a28a942768
"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> |
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