"Division by invariant integers using multiplication" paper
by Granlund and Montgomery contains a method for directly computing
divisibility (x%c == 0 for c constant) by means of the modular inverse.
The method is further elaborated in "Hacker's Delight" by Warren Section 10-17

This general rule can compute divisibilty by one multiplication and a compare
for odd divisors and an additional rotate for even divisors.

To apply the divisibility rule, we must take into account
the rules to rewrite x%c = x-((x/c)*c) and (x/c) for c constant on the first
optimization pass "opt".  This complicates the matching as we want to match
only in the cases where the result of (x/c) is not also available.
So, we must match on the expanded form of (x/c) in the expression x == c*(x/c)
in the "late opt" pass after common subexpresion elimination.

Note, that if there is an intermediate opt pass introduced in the future we
could simplify these rules by delaying the magic division rewrite to "late opt"
and matching directly on (x/c) in the intermediate opt pass.

Additional rules to lower the generic RotateLeft* ops were also applied.

On amd64, the divisibility check is 25-50% faster.

name                     old time/op  new time/op  delta
DivconstI64-4            2.08ns ± 0%  2.08ns ± 1%     ~     (p=0.881 n=5+5)
DivisibleconstI64-4      2.67ns ± 0%  2.67ns ± 1%     ~     (p=1.000 n=5+5)
DivisibleWDivconstI64-4  2.67ns ± 0%  2.67ns ± 0%     ~     (p=0.683 n=5+5)
DivconstU64-4            2.08ns ± 1%  2.08ns ± 1%     ~     (p=1.000 n=5+5)
DivisibleconstU64-4      2.77ns ± 1%  1.55ns ± 2%  -43.90%  (p=0.008 n=5+5)
DivisibleWDivconstU64-4  2.99ns ± 1%  2.99ns ± 1%     ~     (p=1.000 n=5+5)
DivconstI32-4            1.53ns ± 2%  1.53ns ± 0%     ~     (p=1.000 n=5+5)
DivisibleconstI32-4      2.23ns ± 0%  2.25ns ± 3%     ~     (p=0.167 n=5+5)
DivisibleWDivconstI32-4  2.27ns ± 1%  2.27ns ± 1%     ~     (p=0.429 n=5+5)
DivconstU32-4            1.78ns ± 0%  1.78ns ± 1%     ~     (p=1.000 n=4+5)
DivisibleconstU32-4      2.52ns ± 2%  1.26ns ± 0%  -49.96%  (p=0.000 n=5+4)
DivisibleWDivconstU32-4  2.63ns ± 0%  2.85ns ±10%   +8.29%  (p=0.016 n=4+5)
DivconstI16-4            1.54ns ± 0%  1.54ns ± 0%     ~     (p=0.333 n=4+5)
DivisibleconstI16-4      2.10ns ± 0%  2.10ns ± 1%     ~     (p=0.571 n=4+5)
DivisibleWDivconstI16-4  2.22ns ± 0%  2.23ns ± 1%     ~     (p=0.556 n=4+5)
DivconstU16-4            1.09ns ± 0%  1.01ns ± 1%   -7.74%  (p=0.000 n=4+5)
DivisibleconstU16-4      1.83ns ± 0%  1.26ns ± 0%  -31.52%  (p=0.008 n=5+5)
DivisibleWDivconstU16-4  1.88ns ± 0%  1.89ns ± 1%     ~     (p=0.365 n=5+5)
DivconstI8-4             1.54ns ± 1%  1.54ns ± 1%     ~     (p=1.000 n=5+5)
DivisibleconstI8-4       2.10ns ± 0%  2.11ns ± 0%     ~     (p=0.238 n=5+4)
DivisibleWDivconstI8-4   2.22ns ± 0%  2.23ns ± 2%     ~     (p=0.762 n=5+5)
DivconstU8-4             0.92ns ± 1%  0.94ns ± 1%   +2.65%  (p=0.008 n=5+5)
DivisibleconstU8-4       1.66ns ± 0%  1.26ns ± 1%  -24.28%  (p=0.008 n=5+5)
DivisibleWDivconstU8-4   1.79ns ± 0%  1.80ns ± 1%     ~     (p=0.079 n=4+5)

A follow-up change will address the signed division case.

Updates #30282

Change-Id: I7e995f167179aa5c76bb10fbcbeb49c520943403
Reviewed-on: https://go-review.googlesource.com/c/go/+/168037


Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>