\dotequivIdentical With Dot Above
    U+02A6A⩪\dotsimTilde Operator With Dot Above
    U+02A6B⩫\simrdotsTilde Operator With Rising Dots
    U+02A6C⩬\simminussimSimilar Minus Similar
    U+02A6D⩭\congdotCongruent With Dot Above
    U+02A6E⩮\asteqEquals With Asterisk
    U+02A6F⩯\hatapproxAlmost Equal To With Circumflex Accent
    U+02A70⩰\approxeqqApproximately Equal Or Equal To
    U+02A71⩱\eqqplusEquals Sign Above Plus Sign
    U+02A72⩲\pluseqqPlus Sign Above Equals Sign
    U+02A73⩳\eqqsimEquals Sign Above Tilde Operator
    U+02A74⩴\ColoneqDouble Colon Equal
    U+02A75⩵\EqualTwo Consecutive Equals Signs
    U+02A76⩶\eqeqeqThree Consecutive Equals Signs
    U+02A77⩷\ddotseqEquals Sign With Two Dots Above And Two Dots Below
    U+02A78⩸\equivDDEquivalent With Four Dots Above
    U+02A79⩹\ltcirLess-Than With Circle Inside
    U+02A7A⩺\gtcirGreater-Than With Circle Inside
    U+02A7B⩻\ltquestLess-Than With Question Mark Above
    U+02A7C⩼\gtquestGreater-Than With Question Mark Above
    U+02A7D⩽\leqslantLess-Than Or Slanted Equal To
    U+02A7D + U+00338⩽̸\nleqslantLess-Than Or Slanted Equal To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02A7E⩾\geqslantGreater-Than Or Slanted Equal To
    U+02A7E + U+00338⩾̸\ngeqslantGreater-Than Or Slanted Equal To + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02A7F⩿\lesdotLess-Than Or Slanted Equal To With Dot Inside
    U+02A80⪀\gesdotGreater-Than Or Slanted Equal To With Dot Inside
    U+02A81⪁\lesdotoLess-Than Or Slanted Equal To With Dot Above
    U+02A82⪂\gesdotoGreater-Than Or Slanted Equal To With Dot Above
    U+02A83⪃\lesdotorLess-Than Or Slanted Equal To With Dot Above Right
    U+02A84⪄\gesdotolGreater-Than Or Slanted Equal To With Dot Above Left
    U+02A85⪅\lessapproxLess-Than Or Approximate
    U+02A86⪆\gtrapproxGreater-Than Or Approximate
    U+02A87⪇\lneqLess-Than And Single-Line Not Equal To
    U+02A88⪈\gneqGreater-Than And Single-Line Not Equal To
    U+02A89⪉\lnapproxLess-Than And Not Approximate
    U+02A8A⪊\gnapproxGreater-Than And Not Approximate
    U+02A8B⪋\lesseqqgtrLess-Than Above Double-Line Equal Above Greater-Than
    U+02A8C⪌\gtreqqlessGreater-Than Above Double-Line Equal Above Less-Than
    U+02A8D⪍\lsimeLess-Than Above Similar Or Equal
    U+02A8E⪎\gsimeGreater-Than Above Similar Or Equal
    U+02A8F⪏\lsimgLess-Than Above Similar Above Greater-Than
    U+02A90⪐\gsimlGreater-Than Above Similar Above Less-Than
    U+02A91⪑\lgELess-Than Above Greater-Than Above Double-Line Equal
    U+02A92⪒\glEGreater-Than Above Less-Than Above Double-Line Equal
    U+02A93⪓\lesgesLess-Than Above Slanted Equal Above Greater-Than Above Slanted Equal
    U+02A94⪔\geslesGreater-Than Above Slanted Equal Above Less-Than Above Slanted Equal
    U+02A95⪕\eqslantlessSlanted Equal To Or Less-Than
    U+02A96⪖\eqslantgtrSlanted Equal To Or Greater-Than
    U+02A97⪗\elsdotSlanted Equal To Or Less-Than With Dot Inside
    U+02A98⪘\egsdotSlanted Equal To Or Greater-Than With Dot Inside
    U+02A99⪙\eqqlessDouble-Line Equal To Or Less-Than
    U+02A9A⪚\eqqgtrDouble-Line Equal To Or Greater-Than
    U+02A9B⪛\eqqslantlessDouble-Line Slanted Equal To Or Less-Than
    U+02A9C⪜\eqqslantgtrDouble-Line Slanted Equal To Or Greater-Than
    U+02A9D⪝\simlessSimilar Or Less-Than
    U+02A9E⪞\simgtrSimilar Or Greater-Than
    U+02A9F⪟\simlESimilar Above Less-Than Above Equals Sign
    U+02AA0⪠\simgESimilar Above Greater-Than Above Equals Sign
    U+02AA1⪡\NestedLessLessDouble Nested Less-Than
    U+02AA1 + U+00338⪡̸\NotNestedLessLessDouble Nested Less-Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AA2⪢\NestedGreaterGreaterDouble Nested Greater-Than
    U+02AA2 + U+00338⪢̸\NotNestedGreaterGreaterDouble Nested Greater-Than + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AA3⪣\partialmeetcontractionDouble Nested Less-Than With Underbar
    U+02AA4⪤\gljGreater-Than Overlapping Less-Than
    U+02AA5⪥\glaGreater-Than Beside Less-Than
    U+02AA6⪦\ltccLess-Than Closed By Curve
    U+02AA7⪧\gtccGreater-Than Closed By Curve
    U+02AA8⪨\lesccLess-Than Closed By Curve Above Slanted Equal
    U+02AA9⪩\gesccGreater-Than Closed By Curve Above Slanted Equal
    U+02AAA⪪\smtSmaller Than
    U+02AAB⪫\latLarger Than
    U+02AAC⪬\smteSmaller Than Or Equal To
    U+02AAD⪭\lateLarger Than Or Equal To
    U+02AAE⪮\bumpeqqEquals Sign With Bumpy Above
    U+02AAF⪯\preceqPrecedes Above Single-Line Equals Sign
    U+02AAF + U+00338⪯̸\npreceqPrecedes Above Single-Line Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AB0⪰\succeqSucceeds Above Single-Line Equals Sign
    U+02AB0 + U+00338⪰̸\nsucceqSucceeds Above Single-Line Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AB1⪱\precneqPrecedes Above Single-Line Not Equal To
    U+02AB2⪲\succneqSucceeds Above Single-Line Not Equal To
    U+02AB3⪳\preceqqPrecedes Above Equals Sign
    U+02AB4⪴\succeqqSucceeds Above Equals Sign
    U+02AB5⪵\precneqqPrecedes Above Not Equal To
    U+02AB6⪶\succneqqSucceeds Above Not Equal To
    U+02AB7⪷\precapproxPrecedes Above Almost Equal To
    U+02AB8⪸\succapproxSucceeds Above Almost Equal To
    U+02AB9⪹\precnapproxPrecedes Above Not Almost Equal To
    U+02ABA⪺\succnapproxSucceeds Above Not Almost Equal To
    U+02ABB⪻\PrecDouble Precedes
    U+02ABC⪼\SuccDouble Succeeds
    U+02ABD⪽\subsetdotSubset With Dot
    U+02ABE⪾\supsetdotSuperset With Dot
    U+02ABF⪿\subsetplusSubset With Plus Sign Below
    U+02AC0⫀\supsetplusSuperset With Plus Sign Below
    U+02AC1⫁\submultSubset With Multiplication Sign Below
    U+02AC2⫂\supmultSuperset With Multiplication Sign Below
    U+02AC3⫃\subedotSubset Of Or Equal To With Dot Above
    U+02AC4⫄\supedotSuperset Of Or Equal To With Dot Above
    U+02AC5⫅\subseteqqSubset Of Above Equals Sign
    U+02AC5 + U+00338⫅̸\nsubseteqqSubset Of Above Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AC6⫆\supseteqqSuperset Of Above Equals Sign
    U+02AC6 + U+00338⫆̸\nsupseteqqSuperset Of Above Equals Sign + Combining Long Solidus Overlay / Non-Spacing Long Slash Overlay
    U+02AC7⫇\subsimSubset Of Above Tilde Operator
    U+02AC8⫈\supsimSuperset Of Above Tilde Operator
    U+02AC9⫉\subsetapproxSubset Of Above Almost Equal To
    U+02ACA⫊\supsetapproxSuperset Of Above Almost Equal To
    U+02ACB⫋\subsetneqqSubset Of Above Not Equal To
    U+02ACC⫌\supsetneqqSuperset Of Above Not Equal To
    U+02ACD⫍\lsqhookSquare Left Open Box Operator
    U+02ACE⫎\rsqhookSquare Right Open Box Operator
    U+02ACF⫏\csubClosed Subset
    U+02AD0⫐\csupClosed Superset
    U+02AD1⫑\csubeClosed Subset Or Equal To
    U+02AD2⫒\csupeClosed Superset Or Equal To
    U+02AD3⫓\subsupSubset Above Superset
    U+02AD4⫔\supsubSuperset Above Subset
    U+02AD5⫕\subsubSubset Above Subset
    U+02AD6⫖\supsupSuperset Above Superset
    U+02AD7⫗\suphsubSuperset Beside Subset
    U+02AD8⫘\supdsubSuperset Beside And Joined By Dash With Subset
    U+02AD9⫙\forkvElement Of Opening Downwards
    U+02ADB⫛\mlcpTransversal Intersection
    U+02ADC⫝̸\forksForking
    U+02ADD⫝\forksnotNonforking
    U+02AE3⫣\dashVDouble Vertical Bar Left Turnstile
    U+02AE4⫤\DashvVertical Bar Double Left Turnstile
    U+02AEA⫪\Top, \downvDashDouble Down Tack
    U+02AEB⫫\upvDash, \Bot, \indepDouble Up Tack
    U+02AF4⫴\interleaveTriple Vertical Bar Binary Relation
    U+02AF6⫶\tdcolTriple Colon Operator
    U+02AF7⫷\lllnestTriple Nested Less-Than
    U+02AF8⫸\gggnestTriple Nested Greater-Than
    U+02AF9⫹\leqqslantDouble-Line Slanted Less-Than Or Equal To
    U+02AFA⫺\geqqslantDouble-Line Slanted Greater-Than Or Equal To
    U+02B05⬅\:arrow_left:Leftwards Black Arrow
    U+02B06⬆\:arrow_up:Upwards Black Arrow
    U+02B07⬇\:arrow_down:Downwards Black Arrow
    U+02B12⬒\squaretopblackSquare With Top Half Black
    U+02B13⬓\squarebotblackSquare With Bottom Half Black
    U+02B14⬔\squareurblackSquare With Upper Right Diagonal Half Black
    U+02B15⬕\squarellblackSquare With Lower Left Diagonal Half Black
    U+02B16⬖\diamondleftblackDiamond With Left Half Black
    U+02B17⬗\diamondrightblackDiamond With Right Half Black
    U+02B18⬘\diamondtopblackDiamond With Top Half Black
    U+02B19⬙\diamondbotblackDiamond With Bottom Half Black
    U+02B1A⬚\dottedsquareDotted Square
    U+02B1B⬛\lgblksquare, \:black_large_square:Black Large Square
    U+02B1C⬜\lgwhtsquare, \:white_large_square:White Large Square
    U+02B1D⬝\vysmblksquareBlack Very Small Square
    U+02B1E⬞\vysmwhtsquareWhite Very Small Square
    U+02B1F⬟\pentagonblackBlack Pentagon
    U+02B20⬠\pentagonWhite Pentagon
    U+02B21⬡\varhexagonWhite Hexagon
    U+02B22⬢\varhexagonblackBlack Hexagon
    U+02B23⬣\hexagonblackHorizontal Black Hexagon
    U+02B24⬤\lgblkcircleBlack Large Circle
    U+02B25⬥\mdblkdiamondBlack Medium Diamond
    U+02B26⬦\mdwhtdiamondWhite Medium Diamond
    U+02B27⬧\mdblklozengeBlack Medium Lozenge
    U+02B28⬨\mdwhtlozengeWhite Medium Lozenge
    U+02B29⬩\smblkdiamondBlack Small Diamond
    U+02B2A⬪\smblklozengeBlack Small Lozenge
    U+02B2B⬫\smwhtlozengeWhite Small Lozenge
    U+02B2C⬬\blkhorzovalBlack Horizontal Ellipse
    U+02B2D⬭\whthorzovalWhite Horizontal Ellipse
    U+02B2E⬮\blkvertovalBlack Vertical Ellipse
    U+02B2F⬯\whtvertovalWhite Vertical Ellipse
    U+02B30⬰\circleonleftarrowLeft Arrow With Small Circle
    U+02B31⬱\leftthreearrowsThree Leftwards Arrows
    U+02B32⬲\leftarrowonoplusLeft Arrow With Circled Plus
    U+02B33⬳\longleftsquigarrowLong Leftwards Squiggle Arrow
    U+02B34⬴\nvtwoheadleftarrowLeftwards Two-Headed Arrow With Vertical Stroke
    U+02B35⬵\nVtwoheadleftarrowLeftwards Two-Headed Arrow With Double Vertical Stroke
    U+02B36⬶\twoheadmapsfromLeftwards Two-Headed Arrow From Bar
    U+02B37⬷\twoheadleftdbkarrowLeftwards Two-Headed Triple Dash Arrow
    U+02B38⬸\leftdotarrowLeftwards Arrow With Dotted Stem
    U+02B39⬹\nvleftarrowtailLeftwards Arrow With Tail With Vertical Stroke
    U+02B3A⬺\nVleftarrowtailLeftwards Arrow With Tail With Double Vertical Stroke
    U+02B3B⬻\twoheadleftarrowtailLeftwards Two-Headed Arrow With Tail
    U+02B3C⬼\nvtwoheadleftarrowtailLeftwards Two-Headed Arrow With Tail With Vertical Stroke
    U+02B3D⬽\nVtwoheadleftarrowtailLeftwards Two-Headed Arrow With Tail With Double Vertical Stroke
    U+02B3E⬾\leftarrowxLeftwards Arrow Through X
    U+02B3F⬿\leftcurvedarrowWave Arrow Pointing Directly Left
    U+02B40⭀\equalleftarrowEquals Sign Above Leftwards Arrow
    U+02B41⭁\bsimilarleftarrowReverse Tilde Operator Above Leftwards Arrow
    U+02B42⭂\leftarrowbackapproxLeftwards Arrow Above Reverse Almost Equal To
    U+02B43⭃\rightarrowgtrRightwards Arrow Through Greater-Than
    U+02B44⭄\rightarrowsupsetRightwards Arrow Through Superset
    U+02B45⭅\LLeftarrowLeftwards Quadruple Arrow
    U+02B46⭆\RRightarrowRightwards Quadruple Arrow
    U+02B47⭇\bsimilarrightarrowReverse Tilde Operator Above Rightwards Arrow
    U+02B48⭈\rightarrowbackapproxRightwards Arrow Above Reverse Almost Equal To
    U+02B49⭉\similarleftarrowTilde Operator Above Leftwards Arrow
    U+02B4A⭊\leftarrowapproxLeftwards Arrow Above Almost Equal To
    U+02B4B⭋\leftarrowbsimilarLeftwards Arrow Above Reverse Tilde Operator
    U+02B4C⭌\rightarrowbsimilarRightwards Arrow Above Reverse Tilde Operator
    U+02B50⭐\medwhitestar, \:star:White Medium Star
    U+02B51⭑\medblackstarBlack Small Star
    U+02B52⭒\smwhitestarWhite Small Star
    U+02B53⭓\rightpentagonblackBlack Right-Pointing Pentagon
    U+02B54⭔\rightpentagonWhite Right-Pointing Pentagon
    U+02B55⭕\:o:Heavy Large Circle
    U+02C7Cⱼ\_jLatin Subscript Small Letter J
    U+02C7Dⱽ\^VModifier Letter Capital V
    U+03012〒\postalmarkPostal Mark
    U+03030〰\:wavy_dash:Wavy Dash
    U+0303D〽\:part_alternation_mark:Part Alternation Mark
    U+03297㊗\:congratulations:Circled Ideograph Congratulation
    U+03299㊙\:secret:Circled Ideograph Secret
    U+0A71Bꜛ\^uparrowModifier Letter Raised Up Arrow
    U+0A71Cꜜ\^downarrowModifier Letter Raised Down Arrow
    U+0A71Dꜝ\^!Modifier Letter Raised Exclamation Mark
    U+1D400𝐀\bfAMathematical Bold Capital A
    U+1D401𝐁\bfBMathematical Bold Capital B
    U+1D402𝐂\bfCMathematical Bold Capital C
    U+1D403𝐃\bfDMathematical Bold Capital D
    U+1D404𝐄\bfEMathematical Bold Capital E
    U+1D405𝐅\bfFMathematical Bold Capital F
    U+1D406𝐆\bfGMathematical Bold Capital G
    U+1D407𝐇\bfHMathematical Bold Capital H
    U+1D408𝐈\bfIMathematical Bold Capital I
    U+1D409𝐉\bfJMathematical Bold Capital J
    U+1D40A𝐊\bfKMathematical Bold Capital K
    U+1D40B𝐋\bfLMathematical Bold Capital L
    U+1D40C𝐌\bfMMathematical Bold Capital M
    U+1D40D𝐍\bfNMathematical Bold Capital N
    U+1D40E𝐎\bfOMathematical Bold Capital O
    U+1D40F𝐏\bfPMathematical Bold Capital P
    U+1D410𝐐\bfQMathematical Bold Capital Q
    U+1D411𝐑\bfRMathematical Bold Capital R
    U+1D412𝐒\bfSMathematical Bold Capital S
    U+1D413𝐓\bfTMathematical Bold Capital T
    U+1D414𝐔\bfUMathematical Bold Capital U
    U+1D415𝐕\bfVMathematical Bold Capital V
    U+1D416𝐖\bfWMathematical Bold Capital W
    U+1D417𝐗\bfXMathematical Bold Capital X
    U+1D418𝐘\bfYMathematical Bold Capital Y
    U+1D419𝐙\bfZMathematical Bold Capital Z
    U+1D41A𝐚\bfaMathematical Bold Small A
    U+1D41B𝐛\bfbMathematical Bold Small B
    U+1D41C𝐜\bfcMathematical Bold Small C
    U+1D41D𝐝\bfdMathematical Bold Small D
    U+1D41E𝐞\bfeMathematical Bold Small E
    U+1D41F𝐟\bffMathematical Bold Small F
    U+1D420𝐠\bfgMathematical Bold Small G
    U+1D421𝐡\bfhMathematical Bold Small H
    U+1D422𝐢\bfiMathematical Bold Small I
    U+1D423𝐣\bfjMathematical Bold Small J
    U+1D424𝐤\bfkMathematical Bold Small K
    U+1D425𝐥\bflMathematical Bold Small L
    U+1D426𝐦\bfmMathematical Bold Small M
    U+1D427𝐧\bfnMathematical Bold Small N
    U+1D428𝐨\bfoMathematical Bold Small O
    U+1D429𝐩\bfpMathematical Bold Small P
    U+1D42A𝐪\bfqMathematical Bold Small Q
    U+1D42B𝐫\bfrMathematical Bold Small R
    U+1D42C𝐬\bfsMathematical Bold Small S
    U+1D42D𝐭\bftMathematical Bold Small T
    U+1D42E𝐮\bfuMathematical Bold Small U
    U+1D42F𝐯\bfvMathematical Bold Small V
    U+1D430𝐰\bfwMathematical Bold Small W
    U+1D431𝐱\bfxMathematical Bold Small X
    U+1D432𝐲\bfyMathematical Bold Small Y
    U+1D433𝐳\bfzMathematical Bold Small Z
    U+1D434𝐴\itAMathematical Italic Capital A
    U+1D435𝐵\itBMathematical Italic Capital B
    U+1D436𝐶\itCMathematical Italic Capital C
    U+1D437𝐷\itDMathematical Italic Capital D
    U+1D438𝐸\itEMathematical Italic Capital E
    U+1D439𝐹\itFMathematical Italic Capital F
    U+1D43A𝐺\itGMathematical Italic Capital G
    U+1D43B𝐻\itHMathematical Italic Capital H
    U+1D43C𝐼\itIMathematical Italic Capital I
    U+1D43D𝐽\itJMathematical Italic Capital J
    U+1D43E𝐾\itKMathematical Italic Capital K
    U+1D43F𝐿\itLMathematical Italic Capital L
    U+1D440𝑀\itMMathematical Italic Capital M
    U+1D441𝑁\itNMathematical Italic Capital N
    U+1D442𝑂\itOMathematical Italic Capital O
    U+1D443𝑃\itPMathematical Italic Capital P
    U+1D444𝑄\itQMathematical Italic Capital Q
    U+1D445𝑅\itRMathematical Italic Capital R
    U+1D446𝑆\itSMathematical Italic Capital S
    U+1D447𝑇\itTMathematical Italic Capital T
    U+1D448𝑈\itUMathematical Italic Capital U
    U+1D449𝑉\itVMathematical Italic Capital V
    U+1D44A𝑊\itWMathematical Italic Capital W
    U+1D44B𝑋\itXMathematical Italic Capital X
    U+1D44C𝑌\itYMathematical Italic Capital Y
    U+1D44D𝑍\itZMathematical Italic Capital Z
    U+1D44E𝑎\itaMathematical Italic Small A
    U+1D44F𝑏\itbMathematical Italic Small B
    U+1D450𝑐\itcMathematical Italic Small C
    U+1D451𝑑\itdMathematical Italic Small D
    U+1D452𝑒\iteMathematical Italic Small E
    U+1D453𝑓\itfMathematical Italic Small F
    U+1D454𝑔\itgMathematical Italic Small G
    U+1D456𝑖\itiMathematical Italic Small I
    U+1D457𝑗\itjMathematical Italic Small J
    U+1D458𝑘\itkMathematical Italic Small K
    U+1D459𝑙\itlMathematical Italic Small L
    U+1D45A𝑚\itmMathematical Italic Small M
    U+1D45B𝑛\itnMathematical Italic Small N
    U+1D45C𝑜\itoMathematical Italic Small O
    U+1D45D𝑝\itpMathematical Italic Small P
    U+1D45E𝑞\itqMathematical Italic Small Q
    U+1D45F𝑟\itrMathematical Italic Small R
    U+1D460𝑠\itsMathematical Italic Small S
    U+1D461𝑡\ittMathematical Italic Small T
    U+1D462𝑢\ituMathematical Italic Small U
    U+1D463𝑣\itvMathematical Italic Small V
    U+1D464𝑤\itwMathematical Italic Small W
    U+1D465𝑥\itxMathematical Italic Small X
    U+1D466𝑦\ityMathematical Italic Small Y
    U+1D467𝑧\itzMathematical Italic Small Z
    U+1D468𝑨\biAMathematical Bold Italic Capital A
    U+1D469𝑩\biBMathematical Bold Italic Capital B
    U+1D46A𝑪\biCMathematical Bold Italic Capital C
    U+1D46B𝑫\biDMathematical Bold Italic Capital D
    U+1D46C𝑬\biEMathematical Bold Italic Capital E
    U+1D46D𝑭\biFMathematical Bold Italic Capital F
    U+1D46E𝑮\biGMathematical Bold Italic Capital G
    U+1D46F𝑯\biHMathematical Bold Italic Capital H
    U+1D470𝑰\biIMathematical Bold Italic Capital I
    U+1D471𝑱\biJMathematical Bold Italic Capital J
    U+1D472𝑲\biKMathematical Bold Italic Capital K
    U+1D473𝑳\biLMathematical Bold Italic Capital L
    U+1D474𝑴\biMMathematical Bold Italic Capital M
    U+1D475𝑵\biNMathematical Bold Italic Capital N
    U+1D476𝑶\biOMathematical Bold Italic Capital O
    U+1D477𝑷\biPMathematical Bold Italic Capital P
    U+1D478𝑸\biQMathematical Bold Italic Capital Q
    U+1D479𝑹\biRMathematical Bold Italic Capital R
    U+1D47A𝑺\biSMathematical Bold Italic Capital S
    U+1D47B𝑻\biTMathematical Bold Italic Capital T
    U+1D47C𝑼\biUMathematical Bold Italic Capital U
    U+1D47D𝑽\biVMathematical Bold Italic Capital V
    U+1D47E𝑾\biWMathematical Bold Italic Capital W
    U+1D47F𝑿\biXMathematical Bold Italic Capital X
    U+1D480𝒀\biYMathematical Bold Italic Capital Y
    U+1D481𝒁\biZMathematical Bold Italic Capital Z
    U+1D482𝒂\biaMathematical Bold Italic Small A
    U+1D483𝒃\bibMathematical Bold Italic Small B
    U+1D484𝒄\bicMathematical Bold Italic Small C
    U+1D485𝒅\bidMathematical Bold Italic Small D
    U+1D486𝒆\bieMathematical Bold Italic Small E
    U+1D487𝒇\bifMathematical Bold Italic Small F
    U+1D488𝒈\bigMathematical Bold Italic Small G
    U+1D489𝒉\bihMathematical Bold Italic Small H
    U+1D48A𝒊\biiMathematical Bold Italic Small I
    U+1D48B𝒋\bijMathematical Bold Italic Small J
    U+1D48C𝒌\bikMathematical Bold Italic Small K
    U+1D48D𝒍\bilMathematical Bold Italic Small L
    U+1D48E𝒎\bimMathematical Bold Italic Small M
    U+1D48F𝒏\binMathematical Bold Italic Small N
    U+1D490𝒐\bioMathematical Bold Italic Small O
    U+1D491𝒑\bipMathematical Bold Italic Small P
    U+1D492𝒒\biqMathematical Bold Italic Small Q
    U+1D493𝒓\birMathematical Bold Italic Small R
    U+1D494𝒔\bisMathematical Bold Italic Small S
    U+1D495𝒕\bitMathematical Bold Italic Small T
    U+1D496𝒖\biuMathematical Bold Italic Small U
    U+1D497𝒗\bivMathematical Bold Italic Small V
    U+1D498𝒘\biwMathematical Bold Italic Small W
    U+1D499𝒙\bixMathematical Bold Italic Small X
    U+1D49A𝒚\biyMathematical Bold Italic Small Y
    U+1D49B𝒛\bizMathematical Bold Italic Small Z
    U+1D49C𝒜\scrAMathematical Script Capital A
    U+1D49E𝒞\scrCMathematical Script Capital C
    U+1D49F𝒟\scrDMathematical Script Capital D
    U+1D4A2𝒢\scrGMathematical Script Capital G
    U+1D4A5𝒥\scrJMathematical Script Capital J
    U+1D4A6𝒦\scrKMathematical Script Capital K
    U+1D4A9𝒩\scrNMathematical Script Capital N
    U+1D4AA𝒪\scrOMathematical Script Capital O
    U+1D4AB𝒫\scrPMathematical Script Capital P
    U+1D4AC𝒬\scrQMathematical Script Capital Q
    U+1D4AE𝒮\scrSMathematical Script Capital S
    U+1D4AF𝒯\scrTMathematical Script Capital T
    U+1D4B0𝒰\scrUMathematical Script Capital U
    U+1D4B1𝒱\scrVMathematical Script Capital V
    U+1D4B2𝒲\scrWMathematical Script Capital W
    U+1D4B3𝒳\scrXMathematical Script Capital X
    U+1D4B4𝒴\scrYMathematical Script Capital Y
    U+1D4B5𝒵\scrZMathematical Script Capital Z
    U+1D4B6𝒶\scraMathematical Script Small A
    U+1D4B7𝒷\scrbMathematical Script Small B
    U+1D4B8𝒸\scrcMathematical Script Small C
    U+1D4B9𝒹\scrdMathematical Script Small D
    U+1D4BB𝒻\scrfMathematical Script Small F
    U+1D4BD𝒽\scrhMathematical Script Small H
    U+1D4BE𝒾\scriMathematical Script Small I
    U+1D4BF𝒿\scrjMathematical Script Small J
    U+1D4C0𝓀\scrkMathematical Script Small K
    U+1D4C1𝓁\scrlMathematical Script Small L
    U+1D4C2𝓂\scrmMathematical Script Small M
    U+1D4C3𝓃\scrnMathematical Script Small N
    U+1D4C5𝓅\scrpMathematical Script Small P
    U+1D4C6𝓆\scrqMathematical Script Small Q
    U+1D4C7𝓇\scrrMathematical Script Small R
    U+1D4C8𝓈\scrsMathematical Script Small S
    U+1D4C9𝓉\scrtMathematical Script Small T
    U+1D4CA𝓊\scruMathematical Script Small U
    U+1D4CB𝓋\scrvMathematical Script Small V
    U+1D4CC𝓌\scrwMathematical Script Small W
    U+1D4CD𝓍\scrxMathematical Script Small X
    U+1D4CE𝓎\scryMathematical Script Small Y
    U+1D4CF𝓏\scrzMathematical Script Small Z
    U+1D4D0𝓐\bscrAMathematical Bold Script Capital A
    U+1D4D1𝓑\bscrBMathematical Bold Script Capital B
    U+1D4D2𝓒\bscrCMathematical Bold Script Capital C
    U+1D4D3𝓓\bscrDMathematical Bold Script Capital D
    U+1D4D4𝓔\bscrEMathematical Bold Script Capital E
    U+1D4D5𝓕\bscrFMathematical Bold Script Capital F
    U+1D4D6𝓖\bscrGMathematical Bold Script Capital G
    U+1D4D7𝓗\bscrHMathematical Bold Script Capital H
    U+1D4D8𝓘\bscrIMathematical Bold Script Capital I
    U+1D4D9𝓙\bscrJMathematical Bold Script Capital J
    U+1D4DA𝓚\bscrKMathematical Bold Script Capital K
    U+1D4DB𝓛\bscrLMathematical Bold Script Capital L
    U+1D4DC𝓜\bscrMMathematical Bold Script Capital M
    U+1D4DD𝓝\bscrNMathematical Bold Script Capital N
    U+1D4DE𝓞\bscrOMathematical Bold Script Capital O
    U+1D4DF𝓟\bscrPMathematical Bold Script Capital P
    U+1D4E0𝓠\bscrQMathematical Bold Script Capital Q
    U+1D4E1𝓡\bscrRMathematical Bold Script Capital R
    U+1D4E2𝓢\bscrSMathematical Bold Script Capital S
    U+1D4E3𝓣\bscrTMathematical Bold Script Capital T
    U+1D4E4𝓤\bscrUMathematical Bold Script Capital U
    U+1D4E5𝓥\bscrVMathematical Bold Script Capital V
    U+1D4E6𝓦\bscrWMathematical Bold Script Capital W
    U+1D4E7𝓧\bscrXMathematical Bold Script Capital X
    U+1D4E8𝓨\bscrYMathematical Bold Script Capital Y
    U+1D4E9𝓩\bscrZMathematical Bold Script Capital Z
    U+1D4EA𝓪\bscraMathematical Bold Script Small A
    U+1D4EB𝓫\bscrbMathematical Bold Script Small B
    U+1D4EC𝓬\bscrcMathematical Bold Script Small C
    U+1D4ED𝓭\bscrdMathematical Bold Script Small D
    U+1D4EE𝓮\bscreMathematical Bold Script Small E
    U+1D4EF𝓯\bscrfMathematical Bold Script Small F
    U+1D4F0𝓰\bscrgMathematical Bold Script Small G
    U+1D4F1𝓱\bscrhMathematical Bold Script Small H
    U+1D4F2𝓲\bscriMathematical Bold Script Small I
    U+1D4F3𝓳\bscrjMathematical Bold Script Small J
    U+1D4F4𝓴\bscrkMathematical Bold Script Small K
    U+1D4F5𝓵\bscrlMathematical Bold Script Small L
    U+1D4F6𝓶\bscrmMathematical Bold Script Small M
    U+1D4F7𝓷\bscrnMathematical Bold Script Small N
    U+1D4F8𝓸\bscroMathematical Bold Script Small O
    U+1D4F9𝓹\bscrpMathematical Bold Script Small P
    U+1D4FA𝓺\bscrqMathematical Bold Script Small Q
    U+1D4FB𝓻\bscrrMathematical Bold Script Small R
    U+1D4FC𝓼\bscrsMathematical Bold Script Small S
    U+1D4FD𝓽\bscrtMathematical Bold Script Small T
    U+1D4FE𝓾\bscruMathematical Bold Script Small U
    U+1D4FF𝓿\bscrvMathematical Bold Script Small V
    U+1D500𝔀\bscrwMathematical Bold Script Small W
    U+1D501𝔁\bscrxMathematical Bold Script Small X
    U+1D502𝔂\bscryMathematical Bold Script Small Y
    U+1D503𝔃\bscrzMathematical Bold Script Small Z
    U+1D504𝔄\frakAMathematical Fraktur Capital A
    U+1D505𝔅\frakBMathematical Fraktur Capital B
    U+1D507𝔇\frakDMathematical Fraktur Capital D
    U+1D508𝔈\frakEMathematical Fraktur Capital E
    U+1D509𝔉\frakFMathematical Fraktur Capital F
    U+1D50A𝔊\frakGMathematical Fraktur Capital G
    U+1D50D𝔍\frakJMathematical Fraktur Capital J
    U+1D50E𝔎\frakKMathematical Fraktur Capital K
    U+1D50F𝔏\frakLMathematical Fraktur Capital L
    U+1D510𝔐\frakMMathematical Fraktur Capital M
    U+1D511𝔑\frakNMathematical Fraktur Capital N
    U+1D512𝔒\frakOMathematical Fraktur Capital O
    U+1D513𝔓\frakPMathematical Fraktur Capital P
    U+1D514𝔔\frakQMathematical Fraktur Capital Q
    U+1D516𝔖\frakSMathematical Fraktur Capital S
    U+1D517𝔗\frakTMathematical Fraktur Capital T
    U+1D518𝔘\frakUMathematical Fraktur Capital U
    U+1D519𝔙\frakVMathematical Fraktur Capital V
    U+1D51A𝔚\frakWMathematical Fraktur Capital W
    U+1D51B𝔛\frakXMathematical Fraktur Capital X
    U+1D51C𝔜\frakYMathematical Fraktur Capital Y
    U+1D51E𝔞\frakaMathematical Fraktur Small A
    U+1D51F𝔟\frakbMathematical Fraktur Small B
    U+1D520𝔠\frakcMathematical Fraktur Small C
    U+1D521𝔡\frakdMathematical Fraktur Small D
    U+1D522𝔢\frakeMathematical Fraktur Small E
    U+1D523𝔣\frakfMathematical Fraktur Small F
    U+1D524𝔤\frakgMathematical Fraktur Small G
    U+1D525𝔥\frakhMathematical Fraktur Small H
    U+1D526𝔦\frakiMathematical Fraktur Small I
    U+1D527𝔧\frakjMathematical Fraktur Small J
    U+1D528𝔨\frakkMathematical Fraktur Small K
    U+1D529𝔩\fraklMathematical Fraktur Small L
    U+1D52A𝔪\frakmMathematical Fraktur Small M
    U+1D52B𝔫\fraknMathematical Fraktur Small N
    U+1D52C𝔬\frakoMathematical Fraktur Small O
    U+1D52D𝔭\frakpMathematical Fraktur Small P
    U+1D52E𝔮\frakqMathematical Fraktur Small Q
    U+1D52F𝔯\frakrMathematical Fraktur Small R
    U+1D530𝔰\fraksMathematical Fraktur Small S
    U+1D531𝔱\fraktMathematical Fraktur Small T
    U+1D532𝔲\frakuMathematical Fraktur Small U
    U+1D533𝔳\frakvMathematical Fraktur Small V
    U+1D534𝔴\frakwMathematical Fraktur Small W
    U+1D535𝔵\frakxMathematical Fraktur Small X
    U+1D536𝔶\frakyMathematical Fraktur Small Y
    U+1D537𝔷\frakzMathematical Fraktur Small Z
    U+1D538𝔸\bbAMathematical Double-Struck Capital A
    U+1D539𝔹\bbBMathematical Double-Struck Capital B
    U+1D53B𝔻\bbDMathematical Double-Struck Capital D
    U+1D53C𝔼\bbEMathematical Double-Struck Capital E
    U+1D53D𝔽\bbFMathematical Double-Struck Capital F
    U+1D53E𝔾\bbGMathematical Double-Struck Capital G
    U+1D540𝕀\bbIMathematical Double-Struck Capital I
    U+1D541𝕁\bbJMathematical Double-Struck Capital J
    U+1D542𝕂\bbKMathematical Double-Struck Capital K
    U+1D543𝕃\bbLMathematical Double-Struck Capital L
    U+1D544𝕄\bbMMathematical Double-Struck Capital M
    U+1D546𝕆\bbOMathematical Double-Struck Capital O
    U+1D54A𝕊\bbSMathematical Double-Struck Capital S
    U+1D54B𝕋\bbTMathematical Double-Struck Capital T
    U+1D54C𝕌\bbUMathematical Double-Struck Capital U
    U+1D54D𝕍\bbVMathematical Double-Struck Capital V
    U+1D54E𝕎\bbWMathematical Double-Struck Capital W
    U+1D54F𝕏\bbXMathematical Double-Struck Capital X
    U+1D550𝕐\bbYMathematical Double-Struck Capital Y
    U+1D552𝕒\bbaMathematical Double-Struck Small A
    U+1D553𝕓\bbbMathematical Double-Struck Small B
    U+1D554𝕔\bbcMathematical Double-Struck Small C
    U+1D555𝕕\bbdMathematical Double-Struck Small D
    U+1D556𝕖\bbeMathematical Double-Struck Small E
    U+1D557𝕗\bbfMathematical Double-Struck Small F
    U+1D558𝕘\bbgMathematical Double-Struck Small G
    U+1D559𝕙\bbhMathematical Double-Struck Small H
    U+1D55A𝕚\bbiMathematical Double-Struck Small I
    U+1D55B𝕛\bbjMathematical Double-Struck Small J
    U+1D55C𝕜\bbkMathematical Double-Struck Small K
    U+1D55D𝕝\bblMathematical Double-Struck Small L
    U+1D55E𝕞\bbmMathematical Double-Struck Small M
    U+1D55F𝕟\bbnMathematical Double-Struck Small N
    U+1D560𝕠\bboMathematical Double-Struck Small O
    U+1D561𝕡\bbpMathematical Double-Struck Small P
    U+1D562𝕢\bbqMathematical Double-Struck Small Q
    U+1D563𝕣\bbrMathematical Double-Struck Small R
    U+1D564𝕤\bbsMathematical Double-Struck Small S
    U+1D565𝕥\bbtMathematical Double-Struck Small T
    U+1D566𝕦\bbuMathematical Double-Struck Small U
    U+1D567𝕧\bbvMathematical Double-Struck Small V
    U+1D568𝕨\bbwMathematical Double-Struck Small W
    U+1D569𝕩\bbxMathematical Double-Struck Small X
    U+1D56A𝕪\bbyMathematical Double-Struck Small Y
    U+1D56B𝕫\bbzMathematical Double-Struck Small Z
    U+1D56C𝕬\bfrakAMathematical Bold Fraktur Capital A
    U+1D56D𝕭\bfrakBMathematical Bold Fraktur Capital B
    U+1D56E𝕮\bfrakCMathematical Bold Fraktur Capital C
    U+1D56F𝕯\bfrakDMathematical Bold Fraktur Capital D
    U+1D570𝕰\bfrakEMathematical Bold Fraktur Capital E
    U+1D571𝕱\bfrakFMathematical Bold Fraktur Capital F
    U+1D572𝕲\bfrakGMathematical Bold Fraktur Capital G
    U+1D573𝕳\bfrakHMathematical Bold Fraktur Capital H
    U+1D574𝕴\bfrakIMathematical Bold Fraktur Capital I
    U+1D575𝕵\bfrakJMathematical Bold Fraktur Capital J
    U+1D576𝕶\bfrakKMathematical Bold Fraktur Capital K
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    U+1D578𝕸\bfrakMMathematical Bold Fraktur Capital M
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    U+1D6AA𝚪\bfGammaMathematical Bold Capital Gamma
    U+1D6AB𝚫\bfDeltaMathematical Bold Capital Delta
    U+1D6AC𝚬\bfEpsilonMathematical Bold Capital Epsilon
    U+1D6AD𝚭\bfZetaMathematical Bold Capital Zeta
    U+1D6AE𝚮\bfEtaMathematical Bold Capital Eta
    U+1D6AF𝚯\bfThetaMathematical Bold Capital Theta
    U+1D6B0𝚰\bfIotaMathematical Bold Capital Iota
    U+1D6B1𝚱\bfKappaMathematical Bold Capital Kappa
    U+1D6B2𝚲\bfLambdaMathematical Bold Capital Lamda
    U+1D6B3𝚳\bfMuMathematical Bold Capital Mu
    U+1D6B4𝚴\bfNuMathematical Bold Capital Nu
    U+1D6B5𝚵\bfXiMathematical Bold Capital Xi
    U+1D6B6𝚶\bfOmicronMathematical Bold Capital Omicron
    U+1D6B7𝚷\bfPiMathematical Bold Capital Pi
    U+1D6B8𝚸\bfRhoMathematical Bold Capital Rho
    U+1D6B9𝚹\bfvarThetaMathematical Bold Capital Theta Symbol
    U+1D6BA𝚺\bfSigmaMathematical Bold Capital Sigma
    U+1D6BB𝚻\bfTauMathematical Bold Capital Tau
    U+1D6BC𝚼\bfUpsilonMathematical Bold Capital Upsilon
    U+1D6BD𝚽\bfPhiMathematical Bold Capital Phi
    U+1D6BE𝚾\bfChiMathematical Bold Capital Chi
    U+1D6BF𝚿\bfPsiMathematical Bold Capital Psi
    U+1D6C0𝛀\bfOmegaMathematical Bold Capital Omega
    U+1D6C1𝛁\bfnablaMathematical Bold Nabla
    U+1D6C2𝛂\bfalphaMathematical Bold Small Alpha
    U+1D6C3𝛃\bfbetaMathematical Bold Small Beta
    U+1D6C4𝛄\bfgammaMathematical Bold Small Gamma
    U+1D6C5𝛅\bfdeltaMathematical Bold Small Delta
    U+1D6C6𝛆\bfvarepsilonMathematical Bold Small Epsilon
    U+1D6C7𝛇\bfzetaMathematical Bold Small Zeta
    U+1D6C8𝛈\bfetaMathematical Bold Small Eta
