rational powers (fixes #18114) #18118
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| @@ -2137,7 +2137,8 @@ rationalize(nextfloat(0.0)) == 0//1 | |||
| # rational-exponent promotion rules (issue #3155): | |||
| @test 2.0f0^(1//3) == 2.0f0^(1.0f0/3) | |||
| @test 2^(1//3) == 2^(1/3) | |||
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| # no loss of precision for rational powers (issue #18114) | |||
| @test_approx_eq_eps BigFloat(2)^(BigFloat(1)/BigFloat(3)) BigFloat(2)^(1//3) 1e-20 | |||
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Cleaner to do @test BigFloat(2)^(BigFloat(1)/BigFloat(3)) ≈ BigFloat(2)^(1//3) ... this will test to sqrt(eps) precision by default, about 4e-39 for the default eps(BigFloat).
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I think even == should work in this case.
| ^{T<:AbstractFloat}(x::T, y::Rational) = x^(convert(T, y.num / y.den)) | ||
| ^{T<:AbstractFloat}(x::Complex{T}, y::Rational) = x^(convert(T, y.num / y.den)) | ||
| ^{T<:AbstractFloat}(x::T, y::Rational) = x^(convert(T,y.num)/convert(T,y.den)) | ||
| ^{T<:AbstractFloat}(x::Complex{T}, y::Rational) = x^(convert(T,y.num)/convert(T,y.den)) |
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You could probably simplify these to x^convert(T,y)
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My thinking here was that there is a higher chance to have a conversion from Int then from Rational. But if you think it's ok to have x^convert(T,y) I can change it.
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convert(T,y) is safe, because there is a generic conversion from Rational to AbstractFloat.
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It will dispatch to this method:
Lines 71 to 74 in b506041
which actually will be better, as it will handle, e.g.
^(x::Float64, y::Rational{BigInt}) by promoting to BigFloat.
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Maybe I don't see the whole picture, but why is there even a specialization for AbstractFloat at all? Can't this case be treated by ^(x::Number, y::Number) = ^(promote(x,y)...)?
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No, because then it will call ^(x::Number, y::Rational) instead. (Remember, Julia always calls the most specific method.)
Simplified the definition of `^`
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Thanks! |
Fixes precision problem for rational powers of BigFloats (JuliaLang#18114)
Fixes #18114