]> Cypherpunks repositories - gostls13.git/commitdiff
math/bits: added package for bit-level counting and manipulation
authorRobert Griesemer <gri@golang.org>
Fri, 3 Feb 2017 00:59:34 +0000 (16:59 -0800)
committerRobert Griesemer <gri@golang.org>
Thu, 16 Feb 2017 21:54:59 +0000 (21:54 +0000)
Initial platform-independent implementation.

For #18616.

Change-Id: I4585c55b963101af9059c06c1b8a866cb384754c
Reviewed-on: https://go-review.googlesource.com/36315
Reviewed-by: Keith Randall <khr@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>
src/math/bits/bits.go [new file with mode: 0644]
src/math/bits/bits_impl.go [new file with mode: 0644]
src/math/bits/bits_test.go [new file with mode: 0644]

diff --git a/src/math/bits/bits.go b/src/math/bits/bits.go
new file mode 100644 (file)
index 0000000..b342d3e
--- /dev/null
@@ -0,0 +1,77 @@
+// 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)) }
diff --git a/src/math/bits/bits_impl.go b/src/math/bits/bits_impl.go
new file mode 100644 (file)
index 0000000..6f7a49b
--- /dev/null
@@ -0,0 +1,132 @@
+// 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
+}
diff --git a/src/math/bits/bits_test.go b/src/math/bits/bits_test.go
new file mode 100644 (file)
index 0000000..b930300
--- /dev/null
@@ -0,0 +1,518 @@
+// 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
+
+import (
+       "testing"
+       "unsafe"
+)
+
+func TestUintSize(t *testing.T) {
+       var x uint
+       if want := unsafe.Sizeof(x) * 8; UintSize != want {
+               t.Fatalf("UintSize = %d; want %d", UintSize, want)
+       }
+}
+
+func TestLeadingZeros(t *testing.T) {
+       for i := 0; i < 256; i++ {
+               nlz := tab[i].nlz
+               for k := 0; k < 64-8; k++ {
+                       x := uint64(i) << uint(k)
+                       if x <= 1<<8-1 {
+                               got := LeadingZeros8(uint8(x))
+                               want := nlz - k + (8 - 8)
+                               if x == 0 {
+                                       want = 8
+                               }
+                               if got != want {
+                                       t.Fatalf("LeadingZeros8(%#02x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<16-1 {
+                               got := LeadingZeros16(uint16(x))
+                               want := nlz - k + (16 - 8)
+                               if x == 0 {
+                                       want = 16
+                               }
+                               if got != want {
+                                       t.Fatalf("LeadingZeros16(%#04x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<32-1 {
+                               got := LeadingZeros32(uint32(x))
+                               want := nlz - k + (32 - 8)
+                               if x == 0 {
+                                       want = 32
+                               }
+                               if got != want {
+                                       t.Fatalf("LeadingZeros32(%#08x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 32 {
+                                       got = LeadingZeros(uint(x))
+                                       if got != want {
+                                               t.Fatalf("LeadingZeros(%#08x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+
+                       if x <= 1<<64-1 {
+                               got := LeadingZeros64(uint64(x))
+                               want := nlz - k + (64 - 8)
+                               if x == 0 {
+                                       want = 64
+                               }
+                               if got != want {
+                                       t.Fatalf("LeadingZeros64(%#016x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 64 {
+                                       got = LeadingZeros(uint(x))
+                                       if got != want {
+                                               t.Fatalf("LeadingZeros(%#016x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+               }
+       }
+}
+
+func TestTrailingZeros(t *testing.T) {
+       for i := 0; i < 256; i++ {
+               ntz := tab[i].ntz
+               for k := 0; k < 64-8; k++ {
+                       x := uint64(i) << uint(k)
+                       want := ntz + k
+                       if x <= 1<<8-1 {
+                               got := TrailingZeros8(uint8(x))
+                               if x == 0 {
+                                       want = 8
+                               }
+                               if got != want {
+                                       t.Fatalf("TrailingZeros8(%#02x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<16-1 {
+                               got := TrailingZeros16(uint16(x))
+                               if x == 0 {
+                                       want = 16
+                               }