    U+1D6C9𝛉\bfthetaMathematical Bold Small Theta
    U+1D6CA𝛊\bfiotaMathematical Bold Small Iota
    U+1D6CB𝛋\bfkappaMathematical Bold Small Kappa
    U+1D6CC𝛌\bflambdaMathematical Bold Small Lamda
    U+1D6CD𝛍\bfmuMathematical Bold Small Mu
    U+1D6CE𝛎\bfnuMathematical Bold Small Nu
    U+1D6CF𝛏\bfxiMathematical Bold Small Xi
    U+1D6D0𝛐\bfomicronMathematical Bold Small Omicron
    U+1D6D1𝛑\bfpiMathematical Bold Small Pi
    U+1D6D2𝛒\bfrhoMathematical Bold Small Rho
    U+1D6D3𝛓\bfvarsigmaMathematical Bold Small Final Sigma
    U+1D6D4𝛔\bfsigmaMathematical Bold Small Sigma
    U+1D6D5𝛕\bftauMathematical Bold Small Tau
    U+1D6D6𝛖\bfupsilonMathematical Bold Small Upsilon
    U+1D6D7𝛗\bfvarphiMathematical Bold Small Phi
    U+1D6D8𝛘\bfchiMathematical Bold Small Chi
    U+1D6D9𝛙\bfpsiMathematical Bold Small Psi
    U+1D6DA𝛚\bfomegaMathematical Bold Small Omega
    U+1D6DB𝛛\bfpartialMathematical Bold Partial Differential
    U+1D6DC𝛜\bfepsilonMathematical Bold Epsilon Symbol
    U+1D6DD𝛝\bfvarthetaMathematical Bold Theta Symbol
    U+1D6DE𝛞\bfvarkappaMathematical Bold Kappa Symbol
    U+1D6DF𝛟\bfphiMathematical Bold Phi Symbol
    U+1D6E0𝛠\bfvarrhoMathematical Bold Rho Symbol
    U+1D6E1𝛡\bfvarpiMathematical Bold Pi Symbol
    U+1D6E2𝛢\itAlphaMathematical Italic Capital Alpha
    U+1D6E3𝛣\itBetaMathematical Italic Capital Beta
    U+1D6E4𝛤\itGammaMathematical Italic Capital Gamma
    U+1D6E5𝛥\itDeltaMathematical Italic Capital Delta
    U+1D6E6𝛦\itEpsilonMathematical Italic Capital Epsilon
    U+1D6E7𝛧\itZetaMathematical Italic Capital Zeta
    U+1D6E8𝛨\itEtaMathematical Italic Capital Eta
    U+1D6E9𝛩\itThetaMathematical Italic Capital Theta
    U+1D6EA𝛪\itIotaMathematical Italic Capital Iota
    U+1D6EB𝛫\itKappaMathematical Italic Capital Kappa
    U+1D6EC𝛬\itLambdaMathematical Italic Capital Lamda
    U+1D6ED𝛭\itMuMathematical Italic Capital Mu
    U+1D6EE𝛮\itNuMathematical Italic Capital Nu
    U+1D6EF𝛯\itXiMathematical Italic Capital Xi
    U+1D6F0𝛰\itOmicronMathematical Italic Capital Omicron
    U+1D6F1𝛱\itPiMathematical Italic Capital Pi
    U+1D6F2𝛲\itRhoMathematical Italic Capital Rho
    U+1D6F3𝛳\itvarThetaMathematical Italic Capital Theta Symbol
    U+1D6F4𝛴\itSigmaMathematical Italic Capital Sigma
    U+1D6F5𝛵\itTauMathematical Italic Capital Tau
    U+1D6F6𝛶\itUpsilonMathematical Italic Capital Upsilon
    U+1D6F7𝛷\itPhiMathematical Italic Capital Phi
    U+1D6F8𝛸\itChiMathematical Italic Capital Chi
    U+1D6F9𝛹\itPsiMathematical Italic Capital Psi
    U+1D6FA𝛺\itOmegaMathematical Italic Capital Omega
    U+1D6FB𝛻\itnablaMathematical Italic Nabla
    U+1D6FC𝛼\italphaMathematical Italic Small Alpha
    U+1D6FD𝛽\itbetaMathematical Italic Small Beta
    U+1D6FE𝛾\itgammaMathematical Italic Small Gamma
    U+1D6FF𝛿\itdeltaMathematical Italic Small Delta
    U+1D700𝜀\itvarepsilonMathematical Italic Small Epsilon
    U+1D701𝜁\itzetaMathematical Italic Small Zeta
    U+1D702𝜂\itetaMathematical Italic Small Eta
    U+1D703𝜃\itthetaMathematical Italic Small Theta
    U+1D704𝜄\itiotaMathematical Italic Small Iota
    U+1D705𝜅\itkappaMathematical Italic Small Kappa
    U+1D706𝜆\itlambdaMathematical Italic Small Lamda
    U+1D707𝜇\itmuMathematical Italic Small Mu
    U+1D708𝜈\itnuMathematical Italic Small Nu
    U+1D709𝜉\itxiMathematical Italic Small Xi
    U+1D70A𝜊\itomicronMathematical Italic Small Omicron
    U+1D70B𝜋\itpiMathematical Italic Small Pi
    U+1D70C𝜌\itrhoMathematical Italic Small Rho
    U+1D70D𝜍\itvarsigmaMathematical Italic Small Final Sigma
    U+1D70E𝜎\itsigmaMathematical Italic Small Sigma
    U+1D70F𝜏\ittauMathematical Italic Small Tau
    U+1D710𝜐\itupsilonMathematical Italic Small Upsilon
    U+1D711𝜑\itvarphiMathematical Italic Small Phi
    U+1D712𝜒\itchiMathematical Italic Small Chi
    U+1D713𝜓\itpsiMathematical Italic Small Psi
    U+1D714𝜔\itomegaMathematical Italic Small Omega
    U+1D715𝜕\itpartialMathematical Italic Partial Differential
    U+1D716𝜖\itepsilonMathematical Italic Epsilon Symbol
    U+1D717𝜗\itvarthetaMathematical Italic Theta Symbol
    U+1D718𝜘\itvarkappaMathematical Italic Kappa Symbol
    U+1D719𝜙\itphiMathematical Italic Phi Symbol
    U+1D71A𝜚\itvarrhoMathematical Italic Rho Symbol
    U+1D71B𝜛\itvarpiMathematical Italic Pi Symbol
    U+1D71C𝜜\biAlphaMathematical Bold Italic Capital Alpha
    U+1D71D𝜝\biBetaMathematical Bold Italic Capital Beta
    U+1D71E𝜞\biGammaMathematical Bold Italic Capital Gamma
    U+1D71F𝜟\biDeltaMathematical Bold Italic Capital Delta
    U+1D720𝜠\biEpsilonMathematical Bold Italic Capital Epsilon
    U+1D721𝜡\biZetaMathematical Bold Italic Capital Zeta
    U+1D722𝜢\biEtaMathematical Bold Italic Capital Eta
    U+1D723𝜣\biThetaMathematical Bold Italic Capital Theta
    U+1D724𝜤\biIotaMathematical Bold Italic Capital Iota
    U+1D725𝜥\biKappaMathematical Bold Italic Capital Kappa
    U+1D726𝜦\biLambdaMathematical Bold Italic Capital Lamda
    U+1D727𝜧\biMuMathematical Bold Italic Capital Mu
    U+1D728𝜨\biNuMathematical Bold Italic Capital Nu
    U+1D729𝜩\biXiMathematical Bold Italic Capital Xi
    U+1D72A𝜪\biOmicronMathematical Bold Italic Capital Omicron
    U+1D72B𝜫\biPiMathematical Bold Italic Capital Pi
    U+1D72C𝜬\biRhoMathematical Bold Italic Capital Rho
    U+1D72D𝜭\bivarThetaMathematical Bold Italic Capital Theta Symbol
    U+1D72E𝜮\biSigmaMathematical Bold Italic Capital Sigma
    U+1D72F𝜯\biTauMathematical Bold Italic Capital Tau
    U+1D730𝜰\biUpsilonMathematical Bold Italic Capital Upsilon
    U+1D731𝜱\biPhiMathematical Bold Italic Capital Phi
    U+1D732𝜲\biChiMathematical Bold Italic Capital Chi
    U+1D733𝜳\biPsiMathematical Bold Italic Capital Psi
    U+1D734𝜴\biOmegaMathematical Bold Italic Capital Omega
    U+1D735𝜵\binablaMathematical Bold Italic Nabla
    U+1D736𝜶\bialphaMathematical Bold Italic Small Alpha
    U+1D737𝜷\bibetaMathematical Bold Italic Small Beta
    U+1D738𝜸\bigammaMathematical Bold Italic Small Gamma
    U+1D739𝜹\bideltaMathematical Bold Italic Small Delta
    U+1D73A𝜺\bivarepsilonMathematical Bold Italic Small Epsilon
    U+1D73B𝜻\bizetaMathematical Bold Italic Small Zeta
    U+1D73C𝜼\bietaMathematical Bold Italic Small Eta
    U+1D73D𝜽\bithetaMathematical Bold Italic Small Theta
    U+1D73E𝜾\biiotaMathematical Bold Italic Small Iota
    U+1D73F𝜿\bikappaMathematical Bold Italic Small Kappa
    U+1D740𝝀\bilambdaMathematical Bold Italic Small Lamda
    U+1D741𝝁\bimuMathematical Bold Italic Small Mu
    U+1D742𝝂\binuMathematical Bold Italic Small Nu
    U+1D743𝝃\bixiMathematical Bold Italic Small Xi
    U+1D744𝝄\biomicronMathematical Bold Italic Small Omicron
    U+1D745𝝅\bipiMathematical Bold Italic Small Pi
    U+1D746𝝆\birhoMathematical Bold Italic Small Rho
    U+1D747𝝇\bivarsigmaMathematical Bold Italic Small Final Sigma
    U+1D748𝝈\bisigmaMathematical Bold Italic Small Sigma
    U+1D749𝝉\bitauMathematical Bold Italic Small Tau
    U+1D74A𝝊\biupsilonMathematical Bold Italic Small Upsilon
    U+1D74B𝝋\bivarphiMathematical Bold Italic Small Phi
    U+1D74C𝝌\bichiMathematical Bold Italic Small Chi
    U+1D74D𝝍\bipsiMathematical Bold Italic Small Psi
    U+1D74E𝝎\biomegaMathematical Bold Italic Small Omega
    U+1D74F𝝏\bipartialMathematical Bold Italic Partial Differential
    U+1D750𝝐\biepsilonMathematical Bold Italic Epsilon Symbol
    U+1D751𝝑\bivarthetaMathematical Bold Italic Theta Symbol
    U+1D752𝝒\bivarkappaMathematical Bold Italic Kappa Symbol
    U+1D753𝝓\biphiMathematical Bold Italic Phi Symbol
    U+1D754𝝔\bivarrhoMathematical Bold Italic Rho Symbol
    U+1D755𝝕\bivarpiMathematical Bold Italic Pi Symbol
    U+1D756𝝖\bsansAlphaMathematical Sans-Serif Bold Capital Alpha
    U+1D757𝝗\bsansBetaMathematical Sans-Serif Bold Capital Beta
    U+1D758𝝘\bsansGammaMathematical Sans-Serif Bold Capital Gamma
    U+1D759𝝙\bsansDeltaMathematical Sans-Serif Bold Capital Delta
    U+1D75A𝝚\bsansEpsilonMathematical Sans-Serif Bold Capital Epsilon
    U+1D75B𝝛\bsansZetaMathematical Sans-Serif Bold Capital Zeta
    U+1D75C𝝜\bsansEtaMathematical Sans-Serif Bold Capital Eta
    U+1D75D𝝝\bsansThetaMathematical Sans-Serif Bold Capital Theta
    U+1D75E𝝞\bsansIotaMathematical Sans-Serif Bold Capital Iota
    U+1D75F𝝟\bsansKappaMathematical Sans-Serif Bold Capital Kappa
    U+1D760𝝠\bsansLambdaMathematical Sans-Serif Bold Capital Lamda
    U+1D761𝝡\bsansMuMathematical Sans-Serif Bold Capital Mu
    U+1D762𝝢\bsansNuMathematical Sans-Serif Bold Capital Nu
    U+1D763𝝣\bsansXiMathematical Sans-Serif Bold Capital Xi
    U+1D764𝝤\bsansOmicronMathematical Sans-Serif Bold Capital Omicron
    U+1D765𝝥\bsansPiMathematical Sans-Serif Bold Capital Pi
    U+1D766𝝦\bsansRhoMathematical Sans-Serif Bold Capital Rho
    U+1D767𝝧\bsansvarThetaMathematical Sans-Serif Bold Capital Theta Symbol
    U+1D768𝝨\bsansSigmaMathematical Sans-Serif Bold Capital Sigma
    U+1D769𝝩\bsansTauMathematical Sans-Serif Bold Capital Tau
    U+1D76A𝝪\bsansUpsilonMathematical Sans-Serif Bold Capital Upsilon
    U+1D76B𝝫\bsansPhiMathematical Sans-Serif Bold Capital Phi
    U+1D76C𝝬\bsansChiMathematical Sans-Serif Bold Capital Chi
    U+1D76D𝝭\bsansPsiMathematical Sans-Serif Bold Capital Psi
    U+1D76E𝝮\bsansOmegaMathematical Sans-Serif Bold Capital Omega
    U+1D76F𝝯\bsansnablaMathematical Sans-Serif Bold Nabla
    U+1D770𝝰\bsansalphaMathematical Sans-Serif Bold Small Alpha
    U+1D771𝝱\bsansbetaMathematical Sans-Serif Bold Small Beta
    U+1D772𝝲\bsansgammaMathematical Sans-Serif Bold Small Gamma
    U+1D773𝝳\bsansdeltaMathematical Sans-Serif Bold Small Delta
    U+1D774𝝴\bsansvarepsilonMathematical Sans-Serif Bold Small Epsilon
    U+1D775𝝵\bsanszetaMathematical Sans-Serif Bold Small Zeta
    U+1D776𝝶\bsansetaMathematical Sans-Serif Bold Small Eta
    U+1D777𝝷\bsansthetaMathematical Sans-Serif Bold Small Theta
    U+1D778𝝸\bsansiotaMathematical Sans-Serif Bold Small Iota
    U+1D779𝝹\bsanskappaMathematical Sans-Serif Bold Small Kappa
    U+1D77A𝝺\bsanslambdaMathematical Sans-Serif Bold Small Lamda
    U+1D77B𝝻\bsansmuMathematical Sans-Serif Bold Small Mu
    U+1D77C𝝼\bsansnuMathematical Sans-Serif Bold Small Nu
    U+1D77D𝝽\bsansxiMathematical Sans-Serif Bold Small Xi
    U+1D77E𝝾\bsansomicronMathematical Sans-Serif Bold Small Omicron
    U+1D77F𝝿\bsanspiMathematical Sans-Serif Bold Small Pi
    U+1D780𝞀\bsansrhoMathematical Sans-Serif Bold Small Rho
    U+1D781𝞁\bsansvarsigmaMathematical Sans-Serif Bold Small Final Sigma
    U+1D782𝞂\bsanssigmaMathematical Sans-Serif Bold Small Sigma
    U+1D783𝞃\bsanstauMathematical Sans-Serif Bold Small Tau
    U+1D784𝞄\bsansupsilonMathematical Sans-Serif Bold Small Upsilon
    U+1D785𝞅\bsansvarphiMathematical Sans-Serif Bold Small Phi
    U+1D786𝞆\bsanschiMathematical Sans-Serif Bold Small Chi
    U+1D787𝞇\bsanspsiMathematical Sans-Serif Bold Small Psi
    U+1D788𝞈\bsansomegaMathematical Sans-Serif Bold Small Omega
    U+1D789𝞉\bsanspartialMathematical Sans-Serif Bold Partial Differential
    U+1D78A𝞊\bsansepsilonMathematical Sans-Serif Bold Epsilon Symbol
    U+1D78B𝞋\bsansvarthetaMathematical Sans-Serif Bold Theta Symbol
    U+1D78C𝞌\bsansvarkappaMathematical Sans-Serif Bold Kappa Symbol
    U+1D78D𝞍\bsansphiMathematical Sans-Serif Bold Phi Symbol
    U+1D78E𝞎\bsansvarrhoMathematical Sans-Serif Bold Rho Symbol
    U+1D78F𝞏\bsansvarpiMathematical Sans-Serif Bold Pi Symbol
    U+1D790𝞐\bisansAlphaMathematical Sans-Serif Bold Italic Capital Alpha
    U+1D791𝞑\bisansBetaMathematical Sans-Serif Bold Italic Capital Beta
    U+1D792𝞒\bisansGammaMathematical Sans-Serif Bold Italic Capital Gamma
    U+1D793𝞓\bisansDeltaMathematical Sans-Serif Bold Italic Capital Delta
    U+1D794𝞔\bisansEpsilonMathematical Sans-Serif Bold Italic Capital Epsilon
    U+1D795𝞕\bisansZetaMathematical Sans-Serif Bold Italic Capital Zeta
    U+1D796𝞖\bisansEtaMathematical Sans-Serif Bold Italic Capital Eta
    U+1D797𝞗\bisansThetaMathematical Sans-Serif Bold Italic Capital Theta
    U+1D798𝞘\bisansIotaMathematical Sans-Serif Bold Italic Capital Iota
    U+1D799𝞙\bisansKappaMathematical Sans-Serif Bold Italic Capital Kappa
    U+1D79A𝞚\bisansLambdaMathematical Sans-Serif Bold Italic Capital Lamda
    U+1D79B𝞛\bisansMuMathematical Sans-Serif Bold Italic Capital Mu
    U+1D79C𝞜\bisansNuMathematical Sans-Serif Bold Italic Capital Nu
    U+1D79D𝞝\bisansXiMathematical Sans-Serif Bold Italic Capital Xi
    U+1D79E𝞞\bisansOmicronMathematical Sans-Serif Bold Italic Capital Omicron
    U+1D79F𝞟\bisansPiMathematical Sans-Serif Bold Italic Capital Pi
    U+1D7A0𝞠\bisansRhoMathematical Sans-Serif Bold Italic Capital Rho
    U+1D7A1𝞡\bisansvarThetaMathematical Sans-Serif Bold Italic Capital Theta Symbol
    U+1D7A2𝞢\bisansSigmaMathematical Sans-Serif Bold Italic Capital Sigma
    U+1D7A3𝞣\bisansTauMathematical Sans-Serif Bold Italic Capital Tau
    U+1D7A4𝞤\bisansUpsilonMathematical Sans-Serif Bold Italic Capital Upsilon
    U+1D7A5𝞥\bisansPhiMathematical Sans-Serif Bold Italic Capital Phi
    U+1D7A6𝞦\bisansChiMathematical Sans-Serif Bold Italic Capital Chi
    U+1D7A7𝞧\bisansPsiMathematical Sans-Serif Bold Italic Capital Psi
    U+1D7A8𝞨\bisansOmegaMathematical Sans-Serif Bold Italic Capital Omega
    U+1D7A9𝞩\bisansnablaMathematical Sans-Serif Bold Italic Nabla
    U+1D7AA𝞪\bisansalphaMathematical Sans-Serif Bold Italic Small Alpha
    U+1D7AB𝞫\bisansbetaMathematical Sans-Serif Bold Italic Small Beta
    U+1D7AC𝞬\bisansgammaMathematical Sans-Serif Bold Italic Small Gamma
    U+1D7AD𝞭\bisansdeltaMathematical Sans-Serif Bold Italic Small Delta
    U+1D7AE𝞮\bisansvarepsilonMathematical Sans-Serif Bold Italic Small Epsilon
    U+1D7AF𝞯\bisanszetaMathematical Sans-Serif Bold Italic Small Zeta
    U+1D7B0𝞰\bisansetaMathematical Sans-Serif Bold Italic Small Eta
    U+1D7B1𝞱\bisansthetaMathematical Sans-Serif Bold Italic Small Theta
    U+1D7B2𝞲\bisansiotaMathematical Sans-Serif Bold Italic Small Iota
    U+1D7B3𝞳\bisanskappaMathematical Sans-Serif Bold Italic Small Kappa
    U+1D7B4𝞴\bisanslambdaMathematical Sans-Serif Bold Italic Small Lamda
    U+1D7B5𝞵\bisansmuMathematical Sans-Serif Bold Italic Small Mu
    U+1D7B6𝞶\bisansnuMathematical Sans-Serif Bold Italic Small Nu
    U+1D7B7𝞷\bisansxiMathematical Sans-Serif Bold Italic Small Xi
    U+1D7B8𝞸\bisansomicronMathematical Sans-Serif Bold Italic Small Omicron
    U+1D7B9𝞹\bisanspiMathematical Sans-Serif Bold Italic Small Pi
    U+1D7BA𝞺\bisansrhoMathematical Sans-Serif Bold Italic Small Rho
    U+1D7BB𝞻\bisansvarsigmaMathematical Sans-Serif Bold Italic Small Final Sigma
    U+1D7BC𝞼\bisanssigmaMathematical Sans-Serif Bold Italic Small Sigma
    U+1D7BD𝞽\bisanstauMathematical Sans-Serif Bold Italic Small Tau
    U+1D7BE𝞾\bisansupsilonMathematical Sans-Serif Bold Italic Small Upsilon
    U+1D7BF𝞿\bisansvarphiMathematical Sans-Serif Bold Italic Small Phi
    U+1D7C0𝟀\bisanschiMathematical Sans-Serif Bold Italic Small Chi
    U+1D7C1𝟁\bisanspsiMathematical Sans-Serif Bold Italic Small Psi
    U+1D7C2𝟂\bisansomegaMathematical Sans-Serif Bold Italic Small Omega
    U+1D7C3𝟃\bisanspartialMathematical Sans-Serif Bold Italic Partial Differential
    U+1D7C4𝟄\bisansepsilonMathematical Sans-Serif Bold Italic Epsilon Symbol
    U+1D7C5𝟅\bisansvarthetaMathematical Sans-Serif Bold Italic Theta Symbol
    U+1D7C6𝟆\bisansvarkappaMathematical Sans-Serif Bold Italic Kappa Symbol
    U+1D7C7𝟇\bisansphiMathematical Sans-Serif Bold Italic Phi Symbol
    U+1D7C8𝟈\bisansvarrhoMathematical Sans-Serif Bold Italic Rho Symbol
    U+1D7C9𝟉\bisansvarpiMathematical Sans-Serif Bold Italic Pi Symbol
    U+1D7CA𝟊\bfDigammaMathematical Bold Capital Digamma
    U+1D7CB𝟋\bfdigammaMathematical Bold Small Digamma
    U+1D7CE𝟎\bfzeroMathematical Bold Digit Zero
    U+1D7CF𝟏\bfoneMathematical Bold Digit One
    U+1D7D0𝟐\bftwoMathematical Bold Digit Two
    U+1D7D1𝟑\bfthreeMathematical Bold Digit Three
    U+1D7D2𝟒\bffourMathematical Bold Digit Four
    U+1D7D3𝟓\bffiveMathematical Bold Digit Five
    U+1D7D4𝟔\bfsixMathematical Bold Digit Six
    U+1D7D5𝟕\bfsevenMathematical Bold Digit Seven
    U+1D7D6𝟖\bfeightMathematical Bold Digit Eight
    U+1D7D7𝟗\bfnineMathematical Bold Digit Nine
    U+1D7D8𝟘\bbzeroMathematical Double-Struck Digit Zero
    U+1D7D9𝟙\bboneMathematical Double-Struck Digit One
    U+1D7DA𝟚\bbtwoMathematical Double-Struck Digit Two
    U+1D7DB𝟛\bbthreeMathematical Double-Struck Digit Three
    U+1D7DC𝟜\bbfourMathematical Double-Struck Digit Four
    U+1D7DD𝟝\bbfiveMathematical Double-Struck Digit Five
    U+1D7DE𝟞\bbsixMathematical Double-Struck Digit Six
    U+1D7DF𝟟\bbsevenMathematical Double-Struck Digit Seven
    U+1D7E0𝟠\bbeightMathematical Double-Struck Digit Eight
    U+1D7E1𝟡\bbnineMathematical Double-Struck Digit Nine
    U+1D7E2𝟢\sanszeroMathematical Sans-Serif Digit Zero
    U+1D7E3𝟣\sansoneMathematical Sans-Serif Digit One
    U+1D7E4𝟤\sanstwoMathematical Sans-Serif Digit Two
    U+1D7E5𝟥\sansthreeMathematical Sans-Serif Digit Three
    U+1D7E6𝟦\sansfourMathematical Sans-Serif Digit Four
    U+1D7E7𝟧\sansfiveMathematical Sans-Serif Digit Five
    U+1D7E8𝟨\sanssixMathematical Sans-Serif Digit Six
    U+1D7E9𝟩\sanssevenMathematical Sans-Serif Digit Seven
    U+1D7EA𝟪\sanseightMathematical Sans-Serif Digit Eight
    U+1D7EB𝟫\sansnineMathematical Sans-Serif Digit Nine
    U+1D7EC𝟬\bsanszeroMathematical Sans-Serif Bold Digit Zero
    U+1D7ED𝟭\bsansoneMathematical Sans-Serif Bold Digit One
    U+1D7EE𝟮\bsanstwoMathematical Sans-Serif Bold Digit Two
    U+1D7EF𝟯\bsansthreeMathematical Sans-Serif Bold Digit Three
    U+1D7F0𝟰\bsansfourMathematical Sans-Serif Bold Digit Four
    U+1D7F1𝟱\bsansfiveMathematical Sans-Serif Bold Digit Five
    U+1D7F2𝟲\bsanssixMathematical Sans-Serif Bold Digit Six
    U+1D7F3𝟳\bsanssevenMathematical Sans-Serif Bold Digit Seven
    U+1D7F4𝟴\bsanseightMathematical Sans-Serif Bold Digit Eight
    U+1D7F5𝟵\bsansnineMathematical Sans-Serif Bold Digit Nine
    U+1D7F6𝟶\ttzeroMathematical Monospace Digit Zero
    U+1D7F7𝟷\ttoneMathematical Monospace Digit One
    U+1D7F8𝟸\tttwoMathematical Monospace Digit Two
    U+1D7F9𝟹\ttthreeMathematical Monospace Digit Three
    U+1D7FA𝟺\ttfourMathematical Monospace Digit Four
    U+1D7FB𝟻\ttfiveMathematical Monospace Digit Five
    U+1D7FC𝟼\ttsixMathematical Monospace Digit Six
    U+1D7FD𝟽\ttsevenMathematical Monospace Digit Seven
    U+1D7FE𝟾\tteightMathematical Monospace Digit Eight
    U+1D7FF𝟿\ttnineMathematical Monospace Digit Nine
    U+1F004🀄\:mahjong:Mahjong Tile Red Dragon
    U+1F0CF🃏\:black_joker:Playing Card Black Joker
    U+1F170🅰\:a:Negative Squared Latin Capital Letter A
    U+1F171🅱\:b:Negative Squared Latin Capital Letter B
    U+1F17E🅾\:o2:Negative Squared Latin Capital Letter O
    U+1F17F🅿\:parking:Negative Squared Latin Capital Letter P
    U+1F18E🆎\:ab:Negative Squared Ab
    U+1F191🆑\:cl:Squared Cl
    U+1F192🆒\:cool:Squared Cool
    U+1F193🆓\:free:Squared Free
    U+1F194🆔\:id:Squared Id
    U+1F195🆕\:new:Squared New
    U+1F196🆖\:ng:Squared Ng
    U+1F197🆗\:ok:Squared Ok
    U+1F198🆘\:sos:Squared Sos
    U+1F199🆙\:up:Squared Up With Exclamation Mark
    U+1F19A🆚\:vs:Squared Vs
    U+1F201🈁\:koko:Squared Katakana Koko
    U+1F202🈂\:sa:Squared Katakana Sa
    U+1F21A🈚\:u7121:Squared Cjk Unified Ideograph-7121
    U+1F22F🈯\:u6307:Squared Cjk Unified Ideograph-6307
    U+1F232🈲\:u7981:Squared Cjk Unified Ideograph-7981
    U+1F233🈳\:u7a7a:Squared Cjk Unified Ideograph-7A7A
    U+1F234🈴\:u5408:Squared Cjk Unified Ideograph-5408
    U+1F235🈵\:u6e80:Squared Cjk Unified Ideograph-6E80
    U+1F236🈶\:u6709:Squared Cjk Unified Ideograph-6709
    U+1F237🈷\:u6708:Squared Cjk Unified Ideograph-6708
    U+1F238🈸\:u7533:Squared Cjk Unified Ideograph-7533
    U+1F239🈹\:u5272:Squared Cjk Unified Ideograph-5272
    U+1F23A🈺\:u55b6:Squared Cjk Unified Ideograph-55B6
    U+1F250🉐\:ideograph_advantage:Circled Ideograph Advantage
    U+1F251🉑\:accept:Circled Ideograph Accept
    U+1F300🌀\:cyclone:Cyclone
    U+1F301🌁\:foggy:Foggy
    U+1F302🌂\:closed_umbrella:Closed Umbrella
    U+1F303🌃\:night_with_stars:Night With Stars
    U+1F304🌄\:sunrise_over_mountains:Sunrise Over Mountains
    U+1F305🌅\:sunrise:Sunrise
    U+1F306🌆\:city_sunset:Cityscape At Dusk
    U+1F307🌇\:city_sunrise:Sunset Over Buildings
    U+1F308🌈\:rainbow:Rainbow
    U+1F309🌉\:bridge_at_night:Bridge At Night
    U+1F30A🌊\:ocean:Water Wave
    U+1F30B🌋\:volcano:Volcano
    U+1F30C🌌\:milky_way:Milky Way
    U+1F30D🌍\:earth_africa:Earth Globe Europe-Africa
    U+1F30E🌎\:earth_americas:Earth Globe Americas
    U+1F30F🌏\:earth_asia:Earth Globe Asia-Australia
    U+1F310🌐\:globe_with_meridians:Globe With Meridians
    U+1F311🌑\:new_moon:New Moon Symbol
    U+1F312🌒\:waxing_crescent_moon:Waxing Crescent Moon Symbol
    U+1F313🌓\:first_quarter_moon:First Quarter Moon Symbol
    U+1F314🌔\:moon:Waxing Gibbous Moon Symbol
    U+1F315🌕\:full_moon:Full Moon Symbol
    U+1F316🌖\:waning_gibbous_moon:Waning Gibbous Moon Symbol
    U+1F317🌗\:last_quarter_moon:Last Quarter Moon Symbol
    U+1F318🌘\:waning_crescent_moon:Waning Crescent Moon Symbol
    U+1F319🌙\:crescent_moon:Crescent Moon
    U+1F31A🌚\:new_moon_with_face:New Moon With Face
    U+1F31B🌛\:first_quarter_moon_with_face:First Quarter Moon With Face
    U+1F31C🌜\:last_quarter_moon_with_face:Last Quarter Moon With Face
    U+1F31D🌝\:full_moon_with_face:Full Moon With Face
    U+1F31E🌞\:sun_with_face:Sun With Face
    U+1F31F🌟\:star2:Glowing Star
    U+1F320🌠\:stars:Shooting Star
    U+1F32D🌭\:hotdog:Hot Dog
    U+1F32E🌮\:taco:Taco
    U+1F32F🌯\:burrito:Burrito
    U+1F330🌰\:chestnut:Chestnut
    U+1F331🌱\:seedling:Seedling
    U+1F332🌲\:evergreen_tree:Evergreen Tree
    U+1F333🌳\:deciduous_tree:Deciduous Tree
    U+1F334🌴\:palm_tree:Palm Tree
    U+1F335🌵\:cactus:Cactus
    U+1F337🌷\:tulip:Tulip
    U+1F338🌸\:cherry_blossom:Cherry Blossom
    U+1F339🌹\:rose:Rose
    U+1F33A🌺\:hibiscus:Hibiscus
    U+1F33B🌻\:sunflower:Sunflower
    U+1F33C🌼\:blossom:Blossom
    U+1F33D🌽\:corn:Ear Of Maize
    U+1F33E🌾\:ear_of_rice:Ear Of Rice
    U+1F33F🌿\:herb:Herb
    U+1F340🍀\:four_leaf_clover:Four Leaf Clover
    U+1F341🍁\:maple_leaf:Maple Leaf
    U+1F342🍂\:fallen_leaf:Fallen Leaf
    U+1F343🍃\:leaves:Leaf Fluttering In Wind
    U+1F344🍄\:mushroom:Mushroom
    U+1F345🍅\:tomato:Tomato
    U+1F346🍆\:eggplant:Aubergine
    U+1F347🍇\:grapes:Grapes
    U+1F348🍈\:melon:Melon
    U+1F349🍉\:watermelon:Watermelon
    U+1F34A🍊\:tangerine:Tangerine
    U+1F34B🍋\:lemon:Lemon
    U+1F34C🍌\:banana:Banana
    U+1F34D🍍\:pineapple:Pineapple
    U+1F34E🍎\:apple:Red Apple
    U+1F34F🍏\:green_apple:Green Apple
    U+1F350🍐\:pear:Pear
    U+1F351🍑\:peach:Peach
    U+1F352🍒\:cherries:Cherries
    U+1F353🍓\:strawberry:Strawberry
    U+1F354🍔\:hamburger:Hamburger
    U+1F355🍕\:pizza:Slice Of Pizza
    U+1F356🍖\:meat_on_bone:Meat On Bone
    U+1F357🍗\:poultry_leg:Poultry Leg
    U+1F358🍘\:rice_cracker:Rice Cracker
    U+1F359🍙\:rice_ball:Rice Ball
    U+1F35A🍚\:rice:Cooked Rice
    U+1F35B🍛\:curry:Curry And Rice
    U+1F35C🍜\:ramen:Steaming Bowl
    U+1F35D🍝\:spaghetti:Spaghetti
    U+1F35E🍞\:bread:Bread
    U+1F35F🍟\:fries:French Fries
    U+1F360🍠\:sweet_potato:Roasted Sweet Potato
    U+1F361🍡\:dango:Dango
    U+1F362🍢\:oden:Oden
    U+1F363🍣\:sushi:Sushi
    U+1F364🍤\:fried_shrimp:Fried Shrimp
    U+1F365🍥\:fish_cake:Fish Cake With Swirl Design
    U+1F366🍦\:icecream:Soft Ice Cream
    U+1F367🍧\:shaved_ice:Shaved Ice
    U+1F368🍨\:ice_cream:Ice Cream
    U+1F369🍩\:doughnut:Doughnut
    U+1F36A🍪\:cookie:Cookie
    U+1F36B🍫\:chocolate_bar:Chocolate Bar
    U+1F36C🍬\:candy:Candy
    U+1F36D🍭\:lollipop:Lollipop
    U+1F36E🍮\:custard:Custard
    U+1F36F🍯\:honey_pot:Honey Pot
    U+1F370🍰\:cake:Shortcake
    U+1F371🍱\:bento:Bento Box
    U+1F372🍲\:stew:Pot Of Food
    U+1F373🍳\:fried_egg:Cooking
    U+1F374🍴\:fork_and_knife:Fork And Knife
    U+1F375🍵\:tea:Teacup Without Handle
    U+1F376🍶\:sake:Sake Bottle And Cup
    U+1F377🍷\:wine_glass:Wine Glass
    U+1F378🍸\:cocktail:Cocktail Glass
    U+1F379🍹\:tropical_drink:Tropical Drink
    U+1F37A🍺\:beer:Beer Mug
    U+1F37B🍻\:beers:Clinking Beer Mugs
    U+1F37C🍼\:baby_bottle:Baby Bottle
    U+1F37E🍾\:champagne:Bottle With Popping Cork
    U+1F37F🍿\:popcorn:Popcorn
    U+1F380🎀\:ribbon:Ribbon
    U+1F381🎁\:gift:Wrapped Present
    U+1F382🎂\:birthday:Birthday Cake
    U+1F383🎃\:jack_o_lantern:Jack-O-Lantern
    U+1F384🎄\:christmas_tree:Christmas Tree
    U+1F385🎅\:santa:Father Christmas
    U+1F386🎆\:fireworks:Fireworks
    U+1F387🎇\:sparkler:Firework Sparkler
    U+1F388🎈\:balloon:Balloon
    U+1F389🎉\:tada:Party Popper
    U+1F38A🎊\:confetti_ball:Confetti Ball
    U+1F38B🎋\:tanabata_tree:Tanabata Tree
    U+1F38C🎌\:crossed_flags:Crossed Flags
    U+1F38D🎍\:bamboo:Pine Decoration
    U+1F38E🎎\:dolls:Japanese Dolls
    U+1F38F🎏\:flags:Carp Streamer
    U+1F390🎐\:wind_chime:Wind Chime
    U+1F391🎑\:rice_scene:Moon Viewing Ceremony
    U+1F392🎒\:school_satchel:School Satchel
    U+1F393🎓\:mortar_board:Graduation Cap
    U+1F3A0🎠\:carousel_horse:Carousel Horse
    U+1F3A1🎡\:ferris_wheel:Ferris Wheel
    U+1F3A2🎢\:roller_coaster:Roller Coaster
    U+1F3A3🎣\:fishing_pole_and_fish:Fishing Pole And Fish
    U+1F3A4🎤\:microphone:Microphone
    U+1F3A5🎥\:movie_camera:Movie Camera
    U+1F3A6🎦\:cinema:Cinema
    U+1F3A7🎧\:headphones:Headphone
    U+1F3A8🎨\:art:Artist Palette
    U+1F3A9🎩\:tophat:Top Hat
    U+1F3AA🎪\:circus_tent:Circus Tent
    U+1F3AB🎫\:ticket:Ticket
    U+1F3AC🎬\:clapper:Clapper Board
    U+1F3AD🎭\:performing_arts:Performing Arts
    U+1F3AE🎮\:video_game:Video Game
    U+1F3AF🎯\:dart:Direct Hit
    U+1F3B0🎰\:slot_machine:Slot Machine
    U+1F3B1🎱\:8ball:Billiards
    U+1F3B2🎲\:game_die:Game Die
    U+1F3B3🎳\:bowling:Bowling
    U+1F3B4🎴\:flower_playing_cards:Flower Playing Cards
    U+1F3B5🎵\:musical_note:Musical Note
    U+1F3B6🎶\:notes:Multiple Musical Notes
    U+1F3B7🎷\:saxophone:Saxophone
    U+1F3B8🎸\:guitar:Guitar
    U+1F3B9🎹\:musical_keyboard:Musical Keyboard
    U+1F3BA🎺\:trumpet:Trumpet
    U+1F3BB🎻\:violin:Violin
    U+1F3BC🎼\:musical_score:Musical Score
    U+1F3BD🎽\:running_shirt_with_sash:Running Shirt With Sash
    U+1F3BE🎾\:tennis:Tennis Racquet And Ball
    U+1F3BF🎿\:ski:Ski And Ski Boot
    U+1F3C0🏀\:basketball:Basketball And Hoop
    U+1F3C1🏁\:checkered_flag:Chequered Flag
    U+1F3C2🏂\:snowboarder:Snowboarder
    U+1F3C3🏃\:runner:Runner
    U+1F3C4🏄\:surfer:Surfer
    U+1F3C5🏅\:sports_medal:Sports Medal
    U+1F3C6🏆\:trophy:Trophy
    U+1F3C7🏇\:horse_racing:Horse Racing
    U+1F3C8🏈\:football:American Football
    U+1F3C9🏉\:rugby_football:Rugby Football
    U+1F3CA🏊\:swimmer:Swimmer
    U+1F3CF🏏\:cricket_bat_and_ball:Cricket Bat And Ball
    U+1F3D0🏐\:volleyball:Volleyball
    U+1F3D1🏑\:field_hockey_stick_and_ball:Field Hockey Stick And Ball
    U+1F3D2🏒\:ice_hockey_stick_and_puck:Ice Hockey Stick And Puck
    U+1F3D3🏓\:table_tennis_paddle_and_ball:Table Tennis Paddle And Ball
    U+1F3E0🏠\:house:House Building
    U+1F3E1🏡\:house_with_garden:House With Garden
    U+1F3E2🏢\:office:Office Building
    U+1F3E3🏣\:post_office:Japanese Post Office
    U+1F3E4🏤\:european_post_office:European Post Office
    U+1F3E5🏥\:hospital:Hospital
    U+1F3E6🏦\:bank:Bank
    U+1F3E7🏧\:atm:Automated Teller Machine
    U+1F3E8🏨\:hotel:Hotel
    U+1F3E9🏩\:love_hotel:Love Hotel
    U+1F3EA🏪\:convenience_store:Convenience Store
    U+1F3EB🏫\:school:School
    U+1F3EC🏬\:department_store:Department Store
    U+1F3ED🏭\:factory:Factory
    U+1F3EE🏮\:izakaya_lantern:Izakaya Lantern
    U+1F3EF🏯\:japanese_castle:Japanese Castle
    U+1F3F0🏰\:european_castle:European Castle
    U+1F3F4🏴\:waving_black_flag:Waving Black Flag
    U+1F3F8🏸\:badminton_racquet_and_shuttlecock:Badminton Racquet And Shuttlecock
    U+1F3F9🏹\:bow_and_arrow:Bow And Arrow
    U+1F3FA🏺\:amphora:Amphora
    U+1F3FB🏻\:skin-tone-2:Emoji Modifier Fitzpatrick Type-1-2
    U+1F3FC🏼\:skin-tone-3:Emoji Modifier Fitzpatrick Type-3
    U+1F3FD🏽\:skin-tone-4:Emoji Modifier Fitzpatrick Type-4
    U+1F3FE🏾\:skin-tone-5:Emoji Modifier Fitzpatrick Type-5
    U+1F3FF🏿\:skin-tone-6:Emoji Modifier Fitzpatrick Type-6
    U+1F400🐀\:rat:Rat
    U+1F401🐁\:mouse2:Mouse
    U+1F402🐂\:ox:Ox
    U+1F403🐃\:water_buffalo:Water Buffalo
    U+1F404🐄\:cow2:Cow
    U+1F405🐅\:tiger2:Tiger
    U+1F406🐆\:leopard:Leopard
    U+1F407🐇\:rabbit2:Rabbit
    U+1F408🐈\:cat2:Cat
    U+1F409🐉\:dragon:Dragon
    U+1F40A🐊\:crocodile:Crocodile
    U+1F40B🐋\:whale2:Whale
    U+1F40C🐌\:snail:Snail
    U+1F40D🐍\:snake:Snake
    U+1F40E🐎\:racehorse:Horse
    U+1F40F🐏\:ram:Ram
    U+1F410🐐\:goat:Goat
    U+1F411🐑\:sheep:Sheep
    U+1F412🐒\:monkey:Monkey
    U+1F413🐓\:rooster:Rooster
    U+1F414🐔\:chicken:Chicken
    U+1F415🐕\:dog2:Dog
    U+1F416🐖\:pig2:Pig
    U+1F417🐗\:boar:Boar
    U+1F418🐘\:elephant:Elephant
    U+1F419🐙\:octopus:Octopus
    U+1F41A🐚\:shell:Spiral Shell
    U+1F41B🐛\:bug:Bug
    U+1F41C🐜\:ant:Ant
    U+1F41D🐝\:bee:Honeybee
    U+1F41E🐞\:ladybug:Lady Beetle
    U+1F41F🐟\:fish:Fish
    U+1F420🐠\:tropical_fish:Tropical Fish
    U+1F421🐡\:blowfish:Blowfish
    U+1F422🐢\:turtle:Turtle
    U+1F423🐣\:hatching_chick:Hatching Chick
    U+1F424🐤\:baby_chick:Baby Chick
    U+1F425🐥\:hatched_chick:Front-Facing Baby Chick
    U+1F426🐦\:bird:Bird
    U+1F427🐧\:penguin:Penguin
    U+1F428🐨\:koala:Koala
    U+1F429🐩\:poodle:Poodle
    U+1F42A🐪\:dromedary_camel:Dromedary Camel
    U+1F42B🐫\:camel:Bactrian Camel
    U+1F42C🐬\:dolphin:Dolphin
    U+1F42D🐭\:mouse:Mouse Face
    U+1F42E🐮\:cow:Cow Face
    U+1F42F🐯\:tiger:Tiger Face
    U+1F430🐰\:rabbit:Rabbit Face
    U+1F431🐱\:cat:Cat Face
    U+1F432🐲\:dragon_face:Dragon Face
    U+1F433🐳\:whale:Spouting Whale
    U+1F434🐴\:horse:Horse Face
    U+1F435🐵\:monkey_face:Monkey Face
    U+1F436🐶\:dog:Dog Face
    U+1F437🐷\:pig:Pig Face
    U+1F438🐸\:frog:Frog Face
    U+1F439🐹\:hamster:Hamster Face
    U+1F43A🐺\:wolf:Wolf Face
    U+1F43B🐻\:bear:Bear Face
    U+1F43C🐼\:panda_face:Panda Face
    U+1F43D🐽\:pig_nose:Pig Nose
    U+1F43E🐾\:feet:Paw Prints
    U+1F440👀\:eyes:Eyes
    U+1F442👂\:ear:Ear
    U+1F443👃\:nose:Nose
    U+1F444👄\:lips:Mouth
    U+1F445👅\:tongue:Tongue
    U+1F446👆\:point_up_2:White Up Pointing Backhand Index
    U+1F447👇\:point_down:White Down Pointing Backhand Index
    U+1F448👈\:point_left:White Left Pointing Backhand Index
    U+1F449👉\:point_right:White Right Pointing Backhand Index
    U+1F44A👊\:facepunch:Fisted Hand Sign
    U+1F44B👋\:wave:Waving Hand Sign
    U+1F44C👌\:ok_hand:Ok Hand Sign
    U+1F44D👍\:+1:Thumbs Up Sign
    U+1F44E👎\:-1:Thumbs Down Sign
    U+1F44F👏\:clap:Clapping Hands Sign
    U+1F450👐\:open_hands:Open Hands Sign
    U+1F451👑\:crown:Crown
    U+1F452👒\:womans_hat:Womans Hat
    U+1F453👓\:eyeglasses:Eyeglasses
    U+1F454👔\:necktie:Necktie
    U+1F455👕\:shirt:T-Shirt
