Remove some special functions from Base (#20427)

Author: ararslan

base/deprecated.jl

@@ -228,14 +228,9 @@ for f in (
         # base/special/log.jl
         :log, :log1p,
         # base/special/gamma.jl
-        :gamma, :lfact, :digamma, :trigamma, :zeta, :eta,
-        # base/special/erf.jl
-        :erfcx, :erfi, :dawson,
-        # base/special/bessel.jl
-        :airyai, :airyaiprime, :airybi, :airybiprime,
-        :besselj0, :besselj1, :bessely0, :bessely1,
+        :gamma, :lfact,
         # base/math.jl
-        :cbrt, :sinh, :cosh, :tanh, :atan, :asinh, :exp, :erf, :erfc, :exp2,
+        :cbrt, :sinh, :cosh, :tanh, :atan, :asinh, :exp, :exp2,
         :expm1, :exp10, :sin, :cos, :tan, :asin, :acos, :acosh, :atanh,
         #=:log,=# :log2, :log10, :lgamma, #=:log1p,=# :sqrt,
         # base/floatfuncs.jl
@@ -254,8 +249,6 @@ for f in ( :acos_fast, :acosh_fast, :angle_fast, :asin_fast, :asinh_fast,
     @eval FastMath Base.@dep_vectorize_1arg Number $f
 end
 for f in (
-        :invdigamma, # base/special/gamma.jl
-        :erfinc, :erfcinv, # base/special/erf.jl
         :trunc, :floor, :ceil, :round, # base/floatfuncs.jl
         :rad2deg, :deg2rad, :exponent, :significand, # base/math.jl
         :sind, :cosd, :tand, :asind, :acosd, :atand, :asecd, :acscd, :acotd, # base/special/trig.jl
@@ -294,11 +287,7 @@ end
 # Deprecate @vectorize_2arg-vectorized functions from...
 for f in (
         # base/special/gamma.jl
-        :polygamma, :zeta, :beta, :lbeta,
-        # base/special/bessel.jl
-        :besseli, :besselix, :besselj, :besseljx,
-        :besselk, :besselkx, :bessely, :besselyx, :besselh,
-        :besselhx, :hankelh1, :hankelh2, :hankelh1x, :hankelh2x,
+        :beta, :lbeta,
         # base/math.jl
         :log, :hypot, :atan2,
     )
@@ -674,65 +663,6 @@ end
 # Deprecate isimag (#19947).
 @deprecate isimag(z::Number) iszero(real(z))
 
