math/big: remove bounds checks for shrVU_g inner loop

Make explicit a shrVU_g precondition.
Replace i with i+1 throughout the loop.
The resulting loop is functionally identical,
but the compiler can do better BCE without the i-1 slice offset.

Benchmarks results on amd64 with -tags=math_big_pure_go.

name                          old time/op  new time/op  delta
NonZeroShifts/1/shrVU-8       4.55ns ± 2%  4.45ns ± 3%   -2.27%  (p=0.000 n=28+30)
NonZeroShifts/1/shlVU-8       4.07ns ± 1%  4.13ns ± 4%   +1.55%  (p=0.000 n=26+29)
NonZeroShifts/2/shrVU-8       6.12ns ± 1%  5.55ns ± 1%   -9.30%  (p=0.000 n=28+28)
NonZeroShifts/2/shlVU-8       5.65ns ± 3%  5.70ns ± 2%   +0.92%  (p=0.008 n=30+29)
NonZeroShifts/3/shrVU-8       7.58ns ± 2%  6.79ns ± 2%  -10.46%  (p=0.000 n=28+28)
NonZeroShifts/3/shlVU-8       6.62ns ± 2%  6.69ns ± 1%   +1.07%  (p=0.000 n=29+28)
NonZeroShifts/4/shrVU-8       9.02ns ± 1%  7.79ns ± 2%  -13.59%  (p=0.000 n=27+30)
NonZeroShifts/4/shlVU-8       7.74ns ± 1%  7.82ns ± 1%   +0.92%  (p=0.000 n=26+28)
NonZeroShifts/5/shrVU-8       10.6ns ± 1%   8.9ns ± 3%  -16.31%  (p=0.000 n=25+29)
NonZeroShifts/5/shlVU-8       8.59ns ± 1%  8.68ns ± 1%   +1.13%  (p=0.000 n=27+29)
NonZeroShifts/10/shrVU-8      18.2ns ± 2%  14.4ns ± 1%  -20.96%  (p=0.000 n=27+28)
NonZeroShifts/10/shlVU-8      14.1ns ± 1%  14.1ns ± 1%   +0.46%  (p=0.001 n=26+28)
NonZeroShifts/100/shrVU-8      161ns ± 2%   118ns ± 1%  -26.83%  (p=0.000 n=29+30)
NonZeroShifts/100/shlVU-8      119ns ± 2%   120ns ± 2%   +0.92%  (p=0.000 n=29+29)
NonZeroShifts/1000/shrVU-8    1.54µs ± 1%  1.10µs ± 1%  -28.63%  (p=0.000 n=29+29)
NonZeroShifts/1000/shlVU-8    1.10µs ± 1%  1.10µs ± 2%     ~     (p=0.701 n=28+29)
NonZeroShifts/10000/shrVU-8   15.3µs ± 2%  10.9µs ± 1%  -28.68%  (p=0.000 n=28+28)
NonZeroShifts/10000/shlVU-8   10.9µs ± 2%  10.9µs ± 2%   -0.57%  (p=0.003 n=26+29)
NonZeroShifts/100000/shrVU-8   154µs ± 1%   111µs ± 2%  -28.04%  (p=0.000 n=27+28)
NonZeroShifts/100000/shlVU-8   113µs ± 2%   113µs ± 2%     ~     (p=0.790 n=30+30)

Change-Id: Ib6a621ee7c88b27f0f18121fb2cba3606c40c9b0
Reviewed-on: https://go-review.googlesource.com/c/go/+/297049
Trust: Josh Bleecher Snyder <[email protected]>
Run-TryBot: Josh Bleecher Snyder <[email protected]>
TryBot-Result: Go Bot <[email protected]>
Reviewed-by: Robert Griesemer <[email protected]>

src/math/big/arith.go

@@ -170,12 +170,16 @@ func shrVU_g(z, x []Word, s uint) (c Word) {
 	if len(z) == 0 {
 		return
 	}
+	if len(x) != len(z) {
+		// This is an invariant guaranteed by the caller.
+		panic("len(x) != len(z)")
+	}
 	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
 	ŝ := _W - s
 	ŝ &= _W - 1 // ditto
 	c = x[0] << ŝ
-	for i := 0; i < len(z)-1; i++ {
-		z[i] = x[i]>>s | x[i+1]<<ŝ
+	for i := 1; i < len(z); i++ {
+		z[i-1] = x[i-1]>>s | x[i]<<ŝ
 	}
 	z[len(z)-1] = x[len(z)-1] >> s
 	return