    U+1F456👖\:jeans:Jeans
    U+1F457👗\:dress:Dress
    U+1F458👘\:kimono:Kimono
    U+1F459👙\:bikini:Bikini
    U+1F45A👚\:womans_clothes:Womans Clothes
    U+1F45B👛\:purse:Purse
    U+1F45C👜\:handbag:Handbag
    U+1F45D👝\:pouch:Pouch
    U+1F45E👞\:mans_shoe:Mans Shoe
    U+1F45F👟\:athletic_shoe:Athletic Shoe
    U+1F460👠\:high_heel:High-Heeled Shoe
    U+1F461👡\:sandal:Womans Sandal
    U+1F462👢\:boot:Womans Boots
    U+1F463👣\:footprints:Footprints
    U+1F464👤\:bust_in_silhouette:Bust In Silhouette
    U+1F465👥\:busts_in_silhouette:Busts In Silhouette
    U+1F466👦\:boy:Boy
    U+1F467👧\:girl:Girl
    U+1F468👨\:man:Man
    U+1F469👩\:woman:Woman
    U+1F46A👪\:family:Family
    U+1F46B👫\:couple:, \:man_and_woman_holding_hands:Man And Woman Holding Hands
    U+1F46C👬\:two_men_holding_hands:Two Men Holding Hands
    U+1F46D👭\:two_women_holding_hands:Two Women Holding Hands
    U+1F46E👮\:cop:Police Officer
    U+1F46F👯\:dancers:Woman With Bunny Ears
    U+1F470👰\:bride_with_veil:Bride With Veil
    U+1F471👱\:person_with_blond_hair:Person With Blond Hair
    U+1F472👲\:man_with_gua_pi_mao:Man With Gua Pi Mao
    U+1F473👳\:man_with_turban:Man With Turban
    U+1F474👴\:older_man:Older Man
    U+1F475👵\:older_woman:Older Woman
    U+1F476👶\:baby:Baby
    U+1F477👷\:construction_worker:Construction Worker
    U+1F478👸\:princess:Princess
    U+1F479👹\:japanese_ogre:Japanese Ogre
    U+1F47A👺\:japanese_goblin:Japanese Goblin
    U+1F47B👻\:ghost:Ghost
    U+1F47C👼\:angel:Baby Angel
    U+1F47D👽\:alien:Extraterrestrial Alien
    U+1F47E👾\:space_invader:Alien Monster
    U+1F47F👿\:imp:Imp
    U+1F480💀\:skull:Skull
    U+1F481💁\:information_desk_person:Information Desk Person
    U+1F482💂\:guardsman:Guardsman
    U+1F483💃\:dancer:Dancer
    U+1F484💄\:lipstick:Lipstick
    U+1F485💅\:nail_care:Nail Polish
    U+1F486💆\:massage:Face Massage
    U+1F487💇\:haircut:Haircut
    U+1F488💈\:barber:Barber Pole
    U+1F489💉\:syringe:Syringe
    U+1F48A💊\:pill:Pill
    U+1F48B💋\:kiss:Kiss Mark
    U+1F48C💌\:love_letter:Love Letter
    U+1F48D💍\:ring:Ring
    U+1F48E💎\:gem:Gem Stone
    U+1F48F💏\:couplekiss:Kiss
    U+1F490💐\:bouquet:Bouquet
    U+1F491💑\:couple_with_heart:Couple With Heart
    U+1F492💒\:wedding:Wedding
    U+1F493💓\:heartbeat:Beating Heart
    U+1F494💔\:broken_heart:Broken Heart
    U+1F495💕\:two_hearts:Two Hearts
    U+1F496💖\:sparkling_heart:Sparkling Heart
    U+1F497💗\:heartpulse:Growing Heart
    U+1F498💘\:cupid:Heart With Arrow
    U+1F499💙\:blue_heart:Blue Heart
    U+1F49A💚\:green_heart:Green Heart
    U+1F49B💛\:yellow_heart:Yellow Heart
    U+1F49C💜\:purple_heart:Purple Heart
    U+1F49D💝\:gift_heart:Heart With Ribbon
    U+1F49E💞\:revolving_hearts:Revolving Hearts
    U+1F49F💟\:heart_decoration:Heart Decoration
    U+1F4A0💠\:diamond_shape_with_a_dot_inside:Diamond Shape With A Dot Inside
    U+1F4A1💡\:bulb:Electric Light Bulb
    U+1F4A2💢\:anger:Anger Symbol
    U+1F4A3💣\:bomb:Bomb
    U+1F4A4💤\:zzz:Sleeping Symbol
    U+1F4A5💥\:boom:Collision Symbol
    U+1F4A6💦\:sweat_drops:Splashing Sweat Symbol
    U+1F4A7💧\:droplet:Droplet
    U+1F4A8💨\:dash:Dash Symbol
    U+1F4A9💩\:hankey:Pile Of Poo
    U+1F4AA💪\:muscle:Flexed Biceps
    U+1F4AB💫\:dizzy:Dizzy Symbol
    U+1F4AC💬\:speech_balloon:Speech Balloon
    U+1F4AD💭\:thought_balloon:Thought Balloon
    U+1F4AE💮\:white_flower:White Flower
    U+1F4AF💯\:100:Hundred Points Symbol
    U+1F4B0💰\:moneybag:Money Bag
    U+1F4B1💱\:currency_exchange:Currency Exchange
    U+1F4B2💲\:heavy_dollar_sign:Heavy Dollar Sign
    U+1F4B3💳\:credit_card:Credit Card
    U+1F4B4💴\:yen:Banknote With Yen Sign
    U+1F4B5💵\:dollar:Banknote With Dollar Sign
    U+1F4B6💶\:euro:Banknote With Euro Sign
    U+1F4B7💷\:pound:Banknote With Pound Sign
    U+1F4B8💸\:money_with_wings:Money With Wings
    U+1F4B9💹\:chart:Chart With Upwards Trend And Yen Sign
    U+1F4BA💺\:seat:Seat
    U+1F4BB💻\:computer:Personal Computer
    U+1F4BC💼\:briefcase:Briefcase
    U+1F4BD💽\:minidisc:Minidisc
    U+1F4BE💾\:floppy_disk:Floppy Disk
    U+1F4BF💿\:cd:Optical Disc
    U+1F4C0📀\:dvd:Dvd
    U+1F4C1📁\:file_folder:File Folder
    U+1F4C2📂\:open_file_folder:Open File Folder
    U+1F4C3📃\:page_with_curl:Page With Curl
    U+1F4C4📄\:page_facing_up:Page Facing Up
    U+1F4C5📅\:date:Calendar
    U+1F4C6📆\:calendar:Tear-Off Calendar
    U+1F4C7📇\:card_index:Card Index
    U+1F4C8📈\:chart_with_upwards_trend:Chart With Upwards Trend
    U+1F4C9📉\:chart_with_downwards_trend:Chart With Downwards Trend
    U+1F4CA📊\:bar_chart:Bar Chart
    U+1F4CB📋\:clipboard:Clipboard
    U+1F4CC📌\:pushpin:Pushpin
    U+1F4CD📍\:round_pushpin:Round Pushpin
    U+1F4CE📎\:paperclip:Paperclip
    U+1F4CF📏\:straight_ruler:Straight Ruler
    U+1F4D0📐\:triangular_ruler:Triangular Ruler
    U+1F4D1📑\:bookmark_tabs:Bookmark Tabs
    U+1F4D2📒\:ledger:Ledger
    U+1F4D3📓\:notebook:Notebook
    U+1F4D4📔\:notebook_with_decorative_cover:Notebook With Decorative Cover
    U+1F4D5📕\:closed_book:Closed Book
    U+1F4D6📖\:book:Open Book
    U+1F4D7📗\:green_book:Green Book
    U+1F4D8📘\:blue_book:Blue Book
    U+1F4D9📙\:orange_book:Orange Book
    U+1F4DA📚\:books:Books
    U+1F4DB📛\:name_badge:Name Badge
    U+1F4DC📜\:scroll:Scroll
    U+1F4DD📝\:memo:Memo
    U+1F4DE📞\:telephone_receiver:Telephone Receiver
    U+1F4DF📟\:pager:Pager
    U+1F4E0📠\:fax:Fax Machine
    U+1F4E1📡\:satellite:, \:satellite_antenna:Satellite Antenna
    U+1F4E2📢\:loudspeaker:Public Address Loudspeaker
    U+1F4E3📣\:mega:Cheering Megaphone
    U+1F4E4📤\:outbox_tray:Outbox Tray
    U+1F4E5📥\:inbox_tray:Inbox Tray
    U+1F4E6📦\:package:Package
    U+1F4E7📧\:e-mail:E-Mail Symbol
    U+1F4E8📨\:incoming_envelope:Incoming Envelope
    U+1F4E9📩\:envelope_with_arrow:Envelope With Downwards Arrow Above
    U+1F4EA📪\:mailbox_closed:Closed Mailbox With Lowered Flag
    U+1F4EB📫\:mailbox:Closed Mailbox With Raised Flag
    U+1F4EC📬\:mailbox_with_mail:Open Mailbox With Raised Flag
    U+1F4ED📭\:mailbox_with_no_mail:Open Mailbox With Lowered Flag
    U+1F4EE📮\:postbox:Postbox
    U+1F4EF📯\:postal_horn:Postal Horn
    U+1F4F0📰\:newspaper:Newspaper
    U+1F4F1📱\:iphone:Mobile Phone
    U+1F4F2📲\:calling:Mobile Phone With Rightwards Arrow At Left
    U+1F4F3📳\:vibration_mode:Vibration Mode
    U+1F4F4📴\:mobile_phone_off:Mobile Phone Off
    U+1F4F5📵\:no_mobile_phones:No Mobile Phones
    U+1F4F6📶\:signal_strength:Antenna With Bars
    U+1F4F7📷\:camera:Camera
    U+1F4F8📸\:camera_with_flash:Camera With Flash
    U+1F4F9📹\:video_camera:Video Camera
    U+1F4FA📺\:tv:Television
    U+1F4FB📻\:radio:Radio
    U+1F4FC📼\:vhs:Videocassette
    U+1F4FF📿\:prayer_beads:Prayer Beads
    U+1F500🔀\:twisted_rightwards_arrows:Twisted Rightwards Arrows
    U+1F501🔁\:repeat:Clockwise Rightwards And Leftwards Open Circle Arrows
    U+1F502🔂\:repeat_one:Clockwise Rightwards And Leftwards Open Circle Arrows With Circled One Overlay
    U+1F503🔃\:arrows_clockwise:Clockwise Downwards And Upwards Open Circle Arrows
    U+1F504🔄\:arrows_counterclockwise:Anticlockwise Downwards And Upwards Open Circle Arrows
    U+1F505🔅\:low_brightness:Low Brightness Symbol
    U+1F506🔆\:high_brightness:High Brightness Symbol
    U+1F507🔇\:mute:Speaker With Cancellation Stroke
    U+1F508🔈\:speaker:Speaker
    U+1F509🔉\:sound:Speaker With One Sound Wave
    U+1F50A🔊\:loud_sound:Speaker With Three Sound Waves
    U+1F50B🔋\:battery:Battery
    U+1F50C🔌\:electric_plug:Electric Plug
    U+1F50D🔍\:mag:Left-Pointing Magnifying Glass
    U+1F50E🔎\:mag_right:Right-Pointing Magnifying Glass
    U+1F50F🔏\:lock_with_ink_pen:Lock With Ink Pen
    U+1F510🔐\:closed_lock_with_key:Closed Lock With Key
    U+1F511🔑\:key:Key
    U+1F512🔒\:lock:Lock
    U+1F513🔓\:unlock:Open Lock
    U+1F514🔔\:bell:Bell
    U+1F515🔕\:no_bell:Bell With Cancellation Stroke
    U+1F516🔖\:bookmark:Bookmark
    U+1F517🔗\:link:Link Symbol
    U+1F518🔘\:radio_button:Radio Button
    U+1F519🔙\:back:Back With Leftwards Arrow Above
    U+1F51A🔚\:end:End With Leftwards Arrow Above
    U+1F51B🔛\:on:On With Exclamation Mark With Left Right Arrow Above
    U+1F51C🔜\:soon:Soon With Rightwards Arrow Above
    U+1F51D🔝\:top:Top With Upwards Arrow Above
    U+1F51E🔞\:underage:No One Under Eighteen Symbol
    U+1F51F🔟\:keycap_ten:Keycap Ten
    U+1F520🔠\:capital_abcd:Input Symbol For Latin Capital Letters
    U+1F521🔡\:abcd:Input Symbol For Latin Small Letters
    U+1F522🔢\:1234:Input Symbol For Numbers
    U+1F523🔣\:symbols:Input Symbol For Symbols
    U+1F524🔤\:abc:Input Symbol For Latin Letters
    U+1F525🔥\:fire:Fire
    U+1F526🔦\:flashlight:Electric Torch
    U+1F527🔧\:wrench:Wrench
    U+1F528🔨\:hammer:Hammer
    U+1F529🔩\:nut_and_bolt:Nut And Bolt
    U+1F52A🔪\:hocho:Hocho
    U+1F52B🔫\:gun:Pistol
    U+1F52C🔬\:microscope:Microscope
    U+1F52D🔭\:telescope:Telescope
    U+1F52E🔮\:crystal_ball:Crystal Ball
    U+1F52F🔯\:six_pointed_star:Six Pointed Star With Middle Dot
    U+1F530🔰\:beginner:Japanese Symbol For Beginner
    U+1F531🔱\:trident:Trident Emblem
    U+1F532🔲\:black_square_button:Black Square Button
    U+1F533🔳\:white_square_button:White Square Button
    U+1F534🔴\:red_circle:Large Red Circle
    U+1F535🔵\:large_blue_circle:Large Blue Circle
    U+1F536🔶\:large_orange_diamond:Large Orange Diamond
    U+1F537🔷\:large_blue_diamond:Large Blue Diamond
    U+1F538🔸\:small_orange_diamond:Small Orange Diamond
    U+1F539🔹\:small_blue_diamond:Small Blue Diamond
    U+1F53A🔺\:small_red_triangle:Up-Pointing Red Triangle
    U+1F53B🔻\:small_red_triangle_down:Down-Pointing Red Triangle
    U+1F53C🔼\:arrow_up_small:Up-Pointing Small Red Triangle
    U+1F53D🔽\:arrow_down_small:Down-Pointing Small Red Triangle
    U+1F54B🕋\:kaaba:Kaaba
    U+1F54C🕌\:mosque:Mosque
    U+1F54D🕍\:synagogue:Synagogue
    U+1F54E🕎\:menorah_with_nine_branches:Menorah With Nine Branches
    U+1F550🕐\:clock1:Clock Face One Oclock
    U+1F551🕑\:clock2:Clock Face Two Oclock
    U+1F552🕒\:clock3:Clock Face Three Oclock
    U+1F553🕓\:clock4:Clock Face Four Oclock
    U+1F554🕔\:clock5:Clock Face Five Oclock
    U+1F555🕕\:clock6:Clock Face Six Oclock
    U+1F556🕖\:clock7:Clock Face Seven Oclock
    U+1F557🕗\:clock8:Clock Face Eight Oclock
    U+1F558🕘\:clock9:Clock Face Nine Oclock
    U+1F559🕙\:clock10:Clock Face Ten Oclock
    U+1F55A🕚\:clock11:Clock Face Eleven Oclock
    U+1F55B🕛\:clock12:Clock Face Twelve Oclock
    U+1F55C🕜\:clock130:Clock Face One-Thirty
    U+1F55D🕝\:clock230:Clock Face Two-Thirty
    U+1F55E🕞\:clock330:Clock Face Three-Thirty
    U+1F55F🕟\:clock430:Clock Face Four-Thirty
    U+1F560🕠\:clock530:Clock Face Five-Thirty
    U+1F561🕡\:clock630:Clock Face Six-Thirty
    U+1F562🕢\:clock730:Clock Face Seven-Thirty
    U+1F563🕣\:clock830:Clock Face Eight-Thirty
    U+1F564🕤\:clock930:Clock Face Nine-Thirty
    U+1F565🕥\:clock1030:Clock Face Ten-Thirty
    U+1F566🕦\:clock1130:Clock Face Eleven-Thirty
    U+1F567🕧\:clock1230:Clock Face Twelve-Thirty
    U+1F57A🕺\:man_dancing:Man Dancing
    U+1F595🖕\:middle_finger:Reversed Hand With Middle Finger Extended
    U+1F596🖖\:spock-hand:Raised Hand With Part Between Middle And Ring Fingers
    U+1F5A4🖤\:black_heart:Black Heart
    U+1F5FB🗻\:mount_fuji:Mount Fuji
    U+1F5FC🗼\:tokyo_tower:Tokyo Tower
    U+1F5FD🗽\:statue_of_liberty:Statue Of Liberty
    U+1F5FE🗾\:japan:Silhouette Of Japan
    U+1F5FF🗿\:moyai:Moyai
    U+1F600😀\:grinning:Grinning Face
    U+1F601😁\:grin:Grinning Face With Smiling Eyes
    U+1F602😂\:joy:Face With Tears Of Joy
    U+1F603😃\:smiley:Smiling Face With Open Mouth
    U+1F604😄\:smile:Smiling Face With Open Mouth And Smiling Eyes
    U+1F605😅\:sweat_smile:Smiling Face With Open Mouth And Cold Sweat
    U+1F606😆\:laughing:Smiling Face With Open Mouth And Tightly-Closed Eyes
    U+1F607😇\:innocent:Smiling Face With Halo
    U+1F608😈\:smiling_imp:Smiling Face With Horns
    U+1F609😉\:wink:Winking Face
    U+1F60A😊\:blush:Smiling Face With Smiling Eyes
    U+1F60B😋\:yum:Face Savouring Delicious Food
    U+1F60C😌\:relieved:Relieved Face
    U+1F60D😍\:heart_eyes:Smiling Face With Heart-Shaped Eyes
    U+1F60E😎\:sunglasses:Smiling Face With Sunglasses
    U+1F60F😏\:smirk:Smirking Face
    U+1F610😐\:neutral_face:Neutral Face
    U+1F611😑\:expressionless:Expressionless Face
    U+1F612😒\:unamused:Unamused Face
    U+1F613😓\:sweat:Face With Cold Sweat
    U+1F614😔\:pensive:Pensive Face
    U+1F615😕\:confused:Confused Face
    U+1F616😖\:confounded:Confounded Face
    U+1F617😗\:kissing:Kissing Face
    U+1F618😘\:kissing_heart:Face Throwing A Kiss
    U+1F619😙\:kissing_smiling_eyes:Kissing Face With Smiling Eyes
    U+1F61A😚\:kissing_closed_eyes:Kissing Face With Closed Eyes
    U+1F61B😛\:stuck_out_tongue:Face With Stuck-Out Tongue
    U+1F61C😜\:stuck_out_tongue_winking_eye:Face With Stuck-Out Tongue And Winking Eye
    U+1F61D😝\:stuck_out_tongue_closed_eyes:Face With Stuck-Out Tongue And Tightly-Closed Eyes
    U+1F61E😞\:disappointed:Disappointed Face
    U+1F61F😟\:worried:Worried Face
    U+1F620😠\:angry:Angry Face
    U+1F621😡\:rage:Pouting Face
    U+1F622😢\:cry:Crying Face
    U+1F623😣\:persevere:Persevering Face
    U+1F624😤\:triumph:Face With Look Of Triumph
    U+1F625😥\:disappointed_relieved:Disappointed But Relieved Face
    U+1F626😦\:frowning:Frowning Face With Open Mouth
    U+1F627😧\:anguished:Anguished Face
    U+1F628😨\:fearful:Fearful Face
    U+1F629😩\:weary:Weary Face
    U+1F62A😪\:sleepy:Sleepy Face
    U+1F62B😫\:tired_face:Tired Face
    U+1F62C😬\:grimacing:Grimacing Face
    U+1F62D😭\:sob:Loudly Crying Face
    U+1F62E😮\:open_mouth:Face With Open Mouth
    U+1F62F😯\:hushed:Hushed Face
    U+1F630😰\:cold_sweat:Face With Open Mouth And Cold Sweat
    U+1F631😱\:scream:Face Screaming In Fear
    U+1F632😲\:astonished:Astonished Face
    U+1F633😳\:flushed:Flushed Face
    U+1F634😴\:sleeping:Sleeping Face
    U+1F635😵\:dizzy_face:Dizzy Face
    U+1F636😶\:no_mouth:Face Without Mouth
    U+1F637😷\:mask:Face With Medical Mask
    U+1F638😸\:smile_cat:Grinning Cat Face With Smiling Eyes
    U+1F639😹\:joy_cat:Cat Face With Tears Of Joy
    U+1F63A😺\:smiley_cat:Smiling Cat Face With Open Mouth
    U+1F63B😻\:heart_eyes_cat:Smiling Cat Face With Heart-Shaped Eyes
    U+1F63C😼\:smirk_cat:Cat Face With Wry Smile
    U+1F63D😽\:kissing_cat:Kissing Cat Face With Closed Eyes
    U+1F63E😾\:pouting_cat:Pouting Cat Face
    U+1F63F😿\:crying_cat_face:Crying Cat Face
    U+1F640🙀\:scream_cat:Weary Cat Face
    U+1F641🙁\:slightly_frowning_face:Slightly Frowning Face
    U+1F642🙂\:slightly_smiling_face:Slightly Smiling Face
    U+1F643🙃\:upside_down_face:Upside-Down Face
    U+1F644🙄\:face_with_rolling_eyes:Face With Rolling Eyes
    U+1F645🙅\:no_good:Face With No Good Gesture
    U+1F646🙆\:ok_woman:Face With Ok Gesture
    U+1F647🙇\:bow:Person Bowing Deeply
    U+1F648🙈\:see_no_evil:See-No-Evil Monkey
    U+1F649🙉\:hear_no_evil:Hear-No-Evil Monkey
    U+1F64A🙊\:speak_no_evil:Speak-No-Evil Monkey
    U+1F64B🙋\:raising_hand:Happy Person Raising One Hand
    U+1F64C🙌\:raised_hands:Person Raising Both Hands In Celebration
    U+1F64D🙍\:person_frowning:Person Frowning
    U+1F64E🙎\:person_with_pouting_face:Person With Pouting Face
    U+1F64F🙏\:pray:Person With Folded Hands
    U+1F680🚀\:rocket:Rocket
    U+1F681🚁\:helicopter:Helicopter
    U+1F682🚂\:steam_locomotive:Steam Locomotive
    U+1F683🚃\:railway_car:Railway Car
    U+1F684🚄\:bullettrain_side:High-Speed Train
    U+1F685🚅\:bullettrain_front:High-Speed Train With Bullet Nose
    U+1F686🚆\:train2:Train
    U+1F687🚇\:metro:Metro
    U+1F688🚈\:light_rail:Light Rail
    U+1F689🚉\:station:Station
    U+1F68A🚊\:tram:Tram
    U+1F68B🚋\:train:Tram Car
    U+1F68C🚌\:bus:Bus
    U+1F68D🚍\:oncoming_bus:Oncoming Bus
    U+1F68E🚎\:trolleybus:Trolleybus
    U+1F68F🚏\:busstop:Bus Stop
    U+1F690🚐\:minibus:Minibus
    U+1F691🚑\:ambulance:Ambulance
    U+1F692🚒\:fire_engine:Fire Engine
    U+1F693🚓\:police_car:Police Car
    U+1F694🚔\:oncoming_police_car:Oncoming Police Car
    U+1F695🚕\:taxi:Taxi
    U+1F696🚖\:oncoming_taxi:Oncoming Taxi
    U+1F697🚗\:car:Automobile
    U+1F698🚘\:oncoming_automobile:Oncoming Automobile
    U+1F699🚙\:blue_car:Recreational Vehicle
    U+1F69A🚚\:truck:Delivery Truck
    U+1F69B🚛\:articulated_lorry:Articulated Lorry
    U+1F69C🚜\:tractor:Tractor
    U+1F69D🚝\:monorail:Monorail
    U+1F69E🚞\:mountain_railway:Mountain Railway
    U+1F69F🚟\:suspension_railway:Suspension Railway
    U+1F6A0🚠\:mountain_cableway:Mountain Cableway
    U+1F6A1🚡\:aerial_tramway:Aerial Tramway
    U+1F6A2🚢\:ship:Ship
    U+1F6A3🚣\:rowboat:Rowboat
    U+1F6A4🚤\:speedboat:Speedboat
    U+1F6A5🚥\:traffic_light:Horizontal Traffic Light
    U+1F6A6🚦\:vertical_traffic_light:Vertical Traffic Light
    U+1F6A7🚧\:construction:Construction Sign
    U+1F6A8🚨\:rotating_light:Police Cars Revolving Light
    U+1F6A9🚩\:triangular_flag_on_post:Triangular Flag On Post
    U+1F6AA🚪\:door:Door
    U+1F6AB🚫\:no_entry_sign:No Entry Sign
    U+1F6AC🚬\:smoking:Smoking Symbol
    U+1F6AD🚭\:no_smoking:No Smoking Symbol
    U+1F6AE🚮\:put_litter_in_its_place:Put Litter In Its Place Symbol
    U+1F6AF🚯\:do_not_litter:Do Not Litter Symbol
    U+1F6B0🚰\:potable_water:Potable Water Symbol
    U+1F6B1🚱\:non-potable_water:Non-Potable Water Symbol
    U+1F6B2🚲\:bike:Bicycle
    U+1F6B3🚳\:no_bicycles:No Bicycles
    U+1F6B4🚴\:bicyclist:Bicyclist
    U+1F6B5🚵\:mountain_bicyclist:Mountain Bicyclist
    U+1F6B6🚶\:walking:Pedestrian
    U+1F6B7🚷\:no_pedestrians:No Pedestrians
    U+1F6B8🚸\:children_crossing:Children Crossing
    U+1F6B9🚹\:mens:Mens Symbol
    U+1F6BA🚺\:womens:Womens Symbol
    U+1F6BB🚻\:restroom:Restroom
    U+1F6BC🚼\:baby_symbol:Baby Symbol
    U+1F6BD🚽\:toilet:Toilet
    U+1F6BE🚾\:wc:Water Closet
    U+1F6BF🚿\:shower:Shower
    U+1F6C0🛀\:bath:Bath
    U+1F6C1🛁\:bathtub:Bathtub
    U+1F6C2🛂\:passport_control:Passport Control
    U+1F6C3🛃\:customs:Customs
    U+1F6C4🛄\:baggage_claim:Baggage Claim
    U+1F6C5🛅\:left_luggage:Left Luggage
    U+1F6CC🛌\:sleeping_accommodation:Sleeping Accommodation
    U+1F6D0🛐\:place_of_worship:Place Of Worship
    U+1F6D1🛑\:octagonal_sign:Octagonal Sign
    U+1F6D2🛒\:shopping_trolley:Shopping Trolley
    U+1F6D5🛕\:hindu_temple:Hindu Temple
    U+1F6D6🛖\:hut:Hut
    U+1F6D7🛗\:elevator:Elevator
    U+1F6EB🛫\:airplane_departure:Airplane Departure
    U+1F6EC🛬\:airplane_arriving:Airplane Arriving
    U+1F6F4🛴\:scooter:Scooter
    U+1F6F5🛵\:motor_scooter:Motor Scooter
    U+1F6F6🛶\:canoe:Canoe
    U+1F6F7🛷\:sled:Sled
    U+1F6F8🛸\:flying_saucer:Flying Saucer
    U+1F6F9🛹\:skateboard:Skateboard
    U+1F6FA🛺\:auto_rickshaw:Auto Rickshaw
    U+1F6FB🛻\:pickup_truck:Pickup Truck
    U+1F6FC🛼\:roller_skate:Roller Skate
    U+1F7E0🟠\:large_orange_circle:Large Orange Circle
    U+1F7E1🟡\:large_yellow_circle:Large Yellow Circle
    U+1F7E2🟢\:large_green_circle:Large Green Circle
    U+1F7E3🟣\:large_purple_circle:Large Purple Circle
    U+1F7E4🟤\:large_brown_circle:Large Brown Circle
    U+1F7E5🟥\:large_red_square:Large Red Square
    U+1F7E6🟦\:large_blue_square:Large Blue Square
    U+1F7E7🟧\:large_orange_square:Large Orange Square
    U+1F7E8🟨\:large_yellow_square:Large Yellow Square
    U+1F7E9🟩\:large_green_square:Large Green Square
    U+1F7EA🟪\:large_purple_square:Large Purple Square
    U+1F7EB🟫\:large_brown_square:Large Brown Square
    U+1F90C🤌\:pinched_fingers:Pinched Fingers
    U+1F90D🤍\:white_heart:White Heart
    U+1F90E🤎\:brown_heart:Brown Heart
    U+1F90F🤏\:pinching_hand:Pinching Hand
    U+1F910🤐\:zipper_mouth_face:Zipper-Mouth Face
    U+1F911🤑\:money_mouth_face:Money-Mouth Face
    U+1F912🤒\:face_with_thermometer:Face With Thermometer
    U+1F913🤓\:nerd_face:Nerd Face
    U+1F914🤔\:thinking_face:Thinking Face
    U+1F915🤕\:face_with_head_bandage:Face With Head-Bandage
    U+1F916🤖\:robot_face:Robot Face
    U+1F917🤗\:hugging_face:Hugging Face
    U+1F918🤘\:the_horns:Sign Of The Horns
    U+1F919🤙\:call_me_hand:Call Me Hand
    U+1F91A🤚\:raised_back_of_hand:Raised Back Of Hand
    U+1F91B🤛\:left-facing_fist:Left-Facing Fist
    U+1F91C🤜\:right-facing_fist:Right-Facing Fist
    U+1F91D🤝\:handshake:Handshake
    U+1F91E🤞\:crossed_fingers:Hand With Index And Middle Fingers Crossed
    U+1F91F🤟\:i_love_you_hand_sign:I Love You Hand Sign
    U+1F920🤠\:face_with_cowboy_hat:Face With Cowboy Hat
    U+1F921🤡\:clown_face:Clown Face
    U+1F922🤢\:nauseated_face:Nauseated Face
    U+1F923🤣\:rolling_on_the_floor_laughing:Rolling On The Floor Laughing
    U+1F924🤤\:drooling_face:Drooling Face
    U+1F925🤥\:lying_face:Lying Face
    U+1F926🤦\:face_palm:Face Palm
    U+1F927🤧\:sneezing_face:Sneezing Face
    U+1F928🤨\:face_with_raised_eyebrow:Face With One Eyebrow Raised
    U+1F929🤩\:star-struck:Grinning Face With Star Eyes
    U+1F92A🤪\:zany_face:Grinning Face With One Large And One Small Eye
    U+1F92B🤫\:shushing_face:Face With Finger Covering Closed Lips
    U+1F92C🤬\:face_with_symbols_on_mouth:Serious Face With Symbols Covering Mouth
    U+1F92D🤭\:face_with_hand_over_mouth:Smiling Face With Smiling Eyes And Hand Covering Mouth
    U+1F92E🤮\:face_vomiting:Face With Open Mouth Vomiting
    U+1F92F🤯\:exploding_head:Shocked Face With Exploding Head
    U+1F930🤰\:pregnant_woman:Pregnant Woman
    U+1F931🤱\:breast-feeding:Breast-Feeding
    U+1F932🤲\:palms_up_together:Palms Up Together
    U+1F933🤳\:selfie:Selfie
    U+1F934🤴\:prince:Prince
    U+1F935🤵\:person_in_tuxedo:Man In Tuxedo
    U+1F936🤶\:mrs_claus:Mother Christmas
    U+1F937🤷\:shrug:Shrug
    U+1F938🤸\:person_doing_cartwheel:Person Doing Cartwheel
    U+1F939🤹\:juggling:Juggling
    U+1F93A🤺\:fencer:Fencer
    U+1F93C🤼\:wrestlers:Wrestlers
    U+1F93D🤽\:water_polo:Water Polo
    U+1F93E🤾\:handball:Handball
    U+1F93F🤿\:diving_mask:Diving Mask
    U+1F940🥀\:wilted_flower:Wilted Flower
    U+1F941🥁\:drum_with_drumsticks:Drum With Drumsticks
    U+1F942🥂\:clinking_glasses:Clinking Glasses
    U+1F943🥃\:tumbler_glass:Tumbler Glass
    U+1F944🥄\:spoon:Spoon
    U+1F945🥅\:goal_net:Goal Net
    U+1F947🥇\:first_place_medal:First Place Medal
    U+1F948🥈\:second_place_medal:Second Place Medal
    U+1F949🥉\:third_place_medal:Third Place Medal
    U+1F94A🥊\:boxing_glove:Boxing Glove
    U+1F94B🥋\:martial_arts_uniform:Martial Arts Uniform
    U+1F94C🥌\:curling_stone:Curling Stone
    U+1F94D🥍\:lacrosse:Lacrosse Stick And Ball
    U+1F94E🥎\:softball:Softball
    U+1F94F🥏\:flying_disc:Flying Disc
    U+1F950🥐\:croissant:Croissant
    U+1F951🥑\:avocado:Avocado
    U+1F952🥒\:cucumber:Cucumber
    U+1F953🥓\:bacon:Bacon
    U+1F954🥔\:potato:Potato
    U+1F955🥕\:carrot:Carrot
    U+1F956🥖\:baguette_bread:Baguette Bread
    U+1F957🥗\:green_salad:Green Salad
    U+1F958🥘\:shallow_pan_of_food:Shallow Pan Of Food
    U+1F959🥙\:stuffed_flatbread:Stuffed Flatbread
    U+1F95A🥚\:egg:Egg
    U+1F95B🥛\:glass_of_milk:Glass Of Milk
    U+1F95C🥜\:peanuts:Peanuts
    U+1F95D🥝\:kiwifruit:Kiwifruit
    U+1F95E🥞\:pancakes:Pancakes
    U+1F95F🥟\:dumpling:Dumpling
    U+1F960🥠\:fortune_cookie:Fortune Cookie
    U+1F961🥡\:takeout_box:Takeout Box
    U+1F962🥢\:chopsticks:Chopsticks
    U+1F963🥣\:bowl_with_spoon:Bowl With Spoon
    U+1F964🥤\:cup_with_straw:Cup With Straw
    U+1F965🥥\:coconut:Coconut
    U+1F966🥦\:broccoli:Broccoli
    U+1F967🥧\:pie:Pie
    U+1F968🥨\:pretzel:Pretzel
    U+1F969🥩\:cut_of_meat:Cut Of Meat
    U+1F96A🥪\:sandwich:Sandwich
    U+1F96B🥫\:canned_food:Canned Food
    U+1F96C🥬\:leafy_green:Leafy Green
    U+1F96D🥭\:mango:Mango
    U+1F96E🥮\:moon_cake:Moon Cake
    U+1F96F🥯\:bagel:Bagel
    U+1F970🥰\:smiling_face_with_3_hearts:Smiling Face With Smiling Eyes And Three Hearts
    U+1F971🥱\:yawning_face:Yawning Face
    U+1F972🥲\:smiling_face_with_tear:Smiling Face With Tear
    U+1F973🥳\:partying_face:Face With Party Horn And Party Hat
    U+1F974🥴\:woozy_face:Face With Uneven Eyes And Wavy Mouth
    U+1F975🥵\:hot_face:Overheated Face
    U+1F976🥶\:cold_face:Freezing Face
    U+1F977🥷\:ninja:Ninja
    U+1F978🥸\:disguised_face:Disguised Face
    U+1F97A🥺\:pleading_face:Face With Pleading Eyes
    U+1F97B🥻\:sari:Sari
    U+1F97C🥼\:lab_coat:Lab Coat
    U+1F97D🥽\:goggles:Goggles
    U+1F97E🥾\:hiking_boot:Hiking Boot
    U+1F97F🥿\:womans_flat_shoe:Flat Shoe
    U+1F980🦀\:crab:Crab
    U+1F981🦁\:lion_face:Lion Face
    U+1F982🦂\:scorpion:Scorpion
    U+1F983🦃\:turkey:Turkey
    U+1F984🦄\:unicorn_face:Unicorn Face
    U+1F985🦅\:eagle:Eagle
    U+1F986🦆\:duck:Duck
    U+1F987🦇\:bat:Bat
    U+1F988🦈\:shark:Shark
    U+1F989🦉\:owl:Owl
    U+1F98A🦊\:fox_face:Fox Face
    U+1F98B🦋\:butterfly:Butterfly
    U+1F98C🦌\:deer:Deer
    U+1F98D🦍\:gorilla:Gorilla
    U+1F98E🦎\:lizard:Lizard
    U+1F98F🦏\:rhinoceros:Rhinoceros
    U+1F990🦐\:shrimp:Shrimp
    U+1F991🦑\:squid:Squid
    U+1F992🦒\:giraffe_face:Giraffe Face
    U+1F993🦓\:zebra_face:Zebra Face
    U+1F994🦔\:hedgehog:Hedgehog
    U+1F995🦕\:sauropod:Sauropod
    U+1F996🦖\:t-rex:T-Rex
    U+1F997🦗\:cricket:Cricket
    U+1F998🦘\:kangaroo:Kangaroo
    U+1F999🦙\:llama:Llama
    U+1F99A🦚\:peacock:Peacock
    U+1F99B🦛\:hippopotamus:Hippopotamus
    U+1F99C🦜\:parrot:Parrot
    U+1F99D🦝\:raccoon:Raccoon
    U+1F99E🦞\:lobster:Lobster
    U+1F99F🦟\:mosquito:Mosquito
    U+1F9A0🦠\:microbe:Microbe
    U+1F9A1🦡\:badger:Badger
    U+1F9A2🦢\:swan:Swan
    U+1F9A3🦣\:mammoth:Mammoth
    U+1F9A4🦤\:dodo:Dodo
    U+1F9A5🦥\:sloth:Sloth
    U+1F9A6🦦\:otter:Otter
    U+1F9A7🦧\:orangutan:Orangutan
    U+1F9A8🦨\:skunk:Skunk
    U+1F9A9🦩\:flamingo:Flamingo
    U+1F9AA🦪\:oyster:Oyster
    U+1F9AB🦫\:beaver:Beaver
    U+1F9AC🦬\:bison:Bison
    U+1F9AD🦭\:seal:Seal
    U+1F9AE🦮\:guide_dog:Guide Dog
    U+1F9AF🦯\:probing_cane:Probing Cane
    U+1F9B4🦴\:bone:Bone
    U+1F9B5🦵\:leg:Leg
    U+1F9B6🦶\:foot:Foot
    U+1F9B7🦷\:tooth:Tooth
    U+1F9B8🦸\:superhero:Superhero
    U+1F9B9🦹\:supervillain:Supervillain
    U+1F9BA🦺\:safety_vest:Safety Vest
    U+1F9BB🦻\:ear_with_hearing_aid:Ear With Hearing Aid
    U+1F9BC🦼\:motorized_wheelchair:Motorized Wheelchair
    U+1F9BD🦽\:manual_wheelchair:Manual Wheelchair
    U+1F9BE🦾\:mechanical_arm:Mechanical Arm
    U+1F9BF🦿\:mechanical_leg:Mechanical Leg
    U+1F9C0🧀\:cheese_wedge:Cheese Wedge
    U+1F9C1🧁\:cupcake:Cupcake
    U+1F9C2🧂\:salt:Salt Shaker
    U+1F9C3🧃\:beverage_box:Beverage Box
    U+1F9C4🧄\:garlic:Garlic
    U+1F9C5🧅\:onion:Onion
    U+1F9C6🧆\:falafel:Falafel
    U+1F9C7🧇\:waffle:Waffle
    U+1F9C8🧈\:butter:Butter
    U+1F9C9🧉\:mate_drink:Mate Drink
    U+1F9CA🧊\:ice_cube:Ice Cube
    U+1F9CB🧋\:bubble_tea:Bubble Tea
    U+1F9CD🧍\:standing_person:Standing Person
    U+1F9CE🧎\:kneeling_person:Kneeling Person
    U+1F9CF🧏\:deaf_person:Deaf Person
    U+1F9D0🧐\:face_with_monocle:Face With Monocle
    U+1F9D1🧑\:adult:Adult
    U+1F9D2🧒\:child:Child
    U+1F9D3🧓\:older_adult:Older Adult
    U+1F9D4🧔\:bearded_person:Bearded Person
    U+1F9D5🧕\:person_with_headscarf:Person With Headscarf
    U+1F9D6🧖\:person_in_steamy_room:Person In Steamy Room
    U+1F9D7🧗\:person_climbing:Person Climbing
    U+1F9D8🧘\:person_in_lotus_position:Person In Lotus Position
    U+1F9D9🧙\:mage:Mage
    U+1F9DA🧚\:fairy:Fairy
    U+1F9DB🧛\:vampire:Vampire
    U+1F9DC🧜\:merperson:Merperson
    U+1F9DD🧝\:elf:Elf
    U+1F9DE🧞\:genie:Genie
    U+1F9DF🧟\:zombie:Zombie
    U+1F9E0🧠\:brain:Brain
    U+1F9E1🧡\:orange_heart:Orange Heart
    U+1F9E2🧢\:billed_cap:Billed Cap
    U+1F9E3🧣\:scarf:Scarf
    U+1F9E4🧤\:gloves:Gloves
    U+1F9E5🧥\:coat:Coat
    U+1F9E6🧦\:socks:Socks
    U+1F9E7🧧\:red_envelope:Red Gift Envelope
    U+1F9E8🧨\:firecracker:Firecracker
    U+1F9E9🧩\:jigsaw:Jigsaw Puzzle Piece
    U+1F9EA🧪\:test_tube:Test Tube
    U+1F9EB🧫\:petri_dish:Petri Dish
    U+1F9EC🧬\:dna:Dna Double Helix
    U+1F9ED🧭\:compass:Compass
    U+1F9EE🧮\:abacus:Abacus
    U+1F9EF🧯\:fire_extinguisher:Fire Extinguisher
    U+1F9F0🧰\:toolbox:Toolbox
    U+1F9F1🧱\:bricks:Brick
    U+1F9F2🧲\:magnet:Magnet
    U+1F9F3🧳\:luggage:Luggage
    U+1F9F4🧴\:lotion_bottle:Lotion Bottle
    U+1F9F5🧵\:thread:Spool Of Thread
    U+1F9F6🧶\:yarn:Ball Of Yarn
    U+1F9F7🧷\:safety_pin:Safety Pin
    U+1F9F8🧸\:teddy_bear:Teddy Bear
    U+1F9F9🧹\:broom:Broom
    U+1F9FA🧺\:basket:Basket
    U+1F9FB🧻\:roll_of_paper:Roll Of Paper
    U+1F9FC🧼\:soap:Bar Of Soap
    U+1F9FD🧽\:sponge:Sponge
    U+1F9FE🧾\:receipt:Receipt
    U+1F9FF🧿\:nazar_amulet:Nazar Amulet
    U+1FA70🩰\:ballet_shoes:Ballet Shoes
    U+1FA71🩱\:one-piece_swimsuit:One-Piece Swimsuit
    U+1FA72🩲\:briefs:Briefs
    U+1FA73🩳\:shorts:Shorts
    U+1FA74🩴\:thong_sandal:Thong Sandal
    U+1FA78🩸\:drop_of_blood:Drop Of Blood
    U+1FA79🩹\:adhesive_bandage:Adhesive Bandage
    U+1FA7A🩺\:stethoscope:Stethoscope
    U+1FA80🪀\:yo-yo:Yo-Yo
    U+1FA81🪁\:kite:Kite
    U+1FA82🪂\:parachute:Parachute
    U+1FA83🪃\:boomerang:Boomerang
    U+1FA84🪄\:magic_wand:Magic Wand
    U+1FA85🪅\:pinata:Pinata
    U+1FA86🪆\:nesting_dolls:Nesting Dolls
    U+1FA90🪐\:ringed_planet:Ringed Planet
    U+1FA91🪑\:chair:Chair
    U+1FA92🪒\:razor:Razor
    U+1FA93🪓\:axe:Axe
    U+1FA94🪔\:diya_lamp:Diya Lamp
    U+1FA95🪕\:banjo:Banjo
    U+1FA96🪖\:military_helmet:Military Helmet
    U+1FA97🪗\:accordion:Accordion
    U+1FA98🪘\:long_drum:Long Drum
    U+1FA99🪙\:coin:Coin
    U+1FA9A🪚\:carpentry_saw:Carpentry Saw
    U+1FA9B🪛\:screwdriver:Screwdriver
    U+1FA9C🪜\:ladder:Ladder
    U+1FA9D🪝\:hook:Hook
    U+1FA9E🪞\:mirror:Mirror
    U+1FA9F🪟\:window:Window
    U+1FAA0🪠\:plunger:Plunger
    U+1FAA1🪡\:sewing_needle:Sewing Needle
    U+1FAA2🪢\:knot:Knot
    U+1FAA3🪣\:bucket:Bucket
    U+1FAA4🪤\:mouse_trap:Mouse Trap
    U+1FAA5🪥\:toothbrush:Toothbrush
    U+1FAA6🪦\:headstone:Headstone
    U+1FAA7🪧\:placard:Placard
    U+1FAA8🪨\:rock:Rock
    U+1FAB0🪰\:fly:Fly
    U+1FAB1🪱\:worm:Worm
    U+1FAB2🪲\:beetle:Beetle
    U+1FAB3🪳\:cockroach:Cockroach
    U+1FAB4🪴\:potted_plant:Potted Plant
    U+1FAB5🪵\:wood:Wood
    U+1FAB6🪶\:feather:Feather
    U+1FAC0🫀\:anatomical_heart:Anatomical Heart
    U+1FAC1🫁\:lungs:Lungs
    U+1FAC2🫂\:people_hugging:People Hugging
    U+1FAD0🫐\:blueberries:Blueberries
    U+1FAD1🫑\:bell_pepper:Bell Pepper
    U+1FAD2🫒\:olive:Olive
    U+1FAD3🫓\:flatbread:Flatbread
    U+1FAD4🫔\:tamale:Tamale
    U+1FAD5🫕\:fondue:Fondue
    U+1FAD6🫖\:teapot:Teapot
    diff --git a/dev/manual/variables-and-scoping/index.html b/dev/manual/variables-and-scoping/index.html index 30da9f1a..c42b6279 100644 --- a/dev/manual/variables-and-scoping/index.html +++ b/dev/manual/variables-and-scoping/index.html @@ -301,4 +301,4 @@ julia> global x::Int ERROR: cannot set type for global x. It already has a value or is already set to a different type. Stacktrace: -[...] +[...] diff --git a/dev/manual/variables/index.html b/dev/manual/variables/index.html index 8a33c980..996749a4 100644 --- a/dev/manual/variables/index.html +++ b/dev/manual/variables/index.html @@ -89,4 +89,4 @@ 3-element Vector{Int64}: 42 2 - 3

