Optimise squared, Mul, and Exp

[yperbasis]

name                     old time/op  new time/op  delta
Mul/single/uint256-8     8.23ns ± 2%  6.90ns ± 1%  -16.11%  (p=0.000 n=10+9)
Mul/single/big-8         64.5ns ± 1%  62.8ns ± 1%   -2.65%  (p=0.000 n=9+9)
_Exp/large/big-8         23.7µs ± 1%  23.7µs ± 1%     ~     (p=0.896 n=10+10)
_Exp/large/uint256-8     3.34µs ± 1%  2.72µs ± 3%  -18.63%  (p=0.000 n=8+10)
_Exp/small/big-8         7.12µs ± 2%  7.09µs ± 0%     ~     (p=0.345 n=10+9)
_Exp/small/uint256-8      283ns ± 1%   229ns ± 1%  -19.22%  (p=0.000 n=9+10)
Square/single/uint256-8  6.27ns ± 1%  5.14ns ± 1%  -17.91%  (p=0.000 n=10+10)
Square/single/big-8      60.0ns ± 2%  60.0ns ± 1%     ~     (p=0.781 n=10+10)

[holiman]

Thanks, nice work!

[chfast]

I'm starting to hate Go inliner...

[chfast]

My benchmarks:

name                     old time/op  new time/op  delta
Mul/single/uint256-8     7.95ns ± 0%  6.56ns ± 0%  -17.46%  (p=0.000 n=16+18)
Mul/single/big-8         59.4ns ± 1%  59.2ns ± 0%     ~     (p=0.274 n=19+17)
Square/single/uint256-8  5.76ns ± 0%  4.94ns ± 0%  -14.20%  (p=0.000 n=18+19)
Square/single/big-8      57.5ns ± 0%  57.5ns ± 0%     ~     (p=0.077 n=18+18)
_Exp/large/big-8         21.3µs ± 1%  21.3µs ± 0%     ~     (p=0.925 n=20+18)
_Exp/large/uint256-8     3.00µs ± 0%  2.54µs ± 0%  -15.61%  (p=0.000 n=18+16)
_Exp/small/big-8         6.33µs ± 1%  6.34µs ± 1%     ~     (p=0.361 n=19+20)
_Exp/small/uint256-8      254ns ± 1%   217ns ± 0%  -14.42%  (p=0.000 n=20+15)

[chfast]

The change you reverted in umul() is also worth having.

name                     old time/op  new time/op  delta
MulMod/small/uint256-8   33.6ns ± 0%  32.3ns ± 0%  -3.97%  (p=0.000 n=19+17)
MulMod/mod64/uint256-8   97.5ns ± 1%  96.1ns ± 0%  -1.48%  (p=0.000 n=20+18)
MulMod/mod128/uint256-8   176ns ± 0%   171ns ± 0%  -2.84%  (p=0.000 n=17+17)
MulMod/mod192/uint256-8   173ns ± 0%   168ns ± 0%  -3.15%  (p=0.000 n=20+20)
MulMod/mod256/uint256-8   169ns ± 0%   162ns ± 0%  -4.14%  (p=0.000 n=17+18)

[chfast]

Can you rebase the branch? It contains some already merged commits and a merge commit.

[holiman]

@yperbasis try a git checkout fast_mul && git fetch origin && git rebase -i origin/master , which remove empty merge-commits.
(edited, should be git fetch origin)
And then followed by git push -f if all went well.

[holiman]

(and add back the improvement to umul)

[AlexeyAkhunov]

Test comment

[yperbasis]

@yperbasis try a git checkout fast_mul && git fetch origin && git rebase -i origin/master , which remove empty merge-commits.
(edited, should be git fetch origin)
And then followed by git push -f if all went well.

Done, but some history appears to still linger for some reason.

[yperbasis]

(and add back the improvement to umul)

Done

[holiman]

Ok, don't worry about it - we can always squash-merge.

However, If you do want it explicitly it to be commit-merged, then it needs to be rebased, empty commits removed and/or squashed to relevant commits.

[chfast]

LGTM, but I'd like to clean up git history. I will do it on a side and let you know.

[yperbasis]

Ok, don't worry about it - we can always squash-merge.

However, If you do want it explicitly it to be commit-merged, then it needs to be rebased, empty commits removed and/or squashed to relevant commits.

I'm fine if you squash-merge it.

[chfast]

Done. Thanks a lot.