+                               if got != want {
+                                       t.Fatalf("TrailingZeros16(%#04x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<32-1 {
+                               got := TrailingZeros32(uint32(x))
+                               if x == 0 {
+                                       want = 32
+                               }
+                               if got != want {
+                                       t.Fatalf("TrailingZeros32(%#08x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 32 {
+                                       got = TrailingZeros(uint(x))
+                                       if got != want {
+                                               t.Fatalf("TrailingZeros(%#08x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+
+                       if x <= 1<<64-1 {
+                               got := TrailingZeros64(uint64(x))
+                               if x == 0 {
+                                       want = 64
+                               }
+                               if got != want {
+                                       t.Fatalf("TrailingZeros64(%#016x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 64 {
+                                       got = TrailingZeros(uint(x))
+                                       if got != want {
+                                               t.Fatalf("TrailingZeros(%#016x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+               }
+       }
+}
+
+func TestOnesCount(t *testing.T) {
+       for i := 0; i < 256; i++ {
+               want := tab[i].pop
+               for k := 0; k < 64-8; k++ {
+                       x := uint64(i) << uint(k)
+                       if x <= 1<<8-1 {
+                               got := OnesCount8(uint8(x))
+                               if got != want {
+                                       t.Fatalf("OnesCount8(%#02x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<16-1 {
+                               got := OnesCount16(uint16(x))
+                               if got != want {
+                                       t.Fatalf("OnesCount16(%#04x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<32-1 {
+                               got := OnesCount32(uint32(x))
+                               if got != want {
+                                       t.Fatalf("OnesCount32(%#08x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 32 {
+                                       got = OnesCount(uint(x))
+                                       if got != want {
+                                               t.Fatalf("OnesCount(%#08x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+
+                       if x <= 1<<64-1 {
+                               got := OnesCount64(uint64(x))
+                               if got != want {
+                                       t.Fatalf("OnesCount64(%#016x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 64 {
+                                       got = OnesCount(uint(x))
+                                       if got != want {
+                                               t.Fatalf("OnesCount(%#016x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+               }
+       }
+}
+
+func TestRotateLeft(t *testing.T) {
+       var m uint64 = deBruijn64
+
+       for k := uint(0); k < 128; k++ {
+               x8 := uint8(m)
+               got8 := RotateLeft8(x8, int(k))
+               want8 := x8<<(k&0x7) | x8>>(8-k&0x7)
+               if got8 != want8 {
+                       t.Fatalf("RotateLeft8(%#02x, %d) == %#02x; want %#02x", x8, k, got8, want8)
+               }
+
+               x16 := uint16(m)
+               got16 := RotateLeft16(x16, int(k))
+               want16 := x16<<(k&0xf) | x16>>(16-k&0xf)
+               if got16 != want16 {
+                       t.Fatalf("RotateLeft16(%#04x, %d) == %#04x; want %#04x", x16, k, got16, want16)
+               }
+
+               x32 := uint32(m)
+               got32 := RotateLeft32(x32, int(k))
+               want32 := x32<<(k&0x1f) | x32>>(32-k&0x1f)
+               if got32 != want32 {
+                       t.Fatalf("RotateLeft32(%#08x, %d) == %#08x; want %#08x", x32, k, got32, want32)
+               }
+               if UintSize == 32 {
+                       x := uint(m)
+                       got := RotateLeft(x, int(k))
+                       want := x<<(k&0x1f) | x>>(32-k&0x1f)
+                       if got != want {
+                               t.Fatalf("RotateLeft(%#08x, %d) == %#08x; want %#08x", x, k, got, want)
+                       }
+               }
+
+               x64 := uint64(m)
+               got64 := RotateLeft64(x64, int(k))
+               want64 := x64<<(k&0x3f) | x64>>(64-k&0x3f)
+               if got64 != want64 {
+                       t.Fatalf("RotateLeft64(%#016x, %d) == %#016x; want %#016x", x64, k, got64, want64)
+               }
+               if UintSize == 64 {
