Merge pull request #18 from JuliaMath/more-base

More things from Base

Author: ararslan

src/gamma.jl

@@ -1,8 +1,9 @@
 # This file contains code that was formerly a part of Julia. License is MIT: http://julialang.org/license
 
-using Base.Math: signflip, f16, f32, f64
 using Base.MPFR: ROUNDING_MODE, big_ln2
 
+typealias ComplexOrReal{T} Union{T,Complex{T}}
+
 # Bernoulli numbers B_{2k}, using tabulated numerators and denominators from
 # the online encyclopedia of integer sequences.  (They actually have data
 # up to k=249, but we stop here at k=20.)  Used for generating the polygamma
@@ -16,7 +17,7 @@ using Base.MPFR: ROUNDING_MODE, big_ln2
 
 Compute the digamma function of `x` (the logarithmic derivative of `gamma(x)`).
 """
-function digamma(z::Union{Float64,Complex{Float64}})
+function digamma(z::ComplexOrReal{Float64})
     # Based on eq. (12), without looking at the accompanying source
     # code, of: K. S. Kölbig, "Programs for computing the logarithm of
     # the gamma function, and the digamma function, for complex
@@ -56,7 +57,7 @@ end
 
 Compute the trigamma function of `x` (the logarithmic second derivative of `gamma(x)`).
 """
-function trigamma(z::Union{Float64,Complex{Float64}})
+function trigamma(z::ComplexOrReal{Float64})
     # via the derivative of the Kölbig digamma formulation
     x = real(z)
     if x <= 0 # reflection formula
@@ -79,6 +80,9 @@ function trigamma(z::Union{Float64,Complex{Float64}})
     ψ += t*w * @evalpoly(w,0.16666666666666666,-0.03333333333333333,0.023809523809523808,-0.03333333333333333,0.07575757575757576,-0.2531135531135531,1.1666666666666667,-7.092156862745098)
 end
 
+signflip(m::Number, z) = (-1+0im)^m * z
+signflip(m::Integer, z) = iseven(m) ? z : -z
+
 # (-1)^m d^m/dz^m cot(z) = p_m(cot z), where p_m is a polynomial
 # that satisfies the recurrence p_{m+1}(x) = p_m′(x) * (1 + x^2).
 # Note that p_m(x) has only even powers of x if m is odd, and
@@ -213,8 +217,7 @@ this definition is equivalent to the Hurwitz zeta function
 ``\\sum_{k=0}^\\infty (k+z)^{-s}``.   For ``z=1``, it yields
 the Riemann zeta function ``\\zeta(s)``.
 """
-function zeta(s::Union{Int,Float64,Complex{Float64}},
-              z::Union{Float64,Complex{Float64}})
+function zeta(s::ComplexOrReal{Float64}, z::ComplexOrReal{Float64})
     ζ = zero(promote_type(typeof(s), typeof(z)))
 
     (z == 1 || z == 0) && return oftype(ζ, zeta(s))
@@ -263,7 +266,8 @@ function zeta(s::Union{Int,Float64,Complex{Float64}},
             minus_z = -z
             ζ += pow_oftype(ζ, minus_z, minus_s) # ν = 0 term
             if xf != z
-                ζ += pow_oftype(ζ, z - nx, minus_s) # real(z - nx) > 0, so use correct branch cut
+                ζ += pow_oftype(ζ, z - nx, minus_s)
+                # real(z - nx) > 0, so use correct branch cut
                 # otherwise, if xf==z, then the definition skips this term
             end
             # do loop in different order, depending on the sign of s,
@@ -316,10 +320,10 @@ end
 """
     polygamma(m, x)
 
-Compute the polygamma function of order `m` of argument `x` (the `(m+1)th` derivative of the
+Compute the polygamma function of order `m` of argument `x` (the `(m+1)`th derivative of the
 logarithm of `gamma(x)`)
 """
-function polygamma(m::Integer, z::Union{Float64,Complex{Float64}})
+function polygamma(m::Integer, z::ComplexOrReal{Float64})
     m == 0 && return digamma(z)
     m == 1 && return trigamma(z)
 
@@ -337,40 +341,25 @@ function polygamma(m::Integer, z::Union{Float64,Complex{Float64}})
     # constants. We throw a DomainError() since the definition is unclear.
     real(m) < 0 && throw(DomainError())
 
-    s = m+1
+    s = Float64(m+1)
+    # It is safe to convert any integer (including `BigInt`) to a float here
+    # as underflow occurs before precision issues.
     if real(z) <= 0 # reflection formula
         (zeta(s, 1-z) + signflip(m, cotderiv(m,z))) * (-gamma(s))
     else
         signflip(m, zeta(s,z) * (-gamma(s)))
     end
 end
 