    That is, a[i] = value (an alias for setindex!) mutates an existing array object in memory, accessible via either a or b. Subsequently setting a = 3.14159 does not change this array, it simply binds a to a different object; the array is still accessible via b. The other common syntax to mutate an existing object is a.field = value (an alias for setproperty!), which can be used to change a mutable struct.

    When you call a function in Julia, it behaves as if you assigned the argument values to new variable names corresponding to the function arguments, as discussed in Argument-Passing Behavior. (By convention, functions that mutate one or more of their arguments have names ending with !.)

    命名规范

    虽然 Julia 语言对合法名字的限制非常少，但是遵循以下这些命名规范是非常有用的：

    关于命名规范的更多信息，可查看代码风格指南。

    + 3

    That is, a[i] = value (an alias for setindex!) mutates an existing array object in memory, accessible via either a or b. Subsequently setting a = 3.14159 does not change this array, it simply binds a to a different object; the array is still accessible via b. The other common syntax to mutate an existing object is a.field = value (an alias for setproperty!), which can be used to change a mutable struct.

    When you call a function in Julia, it behaves as if you assigned the argument values to new variable names corresponding to the function arguments, as discussed in Argument-Passing Behavior. (By convention, functions that mutate one or more of their arguments have names ending with !.)

    命名规范

    虽然 Julia 语言对合法名字的限制非常少，但是遵循以下这些命名规范是非常有用的：

    关于命名规范的更多信息，可查看代码风格指南。

    diff --git a/dev/manual/workflow-tips/index.html b/dev/manual/workflow-tips/index.html index fcb99a32..7ec4078f 100644 --- a/dev/manual/workflow-tips/index.html +++ b/dev/manual/workflow-tips/index.html @@ -31,4 +31,4 @@ t("MyPkg")

    这将在 .julia/dev 目录中创建一个空白包"MyPkg"。 请注意，通过它的 Template 构造器，PkgTemplates 允许控制许多不同的选项。

    在下面的第 2 步中，编辑 MyPkg/src/MyPkg.jl 以更改源代码，并编辑 MyPkg/test/runtests.jl 以进行测试。

  • 对于“一次性”项目，您可以通过在临时目录（例如 /tmp）中进行工作来避免任何清理需求。

    切换到临时目录并启动 Julia，然后执行以下操作：

    pkg> generate MyPkg            # type ] to enter pkg mode
 julia> push!(LOAD_PATH, pwd())   # hit backspace to exit pkg mode

    如果你重新启动 Julia 会话，则必须重新发出修改 LOAD_PATH 的命令。

    在下面的第 2 步中，编辑 MyPkg/src/MyPkg.jl 以更改源代码，并创建你选择的任何测试文件。

  • 构建你自己的包

    在加载任何代码之前， 确保 Revise 已经被启用： using Revise 或者按照教程设置自动加载。

    然后切换到包含测试文件（假设文件为"runtests.jl"）的目录下，并：

    julia> using MyPkg
 
-julia> include("runtests.jl")

    你可以修改在 MyPkg 文件夹中的代码然后用include("runtests.jl")重新跑一遍测试。 通常，你可能需要重新启动Julia 会话来使得这些变化生效（受一些 限制）。

    • +julia> include("runtests.jl")

    你可以修改在 MyPkg 文件夹中的代码然后用include("runtests.jl")重新跑一遍测试。 通常，你可能需要重新启动Julia 会话来使得这些变化生效（受一些 限制）。

    diff --git a/dev/stdlib/ArgTools/index.html b/dev/stdlib/ArgTools/index.html index 176b0ef2..31e2a382 100644 --- a/dev/stdlib/ArgTools/index.html +++ b/dev/stdlib/ArgTools/index.html @@ -26,4 +26,4 @@ ## test using `arg` ## end ## post-test cleanup ## -end

    This method is useful if you need to specify path instead of using path name generated by tempname(). Since path is passed from outside of arg_writers, the path is not an argument to the do block in this form.

    ArgTools.@arg_test — Macro
    @arg_test arg1 arg2 ... body

    The @arg_test macro is used to convert arg functions provided by arg_readers and arg_writers into actual argument values. When you write @arg_test arg body it is equivalent to arg(arg -> body).

    +end

    This method is useful if you need to specify path instead of using path name generated by tempname(). Since path is passed from outside of arg_writers, the path is not an argument to the do block in this form.

    ArgTools.@arg_test — Macro
    @arg_test arg1 arg2 ... body

    The @arg_test macro is used to convert arg functions provided by arg_readers and arg_writers into actual argument values. When you write @arg_test arg body it is equivalent to arg(arg -> body).

    diff --git a/dev/stdlib/Artifacts/index.html b/dev/stdlib/Artifacts/index.html index bde743a6..fffc40bf 100644 --- a/dev/stdlib/Artifacts/index.html +++ b/dev/stdlib/Artifacts/index.html @@ -6,4 +6,4 @@
    Repository

    Artifacts

    Starting with Julia 1.6, the artifacts support has moved from Pkg.jl to Julia itself. Until proper documentation can be added here, you can learn more about artifacts in the Pkg.jl manual at https://julialang.github.io/Pkg.jl/v1/artifacts/.

    Julia 1.6

    Julia's artifacts API requires at least Julia 1.6. In Julia versions 1.3 to 1.5, you can use Pkg.Artifacts instead.

    Artifacts.artifact_meta — Function
    artifact_meta(name::String, artifacts_toml::String;
               platform::AbstractPlatform = HostPlatform(),
               pkg_uuid::Union{Base.UUID,Nothing}=nothing)

    Get metadata about a given artifact (identified by name) stored within the given (Julia)Artifacts.toml file. If the artifact is platform-specific, use platform to choose the most appropriate mapping. If none is found, return nothing.

    Julia 1.3

    This function requires at least Julia 1.3.

    Artifacts.artifact_hash — Function
    artifact_hash(name::String, artifacts_toml::String;
-              platform::AbstractPlatform = HostPlatform())

    Thin wrapper around artifact_meta() to return the hash of the specified, platform- collapsed artifact. Returns nothing if no mapping can be found.

    Julia 1.3

    This function requires at least Julia 1.3.

    Artifacts.find_artifacts_toml — Function
    find_artifacts_toml(path::String)

    Given the path to a .jl file, (such as the one returned by __source__.file in a macro context), find the (Julia)Artifacts.toml that is contained within the containing project (if it exists), otherwise return nothing.

    Julia 1.3

    This function requires at least Julia 1.3.

    Artifacts.@artifact_str — Macro
    macro artifact_str(name)

    Return the on-disk path to an artifact. Automatically looks the artifact up by name in the project's (Julia)Artifacts.toml file. Throws an error on if the requested artifact is not present. If run in the REPL, searches for the toml file starting in the current directory, see find_artifacts_toml() for more.

    If the artifact is marked "lazy" and the package has using LazyArtifacts defined, the artifact will be downloaded on-demand with Pkg the first time this macro tries to compute the path. The files will then be left installed locally for later.

    If name contains a forward or backward slash, all elements after the first slash will be taken to be path names indexing into the artifact, allowing for an easy one-liner to access a single file/directory within an artifact. Example:

    ffmpeg_path = @artifact"FFMPEG/bin/ffmpeg"
    Julia 1.3

    This macro requires at least Julia 1.3.

    Julia 1.6

    Slash-indexing requires at least Julia 1.6.

    + platform::AbstractPlatform = HostPlatform())

    Thin wrapper around artifact_meta() to return the hash of the specified, platform- collapsed artifact. Returns nothing if no mapping can be found.

    Julia 1.3

    This function requires at least Julia 1.3.

    Artifacts.find_artifacts_toml — Function
    find_artifacts_toml(path::String)

    Given the path to a .jl file, (such as the one returned by __source__.file in a macro context), find the (Julia)Artifacts.toml that is contained within the containing project (if it exists), otherwise return nothing.

    Julia 1.3

    This function requires at least Julia 1.3.

    Artifacts.@artifact_str — Macro
    macro artifact_str(name)

    Return the on-disk path to an artifact. Automatically looks the artifact up by name in the project's (Julia)Artifacts.toml file. Throws an error on if the requested artifact is not present. If run in the REPL, searches for the toml file starting in the current directory, see find_artifacts_toml() for more.

    If the artifact is marked "lazy" and the package has using LazyArtifacts defined, the artifact will be downloaded on-demand with Pkg the first time this macro tries to compute the path. The files will then be left installed locally for later.

    If name contains a forward or backward slash, all elements after the first slash will be taken to be path names indexing into the artifact, allowing for an easy one-liner to access a single file/directory within an artifact. Example:

    ffmpeg_path = @artifact"FFMPEG/bin/ffmpeg"
    Julia 1.3

    This macro requires at least Julia 1.3.

    Julia 1.6

    Slash-indexing requires at least Julia 1.6.

    diff --git a/dev/stdlib/Base64/index.html b/dev/stdlib/Base64/index.html index c094e288..a7324d52 100644 --- a/dev/stdlib/Base64/index.html +++ b/dev/stdlib/Base64/index.html @@ -37,4 +37,4 @@ 0x21 julia> String(b) -"Hello!"
    Base64.stringmime — Function
    stringmime(mime, x; context=nothing)

    Return an AbstractString containing the representation of x in the requested mime type. This is similar to repr(mime, x) except that binary data is base64-encoded as an ASCII string.

    The optional keyword argument context can be set to :key=>value pair or an IO or IOContext object whose attributes are used for the I/O stream passed to show.

    +"Hello!"
    Base64.stringmime — Function
    stringmime(mime, x; context=nothing)

    Return an AbstractString containing the representation of x in the requested mime type. This is similar to repr(mime, x) except that binary data is base64-encoded as an ASCII string.

    The optional keyword argument context can be set to :key=>value pair or an IO or IOContext object whose attributes are used for the I/O stream passed to show.

    diff --git a/dev/stdlib/CRC32c/index.html b/dev/stdlib/CRC32c/index.html index c905df2b..de673172 100644 --- a/dev/stdlib/CRC32c/index.html +++ b/dev/stdlib/CRC32c/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    CRC32c

    Standard library module for computing the CRC-32c checksum.

    CRC32c.crc32c — Function
    crc32c(data, crc::UInt32=0x00000000)

    Compute the CRC-32c checksum of the given data, which can be an Array{UInt8}, a contiguous subarray thereof, or a String. Optionally, you can pass a starting crc integer to be mixed in with the checksum. The crc parameter can be used to compute a checksum on data divided into chunks: performing crc32c(data2, crc32c(data1)) is equivalent to the checksum of [data1; data2]. (Technically, a little-endian checksum is computed.)

    There is also a method crc32c(io, nb, crc) to checksum nb bytes from a stream io, or crc32c(io, crc) to checksum all the remaining bytes. Hence you can do open(crc32c, filename) to checksum an entire file, or crc32c(seekstart(buf)) to checksum an IOBuffer without calling take!.

    For a String, note that the result is specific to the UTF-8 encoding (a different checksum would be obtained from a different Unicode encoding). To checksum an a::Array of some other bitstype, you can do crc32c(reinterpret(UInt8,a)), but note that the result may be endian-dependent.

    CRC32c.crc32c — Method
    crc32c(io::IO, [nb::Integer,] crc::UInt32=0x00000000)

    Read up to nb bytes from io and return the CRC-32c checksum, optionally mixed with a starting crc integer. If nb is not supplied, then io will be read until the end of the stream.

    +
    Repository

    CRC32c

    Standard library module for computing the CRC-32c checksum.

    CRC32c.crc32c — Function
    crc32c(data, crc::UInt32=0x00000000)

    Compute the CRC-32c checksum of the given data, which can be an Array{UInt8}, a contiguous subarray thereof, or a String. Optionally, you can pass a starting crc integer to be mixed in with the checksum. The crc parameter can be used to compute a checksum on data divided into chunks: performing crc32c(data2, crc32c(data1)) is equivalent to the checksum of [data1; data2]. (Technically, a little-endian checksum is computed.)

    There is also a method crc32c(io, nb, crc) to checksum nb bytes from a stream io, or crc32c(io, crc) to checksum all the remaining bytes. Hence you can do open(crc32c, filename) to checksum an entire file, or crc32c(seekstart(buf)) to checksum an IOBuffer without calling take!.

    For a String, note that the result is specific to the UTF-8 encoding (a different checksum would be obtained from a different Unicode encoding). To checksum an a::Array of some other bitstype, you can do crc32c(reinterpret(UInt8,a)), but note that the result may be endian-dependent.

    CRC32c.crc32c — Method
    crc32c(io::IO, [nb::Integer,] crc::UInt32=0x00000000)

    Read up to nb bytes from io and return the CRC-32c checksum, optionally mixed with a starting crc integer. If nb is not supplied, then io will be read until the end of the stream.

    diff --git a/dev/stdlib/Dates/index.html b/dev/stdlib/Dates/index.html index ee8db47c..15edcf55 100644 --- a/dev/stdlib/Dates/index.html +++ b/dev/stdlib/Dates/index.html @@ -507,4 +507,4 @@ "2018-08-08T12:00:43.001"
    Dates.ISODateFormat — Constant
    Dates.ISODateFormat

    Describes the ISO8601 formatting for a date. This is the default value for Dates.format of a Date.

    Example

    julia> Dates.format(Date(2018, 8, 8), ISODateFormat)
 "2018-08-08"
    Dates.ISOTimeFormat — Constant
    Dates.ISOTimeFormat

    Describes the ISO8601 formatting for a time. This is the default value for Dates.format of a Time.

    Example

    julia> Dates.format(Time(12, 0, 43, 1), ISOTimeFormat)
 "12:00:43.001"
    Dates.RFC1123Format — Constant
    Dates.RFC1123Format

    Describes the RFC1123 formatting for a date and time.

    Example

    julia> Dates.format(DateTime(2018, 8, 8, 12, 0, 43, 1), RFC1123Format)
-"Wed, 08 Aug 2018 12:00:43"
    +"Wed, 08 Aug 2018 12:00:43"
    diff --git a/dev/stdlib/DelimitedFiles/index.html b/dev/stdlib/DelimitedFiles/index.html index 30b02fd2..1825a050 100644 --- a/dev/stdlib/DelimitedFiles/index.html +++ b/dev/stdlib/DelimitedFiles/index.html @@ -125,4 +125,4 @@ 3 7 4 8 -julia> rm("delim_file.txt")source +julia> rm("delim_file.txt")source diff --git a/dev/stdlib/Distributed/index.html b/dev/stdlib/Distributed/index.html index 336b28ec..3211a223 100644 --- a/dev/stdlib/Distributed/index.html +++ b/dev/stdlib/Distributed/index.html @@ -156,4 +156,4 @@ endsource
    Distributed.@everywhere — Macro
    @everywhere [procs()] expr

    Execute an expression under Main on all procs. Errors on any of the processes are collected into a CompositeException and thrown. For example:

    @everywhere bar = 1

    will define Main.bar on all current processes. Any processes added later (say with addprocs()) will not have the expression defined.

    Unlike @spawnat, @everywhere does not capture any local variables. Instead, local variables can be broadcast using interpolation:

    foo = 1
 @everywhere bar = $foo

    The optional argument procs allows specifying a subset of all processes to have execute the expression.

    Similar to calling remotecall_eval(Main, procs, expr), but with two extra features:

    - `using` and `import` statements run on the calling process first, to ensure
   packages are precompiled.
-- The current source file path used by `include` is propagated to other processes.
    source
    Distributed.clear! — Method
    clear!(syms, pids=workers(); mod=Main)

    Clears global bindings in modules by initializing them to nothing. syms should be of type Symbol or a collection of Symbols . pids and mod identify the processes and the module in which global variables are to be reinitialized. Only those names found to be defined under mod are cleared.

    An exception is raised if a global constant is requested to be cleared.

    source
    Distributed.remoteref_id — Function
    remoteref_id(r::AbstractRemoteRef) -> RRID

    Futures and RemoteChannels are identified by fields:

    • where - refers to the node where the underlying object/storage referred to by the reference actually exists.

    • whence - refers to the node the remote reference was created from. Note that this is different from the node where the underlying object referred to actually exists. For example calling RemoteChannel(2) from the master process would result in a where value of 2 and a whence value of 1.

    • id is unique across all references created from the worker specified by whence.

    Taken together, whence and id uniquely identify a reference across all workers.

    remoteref_id is a low-level API which returns a RRID object that wraps whence and id values of a remote reference.

    source
    Distributed.channel_from_id — Function
    channel_from_id(id) -> c

    A low-level API which returns the backing AbstractChannel for an id returned by remoteref_id. The call is valid only on the node where the backing channel exists.

    source
    Distributed.worker_id_from_socket — Function
    worker_id_from_socket(s) -> pid

    A low-level API which, given a IO connection or a Worker, returns the pid of the worker it is connected to. This is useful when writing custom serialize methods for a type, which optimizes the data written out depending on the receiving process id.

    source
    Distributed.cluster_cookie — Method
    cluster_cookie() -> cookie

    Return the cluster cookie.

    source
    Distributed.cluster_cookie — Method
    cluster_cookie(cookie) -> cookie

    Set the passed cookie as the cluster cookie, then returns it.

    source

    Cluster Manager Interface

    This interface provides a mechanism to launch and manage Julia workers on different cluster environments. There are two types of managers present in Base: LocalManager, for launching additional workers on the same host, and SSHManager, for launching on remote hosts via ssh. TCP/IP sockets are used to connect and transport messages between processes. It is possible for Cluster Managers to provide a different transport.

    Distributed.ClusterManager — Type
    ClusterManager

    Supertype for cluster managers, which control workers processes as a cluster. Cluster managers implement how workers can be added, removed and communicated with. SSHManager and LocalManager are subtypes of this.

    source
    Distributed.WorkerConfig — Type
    WorkerConfig

    Type used by ClusterManagers to control workers added to their clusters. Some fields are used by all cluster managers to access a host:

    • io – the connection used to access the worker (a subtype of IO or Nothing)
    • host – the host address (either a String or Nothing)
    • port – the port on the host used to connect to the worker (either an Int or Nothing)

    Some are used by the cluster manager to add workers to an already-initialized host:

    • count – the number of workers to be launched on the host
    • exename – the path to the Julia executable on the host, defaults to "$(Sys.BINDIR)/julia" or "$(Sys.BINDIR)/julia-debug"
    • exeflags – flags to use when launching Julia remotely

    The userdata field is used to store information for each worker by external managers.

    Some fields are used by SSHManager and similar managers:

    • tunnel – true (use tunneling), false (do not use tunneling), or nothing (use default for the manager)
    • multiplex – true (use SSH multiplexing for tunneling) or false
    • forward – the forwarding option used for -L option of ssh
    • bind_addr – the address on the remote host to bind to
    • sshflags – flags to use in establishing the SSH connection
    • max_parallel – the maximum number of workers to connect to in parallel on the host

    Some fields are used by both LocalManagers and SSHManagers:

    • connect_at – determines whether this is a worker-to-worker or driver-to-worker setup call
    • process – the process which will be connected (usually the manager will assign this during addprocs)
    • ospid – the process ID according to the host OS, used to interrupt worker processes
    • environ – private dictionary used to store temporary information by Local/SSH managers
    • ident – worker as identified by the ClusterManager
    • connect_idents – list of worker ids the worker must connect to if using a custom topology
    • enable_threaded_blas – true, false, or nothing, whether to use threaded BLAS or not on the workers
    source
    Distributed.launch — Function
    launch(manager::ClusterManager, params::Dict, launched::Array, launch_ntfy::Condition)

    Implemented by cluster managers. For every Julia worker launched by this function, it should append a WorkerConfig entry to launched and notify launch_ntfy. The function MUST exit once all workers, requested by manager have been launched. params is a dictionary of all keyword arguments addprocs was called with.

    source
    Distributed.manage — Function
    manage(manager::ClusterManager, id::Integer, config::WorkerConfig. op::Symbol)

    Implemented by cluster managers. It is called on the master process, during a worker's lifetime, with appropriate op values:

    • with :register/:deregister when a worker is added / removed from the Julia worker pool.
    • with :interrupt when interrupt(workers) is called. The ClusterManager should signal the appropriate worker with an interrupt signal.
    • with :finalize for cleanup purposes.
    source
    Base.kill — Method
    kill(manager::ClusterManager, pid::Int, config::WorkerConfig)

    Implemented by cluster managers. It is called on the master process, by rmprocs. It should cause the remote worker specified by pid to exit. kill(manager::ClusterManager.....) executes a remote exit() on pid.

    source
    Sockets.connect — Method
    connect(manager::ClusterManager, pid::Int, config::WorkerConfig) -> (instrm::IO, outstrm::IO)

    Implemented by cluster managers using custom transports. It should establish a logical connection to worker with id pid, specified by config and return a pair of IO objects. Messages from pid to current process will be read off instrm, while messages to be sent to pid will be written to outstrm. The custom transport implementation must ensure that messages are delivered and received completely and in order. connect(manager::ClusterManager.....) sets up TCP/IP socket connections in-between workers.

    source
    Distributed.init_worker — Function
    init_worker(cookie::AbstractString, manager::ClusterManager=DefaultClusterManager())

    Called by cluster managers implementing custom transports. It initializes a newly launched process as a worker. Command line argument --worker[=<cookie>] has the effect of initializing a process as a worker using TCP/IP sockets for transport. cookie is a cluster_cookie.

    source
    Distributed.start_worker — Function
    start_worker([out::IO=stdout], cookie::AbstractString=readline(stdin); close_stdin::Bool=true, stderr_to_stdout::Bool=true)

    start_worker is an internal function which is the default entry point for worker processes connecting via TCP/IP. It sets up the process as a Julia cluster worker.

    host:port information is written to stream out (defaults to stdout).

    The function reads the cookie from stdin if required, and listens on a free port (or if specified, the port in the --bind-to command line option) and schedules tasks to process incoming TCP connections and requests. It also (optionally) closes stdin and redirects stderr to stdout.

    It does not return.

    source
    Distributed.process_messages — Function
    process_messages(r_stream::IO, w_stream::IO, incoming::Bool=true)

    Called by cluster managers using custom transports. It should be called when the custom transport implementation receives the first message from a remote worker. The custom transport must manage a logical connection to the remote worker and provide two IO objects, one for incoming messages and the other for messages addressed to the remote worker. If incoming is true, the remote peer initiated the connection. Whichever of the pair initiates the connection sends the cluster cookie and its Julia version number to perform the authentication handshake.

    See also cluster_cookie.

    source
    Distributed.default_addprocs_params — Function
    default_addprocs_params(mgr::ClusterManager) -> Dict{Symbol, Any}

    Implemented by cluster managers. The default keyword parameters passed when calling addprocs(mgr). The minimal set of options is available by calling default_addprocs_params()

    source
    +- The current source file path used by `include` is propagated to other processes.source
    Distributed.clear! — Method
    clear!(syms, pids=workers(); mod=Main)

    Clears global bindings in modules by initializing them to nothing. syms should be of type Symbol or a collection of Symbols . pids and mod identify the processes and the module in which global variables are to be reinitialized. Only those names found to be defined under mod are cleared.

    An exception is raised if a global constant is requested to be cleared.

    source
    Distributed.remoteref_id — Function
    remoteref_id(r::AbstractRemoteRef) -> RRID

    Futures and RemoteChannels are identified by fields:

    • where - refers to the node where the underlying object/storage referred to by the reference actually exists.

    • whence - refers to the node the remote reference was created from. Note that this is different from the node where the underlying object referred to actually exists. For example calling RemoteChannel(2) from the master process would result in a where value of 2 and a whence value of 1.

    • id is unique across all references created from the worker specified by whence.

    Taken together, whence and id uniquely identify a reference across all workers.

    remoteref_id is a low-level API which returns a RRID object that wraps whence and id values of a remote reference.

    source
    Distributed.channel_from_id — Function
    channel_from_id(id) -> c

    A low-level API which returns the backing AbstractChannel for an id returned by remoteref_id. The call is valid only on the node where the backing channel exists.

    source
    Distributed.worker_id_from_socket — Function
    worker_id_from_socket(s) -> pid

    A low-level API which, given a IO connection or a Worker, returns the pid of the worker it is connected to. This is useful when writing custom serialize methods for a type, which optimizes the data written out depending on the receiving process id.

    source
    Distributed.cluster_cookie — Method
    cluster_cookie() -> cookie

    Return the cluster cookie.

    source
    Distributed.cluster_cookie — Method
    cluster_cookie(cookie) -> cookie

    Set the passed cookie as the cluster cookie, then returns it.

    source

    Cluster Manager Interface

    This interface provides a mechanism to launch and manage Julia workers on different cluster environments. There are two types of managers present in Base: LocalManager, for launching additional workers on the same host, and SSHManager, for launching on remote hosts via ssh. TCP/IP sockets are used to connect and transport messages between processes. It is possible for Cluster Managers to provide a different transport.

    Distributed.ClusterManager — Type
    ClusterManager

    Supertype for cluster managers, which control workers processes as a cluster. Cluster managers implement how workers can be added, removed and communicated with. SSHManager and LocalManager are subtypes of this.

    source
    Distributed.WorkerConfig — Type
    WorkerConfig

    Type used by ClusterManagers to control workers added to their clusters. Some fields are used by all cluster managers to access a host:

    • io – the connection used to access the worker (a subtype of IO or Nothing)
    • host – the host address (either a String or Nothing)
    • port – the port on the host used to connect to the worker (either an Int or Nothing)

    Some are used by the cluster manager to add workers to an already-initialized host:

    • count – the number of workers to be launched on the host
    • exename – the path to the Julia executable on the host, defaults to "$(Sys.BINDIR)/julia" or "$(Sys.BINDIR)/julia-debug"
    • exeflags – flags to use when launching Julia remotely

    The userdata field is used to store information for each worker by external managers.

    Some fields are used by SSHManager and similar managers:

    • tunnel – true (use tunneling), false (do not use tunneling), or nothing (use default for the manager)
    • multiplex – true (use SSH multiplexing for tunneling) or false
    • forward – the forwarding option used for -L option of ssh
    • bind_addr – the address on the remote host to bind to
    • sshflags – flags to use in establishing the SSH connection
    • max_parallel – the maximum number of workers to connect to in parallel on the host

    Some fields are used by both LocalManagers and SSHManagers:

    • connect_at – determines whether this is a worker-to-worker or driver-to-worker setup call
    • process – the process which will be connected (usually the manager will assign this during addprocs)
    • ospid – the process ID according to the host OS, used to interrupt worker processes
    • environ – private dictionary used to store temporary information by Local/SSH managers
    • ident – worker as identified by the ClusterManager
    • connect_idents – list of worker ids the worker must connect to if using a custom topology
    • enable_threaded_blas – true, false, or nothing, whether to use threaded BLAS or not on the workers
    source
    Distributed.launch — Function
    launch(manager::ClusterManager, params::Dict, launched::Array, launch_ntfy::Condition)

    Implemented by cluster managers. For every Julia worker launched by this function, it should append a WorkerConfig entry to launched and notify launch_ntfy. The function MUST exit once all workers, requested by manager have been launched. params is a dictionary of all keyword arguments addprocs was called with.

    source
    Distributed.manage — Function
    manage(manager::ClusterManager, id::Integer, config::WorkerConfig. op::Symbol)

    Implemented by cluster managers. It is called on the master process, during a worker's lifetime, with appropriate op values:

    • with :register/:deregister when a worker is added / removed from the Julia worker pool.
    • with :interrupt when interrupt(workers) is called. The ClusterManager should signal the appropriate worker with an interrupt signal.
    • with :finalize for cleanup purposes.
    source
    Base.kill — Method
    kill(manager::ClusterManager, pid::Int, config::WorkerConfig)

    Implemented by cluster managers. It is called on the master process, by rmprocs. It should cause the remote worker specified by pid to exit. kill(manager::ClusterManager.....) executes a remote exit() on pid.

    source
    Sockets.connect — Method
    connect(manager::ClusterManager, pid::Int, config::WorkerConfig) -> (instrm::IO, outstrm::IO)

    Implemented by cluster managers using custom transports. It should establish a logical connection to worker with id pid, specified by config and return a pair of IO objects. Messages from pid to current process will be read off instrm, while messages to be sent to pid will be written to outstrm. The custom transport implementation must ensure that messages are delivered and received completely and in order. connect(manager::ClusterManager.....) sets up TCP/IP socket connections in-between workers.

    source
    Distributed.init_worker — Function
    init_worker(cookie::AbstractString, manager::ClusterManager=DefaultClusterManager())

    Called by cluster managers implementing custom transports. It initializes a newly launched process as a worker. Command line argument --worker[=<cookie>] has the effect of initializing a process as a worker using TCP/IP sockets for transport. cookie is a cluster_cookie.

    source
    Distributed.start_worker — Function
    start_worker([out::IO=stdout], cookie::AbstractString=readline(stdin); close_stdin::Bool=true, stderr_to_stdout::Bool=true)

    start_worker is an internal function which is the default entry point for worker processes connecting via TCP/IP. It sets up the process as a Julia cluster worker.

    host:port information is written to stream out (defaults to stdout).

