fix spurious overflow for Float16(::Rational)#52395
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nsajko
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Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
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Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
nsajko
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Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
nsajko
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Jan 14, 2024
Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
nsajko
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Jan 14, 2024
Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
nsajko
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Jan 15, 2024
Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
nsajko
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Jan 15, 2024
Constructing a floating-point number from a `Rational` should now be correctly rounded. Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
nsajko
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Jan 15, 2024
Constructing a floating-point number from a `Rational` should now be correctly rounded. Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
fingolfin
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Feb 7, 2024
vtjnash
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Feb 7, 2024
| 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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Wouldn't these suffer from double-rounding accuracy loss? @oscardssmith
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they would. Doing this properly is fairly hard though.
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Also worth noting that Float16(num)/Float16(den) also potentially has triple rounding.
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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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we should merge and improve later.
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That was my thought as well, but want to confirm.
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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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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.)
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Was there a point to merging this? This PR was just a quick fix compared to the thorough fix of #49749. |
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Primarily that it was a quick fix, compared to the thorough fix of #49749 :). To be slightly more serious, I think we should merge the more thorough fix, but this was an improvement that was ready to merge first. |
nsajko
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Constructing a floating-point number from a `Rational` should now be correctly rounded. Implementation approach: 1. Convert the (numerator, denominator) pair to a (sign bit, integral significand, exponent) triplet using integer arithmetic. The integer type in question must be wide enough. 2. Convert the above triplet into an instance of the chosen FP type. There is special support for IEEE 754 floating-point and for `BigFloat`, otherwise a fallback using `ldexp` is used. As a bonus, constructing a `BigFloat` from a `Rational` should now be thread-safe when the rounding mode and precision are provided to the constructor, because there is no access to the global precision or rounding mode settings. Updates JuliaLang#45213 Updates JuliaLang#50940 Updates JuliaLang#52507 Fixes JuliaLang#52394 Closes JuliaLang#52395 Fixes JuliaLang#52859
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Fixes #52394.
Update: also fixes
Float32forUInt128, since currentlyFloat32((typemax(UInt128)-0x01) // typemax(UInt128))givesNan32.