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fix inverse(^) domain #34

Merged
merged 11 commits into from
Sep 16, 2024
Merged

fix inverse(^) domain #34

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ff3852c
fix inverse(^) domain
aplavin Jul 13, 2023
ba8e13d
more inverse domain fixes
aplavin Nov 25, 2023
a23b811
Update src/functions.jl
aplavin Aug 20, 2024
3d4be83
Update src/functions.jl
aplavin Aug 20, 2024
7db1ae3
Update src/inverse.jl
aplavin Aug 20, 2024
415d4c3
Update src/inverse.jl
aplavin Aug 20, 2024
157f7f0
fix
aplavin Aug 21, 2024
3f093b8
add tests
aplavin Sep 13, 2024
504cc39
Merge branch 'master' into patch-2
aplavin Sep 13, 2024
d99f067
test
aplavin Sep 14, 2024
50f3fca
bump
aplavin Sep 16, 2024
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20 changes: 13 additions & 7 deletions src/functions.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -13,18 +13,20 @@
end



function invpow_arg2(x::Number, p::Real)
if is_real_type(typeof(x))
x ≥ zero(x) ? x^inv(p) : # x > 0 - trivially invertible
isinteger(p) && isodd(Integer(p)) ? copysign(abs(x)^inv(p), x) : # p odd - invertible even for x < 0
throw(DomainError(x, "inverse for x^$p is not defined at $x"))
else
# complex x^p is invertible only for p = 1/n
# complex x^p is only invertible for p = 1/n
isinteger(inv(p)) ? x^inv(p) : throw(DomainError(x, "inverse for x^$p is not defined at $x"))
end
end

function invpow_arg1(b::Real, x::Real)
# b < 0 should never happen in actual use: this check is done in inverse(f)
if b ≥ zero(b) && x ≥ zero(x)
log(b, x)
else
Expand All @@ -33,15 +35,19 @@
end

function invlog_arg1(b::Real, x::Real)
if b ≥ zero(b)
b^x
else
throw(DomainError(x, "inverse for log($b, x) is not defined at $x"))
end
# exception may happen here: check cannot be done in inverse(f) because of log(Real, Complex)
b > zero(b) && !isone(b) || throw(DomainError(x, "inverse for log($b, x) is not defined at $x"))
b^x
end
invlog_arg1(b::Number, x::Number) = b^x

invlog_arg2(b::Number, x::Number) = x^inv(b)

function invlog_arg2(b::Real, x::Real)
# exception may happen here: check cannot be done in inverse(f) because of log(Complex, Real)
x > zero(x) && !isone(x) || throw(DomainError(x, "inverse for log($b, x) is not defined at $x"))
x^inv(b)
end
invlog_arg2(b, x) = x^inv(b)

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function invdivrem((q, r)::NTuple{2,Number}, divisor::Number)
Expand Down
11 changes: 9 additions & 2 deletions src/inverse.jl
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Expand Up @@ -159,17 +159,24 @@ inverse(::typeof(sqrt)) = square
inverse(::typeof(square)) = sqrt

inverse(::typeof(cbrt)) = Base.Fix2(^, 3)

inverse(f::Base.Fix2{typeof(^)}) = iszero(f.x) ? throw(DomainError(f.x, "Cannot invert x^$(f.x)")) : Base.Fix2(invpow_arg2, f.x)
inverse(f::Base.Fix2{typeof(^), <:Integer}) = isodd(f.x) ? Base.Fix2(invpow_arg2, f.x) : throw(DomainError(f.x, "Cannot invert x^$(f.x)"))
inverse(f::Base.Fix2{typeof(invpow_arg2)}) = Base.Fix2(^, f.x)

inverse(f::Base.Fix1{typeof(^), <:Real}) = f.x > zero(f.x) ? Base.Fix1(invpow_arg1, f.x) : throw(DomainError(f.x, "Cannot invert $(f.x)^x"))
inverse(f::Base.Fix1{typeof(^)}) = Base.Fix1(invpow_arg1, f.x)
inverse(f::Base.Fix1{typeof(invpow_arg1)}) = Base.Fix1(^, f.x)
inverse(f::Base.Fix1{typeof(log)}) = Base.Fix1(invlog_arg1, f.x)
inverse(f::Base.Fix1{typeof(log)}) = isone(f.x) ? throw(DomainError(f.x, "Cannot invert log($(f.x), x)")) : Base.Fix1(invlog_arg1, f.x)
inverse(f::Base.Fix1{typeof(invlog_arg1)}) = Base.Fix1(log, f.x)
inverse(f::Base.Fix2{typeof(log)}) = Base.Fix2(invlog_arg2, f.x)

