added a rule and tests for sincospi

Author: RainerHeintzmann

src/rulesets/Base/fastmath_able.jl

@@ -48,6 +48,8 @@ let
         # Trig-Multivariate
         @scalar_rule atan(y, x) @setup(u = x ^ 2 + y ^ 2) (x / u, -y / u)
         @scalar_rule sincos(x) @setup((sinx, cosx) = Ω) cosx -sinx
+        # the position of the minus sign below warrants the correct type for π  
+        @scalar_rule sincospi(x) @setup((sinpix, cospix) = Ω) (π * cospix, π * (-sinpix))
 
         # exponents
         @scalar_rule cbrt(x) inv(3 * Ω ^ 2)

test/rulesets/Base/fastmath_able.jl

@@ -64,6 +64,12 @@ const FASTABLE_AST = quote
                 test_frule(sincos, randn(T))
                 test_rrule(sincos, randn(T); output_tangent=Δz)
             end
+            @testset "sincospi(x::$T)" for T in (Float64, ComplexF64)
+                Δz = Tangent{Tuple{T,T}}(randn(T), randn(T))
+
+                test_frule(sincospi, randn(T))
+                test_rrule(sincospi, randn(T); output_tangent=Δz)
+            end
         end
     end