internal void SubtractPositive(Integer Result, Integer ToSub)
{
if (ToSub.IsULong())
{
SubtractULong(Result, ToSub.GetAsULong());
return;
}
if (ToSub.GetIndex() > Result.GetIndex())
{
throw(new Exception("In Subtract() ToSub.Index > Index."));
}
int Max = ToSub.GetIndex();
for (int Count = 0; Count <= Max; Count++)
{
SignedD[Count] = (long)Result.GetD(Count) - (long)ToSub.GetD(Count);
}
Max = Result.GetIndex();
for (int Count = ToSub.GetIndex() + 1; Count <= Max; Count++)
{
SignedD[Count] = (long)Result.GetD(Count);
}
Max = Result.GetIndex();
for (int Count = 0; Count < Max; Count++)
{
if (SignedD[Count] < 0)
{
SignedD[Count] += (long)0xFFFFFFFF + 1;
SignedD[Count + 1]--;
}
}
if (SignedD[Result.GetIndex()] < 0)
{
throw(new Exception("Subtract() SignedD[Index] < 0."));
}
Max = Result.GetIndex();
for (int Count = 0; Count <= Max; Count++)
{
Result.SetD(Count, (ulong)SignedD[Count]);
}
for (int Count = Result.GetIndex(); Count >= 0; Count--)
{
if (Result.GetD(Count) != 0)
{
Result.SetIndex(Count);
return;
}
}
// If it never found a non-zero digit it would get down to here.
Result.SetIndex(0);
}
// This is a variation on ShortDivide that returns
// the remainder.
// Also, DivideBy is a ulong.
internal ulong ShortDivideRem(Integer ToDivideOriginal,
ulong DivideByU,
Integer Quotient)
{
if (ToDivideOriginal.IsULong())
{
ulong ToDiv = ToDivideOriginal.GetAsULong();
ulong Q = ToDiv / DivideByU;
Quotient.SetFromULong(Q);
return(ToDiv % DivideByU);
}
ToDivide.Copy(ToDivideOriginal);
Quotient.Copy(ToDivide);
ulong RemainderU = 0;
if (DivideByU > Quotient.GetD(Quotient.GetIndex()))
{
Quotient.SetD(Quotient.GetIndex(), 0);
}
else
{
ulong OneDigit = Quotient.GetD(Quotient.GetIndex());
Quotient.SetD(Quotient.GetIndex(), OneDigit / DivideByU);
RemainderU = OneDigit % DivideByU;
ToDivide.SetD(ToDivide.GetIndex(), RemainderU);
}
for (int Count = Quotient.GetIndex(); Count >= 1; Count--)
{
ulong TwoDigits = ToDivide.GetD(Count);
TwoDigits <<= 32;
TwoDigits |= ToDivide.GetD(Count - 1);
Quotient.SetD(Count - 1, TwoDigits / DivideByU);
RemainderU = TwoDigits % DivideByU;
ToDivide.SetD(Count, 0);
ToDivide.SetD(Count - 1, RemainderU);
}
for (int Count = Quotient.GetIndex(); Count >= 0; Count--)
{
if (Quotient.GetD(Count) != 0)
{
Quotient.SetIndex(Count);
break;
}
}
return(RemainderU);
}
internal string ToString10(Integer From)
{
if (From.IsULong())
{
ulong N = From.GetAsULong();
if (From.IsNegative)
{
return("-" + N.ToString("N0"));
}
else
{
return(N.ToString("N0"));
}
}
string Result = "";
ToDivide.Copy(From);
int CommaCount = 0;
while (!ToDivide.IsZero())
{
uint Digit = (uint)Divider.ShortDivideRem(ToDivide, 10, Quotient);
ToDivide.Copy(Quotient);
if (((CommaCount % 3) == 0) && (CommaCount != 0))
{
Result = Digit.ToString() + "," + Result; // Or use a StringBuilder.
