private OmgNum _FermaFactorization(Dictionary <OmgNum, OmgNum> result, OmgNum num)
{
OmgNum factor = null;
if (OmgOp.DivMod(num, 2.ToOmgNum()).mod.IsZero())
{
factor = 2.ToOmgNum();
}
if (factor == null)
{
OmgNum a = OmgOp.Sqrt(num);
OmgNum aSq = OmgOp.Multiply(a, a);
bool isSquare = OmgOp.Equal(num, aSq);
if (isSquare)
{
factor = a;
}
a.Inc();
aSq = OmgOp.Multiply(a, a);
var s = OmgOp.Subtract(aSq, num);
while (factor == null)
{
var testSqrt = OmgOp.Sqrt(s);
if (OmgOp.Equal(s, OmgOp.Multiply(testSqrt, testSqrt)))
{
factor = (OmgOp.Equal(testSqrt, a)) ? OmgOp.Add(a, a) : OmgOp.Subtract(a, testSqrt);
break;
}
a.Inc();
aSq = OmgOp.Multiply(a, a);
s = OmgOp.Subtract(aSq, num);
}
}
if (factor == null || factor.IsOne())
{
return(num);
}
OmgNum pow = _FindPow(ref num, factor);
if (result.ContainsKey(factor))
{
result[factor] = OmgOp.Add(result[factor], pow);
}
else
{
result[factor] = pow;
}
return(num);
}
private void _FactorPowerOfTwo(OmgNum num)
{
m_powerOfTwo?.Release();
m_initialTested?.Release();
var n = OmgOp.Subtract(num, OmgNum.GetConst(1));
m_powerOfTwo = 0.ToOmgNum();
(OmgNum div, OmgNum mod)divMod = OmgOp.DivMod(n, OmgNum.GetConst(2));
while (divMod.mod.IsZero())
{
n.Release();
divMod.mod.Release();
n = divMod.div;
m_powerOfTwo.Inc();
divMod = OmgOp.DivMod(n, OmgNum.GetConst(2));
}
divMod.div.Release();
divMod.mod.Release();
m_initialTested = n;
}
private OmgNum _FindPow(ref OmgNum num, OmgNum factor)
{
OmgNum pow = 0.ToOmgNum();
while (true)
{
var divMod = OmgOp.DivMod(num, factor);
if (!divMod.mod.IsZero())
{
break;
}
pow.Inc();
divMod.mod.Release();
num.Release();
num = divMod.div;
}
if (pow.IsZero())
{
throw new Exception();
}
return(pow);
}
private OmgNum _SelectExponent(OmgNum carmN)
{
OmgNum candidate = ((1 << 16) + 1).ToOmgNum();
OmgNum gcd = OmgOp.Gcd(candidate, carmN);
while (!gcd.IsOne())
{
gcd = OmgOp.Gcd(candidate.Inc(), carmN);
}
gcd.Release();
return(candidate);
}
public OmgNum FindFactor(OmgNum n, int maxIterations = -1)
{
m_iterations = 0;
m_current = n;
OmgNum x = OmgOp.Random(1.ToOmgNum(), OmgOp.Subtract(n, 2.ToOmgNum()));
OmgNum y = 1.ToOmgNum();
OmgNum i = 0.ToOmgNum();
OmgNum stage = 2.ToOmgNum();
OmgNum sub = OmgOp.Subtract(x, y).MakeAbs();
OmgNum gcd = OmgOp.Gcd(n, sub);
sub.Release();
while (gcd.IsOne())
{
if (maxIterations >= 0 && m_iterations++ > maxIterations)
{
return(null);
}
if (OmgOp.Equal(i, stage))
{
y.Release();
y = new OmgNum(x);
stage.MultByTwo();
}
OmgNum xSquare = OmgOp.Multiply(x, x).Inc();
x.Release();
x = OmgOp.Mod(xSquare, n);
xSquare.Release();
i.Inc();
sub = OmgOp.Subtract(x, y).MakeAbs();
gcd.Release();
gcd = OmgOp.Gcd(n, sub);
sub.Release();
}
return(gcd);
}
