Commit 83bc4a2f authored by Robert Griesemer's avatar Robert Griesemer

math/bits: faster LeadingZeros and Len functions

benchmark                     old ns/op     new ns/op     delta
BenchmarkLeadingZeros-8       8.43          3.10          -63.23%
BenchmarkLeadingZeros8-8      8.13          1.33          -83.64%
BenchmarkLeadingZeros16-8     7.34          2.07          -71.80%
BenchmarkLeadingZeros32-8     7.99          2.87          -64.08%
BenchmarkLeadingZeros64-8     8.13          2.96          -63.59%

Measured on 2.3 GHz Intel Core i7 running macOS 10.12.3.

Change-Id: Id343531b408d42ac45f10c76f60e85bdb977f91e
Reviewed-on: https://go-review.googlesource.com/37582Reviewed-by: default avatarBrad Fitzpatrick <bradfitz@golang.org>
parent 9515cb51
......@@ -14,19 +14,19 @@ 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 - blen(uint64(x)) }
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 - blen(uint64(x)) }
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 - blen(uint64(x)) }
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 - blen(uint64(x)) }
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 - blen(uint64(x)) }
func LeadingZeros64(x uint64) int { return 64 - Len64(x) }
// --- TrailingZeros ---
......@@ -281,16 +281,53 @@ func ReverseBytes64(x uint64) uint64 {
// --- Len ---
// Len returns the minimum number of bits required to represent x; the result is 0 for x == 0.
func Len(x uint) int { return blen(uint64(x)) }
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 blen(uint64(x)) }
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) int { return blen(uint64(x)) }
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) int { return blen(uint64(x)) }
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) int { return blen(uint64(x)) }
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])
}
......@@ -65,25 +65,3 @@ func ntz64(x uint64) int {
// (Knuth, volume 4, section 7.3.1)
return int(deBruijn64tab[(x&-x)*deBruijn64>>(64-6)])
}
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
}
......@@ -62,3 +62,22 @@ var rev8tab = [256]uint8{
0x07, 0x87, 0x47, 0xc7, 0x27, 0xa7, 0x67, 0xe7, 0x17, 0x97, 0x57, 0xd7, 0x37, 0xb7, 0x77, 0xf7,
0x0f, 0x8f, 0x4f, 0xcf, 0x2f, 0xaf, 0x6f, 0xef, 0x1f, 0x9f, 0x5f, 0xdf, 0x3f, 0xbf, 0x7f, 0xff,
}
var len8tab = [256]uint8{
0x00, 0x01, 0x02, 0x02, 0x03, 0x03, 0x03, 0x03, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04, 0x04,
0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05, 0x05,
0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06,
0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06, 0x06,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07, 0x07,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08, 0x08,
}
......@@ -33,7 +33,7 @@ func main() {
gen(buf, "ntz8tab", ntz8)
gen(buf, "pop8tab", pop8)
gen(buf, "rev8tab", rev8)
// add more tables as needed
gen(buf, "len8tab", len8)
out, err := format.Source(buf.Bytes())
if err != nil {
......@@ -82,3 +82,11 @@ func rev8(x uint8) (r uint8) {
}
return
}
func len8(x uint8) (n uint8) {
for x != 0 {
x >>= 1
n++
}
return
}
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