Special functions (mad!) (#367)

* Fix for mad!

Drops SpecialFunctions

* Why the segerrs?

* Revert "Why the segerrs?"

This reverts commit faa2162.

* Possible workaround

JuliaLang/julia/issues/22108

* Addressed comments

Will check if it solves the BigFloat issue.

* Fix syntax

* Remove unused constant definition

* Restore Real

* Attempt irrational

* Implied rational precision.

* Named scale factor `mad_constant`

REQUIRE

@@ -1,6 +1,5 @@
 julia 0.6
 DataStructures 0.5.0
-SpecialFunctions 0.1.0
 SortingAlgorithms
 Compat 0.61.0
 Missings

src/StatsBase.jl

@@ -3,10 +3,9 @@ __precompile__()
 module StatsBase
     import Base: length, isempty, eltype, values, sum, mean, mean!, show, quantile
     import Base.Cartesian: @nloops, @nref, @nextract
+    using Base: @irrational
     import DataStructures: heapify!, heappop!, percolate_down!
 
-    import SpecialFunctions: erfcinv
-
     using Compat, SortingAlgorithms, Missings
     using Compat.LinearAlgebra
     using Compat.Random

src/deprecates.jl

@@ -85,6 +85,6 @@ rand(s::RandIntSampler) = rand(Compat.Random.GLOBAL_RNG, s)
 @deprecate randi(rng::AbstractRNG, a::Int, b::Int) rand(rng, a:b)
 @deprecate randi(a::Int, b::Int) rand(a:b)
 
-@deprecate(mad!(v::AbstractArray{T}, center;
-                constant::Real = 1 / (-sqrt(2 * one(T)) * erfcinv(3 * one(T) / 2))) where T<:Real,
+@deprecate(mad!(v::AbstractArray{<:Real}, center;
+                constant::Real = BigFloat("1.482602218505601860547076529360423431326703202590312896536266275245674447622701")),
            mad!(v, center=center, constant=constant))

src/scalarstats.jl

@@ -263,7 +263,7 @@ function mad(v::AbstractArray{T};
     mad!(v2, center=center === nothing ? median!(v2) : center, normalize=normalize)
 end
 
-
+@irrational mad_constant 1.4826022185056018 BigFloat("1.482602218505601860547076529360423431326703202590312896536266275245674447622701")
 """
     StatsBase.mad!(v; center=median!(v), normalize=true)
 
@@ -274,25 +274,24 @@ If `normalize` is set to `true`, the MAD is multiplied by
 `1 / quantile(Normal(), 3/4) ≈ 1.4826`, in order to obtain a consistent estimator
 of the standard deviation under the assumption that the data is normally distributed.
 """
-function mad!(v::AbstractArray{T};
+function mad!(v::AbstractArray{<:Real};
               center::Real=median!(v),
               normalize::Union{Bool,Nothing}=true,
-              constant=nothing) where T<:Real
-    for i in 1:length(v)
-        @inbounds v[i] = abs(v[i]-center)
-    end
-    k = 1 / (-sqrt(2 * one(T)) * erfcinv(3 * one(T) / 2))
-    if normalize === nothing
+              constant=nothing)
+    isempty(v) && throw(ArgumentError("mad is not defined for empty arrays"))
+    v .= abs.(v .- center)
+    m = median!(v)
+    if normalize isa Nothing
         Base.depwarn("the `normalize` keyword argument will be false by default in future releases: set it explicitly to silence this deprecation", :mad)
         normalize = true
     end
-    if constant !== nothing
+    if !isa(constant, Nothing)
         Base.depwarn("keyword argument `constant` is deprecated, use `normalize` instead or apply the multiplication directly", :mad)
-        constant * median!(v)
+        m * constant
     elseif normalize
-        k * median!(v)
+        m * mad_constant
     else
-        one(k) * median!(v)
+        m
     end
 end