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improve support for custom Number types (#50)
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@aplavin
aplavin authored Jul 16, 2024
1 parent 1d4cbb7 commit 5f6b4da
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5 changes: 3 additions & 2 deletions Project.toml
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@@ -1,6 +1,6 @@
name = "InverseFunctions"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.14"
version = "0.1.15"

[deps]
Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
Expand All @@ -18,6 +18,7 @@ julia = "1"
[extras]
Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[targets]
test = ["Dates", "Documenter"]
test = ["Dates", "Documenter", "Unitful"]
53 changes: 25 additions & 28 deletions src/functions.jl
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Expand Up @@ -5,57 +5,46 @@
Inverse of `sqrt(x)` for non-negative `x`.
"""
square(x) = x^2
function square(x::Real)
x < zero(x) && throw(DomainError(x, "`square` is defined as the inverse of `sqrt` and can only be evaluated for non-negative values"))
function square(x)
if is_real_type(typeof(x)) && x < zero(x)
throw(DomainError(x, "`square` is defined as the inverse of `sqrt` and can only be evaluated for non-negative values"))
end
return x^2
end


function invpow2(x::Real, p::Integer)
if x ≥ zero(x) || isodd(p)
copysign(abs(x)^inv(p), x)
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 $x"))
else
throw(DomainError(x, "inverse for x^$p is not defined at $x"))
end
end
function invpow2(x::Real, p::Real)
if x ≥ zero(x)
x^inv(p)
else
throw(DomainError(x, "inverse for x^$p is not defined at $x"))
end
end
function invpow2(x, p::Real)
# complex x^p is only invertible for p = 1/n
if isinteger(inv(p))
x^inv(p)
else
throw(DomainError(x, "inverse for x^$p is not defined at $x"))
# complex x^p is invertible only for p = 1/n
isinteger(inv(p)) ? x^inv(p) : throw(DomainError(x, "inverse for x^$p is not defined at $x"))
end
end

function invpow1(b::Real, x::Real)
function invpow_arg1(b::Real, x::Real)
if b ≥ zero(b) && x ≥ zero(x)
log(b, x)
else
throw(DomainError(x, "inverse for $b^x is not defined at $x"))
end
end

function invlog1(b::Real, x::Real)
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
end
invlog1(b, x) = b^x
invlog_arg1(b::Number, x::Number) = b^x

invlog2(b, x) = x^inv(b)
invlog_arg2(b::Number, x::Number) = x^inv(b)


function invdivrem((q, r), divisor)
function invdivrem((q, r)::NTuple{2,Number}, divisor::Number)
res = muladd(q, divisor, r)
if abs(r) ≤ abs(divisor) && (iszero(r) || sign(r) == sign(res))
res
Expand All @@ -64,10 +53,18 @@ function invdivrem((q, r), divisor)
end
end

function invfldmod((q, r), divisor)
function invfldmod((q, r)::NTuple{2,Number}, divisor::Number)
if abs(r) ≤ abs(divisor) && (iszero(r) || sign(r) == sign(divisor))
muladd(q, divisor, r)
else
throw(DomainError((q, r), "inverse for fldmod(x) is not defined at this point"))
end
end


# check if T is a real-Number type
# this is not the same as T <: Real which immediately excludes custom Number subtypes such as unitful numbers
# also, isreal(x) != is_real_type(typeof(x)): the former is true for complex numbers with zero imaginary part
@inline is_real_type(@nospecialize _::Type{<:Real}) = true
@inline is_real_type(::Type{T}) where {T<:Number} = real(T) == T
@inline is_real_type(@nospecialize _::Type) = false
16 changes: 8 additions & 8 deletions src/inverse.jl
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Expand Up @@ -159,14 +159,14 @@ 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^$(f.x)")) : Base.Fix2(invpow2, f.x)
inverse(f::Base.Fix2{typeof(invpow2)}) = Base.Fix2(^, f.x)
inverse(f::Base.Fix1{typeof(^)}) = Base.Fix1(invpow1, f.x)
inverse(f::Base.Fix1{typeof(invpow1)}) = Base.Fix1(^, f.x)
inverse(f::Base.Fix1{typeof(log)}) = Base.Fix1(invlog1, f.x)
inverse(f::Base.Fix1{typeof(invlog1)}) = Base.Fix1(log, f.x)
inverse(f::Base.Fix2{typeof(log)}) = Base.Fix2(invlog2, f.x)
inverse(f::Base.Fix2{typeof(invlog2)}) = Base.Fix2(log, f.x)
inverse(f::Base.Fix2{typeof(^)}) = iszero(f.x) ? throw(DomainError(f.x, "Cannot invert x^$(f.x)")) : Base.Fix2(invpow_arg2, f.x)
inverse(f::Base.Fix2{typeof(invpow_arg2)}) = Base.Fix2(^, f.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(invlog_arg1)}) = Base.Fix1(log, f.x)
inverse(f::Base.Fix2{typeof(log)}) = 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)
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20 changes: 20 additions & 0 deletions test/test_inverse.jl
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Expand Up @@ -2,6 +2,7 @@

using Test
using InverseFunctions
using Unitful
using Dates


Expand Down Expand Up @@ -79,14 +80,19 @@ end
end

# ensure that inverses have domains compatible with original functions
@test_throws DomainError inverse(sqrt)(-1.0)
InverseFunctions.test_inverse(sqrt, complex(-1.0))
InverseFunctions.test_inverse(sqrt, complex(1.0))
@test_throws DomainError inverse(Base.Fix1(*, 0))
@test_throws DomainError inverse(Base.Fix2(^, 0))
@test_throws DomainError inverse(Base.Fix1(log, -2))(5)
@test_throws DomainError inverse(Base.Fix1(log, 2))(-5)
InverseFunctions.test_inverse(inverse(Base.Fix1(log, 2)), complex(-5))
@test_throws DomainError inverse(Base.Fix2(^, 0.5))(-5)
@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))
InverseFunctions.test_inverse(Base.Fix2(^, -1), complex(-5.))
@test_throws DomainError inverse(Base.Fix2(^, 2))(-5)
@test_throws DomainError inverse(Base.Fix1(^, 2))(-5)
@test_throws DomainError inverse(Base.Fix1(^, -2))(3)
Expand Down Expand Up @@ -130,6 +136,20 @@ end
end
end

@testset "unitful" begin
# the majority of inverse just propagate to underlying mathematical functions and don't have any issues with unitful numbers
# only those that behave treat real numbers differently have to be tested here
x = rand()u"m"
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)
end

@testset "dates" begin
InverseFunctions.test_inverse(Dates.date2epochdays, Date(2020, 1, 2); compare = ===)
InverseFunctions.test_inverse(Dates.datetime2epochms, DateTime(2020, 1, 2, 12, 34, 56); compare = ===)
Expand Down

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Registration pull request created: JuliaRegistries/General/111164

Tip: Release Notes

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"Release notes:" and it will be added to the registry PR, and if TagBot is installed it will also be added to the
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Release notes:

## Breaking changes

- blah

To add them here just re-invoke and the PR will be updated.

Tagging

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v0.1.15 -m "<description of version>" 5f6b4dad6a6470d730957388e63502c2d50d45df
git push origin v0.1.15

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