// 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)
}
// a few tests on the zero object
func TestZero(t *testing.T) {
// test Limit() on zero object
var s sieve.Sieve
n := s.Limit()
if n != 0 {
t.Error("zero object Limit() = ", n)
}
// test Iterate succeeds on zero object
if !s.Iterate(0, 0, func(uint64) bool {
return false
}) {
t.Error("Iterate fails on zero object")
}
// test Iterate fails on request > limit
if s.Iterate(0, 1, func(uint64) bool {
return false
}) {
t.Error("Iterate attempts request > limit on zero object")
}
}