-@deprecate airy(z::Number) airyai(z)
-@deprecate airyx(z::Number) airyaix(z)
-@deprecate airyprime(z::Number) airyaiprime(z)
-@deprecate airy(x::AbstractArray{<:Number}) airyai.(x)
-@deprecate airyx(x::AbstractArray{<:Number}) airyaix.(x)
-@deprecate airyprime(x::AbstractArray{<:Number}) airyprime.(x)
-
-function _airy(k::Integer, z::Complex128)
-    depwarn("`airy(k,x)` is deprecated, use `airyai(x)`, `airyaiprime(x)`, `airybi(x)` or `airybiprime(x)` instead.",:airy)
-    id = Int32(k==1 || k==3)
-    if k == 0 || k == 1
-        return Base.Math._airy(z, id, Int32(1))
-    elseif k == 2 || k == 3
-        return Base.Math._biry(z, id, Int32(1))
-    else
-        throw(ArgumentError("k must be between 0 and 3"))
-    end
-end
-function _airyx(k::Integer, z::Complex128)
-    depwarn("`airyx(k,x)` is deprecated, use `airyaix(x)`, `airyaiprimex(x)`, `airybix(x)` or `airybiprimex(x)` instead.",:airyx)
-    id = Int32(k==1 || k==3)
-    if k == 0 || k == 1
-        return Base.Math._airy(z, id, Int32(2))
-    elseif k == 2 || k == 3
-        return Base.Math._biry(z, id, Int32(2))
-    else
-        throw(ArgumentError("k must be between 0 and 3"))
-    end
-end
-
-for afn in (:airy,:airyx)
-    _afn = Symbol("_"*string(afn))
-    suf  = string(afn)[5:end]
-    @eval begin
-        function $afn(k::Integer, z::Complex128)
-            afn = $(QuoteNode(afn))
-            suf = $(QuoteNode(suf))
-            depwarn("`$afn(k,x)` is deprecated, use `airyai$suf(x)`, `airyaiprime$suf(x)`, `airybi$suf(x)` or `airybiprime$suf(x)` instead.",$(QuoteNode(afn)))
-            $_afn(k,z)
-        end
-
-        $afn(k::Integer, z::Complex) = $afn(k, float(z))
-        $afn(k::Integer, z::Complex{<:AbstractFloat}) = throw(MethodError($afn,(k,z)))
-        $afn(k::Integer, z::Complex64) = Complex64($afn(k, Complex128(z)))
-        $afn(k::Integer, x::Real) = $afn(k, float(x))
-        $afn(k::Integer, x::AbstractFloat) = real($afn(k, complex(x)))
-
-        function $afn(k::Number, x::AbstractArray{<:Number})
-            $afn.(k,x)
-        end
-        function $afn(k::AbstractArray{<:Number}, x::Number)
-            $afn.(k,x)
-        end
-        function $afn(k::AbstractArray{<:Number}, x::AbstractArray{<:Number})
-            $afn.(k,x)
-        end
-    end
-end
-
 # Deprecate vectorized xor in favor of compact broadcast syntax
 @deprecate xor(a::Bool, B::BitArray)                xor.(a, B)
 @deprecate xor(A::BitArray, b::Bool)                xor.(A, b)
@@ -1231,6 +1161,24 @@ end
 
 # TODO: remove warning for using `_` in parse_input_line in base/client.jl
 
+# Special functions have been moved to a package
+for f in (:airyai, :airyaiprime, :airybi, :airybiprime, :airyaix, :airyaiprimex, :airybix, :airybiprimex,
+          :besselh, :besselhx, :besseli, :besselix, :besselj, :besselj0, :besselj1, :besseljx, :besselk,
+          :besselkx, :bessely, :bessely0, :bessely1, :besselyx,
+          :dawson, :erf, :erfc, :erfcinv, :erfcx, :erfi, :erfinv,
+          :eta, :zeta, :digamma, :invdigamma, :polygamma, :trigamma,
+          :hankelh1, :hankelh1x, :hankelh2, :hankelh2x,
+          :airy, :airyx, :airyprime)
+    @eval begin
+        function $f(args...; kwargs...)
+            error(string($f, args, " has been moved to the package SpecialFunctions.jl.\n",
+                         "Run Pkg.add(\"SpecialFunctions\") to install SpecialFunctions on Julia v0.6 and later,\n",
+                         "and then run `using SpecialFunctions`."))
+        end
+        export $f
+    end
+end
+
 # END 0.6 deprecations
 
 # BEGIN 1.0 deprecations

base/docs/helpdb/Base.jl

@@ -304,13 +304,6 @@ This would create a 25-by-30000 `BitArray`, linked to the file associated with s
 """
 Mmap.mmap(io, ::BitArray, dims = ?, offset = ?)
 
-"""
-    bessely0(x)
-
-Bessel function of the second kind of order 0, ``Y_0(x)``.
-"""
-bessely0
-
 """
     filter!(function, collection)
 
@@ -647,13 +640,6 @@ for use in `Mmap.mmap`. Used by `SharedArray` for creating shared memory arrays.
 """
 Mmap.Anonymous
 
-"""
-    erfi(x)
-
-Compute the imaginary error function of `x`, defined by ``-i \\operatorname{erf}(ix)``.
-"""
-erfi
-
 """
     floor([T,] x, [digits, [base]])
 
@@ -695,13 +681,6 @@ The item or field is not defined for the given object.
 """
 UndefRefError
 
-"""
-    bessely1(x)
-
-Bessel function of the second kind of order 1, ``Y_1(x)``.
-"""
-bessely1
-
 """
     append!(collection, collection2) -> collection.
 