+                       x := uint(m)
+                       got := RotateLeft(x, int(k))
+                       want := x<<(k&0x3f) | x>>(64-k&0x3f)
+                       if got != want {
+                               t.Fatalf("RotateLeft(%#016x, %d) == %#016x; want %#016x", x, k, got, want)
+                       }
+               }
+       }
+}
+
+func TestRotateRight(t *testing.T) {
+       var m uint64 = deBruijn64
+
+       for k := uint(0); k < 128; k++ {
+               x8 := uint8(m)
+               got8 := RotateRight8(x8, int(k))
+               want8 := x8>>(k&0x7) | x8<<(8-k&0x7)
+               if got8 != want8 {
+                       t.Fatalf("RotateRight8(%#02x, %d) == %#02x; want %#02x", x8, k, got8, want8)
+               }
+
+               x16 := uint16(m)
+               got16 := RotateRight16(x16, int(k))
+               want16 := x16>>(k&0xf) | x16<<(16-k&0xf)
+               if got16 != want16 {
+                       t.Fatalf("RotateRight16(%#04x, %d) == %#04x; want %#04x", x16, k, got16, want16)
+               }
+
+               x32 := uint32(m)
+               got32 := RotateRight32(x32, int(k))
+               want32 := x32>>(k&0x1f) | x32<<(32-k&0x1f)
+               if got32 != want32 {
+                       t.Fatalf("RotateRight32(%#08x, %d) == %#08x; want %#08x", x32, k, got32, want32)
+               }
+               if UintSize == 32 {
+                       x := uint(m)
+                       got := RotateRight(x, int(k))
+                       want := x>>(k&0x1f) | x<<(32-k&0x1f)
+                       if got != want {
+                               t.Fatalf("RotateRight(%#08x, %d) == %#08x; want %#08x", x, k, got, want)
+                       }
+               }
+
+               x64 := uint64(m)
+               got64 := RotateRight64(x64, int(k))
+               want64 := x64>>(k&0x3f) | x64<<(64-k&0x3f)
+               if got64 != want64 {
+                       t.Fatalf("RotateRight64(%#016x, %d) == %#016x; want %#016x", x64, k, got64, want64)
+               }
+               if UintSize == 64 {
+                       x := uint(m)
+                       got := RotateRight(x, int(k))
+                       want := x>>(k&0x3f) | x<<(64-k&0x3f)
+                       if got != want {
+                               t.Fatalf("RotateRight(%#016x, %d) == %#016x; want %#016x", x, k, got, want)
+                       }
+               }
+       }
+}
+
+func TestReverse(t *testing.T) {
+       // test each bit
+       for i := uint(0); i < 64; i++ {
+               testReverse(t, uint64(1)<<i, uint64(1)<<(63-i))
+       }
+
+       // test a few patterns
+       for _, test := range []struct {
+               x, r uint64
+       }{
+               {0, 0},
+               {0x1, 0x8 << 60},
+               {0x2, 0x4 << 60},
+               {0x3, 0xc << 60},
+               {0x4, 0x2 << 60},
+               {0x5, 0xa << 60},
+               {0x6, 0x6 << 60},
+               {0x7, 0xe << 60},
+               {0x8, 0x1 << 60},
+               {0x9, 0x9 << 60},
+               {0xa, 0x5 << 60},
+               {0xb, 0xd << 60},
+               {0xc, 0x3 << 60},
+               {0xd, 0xb << 60},
+               {0xe, 0x7 << 60},
+               {0xf, 0xf << 60},
+               {0x5686487, 0xe12616a000000000},
+               {0x0123456789abcdef, 0xf7b3d591e6a2c480},
+       } {
+               testReverse(t, test.x, test.r)
+               testReverse(t, test.r, test.x)
+       }
+}
+
+func testReverse(t *testing.T, x64, want64 uint64) {
+       x8 := uint8(x64)
+       got8 := Reverse8(x8)
+       want8 := uint8(want64 >> (64 - 8))
+       if got8 != want8 {
+               t.Fatalf("Reverse8(%#02x) == %#02x; want %#02x", x8, got8, want8)
+       }
+
+       x16 := uint16(x64)
+       got16 := Reverse16(x16)
+       want16 := uint16(want64 >> (64 - 16))
+       if got16 != want16 {
+               t.Fatalf("Reverse16(%#04x) == %#04x; want %#04x", x16, got16, want16)
+       }
+
+       x32 := uint32(x64)
+       got32 := Reverse32(x32)
+       want32 := uint32(want64 >> (64 - 32))
+       if got32 != want32 {
+               t.Fatalf("Reverse32(%#08x) == %#08x; want %#08x", x32, got32, want32)
+       }
+       if UintSize == 32 {
+               x := uint(x32)
+               got := Reverse(x)
+               want := uint(want32)
+               if got != want {
+                       t.Fatalf("Reverse(%#08x) == %#08x; want %#08x", x, got, want)
+               }
+       }
+
+       got64 := Reverse64(x64)
+       if got64 != want64 {
+               t.Fatalf("Reverse64(%#016x) == %#016x; want %#016x", x64, got64, want64)
+       }
+       if UintSize == 64 {
+               x := uint(x64)
+               got := Reverse(x)
+               want := uint(want64)
+               if got != want {
+                       t.Fatalf("Reverse(%#08x) == %#016x; want %#016x", x, got, want)
+               }
+       }
+}
+
+func TestReverseBytes(t *testing.T) {
