math/big: use math/bits where appropriate

This change adds math/bits as a new dependency of math/big.

- use bits.LeadingZeroes instead of local implementation
  (they are identical, so there's no performance loss here)

- leave other functionality local (ntz, bitLen) since there's
  faster implementations in math/big at the moment

Change-Id: I1218aa8a1df0cc9783583b090a4bb5a8a145c4a2
Reviewed-on: https://go-review.googlesource.com/37141Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

src/cmd/dist/buildtool.go

@@ -68,6 +68,7 @@ var bootstrapDirs = []string{
 	"cmd/link/internal/x86",
 	"debug/pe",
 	"math/big",
+	"math/bits",
 }
 
 // File prefixes that are ignored by go/build anyway, and cause

src/go/build/deps_test.go

@@ -260,7 +260,7 @@ var pkgDeps = map[string][]string{
 	"internal/singleflight":     {"sync"},
 	"internal/trace":            {"L4", "OS"},
 	"internal/pprof/profile":    {"L4", "OS", "compress/gzip", "regexp"},
-	"math/big":                  {"L4"},
+	"math/big":                  {"L4", "math/bits"},
 	"mime":                      {"L4", "OS", "syscall", "internal/syscall/windows/registry"},
 	"mime/quotedprintable":      {"L4"},
 	"net/internal/socktest":     {"L4", "OS", "syscall"},

src/math/big/arith.go

@@ -8,18 +8,17 @@
 
 package big
 
+import "math/bits"
+
 // A Word represents a single digit of a multi-precision unsigned integer.
 type Word uint
 
 const (
-	// Compute the size _S of a Word in bytes.
-	_m    = ^Word(0)
-	_logS = _m>>8&1 + _m>>16&1 + _m>>32&1
-	_S    = 1 << _logS
+	_S = _W / 8 // word size in bytes
 
-	_W = _S << 3 // word size in bits
-	_B = 1 << _W // digit base
-	_M = _B - 1  // digit mask
+	_W = bits.UintSize // word size in bits
+	_B = 1 << _W       // digit base
+	_M = _B - 1        // digit mask
 
 	_W2 = _W / 2   // half word size in bits
 	_B2 = 1 << _W2 // half digit base
@@ -78,42 +77,30 @@ func mulAddWWW_g(x, y, c Word) (z1, z0 Word) {
 }
 
 // Length of x in bits.
-func bitLen_g(x Word) (n int) {
-	for ; x >= 0x8000; x >>= 16 {
-		n += 16
-	}
-	if x >= 0x80 {
-		x >>= 8
-		n += 8
-	}
-	if x >= 0x8 {
-		x >>= 4
-		n += 4
-	}
-	if x >= 0x2 {
-		x >>= 2
-		n += 2
-	}
-	if x >= 0x1 {
-		n++
-	}
-	return
+func bitLen_g(x Word) int {
+	return bits.Len(uint(x))
 }
 
 // log2 computes the integer binary logarithm of x.
 // The result is the integer n for which 2^n <= x < 2^(n+1).
 // If x == 0, the result is -1.
 func log2(x Word) int {
+	// TODO(gri) Replace with call to bits.Len once we have a fast
+	// implementation for the same platforms currently supporting math/big.
 	return bitLen(x) - 1
 }
 
 // nlz returns the number of leading zeros in x.
 func nlz(x Word) uint {
+	// TODO(gri) Replace with call to bits.LeadingZeros once we have a fast
+	// implementation for the same platforms currently supporting math/big.
 	return uint(_W - bitLen(x))
 }
 
 // nlz64 returns the number of leading zeros in x.
 func nlz64(x uint64) uint {
+	// TODO(gri) Replace with call to bits.LeadingZeros64 once we have a fast
+	// implementation for the same platforms currently supporting math/big.
 	switch _W {
 	case 32:
 		w := x >> 32

src/math/big/nat.go

@@ -9,6 +9,7 @@
 package big
 
 import (
+	"math/bits"
 	"math/rand"
 	"sync"
 )
@@ -658,44 +659,6 @@ func (x nat) bitLen() int {
 	return 0
 }
 
