Adding upstream version 1.20.14.upstream/1.20.14upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

10 files changed, 2688 insertions, 0 deletions

diff --git a/src/math/bits/bits.go b/src/math/bits/bits.go
new file mode 100644
index 0000000..c1c7b79
--- /dev/null
+++ b/src/math/bits/bits.go
@@ -0,0 +1,599 @@
+// 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.
+
+//go:generate go run make_tables.go
+
+// Package bits implements bit counting and manipulation
+// functions for the predeclared unsigned integer types.
+//
+// Functions in this package may be implemented directly by
+// the compiler, for better performance. For those functions
+// the code in this package will not be used. Which
+// functions are implemented by the compiler depends on the
+// architecture and the Go release.
+package bits
+
+const uintSize = 32 << (^uint(0) >> 63) // 32 or 64
+
+// UintSize is the size of a uint in bits.
+const UintSize = uintSize
+
+// --- LeadingZeros ---
+
+// LeadingZeros returns the number of leading zero bits in x; the result is UintSize for x == 0.
+func LeadingZeros(x uint) int { return UintSize - Len(x) }
+
+// LeadingZeros8 returns the number of leading zero bits in x; the result is 8 for x == 0.
+func LeadingZeros8(x uint8) int { return 8 - Len8(x) }
+
+// LeadingZeros16 returns the number of leading zero bits in x; the result is 16 for x == 0.
+func LeadingZeros16(x uint16) int { return 16 - Len16(x) }
+
+// LeadingZeros32 returns the number of leading zero bits in x; the result is 32 for x == 0.
+func LeadingZeros32(x uint32) int { return 32 - Len32(x) }
+
+// LeadingZeros64 returns the number of leading zero bits in x; the result is 64 for x == 0.
+func LeadingZeros64(x uint64) int { return 64 - Len64(x) }
+
+// --- TrailingZeros ---
+
+// 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,
+}
+
+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,
+}
+
+// TrailingZeros returns the number of trailing zero bits in x; the result is UintSize for x == 0.
+func TrailingZeros(x uint) int {
+	if UintSize == 32 {
+		return TrailingZeros32(uint32(x))
+	}
+	return TrailingZeros64(uint64(x))
+}
+
+// TrailingZeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
+func TrailingZeros8(x uint8) int {
+	return int(ntz8tab[x])
+}
+
+// TrailingZeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0.
+func TrailingZeros16(x uint16) int {
+	if x == 0 {
+		return 16
+	}
+	// see comment in TrailingZeros64
+	return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)])
+}
+
+// TrailingZeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0.
+func TrailingZeros32(x uint32) int {
+	if x == 0 {
+		return 32
+	}
+	// see comment in TrailingZeros64
+	return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)])
+}
+
+// TrailingZeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0.
+func TrailingZeros64(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)])
+}
+
+// --- OnesCount ---
+
+const m0 = 0x5555555555555555 // 01010101 ...
+const m1 = 0x3333333333333333 // 00110011 ...
+const m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ...
+const m3 = 0x00ff00ff00ff00ff // etc.
+const m4 = 0x0000ffff0000ffff
+
+// OnesCount returns the number of one bits ("population count") in x.
+func OnesCount(x uint) int {
+	if UintSize == 32 {
+		return OnesCount32(uint32(x))
+	}
+	return OnesCount64(uint64(x))
+}
+
+// OnesCount8 returns the number of one bits ("population count") in x.
+func OnesCount8(x uint8) int {
+	return int(pop8tab[x])
+}
+
+// OnesCount16 returns the number of one bits ("population count") in x.
+func OnesCount16(x uint16) int {
+	return int(pop8tab[x>>8] + pop8tab[x&0xff])
+}
+
+// OnesCount32 returns the number of one bits ("population count") in x.
+func OnesCount32(x uint32) int {
+	return int(pop8tab[x>>24] + pop8tab[x>>16&0xff] + pop8tab[x>>8&0xff] + pop8tab[x&0xff])
+}
+
+// OnesCount64 returns the number of one bits ("population count") in x.
+func OnesCount64(x uint64) int {
+	// Implementation: Parallel summing of adjacent bits.
+	// See "Hacker's Delight", Chap. 5: Counting Bits.
+	// The following pattern shows the general approach:
+	//
+	//   x = x>>1&(m0&m) + x&(m0&m)
+	//   x = x>>2&(m1&m) + x&(m1&m)
+	//   x = x>>4&(m2&m) + x&(m2&m)
+	//   x = x>>8&(m3&m) + x&(m3&m)
+	//   x = x>>16&(m4&m) + x&(m4&m)
+	//   x = x>>32&(m5&m) + x&(m5&m)
+	//   return int(x)
+	//
+	// Masking (& operations) can be left away when there's no
+	// danger that a field's sum will carry over into the next
+	// field: Since the result cannot be > 64, 8 bits is enough
+	// and we can ignore the masks for the shifts by 8 and up.
+	// Per "Hacker's Delight", the first line can be simplified
+	// more, but it saves at best one instruction, so we leave
+	// it alone for clarity.
+	const m = 1<<64 - 1
+	x = x>>1&(m0&m) + x&(m0&m)
+	x = x>>2&(m1&m) + x&(m1&m)
+	x = (x>>4 + x) & (m2 & m)
+	x += x >> 8
+	x += x >> 16
+	x += x >> 32
+	return int(x) & (1<<7 - 1)
+}
+
+// --- RotateLeft ---
+
+// RotateLeft returns the value of x rotated left by (k mod UintSize) bits.
+// To rotate x right by k bits, call RotateLeft(x, -k).
+//
+// This function's execution time does not depend on the inputs.
+func RotateLeft(x uint, k int) uint {
+	if UintSize == 32 {
+		return uint(RotateLeft32(uint32(x), k))
+	}
+	return uint(RotateLeft64(uint64(x), k))
+}
+
+// RotateLeft8 returns the value of x rotated left by (k mod 8) bits.
+// To rotate x right by k bits, call RotateLeft8(x, -k).
+//
+// This function's execution time does not depend on the inputs.
+func RotateLeft8(x uint8, k int) uint8 {
+	const n = 8
+	s := uint(k) & (n - 1)
+	return x<<s | x>>(n-s)
+}
+
+// RotateLeft16 returns the value of x rotated left by (k mod 16) bits.
+// To rotate x right by k bits, call RotateLeft16(x, -k).
+//
+// This function's execution time does not depend on the inputs.
+func RotateLeft16(x uint16, k int) uint16 {
+	const n = 16
+	s := uint(k) & (n - 1)
+	return x<<s | x>>(n-s)
+}
+
+// RotateLeft32 returns the value of x rotated left by (k mod 32) bits.
+// To rotate x right by k bits, call RotateLeft32(x, -k).
+//
+// This function's execution time does not depend on the inputs.
+func RotateLeft32(x uint32, k int) uint32 {
+	const n = 32
+	s := uint(k) & (n - 1)
+	return x<<s | x>>(n-s)
+}
+
+// RotateLeft64 returns the value of x rotated left by (k mod 64) bits.
+// To rotate x right by k bits, call RotateLeft64(x, -k).
+//
+// This function's execution time does not depend on the inputs.
+func RotateLeft64(x uint64, k int) uint64 {
+	const n = 64
+	s := uint(k) & (n - 1)
+	return x<<s | x>>(n-s)
+}
+
+// --- Reverse ---
+
+// Reverse returns the value of x with its bits in reversed order.
+func Reverse(x uint) uint {
+	if UintSize == 32 {
+		return uint(Reverse32(uint32(x)))
+	}
+	return uint(Reverse64(uint64(x)))
+}
+
+// Reverse8 returns the value of x with its bits in reversed order.
+func Reverse8(x uint8) uint8 {
+	return rev8tab[x]
+}
+
+// Reverse16 returns the value of x with its bits in reversed order.
+func Reverse16(x uint16) uint16 {
+	return uint16(rev8tab[x>>8]) | uint16(rev8tab[x&0xff])<<8
+}
+
+// Reverse32 returns the value of x with its bits in reversed order.
+func Reverse32(x uint32) uint32 {
+	const m = 1<<32 - 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 ReverseBytes32(x)
+}
+
+// Reverse64 returns the value of x with its bits in reversed order.
+func Reverse64(x uint64) uint64 {
+	const m = 1<<64 - 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 ReverseBytes64(x)
+}
+
+// --- ReverseBytes ---
+
+// ReverseBytes returns the value of x with its bytes in reversed order.
+//
+// This function's execution time does not depend on the inputs.
+func ReverseBytes(x uint) uint {
+	if UintSize == 32 {
+		return uint(ReverseBytes32(uint32(x)))
+	}
+	return uint(ReverseBytes64(uint64(x)))
+}
+
+// ReverseBytes16 returns the value of x with its bytes in reversed order.
+//
+// This function's execution time does not depend on the inputs.
+func ReverseBytes16(x uint16) uint16 {
+	return x>>8 | x<<8
+}
+
+// ReverseBytes32 returns the value of x with its bytes in reversed order.
+//
+// This function's execution time does not depend on the inputs.
+func ReverseBytes32(x uint32) uint32 {
+	const m = 1<<32 - 1
+	x = x>>8&(m3&m) | x&(m3&m)<<8
+	return x>>16 | x<<16
+}
+
+// ReverseBytes64 returns the value of x with its bytes in reversed order.
+//
+// This function's execution time does not depend on the inputs.
+func ReverseBytes64(x uint64) uint64 {
+	const m = 1<<64 - 1
+	x = x>>8&(m3&m) | x&(m3&m)<<8
+	x = x>>16&(m4&m) | x&(m4&m)<<16
+	return x>>32 | x<<32
+}
+
+// --- Len ---
+
+// Len returns the minimum number of bits required to represent x; the result is 0 for x == 0.
