Merge pull request #21589 from JuliaLang/yyc/cis

Use `sincos` from libm in `cis`

base/complex.jl

@@ -424,7 +424,10 @@ sqrt(z::Complex) = sqrt(float(z))
 # end
 
 # compute exp(im*theta)
-cis(theta::Real) = Complex(cos(theta),sin(theta))
+function cis(theta::Real)
+    s, c = sincos(theta)
+    Complex(c, s)
+end
 
 """
     cis(z)
@@ -433,7 +436,8 @@ Return ``\\exp(iz)``.
 """
 function cis(z::Complex)
     v = exp(-imag(z))
-    Complex(v*cos(real(z)), v*sin(real(z)))
+    s, c = sincos(real(z))
+    Complex(v * c, v * s)
 end
 
 """
@@ -510,7 +514,8 @@ function exp(z::Complex)
         if iszero(zi)
             Complex(er, zi)
         else
-            Complex(er*cos(zi), er*sin(zi))
+            s, c = sincos(zi)
+            Complex(er * c, er * s)
         end
     end
 end
@@ -538,7 +543,8 @@ function expm1(z::Complex{T}) where T<:Real
                 wr = erm1 - 2 * er * (sin(convert(Tf, 0.5) * zi))^2
                 return Complex(wr, er * sin(zi))
             else
-                return Complex(er * cos(zi), er * sin(zi))
+                s, c = sincos(zi)
+                return Complex(er * c, er * s)
             end
         end
     end
@@ -600,13 +606,15 @@ end
 function exp2(z::Complex{T}) where T
     er = exp2(real(z))
     theta = imag(z) * log(convert(T, 2))
-    Complex(er*cos(theta), er*sin(theta))
+    s, c = sincos(theta)
+    Complex(er * c, er * s)
 end
 
 function exp10(z::Complex{T}) where T
     er = exp10(real(z))
     theta = imag(z) * log(convert(T, 10))
-    Complex(er*cos(theta), er*sin(theta))
+    s, c = sincos(theta)
+    Complex(er * c, er * s)
 end
 
 function ^(z::T, p::T) where T<:Complex
@@ -628,8 +636,7 @@ function ^(z::T, p::T) where T<:Complex
         rp = rp*exp(-pim*theta)
         ntheta = ntheta + pim*log(r)
     end
-    cosntheta = cos(ntheta)
-    sinntheta = sin(ntheta)
+    sinntheta, cosntheta = sincos(ntheta)
     re, im = rp*cosntheta, rp*sinntheta
     if isinf(rp)
         if isnan(re)
@@ -689,7 +696,8 @@ function sin(z::Complex{T}) where T
             Complex(F(NaN), F(NaN))
         end
     else
-        Complex(sin(zr)*cosh(zi), cos(zr)*sinh(zi))
+        s, c = sincos(zr)
+        Complex(s * cosh(zi), c * sinh(zi))
     end
 end
 
@@ -708,7 +716,8 @@ function cos(z::Complex{T}) where T
             Complex(F(NaN), F(NaN))
         end
     else
-        Complex(cos(zr)*cosh(zi), -sin(zr)*sinh(zi))
+        s, c = sincos(zr)
+        Complex(c * cosh(zi), -s * sinh(zi))
     end
 end
 

base/exports.jl

@@ -405,6 +405,7 @@ export
     significand,
     sin,
     sinc,
+    sincos,
     sind,
     sinh,
     sinpi,

base/fastmath.jl

@@ -76,6 +76,7 @@ const fast_op =
          :min => :min_fast,
          :minmax => :minmax_fast,
          :sin => :sin_fast,
+         :sincos => :sincos_fast,
          :sinh => :sinh_fast,
          :sqrt => :sqrt_fast,
          :tan => :tan_fast,
@@ -273,6 +274,45 @@ atan2_fast(x::Float64, y::Float64) =
 
 # explicit implementations
 
+# FIXME: Change to `ccall((:sincos, libm))` when `Ref` calling convention can be
+#        stack allocated.
+@inline function sincos_fast(v::Float64)
+    return Base.llvmcall("""
+    %f = bitcast i8 *%1 to void (double, double *, double *)*
+    %ps = alloca double
+    %pc = alloca double
+    call void %f(double %0, double *%ps, double *%pc)
+    %s = load double, double* %ps
+    %c = load double, double* %pc
+    %res0 = insertvalue [2 x double] undef, double %s, 0
+    %res = insertvalue [2 x double] %res0, double %c, 1
+    ret [2 x double] %res
+    """, Tuple{Float64,Float64}, Tuple{Float64,Ptr{Void}}, v, cglobal((:sincos, libm)))
+end
+
+@inline function sincos_fast(v::Float32)
+    return Base.llvmcall("""
+    %f = bitcast i8 *%1 to void (float, float *, float *)*
+    %ps = alloca float
+    %pc = alloca float
+    call void %f(float %0, float *%ps, float *%pc)
+    %s = load float, float* %ps
+    %c = load float, float* %pc
+    %res0 = insertvalue [2 x float] undef, float %s, 0
+    %res = insertvalue [2 x float] %res0, float %c, 1
+    ret [2 x float] %res
+    """, Tuple{Float32,Float32}, Tuple{Float32,Ptr{Void}}, v, cglobal((:sincosf, libm)))
+end
+
+@inline function sincos_fast(v::Float16)
+    s, c = sincos_fast(Float32(v))
+    return Float16(s), Float16(c)
+end
+
+sincos_fast(v::AbstractFloat) = (sin_fast(v), cos_fast(v))
+sincos_fast(v::Real) = sincos_fast(float(v)::AbstractFloat)
+sincos_fast(v) = (sin_fast(v), cos_fast(v))
+
 @fastmath begin
     exp10_fast(x::T) where {T<:FloatTypes} = exp2(log2(T(10))*x)
     exp10_fast(x::Integer) = exp10(float(x))
@@ -287,7 +327,10 @@ atan2_fast(x::Float64, y::Float64) =
 
