This commit implements num-integer::Roots trait
for BigInt and BigUint types, and also adds sqrt,
cbrt, nth_root as inherent methods to allow access
to them without importing Roots trait. For each
type tests were added as submodules in the roots
test module.
Signed-off-by: Manca Bizjak <manca.bizjak@xlab.si>
We don't actually support `no_std` yet, and probably won't until `alloc`
is stable. We're just reserving this ability with the "std" feature
now, and compilation will fail without.
It was pointed out in the blog post [Big Integers in Zig] that we don't
have a special case in `num-bigint` for single-digit divisors. While
you can already get this optimization by dividing directly by `u32`,
it's easy to make small `BigUint` divisors work like this too.
$ cargo benchcmp baseline single-div
name baseline ns/iter single-div ns/iter diff ns/iter diff % speedup
factorial_div_biguint 5,638,353 1,005,488 -4,632,865 -82.17% x 5.61
`BigInt` will also gain from this, since it uses `BigUint` division
internally.
Running [zig-bn's facdiv-rs] shows a nice improvement too. My i7-7700K
with Rust 1.26 goes from 4.15 seconds to just 0.65 -- a 6.38x speedup!
[Big Integers in Zig]: https://tiehuis.github.io/big-integers-in-zig#division-test-single-limb
[zig-bn's facdiv-rs]: https://github.com/tiehuis/zig-bn/tree/master/bench/facdiv/crate-facdiv-rs
Serde 0.7 dropped it's dependency on num, so this patch moves
the implementations here. For the sake of a better implementation,
this just serializes BigUint as a `Vec<u32>`, `BigInt` as a
`(u8, Vec<u32>)`, `Complex<T>` as a `(T, T)`, and `Ratio<T>`
as a `(T, T)`.
