func (ps *Swing) OddSwing(z *big.Int, k uint) *big.Int {
if k < uint(len(SmallOddSwing)) {
return z.SetInt64(SmallOddSwing[k])
}
rootK := xmath.FloorSqrt(k)
ps.factors = ps.factors[:0] // reset length, reusing existing capacity
ps.Sieve.Iterate(3, uint64(rootK), func(p uint64) (terminate bool) {
q := uint64(k) / p
for q > 0 {
if q&1 == 1 {
ps.factors = append(ps.factors, p)
}
q /= p
}
return
})
ps.Sieve.Iterate(uint64(rootK+1), uint64(k/3), func(p uint64) (term bool) {
if (uint64(k) / p & 1) == 1 {
ps.factors = append(ps.factors, p)
}
return
})
ps.Sieve.Iterate(uint64(k/2+1), uint64(k), func(p uint64) (term bool) {
ps.factors = append(ps.factors, p)
return
})
return xmath.Product(z, ps.factors)
}
// BinomialS computes the binomial coefficient C(n,k) using prime number
// sieve p. BinomialS returns nil if p is too small. Otherwise it leaves
// the result in z, replacing the existing value of z, and returning z.
func BinomialS(z *big.Int, p *sieve.Sieve, n, k uint) *big.Int {
if uint64(n) > p.Lim {
return nil
}
if k > n {
return z.SetInt64(0)
}
if k > n/2 {
k = n - k
}
if k < 3 {
switch k {
case 0:
return z.SetInt64(1)
case 1:
return z.SetInt64(int64(n))
case 2:
var n1 big.Int
return z.Rsh(z.Mul(z.SetInt64(int64(n)), n1.SetInt64(int64(n-1))), 1)
}
}
rootN := uint64(xmath.FloorSqrt(n))
var factors []uint64
p.Iterate(2, rootN, func(p uint64) (terminate bool) {
var r, nn, kk uint64 = 0, uint64(n), uint64(k)
for nn > 0 {
if nn%p < kk%p+r {
r = 1
factors = append(factors, p)
} else {
r = 0
}
nn /= p
kk /= p
}
return
})
p.Iterate(rootN+1, uint64(n/2), func(p uint64) (terminate bool) {
if uint64(n)%p < uint64(k)%p {
factors = append(factors, p)
}
return
})
p.Iterate(uint64(n-k+1), uint64(n), func(p uint64) (terminate bool) {
factors = append(factors, p)
return
})
return xmath.Product(z, factors)
}
func TestFloorSqrt(t *testing.T) {
tcs := []struct {
n, s uint
}{
{0, 0},
{1, 1},
{2, 1},
{3, 1},
{4, 2},
{5, 2},
{7, 2},
{1<<20 - 1, 1<<10 - 1},
{1 << 20, 1 << 10},
{1<<20 + 1, 1 << 10},
{math.MaxUint32 - 1, math.MaxUint16},
}
for _, tc := range tcs {
if s := xmath.FloorSqrt(tc.n); s != tc.s {
t.Errorf("FloorSqrt(%d) expected to be %d. got %d", tc.n, tc.s, s)
}
}
}