cmd/compile: add unsigned divisibility rules

"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>

1 files changed, 20 insertions, 0 deletions

diff --git a/test/codegen/arithmetic.go b/test/codegen/arithmetic.go
index a937be7fe5..16158b2f4b 100644
--- a/test/codegen/arithmetic.go
+++ b/test/codegen/arithmetic.go
@@ -215,6 +215,26 @@ func ConstMods(n1 uint, n2 int) (uint, int) {
 	return a, b
 }
 
+// Check that divisibility checks x%c==0 are converted to MULs and rotates
+func Divisible(n uint) (even, odd bool) {
+	// amd64:"MOVQ\t[$]-6148914691236517205","IMULQ","ROLQ\t[$]63",-"DIVQ"
+	// 386:"IMUL3L\t[$]-1431655765","ROLL\t[$]31",-"DIVQ"
+	// arm64:"MOVD\t[$]-6148914691236517205","MUL","ROR",-"DIV"
+	// arm:"MUL","CMP\t[$]715827882",-".*udiv"
+	// ppc64:"MULLD","ROTL\t[$]63"
+	// ppc64le:"MULLD","ROTL\t[$]63"
+	even = n%6 == 0
+
+	// amd64:"MOVQ\t[$]-8737931403336103397","IMULQ",-"ROLQ",-"DIVQ"
+	// 386:"IMUL3L\t[$]678152731",-"ROLL",-"DIVQ"
+	// arm64:"MOVD\t[$]-8737931403336103397","MUL",-"ROR",-"DIV"
+	// arm:"MUL","CMP\t[$]226050910",-".*udiv"
+	// ppc64:"MULLD",-"ROTL"
+	// ppc64le:"MULLD",-"ROTL"
+	odd = n%19 == 0
+	return
+}
+
 // Check that fix-up code is not generated for divisions where it has been proven that
 // that the divisor is not -1 or that the dividend is > MinIntNN.
 func NoFix64A(divr int64) (int64, int64) {