public XInt Factorial(int N)
{
var n = (uint)N;
var exp2 = (int)(n - MathFun.BitCount(n));
if (n < SmallOddFactorial.Length)
{
return(new XInt(SmallOddFactorial[n]) << exp2);
}
if (n >= SmallOddSwing.Length)
{
this.prime = new Primes(n);
this.factors = new Factors(n);
}
return(this.OddFactorial(n) << exp2);
}
//// Swing(n) = OddSwing(n) << (int)MathFun.BitCount(n);
private XInt OddSwing(uint n)
{
if (n < SmallOddSwing.Length)
{
return(new XInt(SmallOddSwing[n]));
}
var rootN = MathFun.FloorSqrt(n);
this.factors.Init();
this.factors.SetMax(rootN);
this.prime.Factorizer(3, rootN, p =>
{
var q = n;
while ((q /= p) > 0)
{
if ((q & 1) == 1)
{
this.factors.Add(p);
}
}
});
this.factors.SetMax(n / 3);
this.prime.Factorizer(rootN + 1, n / 3, p =>
{
if (((n / p) & 1) == 1)
{
this.factors.Add(p);
}
});
this.factors.SetMax(n);
this.prime.Factorizer(n / 2 + 1, n, p =>
{
this.factors.Add(p);
});
return(this.factors.Product());
}
public XInt GetPrimorial(uint min, uint max)
{
var mem = (int)(0.63 * max / System.Math.Log(max));
var plist = new long[mem];
var size = 0;
if (min <= 2)
{
plist[size++] = 2;
}
if (min <= 3)
{
plist[size++] = 3;
}
var absPos = (int)((min + (min + 1) % 2) / 3 - 1);
var index = absPos / BitsPerInt;
var bitPos = absPos % BitsPerInt;
bool toggle = (bitPos & 1) == 1;
var prime = (uint)(5 + 3 * (BitsPerInt * index + bitPos) - (bitPos & 1));
while (prime <= max)
{
var bitField = this.isComposite[index++] >> bitPos;
for (; bitPos < BitsPerInt; bitPos++)
{
if ((bitField & 1) == 0)
{
plist[size++] = prime;
}
prime += (toggle = !toggle) ? 2u : 4u;
if (prime > max)
{
return(MathFun.Product(plist, 0, size));
}
bitField >>= 1;
}
bitPos = 0;
}
return(XInt.Zero);
}
public XInt Product()
{
this.factors[this.count++] = this.prod;
return(MathFun.Product(this.factors, 0, this.count));
}
