math/bits: faster TrailingZeroes8

For sizes > 8, the existing code is faster.

benchmark                     old ns/op     new ns/op     delta
BenchmarkTrailingZeros8-8     1.95          1.29          -33.85%

Measured on 2.3 GHz Intel Core i7 running macOS 10.12.3.

Change-Id: I6f3a33ec633a2c544ec29693c141f2f99335c745
Reviewed-on: https://go-review.googlesource.com/37581Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

src/math/bits/bits.go

@@ -34,7 +34,7 @@ func LeadingZeros64(x uint64) int { return 64 - blen(uint64(x)) }
 func TrailingZeros(x uint) int { return ntz(x) }
 
 // TrailingZeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
-func TrailingZeros8(x uint8) int { return ntz8(x) }
+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 { return ntz16(x) }

src/math/bits/bits_impl.go

@@ -23,14 +23,6 @@ var deBruijn32tab = [32]byte{
 	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

src/math/bits/bits_tables.go

@@ -6,6 +6,25 @@
 
 package bits
 
+var ntz8tab = [256]uint8{
+	0x08, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x06, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x07, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x06, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x05, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+	0x04, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00, 0x03, 0x00, 0x01, 0x00, 0x02, 0x00, 0x01, 0x00,
+}
+
 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,

src/math/bits/make_tables.go

@@ -30,6 +30,7 @@ package bits
 func main() {
 	buf := bytes.NewBuffer(header)
 
+	gen(buf, "ntz8tab", ntz8)
 	gen(buf, "pop8tab", pop8)
 	gen(buf, "rev8tab", rev8)
 	// add more tables as needed
@@ -58,6 +59,14 @@ func gen(w io.Writer, name string, f func(uint8) uint8) {
 	fmt.Fprint(w, "\n}\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