+func Len(x uint) int {
+	if UintSize == 32 {
+		return Len32(uint32(x))
+	}
+	return Len64(uint64(x))
+}
+
+// Len8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
+func Len8(x uint8) int {
+	return int(len8tab[x])
+}
+
+// Len16 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
+func Len16(x uint16) (n int) {
+	if x >= 1<<8 {
+		x >>= 8
+		n = 8
+	}
+	return n + int(len8tab[x])
+}
+
+// Len32 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
+func Len32(x uint32) (n int) {
+	if x >= 1<<16 {
+		x >>= 16
+		n = 16
+	}
+	if x >= 1<<8 {
+		x >>= 8
+		n += 8
+	}
+	return n + int(len8tab[x])
+}
+
+// Len64 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
+func Len64(x uint64) (n int) {
+	if x >= 1<<32 {
+		x >>= 32
+		n = 32
+	}
+	if x >= 1<<16 {
+		x >>= 16
+		n += 16
+	}
+	if x >= 1<<8 {
+		x >>= 8
+		n += 8
+	}
+	return n + int(len8tab[x])
+}
+
+// --- Add with carry ---
+
+// Add returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+func Add(x, y, carry uint) (sum, carryOut uint) {
+	if UintSize == 32 {
+		s32, c32 := Add32(uint32(x), uint32(y), uint32(carry))
+		return uint(s32), uint(c32)
+	}
+	s64, c64 := Add64(uint64(x), uint64(y), uint64(carry))
+	return uint(s64), uint(c64)
+}
+
+// Add32 returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+func Add32(x, y, carry uint32) (sum, carryOut uint32) {
+	sum64 := uint64(x) + uint64(y) + uint64(carry)
+	sum = uint32(sum64)
+	carryOut = uint32(sum64 >> 32)
+	return
+}
+
+// Add64 returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+func Add64(x, y, carry uint64) (sum, carryOut uint64) {
+	sum = x + y + carry
+	// The sum will overflow if both top bits are set (x & y) or if one of them
+	// is (x | y), and a carry from the lower place happened. If such a carry
+	// happens, the top bit will be 1 + 0 + 1 = 0 (&^ sum).
+	carryOut = ((x & y) | ((x | y) &^ sum)) >> 63
+	return
+}
+
+// --- Subtract with borrow ---
+
+// Sub returns the difference of x, y and borrow: diff = x - y - borrow.
+// The borrow input must be 0 or 1; otherwise the behavior is undefined.
+// The borrowOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+func Sub(x, y, borrow uint) (diff, borrowOut uint) {
+	if UintSize == 32 {
+		d32, b32 := Sub32(uint32(x), uint32(y), uint32(borrow))
+		return uint(d32), uint(b32)
+	}
+	d64, b64 := Sub64(uint64(x), uint64(y), uint64(borrow))
+	return uint(d64), uint(b64)
+}
+
+// Sub32 returns the difference of x, y and borrow, diff = x - y - borrow.
+// The borrow input must be 0 or 1; otherwise the behavior is undefined.
+// The borrowOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+func Sub32(x, y, borrow uint32) (diff, borrowOut uint32) {
+	diff = x - y - borrow
+	// The difference will underflow if the top bit of x is not set and the top
+	// bit of y is set (^x & y) or if they are the same (^(x ^ y)) and a borrow
+	// from the lower place happens. If that borrow happens, the result will be
+	// 1 - 1 - 1 = 0 - 0 - 1 = 1 (& diff).
+	borrowOut = ((^x & y) | (^(x ^ y) & diff)) >> 31
+	return
+}
+
+// Sub64 returns the difference of x, y and borrow: diff = x - y - borrow.
+// The borrow input must be 0 or 1; otherwise the behavior is undefined.
+// The borrowOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+func Sub64(x, y, borrow uint64) (diff, borrowOut uint64) {
+	diff = x - y - borrow
+	// See Sub32 for the bit logic.
+	borrowOut = ((^x & y) | (^(x ^ y) & diff)) >> 63
+	return
+}
+
+// --- Full-width multiply ---
+
+// Mul returns the full-width product of x and y: (hi, lo) = x * y
+// with the product bits' upper half returned in hi and the lower
+// half returned in lo.
+//
+// This function's execution time does not depend on the inputs.
+func Mul(x, y uint) (hi, lo uint) {
+	if UintSize == 32 {
+		h, l := Mul32(uint32(x), uint32(y))
+		return uint(h), uint(l)
+	}
+	h, l := Mul64(uint64(x), uint64(y))
+	return uint(h), uint(l)
+}
+
+// Mul32 returns the 64-bit product of x and y: (hi, lo) = x * y
+// with the product bits' upper half returned in hi and the lower
+// half returned in lo.
+//
+// This function's execution time does not depend on the inputs.
+func Mul32(x, y uint32) (hi, lo uint32) {
+	tmp := uint64(x) * uint64(y)
+	hi, lo = uint32(tmp>>32), uint32(tmp)
+	return
+}
+
+// Mul64 returns the 128-bit product of x and y: (hi, lo) = x * y
+// with the product bits' upper half returned in hi and the lower
+// half returned in lo.
+//
+// This function's execution time does not depend on the inputs.
+func Mul64(x, y uint64) (hi, lo uint64) {
+	const mask32 = 1<<32 - 1
+	x0 := x & mask32
+	x1 := x >> 32
+	y0 := y & mask32
+	y1 := y >> 32
+	w0 := x0 * y0
+	t := x1*y0 + w0>>32
+	w1 := t & mask32
+	w2 := t >> 32
+	w1 += x0 * y1
+	hi = x1*y1 + w2 + w1>>32
+	lo = x * y
+	return
+}
+
+// --- Full-width divide ---
+
+// Div returns the quotient and remainder of (hi, lo) divided by y:
+// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
+// half in parameter hi and the lower half in parameter lo.
+// Div panics for y == 0 (division by zero) or y <= hi (quotient overflow).
+func Div(hi, lo, y uint) (quo, rem uint) {
+	if UintSize == 32 {
+		q, r := Div32(uint32(hi), uint32(lo), uint32(y))
+		return uint(q), uint(r)
+	}
+	q, r := Div64(uint64(hi), uint64(lo), uint64(y))
+	return uint(q), uint(r)
+}
+
+// Div32 returns the quotient and remainder of (hi, lo) divided by y:
+// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
+// half in parameter hi and the lower half in parameter lo.
+// Div32 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
+func Div32(hi, lo, y uint32) (quo, rem uint32) {
+	if y != 0 && y <= hi {
+		panic(overflowError)
+	}
+	z := uint64(hi)<<32 | uint64(lo)
+	quo, rem = uint32(z/uint64(y)), uint32(z%uint64(y))
+	return
+}
+
+// Div64 returns the quotient and remainder of (hi, lo) divided by y:
+// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
+// half in parameter hi and the lower half in parameter lo.
+// Div64 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
+func Div64(hi, lo, y uint64) (quo, rem uint64) {
+	if y == 0 {
+		panic(divideError)
+	}
+	if y <= hi {
+		panic(overflowError)
+	}
+
+	// If high part is zero, we can directly return the results.
+	if hi == 0 {
+		return lo / y, lo % y
+	}
+
+	s := uint(LeadingZeros64(y))
+	y <<= s
+
+	const (
+		two32  = 1 << 32
+		mask32 = two32 - 1
+	)
+	yn1 := y >> 32
+	yn0 := y & mask32
+	un32 := hi<<s | lo>>(64-s)
+	un10 := lo << s
+	un1 := un10 >> 32
+	un0 := un10 & mask32
+	q1 := un32 / yn1
+	rhat := un32 - q1*yn1
+
+	for q1 >= two32 || q1*yn0 > two32*rhat+un1 {
+		q1--
+		rhat += yn1
+		if rhat >= two32 {
+			break
+		}
+	}
+
+	un21 := un32*two32 + un1 - q1*y
+	q0 := un21 / yn1
+	rhat = un21 - q0*yn1
+
+	for q0 >= two32 || q0*yn0 > two32*rhat+un0 {
+		q0--
+		rhat += yn1
+		if rhat >= two32 {
+			break
+		}
+	}
+
+	return q1*two32 + q0, (un21*two32 + un0 - q0*y) >> s
+}
+
+// Rem returns the remainder of (hi, lo) divided by y. Rem panics for
+// y == 0 (division by zero) but, unlike Div, it doesn't panic on a
+// quotient overflow.
+func Rem(hi, lo, y uint) uint {
+	if UintSize == 32 {
+		return uint(Rem32(uint32(hi), uint32(lo), uint32(y)))
+	}
+	return uint(Rem64(uint64(hi), uint64(lo), uint64(y)))
+}
+
+// Rem32 returns the remainder of (hi, lo) divided by y. Rem32 panics
+// for y == 0 (division by zero) but, unlike Div32, it doesn't panic
+// on a quotient overflow.
+func Rem32(hi, lo, y uint32) uint32 {
+	return uint32((uint64(hi)<<32 | uint64(lo)) % uint64(y))
+}
+
+// Rem64 returns the remainder of (hi, lo) divided by y. Rem64 panics
+// for y == 0 (division by zero) but, unlike Div64, it doesn't panic
+// on a quotient overflow.
+func Rem64(hi, lo, y uint64) uint64 {
+	// We scale down hi so that hi < y, then use Div64 to compute the
+	// rem with the guarantee that it won't panic on quotient overflow.
+	// Given that
+	//   hi ≡ hi%y    (mod y)
+	// we have
+	//   hi<<64 + lo ≡ (hi%y)<<64 + lo    (mod y)
+	_, rem := Div64(hi%y, lo, y)
+	return rem
+}
diff --git a/src/math/bits/bits_errors.go b/src/math/bits/bits_errors.go
new file mode 100644
index 0000000..61cb5c9
--- /dev/null
+++ b/src/math/bits/bits_errors.go
@@ -0,0 +1,16 @@
+// Copyright 2019 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.
+
+//go:build !compiler_bootstrap
+// +build !compiler_bootstrap
+
+package bits
+
+import _ "unsafe"
+
+//go:linkname overflowError runtime.overflowError
+var overflowError error
+
+//go:linkname divideError runtime.divideError
+var divideError error
diff --git a/src/math/bits/bits_errors_bootstrap.go b/src/math/bits/bits_errors_bootstrap.go
new file mode 100644
index 0000000..4d610d3
--- /dev/null
+++ b/src/math/bits/bits_errors_bootstrap.go
@@ -0,0 +1,23 @@
+// Copyright 2019 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.
+
+//go:build compiler_bootstrap
+// +build compiler_bootstrap
+
+// This version used only for bootstrap (on this path we want
+// to avoid use of go:linkname as applied to variables).