-const deBruijn32 = 0x077CB531
-
-var deBruijn32Lookup = [...]byte{
-	0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
-	31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
-}
-
-const deBruijn64 = 0x03f79d71b4ca8b09
-
-var deBruijn64Lookup = [...]byte{
-	0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
-	62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
-	63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
-	54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
-}
-
-// trailingZeroBits returns the number of consecutive least significant zero
-// bits of x.
-func trailingZeroBits(x Word) uint {
-	// x & -x leaves only the right-most bit set in the word. Let k be the
-	// index of that bit. Since only a single bit is set, the value is two
-	// to the power of k. Multiplying by a power of two is equivalent to
-	// left shifting, in this case by k bits. The de Bruijn constant is
-	// such that all six bit, consecutive substrings are distinct.
-	// Therefore, if we have a left shifted version of this constant we can
-	// find by how many bits it was shifted by looking at which six bit
-	// substring ended up at the top of the word.
-	// (Knuth, volume 4, section 7.3.1)
-	switch _W {
-	case 32:
-		return uint(deBruijn32Lookup[((x&-x)*deBruijn32)>>27])
-	case 64:
-		return uint(deBruijn64Lookup[((x&-x)*(deBruijn64&_M))>>58])
-	default:
-		panic("unknown word size")
-	}
-}
-
 // trailingZeroBits returns the number of consecutive least significant zero
 // bits of x.
 func (x nat) trailingZeroBits() uint {
@@ -707,7 +670,7 @@ func (x nat) trailingZeroBits() uint {
 		i++
 	}
 	// x[i] != 0
-	return i*_W + trailingZeroBits(x[i])
+	return i*_W + uint(bits.TrailingZeros(uint(x[i])))
 }
 
 // z = x << s

src/math/big/nat_test.go

@@ -303,36 +303,6 @@ func TestModW(t *testing.T) {
 	}
 }
 
-func TestTrailingZeroBits(t *testing.T) {
-	// test 0 case explicitly
-	if n := trailingZeroBits(0); n != 0 {
-		t.Errorf("got trailingZeroBits(0) = %d; want 0", n)
-	}
-
-	x := Word(1)
-	for i := uint(0); i < _W; i++ {
-		n := trailingZeroBits(x)
-		if n != i {
-			t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W)
-		}
-		x <<= 1
-	}
-
-	// test 0 case explicitly
-	if n := nat(nil).trailingZeroBits(); n != 0 {
-		t.Errorf("got nat(nil).trailingZeroBits() = %d; want 0", n)
-	}
-
-	y := nat(nil).set(natOne)
-	for i := uint(0); i <= 3*_W; i++ {
-		n := y.trailingZeroBits()
-		if n != i {
-			t.Errorf("got 0x%s.trailingZeroBits() = %d; want %d", y.utoa(16), n, i)
-		}
-		y = y.shl(y, 1)
-	}
-}
-
 var montgomeryTests = []struct {
 	x, y, m      string
 	k0           uint64

src/math/big/natconv.go

@@ -11,6 +11,7 @@ import (
 	"fmt"
 	"io"
 	"math"
+	"math/bits"
 	"sync"
 )
 
@@ -262,7 +263,7 @@ func (x nat) itoa(neg bool, base int) []byte {
 	// convert power of two and non power of two bases separately
 	if b := Word(base); b == b&-b {
 		// shift is base b digit size in bits
-		shift := trailingZeroBits(b) // shift > 0 because b >= 2
+		shift := uint(bits.TrailingZeros(uint(b))) // shift > 0 because b >= 2
 		mask := Word(1<<shift - 1)
 		w := x[0]         // current word
 		nbits := uint(_W) // number of unprocessed bits in w