math/bits: added package for bit-level counting and manipulation

Initial platform-independent implementation.

For #18616.

Change-Id: I4585c55b963101af9059c06c1b8a866cb384754c
Reviewed-on: https://go-review.googlesource.com/36315Reviewed-by: Keith Randall <khr@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>

src/math/bits/bits.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.
+
+// Package bits implements bit counting and manipulation
+// functions for the predeclared unsigned integer types.
+package bits
+
+// UintSize is the size of a uint in bits.
+const UintSize = uintSize
+
+// LeadingZerosN returns the number of leading zero bits in x.
+// N is absent for uint, or one of 8, 16, 32, 64.
+// The result is the size of x in bits for x == 0.
+func LeadingZeros(x uint) int     { return UintSize - blen(uint64(x)) }
+func LeadingZeros8(x uint8) int   { return 8 - blen(uint64(x)) }
+func LeadingZeros16(x uint16) int { return 16 - blen(uint64(x)) }
+func LeadingZeros32(x uint32) int { return 32 - blen(uint64(x)) }
+func LeadingZeros64(x uint64) int { return 64 - blen(uint64(x)) }
+
+// TrailingZerosN returns the number of trailing zero bits in x.
+// N is absent for uint, or one of 8, 16, 32, 64.
+// The result is the size of x in bits for x == 0.
+func TrailingZeros(x uint) int     { return ntz(x) }
+func TrailingZeros8(x uint8) int   { return ntz8(x) }
+func TrailingZeros16(x uint16) int { return ntz16(x) }
+func TrailingZeros32(x uint32) int { return ntz32(x) }
+func TrailingZeros64(x uint64) int { return ntz64(x) }
+
+// OnesCountN returns the number of one bits ("population count") in x.
+// N is absent for uint, or one of 8, 16, 32, 64.
+func OnesCount(x uint) int     { return pop(uint64(x)) }
+func OnesCount8(x uint8) int   { return pop(uint64(x)) }
+func OnesCount16(x uint16) int { return pop(uint64(x)) }
+func OnesCount32(x uint32) int { return pop(uint64(x)) }
+func OnesCount64(x uint64) int { return pop(uint64(x)) }
+
+// RotateLeftN returns the value of x rotated left by k bits; k must not be negative.
+// N is absent for uint, or one of 8, 16, 32, 64.
+func RotateLeft(x uint, k int) uint       { return uint(rot(uint64(x), UintSize, pos(k)%UintSize)) }
+func RotateLeft8(x uint8, k int) uint8    { return uint8(rot(uint64(x), 8, pos(k)%8)) }
+func RotateLeft16(x uint16, k int) uint16 { return uint16(rot(uint64(x), 16, pos(k)%16)) }
+func RotateLeft32(x uint32, k int) uint32 { return uint32(rot(uint64(x), 32, pos(k)%32)) }
+func RotateLeft64(x uint64, k int) uint64 { return uint64(rot(uint64(x), 64, pos(k)%64)) }
+
+// RotateRightN returns the value of x rotated right by k bits; k must not be negative.
+// N is absent for uint, or one of 8, 16, 32, 64.
+func RotateRight(x uint, k int) uint       { return uint(rot(uint64(x), UintSize, UintSize-pos(k)%UintSize)) }
+func RotateRight8(x uint8, k int) uint8    { return uint8(rot(uint64(x), 8, 8-pos(k)%8)) }
+func RotateRight16(x uint16, k int) uint16 { return uint16(rot(uint64(x), 16, 16-pos(k)%16)) }
+func RotateRight32(x uint32, k int) uint32 { return uint32(rot(uint64(x), 32, 32-pos(k)%32)) }
+func RotateRight64(x uint64, k int) uint64 { return uint64(rot(uint64(x), 64, 64-pos(k)%64)) }
+
+// ReverseN returns the value of x with its bits in reversed order.
+// N is absent for uint, or one of 8, 16, 32, 64.
+func Reverse(x uint) uint       { return uint(rev(uint64(x), UintSize)) }
+func Reverse8(x uint8) uint8    { return uint8(rev(uint64(x), 8)) }
+func Reverse16(x uint16) uint16 { return uint16(rev(uint64(x), 16)) }
+func Reverse32(x uint32) uint32 { return uint32(rev(uint64(x), 32)) }
+func Reverse64(x uint64) uint64 { return uint64(rev(uint64(x), 64)) }
+
+// ReverseBytesN returns the value of x with its bytes in reversed order.
+// N is absent for uint, or one of 8, 16, 32, 64.
+func ReverseBytes(x uint) uint       { return uint(swap(uint64(x), UintSize)) }
+func ReverseBytes16(x uint16) uint16 { return uint16(swap(uint64(x), 16)) }
+func ReverseBytes32(x uint32) uint32 { return uint32(swap(uint64(x), 32)) }
+func ReverseBytes64(x uint64) uint64 { return uint64(swap(uint64(x), 64)) }
+
+// LenN returns the minimum number of bits required to represent x.
+// LenN(x) - 1 is the index of the most significant bit of x.
+// N is absent for uint, or one of 8, 16, 32, 64.
+// The result is 0 for x == 0.
+func Len(x uint) int     { return blen(uint64(x)) }
+func Len8(x uint8) int   { return blen(uint64(x)) }
+func Len16(x uint16) int { return blen(uint64(x)) }
+func Len32(x uint32) int { return blen(uint64(x)) }
+func Len64(x uint64) int { return blen(uint64(x)) }

