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Avoid silent overflow in /(x::Rational, y::Complex{Int}) #53453

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Avoid silent overflow in /(x::Rational, y::Complex{Int}) #53453

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22643eb
complex division by rational inf
nhz2 Feb 23, 2024
b332488
add overflow test
nhz2 Feb 23, 2024
fe0fd94
fix whitespace
nhz2 Feb 23, 2024
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Merge branch 'master' into nz/complex-rational-div-1
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More specific fix
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Merge branch 'master' into nz/complex-rational-div-1
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Merge branch 'master' into nz/complex-rational-div-1
nhz2 Mar 3, 2024
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simplify changes
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Merge branch 'master' into nz/complex-rational-div-1
nhz2 Sep 14, 2024
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remove added whitespace
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Merge branch 'master' into nz/complex-rational-div-1
nhz2 Oct 19, 2024
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Update base/rational.jl
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Merge branch 'master' into nz/complex-rational-div-1
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2 changes: 1 addition & 1 deletion base/complex.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -351,7 +351,7 @@ muladd(z::Complex, w::Complex, x::Real) =
Complex(muladd(real(z), real(w), -muladd(imag(z), imag(w), -x)),
muladd(real(z), imag(w), imag(z) * real(w)))

/(a::R, z::S) where {R<:Real,S<:Complex} = (T = promote_type(R,S); a*inv(T(z)))
/(a::R, z::S) where {R<:Real, S<:Complex} = (T = promote_type(R,S); a*inv(T(z)))
/(z::Complex, x::Real) = Complex(real(z)/x, imag(z)/x)

function /(a::Complex{T}, b::Complex{T}) where T<:Real
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18 changes: 15 additions & 3 deletions base/rational.jl
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Expand Up @@ -401,9 +401,21 @@ function *(y::Integer, x::Rational)
yn, xd = divgcd(promote(y, x.den)...)
unsafe_rational(checked_mul(yn, x.num), xd)
end
/(x::Rational, y::Union{Rational, Integer, Complex{<:Union{Integer,Rational}}}) = x//y
/(x::Union{Integer, Complex{<:Union{Integer,Rational}}}, y::Rational) = x//y
inv(x::Rational{T}) where {T} = checked_den(x.den, x.num)
/(x::Rational, y::Union{Rational, Integer}) = x//y
/(x::Integer, y::Rational) = x//y
# Avoid overflow for Rational math if result is zero.
# This method is needed because previously this method didn't check for overflows
# but would return the correct answer if `a` was zero even if 1//z was wrong.
function /(a::Rational, z::Complex{<:Integer})
z_r = complex(Rational(real(z)), Rational(imag(z)))
if iszero(a) && !iszero(z)
a/oneunit(z_r)
else
a/z_r
end
end

inv(x::Rational) = checked_den(x.den, x.num)
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fma(x::Rational, y::Rational, z::Rational) = x*y+z

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16 changes: 16 additions & 0 deletions test/rational.jl
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Expand Up @@ -203,6 +203,22 @@ end
end

@test Rational(rand_int, 3)/Complex(3, 2) == Complex(Rational(rand_int, 13), -Rational(rand_int*2, 39))
@test iszero(zero(Rational{Int8}) / complex(Int8(100), Int8(100)))
@test (true//true) / complex(false, true) === 0//1 - 1//1*im
@test (false//true) / complex(false, true) === 0//1 + 0//1*im
@test (false//true) / complex(true, false) === 0//1 + 0//1*im
@test (false//true) / complex(true, true) === 0//1 + 0//1*im
@test (true//true) / complex(true, true) === 1//2 - 1//2*im
@test (false//true) / complex(true//true, true//true) === 0//1 + 0//1*im
@test (true//true) / complex(true//true, true//true) === 1//2 - 1//2*im
@test (false//true) / complex(true//false, false//true) === 0//1 + 0//1*im
@test (true//true) / complex(true//true, true//false) === 0//1 + 0//1*im
@test_throws DivideError (0//1) / complex(0, 0)
@test_throws DivideError (1//1) / complex(0, 0)
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@nsajko nsajko Oct 19, 2024 •
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This is wrong. The correct result is positive infinity, just like here:

julia> (1 // 1) / 0
1//0

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With complex numbers, there are many possible infinities, I'm not sure what infinity is correct.

julia> 1.0/(0.0im)
NaN + NaN*im

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Ref: #22983
https://discourse.julialang.org/t/why-inv-complex-0-0-0-0-returns-complex-nan-nan/92694/1

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You're right, sorry.

@test_throws DivideError (1//0) / complex(0, 0)

# 1//200 - 1//200*im cannot be represented as Complex{Rational{Int8}}
@test_throws OverflowError (Int8(1)//Int8(1)) / (Int8(100) + Int8(100)im)

@test Complex(rand_int, 0) == Rational(rand_int)
@test Rational(rand_int) == Complex(rand_int, 0)
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