// FactorialS computes n! given an existing swing.Swing object.
//
// It allows multiple factorials to be computed after computing prime numbers
// just once. The swing.Swing object encapsulates a prime number sieve.
//
// For computing factorials up to n, the swing.Swing object should be
// constructed with with the same or greater n.
//
// FactorialS returns nil if the sieve is not big enough.
func FactorialS(z *big.Int, ps *swing.Swing, n uint) *big.Int {
var oddFactorial func(*big.Int, uint) *big.Int
oddFactorial = func(z *big.Int, n uint) *big.Int {
if n < uint(len(swing.SmallOddFactorial)) {
return z.SetInt64(swing.SmallOddFactorial[n])
}
oddFactorial(z, n/2)
var os big.Int
return z.Mul(z.Mul(z, z), ps.OddSwing(&os, n))
}
return z.Lsh(oddFactorial(z, n), n-xmath.BitCount32(uint32(n)))
}
func init() {
smallPiLimit = 2
for _, w := range smallComposites {
smallPiLimit += uint64(32 - xmath.BitCount32(w))
}
}
// SwingingFactorial member computes n≀ on a Swing object.
func (ps *Swing) SwingingFactorial(z *big.Int, n uint) *big.Int {
if uint64(n) > ps.Sieve.Lim {
return nil
}
return z.Lsh(ps.OddSwing(z, n), xmath.BitCount32(uint32(n>>1)))
}