src/math/bits/bits_impl.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.
+
+// This file provides basic implementations of the bits functions.
+
+package bits
+
+const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64
+
+func ntz(x uint) (n int) {
+	if UintSize == 32 {
+		return ntz32(uint32(x))
+	}
+	return ntz64(uint64(x))
+}
+
+// See http://supertech.csail.mit.edu/papers/debruijn.pdf
+const deBruijn32 = 0x077CB531
+
+var deBruijn32tab = [32]byte{
+	0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
+	31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
+}
+
+func ntz8(x uint8) (n int) {
+	if x == 0 {
+		return 8
+	}
+	// see comment in ntz64
+	return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)])
+}
+
+func ntz16(x uint16) (n int) {
+	if x == 0 {
+		return 16
+	}
+	// see comment in ntz64
+	return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)])
+}
+
+func ntz32(x uint32) int {
+	if x == 0 {
+		return 32
+	}
+	// see comment in ntz64
+	return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)])
+}
+
+const deBruijn64 = 0x03f79d71b4ca8b09
+
+var deBruijn64tab = [64]byte{
+	0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
+	62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
+	63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
+	54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
+}
+
+func ntz64(x uint64) int {
+	if x == 0 {
+		return 64
+	}
+	// If popcount is fast, replace code below with return popcount(^x & (x - 1)).
+	//
+	// x & -x leaves only the right-most bit set in the word. Let k be the
+	// index of that bit. Since only a single bit is set, the value is two
+	// to the power of k. Multiplying by a power of two is equivalent to
+	// left shifting, in this case by k bits. The de Bruijn (64 bit) constant
+	// is such that all six bit, consecutive substrings are distinct.
+	// Therefore, if we have a left shifted version of this constant we can
+	// find by how many bits it was shifted by looking at which six bit
+	// substring ended up at the top of the word.
+	// (Knuth, volume 4, section 7.3.1)
+	return int(deBruijn64tab[(x&-x)*deBruijn64>>(64-6)])
+}
+
+func pop(x uint64) (n int) {
+	for x != 0 {
+		n++
+		x &= x - 1
+	}
+	return
+}
+
+func pos(k int) uint {
+	if k < 0 {
+		panic("negative rotation count")
+	}
+	return uint(k)
+}
+
+func rot(x uint64, size, k uint) uint64 {
+	return x<<k | x>>(size-k)&(1<<k-1)
+}
+
+func rev(x uint64, size uint) (r uint64) {
+	for i := size; i > 0; i-- {
+		r = r<<1 | x&1
+		x >>= 1
+	}
+	return
+}
+
+func swap(x uint64, size uint) (r uint64) {
+	for i := size / 8; i > 0; i-- {
+		r = r<<8 | x&0xff
+		x >>= 8
+	}
+	return
+}
+
+func blen(x uint64) (i int) {
+	for ; x >= 1<<(16-1); x >>= 16 {
+		i += 16
+	}
+	if x >= 1<<(8-1) {
+		x >>= 8
+		i += 8
+	}
+	if x >= 1<<(4-1) {
+		x >>= 4
+		i += 4
+	}
+	if x >= 1<<(2-1) {
+		x >>= 2
+		i += 2
+	}
+	if x >= 1<<(1-1) {
+		i++
+	}
+	return
+}