math/big: optimize shlVU_g and shrVU_g

Special case shifts by zero.
Provide hints to the compiler that shifts are bounded.

There are no existing benchmarks for shifts,
but the Float implementation uses shifts,
so we can use those.

Benchmarks on amd64 with -tags=math_big_pure_go.

name                  old time/op    new time/op    delta
FloatString/100-8        869ns ± 3%     872ns ± 4%   +0.40%  (p=0.001 n=94+83)
FloatString/1000-8      26.5µs ± 1%    26.4µs ± 1%   -0.46%  (p=0.000 n=87+96)
FloatString/10000-8     2.18ms ± 2%    2.18ms ± 2%     ~     (p=0.687 n=90+89)
FloatString/100000-8     200ms ± 7%     197ms ± 5%   -1.47%  (p=0.000 n=100+90)
FloatAdd/10-8           65.9ns ± 4%    64.0ns ± 4%   -2.94%  (p=0.000 n=92+93)
FloatAdd/100-8          71.3ns ± 4%    67.4ns ± 4%   -5.51%  (p=0.000 n=96+93)
FloatAdd/1000-8          128ns ± 1%     121ns ± 0%   -5.69%  (p=0.000 n=91+80)
FloatAdd/10000-8         718ns ± 4%     626ns ± 4%  -12.83%  (p=0.000 n=99+99)
FloatAdd/100000-8       6.43µs ± 3%    5.50µs ± 1%  -14.50%  (p=0.000 n=98+83)
FloatSub/10-8           57.7ns ± 2%    57.0ns ± 4%   -1.20%  (p=0.000 n=89+96)
FloatSub/100-8          59.9ns ± 3%    58.7ns ± 4%   -2.10%  (p=0.000 n=100+98)
FloatSub/1000-8         94.5ns ± 1%    88.6ns ± 0%   -6.16%  (p=0.000 n=74+70)
FloatSub/10000-8         456ns ± 1%     416ns ± 5%   -8.83%  (p=0.000 n=87+95)
FloatSub/100000-8       4.00µs ± 1%    3.57µs ± 1%  -10.87%  (p=0.000 n=68+85)
FloatSqrt/64-8           585ns ± 1%     579ns ± 1%   -0.99%  (p=0.000 n=92+90)
FloatSqrt/128-8         1.26µs ± 1%    1.23µs ± 2%   -2.42%  (p=0.000 n=91+81)
FloatSqrt/256-8         1.45µs ± 3%    1.40µs ± 1%   -3.61%  (p=0.000 n=96+90)
FloatSqrt/1000-8        4.03µs ± 1%    3.91µs ± 1%   -3.05%  (p=0.000 n=90+93)
FloatSqrt/10000-8       48.0µs ± 0%    47.3µs ± 1%   -1.55%  (p=0.000 n=90+90)
FloatSqrt/100000-8      1.23ms ± 3%    1.22ms ± 4%   -1.00%  (p=0.000 n=99+99)
FloatSqrt/1000000-8     96.7ms ± 4%    98.0ms ±10%     ~     (p=0.322 n=89+99)

Change-Id: I0f941c05b7c324256d7f0674559b6ba906e92ba8
Reviewed-on: https://go-review.googlesource.com/c/go/+/164967
Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>

src/math/big/arith.go

@@ -204,32 +204,46 @@ func subVW_g(z, x []Word, y Word) (c Word) {
 }
 
 func shlVU_g(z, x []Word, s uint) (c Word) {
-	if n := len(z); n > 0 {
+	if s == 0 {
+		copy(z, x)
+		return
+	}
+	if len(z) == 0 {
+		return
+	}
+	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
 	ŝ := _W - s
-		w1 := x[n-1]
+	ŝ &= _W - 1 // ditto
+	w1 := x[len(z)-1]
 	c = w1 >> ŝ
-		for i := n - 1; i > 0; i-- {
+	for i := len(z) - 1; i > 0; i-- {
 		w := w1
 		w1 = x[i-1]
 		z[i] = w<<s | w1>>ŝ
 	}
 	z[0] = w1 << s
-	}
 	return
 }
 
 func shrVU_g(z, x []Word, s uint) (c Word) {
-	if n := len(z); n > 0 {
+	if s == 0 {
+		copy(z, x)
+		return
+	}
+	if len(z) == 0 {
+		return
+	}
+	s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
 	ŝ := _W - s
+	ŝ &= _W - 1 // ditto
 	w1 := x[0]
 	c = w1 << ŝ
-		for i := 0; i < n-1; i++ {
+	for i := 0; i < len(z)-1; i++ {
 		w := w1
 		w1 = x[i+1]
 		z[i] = w>>s | w1<<ŝ
 	}
-		z[n-1] = w1 >> s
-	}
+	z[len(z)-1] = w1 >> s
 	return
 }