+
+package bits
+
+type errorString string
+
+func (e errorString) RuntimeError() {}
+
+func (e errorString) Error() string {
+	return "runtime error: " + string(e)
+}
+
+var overflowError = error(errorString("integer overflow"))
+
+var divideError = error(errorString("integer divide by zero"))
diff --git a/src/math/bits/bits_tables.go b/src/math/bits/bits_tables.go
new file mode 100644
index 0000000..f869b8d
--- /dev/null
+++ b/src/math/bits/bits_tables.go
@@ -0,0 +1,79 @@
+// 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
+
+const ntz8tab = "" +
+	"\x08\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x05\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x06\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x05\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x07\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x05\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x06\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x05\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00" +
+	"\x04\x00\x01\x00\x02\x00\x01\x00\x03\x00\x01\x00\x02\x00\x01\x00"
+
+const pop8tab = "" +
+	"\x00\x01\x01\x02\x01\x02\x02\x03\x01\x02\x02\x03\x02\x03\x03\x04" +
+	"\x01\x02\x02\x03\x02\x03\x03\x04\x02\x03\x03\x04\x03\x04\x04\x05" +
+	"\x01\x02\x02\x03\x02\x03\x03\x04\x02\x03\x03\x04\x03\x04\x04\x05" +
+	"\x02\x03\x03\x04\x03\x04\x04\x05\x03\x04\x04\x05\x04\x05\x05\x06" +
+	"\x01\x02\x02\x03\x02\x03\x03\x04\x02\x03\x03\x04\x03\x04\x04\x05" +
+	"\x02\x03\x03\x04\x03\x04\x04\x05\x03\x04\x04\x05\x04\x05\x05\x06" +
+	"\x02\x03\x03\x04\x03\x04\x04\x05\x03\x04\x04\x05\x04\x05\x05\x06" +
+	"\x03\x04\x04\x05\x04\x05\x05\x06\x04\x05\x05\x06\x05\x06\x06\x07" +
+	"\x01\x02\x02\x03\x02\x03\x03\x04\x02\x03\x03\x04\x03\x04\x04\x05" +
+	"\x02\x03\x03\x04\x03\x04\x04\x05\x03\x04\x04\x05\x04\x05\x05\x06" +
+	"\x02\x03\x03\x04\x03\x04\x04\x05\x03\x04\x04\x05\x04\x05\x05\x06" +
+	"\x03\x04\x04\x05\x04\x05\x05\x06\x04\x05\x05\x06\x05\x06\x06\x07" +
+	"\x02\x03\x03\x04\x03\x04\x04\x05\x03\x04\x04\x05\x04\x05\x05\x06" +
+	"\x03\x04\x04\x05\x04\x05\x05\x06\x04\x05\x05\x06\x05\x06\x06\x07" +
+	"\x03\x04\x04\x05\x04\x05\x05\x06\x04\x05\x05\x06\x05\x06\x06\x07" +
+	"\x04\x05\x05\x06\x05\x06\x06\x07\x05\x06\x06\x07\x06\x07\x07\x08"
+
+const rev8tab = "" +
+	"\x00\x80\x40\xc0\x20\xa0\x60\xe0\x10\x90\x50\xd0\x30\xb0\x70\xf0" +
+	"\x08\x88\x48\xc8\x28\xa8\x68\xe8\x18\x98\x58\xd8\x38\xb8\x78\xf8" +
+	"\x04\x84\x44\xc4\x24\xa4\x64\xe4\x14\x94\x54\xd4\x34\xb4\x74\xf4" +
+	"\x0c\x8c\x4c\xcc\x2c\xac\x6c\xec\x1c\x9c\x5c\xdc\x3c\xbc\x7c\xfc" +
+	"\x02\x82\x42\xc2\x22\xa2\x62\xe2\x12\x92\x52\xd2\x32\xb2\x72\xf2" +
+	"\x0a\x8a\x4a\xca\x2a\xaa\x6a\xea\x1a\x9a\x5a\xda\x3a\xba\x7a\xfa" +
+	"\x06\x86\x46\xc6\x26\xa6\x66\xe6\x16\x96\x56\xd6\x36\xb6\x76\xf6" +
+	"\x0e\x8e\x4e\xce\x2e\xae\x6e\xee\x1e\x9e\x5e\xde\x3e\xbe\x7e\xfe" +
+	"\x01\x81\x41\xc1\x21\xa1\x61\xe1\x11\x91\x51\xd1\x31\xb1\x71\xf1" +
+	"\x09\x89\x49\xc9\x29\xa9\x69\xe9\x19\x99\x59\xd9\x39\xb9\x79\xf9" +
+	"\x05\x85\x45\xc5\x25\xa5\x65\xe5\x15\x95\x55\xd5\x35\xb5\x75\xf5" +
+	"\x0d\x8d\x4d\xcd\x2d\xad\x6d\xed\x1d\x9d\x5d\xdd\x3d\xbd\x7d\xfd" +
+	"\x03\x83\x43\xc3\x23\xa3\x63\xe3\x13\x93\x53\xd3\x33\xb3\x73\xf3" +
+	"\x0b\x8b\x4b\xcb\x2b\xab\x6b\xeb\x1b\x9b\x5b\xdb\x3b\xbb\x7b\xfb" +
+	"\x07\x87\x47\xc7\x27\xa7\x67\xe7\x17\x97\x57\xd7\x37\xb7\x77\xf7" +
+	"\x0f\x8f\x4f\xcf\x2f\xaf\x6f\xef\x1f\x9f\x5f\xdf\x3f\xbf\x7f\xff"
+
+const len8tab = "" +
+	"\x00\x01\x02\x02\x03\x03\x03\x03\x04\x04\x04\x04\x04\x04\x04\x04" +
+	"\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05\x05" +
+	"\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06" +
+	"\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06\x06" +
+	"\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07" +
+	"\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07" +
+	"\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07" +
+	"\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07\x07" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08" +
+	"\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08\x08"
diff --git a/src/math/bits/bits_test.go b/src/math/bits/bits_test.go
new file mode 100644
index 0000000..23b4539
--- /dev/null
+++ b/src/math/bits/bits_test.go
@@ -0,0 +1,1347 @@
+// 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_test
+
+import (
+	. "math/bits"
+	"runtime"
+	"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)
+					}
+				}
+			}
+		}
+	}
+}
+
+// Exported (global) variable serving as input for some
+// of the benchmarks to ensure side-effect free calls
+// are not optimized away.
+var Input uint64 = DeBruijn64
+
+// Exported (global) variable to store function results
+// during benchmarking to ensure side-effect free calls
+// are not optimized away.
+var Output int
+
+func BenchmarkLeadingZeros(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += LeadingZeros(uint(Input) >> (uint(i) % UintSize))
+	}
+	Output = s
+}
+
+func BenchmarkLeadingZeros8(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += LeadingZeros8(uint8(Input) >> (uint(i) % 8))
+	}
+	Output = s
+}
+
+func BenchmarkLeadingZeros16(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += LeadingZeros16(uint16(Input) >> (uint(i) % 16))
+	}
+	Output = s
+}
+
+func BenchmarkLeadingZeros32(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += LeadingZeros32(uint32(Input) >> (uint(i) % 32))
+	}
+	Output = s
+}
+
+func BenchmarkLeadingZeros64(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += LeadingZeros64(uint64(Input) >> (uint(i) % 64))
+	}
+	Output = s
+}
+
+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 BenchmarkTrailingZeros(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += TrailingZeros(uint(Input) << (uint(i) % UintSize))
+	}
+	Output = s
+}
+
+func BenchmarkTrailingZeros8(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += TrailingZeros8(uint8(Input) << (uint(i) % 8))
+	}
+	Output = s
+}
+
+func BenchmarkTrailingZeros16(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += TrailingZeros16(uint16(Input) << (uint(i) % 16))
+	}
+	Output = s
+}
+
+func BenchmarkTrailingZeros32(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += TrailingZeros32(uint32(Input) << (uint(i) % 32))
+	}
+	Output = s
+}
+
+func BenchmarkTrailingZeros64(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += TrailingZeros64(uint64(Input) << (uint(i) % 64))
+	}
+	Output = s
+}
+
+func TestOnesCount(t *testing.T) {
+	var x uint64
+	for i := 0; i <= 64; i++ {
+		testOnesCount(t, x, i)
+		x = x<<1 | 1
+	}
+
+	for i := 64; i >= 0; i-- {
+		testOnesCount(t, x, i)
+		x = x << 1
+	}
+
+	for i := 0; i < 256; i++ {
+		for k := 0; k < 64-8; k++ {
+			testOnesCount(t, uint64(i)<<uint(k), tab[i].pop)
+		}
+	}
+}
+
+func testOnesCount(t *testing.T, x uint64, want int) {
+	if x <= 1<<8-1 {
+		got := OnesCount8(uint8(x))
+		if got != want {
+			t.Fatalf("OnesCount8(%#02x) == %d; want %d", uint8(x), got, want)
+		}
+	}
+
+	if x <= 1<<16-1 {
+		got := OnesCount16(uint16(x))
+		if got != want {
+			t.Fatalf("OnesCount16(%#04x) == %d; want %d", uint16(x), got, want)
+		}
+	}
+
+	if x <= 1<<32-1 {
+		got := OnesCount32(uint32(x))
+		if got != want {
+			t.Fatalf("OnesCount32(%#08x) == %d; want %d", uint32(x), got, want)
+		}
+		if UintSize == 32 {
+			got = OnesCount(uint(x))
+			if got != want {
+				t.Fatalf("OnesCount(%#08x) == %d; want %d", uint32(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 BenchmarkOnesCount(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += OnesCount(uint(Input))
+	}
+	Output = s
+}
+
+func BenchmarkOnesCount8(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += OnesCount8(uint8(Input))
+	}
+	Output = s
+}
+
+func BenchmarkOnesCount16(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += OnesCount16(uint16(Input))
+	}
+	Output = s
+}
+
+func BenchmarkOnesCount32(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += OnesCount32(uint32(Input))
