Fix roundoff bugs in prevpow/nextpow
#45067
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Welcome @milkmoore. Great to have you contribute to Julia! |
| wp = a^n | ||
| wp > p || throw(OverflowError("result is beyond the range of type of the base")) | ||
| wp >= x && return wp | ||
| wwp = a^(n+1) |
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what about wp*a powers are relatively expensive.
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I considered that but it's only valid for integers. For floats there's no guarantee that x*x^n == x^(n+1).
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For IEEEFloat types, bases that are powers of 2 can be done very efficiently with some bit-twiddling. I'll get around to it sooner or later but for now I was focused on correctness.
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I think you can possibly do stuff both correct and fast with a modification of the pow implimentation which uses Double-double internally. It would be a bit of a pain though.
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Given @oscardssmith's approval, should we merge this? Any remaining concerns? |
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Unless somebody had suggestions, there wasn't anything else I had plans to do. |
This PR fixes a bug where
prevpow(2.0,prevfloat(1024.0)) == 1024.0and a matching bug fornextpow. The previous implementation didn't cover all the possible cases of roundoff in the logarithm, (eg: didn't consider thatlog(2.0,prevfloat(1024.0))==10.0, whichfloors to 10 instead of the mathematically correct 9).It also adds a
DomainErrorin the case that the input is beyond the range of the returned type. Previously, for example,prevpow(Int8(4),200) == 0was a silent incorrect result. The only exception is a base of2::Integerfor anyInteger, which has its own special case. One could technically only throw an error when the result is out-of-range (eg,prevpow(Int8(4),200)could correctly return64even though200>typemax(Int8)), but that was more complicated (and the previous behavior was to return0).It also adds an
OverflowErrortonextpowwhen the result is not representable. Previously,nextpow(Int8(4),65) == 0.The added errors could be considered breaking. It's hard to imagine anybody was intentionally using this behavior, but they could be split off if controversial.