-# If we really cared about single precision, we could make a faster
-# Float32 version by truncating the Stirling series at a smaller cutoff.
-for (f,T) in ((:f32,Float32),(:f16,Float16))
-    @eval begin
-        zeta(s::Integer, z::Union{$T,Complex{$T}}) = $f(zeta(Int(s), f64(z)))
-        zeta(s::Union{Float64,Complex128}, z::Union{$T,Complex{$T}}) = zeta(s, f64(z))
-        zeta(s::Number, z::Union{$T,Complex{$T}}) = $f(zeta(f64(s), f64(z)))
-        polygamma(m::Integer, z::Union{$T,Complex{$T}}) = $f(polygamma(Int(m), f64(z)))
-        digamma(z::Union{$T,Complex{$T}}) = $f(digamma(f64(z)))
-        trigamma(z::Union{$T,Complex{$T}}) = $f(trigamma(f64(z)))
-    end
-end
-
-zeta(s::Integer, z::Number) = zeta(Int(s), f64(z))
-zeta(s::Number, z::Number) = zeta(f64(s), f64(z))
-for f in (:digamma, :trigamma)
-    @eval begin
-        $f(z::Number) = $f(f64(z))
-    end
-end
-polygamma(m::Integer, z::Number) = polygamma(m, f64(z))
+"""
+    invdigamma(x)
 
-# Inverse digamma function:
-# Implementation of fixed point algorithm described in
-#  "Estimating a Dirichlet distribution" by Thomas P. Minka, 2000
+Compute the inverse [`digamma`](@ref) function of `x`.
+"""
 function invdigamma(y::Float64)
+    # Implementation of fixed point algorithm described in
+    # "Estimating a Dirichlet distribution" by Thomas P. Minka, 2000
+
     # Closed form initial estimates
     if y >= -2.22
         x_old = exp(y) + 0.5
@@ -392,18 +381,16 @@ function invdigamma(y::Float64)
 
     return x_new
 end
-invdigamma(x::Float32) = Float32(invdigamma(Float64(x)))
 
 """
-    invdigamma(x)
+    zeta(s)
 
-Compute the inverse [`digamma`](@ref) function of `x`.
+Riemann zeta function ``\\zeta(s)``.
 """
-invdigamma(x::Real) = invdigamma(Float64(x))
+function zeta(s::ComplexOrReal{Float64})
+    # Riemann zeta function; algorithm is based on specializing the Hurwitz
+    # zeta function above for z==1.
 
-# Riemann zeta function; algorithm is based on specializing the Hurwitz
-# zeta function above for z==1.
-function zeta(s::Union{Float64,Complex{Float64}})
     # blows up to ±Inf, but get correct sign of imaginary zero
     s == 1 && return NaN + zero(s) * imag(s)
 
@@ -448,23 +435,18 @@ function zeta(s::Union{Float64,Complex{Float64}})
     return ζ
 end
 
-zeta(x::Integer) = zeta(Float64(x))
-zeta(x::Real)    = oftype(float(x),zeta(Float64(x)))
-
-"""
-    zeta(s)
-
-Riemann zeta function ``\\zeta(s)``.
-"""
-zeta(z::Complex) = oftype(float(z),zeta(Complex128(z)))
-
 function zeta(x::BigFloat)
     z = BigFloat()
     ccall((:mpfr_zeta, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Int32), &z, &x, ROUNDING_MODE[])
     return z
 end
 
-function eta(z::Union{Float64,Complex{Float64}})
+"""
+    eta(x)
+
+Dirichlet eta function ``\\eta(s) = \\sum^\\infty_{n=1}(-1)^{n-1}/n^{s}``.
+"""
+function eta(z::ComplexOrReal{Float64})
     δz = 1 - z
     if abs(real(δz)) + abs(imag(δz)) < 7e-3 # Taylor expand around z==1
         return 0.6931471805599453094172321214581765 *
@@ -478,17 +460,82 @@ function eta(z::Union{Float64,Complex{Float64}})
         return -zeta(z) * expm1(0.6931471805599453094172321214581765*δz)
     end
 end
-eta(x::Integer) = eta(Float64(x))
-eta(x::Real)    = oftype(float(x),eta(Float64(x)))
-
-"""
-    eta(x)
-
-Dirichlet eta function ``\\eta(s) = \\sum^\\infty_{n=1}(-1)^{n-1}/n^{s}``.
-"""
-eta(z::Complex) = oftype(float(z),eta(Complex128(z)))
 
