public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 7)
{
return((XInt)(new[] { 1, 1, 2, 6, 24, 120, 720 })[n]);
}
long h = n / 2;
var q = h * h;
var f = new long[(int)h];
f[0] = (n & 1) == 1 ? 2 * q * n : 2 * q;
var i = 1;
for (var d = 1; d < n - 2; d += 2)
{
f[i++] = q -= d;
}
return(XMath.Product(f, f.Length));
}
public void WriteFactors(TextWriter file)
{
if (file == null)
{
return;
}
file.WriteLine("The prime factors of {0}! ", this.n);
var sum = this.n - XMath.BitCount(this.n);
file.Write("2^{0}", sum);
for (var p = 0; p < this.card; p++)
{
int f = this.primeList[p], m = this.multiList[p];
sum += m;
if (m > 1)
{
file.Write("*{0}^{1}", f, m);
}
else
{
file.Write("*{0}", f);
}
}
file.WriteLine();
file.WriteLine("Number of different factors: {0} ", this.card);
file.WriteLine("Number of all factors: {0} ", sum);
}
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 XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
int r = n % 8, s = n / 8 + 1;
var rf = (long)(new int[] { 1, 1, 2, 6, 24, 120, 720, 5040 })[r];
if (n < 8)
{
return(rf);
}
var factors = new XInt[s];
factors[s - 1] = rf;
Parallel.For(0, s - 1, i =>
{
factors[i] = CPpoly(i * 8 + r + 1);
});
return(XMath.Product(factors, 0, s));
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
this.sieve = new PrimeSieve(n);
return(this.RecFactorial(n));
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new ArithmeticException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
this.oddFactNdiv4 = this.oddFactNdiv2 = XInt.One;
return(this.OddFactorial(n) << (n - XMath.BitCount(n)));
}
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));
}
private XInt Swing(int n)
{
if (n < 33)
{
return(SmallOddSwing[n]);
}
var count = 0;
var rootN = XMath.FloorSqrt(n);
var j = 1;
var prod = XInt.One;
int high;
while (true)
{
high = n / j++;
var low = n / j++;
if (low < rootN)
{
low = rootN;
}
if (high - low < 32)
{
break;
}
var primorial = this.GetPrimorial(low + 1, high);
prod *= primorial;
}
var primes = this.sieve.GetPrimeCollection(3, high);
foreach (var prime in primes)
{
int q = n, p = 1;
while ((q /= prime) > 0)
{
if ((q & 1) == 1)
{
p *= prime;
}
}
if (p > 1)
{
this.primeList[count++] = p;
}
}
return(prod * XMath.Product(this.primeList, 0, count));
}
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)));
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
this.cache = new Dictionary <int, CachedPrimorial>();
this.sieve = new PrimeSieve(n);
var pLen = (int)(2.0 * (XMath.FloorSqrt(n)
+ (double)n / (XMath.Log2(n) - 1)));
this.primeList = new int[pLen];
var exp2 = n - XMath.BitCount(n);
return(this.RecFactorial(n) << exp2);
}
private XInt Swing(int n)
{
if (n < 33)
{
return(SmallOddSwing[n]);
}
var primorial = Task.Factory.StartNew(() => this.sieve.GetPrimorial(n / 2 + 1, n));
var count = 0;
var rootN = XMath.FloorSqrt(n);
var aPrimes = this.sieve.GetPrimeCollection(3, rootN);
var bPrimes = this.sieve.GetPrimeCollection(rootN + 1, n / 3);
var piN = aPrimes.NumberOfPrimes + bPrimes.NumberOfPrimes;
var primeList = new int[piN];
foreach (var prime in aPrimes)
{
int q = n, p = 1;
while ((q /= prime) > 0)
{
if ((q & 1) == 1)
{
p *= prime;
}
}
if (p > 1)
{
primeList[count++] = p;
}
}
foreach (var prime in bPrimes.Where(prime => ((n / prime) & 1) == 1))
{
primeList[count++] = prime;
}
var primeProduct = XMath.Product(primeList, 0, count);
return(primeProduct * primorial.Result);
}
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 < 7)
{
return((XInt)(new int[] { 1, 1, 2, 6, 24, 120, 720 })[n]);
}
int i = 1, loop = n / 2;
var f = new long[loop + (n & 1)];
f[0] = loop;
if ((n & 1) == 1)
{
f[loop] = n;
}
long s = loop;
for (var inc = loop - 1; inc > 0; inc--)
{
s += inc;
var t = s;
while ((t & 1) == 0)
{
t /= 2;
loop++;
}
f[i++] = t;
}
return(XMath.Product(f) << loop);
}
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)));
}
private static XInt Swing(PrimeSieve sieve, int n)
{
var primorial = Task.Factory.StartNew <XInt>(() => sieve.GetPrimorial(n / 2 + 1, n));
var count = 0;
var rootN = XMath.FloorSqrt(n);
var aPrimes = sieve.GetPrimeCollection(3, rootN);
var bPrimes = sieve.GetPrimeCollection(rootN + 1, n / 3);
var primeList = new int[aPrimes.NumberOfPrimes + bPrimes.NumberOfPrimes];
foreach (var prime in aPrimes)
{
int q = n, p = 1;
while ((q /= prime) > 0)
{
if ((q & 1) == 1)
{
p *= prime;
}
}
if (p > 1)
{
primeList[count++] = p;
}
}
foreach (var prime in bPrimes.Where(prime => ((n / prime) & 1) == 1))
{
primeList[count++] = prime;
}
var primeProduct = XMath.Product(primeList, 0, count);
return(primeProduct * primorial.Result);
}
private XInt RepeatedSquare(int len, int k)
{
if (len == 0)
{
return(XInt.One);
}
int i = 0, mult = this.multiList[0];
while (mult > 1)
{
if ((mult & 1) == 1) // is mult odd ?
{
this.primeList[len++] = this.primeList[i];
}
this.multiList[i++] = mult >> 1;
mult = this.multiList[i];
}
var p = XMath.Product(this.primeList, i, len - i);
return(XInt.Pow(p, k) * this.RepeatedSquare(i, 2 * k));
}
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);
}
private XInt MiddleBinomial(int n) // assuming n = 2k
{
if (n < 50)
{
return(new XInt(Binomial[n / 2]));
}
int k = n / 2, pc = 0, pp = 0;
var rootN = XMath.FloorSqrt(n);
var bigPrimes = this.sieve.GetPrimorial(k + 1, n);
var smallPrimes = this.sieve.GetPrimorial(k / 2 + 1, n / 3);
var primes = this.sieve.GetPrimeCollection(rootN + 1, n / 5);
var primeList = new int[primes.NumberOfPrimes];
foreach (var prime in primes.Where(prime => (n / prime & 1) == 1))
{
primeList[pc++] = prime;
}
var prodPrimes = XMath.Product(primeList, 0, pc);
primes = this.sieve.GetPrimeCollection(1, rootN);
var primePowers = new XInt[primes.NumberOfPrimes];
var exp = 0;
foreach (var prime in primes.Where(prime => (exp = ExpSum(prime, n)) > 0))
{
primePowers[pp++] = XInt.Pow(prime, exp);
}
var powerPrimes = XMath.Product(primePowers, 0, pp);
return(bigPrimes * smallPrimes * prodPrimes * powerPrimes);
}
