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Adds an expm1 function for complex values. #6539

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May 20, 2014
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Adds an expm1 function for complex values. #6539

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This adds an expm1 function for complex values. It uses the property …
simonbyrne Apr 16, 2014
2bc0df7
add more tests
simonbyrne May 20, 2014
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52 changes: 42 additions & 10 deletions base/complex.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -328,16 +328,48 @@ log2(z::Complex) = log(z)/oftype(real(z),0.6931471805599453)

function exp(z::Complex)
zr, zi = reim(z)
if isfinite(zr) && !isfinite(zi) return Complex(oftype(zr, NaN), oftype(zi, NaN)) end
if zr==Inf && zi==0 return Complex(zr, zi) end
if zr==-Inf && !isfinite(zi) return Complex(-zero(zr), copysign(zero(zi), zi)) end
if zr==Inf && !isfinite(zi) return Complex(-zr, oftype(zr, NaN)) end
if isnan(zr) return Complex(zr, zi==0 ? zi : zr) end
er = exp(zr)
zi==0 && return Complex(er, zi)
wr = er*(isfinite(zi) ? cos(zi) : zi)
wi = er*(isfinite(zi) ? sin(zi) : zi)
Complex(wr, wi)
if isnan(zr)
Complex(zr, zi==zero(zi) ? zi : zr)
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Not important but just FYI, zero() is not necessary in this context (since it's an argument and not a return value).

elseif !isfinite(zi)
if zr == inf(zr)
Complex(-zr, nan(zr))
elseif zr == -inf(zr)
Complex(-zero(zr), copysign(zero(zi), zi))
else
Complex(nan(zr), nan(zi))
end
else
er = exp(zr)
if zi == zero(zi)
Complex(er, zi)
else
Complex(er*cos(zi), er*sin(zi))
end
end
end

function expm1(z::Complex)
zr,zi = reim(z)
if isnan(zr)
Complex(zr, zi==zero(zi) ? zi : zr)
elseif !isfinite(zi)
if zr == inf(zr)
Complex(-zr, nan(zr))
elseif zr == -inf(zr)
Complex(-one(zr), copysign(zero(zi), zi))
else
Complex(nan(zr), nan(zi))
end
else
erm1 = expm1(zr)
if zi == zero(zi)
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))
end
end
end

function ^{T<:FloatingPoint}(z::Complex{T}, p::Complex{T})
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3 changes: 2 additions & 1 deletion base/math.jl
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Expand Up @@ -20,7 +20,8 @@ export sin, cos, tan, sinh, cosh, tanh, asin, acos, atan,

import Base: log, exp, sin, cos, tan, sinh, cosh, tanh, asin,
acos, atan, asinh, acosh, atanh, sqrt, log2, log10,
max, min, minmax, ceil, floor, trunc, round, ^, exp2, exp10
max, min, minmax, ceil, floor, trunc, round, ^, exp2,
exp10, expm1

import Core.Intrinsics: nan_dom_err, sqrt_llvm, box, unbox, powi_llvm

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49 changes: 49 additions & 0 deletions test/complex.jl
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Expand Up @@ -103,6 +103,55 @@
@test isequal(exp(complex( NaN, 5.0)), complex( NaN, NaN))
@test isequal(exp(complex( NaN, NaN)), complex( NaN, NaN))

# expm1:
# expm1(conj(z)) = conj(expm1(z))

@test isequal(expm1(complex( 0.0, 0.0)), complex(0.0, 0.0))
@test isequal(expm1(complex( 0.0,-0.0)), complex(0.0,-0.0))
@test isequal(expm1(complex( 0.0, Inf)), complex(NaN, NaN))
@test isequal(expm1(complex( 0.0,-Inf)), complex(NaN, NaN))
@test isequal(expm1(complex( 0.0, NaN)), complex(NaN, NaN))

@test isequal(expm1(complex(-0.0, 0.0)), complex(-0.0, 0.0))
@test isequal(expm1(complex(-0.0,-0.0)), complex(-0.0,-0.0))

@test isequal(expm1(complex( 5.0, Inf)), complex(NaN, NaN))

@test isequal(expm1(complex( Inf, 0.0)), complex(Inf, 0.0))
@test isequal(expm1(complex( Inf,-0.0)), complex(Inf,-0.0))
@test isequal(expm1(complex( Inf, 5.0)), complex(cos(5.0)*Inf,sin(5.0)* Inf))
@test isequal(expm1(complex( Inf,-5.0)), complex(cos(5.0)*Inf,sin(5.0)*-Inf))
@test isequal(expm1(complex( Inf, NaN)), complex(-Inf, NaN))
@test isequal(expm1(complex( Inf, Inf)), complex(-Inf, NaN))
@test isequal(expm1(complex( Inf,-Inf)), complex(-Inf, NaN))

@test isequal(expm1(complex(-Inf, 0.0)), complex(-1.0, 0.0))
@test isequal(expm1(complex(-Inf,-0.0)), complex(-1.0,-0.0))
@test isequal(expm1(complex(-Inf, 5.0)), complex(-1.0,sin(5.0)* 0.0))
@test isequal(expm1(complex(-Inf,-5.0)), complex(-1.0,sin(5.0)*-0.0))
@test isequal(expm1(complex(-Inf, Inf)), complex(-1.0, 0.0))
@test isequal(expm1(complex(-Inf,-Inf)), complex(-1.0,-0.0))
@test isequal(expm1(complex(-Inf, NaN)), complex(-1.0, 0.0))

@test isequal(expm1(complex( NaN, 0.0)), complex( NaN, 0.0))
@test isequal(expm1(complex( NaN,-0.0)), complex( NaN,-0.0))
@test isequal(expm1(complex( NaN, 5.0)), complex( NaN, NaN))
@test isequal(expm1(complex( NaN, NaN)), complex( NaN, NaN))

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These tests are great but they don't seem to test any "normal" argument values.

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Thanks, I've added some more tests.

@test isequal(expm1(complex( 1e-20, 0.0)), complex(expm1( 1e-20), 0.0))
@test isequal(expm1(complex(-1e-20, 0.0)), complex(expm1(-1e-20), 0.0))

@test_approx_eq expm1(complex( 1e-20, 1e-10)) complex( 5e-21, 1e-10)
@test_approx_eq expm1(complex( 1e-20,-1e-10)) complex( 5e-21,-1e-10)
@test_approx_eq expm1(complex(-1e-20, 1e-10)) complex(-1.5e-20, 1e-10)
@test_approx_eq expm1(complex(-1e-20,-1e-10)) complex(-1.5e-20,-1e-10)

@test_approx_eq expm1(complex( 10.0, 10.0)) exp(complex( 10.0, 10.0))-1
@test_approx_eq expm1(complex( 10.0,-10.0)) exp(complex( 10.0,-10.0))-1
@test_approx_eq expm1(complex(-10.0, 10.0)) exp(complex(-10.0, 10.0))-1
@test_approx_eq expm1(complex(-10.0,-10.0)) exp(complex(-10.0,-10.0))-1


# ^ (cpow)
# equivalent to exp(y*log(x))
# except for 0^0?
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