Support computing values for all rational powers #213
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I thought we would need to wait for a `constexpr` version of `std::powl`, but I was wrong. Instead, we can get away with a `root` function. Note that there's no guarantee that `std::powl` would be better in all cases, even if we _could_ just use it. After all, its second argument is `1.0l / n`, which is a lossy representation of the Nth root. On the implementation side, we take advantage of the fact that this function is only ever meant to be called at compile time, which lets us prioritize accuracy over "speed" (because the runtime speed is always essentially infinite). We do a binary search between 1 and `x` after checking that `x > 1` (and `n > 1`). When we end up with two neighboring floating point values, we pick whichever gives the closest result when we run it through `checked_int_pow`. This algorithm is guaranteed to produce the best representable result for a "pure root". For other rational powers, it's technically possible that we could have some lossiness in the `checked_int_pow` computation, if we enter a floating point realm that is high enough such that not all integer values can be represented. That said, I tried a bunch of test cases to compare it to `powl`, and it's passed all the ones that I was able to come up with. Fixes #116.
chiphogg
added
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release notes: 🐛 lib (bugfix)
gcc is not standards compliant (!!) https://stackoverflow.com/a/5483978/15777264
geoffviola
reviewed
Dec 18, 2023
geoffviola
approved these changes
Dec 19, 2023
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I thought we would need to wait for a
constexprversion ofstd::powl, but I was wrong. Instead, we can get away with arootfunction. Note that there's no guarantee that
std::powlwould bebetter in all cases, even if we could just use it. After all, its
second argument is
1.0l / n, which is a lossy representation of theNth root.
On the implementation side, we take advantage of the fact that this
function is only ever meant to be called at compile time, which lets us
prioritize accuracy over "speed" (because the runtime speed is always
essentially infinite). We do a binary search between 1 and
xafterchecking that
x > 1(andn > 1). When we end up with twoneighboring floating point values, we pick whichever gives the closest
result when we run it through
checked_int_pow.This algorithm is guaranteed to produce the best representable result
for a "pure root". For other rational powers, it's technically possible
that we could have some lossiness in the
checked_int_powcomputation,if we enter a floating point realm that is high enough such that not all
integer values can be represented. That said, I tried a bunch of test
cases to compare it to
powl, and it's passed all the ones that I wasable to come up with.
Fixes #116.