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: Brad Fitzpatrick <bradfitz@golang.org>

src/math/bits/bits.go

@@ -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])
+}

src/math/bits/bits_impl.go

@@ -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
-}

src/math/bits/bits_tables.go

@@ -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,
+}

src/math/bits/make_tables.go

@@ -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
+}