    The function reads the cookie from stdin if required, and listens on a free port (or if specified, the port in the --bind-to command line option) and schedules tasks to process incoming TCP connections and requests. It also (optionally) closes stdin and redirects stderr to stdout.

    It does not return.

    source
    Distributed.process_messages — Function
    process_messages(r_stream::IO, w_stream::IO, incoming::Bool=true)

    Called by cluster managers using custom transports. It should be called when the custom transport implementation receives the first message from a remote worker. The custom transport must manage a logical connection to the remote worker and provide two IO objects, one for incoming messages and the other for messages addressed to the remote worker. If incoming is true, the remote peer initiated the connection. Whichever of the pair initiates the connection sends the cluster cookie and its Julia version number to perform the authentication handshake.

    See also cluster_cookie.

    source
    Distributed.default_addprocs_params — Function
    default_addprocs_params(mgr::ClusterManager) -> Dict{Symbol, Any}

    Implemented by cluster managers. The default keyword parameters passed when calling addprocs(mgr). The minimal set of options is available by calling default_addprocs_params()

    source
    diff --git a/dev/stdlib/Downloads/index.html b/dev/stdlib/Downloads/index.html index 7f9a1e28..bef974ad 100644 --- a/dev/stdlib/Downloads/index.html +++ b/dev/stdlib/Downloads/index.html @@ -60,4 +60,4 @@ code :: Int message :: String response :: Response -end

    RequestError is a type capturing the properties of a failed response to a request as an exception object:

    The same RequestError type is thrown by download if the request was successful but there was a protocol-level error indicated by a status code that is not in the 2xx range, in which case code will be zero and the message field will be the empty string. The request API only throws a RequestError if the libcurl error code is non-zero, in which case the included response object is likely to have a status of zero and an empty message. There are, however, situations where a curl-level error is thrown due to a protocol error, in which case both the inner and outer code and message may be of interest.

    Downloads.Downloader — Type
    Downloader(; [ grace::Real = 30 ])

    Downloader objects are used to perform individual download operations. Connections, name lookups and other resources are shared within a Downloader. These connections and resources are cleaned up after a configurable grace period (default: 30 seconds) since anything was downloaded with it, or when it is garbage collected, whichever comes first. If the grace period is set to zero, all resources will be cleaned up immediately as soon as there are no more ongoing downloads in progress. If the grace period is set to Inf then resources are not cleaned up until Downloader is garbage collected.

    +end

    RequestError is a type capturing the properties of a failed response to a request as an exception object:

    The same RequestError type is thrown by download if the request was successful but there was a protocol-level error indicated by a status code that is not in the 2xx range, in which case code will be zero and the message field will be the empty string. The request API only throws a RequestError if the libcurl error code is non-zero, in which case the included response object is likely to have a status of zero and an empty message. There are, however, situations where a curl-level error is thrown due to a protocol error, in which case both the inner and outer code and message may be of interest.

    Downloads.Downloader — Type
    Downloader(; [ grace::Real = 30 ])

    Downloader objects are used to perform individual download operations. Connections, name lookups and other resources are shared within a Downloader. These connections and resources are cleaned up after a configurable grace period (default: 30 seconds) since anything was downloaded with it, or when it is garbage collected, whichever comes first. If the grace period is set to zero, all resources will be cleaned up immediately as soon as there are no more ongoing downloads in progress. If the grace period is set to Inf then resources are not cleaned up until Downloader is garbage collected.

    diff --git a/dev/stdlib/FileWatching/index.html b/dev/stdlib/FileWatching/index.html index 742702cd..644a1d2a 100644 --- a/dev/stdlib/FileWatching/index.html +++ b/dev/stdlib/FileWatching/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    文件相关事件

    FileWatching.poll_fd — Function
    poll_fd(fd, timeout_s::Real=-1; readable=false, writable=false)

    Monitor a file descriptor fd for changes in the read or write availability, and with a timeout given by timeout_s seconds.

    The keyword arguments determine which of read and/or write status should be monitored; at least one of them must be set to true.

    The returned value is an object with boolean fields readable, writable, and timedout, giving the result of the polling.

    FileWatching.poll_file — Function
    poll_file(path::AbstractString, interval_s::Real=5.007, timeout_s::Real=-1) -> (previous::StatStruct, current)

    Monitor a file for changes by polling every interval_s seconds until a change occurs or timeout_s seconds have elapsed. The interval_s should be a long period; the default is 5.007 seconds.

    Returns a pair of status objects (previous, current) when a change is detected. The previous status is always a StatStruct, but it may have all of the fields zeroed (indicating the file didn't previously exist, or wasn't previously accessible).

    The current status object may be a StatStruct, an EOFError (indicating the timeout elapsed), or some other Exception subtype (if the stat operation failed - for example, if the path does not exist).

    To determine when a file was modified, compare current isa StatStruct && mtime(prev) != mtime(current) to detect notification of changes. However, using watch_file for this operation is preferred, since it is more reliable and efficient, although in some situations it may not be available.

    FileWatching.watch_file — Function
    watch_file(path::AbstractString, timeout_s::Real=-1)

    Watch file or directory path for changes until a change occurs or timeout_s seconds have elapsed. This function does not poll the file system and instead uses platform-specific functionality to receive notifications from the operating system (e.g. via inotify on Linux). See the NodeJS documentation linked below for details.

    The returned value is an object with boolean fields renamed, changed, and timedout, giving the result of watching the file.

    This behavior of this function varies slightly across platforms. See https://nodejs.org/api/fs.html#fs_caveats for more detailed information.

    FileWatching.watch_folder — Function
    watch_folder(path::AbstractString, timeout_s::Real=-1)

    Watches a file or directory path for changes until a change has occurred or timeout_s seconds have elapsed. This function does not poll the file system and instead uses platform-specific functionality to receive notifications from the operating system (e.g. via inotify on Linux). See the NodeJS documentation linked below for details.

    This will continuing tracking changes for path in the background until unwatch_folder is called on the same path.

    The returned value is an pair where the first field is the name of the changed file (if available) and the second field is an object with boolean fields renamed, changed, and timedout, giving the event.

    This behavior of this function varies slightly across platforms. See https://nodejs.org/api/fs.html#fs_caveats for more detailed information.

    FileWatching.unwatch_folder — Function
    unwatch_folder(path::AbstractString)

    Stop background tracking of changes for path. It is not recommended to do this while another task is waiting for watch_folder to return on the same path, as the result may be unpredictable.

    Pidfile

    A simple utility tool for creating advisory pidfiles (lock files).

    Primary Functions

    FileWatching.Pidfile.mkpidlock — Function
    mkpidlock([f::Function], at::String, [pid::Cint, proc::Process]; kwopts...)

    Create a pidfile lock for the path "at" for the current process or the process identified by pid or proc. Can take a function to execute once locked, for usage in do blocks, after which the lock will be automatically closed. If the lock fails and wait is false, then an error is thrown.

    The lock will be released by either close, a finalizer, or shortly after proc exits. Make sure the return value is live through the end of the critical section of your program, so the finalizer does not reclaim it early.

    Optional keyword arguments:

    • mode: file access mode (modified by the process umask). Defaults to world-readable.
    • poll_interval: Specify the maximum time to between attempts (if watch_file doesn't work)
    • stale_age: Delete an existing pidfile (ignoring the lock) if it is older than this many seconds, based on its mtime. The file won't be deleted until 5x longer than this if the pid in the file appears that it may be valid. Or 25x longer if refresh is overridden to 0 to disable lock refreshing. By default this is disabled (stale_age = 0), but a typical recommended value would be about 3-5x an estimated normal completion time.
    • refresh: Keeps a lock from becoming stale by updating the mtime every interval of time that passes. By default, this is set to stale_age/2, which is the recommended value.
    • wait: If true, block until we get the lock, if false, raise error if lock fails.
    FileWatching.Pidfile.trymkpidlock — Function
    trymkpidlock([f::Function], at::String, [pid::Cint, proc::Process]; kwopts...)

    Like mkpidlock except returns false instead of waiting if the file is already locked.

    Julia 1.10

    This function requires at least Julia 1.10.

    Base.close — Method
    close(lock::LockMonitor)

    Release a pidfile lock.

    Helper Functions

    FileWatching.Pidfile.open_exclusive — Function
    open_exclusive(path::String; mode, poll_interval, wait, stale_age, refresh) :: File

    Create a new a file for read-write advisory-exclusive access. If wait is false then error out if the lock files exist otherwise block until we get the lock.

    For a description of the keyword arguments, see mkpidlock.

    FileWatching.Pidfile.tryopen_exclusive — Function
    tryopen_exclusive(path::String, mode::Integer = 0o444) :: Union{Void, File}

    Try to create a new file for read-write advisory-exclusive access, return nothing if it already exists.

    FileWatching.Pidfile.parse_pidfile — Function
    parse_pidfile(file::Union{IO, String}) => (pid, hostname, age)

    Attempt to parse our pidfile format, replaced an element with (0, "", 0.0), respectively, for any read that failed.

    FileWatching.Pidfile.stale_pidfile — Function
    stale_pidfile(path::String, stale_age::Real, refresh::Real) :: Bool

    Helper function for open_exclusive for deciding if a pidfile is stale.

    FileWatching.Pidfile.isvalidpid — Function
    isvalidpid(hostname::String, pid::Cuint) :: Bool

    Attempt to conservatively estimate whether pid is a valid process id.

    Base.Filesystem.touch — Method
    Base.touch(::Pidfile.LockMonitor)

    Update the mtime on the lock, to indicate it is still fresh.

    See also the refresh keyword in the mkpidlock constructor.

    +
    Repository

    文件相关事件

    FileWatching.poll_fd — Function
    poll_fd(fd, timeout_s::Real=-1; readable=false, writable=false)

    Monitor a file descriptor fd for changes in the read or write availability, and with a timeout given by timeout_s seconds.

    The keyword arguments determine which of read and/or write status should be monitored; at least one of them must be set to true.

    The returned value is an object with boolean fields readable, writable, and timedout, giving the result of the polling.

    FileWatching.poll_file — Function
    poll_file(path::AbstractString, interval_s::Real=5.007, timeout_s::Real=-1) -> (previous::StatStruct, current)

    Monitor a file for changes by polling every interval_s seconds until a change occurs or timeout_s seconds have elapsed. The interval_s should be a long period; the default is 5.007 seconds.

    Returns a pair of status objects (previous, current) when a change is detected. The previous status is always a StatStruct, but it may have all of the fields zeroed (indicating the file didn't previously exist, or wasn't previously accessible).

    The current status object may be a StatStruct, an EOFError (indicating the timeout elapsed), or some other Exception subtype (if the stat operation failed - for example, if the path does not exist).

    To determine when a file was modified, compare current isa StatStruct && mtime(prev) != mtime(current) to detect notification of changes. However, using watch_file for this operation is preferred, since it is more reliable and efficient, although in some situations it may not be available.

    FileWatching.watch_file — Function
    watch_file(path::AbstractString, timeout_s::Real=-1)

    Watch file or directory path for changes until a change occurs or timeout_s seconds have elapsed. This function does not poll the file system and instead uses platform-specific functionality to receive notifications from the operating system (e.g. via inotify on Linux). See the NodeJS documentation linked below for details.

    The returned value is an object with boolean fields renamed, changed, and timedout, giving the result of watching the file.

    This behavior of this function varies slightly across platforms. See https://nodejs.org/api/fs.html#fs_caveats for more detailed information.

    FileWatching.watch_folder — Function
    watch_folder(path::AbstractString, timeout_s::Real=-1)

    Watches a file or directory path for changes until a change has occurred or timeout_s seconds have elapsed. This function does not poll the file system and instead uses platform-specific functionality to receive notifications from the operating system (e.g. via inotify on Linux). See the NodeJS documentation linked below for details.

    This will continuing tracking changes for path in the background until unwatch_folder is called on the same path.

    The returned value is an pair where the first field is the name of the changed file (if available) and the second field is an object with boolean fields renamed, changed, and timedout, giving the event.

    This behavior of this function varies slightly across platforms. See https://nodejs.org/api/fs.html#fs_caveats for more detailed information.

    FileWatching.unwatch_folder — Function
    unwatch_folder(path::AbstractString)

    Stop background tracking of changes for path. It is not recommended to do this while another task is waiting for watch_folder to return on the same path, as the result may be unpredictable.

    Pidfile

    A simple utility tool for creating advisory pidfiles (lock files).

    Primary Functions

    FileWatching.Pidfile.mkpidlock — Function
    mkpidlock([f::Function], at::String, [pid::Cint, proc::Process]; kwopts...)

    Create a pidfile lock for the path "at" for the current process or the process identified by pid or proc. Can take a function to execute once locked, for usage in do blocks, after which the lock will be automatically closed. If the lock fails and wait is false, then an error is thrown.

    The lock will be released by either close, a finalizer, or shortly after proc exits. Make sure the return value is live through the end of the critical section of your program, so the finalizer does not reclaim it early.

    Optional keyword arguments:

    • mode: file access mode (modified by the process umask). Defaults to world-readable.
    • poll_interval: Specify the maximum time to between attempts (if watch_file doesn't work)
    • stale_age: Delete an existing pidfile (ignoring the lock) if it is older than this many seconds, based on its mtime. The file won't be deleted until 5x longer than this if the pid in the file appears that it may be valid. Or 25x longer if refresh is overridden to 0 to disable lock refreshing. By default this is disabled (stale_age = 0), but a typical recommended value would be about 3-5x an estimated normal completion time.
    • refresh: Keeps a lock from becoming stale by updating the mtime every interval of time that passes. By default, this is set to stale_age/2, which is the recommended value.
    • wait: If true, block until we get the lock, if false, raise error if lock fails.
    FileWatching.Pidfile.trymkpidlock — Function
    trymkpidlock([f::Function], at::String, [pid::Cint, proc::Process]; kwopts...)

    Like mkpidlock except returns false instead of waiting if the file is already locked.

    Julia 1.10

    This function requires at least Julia 1.10.

    Base.close — Method
    close(lock::LockMonitor)

    Release a pidfile lock.

    Helper Functions

    FileWatching.Pidfile.open_exclusive — Function
    open_exclusive(path::String; mode, poll_interval, wait, stale_age, refresh) :: File

    Create a new a file for read-write advisory-exclusive access. If wait is false then error out if the lock files exist otherwise block until we get the lock.

    For a description of the keyword arguments, see mkpidlock.

    FileWatching.Pidfile.tryopen_exclusive — Function
    tryopen_exclusive(path::String, mode::Integer = 0o444) :: Union{Void, File}

    Try to create a new file for read-write advisory-exclusive access, return nothing if it already exists.

    FileWatching.Pidfile.parse_pidfile — Function
    parse_pidfile(file::Union{IO, String}) => (pid, hostname, age)

    Attempt to parse our pidfile format, replaced an element with (0, "", 0.0), respectively, for any read that failed.

    FileWatching.Pidfile.stale_pidfile — Function
    stale_pidfile(path::String, stale_age::Real, refresh::Real) :: Bool

    Helper function for open_exclusive for deciding if a pidfile is stale.

    FileWatching.Pidfile.isvalidpid — Function
    isvalidpid(hostname::String, pid::Cuint) :: Bool

    Attempt to conservatively estimate whether pid is a valid process id.

    Base.Filesystem.touch — Method
    Base.touch(::Pidfile.LockMonitor)

    Update the mtime on the lock, to indicate it is still fresh.

    See also the refresh keyword in the mkpidlock constructor.

    diff --git a/dev/stdlib/Future/index.html b/dev/stdlib/Future/index.html index 4d3525d5..7bd2e1f0 100644 --- a/dev/stdlib/Future/index.html +++ b/dev/stdlib/Future/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    Future

    The Future module implements future behavior of already existing functions, which will replace the current version in a future release of Julia.

    Future.copy! — Function
    Future.copy!(dst, src) -> dst

    Copy src into dst.

    Julia 1.1

    This function has moved to Base with Julia 1.1, consider using copy!(dst, src) instead. Future.copy! will be deprecated in the future.

    Future.randjump — Function
    randjump(r::MersenneTwister, steps::Integer) -> MersenneTwister

    Create an initialized MersenneTwister object, whose state is moved forward (without generating numbers) from r by steps steps. One such step corresponds to the generation of two Float64 numbers. For each different value of steps, a large polynomial has to be generated internally. One is already pre-computed for steps=big(10)^20.

    +
    Repository

    Future

    The Future module implements future behavior of already existing functions, which will replace the current version in a future release of Julia.

    Future.copy! — Function
    Future.copy!(dst, src) -> dst

    Copy src into dst.

    Julia 1.1

    This function has moved to Base with Julia 1.1, consider using copy!(dst, src) instead. Future.copy! will be deprecated in the future.

    Future.randjump — Function
    randjump(r::MersenneTwister, steps::Integer) -> MersenneTwister

    Create an initialized MersenneTwister object, whose state is moved forward (without generating numbers) from r by steps steps. One such step corresponds to the generation of two Float64 numbers. For each different value of steps, a large polynomial has to be generated internally. One is already pre-computed for steps=big(10)^20.

    diff --git a/dev/stdlib/InteractiveUtils/index.html b/dev/stdlib/InteractiveUtils/index.html index 81417857..6eb33e9e 100644 --- a/dev/stdlib/InteractiveUtils/index.html +++ b/dev/stdlib/InteractiveUtils/index.html @@ -29,4 +29,4 @@ 1.8 ms CodecZlib 0.8 ms Compat 13.1 ms FilePathsBase 28.39% compilation time - 1681.2 ms CSV 92.40% compilation time
    Julia 1.8

    This macro requires at least Julia 1.8

    InteractiveUtils.clipboard — Function
    clipboard(x)

    Send a printed form of x to the operating system clipboard ("copy").

    clipboard() -> String

    Return a string with the contents of the operating system clipboard ("paste").

    + 1681.2 ms CSV 92.40% compilation time
    Julia 1.8

    This macro requires at least Julia 1.8

    InteractiveUtils.clipboard — Function
    clipboard(x)

    Send a printed form of x to the operating system clipboard ("copy").

    clipboard() -> String

    Return a string with the contents of the operating system clipboard ("paste").

    diff --git a/dev/stdlib/LazyArtifacts/index.html b/dev/stdlib/LazyArtifacts/index.html index af3e1cdf..448f02cc 100644 --- a/dev/stdlib/LazyArtifacts/index.html +++ b/dev/stdlib/LazyArtifacts/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    Lazy Artifacts

    In order for a package to download artifacts lazily, LazyArtifacts must be explicitly listed as a dependency of that package.

    For further information on artifacts, see Artifacts.

    +
    Repository

    Lazy Artifacts

    In order for a package to download artifacts lazily, LazyArtifacts must be explicitly listed as a dependency of that package.

    For further information on artifacts, see Artifacts.

    diff --git a/dev/stdlib/LibCURL/index.html b/dev/stdlib/LibCURL/index.html index 225c3d9c..0aa68739 100644 --- a/dev/stdlib/LibCURL/index.html +++ b/dev/stdlib/LibCURL/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository
    +
    Repository
    diff --git a/dev/stdlib/LibGit2/index.html b/dev/stdlib/LibGit2/index.html index b9f478f9..84038515 100644 --- a/dev/stdlib/LibGit2/index.html +++ b/dev/stdlib/LibGit2/index.html @@ -239,4 +239,4 @@ julia> LibGit2.url(remote) "https://github.com/JuliaLang/Example.jl"
    LibGit2.version — Function
    version() -> VersionNumber

    Return the version of libgit2 in use, as a VersionNumber.

    LibGit2.with — Function
    with(f::Function, obj)

    Resource management helper function. Applies f to obj, making sure to call close on obj after f successfully returns or throws an error. Ensures that allocated git resources are finalized as soon as they are no longer needed.

    LibGit2.with_warn — Function
    with_warn(f::Function, ::Type{T}, args...)

    Resource management helper function. Apply f to args, first constructing an instance of type T from args. Makes sure to call close on the resulting object after f successfully returns or throws an error. Ensures that allocated git resources are finalized as soon as they are no longer needed. If an error is thrown by f, a warning is shown containing the error.

    LibGit2.workdir — Function
    LibGit2.workdir(repo::GitRepo)

    Return the location of the working directory of repo. This will throw an error for bare repositories.

    Note

    This will typically be the parent directory of gitdir(repo), but can be different in some cases: e.g. if either the core.worktree configuration variable or the GIT_WORK_TREE environment variable is set.

    See also gitdir, path.

    LibGit2.GitObject — Method
    (::Type{T})(te::GitTreeEntry) where T<:GitObject

    Get the git object to which te refers and return it as its actual type (the type entrytype would show), for instance a GitBlob or GitTag.

    Examples

    tree = LibGit2.GitTree(repo, "HEAD^{tree}")
 tree_entry = tree[1]
-blob = LibGit2.GitBlob(tree_entry)
    LibGit2.UserPasswordCredential — Type

    Credential that support only user and password parameters

    LibGit2.SSHCredential — Type

    SSH credential type

    LibGit2.isfilled — Function
    isfilled(cred::AbstractCredential) -> Bool

    Verifies that a credential is ready for use in authentication.

    LibGit2.CachedCredentials — Type

    Caches credential information for re-use

    LibGit2.CredentialPayload — Type
    LibGit2.CredentialPayload

    Retains the state between multiple calls to the credential callback for the same URL. A CredentialPayload instance is expected to be reset! whenever it will be used with a different URL.

    LibGit2.approve — Function
    approve(payload::CredentialPayload; shred::Bool=true) -> Nothing

    Store the payload credential for re-use in a future authentication. Should only be called when authentication was successful.

    The shred keyword controls whether sensitive information in the payload credential field should be destroyed. Should only be set to false during testing.

    LibGit2.reject — Function
    reject(payload::CredentialPayload; shred::Bool=true) -> Nothing

    Discard the payload credential from begin re-used in future authentication. Should only be called when authentication was unsuccessful.

    The shred keyword controls whether sensitive information in the payload credential field should be destroyed. Should only be set to false during testing.

    LibGit2.Consts.GIT_CONFIG — Type

    Priority level of a config file.

    These priority levels correspond to the natural escalation logic (from higher to lower) when searching for config entries in git.

    • CONFIG_LEVEL_DEFAULT - Open the global, XDG and system configuration files if any available.
    • CONFIG_LEVEL_PROGRAMDATA - System-wide on Windows, for compatibility with portable git
    • CONFIG_LEVEL_SYSTEM - System-wide configuration file; /etc/gitconfig on Linux systems
    • CONFIG_LEVEL_XDG - XDG compatible configuration file; typically ~/.config/git/config
    • CONFIG_LEVEL_GLOBAL - User-specific configuration file (also called Global configuration file); typically ~/.gitconfig
    • CONFIG_LEVEL_LOCAL - Repository specific configuration file; $WORK_DIR/.git/config on non-bare repos
    • CONFIG_LEVEL_APP - Application specific configuration file; freely defined by applications
    • CONFIG_HIGHEST_LEVEL - Represents the highest level available config file (i.e. the most specific config file available that actually is loaded)
    +blob = LibGit2.GitBlob(tree_entry)
    LibGit2.UserPasswordCredential — Type

    Credential that support only user and password parameters

    LibGit2.SSHCredential — Type

    SSH credential type

    LibGit2.isfilled — Function
    isfilled(cred::AbstractCredential) -> Bool

    Verifies that a credential is ready for use in authentication.

    LibGit2.CachedCredentials — Type

    Caches credential information for re-use

    LibGit2.CredentialPayload — Type
    LibGit2.CredentialPayload

    Retains the state between multiple calls to the credential callback for the same URL. A CredentialPayload instance is expected to be reset! whenever it will be used with a different URL.

    LibGit2.approve — Function
    approve(payload::CredentialPayload; shred::Bool=true) -> Nothing

    Store the payload credential for re-use in a future authentication. Should only be called when authentication was successful.

    The shred keyword controls whether sensitive information in the payload credential field should be destroyed. Should only be set to false during testing.

    LibGit2.reject — Function
    reject(payload::CredentialPayload; shred::Bool=true) -> Nothing

    Discard the payload credential from begin re-used in future authentication. Should only be called when authentication was unsuccessful.

    The shred keyword controls whether sensitive information in the payload credential field should be destroyed. Should only be set to false during testing.

    LibGit2.Consts.GIT_CONFIG — Type

    Priority level of a config file.

    These priority levels correspond to the natural escalation logic (from higher to lower) when searching for config entries in git.

    • CONFIG_LEVEL_DEFAULT - Open the global, XDG and system configuration files if any available.
    • CONFIG_LEVEL_PROGRAMDATA - System-wide on Windows, for compatibility with portable git
    • CONFIG_LEVEL_SYSTEM - System-wide configuration file; /etc/gitconfig on Linux systems
    • CONFIG_LEVEL_XDG - XDG compatible configuration file; typically ~/.config/git/config
    • CONFIG_LEVEL_GLOBAL - User-specific configuration file (also called Global configuration file); typically ~/.gitconfig
    • CONFIG_LEVEL_LOCAL - Repository specific configuration file; $WORK_DIR/.git/config on non-bare repos
    • CONFIG_LEVEL_APP - Application specific configuration file; freely defined by applications
    • CONFIG_HIGHEST_LEVEL - Represents the highest level available config file (i.e. the most specific config file available that actually is loaded)
    diff --git a/dev/stdlib/Libdl/index.html b/dev/stdlib/Libdl/index.html index d16e22f8..783a8b84 100644 --- a/dev/stdlib/Libdl/index.html +++ b/dev/stdlib/Libdl/index.html @@ -15,4 +15,4 @@ ... do something finally dlclose(hdl) -end

    We define a dlclose() method that accepts a parameter of type Nothing, so that user code does not have to change its behavior for the case that library_name was not found.

    source
    Base.Libc.Libdl.dlext — Constant
    dlext

    File extension for dynamic libraries (e.g. dll, dylib, so) on the current platform.

    source
    Base.Libc.Libdl.dllist — Function
    dllist()

    Return the paths of dynamic libraries currently loaded in a Vector{String}.

    source
    Base.Libc.Libdl.dlpath — Function
    dlpath(handle::Ptr{Cvoid})

    Given a library handle from dlopen, return the full path.

    source
    dlpath(libname::Union{AbstractString, Symbol})

    Get the full path of the library libname.

    Example

    julia> dlpath("libjulia")
    source
    Base.Libc.Libdl.find_library — Function
    find_library(names [, locations])

    Searches for the first library in names in the paths in the locations list, DL_LOAD_PATH, or system library paths (in that order) which can successfully be dlopen'd. On success, the return value will be one of the names (potentially prefixed by one of the paths in locations). This string can be assigned to a global const and used as the library name in future ccall's. On failure, it returns the empty string.

    source
    Base.DL_LOAD_PATH — Constant
    DL_LOAD_PATH

    When calling dlopen, the paths in this list will be searched first, in order, before searching the system locations for a valid library handle.

    source
    +end

    We define a dlclose() method that accepts a parameter of type Nothing, so that user code does not have to change its behavior for the case that library_name was not found.

    source
    Base.Libc.Libdl.dlext — Constant
    dlext

    File extension for dynamic libraries (e.g. dll, dylib, so) on the current platform.

    source
    Base.Libc.Libdl.dllist — Function
    dllist()

    Return the paths of dynamic libraries currently loaded in a Vector{String}.

    source
    Base.Libc.Libdl.dlpath — Function
    dlpath(handle::Ptr{Cvoid})

    Given a library handle from dlopen, return the full path.

    source
    dlpath(libname::Union{AbstractString, Symbol})

    Get the full path of the library libname.

    Example

    julia> dlpath("libjulia")
    source
    Base.Libc.Libdl.find_library — Function
    find_library(names [, locations])

    Searches for the first library in names in the paths in the locations list, DL_LOAD_PATH, or system library paths (in that order) which can successfully be dlopen'd. On success, the return value will be one of the names (potentially prefixed by one of the paths in locations). This string can be assigned to a global const and used as the library name in future ccall's. On failure, it returns the empty string.

    source
    Base.DL_LOAD_PATH — Constant
    DL_LOAD_PATH

    When calling dlopen, the paths in this list will be searched first, in order, before searching the system locations for a valid library handle.

    source
    diff --git a/dev/stdlib/LinearAlgebra/index.html b/dev/stdlib/LinearAlgebra/index.html index 9c5c4d08..65b53d2a 100644 --- a/dev/stdlib/LinearAlgebra/index.html +++ b/dev/stdlib/LinearAlgebra/index.html @@ -2531,4 +2531,4 @@ 2.0
    LinearAlgebra.BLAS.iamax — Function
    iamax(n, dx, incx)
 iamax(dx)

    Find the index of the element of dx with the maximum absolute value. n is the length of dx, and incx is the stride. If n and incx are not provided, they assume default values of n=length(dx) and incx=stride1(dx).

    Level 2 BLAS functions

    The level 2 BLAS functions were published in [(Dongarra, 1988)][Dongarra-1988], and define matrix-vector operations.

    [Dongarra-1988]: https://dl.acm.org/doi/10.1145/42288.42291

    return a vector

    LinearAlgebra.BLAS.gemv! — Function
    gemv!(tA, alpha, A, x, beta, y)

    Update the vector y as alpha*A*x + beta*y or alpha*A'x + beta*y according to tA. alpha and beta are scalars. Return the updated y.

    LinearAlgebra.BLAS.gemv — Method
    gemv(tA, alpha, A, x)

    Return alpha*A*x or alpha*A'x according to tA. alpha is a scalar.

    LinearAlgebra.BLAS.gemv — Method
    gemv(tA, A, x)

    Return A*x or A'x according to tA.

    LinearAlgebra.BLAS.gbmv! — Function
    gbmv!(trans, m, kl, ku, alpha, A, x, beta, y)

    Update vector y as alpha*A*x + beta*y or alpha*A'*x + beta*y according to trans. The matrix A is a general band matrix of dimension m by size(A,2) with kl sub-diagonals and ku super-diagonals. alpha and beta are scalars. Return the updated y.

    LinearAlgebra.BLAS.gbmv — Function
    gbmv(trans, m, kl, ku, alpha, A, x)

    Return alpha*A*x or alpha*A'*x according to trans. The matrix A is a general band matrix of dimension m by size(A,2) with kl sub-diagonals and ku super-diagonals, and alpha is a scalar.

    LinearAlgebra.BLAS.hemv! — Function
    hemv!(ul, alpha, A, x, beta, y)

    Update the vector y as alpha*A*x + beta*y. A is assumed to be Hermitian. Only the ul triangle of A is used. alpha and beta are scalars. Return the updated y.

    LinearAlgebra.BLAS.hemv — Method
    hemv(ul, alpha, A, x)

    Return alpha*A*x. A is assumed to be Hermitian. Only the ul triangle of A is used. alpha is a scalar.

    LinearAlgebra.BLAS.hemv — Method
    hemv(ul, A, x)

    Return A*x. A is assumed to be Hermitian. Only the ul triangle of A is used.

    LinearAlgebra.BLAS.hpmv! — Function
    hpmv!(uplo, α, AP, x, β, y)

    Update vector y as α*A*x + β*y, where A is a Hermitian matrix provided in packed format AP.

    With uplo = 'U', the array AP must contain the upper triangular part of the Hermitian matrix packed sequentially, column by column, so that AP[1] contains A[1, 1], AP[2] and AP[3] contain A[1, 2] and A[2, 2] respectively, and so on.

    With uplo = 'L', the array AP must contain the lower triangular part of the Hermitian matrix packed sequentially, column by column, so that AP[1] contains A[1, 1], AP[2] and AP[3] contain A[2, 1] and A[3, 1] respectively, and so on.

    The scalar inputs α and β must be complex or real numbers.

    The array inputs x, y and AP must all be of ComplexF32 or ComplexF64 type.

    Return the updated y.

    Julia 1.5

    hpmv! requires at least Julia 1.5.

    LinearAlgebra.BLAS.symv! — Function
    symv!(ul, alpha, A, x, beta, y)

    Update the vector y as alpha*A*x + beta*y. A is assumed to be symmetric. Only the ul triangle of A is used. alpha and beta are scalars. Return the updated y.

    LinearAlgebra.BLAS.symv — Method
    symv(ul, alpha, A, x)

    Return alpha*A*x. A is assumed to be symmetric. Only the ul triangle of A is used. alpha is a scalar.

    LinearAlgebra.BLAS.symv — Method
    symv(ul, A, x)

    Return A*x. A is assumed to be symmetric. Only the ul triangle of A is used.

    LinearAlgebra.BLAS.sbmv! — Function
    sbmv!(uplo, k, alpha, A, x, beta, y)

    Update vector y as alpha*A*x + beta*y where A is a symmetric band matrix of order size(A,2) with k super-diagonals stored in the argument A. The storage layout for A is described the reference BLAS module, level-2 BLAS at http://www.netlib.org/lapack/explore-html/. Only the uplo triangle of A is used.

    Return the updated y.

    LinearAlgebra.BLAS.sbmv — Method
    sbmv(uplo, k, alpha, A, x)

    Return alpha*A*x where A is a symmetric band matrix of order size(A,2) with k super-diagonals stored in the argument A. Only the uplo triangle of A is used.

    LinearAlgebra.BLAS.sbmv — Method
    sbmv(uplo, k, A, x)

    Return A*x where A is a symmetric band matrix of order size(A,2) with k super-diagonals stored in the argument A. Only the uplo triangle of A is used.

    LinearAlgebra.BLAS.spmv! — Function
    spmv!(uplo, α, AP, x, β, y)

    Update vector y as α*A*x + β*y, where A is a symmetric matrix provided in packed format AP.

    With uplo = 'U', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP[1] contains A[1, 1], AP[2] and AP[3] contain A[1, 2] and A[2, 2] respectively, and so on.

    With uplo = 'L', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP[1] contains A[1, 1], AP[2] and AP[3] contain A[2, 1] and A[3, 1] respectively, and so on.

    The scalar inputs α and β must be real.

    The array inputs x, y and AP must all be of Float32 or Float64 type.

    Return the updated y.

    Julia 1.5

    spmv! requires at least Julia 1.5.

    LinearAlgebra.BLAS.trmv! — Function
    trmv!(ul, tA, dA, A, b)

    Return op(A)*b, where op is determined by tA. Only the ul triangle of A is used. dA determines if the diagonal values are read or are assumed to be all ones. The multiplication occurs in-place on b.

    LinearAlgebra.BLAS.trmv — Function
    trmv(ul, tA, dA, A, b)

    Return op(A)*b, where op is determined by tA. Only the ul triangle of A is used. dA determines if the diagonal values are read or are assumed to be all ones.

    LinearAlgebra.BLAS.trsv! — Function
    trsv!(ul, tA, dA, A, b)

    Overwrite b with the solution to A*x = b or one of the other two variants determined by tA and ul. dA determines if the diagonal values are read or are assumed to be all ones. Return the updated b.

    LinearAlgebra.BLAS.trsv — Function
    trsv(ul, tA, dA, A, b)

    Return the solution to A*x = b or one of the other two variants determined by tA and ul. dA determines if the diagonal values are read or are assumed to be all ones.

    return a matrix

    LinearAlgebra.BLAS.ger! — Function
    ger!(alpha, x, y, A)

    Rank-1 update of the matrix A with vectors x and y as alpha*x*y' + A.

    LinearAlgebra.BLAS.her! — Function
    her!(uplo, alpha, x, A)

    Methods for complex arrays only. Rank-1 update of the Hermitian matrix A with vector x as alpha*x*x' + A. uplo controls which triangle of A is updated. Returns A.

    LinearAlgebra.BLAS.syr! — Function
    syr!(uplo, alpha, x, A)

    Rank-1 update of the symmetric matrix A with vector x as alpha*x*transpose(x) + A. uplo controls which triangle of A is updated. Returns A.

    LinearAlgebra.BLAS.spr! — Function
    spr!(uplo, α, x, AP)

    Update matrix A as A+α*x*x', where A is a symmetric matrix provided in packed format AP and x is a vector.

    With uplo = 'U', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP[1] contains A[1, 1], AP[2] and AP[3] contain A[1, 2] and A[2, 2] respectively, and so on.

    With uplo = 'L', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP[1] contains A[1, 1], AP[2] and AP[3] contain A[2, 1] and A[3, 1] respectively, and so on.

    The scalar input α must be real.

    The array inputs x and AP must all be of Float32 or Float64 type. Return the updated AP.

    Julia 1.8

    spr! requires at least Julia 1.8.

    Level 3 BLAS functions

    The level 3 BLAS functions were published in [(Dongarra, 1990)][Dongarra-1990], and define matrix-matrix operations.

    [Dongarra-1990]: https://dl.acm.org/doi/10.1145/77626.79170

    LinearAlgebra.BLAS.gemm! — Function
    gemm!(tA, tB, alpha, A, B, beta, C)

    Update C as alpha*A*B + beta*C or the other three variants according to tA and tB. Return the updated C.

    LinearAlgebra.BLAS.gemm — Method
    gemm(tA, tB, alpha, A, B)

    Return alpha*A*B or the other three variants according to tA and tB.

    LinearAlgebra.BLAS.gemm — Method
    gemm(tA, tB, A, B)

    Return A*B or the other three variants according to tA and tB.

    LinearAlgebra.BLAS.symm! — Function
    symm!(side, ul, alpha, A, B, beta, C)

    Update C as alpha*A*B + beta*C or alpha*B*A + beta*C according to side. A is assumed to be symmetric. Only the ul triangle of A is used. Return the updated C.

    LinearAlgebra.BLAS.symm — Method
    symm(side, ul, alpha, A, B)

    Return alpha*A*B or alpha*B*A according to side. A is assumed to be symmetric. Only the ul triangle of A is used.

    LinearAlgebra.BLAS.symm — Method
    symm(side, ul, A, B)

    Return A*B or B*A according to side. A is assumed to be symmetric. Only the ul triangle of A is used.

    LinearAlgebra.BLAS.hemm! — Function
    hemm!(side, ul, alpha, A, B, beta, C)

    Update C as alpha*A*B + beta*C or alpha*B*A + beta*C according to side. A is assumed to be Hermitian. Only the ul triangle of A is used. Return the updated C.

    LinearAlgebra.BLAS.hemm — Method
    hemm(side, ul, alpha, A, B)

    Return alpha*A*B or alpha*B*A according to side. A is assumed to be Hermitian. Only the ul triangle of A is used.

    LinearAlgebra.BLAS.hemm — Method
    hemm(side, ul, A, B)

    Return A*B or B*A according to side. A is assumed to be Hermitian. Only the ul triangle of A is used.

    LinearAlgebra.BLAS.syrk! — Function
    syrk!(uplo, trans, alpha, A, beta, C)

    Rank-k update of the symmetric matrix C as alpha*A*transpose(A) + beta*C or alpha*transpose(A)*A + beta*C according to trans. Only the uplo triangle of C is used. Return C.

    LinearAlgebra.BLAS.syrk — Function
    syrk(uplo, trans, alpha, A)

    Return either the upper triangle or the lower triangle of A, according to uplo, of alpha*A*transpose(A) or alpha*transpose(A)*A, according to trans.

    LinearAlgebra.BLAS.herk! — Function
    herk!(uplo, trans, alpha, A, beta, C)

    Methods for complex arrays only. Rank-k update of the Hermitian matrix C as alpha*A*A' + beta*C or alpha*A'*A + beta*C according to trans. Only the uplo triangle of C is updated. Returns C.

    LinearAlgebra.BLAS.herk — Function
    herk(uplo, trans, alpha, A)

    Methods for complex arrays only. Returns the uplo triangle of alpha*A*A' or alpha*A'*A, according to trans.

