Esempio n. 1
0
// 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)
}
Esempio n. 2
0
// 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")
	}
}