     # complex numbers
 
-    cis_fast(x::T) where {T<:FloatTypes} = Complex{T}(cos(x), sin(x))
+    function cis_fast(x::T) where {T<:FloatTypes}
+        s, c = sincos_fast(x)
+        Complex{T}(c, s)
+    end
 
     # See <http://en.cppreference.com/w/cpp/numeric/complex>
     pow_fast(x::T, y::T) where {T<:ComplexTypes} = exp(y*log(x))

base/math.jl

@@ -2,7 +2,7 @@
 
 module Math
 
-export sin, cos, tan, sinh, cosh, tanh, asin, acos, atan,
+export sin, cos, sincos, tan, sinh, cosh, tanh, asin, acos, atan,
        asinh, acosh, atanh, sec, csc, cot, asec, acsc, acot,
        sech, csch, coth, asech, acsch, acoth,
        sinpi, cospi, sinc, cosc,
@@ -419,6 +419,19 @@ for f in (:sin, :cos, :tan, :asin, :acos, :acosh, :atanh, :log, :log2, :log10,
     end
 end
 
+"""
+    sincos(x)
+
+Compute sine and cosine of `x`, where `x` is in radians.
+"""
+@inline function sincos(x)
+    res = Base.FastMath.sincos_fast(x)
+    if (isnan(res[1]) | isnan(res[2])) & !isnan(x)
+        throw(DomainError())
+    end
+    return res
+end
+
 sqrt(x::Float64) = sqrt_llvm(x)
 sqrt(x::Float32) = sqrt_llvm(x)
 

base/mpfr.jl

@@ -13,7 +13,7 @@ import
         nextfloat, prevfloat, promote_rule, rem, rem2pi, round, show, float,
         sum, sqrt, string, print, trunc, precision, exp10, expm1,
         gamma, lgamma, log1p,
-        eps, signbit, sin, cos, tan, sec, csc, cot, acos, asin, atan,
+        eps, signbit, sin, cos, sincos, tan, sec, csc, cot, acos, asin, atan,
         cosh, sinh, tanh, sech, csch, coth, acosh, asinh, atanh, atan2,
         cbrt, typemax, typemin, unsafe_trunc, realmin, realmax, rounding,
         setrounding, maxintfloat, widen, significand, frexp, tryparse, iszero, big
@@ -24,6 +24,8 @@ import Base.GMP: ClongMax, CulongMax, CdoubleMax, Limb
 
 import Base.Math.lgamma_r
 
+import Base.FastMath.sincos_fast
+
 function __init__()
     try
         # set exponent to full range by default
@@ -515,6 +517,15 @@ for f in (:exp, :exp2, :exp10, :expm1, :cosh, :sinh, :tanh, :sech, :csch, :coth,
     end
 end
 
+function sincos_fast(v::BigFloat)
+    s = BigFloat()
+    c = BigFloat()
+    ccall((:mpfr_sin_cos, :libmpfr), Int32, (Ptr{BigFloat}, Ptr{BigFloat}, Ptr{BigFloat}, Int32),
+          &s, &c, &v, ROUNDING_MODE[])
+    return (s, c)
+end
+sincos(v::BigFloat) = sincos_fast(v)
+
 # return log(2)
 function big_ln2()
     c = BigFloat()

base/sysimg.jl

@@ -277,6 +277,10 @@ importall .Order
 include("sort.jl")
 importall .Sort
 
+# Fast math
+include("fastmath.jl")
+importall .FastMath
+
 function deepcopy_internal end
 
 # BigInts and BigFloats
@@ -362,10 +366,6 @@ importall .DFT
 include("dsp.jl")
 importall .DSP
 
-# Fast math
-include("fastmath.jl")
-importall .FastMath
-
 # libgit2 support
 include("libgit2/libgit2.jl")
 

doc/src/stdlib/math.md

@@ -58,6 +58,7 @@ Base.:(!)
 Base.isapprox
 Base.sin
 Base.cos
+Base.sincos
 Base.tan
 Base.Math.sind
 Base.Math.cosd

test/fastmath.jl

@@ -9,6 +9,7 @@
 @test macroexpand(:(@fastmath min(1))) == :(Base.FastMath.min_fast(1))
 @test macroexpand(:(@fastmath min)) == :(Base.FastMath.min_fast)
 @test macroexpand(:(@fastmath x.min)) == :(x.min)
+@test macroexpand(:(@fastmath sincos(x))) == :(Base.FastMath.sincos_fast(x))
 
 # basic arithmetic
 

test/math.jl

@@ -627,3 +627,12 @@ end
 @testset "promote Float16 irrational #15359" begin
     @test typeof(Float16(.5) * pi) == Float16
 end
+
+@testset "sincos" begin
+    @test sincos(1.0) === (sin(1.0), cos(1.0))
+    @test sincos(1f0) === (sin(1f0), cos(1f0))
+    @test sincos(Float16(1)) === (sin(Float16(1)), cos(Float16(1)))
+    @test sincos(1) === (sin(1), cos(1))
+    @test sincos(big(1)) == (sin(big(1)), cos(big(1)))
+    @test sincos(big(1.0)) == (sin(big(1.0)), cos(big(1.0)))
+end