+       for _, test := range []struct {
+               x, r uint64
+       }{
+               {0, 0},
+               {0x01, 0x01 << 56},
+               {0x0123, 0x2301 << 48},
+               {0x012345, 0x452301 << 40},
+               {0x01234567, 0x67452301 << 32},
+               {0x0123456789, 0x8967452301 << 24},
+               {0x0123456789ab, 0xab8967452301 << 16},
+               {0x0123456789abcd, 0xcdab8967452301 << 8},
+               {0x0123456789abcdef, 0xefcdab8967452301 << 0},
+       } {
+               testReverseBytes(t, test.x, test.r)
+               testReverseBytes(t, test.r, test.x)
+       }
+}
+
+func testReverseBytes(t *testing.T, x64, want64 uint64) {
+       x16 := uint16(x64)
+       got16 := ReverseBytes16(x16)
+       want16 := uint16(want64 >> (64 - 16))
+       if got16 != want16 {
+               t.Fatalf("ReverseBytes16(%#04x) == %#04x; want %#04x", x16, got16, want16)
+       }
+
+       x32 := uint32(x64)
+       got32 := ReverseBytes32(x32)
+       want32 := uint32(want64 >> (64 - 32))
+       if got32 != want32 {
+               t.Fatalf("ReverseBytes32(%#08x) == %#08x; want %#08x", x32, got32, want32)
+       }
+       if UintSize == 32 {
+               x := uint(x32)
+               got := ReverseBytes(x)
+               want := uint(want32)
+               if got != want {
+                       t.Fatalf("ReverseBytes(%#08x) == %#08x; want %#08x", x, got, want)
+               }
+       }
+
+       got64 := ReverseBytes64(x64)
+       if got64 != want64 {
+               t.Fatalf("ReverseBytes64(%#016x) == %#016x; want %#016x", x64, got64, want64)
+       }
+       if UintSize == 64 {
+               x := uint(x64)
+               got := ReverseBytes(x)
+               want := uint(want64)
+               if got != want {
+                       t.Fatalf("ReverseBytes(%#016x) == %#016x; want %#016x", x, got, want)
+               }
+       }
+}
+
+func TestLen(t *testing.T) {
+       for i := 0; i < 256; i++ {
+               len := 8 - tab[i].nlz
+               for k := 0; k < 64-8; k++ {
+                       x := uint64(i) << uint(k)
+                       want := 0
+                       if x != 0 {
+                               want = len + k
+                       }
+                       if x <= 1<<8-1 {
+                               got := Len8(uint8(x))
+                               if got != want {
+                                       t.Fatalf("Len8(%#02x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<16-1 {
+                               got := Len16(uint16(x))
+                               if got != want {
+                                       t.Fatalf("Len16(%#04x) == %d; want %d", x, got, want)
+                               }
+                       }
+
+                       if x <= 1<<32-1 {
+                               got := Len32(uint32(x))
+                               if got != want {
+                                       t.Fatalf("Len32(%#08x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 32 {
+                                       got := Len(uint(x))
+                                       if got != want {
+                                               t.Fatalf("Len(%#08x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+
+                       if x <= 1<<64-1 {
+                               got := Len64(uint64(x))
+                               if got != want {
+                                       t.Fatalf("Len64(%#016x) == %d; want %d", x, got, want)
+                               }
+                               if UintSize == 64 {
+                                       got := Len(uint(x))
+                                       if got != want {
+                                               t.Fatalf("Len(%#016x) == %d; want %d", x, got, want)
+                                       }
+                               }
+                       }
+               }
+       }
+}
+
+// ----------------------------------------------------------------------------
+// Testing support
+
+type entry = struct {
+       nlz, ntz, pop int
+}
+
+// tab contains results for all uint8 values
+var tab [256]entry
+
+func init() {
+       tab[0] = entry{8, 8, 0}
+       for i := 1; i < len(tab); i++ {
+               // nlz
+               x := i // x != 0
+               n := 0
+               for x&0x80 == 0 {
+                       n++
+                       x <<= 1
+               }
+               tab[i].nlz = n
+
+               // ntz
+               x = i // x != 0
+               n = 0
+               for x&1 == 0 {
+                       n++
+                       x >>= 1
+               }
+               tab[i].ntz = n
+
+               // pop
+               x = i // x != 0
+               n = 0
+               for x != 0 {
+                       n += int(x & 1)
+                       x >>= 1
+               }
+               tab[i].pop = n
+       }
+}