private int PrimeFactors(int n)
{
var sieve = new PrimeSieve(n);
var primes = sieve.GetPrimeCollection(3, n);
int maxBound = n / 2, count = 0;
foreach (var prime in primes)
{
var m = prime > maxBound ? 1 : 0;
if (prime <= maxBound)
{
var q = n;
while (q >= prime)
{
m += q /= prime;
}
}
this.primeList[count] = prime;
this.multiList[count++] = m;
}
return count;
}
private int PrimeFactors(int n)
{
var sieve = new PrimeSieve(n);
var primeCollection = sieve.GetPrimeCollection(2, n);
int maxBound = n / 2, count = 0;
foreach (var prime in primeCollection)
{
var m = prime > maxBound ? 1 : 0;
if (prime <= maxBound)
{
var q = n;
while (q >= prime)
{
m += q /= prime;
}
}
this.primeList[count] = prime;
this.multiList[count++] = m;
}
return(count);
}
private void PrimeFactors(int n)
{
var maxBound = n / 3;
var lastList = this.primeList.Length - 1;
var start = this.tower[1] == 2 ? 1 : 0;
var sieve = new PrimeSieve(n);
for (var section = start; section < this.primeList.Length; section++)
{
var primes = sieve.GetPrimeCollection(this.tower[section] + 1, this.tower[section + 1]);
foreach (var prime in primes)
{
this.primeList[section][this.listLength[section]++] = prime;
if (prime > maxBound) continue;
var np = n;
do
{
var k = lastList;
var q = np /= prime;
do if ((q & 1) == 1) //if q is odd
{
this.primeList[k][this.listLength[k]++] = prime;
}
while (((q >>= 1) > 0) && (prime <= this.bound[--k]));
} while (prime <= np);
}
}
}
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 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 void PrimeFactors(int n)
{
var maxBound = n / 3;
var lastList = this.primeList.Length - 1;
var start = this.tower[1] == 2 ? 1 : 0;
var sieve = new PrimeSieve(n);
for (var section = start; section < this.primeList.Length; section++)
{
var primes = sieve.GetPrimeCollection(this.tower[section] + 1, this.tower[section + 1]);
foreach (var prime in primes)
{
this.primeList[section][this.listLength[section]++] = prime;
if (prime > maxBound)
{
continue;
}
var np = n;
do
{
var k = lastList;
var q = np /= prime;
do
{
if ((q & 1) == 1) //if q is odd
{
this.primeList[k][this.listLength[k]++] = prime;
}
}while (((q >>= 1) > 0) && (prime <= this.bound[--k]));
} while (prime <= np);
}
}
}
public XInt Factorial(int n)
{
if (n < 20) { return XMath.Factorial(n); }
var rootN = XMath.FloorSqrt(n);
var log2N = XMath.FloorLog2(n);
var section = new XInt[log2N + 1];
for (var i = 0; i < section.Length; i++)
{
section[i] = XInt.One;
}
var sieve = new PrimeSieve(n);
var primes = sieve.GetPrimeCollection(3, rootN);
foreach (var prime in primes)
{
int k = 0, m = 0, q = n;
do
{
m += q /= prime;
} while (q >= 1);
while (m > 0)
{
if ((m & 1) == 1)
{
section[k] *= prime;
}
m = m / 2;
k++;
}
}
var j = 2;
var low = n;
while (low != rootN)
{
var high = low;
low = n / j++;
if (low < rootN) { low = rootN; }
var primorial = sieve.GetPrimorial(low + 1, high);
if (primorial != XInt.One)
{
int k = 0, m = j - 2;
while (m > 0)
{
if ((m & 1) == 1)
{
section[k] *= primorial;
}
m = m / 2;
k++;
}
}
}
var factorial = section[log2N];
for (var i = log2N - 1; i >= 0; --i)
{
factorial = XInt.Pow(factorial,2) * section[i];
}
var exp2N = n - XMath.BitCount(n);
return factorial << exp2N;
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
var rootN = XMath.FloorSqrt(n);
var log2N = XMath.FloorLog2(n);
var section = new XInt[log2N + 1];
for (var i = 0; i < section.Length; i++)
{
section[i] = XInt.One;
}
var sieve = new PrimeSieve(n);
var primes = sieve.GetPrimeCollection(3, rootN);
foreach (var prime in primes)
{
int k = 0, m = 0, q = n;
do
{
m += q /= prime;
} while (q >= 1);
while (m > 0)
{
if ((m & 1) == 1)
{
section[k] *= prime;
}
m = m / 2;
k++;
}
}
var j = 2;
var low = n;
while (low != rootN)
{
var high = low;
low = n / j++;
if (low < rootN)
{
low = rootN;
}
var primorial = sieve.GetPrimorial(low + 1, high);
if (primorial != XInt.One)
{
int k = 0, m = j - 2;
while (m > 0)
{
if ((m & 1) == 1)
{
section[k] *= primorial;
}
m = m / 2;
k++;
}
}
}
var factorial = section[log2N];
for (var i = log2N - 1; i >= 0; --i)
{
factorial = XInt.Pow(factorial, 2) * section[i];
}
var exp2N = n - XMath.BitCount(n);
return(factorial << exp2N);
}