+	}
+	Output = s
+}
+
+func BenchmarkOnesCount64(b *testing.B) {
+	var s int
+	for i := 0; i < b.N; i++ {
+		s += OnesCount64(uint64(Input))
+	}
+	Output = s
+}
+
+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)
+		}
+		got8 = RotateLeft8(want8, -int(k))
+		if got8 != x8 {
+			t.Fatalf("RotateLeft8(%#02x, -%d) == %#02x; want %#02x", want8, k, got8, x8)
+		}
+
+		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)
+		}
+		got16 = RotateLeft16(want16, -int(k))
+		if got16 != x16 {
+			t.Fatalf("RotateLeft16(%#04x, -%d) == %#04x; want %#04x", want16, k, got16, x16)
+		}
+
+		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)
+		}
+		got32 = RotateLeft32(want32, -int(k))
+		if got32 != x32 {
+			t.Fatalf("RotateLeft32(%#08x, -%d) == %#08x; want %#08x", want32, k, got32, x32)
+		}
+		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)
+			}
+			got = RotateLeft(want, -int(k))
+			if got != x {
+				t.Fatalf("RotateLeft(%#08x, -%d) == %#08x; want %#08x", want, k, got, x)
+			}
+		}
+
+		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)
+		}
+		got64 = RotateLeft64(want64, -int(k))
+		if got64 != x64 {
+			t.Fatalf("RotateLeft64(%#016x, -%d) == %#016x; want %#016x", want64, k, got64, x64)
+		}
+		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)
+			}
+			got = RotateLeft(want, -int(k))
+			if got != x {
+				t.Fatalf("RotateLeft(%#08x, -%d) == %#08x; want %#08x", want, k, got, x)
+			}
+		}
+	}
+}
+
+func BenchmarkRotateLeft(b *testing.B) {
+	var s uint
+	for i := 0; i < b.N; i++ {
+		s += RotateLeft(uint(Input), i)
+	}
+	Output = int(s)
+}
+
+func BenchmarkRotateLeft8(b *testing.B) {
+	var s uint8
+	for i := 0; i < b.N; i++ {
+		s += RotateLeft8(uint8(Input), i)
+	}
+	Output = int(s)
+}
+
+func BenchmarkRotateLeft16(b *testing.B) {
+	var s uint16
+	for i := 0; i < b.N; i++ {
+		s += RotateLeft16(uint16(Input), i)
+	}
+	Output = int(s)
+}
+
+func BenchmarkRotateLeft32(b *testing.B) {
+	var s uint32
+	for i := 0; i < b.N; i++ {
+		s += RotateLeft32(uint32(Input), i)
+	}
+	Output = int(s)
+}
+
+func BenchmarkRotateLeft64(b *testing.B) {
+	var s uint64
+	for i := 0; i < b.N; i++ {
+		s += RotateLeft64(uint64(Input), i)
+	}
+	Output = int(s)
+}
+
+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 BenchmarkReverse(b *testing.B) {
+	var s uint
+	for i := 0; i < b.N; i++ {
+		s += Reverse(uint(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverse8(b *testing.B) {
+	var s uint8
+	for i := 0; i < b.N; i++ {
+		s += Reverse8(uint8(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverse16(b *testing.B) {
+	var s uint16
+	for i := 0; i < b.N; i++ {
+		s += Reverse16(uint16(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverse32(b *testing.B) {
+	var s uint32
+	for i := 0; i < b.N; i++ {
+		s += Reverse32(uint32(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverse64(b *testing.B) {
+	var s uint64
+	for i := 0; i < b.N; i++ {
+		s += Reverse64(uint64(i))
+	}
+	Output = int(s)
+}
+
+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 BenchmarkReverseBytes(b *testing.B) {
+	var s uint
+	for i := 0; i < b.N; i++ {
+		s += ReverseBytes(uint(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverseBytes16(b *testing.B) {
+	var s uint16
+	for i := 0; i < b.N; i++ {
+		s += ReverseBytes16(uint16(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverseBytes32(b *testing.B) {
+	var s uint32
+	for i := 0; i < b.N; i++ {
+		s += ReverseBytes32(uint32(i))
+	}
+	Output = int(s)
+}
+
+func BenchmarkReverseBytes64(b *testing.B) {
+	var s uint64
+	for i := 0; i < b.N; i++ {
+		s += ReverseBytes64(uint64(i))
+	}
+	Output = int(s)
+}
+
+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)
+					}
+				}
+			}
+		}
+	}
+}
+
+const (
+	_M   = 1<<UintSize - 1
+	_M32 = 1<<32 - 1
+	_M64 = 1<<64 - 1
+)
+
+func TestAddSubUint(t *testing.T) {
+	test := func(msg string, f func(x, y, c uint) (z, cout uint), x, y, c, z, cout uint) {
+		z1, cout1 := f(x, y, c)
+		if z1 != z || cout1 != cout {
+			t.Errorf("%s: got z:cout = %#x:%#x; want %#x:%#x", msg, z1, cout1, z, cout)
+		}
+	}
+	for _, a := range []struct{ x, y, c, z, cout uint }{
+		{0, 0, 0, 0, 0},
+		{0, 1, 0, 1, 0},
+		{0, 0, 1, 1, 0},
+		{0, 1, 1, 2, 0},
+		{12345, 67890, 0, 80235, 0},
+		{12345, 67890, 1, 80236, 0},
+		{_M, 1, 0, 0, 1},
+		{_M, 0, 1, 0, 1},
+		{_M, 1, 1, 1, 1},
+		{_M, _M, 0, _M - 1, 1},
+		{_M, _M, 1, _M, 1},
+	} {
+		test("Add", Add, a.x, a.y, a.c, a.z, a.cout)
+		test("Add symmetric", Add, a.y, a.x, a.c, a.z, a.cout)
+		test("Sub", Sub, a.z, a.x, a.c, a.y, a.cout)
+		test("Sub symmetric", Sub, a.z, a.y, a.c, a.x, a.cout)
+		// The above code can't test intrinsic implementation, because the passed function is not called directly.
+		// The following code uses a closure to test the intrinsic version in case the function is intrinsified.
+		test("Add intrinsic", func(x, y, c uint) (uint, uint) { return Add(x, y, c) }, a.x, a.y, a.c, a.z, a.cout)
+		test("Add intrinsic symmetric", func(x, y, c uint) (uint, uint) { return Add(x, y, c) }, a.y, a.x, a.c, a.z, a.cout)
+		test("Sub intrinsic", func(x, y, c uint) (uint, uint) { return Sub(x, y, c) }, a.z, a.x, a.c, a.y, a.cout)
+		test("Sub intrinsic symmetric", func(x, y, c uint) (uint, uint) { return Sub(x, y, c) }, a.z, a.y, a.c, a.x, a.cout)
+
+	}
+}
+
+func TestAddSubUint32(t *testing.T) {
+	test := func(msg string, f func(x, y, c uint32) (z, cout uint32), x, y, c, z, cout uint32) {
+		z1, cout1 := f(x, y, c)
+		if z1 != z || cout1 != cout {
+			t.Errorf("%s: got z:cout = %#x:%#x; want %#x:%#x", msg, z1, cout1, z, cout)
+		}
+	}
+	for _, a := range []struct{ x, y, c, z, cout uint32 }{
+		{0, 0, 0, 0, 0},
+		{0, 1, 0, 1, 0},
+		{0, 0, 1, 1, 0},
+		{0, 1, 1, 2, 0},
+		{12345, 67890, 0, 80235, 0},
+		{12345, 67890, 1, 80236, 0},
+		{_M32, 1, 0, 0, 1},
+		{_M32, 0, 1, 0, 1},
+		{_M32, 1, 1, 1, 1},
+		{_M32, _M32, 0, _M32 - 1, 1},
+		{_M32, _M32, 1, _M32, 1},
+	} {
+		test("Add32", Add32, a.x, a.y, a.c, a.z, a.cout)
+		test("Add32 symmetric", Add32, a.y, a.x, a.c, a.z, a.cout)
+		test("Sub32", Sub32, a.z, a.x, a.c, a.y, a.cout)
+		test("Sub32 symmetric", Sub32, a.z, a.y, a.c, a.x, a.cout)
+	}
+}
+
+func TestAddSubUint64(t *testing.T) {
+	test := func(msg string, f func(x, y, c uint64) (z, cout uint64), x, y, c, z, cout uint64) {
+		z1, cout1 := f(x, y, c)
+		if z1 != z || cout1 != cout {
+			t.Errorf("%s: got z:cout = %#x:%#x; want %#x:%#x", msg, z1, cout1, z, cout)
+		}
+	}
+	for _, a := range []struct{ x, y, c, z, cout uint64 }{
+		{0, 0, 0, 0, 0},
+		{0, 1, 0, 1, 0},
+		{0, 0, 1, 1, 0},
+		{0, 1, 1, 2, 0},
+		{12345, 67890, 0, 80235, 0},
+		{12345, 67890, 1, 80236, 0},
+		{_M64, 1, 0, 0, 1},
+		{_M64, 0, 1, 0, 1},
+		{_M64, 1, 1, 1, 1},
+		{_M64, _M64, 0, _M64 - 1, 1},
+		{_M64, _M64, 1, _M64, 1},
+	} {
+		test("Add64", Add64, a.x, a.y, a.c, a.z, a.cout)
+		test("Add64 symmetric", Add64, a.y, a.x, a.c, a.z, a.cout)
+		test("Sub64", Sub64, a.z, a.x, a.c, a.y, a.cout)
+		test("Sub64 symmetric", Sub64, a.z, a.y, a.c, a.x, a.cout)
+		// The above code can't test intrinsic implementation, because the passed function is not called directly.
+		// The following code uses a closure to test the intrinsic version in case the function is intrinsified.
+		test("Add64 intrinsic", func(x, y, c uint64) (uint64, uint64) { return Add64(x, y, c) }, a.x, a.y, a.c, a.z, a.cout)
+		test("Add64 intrinsic symmetric", func(x, y, c uint64) (uint64, uint64) { return Add64(x, y, c) }, a.y, a.x, a.c, a.z, a.cout)
+		test("Sub64 intrinsic", func(x, y, c uint64) (uint64, uint64) { return Sub64(x, y, c) }, a.z, a.x, a.c, a.y, a.cout)
+		test("Sub64 intrinsic symmetric", func(x, y, c uint64) (uint64, uint64) { return Sub64(x, y, c) }, a.z, a.y, a.c, a.x, a.cout)
+	}
+}
+
+func TestAdd64OverflowPanic(t *testing.T) {
+	// Test that 64-bit overflow panics fire correctly.
+	// These are designed to improve coverage of compiler intrinsics.
