internal RawNum Sqrt(RawNum left)
{
m_targetSquare = left;
m_targetSquareNum = m_targetSquare.OmgWrapper();
m_rootAprox = OmgPool.GetRawZero();
m_buffer = OmgPool.GetRawZero();
_FillInitialApproximation();
while (!_AproxEqualToBuffer())
{
var aproxCopy = OmgPool.GetRawZero();
aproxCopy.CopyFrom(m_rootAprox);
var bufferCopy = OmgPool.GetRawZero();
bufferCopy.CopyFrom(m_buffer);
_MakeGeronIteration();
if (OmgOp.Equal(aproxCopy.OmgWrapper(), m_buffer.OmgWrapper()) &&
OmgOp.Equal(bufferCopy.OmgWrapper(), m_rootAprox.OmgWrapper()) &&
OmgOp.Less(m_rootAprox.OmgWrapper(), m_buffer.OmgWrapper()))
{
break;
}
OmgPool.ReleaseNumber(bufferCopy);
OmgPool.ReleaseNumber(aproxCopy);
}
OmgPool.ReleaseNumber(m_buffer);
return(m_rootAprox);
}
public (OmgNum div, OmgNum mod) DivMod(OmgNum left, OmgNum right)
{
_InitializeDivModResult();
if (OmgOp.Equal(right, s_two))
{
_DivModByTwo(left);
return(m_divRes, m_modRes);
}
bool isNegative = left.IsNegative != right.IsNegative;
m_divRes.IsNegative = isNegative;
_FindDivModSolution(left.Raw, right.Raw);
if (isNegative)
{
m_divRaw.Inc();
_Subtract(right.Raw, m_modRaw);
}
_RemoveModLeadingZeros();
return(m_divRes, m_modRes);
}
private bool _MakeTest(OmgNum testBase)
{
OmgNum numDec = (new OmgNum(m_tested)).Dec();
OmgNum tested = OmgOp.Pow(testBase, m_initialTested, m_tested);
OmgNum iterationsLeft = new OmgNum(m_powerOfTwo);
try {
if (OmgOp.Equal(tested, OmgNum.GetConst(1)) || OmgOp.Equal(tested, numDec))
{
return(true);
}
while (!iterationsLeft.IsZero())
{
iterationsLeft.Dec();
var nwTested = OmgOp.Multiply(tested, tested, m_tested);
tested.Release();
tested = nwTested;
if (OmgOp.Equal(tested, numDec))
{
return(true);
}
}
return(false);
}
finally {
numDec.Release();
tested.Release();
iterationsLeft.Release();
}
}
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 bool _IsSmallPrime(Dictionary <OmgNum, OmgNum> result, OmgNum num)
{
smallPrimesOmg ??= smallPrimes.Select(x => x.ToOmgNum()).ToArray();
foreach (var prime in smallPrimesOmg)
{
if (OmgOp.Equal(prime, num))
{
result[prime] = 1.ToOmgNum();
return(true);
}
}
return(false);
}
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);
}
private OmgNum _FindFactorsWithPollard(Dictionary <OmgNum, OmgNum> result, OmgNum num)
{
num = num.Copy();
while (!num.IsOne())
{
OmgNum factor = m_polard.FindFactor(num, maxIterations: 100000);
if (factor == null || factor.IsOne() || OmgOp.Equal(factor, num))
{
return(num);
}
OmgNum pow = _FindPow(ref num, factor);
result[factor] = pow;
}
return(num);
}
public bool IsPrime(OmgNum tested)
{
foreach (var prime in s_smallPrimes)
{
if (OmgOp.Less(tested, prime) || OmgOp.Equal(tested, prime))
{
return(true);
}
var mod = OmgOp.Mod(tested, prime);
bool isComposite = mod.IsZero();
mod.Release();
if (isComposite)
{
return(false);
}
}
return(true);
}
private bool _AproxEqualToBuffer()
{
return(OmgOp.Equal(m_rootAprox.OmgWrapper(), m_buffer.OmgWrapper()));
}