Commit 014d036d authored by Robert Griesemer's avatar Robert Griesemer

math/big: added nat.trailingZeroBits, simplified some code

Will simplify implementation of binaryGCD.

R=rsc, cswenson
CC=golang-dev
https://golang.org/cl/6299064
parent 7762a9dc
......@@ -740,7 +740,7 @@ func (x nat) string(charset string) string {
// convert power of two and non power of two bases separately
if b == b&-b {
// shift is base-b digit size in bits
shift := uint(trailingZeroBits(b)) // shift > 0 because b >= 2
shift := trailingZeroBits(b) // shift > 0 because b >= 2
mask := Word(1)<<shift - 1
w := x[0]
nbits := uint(_W) // number of unprocessed bits in w
......@@ -993,10 +993,9 @@ var deBruijn64Lookup = []byte{
54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
}
// trailingZeroBits returns the number of consecutive zero bits on the right
// side of the given Word.
// See Knuth, volume 4, section 7.3.1
func trailingZeroBits(x Word) int {
// 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
......@@ -1005,11 +1004,12 @@ func trailingZeroBits(x Word) int {
// 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 int(deBruijn32Lookup[((x&-x)*deBruijn32)>>27])
return uint(deBruijn32Lookup[((x&-x)*deBruijn32)>>27])
case 64:
return int(deBruijn64Lookup[((x&-x)*(deBruijn64&_M))>>58])
return uint(deBruijn64Lookup[((x&-x)*(deBruijn64&_M))>>58])
default:
panic("Unknown word size")
}
......@@ -1017,6 +1017,20 @@ func trailingZeroBits(x Word) int {
return 0
}
// trailingZeroBits returns the number of consecutive least significant zero
// bits of x.
func (x nat) trailingZeroBits() uint {
if len(x) == 0 {
return 0
}
var i uint
for x[i] == 0 {
i++
}
// x[i] != 0
return i*_W + trailingZeroBits(x[i])
}
// z = x << s
func (z nat) shl(x nat, s uint) nat {
m := len(x)
......@@ -1169,29 +1183,6 @@ func (x nat) modW(d Word) (r Word) {
return divWVW(q, 0, x, d)
}
// powersOfTwoDecompose finds q and k with x = q * 1<<k and q is odd, or q and k are 0.
func (x nat) powersOfTwoDecompose() (q nat, k int) {
if len(x) == 0 {
return x, 0
}
// One of the words must be non-zero by definition,
// so this loop will terminate with i < len(x), and
// i is the number of 0 words.
i := 0
for x[i] == 0 {
i++
}
n := trailingZeroBits(x[i]) // x[i] != 0
q = make(nat, len(x)-i)
shrVU(q, x[i:], uint(n))
q = q.norm()
k = i*_W + n
return
}
// random creates a random integer in [0..limit), using the space in z if
// possible. n is the bit length of limit.
func (z nat) random(rand *rand.Rand, limit nat, n int) nat {
......@@ -1343,8 +1334,9 @@ func (n nat) probablyPrime(reps int) bool {
}
nm1 := nat(nil).sub(n, natOne)
// 1<<k * q = nm1;
q, k := nm1.powersOfTwoDecompose()
// determine q, k such that nm1 = q << k
k := nm1.trailingZeroBits()
q := nat(nil).shr(nm1, k)
nm3 := nat(nil).sub(nm1, natTwo)
rand := rand.New(rand.NewSource(int64(n[0])))
......@@ -1360,7 +1352,7 @@ NextRandom:
if y.cmp(natOne) == 0 || y.cmp(nm1) == 0 {
continue
}
for j := 1; j < k; j++ {
for j := uint(1); j < k; j++ {
y = y.mul(y, y)
quotient, y = quotient.div(y, y, n)
if y.cmp(nm1) == 0 {
......
......@@ -613,14 +613,23 @@ func TestModW(t *testing.T) {
}
func TestTrailingZeroBits(t *testing.T) {
var x Word
x--
for i := 0; i < _W; i++ {
if trailingZeroBits(x) != i {
t.Errorf("Failed at step %d: x: %x got: %d", i, x, trailingZeroBits(x))
x := Word(1)
for i := uint(0); i <= _W; i++ {
n := trailingZeroBits(x)
if n != i%_W {
t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W)
}
x <<= 1
}
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.string(lowercaseDigits[0:16]), n, i)
}
y = y.shl(y, 1)
}
}
var expNNTests = []struct {
......
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