all: faster midpoint computation in binary search

On my machine (3.1 GHz Quad-Core Intel Core i7, macOS 10.15.7 10.15.7), go 1.15.6

benchstat:
name          old time/op  new time/op  delta
SearchInts-8  20.3ns ± 1%  16.6ns ± 6%  -18.37%  (p=0.000 n=9+10)

Change-Id: I346e5955fd6df6ce10254b22267dbc8d5a2b16c0
Reviewed-on: https://go-review.googlesource.com/c/go/+/279439
Reviewed-by: Ben Shi <powerman1st@163.com>
Reviewed-by: Robert Griesemer <gri@golang.org>
Trust: Robert Griesemer <gri@golang.org>

src/go/token/position.go

@@ -540,7 +540,7 @@ func searchInts(a []int, x int) int {
 	// TODO(gri): Remove this when compilers have caught up.
 	i, j := 0, len(a)
 	for i < j {
-		h := i + (j-i)/2 // avoid overflow when computing h
+		h := i + (j-i)>>1 // avoid overflow when computing h
 		// i ≤ h < j
 		if a[h] <= x {
 			i = h + 1

src/go/token/position_bench_test.go

@@ -0,0 +1,24 @@
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package token
+
+import (
+	"testing"
+)
+
+func BenchmarkSearchInts(b *testing.B) {
+	data := make([]int, 10000)
+	for i := 0; i < 10000; i++ {
+		data[i] = i
+	}
+	const x = 8
+	if r := searchInts(data, x); r != x {
+		b.Errorf("got index = %d; want %d", r, x)
+	}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		searchInts(data, x)
+	}
+}

src/reflect/type.go

@@ -1723,7 +1723,7 @@ func typesByString(s string) []*rtype {
 		// This is a copy of sort.Search, with f(h) replaced by (*typ[h].String() >= s).
 		i, j := 0, len(offs)
 		for i < j {
-			h := i + (j-i)/2 // avoid overflow when computing h
+			h := i + (j-i)>>1 // avoid overflow when computing h
 			// i ≤ h < j
 			if !(rtypeOff(section, offs[h]).String() >= s) {
 				i = h + 1 // preserves f(i-1) == false

src/strconv/makeisprint.go

@@ -37,7 +37,7 @@ var (
 func bsearch16(a []uint16, x uint16) int {
 	i, j := 0, len(a)
 	for i < j {
-		h := i + (j-i)/2
+		h := i + (j-i)>>1
 		if a[h] < x {
 			i = h + 1
 		} else {
@@ -52,7 +52,7 @@ func bsearch16(a []uint16, x uint16) int {
 func bsearch32(a []uint32, x uint32) int {
 	i, j := 0, len(a)
 	for i < j {
-		h := i + (j-i)/2
+		h := i + (j-i)>>1
 		if a[h] < x {
 			i = h + 1
 		} else {

src/strconv/quote.go

@@ -440,7 +440,7 @@ func Unquote(s string) (string, error) {
 func bsearch16(a []uint16, x uint16) int {
 	i, j := 0, len(a)
 	for i < j {
-		h := i + (j-i)/2
+		h := i + (j-i)>>1
 		if a[h] < x {
 			i = h + 1
 		} else {
@@ -455,7 +455,7 @@ func bsearch16(a []uint16, x uint16) int {
 func bsearch32(a []uint32, x uint32) int {
 	i, j := 0, len(a)
 	for i < j {
-		h := i + (j-i)/2
+		h := i + (j-i)>>1
 		if a[h] < x {
 			i = h + 1
 		} else {