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Make expm1(::Complex64) type stable. #21896

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merged 1 commit into from
May 16, 2017
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Make expm1(::Complex64) type stable. #21896

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11 changes: 8 additions & 3 deletions base/complex.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -515,7 +515,8 @@ function exp(z::Complex)
end
end

function expm1(z::Complex)
function expm1(z::Complex{T}) where T<:Real
Tf = float(T)
zr,zi = reim(z)
if isnan(zr)
Complex(zr, zi==0 ? zi : zr)
Expand All @@ -533,8 +534,12 @@ function expm1(z::Complex)
Complex(erm1, zi)
else
er = erm1+one(erm1)
wr = isfinite(er) ? erm1 - 2.0*er*(sin(0.5*zi))^2 : er*cos(zi)
Complex(wr, er*sin(zi))
if isfinite(er)
wr = erm1 - 2 * er * (sin(convert(Tf, 0.5) * zi))^2
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@giordano giordano May 17, 2017 •
edited
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I know I'm a bit too late, but why not using zi / 2 instead of converting 0.5? The performance difference is sensible for BigFloat for this operation (not the whole function, though).

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I'm just trying to not change the result for machine types and being conservative about this transformation. I assume this transformation is exact for Float16, Float32 and Float64 (though floating point corner cases frequently surprises me...)? If that's the case then I think we can change this to / 2.

return Complex(wr, er * sin(zi))
else
return Complex(er * cos(zi), er * sin(zi))
end
end
end
end
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7 changes: 7 additions & 0 deletions test/complex.jl
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Expand Up @@ -951,3 +951,10 @@ end
@test log1p(complex(x, x)) ≈ log(1 + complex(x, x))
end
end

@testset "expm1 type stability" begin
x = @inferred expm1(0.1im)
@test x isa Complex128
x = @inferred expm1(0.1f0im)
@test x isa Complex64
end