Better precision for cispi(::Complex) (JuliaLang#45945)

* Better precision for cispi(::Complex) * Fix bug, add test * Update doctest
pcjentsch · Aug 18, 2022 · 728c3a1 · 728c3a1
1 parent 15e0152
commit 728c3a1
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diff --git a/base/complex.jl b/base/complex.jl
@@ -591,7 +591,7 @@ julia> cispi(10000)
 1.0 + 0.0im
 
 julia> cispi(0.25 + 1im)
-0.030556854645952924 + 0.030556854645952924im
+0.030556854645954562 + 0.030556854645954562im
 ```
 
 !!! compat "Julia 1.6"
@@ -601,8 +601,9 @@ function cispi end
 cispi(theta::Real) = Complex(reverse(sincospi(theta))...)
 
 function cispi(z::Complex)
-    sipi, copi = sincospi(z)
-    return complex(real(copi) - imag(sipi), imag(copi) + real(sipi))
+    v = exp(-(pi*imag(z)))
+    s, c = sincospi(real(z))
+    Complex(v * c, v * s)
 end
 
 """

diff --git a/test/complex.jl b/test/complex.jl
@@ -935,6 +935,7 @@ end
     @test cispi(0.0+0.0im) == cispi(0)
     @test cispi(1.0+0.0im) == cispi(1)
     @test cispi(2.0+0.0im) == cispi(2)
+    @test cispi(5im) ≈ exp(-5pi) rtol=1e-10 # https://github.com/JuliaLang/julia/pull/45945
 end
 
 @testset "exp2" begin