}
else
{
Result = Digit.ToString() + Result;
}
CommaCount++;
}
if (From.IsNegative)
{
return("-" + Result);
}
else
{
return(Result);
}
}
// This is a variation on ShortDivide() to get the
// remainder only.
internal ulong GetMod32(Integer ToDivideOriginal, ulong DivideByU)
{
if ((DivideByU >> 32) != 0)
{
throw(new Exception("GetMod32: (DivideByU >> 32) != 0."));
}
// If this is _equal_ to a small prime it would return zero.
if (ToDivideOriginal.IsULong())
{
ulong Result = ToDivideOriginal.GetAsULong();
return(Result % DivideByU);
}
ToDivide.Copy(ToDivideOriginal);
ulong RemainderU = 0;
if (DivideByU <= ToDivide.GetD(ToDivide.GetIndex()))
{
ulong OneDigit = ToDivide.GetD(ToDivide.GetIndex());
RemainderU = OneDigit % DivideByU;
ToDivide.SetD(ToDivide.GetIndex(), RemainderU);
}
for (int Count = ToDivide.GetIndex(); Count >= 1; Count--)
{
ulong TwoDigits = ToDivide.GetD(Count);
TwoDigits <<= 32;
TwoDigits |= ToDivide.GetD(Count - 1);
RemainderU = TwoDigits % DivideByU;
ToDivide.SetD(Count, 0);
ToDivide.SetD(Count - 1, RemainderU);
}
return(RemainderU);
}
internal bool FindMultiplicativeInverseSmall(Integer ToFind, Integer KnownNumber, Integer Modulus)
{
// This method is for: KnownNumber * ToFind = 1 mod Modulus
// An example:
// PublicKeyExponent * X = 1 mod PhiN.
// PublicKeyExponent * X = 1 mod (P - 1)(Q - 1).
// This means that
// (PublicKeyExponent * X) = (Y * PhiN) + 1
// X is less than PhiN.
// So Y is less than PublicKExponent.
// Y can't be zero.
// If this equation can be solved then it can be solved modulo
// any number. So it has to be solvable mod PublicKExponent.
// See: Hasse Principle.
// This also depends on the idea that the KnownNumber is prime and
// that there is one unique modular inverse.
// if( !KnownNumber-is-a-prime )
// then it won't work.
if (!KnownNumber.IsULong())
{
throw(new Exception("FindMultiplicativeInverseSmall() was called with too big of a KnownNumber."));
}
ulong KnownNumberULong = KnownNumber.GetAsULong();
// 65537
if (KnownNumberULong > 1000000)
{
throw(new Exception("KnownNumberULong > 1000000. FindMultiplicativeInverseSmall() was called with too big of an exponent."));
}
// (Y * PhiN) + 1 mod PubKExponent has to be zero if Y is a solution.
ulong ModulusModKnown = Divider.GetMod32(Modulus, KnownNumberULong);
// Worker.ReportProgress( 0, "ModulusModExponent: " + ModulusModKnown.ToString( "N0" ));
// if( Worker.CancellationPending )
// return false;
// Y can't be zero.
// The exponent is a small number like 65537.
for (uint Y = 1; Y < (uint)KnownNumberULong; Y++)
{
ulong X = (ulong)Y * ModulusModKnown;
X++; // Add 1 to it for (Y * PhiN) + 1.
X = X % KnownNumberULong;
if (X == 0)
{
// if( Worker.CancellationPending )
// return false;
// What is PhiN mod 65537?
// That gives me Y.
// The private key exponent is X*65537 + ModPart
// The CipherText raised to that is the PlainText.
// P + zN = C^(X*65537 + ModPart)
// P + zN = C^(X*65537)(C^ModPart)
// P + zN = ((C^65537)^X)(C^ModPart)
// Worker.ReportProgress( 0, "Found Y at: " + Y.ToString( "N0" ));
ToFind.Copy(Modulus);
Multiplier.MultiplyULong(ToFind, Y);
ToFind.AddULong(1);
Divider.Divide(ToFind, KnownNumber, Quotient, Remainder);
if (!Remainder.IsZero())
{
throw(new Exception("This can't happen. !Remainder.IsZero()"));
}
ToFind.Copy(Quotient);
// Worker.ReportProgress( 0, "ToFind: " + ToString10( ToFind ));
break;
}
}
// if( Worker.CancellationPending )
// return false;
TestForModInverse1.Copy(ToFind);
Multiplier.MultiplyULong(TestForModInverse1, KnownNumberULong);
Divider.Divide(TestForModInverse1, Modulus, Quotient, Remainder);
if (!Remainder.IsOne())
{
// The definition is that it's congruent to 1 mod the modulus,
// so this has to be 1.