 function eta(x::BigFloat)
     x == 1 && return big_ln2()
     return -zeta(x) * expm1(big_ln2()*(1-x))
 end
+
+# Converting types that we can convert, and not ones we can not
+# Float16, and Float32 and their Complex equivalents can be converted to Float64
+# and results converted back.
+# Otherwise, we need to make things use their own `float` converting methods
+# and in those cases, we do not convert back either as we assume
+# they also implement their own versions of the functions, with the correct return types.
+# This is the case for BitIntegers (which become `Float64` when `float`ed).
+# Otherwise, if they do not implement their version of the functions we
+# manually throw a `MethodError`.
+# This case occurs, when calling `float` on a type does not change its type,
+# as it is already a `float`, and would have hit own method, if one had existed.
+
+
+# If we really cared about single precision, we could make a faster
+# Float32 version by truncating the Stirling series at a smaller cutoff.
+# and if we really cared about half precision, we could make a faster
+# Float16 version, by using a precomputed table look-up.
+
+
+for T in (Float16, Float32, Float64)
+    @eval f64(x::Complex{$T}) = Complex128(x)
+    @eval f64(x::$T) = Float64(x)
+end
+
+
+for f in (:digamma, :trigamma, :zeta, :eta, :invdigamma)
+    @eval begin
+        function $f(z::Union{ComplexOrReal{Float16}, ComplexOrReal{Float32}})
+            oftype(z, $f(f64(z)))
+        end
+
+        function $f(z::Number)
+            x = float(z)
+            typeof(x) === typeof(z) && throw(MethodError($f, (z,)))
+            # There is nothing to fallback to, as this didn't change the argument types
+            $f(x)
+        end
+    end
+end
+
+
+for T1 in (Float16, Float32, Float64), T2 in (Float16, Float32, Float64)
+    (T1 == T2 == Float64) && continue # Avoid redefining base definition
+
+    @eval function zeta(s::ComplexOrReal{$T1}, z::ComplexOrReal{$T2})
+        ζ = zeta(f64(s), f64(z))
+        convert(promote_type(typeof(s), typeof(z)),  ζ)
+    end
+end
+
+
+function zeta(s::Number, z::Number)
+    t = float(s)
+    x = float(z)
+    if typeof(t) === typeof(s) && typeof(x) === typeof(z)
+        # There is nothing to fallback to, since this didn't work
+        throw(MethodError(zeta,(s,z)))
+    end
+    zeta(t, x)
+end
+
+
+function polygamma(m::Integer, z::Union{ComplexOrReal{Float16}, ComplexOrReal{Float32}})
+    oftype(z, polygamma(m, f64(z)))
+end
+
+
+function polygamma(m::Integer, z::Number)
+    x = float(z)
+    typeof(x) === typeof(z) && throw(MethodError(polygamma, (m,z)))
+    # There is nothing to fallback to, since this didn't work
+    polygamma(m, x)
+end

test/runtests.jl

@@ -454,3 +454,35 @@ end
         @test typeof(SF.erfc(a)) == BigFloat
     end
 end
+
+@testset "Base Julia issue #17474" begin
+    @test SF.f64(complex(1f0,1f0)) === complex(1.0, 1.0)
+    @test SF.f64(1f0) === 1.0
+
+    @test typeof(SF.eta(big"2")) == BigFloat
+    @test typeof(SF.zeta(big"2")) == BigFloat
+    @test typeof(SF.digamma(big"2")) == BigFloat
+
+    @test_throws MethodError SF.trigamma(big"2")
+    @test_throws MethodError SF.trigamma(big"2.0")
+    @test_throws MethodError SF.invdigamma(big"2")
+    @test_throws MethodError SF.invdigamma(big"2.0")
+
+    @test_throws MethodError SF.eta(Complex(big"2"))
+    @test_throws MethodError SF.eta(Complex(big"2.0"))
+    @test_throws MethodError SF.zeta(Complex(big"2"))
+    @test_throws MethodError SF.zeta(Complex(big"2.0"))
+    @test_throws MethodError SF.zeta(1.0,big"2")
+    @test_throws MethodError SF.zeta(1.0,big"2.0")
+    @test_throws MethodError SF.zeta(big"1.0",2.0)
+    @test_throws MethodError SF.zeta(big"1",2.0)
+
+
+    @test typeof(SF.polygamma(3, 0x2)) == Float64
+    @test typeof(SF.polygamma(big"3", 2f0)) == Float32
+    @test typeof(SF.zeta(1, 2.0)) == Float64
+    @test typeof(SF.zeta(1, 2f0)) == Float64 # BitIntegers result in Float64 returns
+    @test typeof(SF.zeta(2f0, complex(2f0,0f0))) == Complex{Float32}
+    @test typeof(SF.zeta(complex(1,1), 2f0)) == Complex{Float64}
+    @test typeof(SF.zeta(complex(1), 2.0)) == Complex{Float64}
+end