public Reducer(UInt32MontgomeryReduction reduction, uint modulus)
: base(reduction, modulus)
{
if ((modulus & 1) == 0)
{
throw new InvalidOperationException("not relatively prime");
}
var nInv = IntegerMath.ModularInversePowerOfTwoModulus(modulus, 32);
k0 = IntegerMath.TwosComplement(nInv);
var rModN = uint.MaxValue % modulus + 1;
rSquaredModN = IntegerMath.ModularProduct(rModN, rModN, modulus);
}
private long Rho(long n, long xInit, long c)
{
if ((n & 1) == 0)
{
return(2);
}
var x = xInit;
var y = xInit;
var ys = y;
var r = 1;
var m = batchSize;
var g = (long)1;
do
{
x = y;
for (int i = 0; i < r; i++)
{
y = F(y, c, n);
}
var k = 0;
while (k < r && g == 1)
{
ys = y;
var limit = Math.Min(m, r - k);
var q = (long)1;
for (int i = 0; i < limit; i++)
{
y = F(y, c, n);
q = IntegerMath.ModularProduct(q, x - y, n);
}
g = IntegerMath.GreatestCommonDivisor(q, n);
k += limit;
}
r <<= 1;
}while (g == 1);
if (g == n)
{
do
{
ys = F(ys, c, n);
g = IntegerMath.GreatestCommonDivisor(x - ys, n);
}while (g == 1);
}
return(g);
}
public Reducer(UInt64MontgomeryReduction reduction, ulong modulus)
: base(reduction, modulus)
{
if ((modulus & 1) == 0)
{
throw new InvalidOperationException("not relatively prime");
}
int rLength = modulus == (uint)modulus ? 32 : 64;
var rMinusOne = rLength == 32 ? uint.MaxValue : ulong.MaxValue;
var rModN = rMinusOne % modulus + 1;
rSquaredModN = IntegerMath.ModularProduct(rModN, rModN, modulus);
var nInv = IntegerMath.ModularInversePowerOfTwoModulus(modulus, rLength);
k0 = (uint)IntegerMath.TwosComplement(nInv);
oneRep = 0;
}
public override Rational ModularProduct(Rational a, Rational b, Rational modulus)
{
return(IntegerMath.ModularProduct((BigInteger)a, (BigInteger)b, (BigInteger)modulus));
}
public override uint ModularProduct(uint a, uint b, uint modulus)
{
return(IntegerMath.ModularProduct(a, b, modulus));
}
public IResidue <int> Multiply(IResidue <int> x)
{
r = IntegerMath.ModularProduct(r, ((Residue)x).r, reducer.Modulus);
return(this);
}
protected static long F(long x, long c, long n)
{
return((IntegerMath.ModularProduct(x, x, n) + c) % n);
}
public override ulong ModularProduct(ulong a, ulong b, ulong modulus)
{
return(IntegerMath.ModularProduct(a, b, modulus));
}
public override double ModularProduct(double a, double b, double modulus)
{
return((double)IntegerMath.ModularProduct(ToBigInteger(a), ToBigInteger(b), ToBigInteger(modulus)));
}
public override Complex ModularProduct(Complex a, Complex b, Complex modulus)
{
return((Complex)IntegerMath.ModularProduct(ToBigInteger(a), ToBigInteger(b), ToBigInteger(modulus)));
}
public override BigInteger ModularProduct(BigInteger a, BigInteger b, BigInteger modulus)
{
return(IntegerMath.ModularProduct(a, b, modulus));
}
public override IResidue <UInt128> Multiply(IResidue <UInt128> x)
{
r = IntegerMath.ModularProduct(r, GetRep(x), reducer.modulus);
return(this);
}