    LinearAlgebra.BLAS.syr2k! — Function
    syr2k!(uplo, trans, alpha, A, B, beta, C)

    Rank-2k update of the symmetric matrix C as alpha*A*transpose(B) + alpha*B*transpose(A) + beta*C or alpha*transpose(A)*B + alpha*transpose(B)*A + beta*C according to trans. Only the uplo triangle of C is used. Returns C.

    LinearAlgebra.BLAS.syr2k — Function
    syr2k(uplo, trans, alpha, A, B)

    Returns the uplo triangle of alpha*A*transpose(B) + alpha*B*transpose(A) or alpha*transpose(A)*B + alpha*transpose(B)*A, according to trans.

    syr2k(uplo, trans, A, B)

    Return the uplo triangle of A*transpose(B) + B*transpose(A) or transpose(A)*B + transpose(B)*A, according to trans.

    LinearAlgebra.BLAS.her2k! — Function
    her2k!(uplo, trans, alpha, A, B, beta, C)

    Rank-2k update of the Hermitian matrix C as alpha*A*B' + alpha*B*A' + beta*C or alpha*A'*B + alpha*B'*A + beta*C according to trans. The scalar beta has to be real. Only the uplo triangle of C is used. Return C.

    LinearAlgebra.BLAS.her2k — Function
    her2k(uplo, trans, alpha, A, B)

    Return the uplo triangle of alpha*A*B' + alpha*B*A' or alpha*A'*B + alpha*B'*A, according to trans.

    her2k(uplo, trans, A, B)

    Return the uplo triangle of A*B' + B*A' or A'*B + B'*A, according to trans.

    LinearAlgebra.BLAS.trmm! — Function
    trmm!(side, ul, tA, dA, alpha, A, B)

    Update B as alpha*A*B or one of the other three variants determined by side and tA. Only the ul triangle of A is used. dA determines if the diagonal values are read or are assumed to be all ones. Return the updated B.

    LinearAlgebra.BLAS.trmm — Function
    trmm(side, ul, tA, dA, alpha, A, B)

    Return alpha*A*B or one of the other three variants determined by side and tA. Only the ul triangle of A is used. dA determines if the diagonal values are read or are assumed to be all ones.

    LinearAlgebra.BLAS.trsm! — Function
    trsm!(side, ul, tA, dA, alpha, A, B)

    Overwrite B with the solution to A*X = alpha*B or one of the other three variants determined by side and tA. Only the ul triangle of A is used. dA determines if the diagonal values are read or are assumed to be all ones. Returns the updated B.

    LinearAlgebra.BLAS.trsm — Function
    trsm(side, ul, tA, dA, alpha, A, B)

    Return the solution to A*X = alpha*B or one of the other three variants determined by determined by side and tA. Only the ul triangle of A is used. dA determines if the diagonal values are read or are assumed to be all ones.

    LAPACK functions

    LinearAlgebra.LAPACK provides wrappers for some of the LAPACK functions for linear algebra. Those functions that overwrite one of the input arrays have names ending in '!'.

    Usually a function has 4 methods defined, one each for Float64, Float32, ComplexF64 and ComplexF32 arrays.

    Note that the LAPACK API provided by Julia can and will change in the future. Since this API is not user-facing, there is no commitment to support/deprecate this specific set of functions in future releases.

    LinearAlgebra.LAPACK — Module

    Interfaces to LAPACK subroutines.

    LinearAlgebra.LAPACK.gbtrf! — Function
    gbtrf!(kl, ku, m, AB) -> (AB, ipiv)

    Compute the LU factorization of a banded matrix AB. kl is the first subdiagonal containing a nonzero band, ku is the last superdiagonal containing one, and m is the first dimension of the matrix AB. Returns the LU factorization in-place and ipiv, the vector of pivots used.

    LinearAlgebra.LAPACK.gbtrs! — Function
    gbtrs!(trans, kl, ku, m, AB, ipiv, B)

    Solve the equation AB * X = B. trans determines the orientation of AB. It may be N (no transpose), T (transpose), or C (conjugate transpose). kl is the first subdiagonal containing a nonzero band, ku is the last superdiagonal containing one, and m is the first dimension of the matrix AB. ipiv is the vector of pivots returned from gbtrf!. Returns the vector or matrix X, overwriting B in-place.

    LinearAlgebra.LAPACK.gebal! — Function
    gebal!(job, A) -> (ilo, ihi, scale)

    Balance the matrix A before computing its eigensystem or Schur factorization. job can be one of N (A will not be permuted or scaled), P (A will only be permuted), S (A will only be scaled), or B (A will be both permuted and scaled). Modifies A in-place and returns ilo, ihi, and scale. If permuting was turned on, A[i,j] = 0 if j > i and 1 < j < ilo or j > ihi. scale contains information about the scaling/permutations performed.

    LinearAlgebra.LAPACK.gebak! — Function
    gebak!(job, side, ilo, ihi, scale, V)

    Transform the eigenvectors V of a matrix balanced using gebal! to the unscaled/unpermuted eigenvectors of the original matrix. Modifies V in-place. side can be L (left eigenvectors are transformed) or R (right eigenvectors are transformed).

    LinearAlgebra.LAPACK.gebrd! — Function
    gebrd!(A) -> (A, d, e, tauq, taup)

    Reduce A in-place to bidiagonal form A = QBP'. Returns A, containing the bidiagonal matrix B; d, containing the diagonal elements of B; e, containing the off-diagonal elements of B; tauq, containing the elementary reflectors representing Q; and taup, containing the elementary reflectors representing P.

    LinearAlgebra.LAPACK.gelqf! — Function
    gelqf!(A, tau)

    Compute the LQ factorization of A, A = LQ. tau contains scalars which parameterize the elementary reflectors of the factorization. tau must have length greater than or equal to the smallest dimension of A.

    Returns A and tau modified in-place.

    gelqf!(A) -> (A, tau)

    Compute the LQ factorization of A, A = LQ.

    Returns A, modified in-place, and tau, which contains scalars which parameterize the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.geqlf! — Function
    geqlf!(A, tau)

    Compute the QL factorization of A, A = QL. tau contains scalars which parameterize the elementary reflectors of the factorization. tau must have length greater than or equal to the smallest dimension of A.

    Returns A and tau modified in-place.

    geqlf!(A) -> (A, tau)

    Compute the QL factorization of A, A = QL.

    Returns A, modified in-place, and tau, which contains scalars which parameterize the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.geqrf! — Function
    geqrf!(A, tau)

    Compute the QR factorization of A, A = QR. tau contains scalars which parameterize the elementary reflectors of the factorization. tau must have length greater than or equal to the smallest dimension of A.

    Returns A and tau modified in-place.

    geqrf!(A) -> (A, tau)

    Compute the QR factorization of A, A = QR.

    Returns A, modified in-place, and tau, which contains scalars which parameterize the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.geqp3! — Function
    geqp3!(A, [jpvt, tau]) -> (A, tau, jpvt)

    Compute the pivoted QR factorization of A, AP = QR using BLAS level 3. P is a pivoting matrix, represented by jpvt. tau stores the elementary reflectors. The arguments jpvt and tau are optional and allow for passing preallocated arrays. When passed, jpvt must have length greater than or equal to n if A is an (m x n) matrix and tau must have length greater than or equal to the smallest dimension of A.

    A, jpvt, and tau are modified in-place.

    LinearAlgebra.LAPACK.gerqf! — Function
    gerqf!(A, tau)

    Compute the RQ factorization of A, A = RQ. tau contains scalars which parameterize the elementary reflectors of the factorization. tau must have length greater than or equal to the smallest dimension of A.

    Returns A and tau modified in-place.

    gerqf!(A) -> (A, tau)

    Compute the RQ factorization of A, A = RQ.

    Returns A, modified in-place, and tau, which contains scalars which parameterize the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.geqrt! — Function
    geqrt!(A, T)

    Compute the blocked QR factorization of A, A = QR. T contains upper triangular block reflectors which parameterize the elementary reflectors of the factorization. The first dimension of T sets the block size and it must be between 1 and n. The second dimension of T must equal the smallest dimension of A.

    Returns A and T modified in-place.

    geqrt!(A, nb) -> (A, T)

    Compute the blocked QR factorization of A, A = QR. nb sets the block size and it must be between 1 and n, the second dimension of A.

    Returns A, modified in-place, and T, which contains upper triangular block reflectors which parameterize the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.geqrt3! — Function
    geqrt3!(A, T)

    Recursively computes the blocked QR factorization of A, A = QR. T contains upper triangular block reflectors which parameterize the elementary reflectors of the factorization. The first dimension of T sets the block size and it must be between 1 and n. The second dimension of T must equal the smallest dimension of A.

    Returns A and T modified in-place.

    geqrt3!(A) -> (A, T)

    Recursively computes the blocked QR factorization of A, A = QR.

    Returns A, modified in-place, and T, which contains upper triangular block reflectors which parameterize the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.getrf! — Function
    getrf!(A) -> (A, ipiv, info)

    Compute the pivoted LU factorization of A, A = LU.

    Returns A, modified in-place, ipiv, the pivoting information, and an info code which indicates success (info = 0), a singular value in U (info = i, in which case U[i,i] is singular), or an error code (info < 0).

    LinearAlgebra.LAPACK.tzrzf! — Function
    tzrzf!(A) -> (A, tau)

    Transforms the upper trapezoidal matrix A to upper triangular form in-place. Returns A and tau, the scalar parameters for the elementary reflectors of the transformation.

    LinearAlgebra.LAPACK.ormrz! — Function
    ormrz!(side, trans, A, tau, C)

    Multiplies the matrix C by Q from the transformation supplied by tzrzf!. Depending on side or trans the multiplication can be left-sided (side = L, Q*C) or right-sided (side = R, C*Q) and Q can be unmodified (trans = N), transposed (trans = T), or conjugate transposed (trans = C). Returns matrix C which is modified in-place with the result of the multiplication.

    LinearAlgebra.LAPACK.gels! — Function
    gels!(trans, A, B) -> (F, B, ssr)

    Solves the linear equation A * X = B, transpose(A) * X = B, or adjoint(A) * X = B using a QR or LQ factorization. Modifies the matrix/vector B in place with the solution. A is overwritten with its QR or LQ factorization. trans may be one of N (no modification), T (transpose), or C (conjugate transpose). gels! searches for the minimum norm/least squares solution. A may be under or over determined. The solution is returned in B.

    LinearAlgebra.LAPACK.gesv! — Function
    gesv!(A, B) -> (B, A, ipiv)

    Solves the linear equation A * X = B where A is a square matrix using the LU factorization of A. A is overwritten with its LU factorization and B is overwritten with the solution X. ipiv contains the pivoting information for the LU factorization of A.

    LinearAlgebra.LAPACK.getrs! — Function
    getrs!(trans, A, ipiv, B)

    Solves the linear equation A * X = B, transpose(A) * X = B, or adjoint(A) * X = B for square A. Modifies the matrix/vector B in place with the solution. A is the LU factorization from getrf!, with ipiv the pivoting information. trans may be one of N (no modification), T (transpose), or C (conjugate transpose).

    LinearAlgebra.LAPACK.getri! — Function
    getri!(A, ipiv)

    Computes the inverse of A, using its LU factorization found by getrf!. ipiv is the pivot information output and A contains the LU factorization of getrf!. A is overwritten with its inverse.

    LinearAlgebra.LAPACK.gesvx! — Function
    gesvx!(fact, trans, A, AF, ipiv, equed, R, C, B) -> (X, equed, R, C, B, rcond, ferr, berr, work)

    Solves the linear equation A * X = B (trans = N), transpose(A) * X = B (trans = T), or adjoint(A) * X = B (trans = C) using the LU factorization of A. fact may be E, in which case A will be equilibrated and copied to AF; F, in which case AF and ipiv from a previous LU factorization are inputs; or N, in which case A will be copied to AF and then factored. If fact = F, equed may be N, meaning A has not been equilibrated; R, meaning A was multiplied by Diagonal(R) from the left; C, meaning A was multiplied by Diagonal(C) from the right; or B, meaning A was multiplied by Diagonal(R) from the left and Diagonal(C) from the right. If fact = F and equed = R or B the elements of R must all be positive. If fact = F and equed = C or B the elements of C must all be positive.

    Returns the solution X; equed, which is an output if fact is not N, and describes the equilibration that was performed; R, the row equilibration diagonal; C, the column equilibration diagonal; B, which may be overwritten with its equilibrated form Diagonal(R)*B (if trans = N and equed = R,B) or Diagonal(C)*B (if trans = T,C and equed = C,B); rcond, the reciprocal condition number of A after equilbrating; ferr, the forward error bound for each solution vector in X; berr, the forward error bound for each solution vector in X; and work, the reciprocal pivot growth factor.

    gesvx!(A, B)

    The no-equilibration, no-transpose simplification of gesvx!.

    LinearAlgebra.LAPACK.gelsd! — Function
    gelsd!(A, B, rcond) -> (B, rnk)

    Computes the least norm solution of A * X = B by finding the SVD factorization of A, then dividing-and-conquering the problem. B is overwritten with the solution X. Singular values below rcond will be treated as zero. Returns the solution in B and the effective rank of A in rnk.

    LinearAlgebra.LAPACK.gelsy! — Function
    gelsy!(A, B, rcond) -> (B, rnk)

    Computes the least norm solution of A * X = B by finding the full QR factorization of A, then dividing-and-conquering the problem. B is overwritten with the solution X. Singular values below rcond will be treated as zero. Returns the solution in B and the effective rank of A in rnk.

    LinearAlgebra.LAPACK.gglse! — Function
    gglse!(A, c, B, d) -> (X,res)

    Solves the equation A * x = c where x is subject to the equality constraint B * x = d. Uses the formula ||c - A*x||^2 = 0 to solve. Returns X and the residual sum-of-squares.

    LinearAlgebra.LAPACK.geev! — Function
    geev!(jobvl, jobvr, A) -> (W, VL, VR)

    Finds the eigensystem of A. If jobvl = N, the left eigenvectors of A aren't computed. If jobvr = N, the right eigenvectors of A aren't computed. If jobvl = V or jobvr = V, the corresponding eigenvectors are computed. Returns the eigenvalues in W, the right eigenvectors in VR, and the left eigenvectors in VL.

    LinearAlgebra.LAPACK.gesdd! — Function
    gesdd!(job, A) -> (U, S, VT)

    Finds the singular value decomposition of A, A = U * S * V', using a divide and conquer approach. If job = A, all the columns of U and the rows of V' are computed. If job = N, no columns of U or rows of V' are computed. If job = O, A is overwritten with the columns of (thin) U and the rows of (thin) V'. If job = S, the columns of (thin) U and the rows of (thin) V' are computed and returned separately.

    LinearAlgebra.LAPACK.gesvd! — Function
    gesvd!(jobu, jobvt, A) -> (U, S, VT)

    Finds the singular value decomposition of A, A = U * S * V'. If jobu = A, all the columns of U are computed. If jobvt = A all the rows of V' are computed. If jobu = N, no columns of U are computed. If jobvt = N no rows of V' are computed. If jobu = O, A is overwritten with the columns of (thin) U. If jobvt = O, A is overwritten with the rows of (thin) V'. If jobu = S, the columns of (thin) U are computed and returned separately. If jobvt = S the rows of (thin) V' are computed and returned separately. jobu and jobvt can't both be O.

    Returns U, S, and Vt, where S are the singular values of A.

    LinearAlgebra.LAPACK.ggsvd! — Function
    ggsvd!(jobu, jobv, jobq, A, B) -> (U, V, Q, alpha, beta, k, l, R)

    Finds the generalized singular value decomposition of A and B, U'*A*Q = D1*R and V'*B*Q = D2*R. D1 has alpha on its diagonal and D2 has beta on its diagonal. If jobu = U, the orthogonal/unitary matrix U is computed. If jobv = V the orthogonal/unitary matrix V is computed. If jobq = Q, the orthogonal/unitary matrix Q is computed. If jobu, jobv or jobq is N, that matrix is not computed. This function is only available in LAPACK versions prior to 3.6.0.

    LinearAlgebra.LAPACK.ggsvd3! — Function
    ggsvd3!(jobu, jobv, jobq, A, B) -> (U, V, Q, alpha, beta, k, l, R)

    Finds the generalized singular value decomposition of A and B, U'*A*Q = D1*R and V'*B*Q = D2*R. D1 has alpha on its diagonal and D2 has beta on its diagonal. If jobu = U, the orthogonal/unitary matrix U is computed. If jobv = V the orthogonal/unitary matrix V is computed. If jobq = Q, the orthogonal/unitary matrix Q is computed. If jobu, jobv, or jobq is N, that matrix is not computed. This function requires LAPACK 3.6.0.

    LinearAlgebra.LAPACK.geevx! — Function
    geevx!(balanc, jobvl, jobvr, sense, A) -> (A, w, VL, VR, ilo, ihi, scale, abnrm, rconde, rcondv)

    Finds the eigensystem of A with matrix balancing. If jobvl = N, the left eigenvectors of A aren't computed. If jobvr = N, the right eigenvectors of A aren't computed. If jobvl = V or jobvr = V, the corresponding eigenvectors are computed. If balanc = N, no balancing is performed. If balanc = P, A is permuted but not scaled. If balanc = S, A is scaled but not permuted. If balanc = B, A is permuted and scaled. If sense = N, no reciprocal condition numbers are computed. If sense = E, reciprocal condition numbers are computed for the eigenvalues only. If sense = V, reciprocal condition numbers are computed for the right eigenvectors only. If sense = B, reciprocal condition numbers are computed for the right eigenvectors and the eigenvectors. If sense = E,B, the right and left eigenvectors must be computed.

    LinearAlgebra.LAPACK.ggev! — Function
    ggev!(jobvl, jobvr, A, B) -> (alpha, beta, vl, vr)

    Finds the generalized eigendecomposition of A and B. If jobvl = N, the left eigenvectors aren't computed. If jobvr = N, the right eigenvectors aren't computed. If jobvl = V or jobvr = V, the corresponding eigenvectors are computed.

    LinearAlgebra.LAPACK.ggev3! — Function
    ggev3!(jobvl, jobvr, A, B) -> (alpha, beta, vl, vr)

    Finds the generalized eigendecomposition of A and B using a blocked algorithm. If jobvl = N, the left eigenvectors aren't computed. If jobvr = N, the right eigenvectors aren't computed. If jobvl = V or jobvr = V, the corresponding eigenvectors are computed. This function requires LAPACK 3.6.0.

    LinearAlgebra.LAPACK.gtsv! — Function
    gtsv!(dl, d, du, B)

    Solves the equation A * X = B where A is a tridiagonal matrix with dl on the subdiagonal, d on the diagonal, and du on the superdiagonal.

    Overwrites B with the solution X and returns it.

    LinearAlgebra.LAPACK.gttrf! — Function
    gttrf!(dl, d, du) -> (dl, d, du, du2, ipiv)

    Finds the LU factorization of a tridiagonal matrix with dl on the subdiagonal, d on the diagonal, and du on the superdiagonal.

    Modifies dl, d, and du in-place and returns them and the second superdiagonal du2 and the pivoting vector ipiv.

    LinearAlgebra.LAPACK.gttrs! — Function
    gttrs!(trans, dl, d, du, du2, ipiv, B)

    Solves the equation A * X = B (trans = N), transpose(A) * X = B (trans = T), or adjoint(A) * X = B (trans = C) using the LU factorization computed by gttrf!. B is overwritten with the solution X.

    LinearAlgebra.LAPACK.orglq! — Function
    orglq!(A, tau, k = length(tau))

    Explicitly finds the matrix Q of a LQ factorization after calling gelqf! on A. Uses the output of gelqf!. A is overwritten by Q.

    LinearAlgebra.LAPACK.orgqr! — Function
    orgqr!(A, tau, k = length(tau))

    Explicitly finds the matrix Q of a QR factorization after calling geqrf! on A. Uses the output of geqrf!. A is overwritten by Q.

    LinearAlgebra.LAPACK.orgql! — Function
    orgql!(A, tau, k = length(tau))

    Explicitly finds the matrix Q of a QL factorization after calling geqlf! on A. Uses the output of geqlf!. A is overwritten by Q.

    LinearAlgebra.LAPACK.orgrq! — Function
    orgrq!(A, tau, k = length(tau))

    Explicitly finds the matrix Q of a RQ factorization after calling gerqf! on A. Uses the output of gerqf!. A is overwritten by Q.

    LinearAlgebra.LAPACK.ormlq! — Function
    ormlq!(side, trans, A, tau, C)

    Computes Q * C (trans = N), transpose(Q) * C (trans = T), adjoint(Q) * C (trans = C) for side = L or the equivalent right-sided multiplication for side = R using Q from a LQ factorization of A computed using gelqf!. C is overwritten.

    LinearAlgebra.LAPACK.ormqr! — Function
    ormqr!(side, trans, A, tau, C)

    Computes Q * C (trans = N), transpose(Q) * C (trans = T), adjoint(Q) * C (trans = C) for side = L or the equivalent right-sided multiplication for side = R using Q from a QR factorization of A computed using geqrf!. C is overwritten.

    LinearAlgebra.LAPACK.ormql! — Function
    ormql!(side, trans, A, tau, C)

    Computes Q * C (trans = N), transpose(Q) * C (trans = T), adjoint(Q) * C (trans = C) for side = L or the equivalent right-sided multiplication for side = R using Q from a QL factorization of A computed using geqlf!. C is overwritten.

    LinearAlgebra.LAPACK.ormrq! — Function
    ormrq!(side, trans, A, tau, C)

    Computes Q * C (trans = N), transpose(Q) * C (trans = T), adjoint(Q) * C (trans = C) for side = L or the equivalent right-sided multiplication for side = R using Q from a RQ factorization of A computed using gerqf!. C is overwritten.

    LinearAlgebra.LAPACK.gemqrt! — Function
    gemqrt!(side, trans, V, T, C)

    Computes Q * C (trans = N), transpose(Q) * C (trans = T), adjoint(Q) * C (trans = C) for side = L or the equivalent right-sided multiplication for side = R using Q from a QR factorization of A computed using geqrt!. C is overwritten.

    LinearAlgebra.LAPACK.posv! — Function
    posv!(uplo, A, B) -> (A, B)

    Finds the solution to A * X = B where A is a symmetric or Hermitian positive definite matrix. If uplo = U the upper Cholesky decomposition of A is computed. If uplo = L the lower Cholesky decomposition of A is computed. A is overwritten by its Cholesky decomposition. B is overwritten with the solution X.

    LinearAlgebra.LAPACK.potrf! — Function
    potrf!(uplo, A)

    Computes the Cholesky (upper if uplo = U, lower if uplo = L) decomposition of positive-definite matrix A. A is overwritten and returned with an info code.

    LinearAlgebra.LAPACK.potri! — Function
    potri!(uplo, A)

    Computes the inverse of positive-definite matrix A after calling potrf! to find its (upper if uplo = U, lower if uplo = L) Cholesky decomposition.

    A is overwritten by its inverse and returned.

    LinearAlgebra.LAPACK.potrs! — Function
    potrs!(uplo, A, B)

    Finds the solution to A * X = B where A is a symmetric or Hermitian positive definite matrix whose Cholesky decomposition was computed by potrf!. If uplo = U the upper Cholesky decomposition of A was computed. If uplo = L the lower Cholesky decomposition of A was computed. B is overwritten with the solution X.

    LinearAlgebra.LAPACK.pstrf! — Function
    pstrf!(uplo, A, tol) -> (A, piv, rank, info)

    Computes the (upper if uplo = U, lower if uplo = L) pivoted Cholesky decomposition of positive-definite matrix A with a user-set tolerance tol. A is overwritten by its Cholesky decomposition.

    Returns A, the pivots piv, the rank of A, and an info code. If info = 0, the factorization succeeded. If info = i > 0, then A is indefinite or rank-deficient.

    LinearAlgebra.LAPACK.ptsv! — Function
    ptsv!(D, E, B)

    Solves A * X = B for positive-definite tridiagonal A. D is the diagonal of A and E is the off-diagonal. B is overwritten with the solution X and returned.

    LinearAlgebra.LAPACK.pttrf! — Function
    pttrf!(D, E)

    Computes the LDLt factorization of a positive-definite tridiagonal matrix with D as diagonal and E as off-diagonal. D and E are overwritten and returned.

    LinearAlgebra.LAPACK.pttrs! — Function
    pttrs!(D, E, B)

    Solves A * X = B for positive-definite tridiagonal A with diagonal D and off-diagonal E after computing A's LDLt factorization using pttrf!. B is overwritten with the solution X.

    LinearAlgebra.LAPACK.trtri! — Function
    trtri!(uplo, diag, A)

    Finds the inverse of (upper if uplo = U, lower if uplo = L) triangular matrix A. If diag = N, A has non-unit diagonal elements. If diag = U, all diagonal elements of A are one. A is overwritten with its inverse.

    LinearAlgebra.LAPACK.trtrs! — Function
    trtrs!(uplo, trans, diag, A, B)

    Solves A * X = B (trans = N), transpose(A) * X = B (trans = T), or adjoint(A) * X = B (trans = C) for (upper if uplo = U, lower if uplo = L) triangular matrix A. If diag = N, A has non-unit diagonal elements. If diag = U, all diagonal elements of A are one. B is overwritten with the solution X.

    LinearAlgebra.LAPACK.trcon! — Function
    trcon!(norm, uplo, diag, A)

    Finds the reciprocal condition number of (upper if uplo = U, lower if uplo = L) triangular matrix A. If diag = N, A has non-unit diagonal elements. If diag = U, all diagonal elements of A are one. If norm = I, the condition number is found in the infinity norm. If norm = O or 1, the condition number is found in the one norm.

    LinearAlgebra.LAPACK.trevc! — Function
    trevc!(side, howmny, select, T, VL = similar(T), VR = similar(T))

    Finds the eigensystem of an upper triangular matrix T. If side = R, the right eigenvectors are computed. If side = L, the left eigenvectors are computed. If side = B, both sets are computed. If howmny = A, all eigenvectors are found. If howmny = B, all eigenvectors are found and backtransformed using VL and VR. If howmny = S, only the eigenvectors corresponding to the values in select are computed.

    LinearAlgebra.LAPACK.trrfs! — Function
    trrfs!(uplo, trans, diag, A, B, X, Ferr, Berr) -> (Ferr, Berr)

    Estimates the error in the solution to A * X = B (trans = N), transpose(A) * X = B (trans = T), adjoint(A) * X = B (trans = C) for side = L, or the equivalent equations a right-handed side = R X * A after computing X using trtrs!. If uplo = U, A is upper triangular. If uplo = L, A is lower triangular. If diag = N, A has non-unit diagonal elements. If diag = U, all diagonal elements of A are one. Ferr and Berr are optional inputs. Ferr is the forward error and Berr is the backward error, each component-wise.

    LinearAlgebra.LAPACK.stev! — Function
    stev!(job, dv, ev) -> (dv, Zmat)

    Computes the eigensystem for a symmetric tridiagonal matrix with dv as diagonal and ev as off-diagonal. If job = N only the eigenvalues are found and returned in dv. If job = V then the eigenvectors are also found and returned in Zmat.

    LinearAlgebra.LAPACK.stebz! — Function
    stebz!(range, order, vl, vu, il, iu, abstol, dv, ev) -> (dv, iblock, isplit)

    Computes the eigenvalues for a symmetric tridiagonal matrix with dv as diagonal and ev as off-diagonal. If range = A, all the eigenvalues are found. If range = V, the eigenvalues in the half-open interval (vl, vu] are found. If range = I, the eigenvalues with indices between il and iu are found. If order = B, eigvalues are ordered within a block. If order = E, they are ordered across all the blocks. abstol can be set as a tolerance for convergence.

    LinearAlgebra.LAPACK.stegr! — Function
    stegr!(jobz, range, dv, ev, vl, vu, il, iu) -> (w, Z)

    Computes the eigenvalues (jobz = N) or eigenvalues and eigenvectors (jobz = V) for a symmetric tridiagonal matrix with dv as diagonal and ev as off-diagonal. If range = A, all the eigenvalues are found. If range = V, the eigenvalues in the half-open interval (vl, vu] are found. If range = I, the eigenvalues with indices between il and iu are found. The eigenvalues are returned in w and the eigenvectors in Z.

    LinearAlgebra.LAPACK.stein! — Function
    stein!(dv, ev_in, w_in, iblock_in, isplit_in)

    Computes the eigenvectors for a symmetric tridiagonal matrix with dv as diagonal and ev_in as off-diagonal. w_in specifies the input eigenvalues for which to find corresponding eigenvectors. iblock_in specifies the submatrices corresponding to the eigenvalues in w_in. isplit_in specifies the splitting points between the submatrix blocks.

    LinearAlgebra.LAPACK.syconv! — Function
    syconv!(uplo, A, ipiv) -> (A, work)

    Converts a symmetric matrix A (which has been factorized into a triangular matrix) into two matrices L and D. If uplo = U, A is upper triangular. If uplo = L, it is lower triangular. ipiv is the pivot vector from the triangular factorization. A is overwritten by L and D.

    LinearAlgebra.LAPACK.sysv! — Function
    sysv!(uplo, A, B) -> (B, A, ipiv)

    Finds the solution to A * X = B for symmetric matrix A. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored. B is overwritten by the solution X. A is overwritten by its Bunch-Kaufman factorization. ipiv contains pivoting information about the factorization.

    LinearAlgebra.LAPACK.sytrf! — Function
    sytrf!(uplo, A) -> (A, ipiv, info)

    Computes the Bunch-Kaufman factorization of a symmetric matrix A. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored.

    Returns A, overwritten by the factorization, a pivot vector ipiv, and the error code info which is a non-negative integer. If info is positive the matrix is singular and the diagonal part of the factorization is exactly zero at position info.

    LinearAlgebra.LAPACK.sytri! — Function
    sytri!(uplo, A, ipiv)

    Computes the inverse of a symmetric matrix A using the results of sytrf!. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored. A is overwritten by its inverse.

    LinearAlgebra.LAPACK.sytrs! — Function
    sytrs!(uplo, A, ipiv, B)

    Solves the equation A * X = B for a symmetric matrix A using the results of sytrf!. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored. B is overwritten by the solution X.

    LinearAlgebra.LAPACK.hesv! — Function
    hesv!(uplo, A, B) -> (B, A, ipiv)

    Finds the solution to A * X = B for Hermitian matrix A. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored. B is overwritten by the solution X. A is overwritten by its Bunch-Kaufman factorization. ipiv contains pivoting information about the factorization.

    LinearAlgebra.LAPACK.hetrf! — Function
    hetrf!(uplo, A) -> (A, ipiv, info)

    Computes the Bunch-Kaufman factorization of a Hermitian matrix A. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored.

    Returns A, overwritten by the factorization, a pivot vector ipiv, and the error code info which is a non-negative integer. If info is positive the matrix is singular and the diagonal part of the factorization is exactly zero at position info.

    LinearAlgebra.LAPACK.hetri! — Function
    hetri!(uplo, A, ipiv)

    Computes the inverse of a Hermitian matrix A using the results of sytrf!. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored. A is overwritten by its inverse.

    LinearAlgebra.LAPACK.hetrs! — Function
    hetrs!(uplo, A, ipiv, B)

    Solves the equation A * X = B for a Hermitian matrix A using the results of sytrf!. If uplo = U, the upper half of A is stored. If uplo = L, the lower half is stored. B is overwritten by the solution X.

    LinearAlgebra.LAPACK.syev! — Function
    syev!(jobz, uplo, A)

    Finds the eigenvalues (jobz = N) or eigenvalues and eigenvectors (jobz = V) of a symmetric matrix A. If uplo = U, the upper triangle of A is used. If uplo = L, the lower triangle of A is used.

    LinearAlgebra.LAPACK.syevr! — Function
    syevr!(jobz, range, uplo, A, vl, vu, il, iu, abstol) -> (W, Z)

    Finds the eigenvalues (jobz = N) or eigenvalues and eigenvectors (jobz = V) of a symmetric matrix A. If uplo = U, the upper triangle of A is used. If uplo = L, the lower triangle of A is used. If range = A, all the eigenvalues are found. If range = V, the eigenvalues in the half-open interval (vl, vu] are found. If range = I, the eigenvalues with indices between il and iu are found. abstol can be set as a tolerance for convergence.

    The eigenvalues are returned in W and the eigenvectors in Z.

    LinearAlgebra.LAPACK.syevd! — Function
    syevd!(jobz, uplo, A)

    Finds the eigenvalues (jobz = N) or eigenvalues and eigenvectors (jobz = V) of a symmetric matrix A. If uplo = U, the upper triangle of A is used. If uplo = L, the lower triangle of A is used.

    Use the divide-and-conquer method, instead of the QR iteration used by syev! or multiple relatively robust representations used by syevr!. See James W. Demmel et al, SIAM J. Sci. Comput. 30, 3, 1508 (2008) for a comparison of the accuracy and performatce of different methods.

    LinearAlgebra.LAPACK.sygvd! — Function
    sygvd!(itype, jobz, uplo, A, B) -> (w, A, B)

    Finds the generalized eigenvalues (jobz = N) or eigenvalues and eigenvectors (jobz = V) of a symmetric matrix A and symmetric positive-definite matrix B. If uplo = U, the upper triangles of A and B are used. If uplo = L, the lower triangles of A and B are used. If itype = 1, the problem to solve is A * x = lambda * B * x. If itype = 2, the problem to solve is A * B * x = lambda * x. If itype = 3, the problem to solve is B * A * x = lambda * x.

    LinearAlgebra.LAPACK.bdsqr! — Function
    bdsqr!(uplo, d, e_, Vt, U, C) -> (d, Vt, U, C)

    Computes the singular value decomposition of a bidiagonal matrix with d on the diagonal and e_ on the off-diagonal. If uplo = U, e_ is the superdiagonal. If uplo = L, e_ is the subdiagonal. Can optionally also compute the product Q' * C.

    Returns the singular values in d, and the matrix C overwritten with Q' * C.

    LinearAlgebra.LAPACK.bdsdc! — Function
    bdsdc!(uplo, compq, d, e_) -> (d, e, u, vt, q, iq)

    Computes the singular value decomposition of a bidiagonal matrix with d on the diagonal and e_ on the off-diagonal using a divide and conqueq method. If uplo = U, e_ is the superdiagonal. If uplo = L, e_ is the subdiagonal. If compq = N, only the singular values are found. If compq = I, the singular values and vectors are found. If compq = P, the singular values and vectors are found in compact form. Only works for real types.

    Returns the singular values in d, and if compq = P, the compact singular vectors in iq.

    LinearAlgebra.LAPACK.gecon! — Function
    gecon!(normtype, A, anorm)

    Finds the reciprocal condition number of matrix A. If normtype = I, the condition number is found in the infinity norm. If normtype = O or 1, the condition number is found in the one norm. A must be the result of getrf! and anorm is the norm of A in the relevant norm.

    LinearAlgebra.LAPACK.gehrd! — Function
    gehrd!(ilo, ihi, A) -> (A, tau)

    Converts a matrix A to Hessenberg form. If A is balanced with gebal! then ilo and ihi are the outputs of gebal!. Otherwise they should be ilo = 1 and ihi = size(A,2). tau contains the elementary reflectors of the factorization.

    LinearAlgebra.LAPACK.orghr! — Function
    orghr!(ilo, ihi, A, tau)

    Explicitly finds Q, the orthogonal/unitary matrix from gehrd!. ilo, ihi, A, and tau must correspond to the input/output to gehrd!.

    LinearAlgebra.LAPACK.gees! — Function
    gees!(jobvs, A) -> (A, vs, w)

    Computes the eigenvalues (jobvs = N) or the eigenvalues and Schur vectors (jobvs = V) of matrix A. A is overwritten by its Schur form.

    Returns A, vs containing the Schur vectors, and w, containing the eigenvalues.

    LinearAlgebra.LAPACK.gges! — Function
    gges!(jobvsl, jobvsr, A, B) -> (A, B, alpha, beta, vsl, vsr)

    Computes the generalized eigenvalues, generalized Schur form, left Schur vectors (jobsvl = V), or right Schur vectors (jobvsr = V) of A and B.

    The generalized eigenvalues are returned in alpha and beta. The left Schur vectors are returned in vsl and the right Schur vectors are returned in vsr.

    LinearAlgebra.LAPACK.gges3! — Function
    gges3!(jobvsl, jobvsr, A, B) -> (A, B, alpha, beta, vsl, vsr)

    Computes the generalized eigenvalues, generalized Schur form, left Schur vectors (jobsvl = V), or right Schur vectors (jobvsr = V) of A and B using a blocked algorithm. This function requires LAPACK 3.6.0.

    The generalized eigenvalues are returned in alpha and beta. The left Schur vectors are returned in vsl and the right Schur vectors are returned in vsr.

    LinearAlgebra.LAPACK.trexc! — Function
    trexc!(compq, ifst, ilst, T, Q) -> (T, Q)
 trexc!(ifst, ilst, T, Q) -> (T, Q)

    Reorder the Schur factorization T of a matrix, such that the diagonal block of T with row index ifst is moved to row index ilst. If compq = V, the Schur vectors Q are reordered. If compq = N they are not modified. The 4-arg method calls the 5-arg method with compq = V.

    LinearAlgebra.LAPACK.trsen! — Function
    trsen!(job, compq, select, T, Q) -> (T, Q, w, s, sep)
-trsen!(select, T, Q) -> (T, Q, w, s, sep)

    Reorder the Schur factorization of a matrix and optionally finds reciprocal condition numbers. If job = N, no condition numbers are found. If job = E, only the condition number for this cluster of eigenvalues is found. If job = V, only the condition number for the invariant subspace is found. If job = B then the condition numbers for the cluster and subspace are found. If compq = V the Schur vectors Q are updated. If compq = N the Schur vectors are not modified. select determines which eigenvalues are in the cluster. The 3-arg method calls the 5-arg method with job = N and compq = V.

    Returns T, Q, reordered eigenvalues in w, the condition number of the cluster of eigenvalues s, and the condition number of the invariant subspace sep.

    LinearAlgebra.LAPACK.tgsen! — Function
    tgsen!(select, S, T, Q, Z) -> (S, T, alpha, beta, Q, Z)

    Reorders the vectors of a generalized Schur decomposition. select specifies the eigenvalues in each cluster.

    LinearAlgebra.LAPACK.trsyl! — Function
    trsyl!(transa, transb, A, B, C, isgn=1) -> (C, scale)

    Solves the Sylvester matrix equation A * X +/- X * B = scale*C where A and B are both quasi-upper triangular. If transa = N, A is not modified. If transa = T, A is transposed. If transa = C, A is conjugate transposed. Similarly for transb and B. If isgn = 1, the equation A * X + X * B = scale * C is solved. If isgn = -1, the equation A * X - X * B = scale * C is solved.

    Returns X (overwriting C) and scale.

    LinearAlgebra.LAPACK.hseqr! — Function
    hseqr!(job, compz, ilo, ihi, H, Z) -> (H, Z, w)

    Computes all eigenvalues and (optionally) the Schur factorization of a matrix reduced to Hessenberg form. If H is balanced with gebal! then ilo and ihi are the outputs of gebal!. Otherwise they should be ilo = 1 and ihi = size(H,2). tau contains the elementary reflectors of the factorization.

    +trsen!(select, T, Q) -> (T, Q, w, s, sep)

    Reorder the Schur factorization of a matrix and optionally finds reciprocal condition numbers. If job = N, no condition numbers are found. If job = E, only the condition number for this cluster of eigenvalues is found. If job = V, only the condition number for the invariant subspace is found. If job = B then the condition numbers for the cluster and subspace are found. If compq = V the Schur vectors Q are updated. If compq = N the Schur vectors are not modified. select determines which eigenvalues are in the cluster. The 3-arg method calls the 5-arg method with job = N and compq = V.

    Returns T, Q, reordered eigenvalues in w, the condition number of the cluster of eigenvalues s, and the condition number of the invariant subspace sep.

    LinearAlgebra.LAPACK.tgsen! — Function
    tgsen!(select, S, T, Q, Z) -> (S, T, alpha, beta, Q, Z)

    Reorders the vectors of a generalized Schur decomposition. select specifies the eigenvalues in each cluster.

    LinearAlgebra.LAPACK.trsyl! — Function
    trsyl!(transa, transb, A, B, C, isgn=1) -> (C, scale)

    Solves the Sylvester matrix equation A * X +/- X * B = scale*C where A and B are both quasi-upper triangular. If transa = N, A is not modified. If transa = T, A is transposed. If transa = C, A is conjugate transposed. Similarly for transb and B. If isgn = 1, the equation A * X + X * B = scale * C is solved. If isgn = -1, the equation A * X - X * B = scale * C is solved.

