Add sincosd function (#30134)

The function `sincosd` simultaneously computes the sine and cosine
in which the input angle is in degrees.

Author: ronisbr

NEWS.md

@@ -6,6 +6,7 @@ New language features
 
 * Support for Unicode 12.1.0 ([#32002]).
 * Methods can now be added to an abstract type ([#31916]).
+* Added `sincosd(x)` to simultaneously compute the sine and cosine of `x`, where `x` is in degrees ([#30134]).
 
 Language changes
 ----------------

base/exports.jl

@@ -324,6 +324,7 @@ export
     sin,
     sinc,
     sincos,
+    sincosd,
     sind,
     sinh,
     sinpi,

base/math.jl

@@ -6,7 +6,7 @@ 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,
-       cosd, cotd, cscd, secd, sind, tand,
+       cosd, cotd, cscd, secd, sind, tand, sincosd,
        acosd, acotd, acscd, asecd, asind, atand,
        rad2deg, deg2rad,
        log, log2, log10, log1p, exponent, exp, exp2, exp10, expm1,

base/special/trig.jl

@@ -1073,6 +1073,28 @@ end
 
 tand(x::Real) = sind(x) / cosd(x)
 
+"""
+    sincosd(x)
+
+Simultaneously compute the sine and cosine of `x`, where `x` is in degrees.
+
+!!! compat "Julia 1.3"
+    This function requires at least Julia 1.3.
+"""
+function sincosd(x::Real)
+    if isinf(x)
+        return throw(DomainError(x, "sincosd(x) is only defined for finite `x`."))
+    elseif isnan(x)
+        return (oftype(x,NaN), oftype(x,NaN))
+    end
+
+    # It turns out that calling those functions separately yielded better
+    # performance than considering each case and calling `sincos_kernel`.
+    return (sind(x), cosd(x))
+end
+
+sincosd(::Missing) = (missing, missing)
+
 for (fd, f, fn) in ((:sind, :sin, "sine"), (:cosd, :cos, "cosine"), (:tand, :tan, "tangent"))
     name = string(fd)
     @eval begin

test/math.jl

@@ -369,9 +369,14 @@ end
 @testset "degree-based trig functions" begin
     @testset "$T" for T = (Float32,Float64,Rational{Int})
         fT = typeof(float(one(T)))
+        fTsc = typeof( (float(one(T)), float(one(T))) )
         for x = -400:40:400
             @test sind(convert(T,x))::fT ≈ convert(fT,sin(pi/180*x)) atol=eps(deg2rad(convert(fT,x)))
             @test cosd(convert(T,x))::fT ≈ convert(fT,cos(pi/180*x)) atol=eps(deg2rad(convert(fT,x)))
+
+            s,c = sincosd(convert(T,x))
+            @test s::fT ≈ convert(fT,sin(pi/180*x)) atol=eps(deg2rad(convert(fT,x)))
+            @test c::fT ≈ convert(fT,cos(pi/180*x)) atol=eps(deg2rad(convert(fT,x)))
         end
         @testset "sind" begin
             @test sind(convert(T,0.0))::fT === zero(fT)
@@ -387,6 +392,16 @@ end
             @test cosd(convert(T,-90))::fT === zero(fT)
             @test cosd(convert(T,-270))::fT === zero(fT)
         end
+        @testset "sincosd" begin
+            @test sincosd(convert(T,-360))::fTsc === ( -zero(fT),  one(fT) )
+            @test sincosd(convert(T,-270))::fTsc === (   one(fT), zero(fT) )
+            @test sincosd(convert(T,-180))::fTsc === ( -zero(fT), -one(fT) )
+            @test sincosd(convert(T, -90))::fTsc === (  -one(fT), zero(fT) )
+            @test sincosd(convert(T,   0))::fTsc === (  zero(fT),  one(fT) )
+            @test sincosd(convert(T,  90))::fTsc === (   one(fT), zero(fT) )
+            @test sincosd(convert(T, 180))::fTsc === (  zero(fT), -one(fT) )
+            @test sincosd(convert(T, 270))::fTsc === (  -one(fT), zero(fT) )
+        end
 
         @testset "sinpi and cospi" begin
             for x = -3:0.3:3