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Rebase of #35792, add cispi function #38449

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merged 5 commits into from
Nov 29, 2020
Merged

Rebase of #35792, add cispi function #38449

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4f166b0
Implement cispi
eschnett May 11, 2020
3a6d7a0
Review comments in #35792
simeonschaub Jun 23, 2020
53ca775
Remove docs relating cispi and signbit
jmert Nov 15, 2020
da83b9c
Review comment, more expressive function doc.
jmert Nov 15, 2020
7973276
Switch examples to show complex outputs
jmert Nov 15, 2020
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24 changes: 24 additions & 0 deletions base/complex.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -541,6 +541,30 @@ function cis(z::Complex)
Complex(v * c, v * s)
end

cispi(theta::Real) = Complex(reverse(sincospi(theta))...)

"""
cispi(z)

Compute ``\\exp(i\\pi x)`` more accurately than `cis(pi*x)`, especially for large `x`.

# Examples
```jldoctest
julia> cispi(1)
-1.0 + 0.0im

julia> cispi(0.25 + 1im)
0.030556854645952924 + 0.030556854645952924im
```

!!! compat "Julia 1.6"
This function requires Julia 1.6 or later.
"""
function cispi(z::Complex)
sipi, copi = sincospi(z)
return complex(real(copi) - imag(sipi), imag(copi) + real(sipi))
end

"""
angle(z)

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1 change: 1 addition & 0 deletions base/exports.jl
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Expand Up @@ -229,6 +229,7 @@ export
cbrt,
ceil,
cis,
cispi,
clamp,
cld,
cmp,
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1 change: 1 addition & 0 deletions doc/src/base/math.md
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Expand Up @@ -162,6 +162,7 @@ Base.reim
Base.conj
Base.angle
Base.cis
Base.cispi
Base.binomial
Base.factorial
Base.gcd
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17 changes: 17 additions & 0 deletions test/complex.jl
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Expand Up @@ -123,6 +123,8 @@ end
@test atanh(x) ≈ atanh(big(x))
@test cis(real(x)) ≈ cis(real(big(x)))
@test cis(x) ≈ cis(big(x))
@test cispi(real(x)) ≈ cispi(real(big(x)))
@test cispi(x) ≈ cispi(big(x))
@test cos(x) ≈ cos(big(x))
@test cosh(x) ≈ cosh(big(x))
@test exp(x) ≈ exp(big(x))
Expand Down Expand Up @@ -918,6 +920,21 @@ end
@test cis(1.0+0.0im) ≈ 0.54030230586813971740093660744297660373231042061+0.84147098480789650665250232163029899962256306079im
@test cis(pi) ≈ -1.0+0.0im
@test cis(pi/2) ≈ 0.0+1.0im
@test cispi(false) == 1
@test cispi(true) == -1
@test cispi(-1) == -1
@test cispi(0) == 1
@test cispi(1) == -1
@test cispi(2) == 1
@test cispi(0.0) == cispi(0)
@test cispi(1.0) == cispi(1)
@test cispi(2.0) == cispi(2)
@test cispi(0.5) == im
@test cispi(1.5) == -im
@test cispi(0.25) ≈ cis(π/4)
@test cispi(0.0+0.0im) == cispi(0)
@test cispi(1.0+0.0im) == cispi(1)
@test cispi(2.0+0.0im) == cispi(2)
end

@testset "exp2" begin
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