+	tests := []func(uint64, uint64) uint64{
+		func(a, b uint64) uint64 {
+			x, c := Add64(a, b, 0)
+			if c > 0 {
+				panic("overflow")
+			}
+			return x
+		},
+		func(a, b uint64) uint64 {
+			x, c := Add64(a, b, 0)
+			if c != 0 {
+				panic("overflow")
+			}
+			return x
+		},
+		func(a, b uint64) uint64 {
+			x, c := Add64(a, b, 0)
+			if c == 1 {
+				panic("overflow")
+			}
+			return x
+		},
+		func(a, b uint64) uint64 {
+			x, c := Add64(a, b, 0)
+			if c != 1 {
+				return x
+			}
+			panic("overflow")
+		},
+		func(a, b uint64) uint64 {
+			x, c := Add64(a, b, 0)
+			if c == 0 {
+				return x
+			}
+			panic("overflow")
+		},
+	}
+	for _, test := range tests {
+		shouldPanic := func(f func()) {
+			defer func() {
+				if err := recover(); err == nil {
+					t.Fatalf("expected panic")
+				}
+			}()
+			f()
+		}
+
+		// overflow
+		shouldPanic(func() { test(_M64, 1) })
+		shouldPanic(func() { test(1, _M64) })
+		shouldPanic(func() { test(_M64, _M64) })
+
+		// no overflow
+		test(_M64, 0)
+		test(0, 0)
+		test(1, 1)
+	}
+}
+
+func TestSub64OverflowPanic(t *testing.T) {
+	// Test that 64-bit overflow panics fire correctly.
+	// These are designed to improve coverage of compiler intrinsics.
+	tests := []func(uint64, uint64) uint64{
+		func(a, b uint64) uint64 {
+			x, c := Sub64(a, b, 0)
+			if c > 0 {
+				panic("overflow")
+			}
+			return x
+		},
+		func(a, b uint64) uint64 {
+			x, c := Sub64(a, b, 0)
+			if c != 0 {
+				panic("overflow")
+			}
+			return x
+		},
+		func(a, b uint64) uint64 {
+			x, c := Sub64(a, b, 0)
+			if c == 1 {
+				panic("overflow")
+			}
+			return x
+		},
+		func(a, b uint64) uint64 {
+			x, c := Sub64(a, b, 0)
+			if c != 1 {
+				return x
+			}
+			panic("overflow")
+		},
+		func(a, b uint64) uint64 {
+			x, c := Sub64(a, b, 0)
+			if c == 0 {
+				return x
+			}
+			panic("overflow")
+		},
+	}
+	for _, test := range tests {
+		shouldPanic := func(f func()) {
+			defer func() {
+				if err := recover(); err == nil {
+					t.Fatalf("expected panic")
+				}
+			}()
+			f()
+		}
+
+		// overflow
+		shouldPanic(func() { test(0, 1) })
+		shouldPanic(func() { test(1, _M64) })
+		shouldPanic(func() { test(_M64-1, _M64) })
+
+		// no overflow
+		test(_M64, 0)
+		test(0, 0)
+		test(1, 1)
+	}
+}
+
+func TestMulDiv(t *testing.T) {
+	testMul := func(msg string, f func(x, y uint) (hi, lo uint), x, y, hi, lo uint) {
+		hi1, lo1 := f(x, y)
+		if hi1 != hi || lo1 != lo {
+			t.Errorf("%s: got hi:lo = %#x:%#x; want %#x:%#x", msg, hi1, lo1, hi, lo)
+		}
+	}
+	testDiv := func(msg string, f func(hi, lo, y uint) (q, r uint), hi, lo, y, q, r uint) {
+		q1, r1 := f(hi, lo, y)
+		if q1 != q || r1 != r {
+			t.Errorf("%s: got q:r = %#x:%#x; want %#x:%#x", msg, q1, r1, q, r)
+		}
+	}
+	for _, a := range []struct {
+		x, y      uint
+		hi, lo, r uint
+	}{
+		{1 << (UintSize - 1), 2, 1, 0, 1},
+		{_M, _M, _M - 1, 1, 42},
+	} {
+		testMul("Mul", Mul, a.x, a.y, a.hi, a.lo)
+		testMul("Mul symmetric", Mul, a.y, a.x, a.hi, a.lo)
+		testDiv("Div", Div, a.hi, a.lo+a.r, a.y, a.x, a.r)
+		testDiv("Div symmetric", Div, a.hi, a.lo+a.r, a.x, a.y, a.r)
+		// The above code can't test intrinsic implementation, because the passed function is not called directly.
+		// The following code uses a closure to test the intrinsic version in case the function is intrinsified.
+		testMul("Mul intrinsic", func(x, y uint) (uint, uint) { return Mul(x, y) }, a.x, a.y, a.hi, a.lo)
+		testMul("Mul intrinsic symmetric", func(x, y uint) (uint, uint) { return Mul(x, y) }, a.y, a.x, a.hi, a.lo)
+		testDiv("Div intrinsic", func(hi, lo, y uint) (uint, uint) { return Div(hi, lo, y) }, a.hi, a.lo+a.r, a.y, a.x, a.r)
+		testDiv("Div intrinsic symmetric", func(hi, lo, y uint) (uint, uint) { return Div(hi, lo, y) }, a.hi, a.lo+a.r, a.x, a.y, a.r)
+	}
+}
+
+func TestMulDiv32(t *testing.T) {
+	testMul := func(msg string, f func(x, y uint32) (hi, lo uint32), x, y, hi, lo uint32) {
+		hi1, lo1 := f(x, y)
+		if hi1 != hi || lo1 != lo {
+			t.Errorf("%s: got hi:lo = %#x:%#x; want %#x:%#x", msg, hi1, lo1, hi, lo)
+		}
+	}
+	testDiv := func(msg string, f func(hi, lo, y uint32) (q, r uint32), hi, lo, y, q, r uint32) {
+		q1, r1 := f(hi, lo, y)
+		if q1 != q || r1 != r {
+			t.Errorf("%s: got q:r = %#x:%#x; want %#x:%#x", msg, q1, r1, q, r)
+		}
+	}
+	for _, a := range []struct {
+		x, y      uint32
+		hi, lo, r uint32
+	}{
+		{1 << 31, 2, 1, 0, 1},
+		{0xc47dfa8c, 50911, 0x98a4, 0x998587f4, 13},
+		{_M32, _M32, _M32 - 1, 1, 42},
+	} {
+		testMul("Mul32", Mul32, a.x, a.y, a.hi, a.lo)
+		testMul("Mul32 symmetric", Mul32, a.y, a.x, a.hi, a.lo)
+		testDiv("Div32", Div32, a.hi, a.lo+a.r, a.y, a.x, a.r)
+		testDiv("Div32 symmetric", Div32, a.hi, a.lo+a.r, a.x, a.y, a.r)
+	}
+}
+
+func TestMulDiv64(t *testing.T) {
+	testMul := func(msg string, f func(x, y uint64) (hi, lo uint64), x, y, hi, lo uint64) {
+		hi1, lo1 := f(x, y)
+		if hi1 != hi || lo1 != lo {
+			t.Errorf("%s: got hi:lo = %#x:%#x; want %#x:%#x", msg, hi1, lo1, hi, lo)
+		}
+	}
+	testDiv := func(msg string, f func(hi, lo, y uint64) (q, r uint64), hi, lo, y, q, r uint64) {
+		q1, r1 := f(hi, lo, y)
+		if q1 != q || r1 != r {
+			t.Errorf("%s: got q:r = %#x:%#x; want %#x:%#x", msg, q1, r1, q, r)
+		}
+	}
+	for _, a := range []struct {
+		x, y      uint64
+		hi, lo, r uint64
+	}{
+		{1 << 63, 2, 1, 0, 1},
+		{0x3626229738a3b9, 0xd8988a9f1cc4a61, 0x2dd0712657fe8, 0x9dd6a3364c358319, 13},
+		{_M64, _M64, _M64 - 1, 1, 42},
+	} {
+		testMul("Mul64", Mul64, a.x, a.y, a.hi, a.lo)
+		testMul("Mul64 symmetric", Mul64, a.y, a.x, a.hi, a.lo)
+		testDiv("Div64", Div64, a.hi, a.lo+a.r, a.y, a.x, a.r)
+		testDiv("Div64 symmetric", Div64, a.hi, a.lo+a.r, a.x, a.y, a.r)
+		// The above code can't test intrinsic implementation, because the passed function is not called directly.
+		// The following code uses a closure to test the intrinsic version in case the function is intrinsified.
