Use better initial guesses for Roots #71
Merged
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When a
BigUint
is small enough to fit in au64
, we use that to compute roots instead.Otherwise, we can get a closer approximation of roots via
f64
. For values that are even too big for that, we can shift them down in multiples ofn
enough that they do fit, and then shift the result back and refine the answer further.Benchmarked with an i7-7700K on Fedora 29,
rustc 1.32.0-nightly (21f268495 2018-12-02)
.Everything is a big win except
nth_1000
, but even the loss there is fast enough that I'm not worried. I doubtnth_root(1000)
would realistically be used anyway -- I just wanted challenging cases.