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fix spurious overflow for Float16(::Rational) #52395

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Merged
merged 6 commits into from
Feb 7, 2024
Merged

fix spurious overflow for Float16(::Rational) #52395

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fe92f1d
fix spurious overflow for Float16(::Rational)
stevengj Dec 5, 2023
e4d8979
typo
stevengj Dec 5, 2023
b24c5ca
Update base/rational.jl
stevengj Dec 13, 2023
6aab59b
Update test/float16.jl
stevengj Dec 13, 2023
ce4b622
Update base/rational.jl
stevengj Dec 13, 2023
c34a75d
Update test/float16.jl
stevengj Dec 13, 2023
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8 changes: 8 additions & 0 deletions base/rational.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -145,6 +145,14 @@ function (::Type{T})(x::Rational{S}) where T<:AbstractFloat where S
P = promote_type(T,S)
convert(T, convert(P,x.num)/convert(P,x.den))::T
end
# avoid spurious overflow (#52394). (Needed for UInt16 or larger;
# we also include Int16 for consistency of accuracy.)
Float16(x::Rational{<:Union{Int16,Int32,Int64,UInt16,UInt32,UInt64}}) =
Float16(Float32(x))
Float16(x::Rational{<:Union{Int128,UInt128}}) =
Float16(Float64(x)) # UInt128 overflows Float32, include Int128 for consistency
Float32(x::Rational{<:Union{Int128,UInt128}}) =
Float32(Float64(x)) # UInt128 overflows Float32, include Int128 for consistency
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@vtjnash vtjnash Feb 7, 2024

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Wouldn't these suffer from double-rounding accuracy loss? @oscardssmith

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@oscardssmith oscardssmith Feb 7, 2024

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they would. Doing this properly is fairly hard though.

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@oscardssmith oscardssmith Feb 7, 2024

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Also worth noting that Float16(num)/Float16(den) also potentially has triple rounding.

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@fingolfin fingolfin Feb 7, 2024

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Question is: is this problem worse than the problem this PR fixes? I.e. should we merge and improve this later, or should this wait until this PR does it "right" (whatever that means?)

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@oscardssmith oscardssmith Feb 7, 2024

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we should merge and improve later.

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@vtjnash vtjnash Feb 7, 2024

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That was my thought as well, but want to confirm.

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@vtjnash vtjnash Feb 7, 2024

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Would doing it "properly" be something like:

a = Float64(x)
b = Float32(a)
# check if we double-rounded in the wrong direction
if x > a && b < a && nextfloat(b) < a
    b = nextfloat(b)
elseif x < a && b > a && prevfloat(b) > a
    b = prevfloat(b)
end
return b

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@stevengj stevengj Feb 7, 2024 •
edited
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A example of a test case where double rounding gives a different result is:

julia> r = 12928845309018111//18014398509481984
12928845309018111//18014398509481984

julia> Float32(r) == Float32(Float64(r))
false

@vtjnash's code doesn't fix this, however — its output matches Float32(Float64(r)) on this example.

(Example constructed by tweaking a number almost exactly halfway between two Float32 values.)


function Rational{T}(x::AbstractFloat) where T<:Integer
r = rationalize(T, x, tol=0)
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5 changes: 5 additions & 0 deletions test/float16.jl
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Expand Up @@ -203,6 +203,11 @@ const minsubf16_32 = Float32(minsubf16)
# issues #33076
@test Float16(1f5) == Inf16

# issue #52394
@test Float16(10^8 // (10^9 + 1)) == convert(Float16, 10^8 // (10^9 + 1)) == Float16(0.1)
@test Float16((typemax(UInt128)-0x01) // typemax(UInt128)) == Float16(1.0)
@test Float32((typemax(UInt128)-0x01) // typemax(UInt128)) == Float32(1.0)

@testset "conversion to Float16 from" begin
for T in (Float32, Float64, BigFloat)
@testset "conversion from $T" begin
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