math/bits: faster Reverse8/16 functions using table lookups

Measured on 2.3 GHz Intel Core i7, running macOS 10.12.3:

benchmark                old ns/op     new ns/op     delta
BenchmarkReverse8-8      1.70          0.99          -41.76%
BenchmarkReverse16-8     2.24          1.32          -41.07%

Fixes #19279.

Change-Id: I398cf8a3513b7fa63c130efc7846a7c5353999d4
Reviewed-on: https://go-review.googlesource.com/37459
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

src/math/bits/bits.go

@@ -2,6 +2,8 @@
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.
 
+//go:generate go run make_tables.go
+
 // Package bits implements bit counting and manipulation
 // functions for the predeclared unsigned integer types.
 package bits
@@ -232,19 +234,12 @@ func Reverse(x uint) uint {
 
 // Reverse8 returns the value of x with its bits in reversed order.
 func Reverse8(x uint8) uint8 {
-	const m = 1<<8 - 1
-	x = x>>1&(m0&m) | x&(m0&m)<<1
-	x = x>>2&(m1&m) | x&(m1&m)<<2
-	return x>>4 | x<<4
+	return rev8tab[x]
 }
 
 // Reverse16 returns the value of x with its bits in reversed order.
 func Reverse16(x uint16) uint16 {
-	const m = 1<<16 - 1
-	x = x>>1&(m0&m) | x&(m0&m)<<1
-	x = x>>2&(m1&m) | x&(m1&m)<<2
-	x = x>>4&(m2&m) | x&(m2&m)<<4
-	return x>>8 | x<<8
+	return uint16(rev8tab[x>>8]) | uint16(rev8tab[x&0xff])<<8
 }
 
 // Reverse32 returns the value of x with its bits in reversed order.

src/math/bits/bits_tables.go

+// Copyright 2017 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.
+
+// Code generated by go run make_tables.go. DO NOT EDIT.
+
+package bits
+
+var rev8tab = [256]uint8{
+	0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0, 0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0,
+	0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8, 0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8,
+	0x04, 0x84, 0x44, 0xc4, 0x24, 0xa4, 0x64, 0xe4, 0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4,
+	0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac, 0x6c, 0xec, 0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc,
+	0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2, 0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2,
+	0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea, 0x1a, 0x9a, 0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa,
+	0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6, 0x16, 0x96, 0x56, 0xd6, 0x36, 0xb6, 0x76, 0xf6,
+	0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee, 0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe, 0x7e, 0xfe,
+	0x01, 0x81, 0x41, 0xc1, 0x21, 0xa1, 0x61, 0xe1, 0x11, 0x91, 0x51, 0xd1, 0x31, 0xb1, 0x71, 0xf1,
+	0x09, 0x89, 0x49, 0xc9, 0x29, 0xa9, 0x69, 0xe9, 0x19, 0x99, 0x59, 0xd9, 0x39, 0xb9, 0x79, 0xf9,
+	0x05, 0x85, 0x45, 0xc5, 0x25, 0xa5, 0x65, 0xe5, 0x15, 0x95, 0x55, 0xd5, 0x35, 0xb5, 0x75, 0xf5,
+	0x0d, 0x8d, 0x4d, 0xcd, 0x2d, 0xad, 0x6d, 0xed, 0x1d, 0x9d, 0x5d, 0xdd, 0x3d, 0xbd, 0x7d, 0xfd,
+	0x03, 0x83, 0x43, 0xc3, 0x23, 0xa3, 0x63, 0xe3, 0x13, 0x93, 0x53, 0xd3, 0x33, 0xb3, 0x73, 0xf3,
+	0x0b, 0x8b, 0x4b, 0xcb, 0x2b, 0xab, 0x6b, 0xeb, 0x1b, 0x9b, 0x5b, 0xdb, 0x3b, 0xbb, 0x7b, 0xfb,
+	0x07, 0x87, 0x47, 0xc7, 0x27, 0xa7, 0x67, 0xe7, 0x17, 0x97, 0x57, 0xd7, 0x37, 0xb7, 0x77, 0xf7,
+	0x0f, 0x8f, 0x4f, 0xcf, 0x2f, 0xaf, 0x6f, 0xef, 0x1f, 0x9f, 0x5f, 0xdf, 0x3f, 0xbf, 0x7f, 0xff,
+}

src/math/bits/make_tables.go

+// Copyright 2017 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.
+
+// +build ignore
+
+// This program generates bits_tables.go.
+
+package main
+
+import (
+	"bytes"
+	"fmt"
+	"go/format"
+	"io"
+	"io/ioutil"
+	"log"
+)
+
+var header = []byte(`// Copyright 2017 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.
+
+// Code generated by go run make_tables.go. DO NOT EDIT.
+
+package bits
+
+`)
+
+func main() {
+	buf := bytes.NewBuffer(header)
+
+	gen(buf, "rev8tab", rev8)
+	// add more tables as needed
+
+	out, err := format.Source(buf.Bytes())
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	err = ioutil.WriteFile("bits_tables.go", out, 0666)
+	if err != nil {
+		log.Fatal(err)
+	}
+}
+
+func gen(w io.Writer, name string, f func(uint8) uint8) {
+	fmt.Fprintf(w, "var %s = [256]uint8{", name)
+	for i := 0; i < 256; i++ {
+		if i%16 == 0 {
+			fmt.Fprint(w, "\n\t")
+		} else {
+			fmt.Fprint(w, " ")
+		}
+		fmt.Fprintf(w, "%#02x,", f(uint8(i)))
+	}
+	fmt.Fprint(w, "\n}\n\n")
+}
+
+func rev8(x uint8) (r uint8) {
+	for i := 8; i > 0; i-- {
+		r = r<<1 | x&1
+		x >>= 1
+	}
+	return
+}