math/bits: faster OnesCount using table lookups for sizes 8,16,32

For uint64, the existing algorithm is faster.

benchmark                  old ns/op     new ns/op     delta
BenchmarkOnesCount8-8      1.95          0.97          -50.26%
BenchmarkOnesCount16-8     2.54          1.39          -45.28%
BenchmarkOnesCount32-8     2.61          1.96          -24.90%

Measured on 2.3 GHz Intel Core i7 running macOS 10.12.3.

Change-Id: I6cc42882fef3d24694720464039161e339a9ae99
Reviewed-on: https://go-review.googlesource.com/37580
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

src/math/bits/bits.go

@@ -63,32 +63,17 @@ func OnesCount(x uint) int {
 
 // OnesCount8 returns the number of one bits ("population count") in x.
 func OnesCount8(x uint8) int {
-	const m = 1<<8 - 1
+	return int(pop8tab[x])
-	x = x>>1&(m0&m) + x&(m0&m)
-	x = x>>2&(m1&m) + x&(m1&m)
-	x += x >> 4
-	return int(x) & (1<<4 - 1)
 }
 
 // OnesCount16 returns the number of one bits ("population count") in x.
 func OnesCount16(x uint16) int {
-	const m = 1<<16 - 1
+	return int(pop8tab[x>>8] + pop8tab[x&0xff])
-	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
-	return int(x) & (1<<5 - 1)
 }
 
 // OnesCount32 returns the number of one bits ("population count") in x.
 func OnesCount32(x uint32) int {
-	const m = 1<<32 - 1
+	return int(pop8tab[x>>24] + pop8tab[x>>16&0xff] + pop8tab[x>>8&0xff] + pop8tab[x&0xff])
-	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
-	return int(x) & (1<<6 - 1)
 }
 
 // OnesCount64 returns the number of one bits ("population count") in x.

src/math/bits/bits_tables.go

@@ -6,6 +6,25 @@
 
 package bits
 
+var pop8tab = [256]uint8{
+	0x00, 0x01, 0x01, 0x02, 0x01, 0x02, 0x02, 0x03, 0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04,
+	0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
+	0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
+	0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
+	0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
+	0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
+	0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
+	0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
+	0x01, 0x02, 0x02, 0x03, 0x02, 0x03, 0x03, 0x04, 0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05,
+	0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
+	0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
+	0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
+	0x02, 0x03, 0x03, 0x04, 0x03, 0x04, 0x04, 0x05, 0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06,
+	0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
+	0x03, 0x04, 0x04, 0x05, 0x04, 0x05, 0x05, 0x06, 0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07,
+	0x04, 0x05, 0x05, 0x06, 0x05, 0x06, 0x06, 0x07, 0x05, 0x06, 0x06, 0x07, 0x06, 0x07, 0x07, 0x08,
+}
+
 var rev8tab = [256]uint8{
 	0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0, 0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0,
 	0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8, 0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8,

src/math/bits/make_tables.go

@@ -30,6 +30,7 @@ package bits
 func main() {
 	buf := bytes.NewBuffer(header)
 
+	gen(buf, "pop8tab", pop8)
 	gen(buf, "rev8tab", rev8)
 	// add more tables as needed
 
@@ -57,6 +58,14 @@ func gen(w io.Writer, name string, f func(uint8) uint8) {
 	fmt.Fprint(w, "\n}\n\n")
 }
 
+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