public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return(XInt.One);
}
var p = XInt.One;
var r = XInt.One;
int h = 0, shift = 0, k = 1;
var log2N = XMath.FloorLog2(n);
while (h != n)
{
shift += h;
h = n >> log2N--;
var high = (h & 1) == 1 ? h : h - 1;
while (k != high)
{
k += 2;
p *= k;
}
r *= p;
}
return(r << shift);
}
public int Factor(int n)
{
this.n = n;
var lgN = XMath.FloorLog2(n);
var piN = 2 + (15 * n) / (8 * (lgN - 1));
this.primeList = new int[piN];
this.multiList = new int[piN];
return(this.card = this.PrimeFactors(n));
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
var log2N = XMath.FloorLog2(n);
var j = log2N;
var hN = n;
this.primeList = new int[log2N][];
this.listLength = new int[log2N];
this.bound = new int[log2N];
this.tower = new int[log2N + 1];
while (true)
{
this.tower[j] = hN;
if (hN == 1)
{
break;
}
this.bound[--j] = hN / 3;
var pLen = hN < 4 ? 6 : (int)(2.0 * (XMath.FloorSqrt(hN)
+ (double)hN / (XMath.Log2(hN) - 1)));
this.primeList[j] = new int[pLen];
hN >>= 1;
}
this.tower[0] = 2;
this.PrimeFactors(n);
var init = this.listLength[0] == 0 ? 1 : 3;
var oddFactorial = new XInt(init);
var results = new XInt[log2N];
Parallel.For(1, log2N, i =>
results[i] = XMath.Product(this.primeList[i], 0, this.listLength[i])
);
for (var i = 1; i < log2N; i++)
{
oddFactorial = XInt.Pow(oddFactorial, 2);
oddFactorial = oddFactorial * results[i];
}
return(oddFactorial << (n - XMath.BitCount(n)));
}
XInt IFactorialFunction.Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return(XInt.One);
}
var log2N = XMath.FloorLog2(n);
ProductDelegate prodDelegate = Product;
var results = new IAsyncResult[log2N];
int high = n, low = n >> 1, shift = low, taskCounter = 0;
// -- It is more efficient to add the big intervals
// -- first and the small ones later!
while ((low + 1) < high)
{
results[taskCounter++] = prodDelegate.BeginInvoke(low + 1, high, null, null);
high = low;
low >>= 1;
shift += low;
}
XInt p = XInt.One, r = XInt.One;
while (--taskCounter >= 0)
{
var I = Task.Factory.StartNew(() => r * p);
var t = p * prodDelegate.EndInvoke(results[taskCounter]);
r = I.Result;
p = t;
}
return((r * p) << shift);
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
this.sieve = new PrimeSieve(n);
var log2N = XMath.FloorLog2(n);
SwingDelegate swingDelegate = this.Swing;
var results = new IAsyncResult[log2N];
int h = 0, shift = 0, taskCounter = 0;
// -- It is more efficient to add the big intervals
// -- first and the small ones later!
while (h != n)
{
shift += h;
h = n >> log2N--;
if (h > 2)
{
results[taskCounter++] = swingDelegate.BeginInvoke(h, null, null);
}
}
XInt p = XInt.One, r = XInt.One, rl = XInt.One;
for (var i = 0; i < taskCounter; i++)
{
var t = rl * swingDelegate.EndInvoke(results[i]);
p = p * t;
rl = r;
r = r * p;
}
return(r << shift);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return(XInt.One);
}
var p = XInt.One;
var r = XInt.One;
this.currentN = XInt.One;
int h = 0, shift = 0, high = 1;
var log2N = XMath.FloorLog2(n);
while (h != n)
{
shift += h;
h = n >> log2N--;
var len = high;
high = (h - 1) | 1;
len = (high - len) / 2;
if (len > 0)
{
p *= this.Product(len);
r *= p;
}
}
return(r << shift);
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
var sieve = new PrimeSieve(n);
this.results = new IAsyncResult[XMath.FloorLog2(n)];
this.swingDelegate = Swing; this.taskCounter = 0;
var N = n;
// -- It is more efficient to add the big swings
// -- first and the small ones later!
while (N >= Smallswing)
{
this.results[this.taskCounter++] = this.swingDelegate.BeginInvoke(sieve, N, null, null);
N >>= 1;
}
return(this.RecFactorial(n) << (n - XMath.BitCount(n)));
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 20)
{
return(XMath.Factorial(n));
}
var lgN = XMath.FloorLog2(n);
var piN = 2 + (15 * n) / (8 * (lgN - 1));
this.primeList = new int[piN];
this.multiList = new int[piN];
var len = this.PrimeFactors(n);
var exp2 = n - XMath.BitCount(n);
return(this.RepeatedSquare(len, 1) << exp2);
}