+		testMul("Mul64 intrinsic", func(x, y uint64) (uint64, uint64) { return Mul64(x, y) }, a.x, a.y, a.hi, a.lo)
+		testMul("Mul64 intrinsic symmetric", func(x, y uint64) (uint64, uint64) { return Mul64(x, y) }, a.y, a.x, a.hi, a.lo)
+		testDiv("Div64 intrinsic", func(hi, lo, y uint64) (uint64, uint64) { return Div64(hi, lo, y) }, a.hi, a.lo+a.r, a.y, a.x, a.r)
+		testDiv("Div64 intrinsic symmetric", func(hi, lo, y uint64) (uint64, uint64) { return Div64(hi, lo, y) }, a.hi, a.lo+a.r, a.x, a.y, a.r)
+	}
+}
+
+const (
+	divZeroError  = "runtime error: integer divide by zero"
+	overflowError = "runtime error: integer overflow"
+)
+
+func TestDivPanicOverflow(t *testing.T) {
+	// Expect a panic
+	defer func() {
+		if err := recover(); err == nil {
+			t.Error("Div should have panicked when y<=hi")
+		} else if e, ok := err.(runtime.Error); !ok || e.Error() != overflowError {
+			t.Errorf("Div expected panic: %q, got: %q ", overflowError, e.Error())
+		}
+	}()
+	q, r := Div(1, 0, 1)
+	t.Errorf("undefined q, r = %v, %v calculated when Div should have panicked", q, r)
+}
+
+func TestDiv32PanicOverflow(t *testing.T) {
+	// Expect a panic
+	defer func() {
+		if err := recover(); err == nil {
+			t.Error("Div32 should have panicked when y<=hi")
+		} else if e, ok := err.(runtime.Error); !ok || e.Error() != overflowError {
+			t.Errorf("Div32 expected panic: %q, got: %q ", overflowError, e.Error())
+		}
+	}()
+	q, r := Div32(1, 0, 1)
+	t.Errorf("undefined q, r = %v, %v calculated when Div32 should have panicked", q, r)
+}
+
+func TestDiv64PanicOverflow(t *testing.T) {
+	// Expect a panic
+	defer func() {
+		if err := recover(); err == nil {
+			t.Error("Div64 should have panicked when y<=hi")
+		} else if e, ok := err.(runtime.Error); !ok || e.Error() != overflowError {
+			t.Errorf("Div64 expected panic: %q, got: %q ", overflowError, e.Error())
+		}
+	}()
+	q, r := Div64(1, 0, 1)
+	t.Errorf("undefined q, r = %v, %v calculated when Div64 should have panicked", q, r)
+}
+
+func TestDivPanicZero(t *testing.T) {
+	// Expect a panic
+	defer func() {
+		if err := recover(); err == nil {
+			t.Error("Div should have panicked when y==0")
+		} else if e, ok := err.(runtime.Error); !ok || e.Error() != divZeroError {
+			t.Errorf("Div expected panic: %q, got: %q ", divZeroError, e.Error())
+		}
+	}()
+	q, r := Div(1, 1, 0)
+	t.Errorf("undefined q, r = %v, %v calculated when Div should have panicked", q, r)
+}
+
+func TestDiv32PanicZero(t *testing.T) {
+	// Expect a panic
+	defer func() {
+		if err := recover(); err == nil {
+			t.Error("Div32 should have panicked when y==0")
+		} else if e, ok := err.(runtime.Error); !ok || e.Error() != divZeroError {
+			t.Errorf("Div32 expected panic: %q, got: %q ", divZeroError, e.Error())
+		}
+	}()
+	q, r := Div32(1, 1, 0)
+	t.Errorf("undefined q, r = %v, %v calculated when Div32 should have panicked", q, r)
+}
+
+func TestDiv64PanicZero(t *testing.T) {
+	// Expect a panic
+	defer func() {
+		if err := recover(); err == nil {
+			t.Error("Div64 should have panicked when y==0")
+		} else if e, ok := err.(runtime.Error); !ok || e.Error() != divZeroError {
+			t.Errorf("Div64 expected panic: %q, got: %q ", divZeroError, e.Error())
+		}
+	}()
+	q, r := Div64(1, 1, 0)
+	t.Errorf("undefined q, r = %v, %v calculated when Div64 should have panicked", q, r)
+}
+
+func TestRem32(t *testing.T) {
+	// Sanity check: for non-oveflowing dividends, the result is the
+	// same as the rem returned by Div32
+	hi, lo, y := uint32(510510), uint32(9699690), uint32(510510+1) // ensure hi < y
+	for i := 0; i < 1000; i++ {
+		r := Rem32(hi, lo, y)
+		_, r2 := Div32(hi, lo, y)
+		if r != r2 {
+			t.Errorf("Rem32(%v, %v, %v) returned %v, but Div32 returned rem %v", hi, lo, y, r, r2)
+		}
+		y += 13
+	}
+}
+
+func TestRem32Overflow(t *testing.T) {
+	// To trigger a quotient overflow, we need y <= hi
+	hi, lo, y := uint32(510510), uint32(9699690), uint32(7)
+	for i := 0; i < 1000; i++ {
+		r := Rem32(hi, lo, y)
+		_, r2 := Div64(0, uint64(hi)<<32|uint64(lo), uint64(y))
+		if r != uint32(r2) {
+			t.Errorf("Rem32(%v, %v, %v) returned %v, but Div64 returned rem %v", hi, lo, y, r, r2)
+		}
+		y += 13
+	}
+}
+
+func TestRem64(t *testing.T) {
+	// Sanity check: for non-oveflowing dividends, the result is the
+	// same as the rem returned by Div64
+	hi, lo, y := uint64(510510), uint64(9699690), uint64(510510+1) // ensure hi < y
+	for i := 0; i < 1000; i++ {
+		r := Rem64(hi, lo, y)
+		_, r2 := Div64(hi, lo, y)
+		if r != r2 {
+			t.Errorf("Rem64(%v, %v, %v) returned %v, but Div64 returned rem %v", hi, lo, y, r, r2)
+		}
+		y += 13
+	}
+}
+
+func TestRem64Overflow(t *testing.T) {
+	Rem64Tests := []struct {
+		hi, lo, y uint64
+		rem       uint64
+	}{
+		// Testcases computed using Python 3, as:
+		//   >>> hi = 42; lo = 1119; y = 42
+		//   >>> ((hi<<64)+lo) % y
+		{42, 1119, 42, 27},
+		{42, 1119, 38, 9},
+		{42, 1119, 26, 23},
+		{469, 0, 467, 271},
+		{469, 0, 113, 58},
+		{111111, 111111, 1171, 803},
+		{3968194946088682615, 3192705705065114702, 1000037, 56067},
+	}
+
+	for _, rt := range Rem64Tests {
+		if rt.hi < rt.y {
+			t.Fatalf("Rem64(%v, %v, %v) is not a test with quo overflow", rt.hi, rt.lo, rt.y)
+		}
+		rem := Rem64(rt.hi, rt.lo, rt.y)
+		if rem != rt.rem {
+			t.Errorf("Rem64(%v, %v, %v) returned %v, wanted %v",
+				rt.hi, rt.lo, rt.y, rem, rt.rem)
+		}
+	}
+}
+
+func BenchmarkAdd(b *testing.B) {
+	var z, c uint
+	for i := 0; i < b.N; i++ {
+		z, c = Add(uint(Input), uint(i), c)
+	}
+	Output = int(z + c)
+}
+
+func BenchmarkAdd32(b *testing.B) {
+	var z, c uint32
+	for i := 0; i < b.N; i++ {
+		z, c = Add32(uint32(Input), uint32(i), c)
+	}
+	Output = int(z + c)
+}
+
+func BenchmarkAdd64(b *testing.B) {
+	var z, c uint64
+	for i := 0; i < b.N; i++ {
+		z, c = Add64(uint64(Input), uint64(i), c)
+	}
+	Output = int(z + c)
+}
+
+func BenchmarkAdd64multiple(b *testing.B) {
+	var z0 = uint64(Input)
+	var z1 = uint64(Input)
+	var z2 = uint64(Input)
+	var z3 = uint64(Input)
+	for i := 0; i < b.N; i++ {
+		var c uint64
+		z0, c = Add64(z0, uint64(i), c)
+		z1, c = Add64(z1, uint64(i), c)
+		z2, c = Add64(z2, uint64(i), c)
+		z3, _ = Add64(z3, uint64(i), c)
+	}
+	Output = int(z0 + z1 + z2 + z3)
+}
+
+func BenchmarkSub(b *testing.B) {
+	var z, c uint
+	for i := 0; i < b.N; i++ {
+		z, c = Sub(uint(Input), uint(i), c)
+	}
+	Output = int(z + c)
+}
+
+func BenchmarkSub32(b *testing.B) {
+	var z, c uint32
+	for i := 0; i < b.N; i++ {
+		z, c = Sub32(uint32(Input), uint32(i), c)
+	}
+	Output = int(z + c)
+}
+
+func BenchmarkSub64(b *testing.B) {
+	var z, c uint64
+	for i := 0; i < b.N; i++ {
+		z, c = Sub64(uint64(Input), uint64(i), c)
+	}
+	Output = int(z + c)
+}
+
+func BenchmarkSub64multiple(b *testing.B) {
+	var z0 = uint64(Input)
+	var z1 = uint64(Input)
+	var z2 = uint64(Input)
+	var z3 = uint64(Input)
+	for i := 0; i < b.N; i++ {
+		var c uint64
+		z0, c = Sub64(z0, uint64(i), c)
+		z1, c = Sub64(z1, uint64(i), c)
+		z2, c = Sub64(z2, uint64(i), c)
+		z3, _ = Sub64(z3, uint64(i), c)
+	}
+	Output = int(z0 + z1 + z2 + z3)
+}
+
+func BenchmarkMul(b *testing.B) {
+	var hi, lo uint
+	for i := 0; i < b.N; i++ {
+		hi, lo = Mul(uint(Input), uint(i))
+	}
+	Output = int(hi + lo)
+}
+
+func BenchmarkMul32(b *testing.B) {
+	var hi, lo uint32
+	for i := 0; i < b.N; i++ {
+		hi, lo = Mul32(uint32(Input), uint32(i))
+	}
+	Output = int(hi + lo)
+}
+
+func BenchmarkMul64(b *testing.B) {
+	var hi, lo uint64
+	for i := 0; i < b.N; i++ {
+		hi, lo = Mul64(uint64(Input), uint64(i))
+	}
+	Output = int(hi + lo)
+}
+
+func BenchmarkDiv(b *testing.B) {
+	var q, r uint
+	for i := 0; i < b.N; i++ {
+		q, r = Div(1, uint(i), uint(Input))
+	}
+	Output = int(q + r)
+}
+
+func BenchmarkDiv32(b *testing.B) {
+	var q, r uint32
+	for i := 0; i < b.N; i++ {
+		q, r = Div32(1, uint32(i), uint32(Input))
+	}
+	Output = int(q + r)
+}
+
+func BenchmarkDiv64(b *testing.B) {
+	var q, r uint64
+	for i := 0; i < b.N; i++ {
+		q, r = Div64(1, uint64(i), uint64(Input))
+	}
+	Output = int(q + r)
+}
+
+// ----------------------------------------------------------------------------
+// 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
+	}
+}
diff --git a/src/math/bits/example_math_test.go b/src/math/bits/example_math_test.go
new file mode 100644
index 0000000..4bb466f
--- /dev/null
+++ b/src/math/bits/example_math_test.go
@@ -0,0 +1,202 @@
+// 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 bits_test
+
+import (
+	"fmt"
+	"math/bits"
+)
+
+func ExampleAdd32() {
+	// First number is 33<<32 + 12
+	n1 := []uint32{33, 12}
+	// Second number is 21<<32 + 23
+	n2 := []uint32{21, 23}
+	// Add them together without producing carry.
+	d1, carry := bits.Add32(n1[1], n2[1], 0)
+	d0, _ := bits.Add32(n1[0], n2[0], carry)
+	nsum := []uint32{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 1<<32 + 2147483648
+	n1 = []uint32{1, 0x80000000}
+	// Second number is 1<<32 + 2147483648
+	n2 = []uint32{1, 0x80000000}
+	// Add them together producing carry.
+	d1, carry = bits.Add32(n1[1], n2[1], 0)
+	d0, _ = bits.Add32(n1[0], n2[0], carry)
+	nsum = []uint32{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 12] + [21 23] = [54 35] (carry bit was 0)
+	// [1 2147483648] + [1 2147483648] = [3 0] (carry bit was 1)
+}
+
+func ExampleAdd64() {
+	// First number is 33<<64 + 12
+	n1 := []uint64{33, 12}
+	// Second number is 21<<64 + 23
+	n2 := []uint64{21, 23}
+	// Add them together without producing carry.
+	d1, carry := bits.Add64(n1[1], n2[1], 0)
+	d0, _ := bits.Add64(n1[0], n2[0], carry)
+	nsum := []uint64{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 1<<64 + 9223372036854775808
+	n1 = []uint64{1, 0x8000000000000000}
+	// Second number is 1<<64 + 9223372036854775808
+	n2 = []uint64{1, 0x8000000000000000}
+	// Add them together producing carry.