    Returns X (overwriting C) and scale.

    LinearAlgebra.LAPACK.hseqr! — Function
    hseqr!(job, compz, ilo, ihi, H, Z) -> (H, Z, w)

    Computes all eigenvalues and (optionally) the Schur factorization of a matrix reduced to Hessenberg form. If H is balanced with gebal! then ilo and ihi are the outputs of gebal!. Otherwise they should be ilo = 1 and ihi = size(H,2). tau contains the elementary reflectors of the factorization.

    diff --git a/dev/stdlib/Logging/index.html b/dev/stdlib/Logging/index.html index f6e6ec7a..53cf6e45 100644 --- a/dev/stdlib/Logging/index.html +++ b/dev/stdlib/Logging/index.html @@ -102,4 +102,4 @@ test(1) test([1,2]) endsource
    Logging.current_logger — Function
    current_logger()

    Return the logger for the current task, or the global logger if none is attached to the task.

    source

    Loggers that are supplied with the system:

    Logging.NullLogger — Type
    NullLogger()

    Logger which disables all messages and produces no output - the logger equivalent of /dev/null.

    source
    Logging.ConsoleLogger — Type
    ConsoleLogger([stream,] min_level=Info; meta_formatter=default_metafmt,
-              show_limited=true, right_justify=0)

    Logger with formatting optimized for readability in a text console, for example interactive work with the Julia REPL.

    Log levels less than min_level are filtered out.

    Message formatting can be controlled by setting keyword arguments:

    • meta_formatter is a function which takes the log event metadata (level, _module, group, id, file, line) and returns a color (as would be passed to printstyled), prefix and suffix for the log message. The default is to prefix with the log level and a suffix containing the module, file and line location.
    • show_limited limits the printing of large data structures to something which can fit on the screen by setting the :limit IOContext key during formatting.
    • right_justify is the integer column which log metadata is right justified at. The default is zero (metadata goes on its own line).
    Logging.SimpleLogger — Type
    SimpleLogger([stream,] min_level=Info)

    Simplistic logger for logging all messages with level greater than or equal to min_level to stream. If stream is closed then messages with log level greater or equal to Warn will be logged to stderr and below to stdout.

    source
    + show_limited=true, right_justify=0)

    Logger with formatting optimized for readability in a text console, for example interactive work with the Julia REPL.

    Log levels less than min_level are filtered out.

    Message formatting can be controlled by setting keyword arguments:

    Logging.SimpleLogger — Type
    SimpleLogger([stream,] min_level=Info)

    Simplistic logger for logging all messages with level greater than or equal to min_level to stream. If stream is closed then messages with log level greater or equal to Warn will be logged to stderr and below to stdout.

    source
    diff --git a/dev/stdlib/Markdown/index.html b/dev/stdlib/Markdown/index.html index fff5c2e3..e5046f28 100644 --- a/dev/stdlib/Markdown/index.html +++ b/dev/stdlib/Markdown/index.html @@ -99,4 +99,4 @@ This warning admonition has a custom title: `"Beware!"`.

    The first word after !!! declares the type of the admonition. There are standard admonition types that should produce special styling. Namely (in order of decreasing severity): danger, warning, info/note, and tip.

    You can also use your own admonition types, as long as the type name only contains lowercase Latin characters (a-z). For example, you could have a terminology block like this:

    !!! terminology "julia vs Julia"
 
     Strictly speaking, "Julia" refers to the language,
-    and "julia" to the standard implementation.

    However, unless the code rendering the Markdown special-cases that particular admonition type, it will get the default styling.

    A custom title for the box can be provided as a string (in double quotes) after the admonition type. If no title text is specified after the admonition type, then the type name will be used as the title (e.g. "Note" for the note admonition).

    Admonitions, like most other toplevel elements, can contain other toplevel elements (e.g. lists, images).

    Markdown Syntax Extensions

    Julia's markdown supports interpolation in a very similar way to basic string literals, with the difference that it will store the object itself in the Markdown tree (as opposed to converting it to a string). When the Markdown content is rendered the usual show methods will be called, and these can be overridden as usual. This design allows the Markdown to be extended with arbitrarily complex features (such as references) without cluttering the basic syntax.

    In principle, the Markdown parser itself can also be arbitrarily extended by packages, or an entirely custom flavour of Markdown can be used, but this should generally be unnecessary.

    + and "julia" to the standard implementation.

    However, unless the code rendering the Markdown special-cases that particular admonition type, it will get the default styling.

    A custom title for the box can be provided as a string (in double quotes) after the admonition type. If no title text is specified after the admonition type, then the type name will be used as the title (e.g. "Note" for the note admonition).

    Admonitions, like most other toplevel elements, can contain other toplevel elements (e.g. lists, images).

    Markdown Syntax Extensions

    Julia's markdown supports interpolation in a very similar way to basic string literals, with the difference that it will store the object itself in the Markdown tree (as opposed to converting it to a string). When the Markdown content is rendered the usual show methods will be called, and these can be overridden as usual. This design allows the Markdown to be extended with arbitrarily complex features (such as references) without cluttering the basic syntax.

    In principle, the Markdown parser itself can also be arbitrarily extended by packages, or an entirely custom flavour of Markdown can be used, but this should generally be unnecessary.

    diff --git a/dev/stdlib/Mmap/index.html b/dev/stdlib/Mmap/index.html index e0c14028..c55aa33f 100644 --- a/dev/stdlib/Mmap/index.html +++ b/dev/stdlib/Mmap/index.html @@ -55,4 +55,4 @@ julia> close(io) -julia> rm("mmap.bin")

    This creates a 25-by-30000 BitArray, linked to the file associated with stream io.

    Mmap.sync! — Function
    Mmap.sync!(array)

    Forces synchronization between the in-memory version of a memory-mapped Array or BitArray and the on-disk version.

    +julia> rm("mmap.bin")

    This creates a 25-by-30000 BitArray, linked to the file associated with stream io.

    Mmap.sync! — Function
    Mmap.sync!(array)

    Forces synchronization between the in-memory version of a memory-mapped Array or BitArray and the on-disk version.

    diff --git a/dev/stdlib/NetworkOptions/index.html b/dev/stdlib/NetworkOptions/index.html index 275cf6f2..a484c0aa 100644 --- a/dev/stdlib/NetworkOptions/index.html +++ b/dev/stdlib/NetworkOptions/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    Network Options

    NetworkOptions.ca_roots — Function
    ca_roots() :: Union{Nothing, String}

    The ca_roots() function tells the caller where, if anywhere, to find a file or directory of PEM-encoded certificate authority roots. By default, on systems like Windows and macOS where the built-in TLS engines know how to verify hosts using the system's built-in certificate verification mechanism, this function will return nothing. On classic UNIX systems (excluding macOS), root certificates are typically stored in a file in /etc: the common places for the current UNIX system will be searched and if one of these paths exists, it will be returned; if none of these typical root certificate paths exist, then the path to the set of root certificates that are bundled with Julia is returned.

    The default value returned by ca_roots() may be overridden by setting the JULIA_SSL_CA_ROOTS_PATH, SSL_CERT_DIR, or SSL_CERT_FILE environment variables, in which case this function will always return the value of the first of these variables that is set (whether the path exists or not). If JULIA_SSL_CA_ROOTS_PATH is set to the empty string, then the other variables are ignored (as if unset); if the other variables are set to the empty string, they behave is if they are not set.

    NetworkOptions.ca_roots_path — Function
    ca_roots_path() :: String

    The ca_roots_path() function is similar to the ca_roots() function except that it always returns a path to a file or directory of PEM-encoded certificate authority roots. When called on a system like Windows or macOS, where system root certificates are not stored in the file system, it will currently return the path to the set of root certificates that are bundled with Julia. (In the future, this function may instead extract the root certificates from the system and save them to a file whose path would be returned.)

    If it is possible to configure a library that uses TLS to use the system certificates that is generally preferable: i.e. it is better to use ca_roots() which returns nothing to indicate that the system certs should be used. The ca_roots_path() function should only be used when configuring libraries which require a path to a file or directory for root certificates.

    The default value returned by ca_roots_path() may be overridden by setting the JULIA_SSL_CA_ROOTS_PATH, SSL_CERT_DIR, or SSL_CERT_FILE environment variables, in which case this function will always return the value of the first of these variables that is set (whether the path exists or not). If JULIA_SSL_CA_ROOTS_PATH is set to the empty string, then the other variables are ignored (as if unset); if the other variables are set to the empty string, they behave is if they are not set.

    NetworkOptions.ssh_dir — Function
    ssh_dir() :: String

    The ssh_dir() function returns the location of the directory where the ssh program keeps/looks for configuration files. By default this is ~/.ssh but this can be overridden by setting the environment variable SSH_DIR.

    NetworkOptions.ssh_key_pass — Function
    ssh_key_pass() :: String

    The ssh_key_pass() function returns the value of the environment variable SSH_KEY_PASS if it is set or nothing if it is not set. In the future, this may be able to find a password by other means, such as secure system storage, so packages that need a password to decrypt an SSH private key should use this API instead of directly checking the environment variable so that they gain such capabilities automatically when they are added.

    NetworkOptions.ssh_key_name — Function
    ssh_key_name() :: String

    The ssh_key_name() function returns the base name of key files that SSH should use for when establishing a connection. There is usually no reason that this function should be called directly and libraries should generally use the ssh_key_path and ssh_pub_key_path functions to get full paths. If the environment variable SSH_KEY_NAME is set then this function returns that; otherwise it returns id_rsa by default.

    NetworkOptions.ssh_key_path — Function
    ssh_key_path() :: String

    The ssh_key_path() function returns the path of the SSH private key file that should be used for SSH connections. If the SSH_KEY_PATH environment variable is set then it will return that value. Otherwise it defaults to returning

    joinpath(ssh_dir(), ssh_key_name())

    This default value in turn depends on the SSH_DIR and SSH_KEY_NAME environment variables.

    NetworkOptions.ssh_pub_key_path — Function
    ssh_pub_key_path() :: String

    The ssh_pub_key_path() function returns the path of the SSH public key file that should be used for SSH connections. If the SSH_PUB_KEY_PATH environment variable is set then it will return that value. If that isn't set but SSH_KEY_PATH is set, it will return that path with the .pub suffix appended. If neither is set, it defaults to returning

    joinpath(ssh_dir(), ssh_key_name() * ".pub")

    This default value in turn depends on the SSH_DIR and SSH_KEY_NAME environment variables.

    NetworkOptions.ssh_known_hosts_files — Function
    ssh_known_hosts_files() :: Vector{String}

    The ssh_known_hosts_files() function returns a vector of paths of SSH known hosts files that should be used when establishing the identities of remote servers for SSH connections. By default this function returns

    [joinpath(ssh_dir(), "known_hosts"), bundled_known_hosts]

    where bundled_known_hosts is the path of a copy of a known hosts file that is bundled with this package (containing known hosts keys for github.com and gitlab.com). If the environment variable SSH_KNOWN_HOSTS_FILES is set, however, then its value is split into paths on the : character (or on ; on Windows) and this vector of paths is returned instead. If any component of this vector is empty, it is expanded to the default known hosts paths.

    Packages that use ssh_known_hosts_files() should ideally look for matching entries by comparing the host name and key types, considering the first entry in any of the files which matches to be the definitive identity of the host. If the caller cannot compare the key type (e.g. because it has been hashes) then it must approximate the above algorithm by looking for all matching entries for a host in each file: if a file has any entries for a host then one of them must match; the caller should only continue to search further known hosts files if there are no entries for the host in question in an earlier file.

    NetworkOptions.ssh_known_hosts_file — Function
    ssh_known_hosts_file() :: String

    The ssh_known_hosts_file() function returns a single path of an SSH known hosts file that should be used when establishing the identities of remote servers for SSH connections. It returns the first path returned by ssh_known_hosts_files that actually exists. Callers who can look in more than one known hosts file should use ssh_known_hosts_files instead and look for host matches in all the files returned as described in that function's docs.

    NetworkOptions.verify_host — Function
    verify_host(url::AbstractString, [transport::AbstractString]) :: Bool

    The verify_host function tells the caller whether the identity of a host should be verified when communicating over secure transports like TLS or SSH. The url argument may be:

    1. a proper URL staring with proto://
    2. an ssh-style bare host name or host name prefixed with user@
    3. an scp-style host as above, followed by : and a path location

    In each case the host name part is parsed out and the decision about whether to verify or not is made based solely on the host name, not anything else about the input URL. In particular, the protocol of the URL does not matter (more below).

    The transport argument indicates the kind of transport that the query is about. The currently known values are SSL/ssl (alias TLS/tls) and SSH/ssh. If the transport is omitted, the query will return true only if the host name should not be verified regardless of transport.

    The host name is matched against the host patterns in the relevant environment variables depending on whether transport is supplied and what its value is:

    • JULIA_NO_VERIFY_HOSTS — hosts that should not be verified for any transport
    • JULIA_SSL_NO_VERIFY_HOSTS — hosts that should not be verified for SSL/TLS
    • JULIA_SSH_NO_VERIFY_HOSTS — hosts that should not be verified for SSH
    • JULIA_ALWAYS_VERIFY_HOSTS — hosts that should always be verified

    The values of each of these variables is a comma-separated list of host name patterns with the following syntax — each pattern is split on . into parts and each part must one of:

    1. A literal domain name component consisting of one or more ASCII letter, digit, hyphen or underscore (technically not part of a legal host name, but sometimes used). A literal domain name component matches only itself.
    2. A **, which matches zero or more domain name components.
    3. A *, which match any one domain name component.

    When matching a host name against a pattern list in one of these variables, the host name is split on . into components and that sequence of words is matched against the pattern: a literal pattern matches exactly one host name component with that value; a * pattern matches exactly one host name component with any value; a ** pattern matches any number of host name components. For example:

    • ** matches any host name
    • **.org matches any host name in the .org top-level domain
    • example.com matches only the exact host name example.com
    • *.example.com matches api.example.com but not example.com or v1.api.example.com
    • **.example.com matches any domain under example.com, including example.com itself, api.example.com and v1.api.example.com
    +
    Repository

    Network Options

    NetworkOptions.ca_roots — Function
    ca_roots() :: Union{Nothing, String}

    The ca_roots() function tells the caller where, if anywhere, to find a file or directory of PEM-encoded certificate authority roots. By default, on systems like Windows and macOS where the built-in TLS engines know how to verify hosts using the system's built-in certificate verification mechanism, this function will return nothing. On classic UNIX systems (excluding macOS), root certificates are typically stored in a file in /etc: the common places for the current UNIX system will be searched and if one of these paths exists, it will be returned; if none of these typical root certificate paths exist, then the path to the set of root certificates that are bundled with Julia is returned.

    The default value returned by ca_roots() may be overridden by setting the JULIA_SSL_CA_ROOTS_PATH, SSL_CERT_DIR, or SSL_CERT_FILE environment variables, in which case this function will always return the value of the first of these variables that is set (whether the path exists or not). If JULIA_SSL_CA_ROOTS_PATH is set to the empty string, then the other variables are ignored (as if unset); if the other variables are set to the empty string, they behave is if they are not set.

    NetworkOptions.ca_roots_path — Function
    ca_roots_path() :: String

    The ca_roots_path() function is similar to the ca_roots() function except that it always returns a path to a file or directory of PEM-encoded certificate authority roots. When called on a system like Windows or macOS, where system root certificates are not stored in the file system, it will currently return the path to the set of root certificates that are bundled with Julia. (In the future, this function may instead extract the root certificates from the system and save them to a file whose path would be returned.)

    If it is possible to configure a library that uses TLS to use the system certificates that is generally preferable: i.e. it is better to use ca_roots() which returns nothing to indicate that the system certs should be used. The ca_roots_path() function should only be used when configuring libraries which require a path to a file or directory for root certificates.

    The default value returned by ca_roots_path() may be overridden by setting the JULIA_SSL_CA_ROOTS_PATH, SSL_CERT_DIR, or SSL_CERT_FILE environment variables, in which case this function will always return the value of the first of these variables that is set (whether the path exists or not). If JULIA_SSL_CA_ROOTS_PATH is set to the empty string, then the other variables are ignored (as if unset); if the other variables are set to the empty string, they behave is if they are not set.

    NetworkOptions.ssh_dir — Function
    ssh_dir() :: String

    The ssh_dir() function returns the location of the directory where the ssh program keeps/looks for configuration files. By default this is ~/.ssh but this can be overridden by setting the environment variable SSH_DIR.

    NetworkOptions.ssh_key_pass — Function
    ssh_key_pass() :: String

    The ssh_key_pass() function returns the value of the environment variable SSH_KEY_PASS if it is set or nothing if it is not set. In the future, this may be able to find a password by other means, such as secure system storage, so packages that need a password to decrypt an SSH private key should use this API instead of directly checking the environment variable so that they gain such capabilities automatically when they are added.

    NetworkOptions.ssh_key_name — Function
    ssh_key_name() :: String

    The ssh_key_name() function returns the base name of key files that SSH should use for when establishing a connection. There is usually no reason that this function should be called directly and libraries should generally use the ssh_key_path and ssh_pub_key_path functions to get full paths. If the environment variable SSH_KEY_NAME is set then this function returns that; otherwise it returns id_rsa by default.

    NetworkOptions.ssh_key_path — Function
    ssh_key_path() :: String

    The ssh_key_path() function returns the path of the SSH private key file that should be used for SSH connections. If the SSH_KEY_PATH environment variable is set then it will return that value. Otherwise it defaults to returning

    joinpath(ssh_dir(), ssh_key_name())

    This default value in turn depends on the SSH_DIR and SSH_KEY_NAME environment variables.

    NetworkOptions.ssh_pub_key_path — Function
    ssh_pub_key_path() :: String

    The ssh_pub_key_path() function returns the path of the SSH public key file that should be used for SSH connections. If the SSH_PUB_KEY_PATH environment variable is set then it will return that value. If that isn't set but SSH_KEY_PATH is set, it will return that path with the .pub suffix appended. If neither is set, it defaults to returning

    joinpath(ssh_dir(), ssh_key_name() * ".pub")

    This default value in turn depends on the SSH_DIR and SSH_KEY_NAME environment variables.

    NetworkOptions.ssh_known_hosts_files — Function
    ssh_known_hosts_files() :: Vector{String}

    The ssh_known_hosts_files() function returns a vector of paths of SSH known hosts files that should be used when establishing the identities of remote servers for SSH connections. By default this function returns

    [joinpath(ssh_dir(), "known_hosts"), bundled_known_hosts]

    where bundled_known_hosts is the path of a copy of a known hosts file that is bundled with this package (containing known hosts keys for github.com and gitlab.com). If the environment variable SSH_KNOWN_HOSTS_FILES is set, however, then its value is split into paths on the : character (or on ; on Windows) and this vector of paths is returned instead. If any component of this vector is empty, it is expanded to the default known hosts paths.

    Packages that use ssh_known_hosts_files() should ideally look for matching entries by comparing the host name and key types, considering the first entry in any of the files which matches to be the definitive identity of the host. If the caller cannot compare the key type (e.g. because it has been hashes) then it must approximate the above algorithm by looking for all matching entries for a host in each file: if a file has any entries for a host then one of them must match; the caller should only continue to search further known hosts files if there are no entries for the host in question in an earlier file.

    NetworkOptions.ssh_known_hosts_file — Function
    ssh_known_hosts_file() :: String

    The ssh_known_hosts_file() function returns a single path of an SSH known hosts file that should be used when establishing the identities of remote servers for SSH connections. It returns the first path returned by ssh_known_hosts_files that actually exists. Callers who can look in more than one known hosts file should use ssh_known_hosts_files instead and look for host matches in all the files returned as described in that function's docs.

    NetworkOptions.verify_host — Function
    verify_host(url::AbstractString, [transport::AbstractString]) :: Bool

    The verify_host function tells the caller whether the identity of a host should be verified when communicating over secure transports like TLS or SSH. The url argument may be:

    1. a proper URL staring with proto://
    2. an ssh-style bare host name or host name prefixed with user@
    3. an scp-style host as above, followed by : and a path location

    In each case the host name part is parsed out and the decision about whether to verify or not is made based solely on the host name, not anything else about the input URL. In particular, the protocol of the URL does not matter (more below).

    The transport argument indicates the kind of transport that the query is about. The currently known values are SSL/ssl (alias TLS/tls) and SSH/ssh. If the transport is omitted, the query will return true only if the host name should not be verified regardless of transport.

    The host name is matched against the host patterns in the relevant environment variables depending on whether transport is supplied and what its value is:

    • JULIA_NO_VERIFY_HOSTS — hosts that should not be verified for any transport
    • JULIA_SSL_NO_VERIFY_HOSTS — hosts that should not be verified for SSL/TLS
    • JULIA_SSH_NO_VERIFY_HOSTS — hosts that should not be verified for SSH
    • JULIA_ALWAYS_VERIFY_HOSTS — hosts that should always be verified

    The values of each of these variables is a comma-separated list of host name patterns with the following syntax — each pattern is split on . into parts and each part must one of:

    1. A literal domain name component consisting of one or more ASCII letter, digit, hyphen or underscore (technically not part of a legal host name, but sometimes used). A literal domain name component matches only itself.
    2. A **, which matches zero or more domain name components.
    3. A *, which match any one domain name component.

    When matching a host name against a pattern list in one of these variables, the host name is split on . into components and that sequence of words is matched against the pattern: a literal pattern matches exactly one host name component with that value; a * pattern matches exactly one host name component with any value; a ** pattern matches any number of host name components. For example:

    • ** matches any host name
    • **.org matches any host name in the .org top-level domain
    • example.com matches only the exact host name example.com
    • *.example.com matches api.example.com but not example.com or v1.api.example.com
    • **.example.com matches any domain under example.com, including example.com itself, api.example.com and v1.api.example.com
    diff --git a/dev/stdlib/Pkg/index.html b/dev/stdlib/Pkg/index.html index 2ef2fe20..bddbb2b7 100644 --- a/dev/stdlib/Pkg/index.html +++ b/dev/stdlib/Pkg/index.html @@ -32,4 +32,4 @@ (tutorial) pkg> status Status `~/tutorial/Project.toml` [7876af07] Example v0.5.3 - [682c06a0] JSON v0.21.3

    We can see that the tutorial environment now contains Example and JSON.

    Note

    If you have the same package (at the same version) installed in multiple environments, the package will only be downloaded and stored on the hard drive once. This makes environments very lightweight and effectively free to create. Using only the default environment with a huge number of packages in it is a common beginners mistake in Julia. Learning how to use environments effectively will improve your experience with Julia packages.

    For more information about environments, see the Working with Environments section of the documentation.

    If you are ever stuck, you can ask Pkg for help:

    (@v1.8) pkg> ?

    You should see a list of available commands along with short descriptions. You can ask for more detailed help by specifying a command:

    (@v1.8) pkg> ?develop

    This guide should help you get started with Pkg. Pkg has much more to offer in terms of powerful package management, read the full manual to learn more!

    + [682c06a0] JSON v0.21.3

    We can see that the tutorial environment now contains Example and JSON.

    Note

    If you have the same package (at the same version) installed in multiple environments, the package will only be downloaded and stored on the hard drive once. This makes environments very lightweight and effectively free to create. Using only the default environment with a huge number of packages in it is a common beginners mistake in Julia. Learning how to use environments effectively will improve your experience with Julia packages.

    For more information about environments, see the Working with Environments section of the documentation.

    If you are ever stuck, you can ask Pkg for help:

    (@v1.8) pkg> ?

    You should see a list of available commands along with short descriptions. You can ask for more detailed help by specifying a command:

    (@v1.8) pkg> ?develop

    This guide should help you get started with Pkg. Pkg has much more to offer in terms of powerful package management, read the full manual to learn more!

    diff --git a/dev/stdlib/Printf/index.html b/dev/stdlib/Printf/index.html index bbb4746c..7dfd3202 100644 --- a/dev/stdlib/Printf/index.html +++ b/dev/stdlib/Printf/index.html @@ -30,4 +30,4 @@ julia> @printf "%.0f %.1f %f" 0.5 0.025 -0.0078125 0 0.0 -0.007812
    Julia 1.8

    Starting in Julia 1.8, %s (string) and %c (character) widths are computed using textwidth, which e.g. ignores zero-width characters (such as combining characters for diacritical marks) and treats certain "wide" characters (e.g. emoji) as width 2.

    Julia 1.10

    Dynamic width specifiers like %*s and %0*.*f require Julia 1.10.

    Printf.@sprintf — Macro
    @sprintf("%Fmt", args...)

    Return @printf formatted output as string.

    Examples

    julia> @sprintf "this is a %s %15.1f" "test" 34.567
-"this is a test            34.6"
    +"this is a test 34.6" diff --git a/dev/stdlib/Profile/index.html b/dev/stdlib/Profile/index.html index 0e57fd18..4a6caed2 100644 --- a/dev/stdlib/Profile/index.html +++ b/dev/stdlib/Profile/index.html @@ -49,4 +49,4 @@ Profile.take_heap_snapshot(filepath::String, all_one::Bool=false) Profile.take_heap_snapshot(all_one::Bool=false; dir::String)

    Write a snapshot of the heap, in the JSON format expected by the Chrome Devtools Heap Snapshot viewer (.heapsnapshot extension) to a file ($pid_$timestamp.heapsnapshot) in the current directory by default (or tempdir if the current directory is unwritable), or in dir if given, or the given full file path, or IO stream.

    If all_one is true, then report the size of every object as one so they can be easily counted. Otherwise, report the actual size.

    source

    The methods in Profile are not exported and need to be called e.g. as Profile.take_heap_snapshot().

    julia> using Profile
 
-julia> Profile.take_heap_snapshot("snapshot.heapsnapshot")

    Traces and records julia objects on the heap. This only records objects known to the Julia garbage collector. Memory allocated by external libraries not managed by the garbage collector will not show up in the snapshot.

    The resulting heap snapshot file can be uploaded to chrome devtools to be viewed. For more information, see the chrome devtools docs.

    +julia> Profile.take_heap_snapshot("snapshot.heapsnapshot")

    Traces and records julia objects on the heap. This only records objects known to the Julia garbage collector. Memory allocated by external libraries not managed by the garbage collector will not show up in the snapshot.

    The resulting heap snapshot file can be uploaded to chrome devtools to be viewed. For more information, see the chrome devtools docs.

    diff --git a/dev/stdlib/REPL/index.html b/dev/stdlib/REPL/index.html index 1b9c7d11..b092d455 100644 --- a/dev/stdlib/REPL/index.html +++ b/dev/stdlib/REPL/index.html @@ -355,4 +355,4 @@ You like the following fruits: - orange - grape - - peach

    Configuration

    REPL.TerminalMenus.Config — Type
    Config(; scroll_wrap=false, ctrl_c_interrupt=true, charset=:ascii, cursor::Char, up_arrow::Char, down_arrow::Char)

    Configure behavior for selection menus via keyword arguments:

    • scroll_wrap, if true, causes the menu to wrap around when scrolling above the first or below the last entry
    • ctrl_c_interrupt, if true, throws an InterruptException if the user hits Ctrl-C during menu selection. If false, TerminalMenus.request will return the default result from TerminalMenus.selected.
    • charset affects the default values for cursor, up_arrow, and down_arrow, and can be :ascii or :unicode
    • cursor is the character printed to indicate the option that will be chosen by hitting "Enter." Defaults are '>' or '→', depending on charset.
    • up_arrow is the character printed when the display does not include the first entry. Defaults are '^' or '↑', depending on charset.
    • down_arrow is the character printed when the display does not include the last entry. Defaults are 'v' or '↓', depending on charset.

    Subtypes of ConfiguredMenu will print cursor, up_arrow, and down_arrow automatically as needed, your writeline method should not print them.

    Julia 1.6

    Config is available as of Julia 1.6. On older releases use the global CONFIG.

    REPL.TerminalMenus.MultiSelectConfig — Type
    MultiSelectConfig(; charset=:ascii, checked::String, unchecked::String, kwargs...)

    Configure behavior for a multiple-selection menu via keyword arguments:

    • checked is the string to print when an option has been selected. Defaults are "[X]" or "✓", depending on charset.
    • unchecked is the string to print when an option has not been selected. Defaults are "[ ]" or "⬚", depending on charset.

    All other keyword arguments are as described for TerminalMenus.Config. checked and unchecked are not printed automatically, and should be printed by your writeline method.

    Julia 1.6

    MultiSelectConfig is available as of Julia 1.6. On older releases use the global CONFIG.

    REPL.TerminalMenus.config — Function
    config( <see arguments> )

    Keyword-only function to configure global menu parameters

    Arguments

    • charset::Symbol=:na: ui characters to use (:ascii or :unicode); overridden by other arguments
    • cursor::Char='>'|'→': character to use for cursor
    • up_arrow::Char='^'|'↑': character to use for up arrow
    • down_arrow::Char='v'|'↓': character to use for down arrow
    • checked::String="[X]"|"✓": string to use for checked
    • unchecked::String="[ ]"|"⬚"): string to use for unchecked
    • scroll::Symbol=:nowrap: If :wrap wrap cursor around top and bottom, if :nowrap do not wrap cursor
    • supress_output::Bool=false: Ignored legacy argument, pass suppress_output as a keyword argument to request instead.
    • ctrl_c_interrupt::Bool=true: If false, return empty on ^C, if true throw InterruptException() on ^C
    Julia 1.6

    As of Julia 1.6, config is deprecated. Use Config or MultiSelectConfig instead.

    User interaction

    REPL.TerminalMenus.request — Function
    request(m::AbstractMenu; cursor=1)

    Display the menu and enter interactive mode. cursor indicates the item number used for the initial cursor position. cursor can be either an Int or a RefValue{Int}. The latter is useful for observation and control of the cursor position from the outside.

    Returns selected(m).

    Julia 1.6

    The cursor argument requires Julia 1.6 or later.

    request([term,] msg::AbstractString, m::AbstractMenu)

    Shorthand for println(msg); request(m).

    AbstractMenu extension interface

    Any subtype of AbstractMenu must be mutable, and must contain the fields pagesize::Int and pageoffset::Int. Any subtype must also implement the following functions:

    REPL.TerminalMenus.pick — Function
    pick(m::AbstractMenu, cursor::Int)

    Defines what happens when a user presses the Enter key while the menu is open. If true is returned, request() will exit. cursor indexes the position of the selection.

    REPL.TerminalMenus.cancel — Function
    cancel(m::AbstractMenu)

    Define what happens when a user cancels ('q' or ctrl-c) a menu. request() will always exit after calling this function.

    REPL.TerminalMenus.writeline — Function
    writeline(buf::IO, m::AbstractMenu, idx::Int, iscursor::Bool)

    Write the option at index idx to buf. iscursor, if true, indicates that this item is at the current cursor position (the one that will be selected by hitting "Enter").

    If m is a ConfiguredMenu, TerminalMenus will print the cursor indicator. Otherwise the callee is expected to handle such printing.

    Julia 1.6

    writeline requires Julia 1.6 or higher.

    On older versions of Julia, this was writeLine(buf::IO, m::AbstractMenu, idx, iscursor::Bool) and m is assumed to be unconfigured. The selection and cursor indicators can be obtained from TerminalMenus.CONFIG.

    This older function is supported on all Julia 1.x versions but will be dropped in Julia 2.0.

    It must also implement either options or numoptions:

    REPL.TerminalMenus.options — Function
    options(m::AbstractMenu)

    Return a list of strings to be displayed as options in the current page.

    Alternatively, implement numoptions, in which case options is not needed.

    REPL.TerminalMenus.numoptions — Function
    numoptions(m::AbstractMenu) -> Int

    Return the number of options in menu m. Defaults to length(options(m)).

    Julia 1.6

    This function requires Julia 1.6 or later.

    If the subtype does not have a field named selected, it must also implement

    REPL.TerminalMenus.selected — Function
    selected(m::AbstractMenu)

    Return information about the user-selected option. By default it returns m.selected.

    The following are optional but can allow additional customization:

    REPL.TerminalMenus.header — Function
    header(m::AbstractMenu) -> String

    Return a header string to be printed above the menu. Defaults to "".

    REPL.TerminalMenus.keypress — Function
    keypress(m::AbstractMenu, i::UInt32) -> Bool

    Handle any non-standard keypress event. If true is returned, TerminalMenus.request will exit. Defaults to false.

    + - peach

    Configuration

    REPL.TerminalMenus.Config — Type
    Config(; scroll_wrap=false, ctrl_c_interrupt=true, charset=:ascii, cursor::Char, up_arrow::Char, down_arrow::Char)

    Configure behavior for selection menus via keyword arguments:

    • scroll_wrap, if true, causes the menu to wrap around when scrolling above the first or below the last entry
    • ctrl_c_interrupt, if true, throws an InterruptException if the user hits Ctrl-C during menu selection. If false, TerminalMenus.request will return the default result from TerminalMenus.selected.
    • charset affects the default values for cursor, up_arrow, and down_arrow, and can be :ascii or :unicode
    • cursor is the character printed to indicate the option that will be chosen by hitting "Enter." Defaults are '>' or '→', depending on charset.
    • up_arrow is the character printed when the display does not include the first entry. Defaults are '^' or '↑', depending on charset.
    • down_arrow is the character printed when the display does not include the last entry. Defaults are 'v' or '↓', depending on charset.

    Subtypes of ConfiguredMenu will print cursor, up_arrow, and down_arrow automatically as needed, your writeline method should not print them.

    Julia 1.6

    Config is available as of Julia 1.6. On older releases use the global CONFIG.

    REPL.TerminalMenus.MultiSelectConfig — Type
    MultiSelectConfig(; charset=:ascii, checked::String, unchecked::String, kwargs...)

    Configure behavior for a multiple-selection menu via keyword arguments:

    • checked is the string to print when an option has been selected. Defaults are "[X]" or "✓", depending on charset.
    • unchecked is the string to print when an option has not been selected. Defaults are "[ ]" or "⬚", depending on charset.

    All other keyword arguments are as described for TerminalMenus.Config. checked and unchecked are not printed automatically, and should be printed by your writeline method.

    Julia 1.6

    MultiSelectConfig is available as of Julia 1.6. On older releases use the global CONFIG.

    REPL.TerminalMenus.config — Function
    config( <see arguments> )

    Keyword-only function to configure global menu parameters

    Arguments

    • charset::Symbol=:na: ui characters to use (:ascii or :unicode); overridden by other arguments
    • cursor::Char='>'|'→': character to use for cursor
    • up_arrow::Char='^'|'↑': character to use for up arrow
    • down_arrow::Char='v'|'↓': character to use for down arrow
    • checked::String="[X]"|"✓": string to use for checked
    • unchecked::String="[ ]"|"⬚"): string to use for unchecked
    • scroll::Symbol=:nowrap: If :wrap wrap cursor around top and bottom, if :nowrap do not wrap cursor
    • supress_output::Bool=false: Ignored legacy argument, pass suppress_output as a keyword argument to request instead.
    • ctrl_c_interrupt::Bool=true: If false, return empty on ^C, if true throw InterruptException() on ^C
    Julia 1.6

    As of Julia 1.6, config is deprecated. Use Config or MultiSelectConfig instead.

    User interaction

    REPL.TerminalMenus.request — Function
    request(m::AbstractMenu; cursor=1)

    Display the menu and enter interactive mode. cursor indicates the item number used for the initial cursor position. cursor can be either an Int or a RefValue{Int}. The latter is useful for observation and control of the cursor position from the outside.

    Returns selected(m).

    Julia 1.6

    The cursor argument requires Julia 1.6 or later.

    request([term,] msg::AbstractString, m::AbstractMenu)

    Shorthand for println(msg); request(m).

    AbstractMenu extension interface

    Any subtype of AbstractMenu must be mutable, and must contain the fields pagesize::Int and pageoffset::Int. Any subtype must also implement the following functions:

    REPL.TerminalMenus.pick — Function
    pick(m::AbstractMenu, cursor::Int)

    Defines what happens when a user presses the Enter key while the menu is open. If true is returned, request() will exit. cursor indexes the position of the selection.

    REPL.TerminalMenus.cancel — Function
    cancel(m::AbstractMenu)

    Define what happens when a user cancels ('q' or ctrl-c) a menu. request() will always exit after calling this function.

    REPL.TerminalMenus.writeline — Function
    writeline(buf::IO, m::AbstractMenu, idx::Int, iscursor::Bool)

    Write the option at index idx to buf. iscursor, if true, indicates that this item is at the current cursor position (the one that will be selected by hitting "Enter").

    If m is a ConfiguredMenu, TerminalMenus will print the cursor indicator. Otherwise the callee is expected to handle such printing.

    Julia 1.6

    writeline requires Julia 1.6 or higher.

    On older versions of Julia, this was writeLine(buf::IO, m::AbstractMenu, idx, iscursor::Bool) and m is assumed to be unconfigured. The selection and cursor indicators can be obtained from TerminalMenus.CONFIG.

    This older function is supported on all Julia 1.x versions but will be dropped in Julia 2.0.

    It must also implement either options or numoptions:

    REPL.TerminalMenus.options — Function
    options(m::AbstractMenu)

    Return a list of strings to be displayed as options in the current page.

    Alternatively, implement numoptions, in which case options is not needed.

    REPL.TerminalMenus.numoptions — Function
    numoptions(m::AbstractMenu) -> Int

    Return the number of options in menu m. Defaults to length(options(m)).

    Julia 1.6

    This function requires Julia 1.6 or later.

    If the subtype does not have a field named selected, it must also implement

    REPL.TerminalMenus.selected — Function
    selected(m::AbstractMenu)

    Return information about the user-selected option. By default it returns m.selected.

    The following are optional but can allow additional customization:

    REPL.TerminalMenus.header — Function
    header(m::AbstractMenu) -> String

    Return a header string to be printed above the menu. Defaults to "".

    REPL.TerminalMenus.keypress — Function
    keypress(m::AbstractMenu, i::UInt32) -> Bool

    Handle any non-standard keypress event. If true is returned, TerminalMenus.request will exit. Defaults to false.

    diff --git a/dev/stdlib/Random/index.html b/dev/stdlib/Random/index.html index d9bd40c9..0e5d4363 100644 --- a/dev/stdlib/Random/index.html +++ b/dev/stdlib/Random/index.html @@ -280,4 +280,4 @@ SamplerSimple(die, Sampler(RNG, 1:die.nsides, r)) rand(rng::AbstractRNG, sp::SamplerSimple{Die}) = rand(rng, sp.data)

    Here, sp.data refers to the second parameter in the call to the SamplerSimple constructor (in this case equal to Sampler(rng, 1:die.nsides, r)), while the Die object can be accessed via sp[].

    Like SamplerDie, any custom sampler must be a subtype of Sampler{T} where T is the type of the generated values. Note that SamplerSimple(x, data) isa Sampler{eltype(x)}, so this constrains what the first argument to SamplerSimple can be (it's recommended to use SamplerSimple like in the Die example, where x is simply forwarded while defining a Sampler method). Similarly, SamplerTrivial(x) isa Sampler{eltype(x)}.

    Another helper type is currently available for other cases, Random.SamplerTag, but is considered as internal API, and can break at any time without proper deprecations.

    Using distinct algorithms for scalar or array generation

    In some cases, whether one wants to generate only a handful of values or a large number of values will have an impact on the choice of algorithm. This is handled with the third parameter of the Sampler constructor. Let's assume we defined two helper types for Die, say SamplerDie1 which should be used to generate only few random values, and SamplerDieMany for many values. We can use those types as follows:

    Sampler(RNG::Type{<:AbstractRNG}, die::Die, ::Val{1}) = SamplerDie1(...)
-Sampler(RNG::Type{<:AbstractRNG}, die::Die, ::Val{Inf}) = SamplerDieMany(...)

    Of course, rand must also be defined on those types (i.e. rand(::AbstractRNG, ::SamplerDie1) and rand(::AbstractRNG, ::SamplerDieMany)). Note that, as usual, SamplerTrivial and SamplerSimple can be used if custom types are not necessary.

    Note: Sampler(rng, x) is simply a shorthand for Sampler(rng, x, Val(Inf)), and Random.Repetition is an alias for Union{Val{1}, Val{Inf}}.

    Creating new generators

    The API is not clearly defined yet, but as a rule of thumb:

    1. any rand method producing "basic" types (isbitstype integer and floating types in Base) should be defined for this specific RNG, if they are needed;
    2. other documented rand methods accepting an AbstractRNG should work out of the box, (provided the methods from 1) what are relied on are implemented), but can of course be specialized for this RNG if there is room for optimization;
    3. copy for pseudo-RNGs should return an independent copy that generates the exact same random sequence as the original from that point when called in the same way. When this is not feasible (e.g. hardware-based RNGs), copy must not be implemented.

    Concerning 1), a rand method may happen to work automatically, but it's not officially supported and may break without warnings in a subsequent release.

