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/37582
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

diff --git a/src/math/bits/bits.go b/src/math/bits/bits.go
index 1aaa9eea9d4c2f4b51ce79dd0538523ea1dc3f45..33a51c9a42b8e1401135e77043e751f142d15798 100644 (file)
--- a/src/math/bits/bits.go
+++ b/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])
+}

diff --git a/src/math/bits/bits_impl.go b/src/math/bits/bits_impl.go
index cf5a12af2b84f081eed89f36b38f15a2fa05aeb2..0a1d8d77950d665d0292923580743a1de570070e 100644 (file)
--- a/src/math/bits/bits_impl.go
+++ b/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
-}

diff --git a/src/math/bits/bits_tables.go b/src/math/bits/bits_tables.go
index f79f83a01e1bcdbd2ed7ef4fa3b9f772e05130a5..f1e15a0d0ea506d3c3c99423ea69befca64ffe7d 100644 (file)
--- a/src/math/bits/bits_tables.go
+++ b/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,
+}

diff --git a/src/math/bits/make_tables.go b/src/math/bits/make_tables.go
index c66afb5a96e41f21872e40571030c673b1ed2e63..ff2fe2e385ed043a92ca232a329ceffb3da18435 100644 (file)
--- a/src/math/bits/make_tables.go
+++ b/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
+}