+	d1, carry = bits.Add64(n1[1], n2[1], 0)
+	d0, _ = bits.Add64(n1[0], n2[0], carry)
+	nsum = []uint64{d0, d1}
+	fmt.Printf("%v + %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 12] + [21 23] = [54 35] (carry bit was 0)
+	// [1 9223372036854775808] + [1 9223372036854775808] = [3 0] (carry bit was 1)
+}
+
+func ExampleSub32() {
+	// First number is 33<<32 + 23
+	n1 := []uint32{33, 23}
+	// Second number is 21<<32 + 12
+	n2 := []uint32{21, 12}
+	// Sub them together without producing carry.
+	d1, carry := bits.Sub32(n1[1], n2[1], 0)
+	d0, _ := bits.Sub32(n1[0], n2[0], carry)
+	nsum := []uint32{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 3<<32 + 2147483647
+	n1 = []uint32{3, 0x7fffffff}
+	// Second number is 1<<32 + 2147483648
+	n2 = []uint32{1, 0x80000000}
+	// Sub them together producing carry.
+	d1, carry = bits.Sub32(n1[1], n2[1], 0)
+	d0, _ = bits.Sub32(n1[0], n2[0], carry)
+	nsum = []uint32{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 23] - [21 12] = [12 11] (carry bit was 0)
+	// [3 2147483647] - [1 2147483648] = [1 4294967295] (carry bit was 1)
+}
+
+func ExampleSub64() {
+	// First number is 33<<64 + 23
+	n1 := []uint64{33, 23}
+	// Second number is 21<<64 + 12
+	n2 := []uint64{21, 12}
+	// Sub them together without producing carry.
+	d1, carry := bits.Sub64(n1[1], n2[1], 0)
+	d0, _ := bits.Sub64(n1[0], n2[0], carry)
+	nsum := []uint64{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+
+	// First number is 3<<64 + 9223372036854775807
+	n1 = []uint64{3, 0x7fffffffffffffff}
+	// Second number is 1<<64 + 9223372036854775808
+	n2 = []uint64{1, 0x8000000000000000}
+	// Sub them together producing carry.
+	d1, carry = bits.Sub64(n1[1], n2[1], 0)
+	d0, _ = bits.Sub64(n1[0], n2[0], carry)
+	nsum = []uint64{d0, d1}
+	fmt.Printf("%v - %v = %v (carry bit was %v)\n", n1, n2, nsum, carry)
+	// Output:
+	// [33 23] - [21 12] = [12 11] (carry bit was 0)
+	// [3 9223372036854775807] - [1 9223372036854775808] = [1 18446744073709551615] (carry bit was 1)
+}
+
+func ExampleMul32() {
+	// First number is 0<<32 + 12
+	n1 := []uint32{0, 12}
+	// Second number is 0<<32 + 12
+	n2 := []uint32{0, 12}
+	// Multiply them together without producing overflow.
+	hi, lo := bits.Mul32(n1[1], n2[1])
+	nsum := []uint32{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+
+	// First number is 0<<32 + 2147483648
+	n1 = []uint32{0, 0x80000000}
+	// Second number is 0<<32 + 2
+	n2 = []uint32{0, 2}
+	// Multiply them together producing overflow.
+	hi, lo = bits.Mul32(n1[1], n2[1])
+	nsum = []uint32{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+	// Output:
+	// 12 * 12 = [0 144]
+	// 2147483648 * 2 = [1 0]
+}
+
+func ExampleMul64() {
+	// First number is 0<<64 + 12
+	n1 := []uint64{0, 12}
+	// Second number is 0<<64 + 12
+	n2 := []uint64{0, 12}
+	// Multiply them together without producing overflow.
+	hi, lo := bits.Mul64(n1[1], n2[1])
+	nsum := []uint64{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+
+	// First number is 0<<64 + 9223372036854775808
+	n1 = []uint64{0, 0x8000000000000000}
+	// Second number is 0<<64 + 2
+	n2 = []uint64{0, 2}
+	// Multiply them together producing overflow.
+	hi, lo = bits.Mul64(n1[1], n2[1])
+	nsum = []uint64{hi, lo}
+	fmt.Printf("%v * %v = %v\n", n1[1], n2[1], nsum)
+	// Output:
+	// 12 * 12 = [0 144]
+	// 9223372036854775808 * 2 = [1 0]
+}
+
+func ExampleDiv32() {
+	// First number is 0<<32 + 6
+	n1 := []uint32{0, 6}
+	// Second number is 0<<32 + 3
+	n2 := []uint32{0, 3}
+	// Divide them together.
+	quo, rem := bits.Div32(n1[0], n1[1], n2[1])
+	nsum := []uint32{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+
+	// First number is 2<<32 + 2147483648
+	n1 = []uint32{2, 0x80000000}
+	// Second number is 0<<32 + 2147483648
+	n2 = []uint32{0, 0x80000000}
+	// Divide them together.
+	quo, rem = bits.Div32(n1[0], n1[1], n2[1])
+	nsum = []uint32{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+	// Output:
+	// [0 6] / 3 = [2 0]
+	// [2 2147483648] / 2147483648 = [5 0]
+}
+
+func ExampleDiv64() {
+	// First number is 0<<64 + 6
+	n1 := []uint64{0, 6}
+	// Second number is 0<<64 + 3
+	n2 := []uint64{0, 3}
+	// Divide them together.
+	quo, rem := bits.Div64(n1[0], n1[1], n2[1])
+	nsum := []uint64{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+
+	// First number is 2<<64 + 9223372036854775808
+	n1 = []uint64{2, 0x8000000000000000}
+	// Second number is 0<<64 + 9223372036854775808
+	n2 = []uint64{0, 0x8000000000000000}
+	// Divide them together.
+	quo, rem = bits.Div64(n1[0], n1[1], n2[1])
+	nsum = []uint64{quo, rem}
+	fmt.Printf("[%v %v] / %v = %v\n", n1[0], n1[1], n2[1], nsum)
+	// Output:
+	// [0 6] / 3 = [2 0]
+	// [2 9223372036854775808] / 9223372036854775808 = [5 0]
+}
diff --git a/src/math/bits/example_test.go b/src/math/bits/example_test.go
new file mode 100644
index 0000000..b2ed2cb
--- /dev/null
+++ b/src/math/bits/example_test.go
@@ -0,0 +1,210 @@
+// 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_examples.go. DO NOT EDIT.
+
+package bits_test
+
+import (
+	"fmt"
+	"math/bits"
+)
+
+func ExampleLeadingZeros8() {
+	fmt.Printf("LeadingZeros8(%08b) = %d\n", 1, bits.LeadingZeros8(1))
+	// Output:
+	// LeadingZeros8(00000001) = 7
+}
+
+func ExampleLeadingZeros16() {
+	fmt.Printf("LeadingZeros16(%016b) = %d\n", 1, bits.LeadingZeros16(1))
+	// Output:
+	// LeadingZeros16(0000000000000001) = 15
+}
+
+func ExampleLeadingZeros32() {
+	fmt.Printf("LeadingZeros32(%032b) = %d\n", 1, bits.LeadingZeros32(1))
+	// Output:
+	// LeadingZeros32(00000000000000000000000000000001) = 31
+}
+
+func ExampleLeadingZeros64() {
+	fmt.Printf("LeadingZeros64(%064b) = %d\n", 1, bits.LeadingZeros64(1))
+	// Output:
+	// LeadingZeros64(0000000000000000000000000000000000000000000000000000000000000001) = 63
+}
+
+func ExampleTrailingZeros8() {
+	fmt.Printf("TrailingZeros8(%08b) = %d\n", 14, bits.TrailingZeros8(14))
+	// Output:
+	// TrailingZeros8(00001110) = 1
+}
+
+func ExampleTrailingZeros16() {
+	fmt.Printf("TrailingZeros16(%016b) = %d\n", 14, bits.TrailingZeros16(14))
+	// Output:
+	// TrailingZeros16(0000000000001110) = 1
+}
+
+func ExampleTrailingZeros32() {
+	fmt.Printf("TrailingZeros32(%032b) = %d\n", 14, bits.TrailingZeros32(14))
+	// Output:
+	// TrailingZeros32(00000000000000000000000000001110) = 1
+}
+
+func ExampleTrailingZeros64() {
+	fmt.Printf("TrailingZeros64(%064b) = %d\n", 14, bits.TrailingZeros64(14))
+	// Output:
+	// TrailingZeros64(0000000000000000000000000000000000000000000000000000000000001110) = 1
+}
+
+func ExampleOnesCount() {
+	fmt.Printf("OnesCount(%b) = %d\n", 14, bits.OnesCount(14))
+	// Output:
+	// OnesCount(1110) = 3
+}
+
+func ExampleOnesCount8() {
+	fmt.Printf("OnesCount8(%08b) = %d\n", 14, bits.OnesCount8(14))
+	// Output:
+	// OnesCount8(00001110) = 3
+}
+
+func ExampleOnesCount16() {
+	fmt.Printf("OnesCount16(%016b) = %d\n", 14, bits.OnesCount16(14))
+	// Output:
+	// OnesCount16(0000000000001110) = 3
+}
+
+func ExampleOnesCount32() {
+	fmt.Printf("OnesCount32(%032b) = %d\n", 14, bits.OnesCount32(14))
+	// Output:
+	// OnesCount32(00000000000000000000000000001110) = 3
+}
+
+func ExampleOnesCount64() {
+	fmt.Printf("OnesCount64(%064b) = %d\n", 14, bits.OnesCount64(14))
+	// Output:
+	// OnesCount64(0000000000000000000000000000000000000000000000000000000000001110) = 3
+}
+
+func ExampleRotateLeft8() {
+	fmt.Printf("%08b\n", 15)
+	fmt.Printf("%08b\n", bits.RotateLeft8(15, 2))
+	fmt.Printf("%08b\n", bits.RotateLeft8(15, -2))
+	// Output:
+	// 00001111
+	// 00111100
+	// 11000011
+}
+
+func ExampleRotateLeft16() {
+	fmt.Printf("%016b\n", 15)
+	fmt.Printf("%016b\n", bits.RotateLeft16(15, 2))
+	fmt.Printf("%016b\n", bits.RotateLeft16(15, -2))
+	// Output:
+	// 0000000000001111
+	// 0000000000111100
+	// 1100000000000011
+}
+
+func ExampleRotateLeft32() {
+	fmt.Printf("%032b\n", 15)
+	fmt.Printf("%032b\n", bits.RotateLeft32(15, 2))
+	fmt.Printf("%032b\n", bits.RotateLeft32(15, -2))
+	// Output:
+	// 00000000000000000000000000001111
+	// 00000000000000000000000000111100
+	// 11000000000000000000000000000011
+}
+
+func ExampleRotateLeft64() {
+	fmt.Printf("%064b\n", 15)
+	fmt.Printf("%064b\n", bits.RotateLeft64(15, 2))
+	fmt.Printf("%064b\n", bits.RotateLeft64(15, -2))
+	// Output:
+	// 0000000000000000000000000000000000000000000000000000000000001111
+	// 0000000000000000000000000000000000000000000000000000000000111100
+	// 1100000000000000000000000000000000000000000000000000000000000011
+}
+
+func ExampleReverse8() {
+	fmt.Printf("%08b\n", 19)
+	fmt.Printf("%08b\n", bits.Reverse8(19))
+	// Output:
+	// 00010011
+	// 11001000
+}
+
+func ExampleReverse16() {
+	fmt.Printf("%016b\n", 19)
+	fmt.Printf("%016b\n", bits.Reverse16(19))
+	// Output:
+	// 0000000000010011
+	// 1100100000000000
+}
+
+func ExampleReverse32() {
+	fmt.Printf("%032b\n", 19)
+	fmt.Printf("%032b\n", bits.Reverse32(19))
+	// Output:
+	// 00000000000000000000000000010011
+	// 11001000000000000000000000000000
+}
+
+func ExampleReverse64() {
+	fmt.Printf("%064b\n", 19)
+	fmt.Printf("%064b\n", bits.Reverse64(19))
+	// Output:
+	// 0000000000000000000000000000000000000000000000000000000000010011
+	// 1100100000000000000000000000000000000000000000000000000000000000
+}
+
+func ExampleReverseBytes16() {
+	fmt.Printf("%016b\n", 15)
+	fmt.Printf("%016b\n", bits.ReverseBytes16(15))
+	// Output:
+	// 0000000000001111
+	// 0000111100000000
+}
+
+func ExampleReverseBytes32() {
+	fmt.Printf("%032b\n", 15)
+	fmt.Printf("%032b\n", bits.ReverseBytes32(15))
+	// Output:
+	// 00000000000000000000000000001111
+	// 00001111000000000000000000000000
+}
+
+func ExampleReverseBytes64() {
+	fmt.Printf("%064b\n", 15)
+	fmt.Printf("%064b\n", bits.ReverseBytes64(15))
+	// Output:
+	// 0000000000000000000000000000000000000000000000000000000000001111
+	// 0000111100000000000000000000000000000000000000000000000000000000
+}
+
+func ExampleLen8() {
+	fmt.Printf("Len8(%08b) = %d\n", 8, bits.Len8(8))
+	// Output:
+	// Len8(00001000) = 4
+}
+
+func ExampleLen16() {
+	fmt.Printf("Len16(%016b) = %d\n", 8, bits.Len16(8))
+	// Output:
+	// Len16(0000000000001000) = 4
+}
+
+func ExampleLen32() {
+	fmt.Printf("Len32(%032b) = %d\n", 8, bits.Len32(8))
+	// Output:
+	// Len32(00000000000000000000000000001000) = 4
+}
+
+func ExampleLen64() {
+	fmt.Printf("Len64(%064b) = %d\n", 8, bits.Len64(8))
+	// Output:
+	// Len64(0000000000000000000000000000000000000000000000000000000000001000) = 4
+}
diff --git a/src/math/bits/export_test.go b/src/math/bits/export_test.go
new file mode 100644
index 0000000..8c6f933
--- /dev/null
+++ b/src/math/bits/export_test.go
@@ -0,0 +1,7 @@
+// Copyright 2018 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
+
+const DeBruijn64 = deBruijn64
diff --git a/src/math/bits/make_examples.go b/src/math/bits/make_examples.go
new file mode 100644
index 0000000..92e9aab
--- /dev/null
+++ b/src/math/bits/make_examples.go
@@ -0,0 +1,113 @@
+// 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.
+
+//go:build ignore
+// +build ignore
+
+// This program generates example_test.go.
+
+package main
+
+import (
+	"bytes"
+	"fmt"
+	"log"
+	"math/bits"
+	"os"
+)
+
+const header = `// 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_examples.go. DO NOT EDIT.
+
+package bits_test
+
+import (
+	"fmt"
+	"math/bits"
+)
+`
+
+func main() {
+	w := bytes.NewBuffer([]byte(header))
+
+	for _, e := range []struct {
+		name string
+		in   int
+		out  [4]any
+		out2 [4]any
+	}{
+		{
+			name: "LeadingZeros",
+			in:   1,
+			out:  [4]any{bits.LeadingZeros8(1), bits.LeadingZeros16(1), bits.LeadingZeros32(1), bits.LeadingZeros64(1)},
+		},
+		{
+			name: "TrailingZeros",
+			in:   14,
+			out:  [4]any{bits.TrailingZeros8(14), bits.TrailingZeros16(14), bits.TrailingZeros32(14), bits.TrailingZeros64(14)},
+		},
+		{
+			name: "OnesCount",
+			in:   14,
+			out:  [4]any{bits.OnesCount8(14), bits.OnesCount16(14), bits.OnesCount32(14), bits.OnesCount64(14)},
+		},
+		{
+			name: "RotateLeft",
+			in:   15,
+			out:  [4]any{bits.RotateLeft8(15, 2), bits.RotateLeft16(15, 2), bits.RotateLeft32(15, 2), bits.RotateLeft64(15, 2)},
+			out2: [4]any{bits.RotateLeft8(15, -2), bits.RotateLeft16(15, -2), bits.RotateLeft32(15, -2), bits.RotateLeft64(15, -2)},
+		},
+		{
+			name: "Reverse",
+			in:   19,
+			out:  [4]any{bits.Reverse8(19), bits.Reverse16(19), bits.Reverse32(19), bits.Reverse64(19)},
+		},
+		{
+			name: "ReverseBytes",
+			in:   15,
+			out:  [4]any{nil, bits.ReverseBytes16(15), bits.ReverseBytes32(15), bits.ReverseBytes64(15)},
+		},
+		{
+			name: "Len",
+			in:   8,
+			out:  [4]any{bits.Len8(8), bits.Len16(8), bits.Len32(8), bits.Len64(8)},
+		},
+	} {
+		for i, size := range []int{8, 16, 32, 64} {
+			if e.out[i] == nil {
+				continue // function doesn't exist
+			}
+			f := fmt.Sprintf("%s%d", e.name, size)
+			fmt.Fprintf(w, "\nfunc Example%s() {\n", f)
+			switch e.name {
+			case "RotateLeft", "Reverse", "ReverseBytes":
+				fmt.Fprintf(w, "\tfmt.Printf(\"%%0%db\\n\", %d)\n", size, e.in)
+				if e.name == "RotateLeft" {
+					fmt.Fprintf(w, "\tfmt.Printf(\"%%0%db\\n\", bits.%s(%d, 2))\n", size, f, e.in)
+					fmt.Fprintf(w, "\tfmt.Printf(\"%%0%db\\n\", bits.%s(%d, -2))\n", size, f, e.in)
+				} else {
+					fmt.Fprintf(w, "\tfmt.Printf(\"%%0%db\\n\", bits.%s(%d))\n", size, f, e.in)
+				}
+				fmt.Fprintf(w, "\t// Output:\n")
+				fmt.Fprintf(w, "\t// %0*b\n", size, e.in)
+				fmt.Fprintf(w, "\t// %0*b\n", size, e.out[i])
+				if e.name == "RotateLeft" && e.out2[i] != nil {
+					fmt.Fprintf(w, "\t// %0*b\n", size, e.out2[i])
+				}
+			default:
+				fmt.Fprintf(w, "\tfmt.Printf(\"%s(%%0%db) = %%d\\n\", %d, bits.%s(%d))\n", f, size, e.in, f, e.in)
+				fmt.Fprintf(w, "\t// Output:\n")
+				fmt.Fprintf(w, "\t// %s(%0*b) = %d\n", f, size, e.in, e.out[i])
+			}
+			fmt.Fprintf(w, "}\n")
+		}
+	}
+
+	if err := os.WriteFile("example_test.go", w.Bytes(), 0666); err != nil {
+		log.Fatal(err)
+	}
+}
diff --git a/src/math/bits/make_tables.go b/src/math/bits/make_tables.go
new file mode 100644
index 0000000..867025e
--- /dev/null
+++ b/src/math/bits/make_tables.go
@@ -0,0 +1,92 @@
+// 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.
+
+//go:build ignore
+// +build ignore
+
+// This program generates bits_tables.go.
+
+package main
+
+import (
+	"bytes"
+	"fmt"
+	"go/format"
+	"io"
+	"log"
+	"os"
+)
+
+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, "ntz8tab", ntz8)
+	gen(buf, "pop8tab", pop8)
+	gen(buf, "rev8tab", rev8)
+	gen(buf, "len8tab", len8)
+
+	out, err := format.Source(buf.Bytes())
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	err = os.WriteFile("bits_tables.go", out, 0666)
+	if err != nil {
+		log.Fatal(err)
+	}
+}
+
+func gen(w io.Writer, name string, f func(uint8) uint8) {
+	// Use a const string to allow the compiler to constant-evaluate lookups at constant index.
+	fmt.Fprintf(w, "const %s = \"\"+\n\"", name)
+	for i := 0; i < 256; i++ {
+		fmt.Fprintf(w, "\\x%02x", f(uint8(i)))
+		if i%16 == 15 && i != 255 {
+			fmt.Fprint(w, "\"+\n\"")
+		}
+	}
+	fmt.Fprint(w, "\"\n\n")
+}
+
+func ntz8(x uint8) (n uint8) {
+	for x&1 == 0 && n < 8 {
+		x >>= 1
+		n++
+	}
+	return
+}
+
+func pop8(x uint8) (n uint8) {
+	for x != 0 {
+		x &= x - 1
+		n++
+	}
+	return
+}
+
+func rev8(x uint8) (r uint8) {
+	for i := 8; i > 0; i-- {
+		r = r<<1 | x&1
+		x >>= 1
+	}
+	return
+}
+
+func len8(x uint8) (n uint8) {
+	for x != 0 {
+		x >>= 1
+		n++
+	}
+	return
+}