@@ -798,13 +777,6 @@ julia> getfield(a, :num)
 """
 getfield
 
-"""
-    besselj1(x)
-
-Bessel function of the first kind of order 1, ``J_1(x)``.
-"""
-besselj1
-
 """
     select!(v, k, [by=<transform>,] [lt=<comparison>,] [rev=false])
 
@@ -933,35 +905,13 @@ behavior, including program corruption or segfaults, at any later time.
 """
 unsafe_convert
 
-"""
-    erfinv(x)
-
-Compute the inverse error function of a real `x`, defined by ``\\operatorname{erf}(\\operatorname{erfinv}(x)) = x``.
-"""
-erfinv
-
 """
     seek(s, pos)
 
 Seek a stream to the given position.
 """
 seek
 
-"""
-    besselj0(x)
-
-Bessel function of the first kind of order 0, ``J_0(x)``.
-"""
-besselj0
-
-"""
-    erfcinv(x)
-
-Compute the inverse error complementary function of a real `x`, defined by
-``\\operatorname{erfc}(\\operatorname{erfcinv}(x)) = x``.
-"""
-erfcinv
-
 """
     popdisplay()
     popdisplay(d::Display)
@@ -1605,14 +1555,6 @@ Equivalent to [`readdlm`](@ref) with `delim` set to comma, and type optionally d
 """
 readcsv
 
-"""
-    erfcx(x)
-
-Compute the scaled complementary error function of `x`, defined by ``e^{x^2} \\operatorname{erfc}(x)``.
-Note also that ``\\operatorname{erfcx}(-ix)`` computes the Faddeeva function ``w(x)``.
-"""
-erfcx
-
 """
     UndefVarError(var::Symbol)
 
@@ -2482,11 +2424,3 @@ seekend
 Integer division was attempted with a denominator value of 0.
 """
 DivideError
-
-"""
-    dawson(x)
-
-Compute the Dawson function (scaled imaginary error function) of `x`, defined by
-``\\frac{\\sqrt{\\pi}}{2} e^{-x^2} \\operatorname{erfi}(x)``.
-"""
-dawson

base/exports.jl

@@ -313,19 +313,11 @@ export
     csc,
     cscd,
     csch,
-    dawson,
     deg2rad,
     denominator,
-    digamma,
     div,
     divrem,
     eps,
-    erf,
-    erfc,
-    erfcinv,
-    erfcx,
-    erfi,
-    erfinv,
     exp,
     exp10,
     exp2,
@@ -349,7 +341,6 @@ export
     hypot,
     imag,
     inv,
-    invdigamma,
     invmod,
     isapprox,
     iseven,
@@ -420,7 +411,6 @@ export
     tanh,
     trailing_ones,
     trailing_zeros,
-    trigamma,
     trunc,
     unsafe_trunc,
     typemax,
@@ -434,37 +424,8 @@ export
     ≉,
 
 # specfun
-    airyai,
-    airyaiprime,
-    airybi,
-    airybiprime,
-    airyaix,
-    airyaiprimex,
-    airybix,
-    airybiprimex,
-    besselh,
-    besselhx,
-    besseli,
-    besselix,
-    besselj,
-    besselj0,
-    besselj1,
-    besseljx,
-    besselk,
-    besselkx,
-    bessely,
-    bessely0,
-    bessely1,
-    besselyx,
     beta,
-    eta,
-    hankelh1,
-    hankelh1x,
-    hankelh2,
-    hankelh2x,
     lbeta,
-    polygamma,
-    zeta,
 
 # arrays
     broadcast!,