static void Main(string[] args)
{
var a = 234234.ToOmgNum();
var b = "85430534954938530495935803495482304983".ToOmgNum();
var c = "100000000000000000000000000000000".ToOmgNum();
var d = "-100000000000000000".ToOmgNum();
var a1 = OmgOp.Add(a, c);
var a2 = OmgOp.Subtract(a, c);
var a3 = OmgOp.Multiply(a, b);
var a4 = OmgOp.DivMod(b, c);
var a6 = OmgOp.Pow(b, c, a);
var a7 = OmgOp.Sqrt(b);
var sys1 = new OmgEqSys();
sys1.AddEq(1287.ToOmgNum(), 447.ToOmgNum(), 516.ToOmgNum());
bool success1 = sys1.TrySolve(out List <(OmgNum root, OmgNum mod)> solution1);
var sys2 = new OmgEqSys();
bool success2 = sys2.TrySolve(out var solution2);
}
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 _MakeGeronIteration()
{
OmgNum rootAprox = m_rootAprox.OmgWrapper();
var res = OmgOp.DivMod(m_targetSquareNum, rootAprox);
res.mod.Release();
OmgNum sum = OmgOp.Add(rootAprox, res.div);
res.div.Release();
sum.Raw.DivByTwo();
OmgPool.ReleaseNumber(m_buffer);
m_buffer = m_rootAprox;
m_rootAprox = sum.Raw;
}
public static IEnumerable <OmgNum> Decode(IEnumerable <OmgNum> code, PrivKey key)
{
foreach (var num in code)
{
OmgNum m1 = OmgOp.Pow(num, key.dP, key.P);
OmgNum m2 = OmgOp.Pow(num, key.dQ, key.Q);
OmgNum mdif = OmgOp.Subtract(m1, m2);
OmgNum h = OmgOp.Multiply(key.qInv, mdif, key.P);
OmgNum hq = OmgOp.Multiply(h, key.Q);
OmgNum m = OmgOp.Add(m2, hq);
m1.Release();
m2.Release();
mdif.Release();
h.Release();
hq.Release();
yield return(m);
}
}
internal RawNum MultiplyKaratsuba(RawNum left, RawNum right)
{
if (left.IsZero() || right.IsZero())
{
return(OmgPool.GetRawZero());
}
int n = Math.Min(left.Size, right.Size);
(RawNum head, RawNum tail)leftSep = _SeparateHead(left, n);
(RawNum head, RawNum tail)rightSep = _SeparateHead(right, n);
RawNum headsProd = Multiply(leftSep.head, rightSep.head);
RawNum tailsProd = Multiply(leftSep.tail, rightSep.tail);
RawNum headTail = Multiply(leftSep.head, rightSep.tail);
RawNum tailHead = Multiply(leftSep.tail, rightSep.head);
OmgNum midSum = OmgOp.Add(new OmgNum(headTail), new OmgNum(tailHead));
m_multRaw = OmgPool.GetRawZero();
m_multRaw.CopyFrom(tailsProd);
midSum.Raw.Digits.InsertRange(0, Enumerable.Repeat <uint>(0, n));
headsProd.Digits.InsertRange(0, Enumerable.Repeat <uint>(0, 2 * n));
OmgNum res = OmgOp.Add(new OmgNum(tailsProd), midSum);
OmgNum finalRes = OmgOp.Add(new OmgNum(headsProd), res);
midSum.Release();
res.Release();
OmgPool.ReleaseNumber(headTail);
OmgPool.ReleaseNumber(tailHead);
return(finalRes.Raw);
}
public Dictionary <OmgNum, OmgNum> Factorize(OmgNum num)
{
var initNum = num.Copy();
var result = new Dictionary <OmgNum, OmgNum>();
if (_IsSmallPrime(result, num))
{
return(result);
}
num = _FindFactorsWithPollard(result, num);
num = _FermaFactorization(result, num);
if (!num.IsOne())
{
result[num] = 1.ToOmgNum();
}
if (result.Count == 1 && result.TryGetValue(initNum, out var power) && power.IsOne())
{
return(result);
}
var nonPrimeFactors = new Stack <OmgNum>(result.Keys);
while (nonPrimeFactors.Count > 0)
{
var factor = nonPrimeFactors.Pop();
if (result[factor].IsZero())
{
result.Remove(factor);
continue;
}
var primeFactors = Factorize(factor);
if (primeFactors.Count == 1 && primeFactors.Values.First().IsOne())
{
continue;
}
var topPower = result[factor];
result.Remove(factor);
foreach (var primeFactor in primeFactors)
{
var pow = OmgOp.Multiply(topPower, primeFactor.Value);
if (result.ContainsKey(primeFactor.Key))
{
result[primeFactor.Key] = OmgOp.Add(result[primeFactor.Key], pow);
}
else
{
result[primeFactor.Key] = pow;
}
}
}
var keys = new List <OmgNum>(result.Keys);
foreach (var key in keys)
{
if (result[key].IsZero())
{
result.Remove(key);
}
}
return(result);
}