    To define a new rand method for an hypothetical MyRNG generator, and a value specification s (e.g. s == Int, or s == 1:10) of type S==typeof(s) or S==Type{s} if s is a type, the same two methods as we saw before must be defined:

    1. Sampler(::Type{MyRNG}, ::S, ::Repetition), which returns an object of type say SamplerS
    2. rand(rng::MyRNG, sp::SamplerS)

    It can happen that Sampler(rng::AbstractRNG, ::S, ::Repetition) is already defined in the Random module. It would then be possible to skip step 1) in practice (if one wants to specialize generation for this particular RNG type), but the corresponding SamplerS type is considered as internal detail, and may be changed without warning.

    Specializing array generation

    In some cases, for a given RNG type, generating an array of random values can be more efficient with a specialized method than by merely using the decoupling technique explained before. This is for example the case for MersenneTwister, which natively writes random values in an array.

    To implement this specialization for MyRNG and for a specification s, producing elements of type S, the following method can be defined: rand!(rng::MyRNG, a::AbstractArray{S}, ::SamplerS), where SamplerS is the type of the sampler returned by Sampler(MyRNG, s, Val(Inf)). Instead of AbstractArray, it's possible to implement the functionality only for a subtype, e.g. Array{S}. The non-mutating array method of rand will automatically call this specialization internally.

    Reproducibility

    By using an RNG parameter initialized with a given seed, you can reproduce the same pseudorandom number sequence when running your program multiple times. However, a minor release of Julia (e.g. 1.3 to 1.4) may change the sequence of pseudorandom numbers generated from a specific seed, in particular if MersenneTwister is used. (Even if the sequence produced by a low-level function like rand does not change, the output of higher-level functions like randsubseq may change due to algorithm updates.) Rationale: guaranteeing that pseudorandom streams never change prohibits many algorithmic improvements.

    If you need to guarantee exact reproducibility of random data, it is advisable to simply save the data (e.g. as a supplementary attachment in a scientific publication). (You can also, of course, specify a particular Julia version and package manifest, especially if you require bit reproducibility.)

    Software tests that rely on specific "random" data should also generally either save the data, embed it into the test code, or use third-party packages like StableRNGs.jl. On the other hand, tests that should pass for most random data (e.g. testing A \ (A*x) ≈ x for a random matrix A = randn(n,n)) can use an RNG with a fixed seed to ensure that simply running the test many times does not encounter a failure due to very improbable data (e.g. an extremely ill-conditioned matrix).

    The statistical distribution from which random samples are drawn is guaranteed to be the same across any minor Julia releases.

    +Sampler(RNG::Type{<:AbstractRNG}, die::Die, ::Val{Inf}) = SamplerDieMany(...)

    Of course, rand must also be defined on those types (i.e. rand(::AbstractRNG, ::SamplerDie1) and rand(::AbstractRNG, ::SamplerDieMany)). Note that, as usual, SamplerTrivial and SamplerSimple can be used if custom types are not necessary.

    Note: Sampler(rng, x) is simply a shorthand for Sampler(rng, x, Val(Inf)), and Random.Repetition is an alias for Union{Val{1}, Val{Inf}}.

    Creating new generators

    The API is not clearly defined yet, but as a rule of thumb:

    1. any rand method producing "basic" types (isbitstype integer and floating types in Base) should be defined for this specific RNG, if they are needed;
    2. other documented rand methods accepting an AbstractRNG should work out of the box, (provided the methods from 1) what are relied on are implemented), but can of course be specialized for this RNG if there is room for optimization;
    3. copy for pseudo-RNGs should return an independent copy that generates the exact same random sequence as the original from that point when called in the same way. When this is not feasible (e.g. hardware-based RNGs), copy must not be implemented.

    Concerning 1), a rand method may happen to work automatically, but it's not officially supported and may break without warnings in a subsequent release.

    To define a new rand method for an hypothetical MyRNG generator, and a value specification s (e.g. s == Int, or s == 1:10) of type S==typeof(s) or S==Type{s} if s is a type, the same two methods as we saw before must be defined:

    1. Sampler(::Type{MyRNG}, ::S, ::Repetition), which returns an object of type say SamplerS
    2. rand(rng::MyRNG, sp::SamplerS)

    It can happen that Sampler(rng::AbstractRNG, ::S, ::Repetition) is already defined in the Random module. It would then be possible to skip step 1) in practice (if one wants to specialize generation for this particular RNG type), but the corresponding SamplerS type is considered as internal detail, and may be changed without warning.

    Specializing array generation

    In some cases, for a given RNG type, generating an array of random values can be more efficient with a specialized method than by merely using the decoupling technique explained before. This is for example the case for MersenneTwister, which natively writes random values in an array.

    To implement this specialization for MyRNG and for a specification s, producing elements of type S, the following method can be defined: rand!(rng::MyRNG, a::AbstractArray{S}, ::SamplerS), where SamplerS is the type of the sampler returned by Sampler(MyRNG, s, Val(Inf)). Instead of AbstractArray, it's possible to implement the functionality only for a subtype, e.g. Array{S}. The non-mutating array method of rand will automatically call this specialization internally.

    Reproducibility

    By using an RNG parameter initialized with a given seed, you can reproduce the same pseudorandom number sequence when running your program multiple times. However, a minor release of Julia (e.g. 1.3 to 1.4) may change the sequence of pseudorandom numbers generated from a specific seed, in particular if MersenneTwister is used. (Even if the sequence produced by a low-level function like rand does not change, the output of higher-level functions like randsubseq may change due to algorithm updates.) Rationale: guaranteeing that pseudorandom streams never change prohibits many algorithmic improvements.

    If you need to guarantee exact reproducibility of random data, it is advisable to simply save the data (e.g. as a supplementary attachment in a scientific publication). (You can also, of course, specify a particular Julia version and package manifest, especially if you require bit reproducibility.)

    Software tests that rely on specific "random" data should also generally either save the data, embed it into the test code, or use third-party packages like StableRNGs.jl. On the other hand, tests that should pass for most random data (e.g. testing A \ (A*x) ≈ x for a random matrix A = randn(n,n)) can use an RNG with a fixed seed to ensure that simply running the test many times does not encounter a failure due to very improbable data (e.g. an extremely ill-conditioned matrix).

    The statistical distribution from which random samples are drawn is guaranteed to be the same across any minor Julia releases.

    diff --git a/dev/stdlib/SHA/index.html b/dev/stdlib/SHA/index.html index b6200fcf..5e7fa34c 100644 --- a/dev/stdlib/SHA/index.html +++ b/dev/stdlib/SHA/index.html @@ -119,4 +119,4 @@ 0x00000000000000000000000000000094 julia> bytes2hex(digest!(ctx)) -"bc49a6f2aa29b27ee5ed1e944edd7f3d153e8a01535d98b5e24dac9a589a6248"

    All HMAC functions

    HMAC context type

    SHA.HMAC_CTX — Type
    HMAC_CTX(ctx::CTX, key::Vector{UInt8}) where {CTX<:SHA_CTX}

    Construct an empty HMAC_CTX context.

    SHA-1

    SHA.hmac_sha1 — Function
    hmac_sha1(key, data)

    Hash data using the sha1 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha1(key, io::IO)

    Hash data from io with the passed key using sha1 algorithm.

    SHA-2

    SHA.hmac_sha224 — Function
    hmac_sha224(key, data)

    Hash data using the sha224 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha224(key, io::IO)

    Hash data from io with the passed key using sha224 algorithm.

    SHA.hmac_sha256 — Function
    hmac_sha256(key, data)

    Hash data using the sha256 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha256(key, io::IO)

    Hash data from io with the passed key using sha256 algorithm.

    SHA.hmac_sha384 — Function
    hmac_sha384(key, data)

    Hash data using the sha384 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha384(key, io::IO)

    Hash data from io with the passed key using sha384 algorithm.

    SHA.hmac_sha512 — Function
    hmac_sha512(key, data)

    Hash data using the sha512 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha512(key, io::IO)

    Hash data from io with the passed key using sha512 algorithm.

    SHA.hmac_sha2_224 — Function
    hmac_sha2_224(key, data)

    Hash data using the sha2_224 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_224(key, io::IO)

    Hash data from io with the passed key using sha2_224 algorithm.

    SHA.hmac_sha2_256 — Function
    hmac_sha2_256(key, data)

    Hash data using the sha2_256 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_256(key, io::IO)

    Hash data from io with the passed key using sha2_256 algorithm.

    SHA.hmac_sha2_384 — Function
    hmac_sha2_384(key, data)

    Hash data using the sha2_384 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_384(key, io::IO)

    Hash data from io with the passed key using sha2_384 algorithm.

    SHA.hmac_sha2_512 — Function
    hmac_sha2_512(key, data)

    Hash data using the sha2_512 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_512(key, io::IO)

    Hash data from io with the passed key using sha2_512 algorithm.

    SHA-3

    SHA.hmac_sha3_224 — Function
    hmac_sha3_224(key, data)

    Hash data using the sha3_224 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_224(key, io::IO)

    Hash data from io with the passed key using sha3_224 algorithm.

    SHA.hmac_sha3_256 — Function
    hmac_sha3_256(key, data)

    Hash data using the sha3_256 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_256(key, io::IO)

    Hash data from io with the passed key using sha3_256 algorithm.

    SHA.hmac_sha3_384 — Function
    hmac_sha3_384(key, data)

    Hash data using the sha3_384 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_384(key, io::IO)

    Hash data from io with the passed key using sha3_384 algorithm.

    SHA.hmac_sha3_512 — Function
    hmac_sha3_512(key, data)

    Hash data using the sha3_512 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_512(key, io::IO)

    Hash data from io with the passed key using sha3_512 algorithm.

    +"bc49a6f2aa29b27ee5ed1e944edd7f3d153e8a01535d98b5e24dac9a589a6248"

    All HMAC functions

    HMAC context type

    SHA.HMAC_CTX — Type
    HMAC_CTX(ctx::CTX, key::Vector{UInt8}) where {CTX<:SHA_CTX}

    Construct an empty HMAC_CTX context.

    SHA-1

    SHA.hmac_sha1 — Function
    hmac_sha1(key, data)

    Hash data using the sha1 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha1(key, io::IO)

    Hash data from io with the passed key using sha1 algorithm.

    SHA-2

    SHA.hmac_sha224 — Function
    hmac_sha224(key, data)

    Hash data using the sha224 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha224(key, io::IO)

    Hash data from io with the passed key using sha224 algorithm.

    SHA.hmac_sha256 — Function
    hmac_sha256(key, data)

    Hash data using the sha256 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha256(key, io::IO)

    Hash data from io with the passed key using sha256 algorithm.

    SHA.hmac_sha384 — Function
    hmac_sha384(key, data)

    Hash data using the sha384 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha384(key, io::IO)

    Hash data from io with the passed key using sha384 algorithm.

    SHA.hmac_sha512 — Function
    hmac_sha512(key, data)

    Hash data using the sha512 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha512(key, io::IO)

    Hash data from io with the passed key using sha512 algorithm.

    SHA.hmac_sha2_224 — Function
    hmac_sha2_224(key, data)

    Hash data using the sha2_224 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_224(key, io::IO)

    Hash data from io with the passed key using sha2_224 algorithm.

    SHA.hmac_sha2_256 — Function
    hmac_sha2_256(key, data)

    Hash data using the sha2_256 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_256(key, io::IO)

    Hash data from io with the passed key using sha2_256 algorithm.

    SHA.hmac_sha2_384 — Function
    hmac_sha2_384(key, data)

    Hash data using the sha2_384 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_384(key, io::IO)

    Hash data from io with the passed key using sha2_384 algorithm.

    SHA.hmac_sha2_512 — Function
    hmac_sha2_512(key, data)

    Hash data using the sha2_512 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha2_512(key, io::IO)

    Hash data from io with the passed key using sha2_512 algorithm.

    SHA-3

    SHA.hmac_sha3_224 — Function
    hmac_sha3_224(key, data)

    Hash data using the sha3_224 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_224(key, io::IO)

    Hash data from io with the passed key using sha3_224 algorithm.

    SHA.hmac_sha3_256 — Function
    hmac_sha3_256(key, data)

    Hash data using the sha3_256 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_256(key, io::IO)

    Hash data from io with the passed key using sha3_256 algorithm.

    SHA.hmac_sha3_384 — Function
    hmac_sha3_384(key, data)

    Hash data using the sha3_384 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_384(key, io::IO)

    Hash data from io with the passed key using sha3_384 algorithm.

    SHA.hmac_sha3_512 — Function
    hmac_sha3_512(key, data)

    Hash data using the sha3_512 algorithm using the passed key. See also HMAC_CTX.

    hmac_sha3_512(key, io::IO)

    Hash data from io with the passed key using sha3_512 algorithm.

    diff --git a/dev/stdlib/Serialization/index.html b/dev/stdlib/Serialization/index.html index f0d92d49..88d0ee9d 100644 --- a/dev/stdlib/Serialization/index.html +++ b/dev/stdlib/Serialization/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash}); -
    Repository

    序列化

    Provides serialization of Julia objects.

    Serialization.serialize — Function
    serialize(stream::IO, value)

    Write an arbitrary value to a stream in an opaque format, such that it can be read back by deserialize. The read-back value will be as identical as possible to the original, but note that Ptr values are serialized as all-zero bit patterns (NULL).

    An 8-byte identifying header is written to the stream first. To avoid writing the header, construct a Serializer and use it as the first argument to serialize instead. See also Serialization.writeheader.

    The data format can change in minor (1.x) Julia releases, but files written by prior 1.x versions will remain readable. The main exception to this is when the definition of a type in an external package changes. If that occurs, it may be necessary to specify an explicit compatible version of the affected package in your environment. Renaming functions, even private functions, inside packages can also put existing files out of sync. Anonymous functions require special care: because their names are automatically generated, minor code changes can cause them to be renamed. Serializing anonymous functions should be avoided in files intended for long-term storage.

    In some cases, the word size (32- or 64-bit) of the reading and writing machines must match. In rarer cases the OS or architecture must also match, for example when using packages that contain platform-dependent code.

    serialize(filename::AbstractString, value)

    Open a file and serialize the given value to it.

    Julia 1.1

    This method is available as of Julia 1.1.

    Serialization.deserialize — Function
    deserialize(stream)

    Read a value written by serialize. deserialize assumes the binary data read from stream is correct and has been serialized by a compatible implementation of serialize. deserialize is designed for simplicity and performance, and so does not validate the data read. Malformed data can result in process termination. The caller must ensure the integrity and correctness of data read from stream.

    deserialize(filename::AbstractString)

    Open a file and deserialize its contents.

    Julia 1.1

    This method is available as of Julia 1.1.

    Serialization.writeheader — Function
    Serialization.writeheader(s::AbstractSerializer)

    Write an identifying header to the specified serializer. The header consists of 8 bytes as follows:

    OffsetDescription
    0tag byte (0x37)
    1-2signature bytes "JL"
    3protocol version
    4bits 0-1: endianness: 0 = little, 1 = big
    4bits 2-3: platform: 0 = 32-bit, 1 = 64-bit
    5-7reserved
    +
    Repository

    序列化

    Provides serialization of Julia objects.

    Serialization.serialize — Function
    serialize(stream::IO, value)

    Write an arbitrary value to a stream in an opaque format, such that it can be read back by deserialize. The read-back value will be as identical as possible to the original, but note that Ptr values are serialized as all-zero bit patterns (NULL).

    An 8-byte identifying header is written to the stream first. To avoid writing the header, construct a Serializer and use it as the first argument to serialize instead. See also Serialization.writeheader.

    The data format can change in minor (1.x) Julia releases, but files written by prior 1.x versions will remain readable. The main exception to this is when the definition of a type in an external package changes. If that occurs, it may be necessary to specify an explicit compatible version of the affected package in your environment. Renaming functions, even private functions, inside packages can also put existing files out of sync. Anonymous functions require special care: because their names are automatically generated, minor code changes can cause them to be renamed. Serializing anonymous functions should be avoided in files intended for long-term storage.

    In some cases, the word size (32- or 64-bit) of the reading and writing machines must match. In rarer cases the OS or architecture must also match, for example when using packages that contain platform-dependent code.

    serialize(filename::AbstractString, value)

    Open a file and serialize the given value to it.

    Julia 1.1

    This method is available as of Julia 1.1.

    Serialization.deserialize — Function
    deserialize(stream)

    Read a value written by serialize. deserialize assumes the binary data read from stream is correct and has been serialized by a compatible implementation of serialize. deserialize is designed for simplicity and performance, and so does not validate the data read. Malformed data can result in process termination. The caller must ensure the integrity and correctness of data read from stream.

    deserialize(filename::AbstractString)

    Open a file and deserialize its contents.

    Julia 1.1

    This method is available as of Julia 1.1.

    Serialization.writeheader — Function
    Serialization.writeheader(s::AbstractSerializer)

    Write an identifying header to the specified serializer. The header consists of 8 bytes as follows:

    OffsetDescription
    0tag byte (0x37)
    1-2signature bytes "JL"
    3protocol version
    4bits 0-1: endianness: 0 = little, 1 = big
    4bits 2-3: platform: 0 = 32-bit, 1 = 64-bit
    5-7reserved
    diff --git a/dev/stdlib/SharedArrays/index.html b/dev/stdlib/SharedArrays/index.html index 99b96ca9..3c48b809 100644 --- a/dev/stdlib/SharedArrays/index.html +++ b/dev/stdlib/SharedArrays/index.html @@ -5,4 +5,4 @@ gtag('config', 'UA-28835595-9', {'page_path': location.pathname + location.search + location.hash});
    Repository

    共享数组

    SharedArray represents an array, which is shared across multiple processes, on a single machine.

    SharedArrays.SharedArray — Type
    SharedArray{T}(dims::NTuple; init=false, pids=Int[])
 SharedArray{T,N}(...)

    Construct a SharedArray of a bits type T and size dims across the processes specified by pids - all of which have to be on the same host. If N is specified by calling SharedArray{T,N}(dims), then N must match the length of dims.

    If pids is left unspecified, the shared array will be mapped across all processes on the current host, including the master. But, localindices and indexpids will only refer to worker processes. This facilitates work distribution code to use workers for actual computation with the master process acting as a driver.

    If an init function of the type initfn(S::SharedArray) is specified, it is called on all the participating workers.

    The shared array is valid as long as a reference to the SharedArray object exists on the node which created the mapping.

    SharedArray{T}(filename::AbstractString, dims::NTuple, [offset=0]; mode=nothing, init=false, pids=Int[])
-SharedArray{T,N}(...)

    Construct a SharedArray backed by the file filename, with element type T (must be a bits type) and size dims, across the processes specified by pids - all of which have to be on the same host. This file is mmapped into the host memory, with the following consequences:

    • The array data must be represented in binary format (e.g., an ASCII format like CSV cannot be supported)

    • Any changes you make to the array values (e.g., A[3] = 0) will also change the values on disk

    If pids is left unspecified, the shared array will be mapped across all processes on the current host, including the master. But, localindices and indexpids will only refer to worker processes. This facilitates work distribution code to use workers for actual computation with the master process acting as a driver.

    mode must be one of "r", "r+", "w+", or "a+", and defaults to "r+" if the file specified by filename already exists, or "w+" if not. If an init function of the type initfn(S::SharedArray) is specified, it is called on all the participating workers. You cannot specify an init function if the file is not writable.

    offset allows you to skip the specified number of bytes at the beginning of the file.

    source
    SharedArrays.indexpids — Function
    indexpids(S::SharedArray)

    Return the current worker's index in the list of workers mapping the SharedArray (i.e. in the same list returned by procs(S)), or 0 if the SharedArray is not mapped locally.

    source
    SharedArrays.localindices — Function
    localindices(S::SharedArray)

    Return a range describing the "default" indices to be handled by the current process. This range should be interpreted in the sense of linear indexing, i.e., as a sub-range of 1:length(S). In multi-process contexts, returns an empty range in the parent process (or any process for which indexpids returns 0).

    It's worth emphasizing that localindices exists purely as a convenience, and you can partition work on the array among workers any way you wish. For a SharedArray, all indices should be equally fast for each worker process.

    source
    +SharedArray{T,N}(...)

    Construct a SharedArray backed by the file filename, with element type T (must be a bits type) and size dims, across the processes specified by pids - all of which have to be on the same host. This file is mmapped into the host memory, with the following consequences:

    If pids is left unspecified, the shared array will be mapped across all processes on the current host, including the master. But, localindices and indexpids will only refer to worker processes. This facilitates work distribution code to use workers for actual computation with the master process acting as a driver.

    mode must be one of "r", "r+", "w+", or "a+", and defaults to "r+" if the file specified by filename already exists, or "w+" if not. If an init function of the type initfn(S::SharedArray) is specified, it is called on all the participating workers. You cannot specify an init function if the file is not writable.

    offset allows you to skip the specified number of bytes at the beginning of the file.

    source
    SharedArrays.SharedVector — Type
    SharedVector

    A one-dimensional SharedArray.

    source
    SharedArrays.SharedMatrix — Type
    SharedMatrix

    A two-dimensional SharedArray.

    source
    Distributed.procs — Method
    procs(S::SharedArray)

    Get the vector of processes mapping the shared array.

    source
    SharedArrays.sdata — Function
    sdata(S::SharedArray)

    Return the actual Array object backing S.

    source
    SharedArrays.indexpids — Function
    indexpids(S::SharedArray)

    Return the current worker's index in the list of workers mapping the SharedArray (i.e. in the same list returned by procs(S)), or 0 if the SharedArray is not mapped locally.

    source
    SharedArrays.localindices — Function
    localindices(S::SharedArray)

    Return a range describing the "default" indices to be handled by the current process. This range should be interpreted in the sense of linear indexing, i.e., as a sub-range of 1:length(S). In multi-process contexts, returns an empty range in the parent process (or any process for which indexpids returns 0).

    It's worth emphasizing that localindices exists purely as a convenience, and you can partition work on the array among workers any way you wish. For a SharedArray, all indices should be equally fast for each worker process.

    source
    diff --git a/dev/stdlib/Sockets/index.html b/dev/stdlib/Sockets/index.html index bdd9d537..2d4973a5 100644 --- a/dev/stdlib/Sockets/index.html +++ b/dev/stdlib/Sockets/index.html @@ -58,4 +58,4 @@ Stacktrace: [...] nested task error: foo -[...]source
    Sockets.send — Function
    send(socket::UDPSocket, host::IPAddr, port::Integer, msg)

    Send msg over socket to host:port.

    Sockets.recv — Function
    recv(socket::UDPSocket)

    Read a UDP packet from the specified socket, and return the bytes received. This call blocks.

    Sockets.recvfrom — Function
    recvfrom(socket::UDPSocket) -> (host_port, data)

    Read a UDP packet from the specified socket, returning a tuple of (host_port, data), where host_port will be an InetAddr{IPv4} or InetAddr{IPv6}, as appropriate.

    Julia 1.3

    Prior to Julia version 1.3, the first returned value was an address (IPAddr). In version 1.3 it was changed to an InetAddr.

    Sockets.setopt — Function
    setopt(sock::UDPSocket; multicast_loop=nothing, multicast_ttl=nothing, enable_broadcast=nothing, ttl=nothing)

    Set UDP socket options.

    • multicast_loop: loopback for multicast packets (default: true).
    • multicast_ttl: TTL for multicast packets (default: nothing).
    • enable_broadcast: flag must be set to true if socket will be used for broadcast messages, or else the UDP system will return an access error (default: false).
    • ttl: Time-to-live of packets sent on the socket (default: nothing).
    Sockets.nagle — Function
    nagle(socket::Union{TCPServer, TCPSocket}, enable::Bool)

    Enables or disables Nagle's algorithm on a given TCP server or socket.

    Julia 1.3

    This function requires Julia 1.3 or later.

    Sockets.quickack — Function
    quickack(socket::Union{TCPServer, TCPSocket}, enable::Bool)

    On Linux systems, the TCP_QUICKACK is disabled or enabled on socket.

    +[...]source
    Sockets.send — Function
    send(socket::UDPSocket, host::IPAddr, port::Integer, msg)

    Send msg over socket to host:port.

    Sockets.recv — Function
    recv(socket::UDPSocket)

    Read a UDP packet from the specified socket, and return the bytes received. This call blocks.

    Sockets.recvfrom — Function
    recvfrom(socket::UDPSocket) -> (host_port, data)

    Read a UDP packet from the specified socket, returning a tuple of (host_port, data), where host_port will be an InetAddr{IPv4} or InetAddr{IPv6}, as appropriate.

    Julia 1.3

    Prior to Julia version 1.3, the first returned value was an address (IPAddr). In version 1.3 it was changed to an InetAddr.

    Sockets.setopt — Function
    setopt(sock::UDPSocket; multicast_loop=nothing, multicast_ttl=nothing, enable_broadcast=nothing, ttl=nothing)

    Set UDP socket options.

    • multicast_loop: loopback for multicast packets (default: true).
    • multicast_ttl: TTL for multicast packets (default: nothing).
    • enable_broadcast: flag must be set to true if socket will be used for broadcast messages, or else the UDP system will return an access error (default: false).
    • ttl: Time-to-live of packets sent on the socket (default: nothing).
    Sockets.nagle — Function
    nagle(socket::Union{TCPServer, TCPSocket}, enable::Bool)

    Enables or disables Nagle's algorithm on a given TCP server or socket.

    Julia 1.3

    This function requires Julia 1.3 or later.

    Sockets.quickack — Function
    quickack(socket::Union{TCPServer, TCPSocket}, enable::Bool)

    On Linux systems, the TCP_QUICKACK is disabled or enabled on socket.

    diff --git a/dev/stdlib/SparseArrays/index.html b/dev/stdlib/SparseArrays/index.html index 5588bfd0..ed4433d9 100644 --- a/dev/stdlib/SparseArrays/index.html +++ b/dev/stdlib/SparseArrays/index.html @@ -256,4 +256,4 @@ [C::AbstractSparseMatrixCSC{Tv,Ti}]) where {Tv,Ti}

    Bilaterally permute A, storing result PAQ (A[p,q]) in X. Stores intermediate result (AQ)^T (transpose(A[:,q])) in optional argument C if present. Requires that none of X, A, and, if present, C alias each other; to store result PAQ back into A, use the following method lacking X:

    permute!(A::AbstractSparseMatrixCSC{Tv,Ti}, p::AbstractVector{<:Integer},
          q::AbstractVector{<:Integer}[, C::AbstractSparseMatrixCSC{Tv,Ti},
          [workcolptr::Vector{Ti}]]) where {Tv,Ti}

    X's dimensions must match those of A (size(X, 1) == size(A, 1) and size(X, 2) == size(A, 2)), and X must have enough storage to accommodate all allocated entries in A (length(rowvals(X)) >= nnz(A) and length(nonzeros(X)) >= nnz(A)). Column-permutation q's length must match A's column count (length(q) == size(A, 2)). Row-permutation p's length must match A's row count (length(p) == size(A, 1)).

    C's dimensions must match those of transpose(A) (size(C, 1) == size(A, 2) and size(C, 2) == size(A, 1)), and C must have enough storage to accommodate all allocated entries in A (length(rowvals(C)) >= nnz(A) and length(nonzeros(C)) >= nnz(A)).

    For additional (algorithmic) information, and for versions of these methods that forgo argument checking, see (unexported) parent methods unchecked_noalias_permute! and unchecked_aliasing_permute!.

    See also permute.

    source
    SparseArrays.halfperm! — Function
    halfperm!(X::AbstractSparseMatrixCSC{Tv,Ti}, A::AbstractSparseMatrixCSC{TvA,Ti},
-          q::AbstractVector{<:Integer}, f::Function = identity) where {Tv,TvA,Ti}

    Column-permute and transpose A, simultaneously applying f to each entry of A, storing the result (f(A)Q)^T (map(f, transpose(A[:,q]))) in X.

    Element type Tv of X must match f(::TvA), where TvA is the element type of A. X's dimensions must match those of transpose(A) (size(X, 1) == size(A, 2) and size(X, 2) == size(A, 1)), and X must have enough storage to accommodate all allocated entries in A (length(rowvals(X)) >= nnz(A) and length(nonzeros(X)) >= nnz(A)). Column-permutation q's length must match A's column count (length(q) == size(A, 2)).

    This method is the parent of several methods performing transposition and permutation operations on SparseMatrixCSCs. As this method performs no argument checking, prefer the safer child methods ([c]transpose[!], permute[!]) to direct use.

    This method implements the HALFPERM algorithm described in F. Gustavson, "Two fast algorithms for sparse matrices: multiplication and permuted transposition," ACM TOMS 4(3), 250-269 (1978). The algorithm runs in O(size(A, 1), size(A, 2), nnz(A)) time and requires no space beyond that passed in.

    source
    SparseArrays.ftranspose! — Function
    ftranspose!(X::AbstractSparseMatrixCSC{Tv,Ti}, A::AbstractSparseMatrixCSC{Tv,Ti}, f::Function) where {Tv,Ti}

    Transpose A and store it in X while applying the function f to the non-zero elements. Does not remove the zeros created by f. size(X) must be equal to size(transpose(A)). No additional memory is allocated other than resizing the rowval and nzval of X, if needed.

    See halfperm!

    source

    Noteworthy external packages

    Several other Julia packages provide sparse matrix implementations that should be mentioned:

    1. SuiteSparseGraphBLAS.jl is a wrapper over the fast, multithreaded SuiteSparse:GraphBLAS C library. On CPU this is typically the fastest option, often significantly outperforming MKLSparse.

    2. CUDA.jl exposes the CUSPARSE library for GPU sparse matrix operations.

    3. SparseMatricesCSR.jl provides a Julia native implementation of the Compressed Sparse Rows (CSR) format.

    4. MKLSparse.jl accelerates SparseArrays sparse-dense matrix operations using Intel's MKL library.

    5. SparseArrayKit.jl available for multidimensional sparse arrays.

    6. LuxurySparse.jl provides static sparse array formats, as well as a coordinate format.

    7. ExtendableSparse.jl enables fast insertion into sparse matrices using a lazy approach to new stored indices.

    + q::AbstractVector{<:Integer}, f::Function = identity) where {Tv,TvA,Ti}

    Column-permute and transpose A, simultaneously applying f to each entry of A, storing the result (f(A)Q)^T (map(f, transpose(A[:,q]))) in X.

    Element type Tv of X must match f(::TvA), where TvA is the element type of A. X's dimensions must match those of transpose(A) (size(X, 1) == size(A, 2) and size(X, 2) == size(A, 1)), and X must have enough storage to accommodate all allocated entries in A (length(rowvals(X)) >= nnz(A) and length(nonzeros(X)) >= nnz(A)). Column-permutation q's length must match A's column count (length(q) == size(A, 2)).

    This method is the parent of several methods performing transposition and permutation operations on SparseMatrixCSCs. As this method performs no argument checking, prefer the safer child methods ([c]transpose[!], permute[!]) to direct use.

    This method implements the HALFPERM algorithm described in F. Gustavson, "Two fast algorithms for sparse matrices: multiplication and permuted transposition," ACM TOMS 4(3), 250-269 (1978). The algorithm runs in O(size(A, 1), size(A, 2), nnz(A)) time and requires no space beyond that passed in.

    source
    SparseArrays.ftranspose! — Function
    ftranspose!(X::AbstractSparseMatrixCSC{Tv,Ti}, A::AbstractSparseMatrixCSC{Tv,Ti}, f::Function) where {Tv,Ti}

    Transpose A and store it in X while applying the function f to the non-zero elements. Does not remove the zeros created by f. size(X) must be equal to size(transpose(A)). No additional memory is allocated other than resizing the rowval and nzval of X, if needed.

    See halfperm!

    source

    Noteworthy external packages

    Several other Julia packages provide sparse matrix implementations that should be mentioned:

    1. SuiteSparseGraphBLAS.jl is a wrapper over the fast, multithreaded SuiteSparse:GraphBLAS C library. On CPU this is typically the fastest option, often significantly outperforming MKLSparse.

    2. CUDA.jl exposes the CUSPARSE library for GPU sparse matrix operations.

    3. SparseMatricesCSR.jl provides a Julia native implementation of the Compressed Sparse Rows (CSR) format.

    4. MKLSparse.jl accelerates SparseArrays sparse-dense matrix operations using Intel's MKL library.

    5. SparseArrayKit.jl available for multidimensional sparse arrays.

    6. LuxurySparse.jl provides static sparse array formats, as well as a coordinate format.

    7. ExtendableSparse.jl enables fast insertion into sparse matrices using a lazy approach to new stored indices.

    diff --git a/dev/stdlib/Statistics/index.html b/dev/stdlib/Statistics/index.html index 3a793524..59ea65c3 100644 --- a/dev/stdlib/Statistics/index.html +++ b/dev/stdlib/Statistics/index.html @@ -120,4 +120,4 @@ 18.000000000000004 julia> quantile(skipmissing([1, 10, missing]), 0.5) -5.5source +5.5source diff --git a/dev/stdlib/TOML/index.html b/dev/stdlib/TOML/index.html index 06f5656e..5e1e26dd 100644 --- a/dev/stdlib/TOML/index.html +++ b/dev/stdlib/TOML/index.html @@ -79,4 +79,4 @@ parse(p::Parser, x::Union{AbstractString, IO})

    Parse the string or stream x, and return the resulting table (dictionary). Throw a ParserError upon failure.

    See also TOML.tryparse.

    TOML.parsefile — Function
    parsefile(f::AbstractString)
 parsefile(p::Parser, f::AbstractString)

    Parse file f and return the resulting table (dictionary). Throw a ParserError upon failure.

    See also TOML.tryparsefile.

    TOML.tryparse — Function
    tryparse(x::Union{AbstractString, IO})
 tryparse(p::Parser, x::Union{AbstractString, IO})

    Parse the string or stream x, and return the resulting table (dictionary). Return a ParserError upon failure.

    See also TOML.parse.

    TOML.tryparsefile — Function
    tryparsefile(f::AbstractString)
-tryparsefile(p::Parser, f::AbstractString)

    Parse file f and return the resulting table (dictionary). Return a ParserError upon failure.

    See also TOML.parsefile.

    TOML.print — Function
    print([to_toml::Function], io::IO [=stdout], data::AbstractDict; sorted=false, by=identity)

    Write data as TOML syntax to the stream io. If the keyword argument sorted is set to true, sort tables according to the function given by the keyword argument by.

    The following data types are supported: AbstractDict, AbstractVector, AbstractString, Integer, AbstractFloat, Bool, Dates.DateTime, Dates.Time, Dates.Date. Note that the integers and floats need to be convertible to Float64 and Int64 respectively. For other data types, pass the function to_toml that takes the data types and returns a value of a supported type.

    TOML.Parser — Type
    Parser()

    Constructor for a TOML Parser. Note that in most cases one does not need to explicitly create a Parser but instead one directly use use TOML.parsefile or TOML.parse. Using an explicit parser will however reuse some internal data structures which can be beneficial for performance if a larger number of small files are parsed.

    TOML.ParserError — Type
    ParserError

    Type that is returned from tryparse and tryparsefile when parsing fails. It contains (among others) the following fields:

    • pos, the position in the string when the error happened
    • table, the result that so far was successfully parsed
    • type, an error type, different for different types of errors
    +tryparsefile(p::Parser, f::AbstractString)

    Parse file f and return the resulting table (dictionary). Return a ParserError upon failure.

    See also TOML.parsefile.

    TOML.print — Function
    print([to_toml::Function], io::IO [=stdout], data::AbstractDict; sorted=false, by=identity)

    Write data as TOML syntax to the stream io. If the keyword argument sorted is set to true, sort tables according to the function given by the keyword argument by.

    The following data types are supported: AbstractDict, AbstractVector, AbstractString, Integer, AbstractFloat, Bool, Dates.DateTime, Dates.Time, Dates.Date. Note that the integers and floats need to be convertible to Float64 and Int64 respectively. For other data types, pass the function to_toml that takes the data types and returns a value of a supported type.

    TOML.Parser — Type
    Parser()

    Constructor for a TOML Parser. Note that in most cases one does not need to explicitly create a Parser but instead one directly use use TOML.parsefile or TOML.parse. Using an explicit parser will however reuse some internal data structures which can be beneficial for performance if a larger number of small files are parsed.

    TOML.ParserError — Type
    ParserError

    Type that is returned from tryparse and tryparsefile when parsing fails. It contains (among others) the following fields:

    • pos, the position in the string when the error happened
    • table, the result that so far was successfully parsed
    • type, an error type, different for different types of errors
    diff --git a/dev/stdlib/Tar/index.html b/dev/stdlib/Tar/index.html index affa9946..6dbeafcc 100644 --- a/dev/stdlib/Tar/index.html +++ b/dev/stdlib/Tar/index.html @@ -50,4 +50,4 @@ mode :: UInt16 # mode/permissions (best viewed in octal) size :: Int64 # size of record data in bytes link :: String # target path of a symlink -end

    Types are represented with the following symbols: file, hardlink, symlink, chardev, blockdev, directory, fifo, or for unknown types, the typeflag character as a symbol. Note that extract refuses to extract records types other than file, symlink and directory; list will only list other kinds of records if called with strict=false.

    The tar format includes various other metadata about records, including user and group IDs, user and group names, and timestamps. The Tar package, by design, completely ignores these. When creating tar files, these fields are always set to zero/empty. When reading tar files, these fields are ignored aside from verifying header checksums for each header record for all fields.

    +end

    Types are represented with the following symbols: file, hardlink, symlink, chardev, blockdev, directory, fifo, or for unknown types, the typeflag character as a symbol. Note that extract refuses to extract records types other than file, symlink and directory; list will only list other kinds of records if called with strict=false.

    The tar format includes various other metadata about records, including user and group IDs, user and group names, and timestamps. The Tar package, by design, completely ignores these. When creating tar files, these fields are always set to zero/empty. When reading tar files, these fields are ignored aside from verifying header checksums for each header record for all fields.

    diff --git a/dev/stdlib/Test/index.html b/dev/stdlib/Test/index.html index dbd7e4b7..2f3029a5 100644 --- a/dev/stdlib/Test/index.html +++ b/dev/stdlib/Test/index.html @@ -349,4 +349,4 @@ Testing Running tests... Test Summary: | Pass Total Example tests | 9 9 - Testing Example tests passed

    And if all went correctly, you should see a similar output as above. Using Test.jl, more complicated tests can be added for packages but this should ideally point developers in the direction of how to get started with testing their own created packages.

    + Testing Example tests passed

    And if all went correctly, you should see a similar output as above. Using Test.jl, more complicated tests can be added for packages but this should ideally point developers in the direction of how to get started with testing their own created packages.

    diff --git a/dev/stdlib/UUIDs/index.html b/dev/stdlib/UUIDs/index.html index 82ddda7a..7a166b86 100644 --- a/dev/stdlib/UUIDs/index.html +++ b/dev/stdlib/UUIDs/index.html @@ -16,4 +16,4 @@ julia> u5 = uuid5(u4, "julia") UUID("086cc5bb-2461-57d8-8068-0aed7f5b5cd1")
    UUIDs.uuid_version — Function
    uuid_version(u::UUID) -> Int

    Inspects the given UUID and returns its version (see RFC 4122).

    Examples

    julia> uuid_version(uuid4())
-4
    +4 diff --git a/dev/stdlib/Unicode/index.html b/dev/stdlib/Unicode/index.html index d24442c9..22f6121f 100644 --- a/dev/stdlib/Unicode/index.html +++ b/dev/stdlib/Unicode/index.html @@ -59,4 +59,4 @@ 'o': ASCII/Unicode U+006F (category Ll: Letter, lowercase) 's': ASCII/Unicode U+0073 (category Ll: Letter, lowercase) 'e': ASCII/Unicode U+0065 (category Ll: Letter, lowercase) - '́': Unicode U+0301 (category Mn: Mark, nonspacing)

    This consists of the 3rd to 7th codepoints (Chars) in "exposé", because the grapheme "é" is actually two Unicode codepoints (an 'e' followed by an acute-accent combining character U+0301).

    Because finding grapheme boundaries requires iteration over the string contents, the graphemes(s, m:n) function requires time proportional to the length of the string (number of codepoints) before the end of the substring.

    Julia 1.9

    The m:n argument of graphemes requires Julia 1.9.

    + '́': Unicode U+0301 (category Mn: Mark, nonspacing)

    This consists of the 3rd to 7th codepoints (Chars) in "exposé", because the grapheme "é" is actually two Unicode codepoints (an 'e' followed by an acute-accent combining character U+0301).

    Because finding grapheme boundaries requires iteration over the string contents, the graphemes(s, m:n) function requires time proportional to the length of the string (number of codepoints) before the end of the substring.

    Julia 1.9

    The m:n argument of graphemes requires Julia 1.9.