inverse(f::Base.Fix2{typeof(log)}) = isone(f.x) ? throw(DomainError(f.x, "Cannot invert log(x, $(f.x))")) : Base.Fix2(invlog_arg2, f.x)
inverse(f::Base.Fix2{typeof(invlog_arg2)}) = Base.Fix2(log, f.x)


inverse(f::Base.Fix2{typeof(divrem)}) = Base.Fix2(invdivrem, f.x)
inverse(f::Base.Fix2{typeof(invdivrem)}) = Base.Fix2(divrem, f.x)

inverse(f::Base.Fix2{typeof(fldmod)}) = Base.Fix2(invfldmod, f.x)
inverse(f::Base.Fix2{typeof(invfldmod)}) = Base.Fix2(fldmod, f.x)

Expand Down
16 changes: 13 additions & 3 deletions test/test_inverse.jl
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Expand Up @@ -49,7 +49,7 @@ end
x = rand()
for f in (
foo, inv_foo, log, log2, log10, log1p, sqrt,
Base.Fix2(^, rand()), Base.Fix2(^, rand([-10:-1; 1:10])), Base.Fix1(^, rand()), Base.Fix1(log, rand()), Base.Fix1(log, 1/rand()), Base.Fix2(log, rand()),
Base.Fix2(^, 3*rand() - 0.5), Base.Fix2(^, rand(float.([-10:-1; 1:10]))), Base.Fix1(^, rand()), Base.Fix1(log, rand()), Base.Fix1(log, 1/rand()), Base.Fix2(log, rand()),
)
InverseFunctions.test_inverse(f, x)
end
Expand Down Expand Up @@ -92,6 +92,17 @@ end
@test_throws DomainError inverse(Base.Fix2(^, 0.51))(complex(-5))
@test_throws DomainError inverse(Base.Fix2(^, 2))(complex(-5))
InverseFunctions.test_inverse(Base.Fix2(^, 0.5), complex(-5))
@test_throws DomainError inverse(Base.Fix2(^, 2))
@test_throws DomainError inverse(Base.Fix2(^, -4))
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Are the errors for Base.Fix1(^ and log tested somewhere?

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@aplavin I think there's not test for that yet, correct?

InverseFunctions.test_inverse(Base.Fix2(^, 2.0), 4)
@test_throws DomainError inverse(Base.Fix1(^, 2.0))(-4)
@test_throws DomainError inverse(Base.Fix1(^, -2.0))(4)
@test_throws DomainError inverse(Base.Fix1(^, 0))(4)
@test_throws DomainError inverse(Base.Fix1(log, -2))(4)
@test_throws DomainError inverse(Base.Fix1(log, 1))(4)
@test_throws DomainError inverse(Base.Fix2(^, 0))(4)
@test_throws DomainError inverse(Base.Fix2(log, -2))(4)
@test_throws DomainError inverse(Base.Fix2(log, 1))(4)
InverseFunctions.test_inverse(Base.Fix2(^, -1), complex(-5.))
@test_throws DomainError inverse(Base.Fix2(^, 2))(-5)
@test_throws DomainError inverse(Base.Fix1(^, 2))(-5)
Expand Down Expand Up @@ -143,11 +154,10 @@ end
InverseFunctions.test_inverse(sqrt, x)
@test_throws DomainError inverse(sqrt)(-x)

InverseFunctions.test_inverse(Base.Fix2(^, 2), x)
@test_throws DomainError inverse(Base.Fix2(^, 2))(-x)
InverseFunctions.test_inverse(Base.Fix2(^, 3), x)
InverseFunctions.test_inverse(Base.Fix2(^, 3), -x)
InverseFunctions.test_inverse(Base.Fix2(^, -3.5), x)
@test_throws DomainError inverse(Base.Fix2(^, 2))(-x)
end

@testset "dates" begin
Expand Down
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