perf: fast divide shorter by longer bigint

[ChALkeR]

Summary

See #1850

This assumes that rhs is canonical

---

There is another low-hanging fruit after this, which is result size calculation
+1 is really useless there and results in a lot of unoptimal operations

Test Plan

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[tmikov]

Can you please make this request against the static_h branch? The main branch is legacy Hermes and is frozen.

[ChALkeR]

@tmikov Rebased

This PR only partially optimizes things, most of the improvement is elsewhere

[ChALkeR]

Updated
This is now ~3x-10x faster for most division operations (and even faster for small / large division)

Will investigate more

[ChALkeR]

Ops/sec in thousands, 3408 means 3_408_000 divisions on an M3 (Release build)
N is 32-byte, s is 16-byte.

Before:

0 / 100 x 3710 ops/sec @ 269μs/op (0ns..1000μs)
0 % 100 x 3897 ops/sec @ 256μs/op (0ns..1999μs)
0 / N x 2874 ops/sec @ 347μs/op (0ns..1000μs)
0 % N x 2906 ops/sec @ 344μs/op (0ns..1000μs)

21 / 100 x 3408 ops/sec @ 293μs/op (0ns..1000μs)
21 % 100 x 3621 ops/sec @ 276μs/op (0ns..1000μs)
100 / 21 x 3437 ops/sec @ 290μs/op (0ns..1000μs)
100 % 21 x 3047 ops/sec @ 328μs/op (0ns..1000μs)

s / (s + 1) x 3559 ops/sec @ 280μs/op (0ns..1000μs)
s % (s + 1) x 3607 ops/sec @ 277μs/op (0ns..1000μs)
(s + 1) / s x 3272 ops/sec @ 305μs/op (0ns..4ms)
(s + 1) % s x 3217 ops/sec @ 310μs/op (0ns..1000μs)

s / N x 2920 ops/sec @ 342μs/op (0ns..1000μs)
s % N x 2959 ops/sec @ 337μs/op (0ns..1000μs)
N / s x 1031 ops/sec @ 969μs/op (0ns..2ms)
N % s x 1036 ops/sec @ 965μs/op (0ns..2ms)

1 / 64 x 3440 ops/sec @ 290μs/op (0ns..1000μs)
1 / N x 2969 ops/sec @ 336μs/op (0ns..1000μs)
64 / 1 x 3308 ops/sec @ 302μs/op (0ns..1000μs)
N / 1 x 659 ops/sec @ 1516μs/op (999μs..2ms)

2 / 64 x 3700 ops/sec @ 270μs/op (0ns..1000μs)
2 / N x 2936 ops/sec @ 340μs/op (0ns..1000μs)
64 / 2 x 3132 ops/sec @ 319μs/op (0ns..1000μs)
N / 2 x 684 ops/sec @ 1462μs/op (999μs..2ms)

Both fast path and size fix (this PR):

0 / 100 x 45351 ops/sec @ 22μs/op (0ns..1000μs)
0 % 100 x 51578 ops/sec @ 19μs/op (0ns..1000μs)
0 / N x 46462 ops/sec @ 21μs/op (0ns..1000μs)
0 % N x 50065 ops/sec @ 19μs/op (0ns..1000μs)

21 / 100 x 12044 ops/sec @ 83μs/op (0ns..1000μs)
21 % 100 x 12481 ops/sec @ 80μs/op (0ns..1000μs)
100 / 21 x 11375 ops/sec @ 87μs/op (0ns..1000μs)
100 % 21 x 12414 ops/sec @ 80μs/op (0ns..1000μs)

s / (s + 1) x 20412 ops/sec @ 48μs/op (0ns..1000μs)
s % (s + 1) x 20212 ops/sec @ 49μs/op (0ns..1000μs)
(s + 1) / s x 21130 ops/sec @ 47μs/op (0ns..1000μs)
(s + 1) % s x 20716 ops/sec @ 48μs/op (0ns..1000μs)

s / N x 46955 ops/sec @ 21μs/op (0ns..1000μs)
s % N x 36831 ops/sec @ 27μs/op (0ns..1000μs)
N / s x 1595 ops/sec @ 626μs/op (0ns..1000μs)
N % s x 1584 ops/sec @ 631μs/op (0ns..1000μs)

1 / 64 x 11580 ops/sec @ 86μs/op (0ns..1000μs)
1 / N x 45354 ops/sec @ 22μs/op (0ns..7ms)
64 / 1 x 11340 ops/sec @ 88μs/op (0ns..1000μs)
N / 1 x 844 ops/sec @ 1184μs/op (999μs..14ms)

2 / 64 x 11754 ops/sec @ 85μs/op (0ns..7ms)
2 / N x 46642 ops/sec @ 21μs/op (0ns..1000μs)
64 / 2 x 11125 ops/sec @ 89μs/op (0ns..1000μs)
N / 2 x 915 ops/sec @ 1092μs/op (999μs..2ms)

Just size fix (#1852):

0 / 100 x 12090 ops/sec @ 82μs/op (0ns..1000μs)
0 % 100 x 12148 ops/sec @ 82μs/op (0ns..5ms)
0 / N x 13027 ops/sec @ 76μs/op (0ns..1000μs)
0 % N x 13961 ops/sec @ 71μs/op (0ns..1000μs)

21 / 100 x 12117 ops/sec @ 82μs/op (0ns..1000μs)
21 % 100 x 12796 ops/sec @ 78μs/op (0ns..1000μs)
100 / 21 x 11611 ops/sec @ 86μs/op (0ns..4ms)
100 % 21 x 11698 ops/sec @ 85μs/op (0ns..2ms)

s / (s + 1) x 20154 ops/sec @ 49μs/op (0ns..1000μs)
s % (s + 1) x 20397 ops/sec @ 49μs/op (0ns..1000μs)
(s + 1) / s x 19873 ops/sec @ 50μs/op (0ns..1000μs)
(s + 1) % s x 21124 ops/sec @ 47μs/op (0ns..1000μs)

s / N x 13008 ops/sec @ 76μs/op (0ns..1000μs)
s % N x 13987 ops/sec @ 71μs/op (0ns..1000μs)
N / s x 1603 ops/sec @ 623μs/op (0ns..1000μs)
N % s x 1601 ops/sec @ 624μs/op (0ns..1000μs)

1 / 64 x 12476 ops/sec @ 80μs/op (0ns..1000μs)
1 / N x 12883 ops/sec @ 77μs/op (0ns..1000μs)
64 / 1 x 11541 ops/sec @ 86μs/op (0ns..1000μs)
N / 1 x 908 ops/sec @ 1101μs/op (999μs..2ms)

2 / 64 x 12249 ops/sec @ 81μs/op (0ns..1000μs)
2 / N x 12934 ops/sec @ 77μs/op (0ns..1000μs)
64 / 2 x 11827 ops/sec @ 84μs/op (0ns..1000μs)
N / 2 x 907 ops/sec @ 1102μs/op (999μs..2ms)

[ChALkeR]

I will file a separate PR with just the size fix
Upd: #1852

[meta-codesync]

@tmikov has imported this pull request. If you are a Meta employee, you can view this in D88049977.

[ChALkeR]

The assumption is incorrect on -(2n**63n)/(2n**63n)
I need to fix that

[ChALkeR]

The easiest way would be just do lhs.numDigits + 1 < rhs.numDigits in both places
And then consider improving the check in a separate PR

[tmikov]

Are you going to publish an updated one?

[ChALkeR]

Pushed a fix
I recommend to go with #1852 first though

[facebook-github-bot]

@ChALkeR has updated the pull request. You must reimport the pull request before landing.