// I've only seen this happen once. Were the primes P and Q not
// really primes?
throw(new Exception("Remainder has to be 1: " + ToString10(Remainder)));
}
return(true);
}
internal void SubtractULong(Integer Result, ulong ToSub)
{
if (Result.IsULong())
{
ulong ResultU = Result.GetAsULong();
if (ToSub > ResultU)
{
throw(new Exception("SubULong() (IsULong() and (ToSub > Result)."));
}
ResultU = ResultU - ToSub;
Result.SetD(0, ResultU & 0xFFFFFFFF);
Result.SetD(1, ResultU >> 32);
if (Result.GetD(1) == 0)
{
Result.SetIndex(0);
}
else
{
Result.SetIndex(1);
}
return;
}
// If it got this far then Index is at least 2.
SignedD[0] = (long)Result.GetD(0) - (long)(ToSub & 0xFFFFFFFF);
SignedD[1] = (long)Result.GetD(1) - (long)(ToSub >> 32);
if ((SignedD[0] >= 0) && (SignedD[1] >= 0))
{
// No need to reorganize it.
Result.SetD(0, (ulong)SignedD[0]);
Result.SetD(1, (ulong)SignedD[1]);
return;
}
int Max = Result.GetIndex();
for (int Count = 2; Count <= Max; Count++)
{
SignedD[Count] = (long)Result.GetD(Count);
}
Max = Result.GetIndex();
for (int Count = 0; Count < Max; Count++)
{
if (SignedD[Count] < 0)
{
SignedD[Count] += (long)0xFFFFFFFF + 1;
SignedD[Count + 1]--;
}
}
if (SignedD[Result.GetIndex()] < 0)
{
throw(new Exception("SubULong() SignedD[Index] < 0."));
}
Max = Result.GetIndex();
for (int Count = 0; Count <= Max; Count++)
{
Result.SetD(Count, (ulong)SignedD[Count]);
}
Max = Result.GetIndex();
for (int Count = Max; Count >= 0; Count--)
{
if (Result.GetD(Count) != 0)
{
Result.SetIndex(Count);
return;
}
}
// If this was zero it wouldn't find a nonzero
// digit to set the Index to and it would end up down here.
Result.SetIndex(0);
}
internal void MakeRSAKeys()
{
int ShowBits = (PrimeIndex + 1) * 32;
// int TestLoops = 0;
Worker.ReportProgress(0, "Making RSA keys.");
Worker.ReportProgress(0, "Bits size is: " + ShowBits.ToString());
// ulong Loops = 0;
while (true)
{
if (Worker.CancellationPending)
{
return;
}
Thread.Sleep(1); // Let other things run.
// Make two prime factors.
// Normally you'd only make new primes when you pay the Certificate
// Authority for a new certificate.
if (!MakeAPrime(PrimeP, PrimeIndex, 20))
{
return;
}
if (Worker.CancellationPending)
{
return;
}
if (!MakeAPrime(PrimeQ, PrimeIndex, 20))
{
return;
}
if (Worker.CancellationPending)
{
return;
}
// This is extremely unlikely.
Integer Gcd = new Integer();
IntMath.GreatestCommonDivisor(PrimeP, PrimeQ, Gcd);
if (!Gcd.IsOne())
{
Worker.ReportProgress(0, "They had a GCD: " + IntMath.ToString10(Gcd));
continue;
}
if (Worker.CancellationPending)
{
return;
}
IntMath.GreatestCommonDivisor(PrimeP, PubKeyExponent, Gcd);
if (!Gcd.IsOne())
{
Worker.ReportProgress(0, "They had a GCD with PubKeyExponent: " + IntMath.ToString10(Gcd));
continue;
}
if (Worker.CancellationPending)
{
return;
}
IntMath.GreatestCommonDivisor(PrimeQ, PubKeyExponent, Gcd);
if (!Gcd.IsOne())
{
Worker.ReportProgress(0, "2) They had a GCD with PubKeyExponent: " + IntMath.ToString10(Gcd));
continue;
}
// For Modular Reduction. This only has to be done
// once, when P and Q are made.
IntMathForP.ModReduction.SetupGeneralBaseArray(PrimeP);
IntMathForQ.ModReduction.SetupGeneralBaseArray(PrimeQ);
PrimePMinus1.Copy(PrimeP);
IntMath.SubtractULong(PrimePMinus1, 1);
PrimeQMinus1.Copy(PrimeQ);
IntMath.SubtractULong(PrimeQMinus1, 1);
if (Worker.CancellationPending)
{
return;
}
// These checks should be more thorough to
// make sure the primes P and Q are numbers
// that can be used in a secure way.
Worker.ReportProgress(0, "The Index of Prime P is: " + PrimeP.GetIndex().ToString());
Worker.ReportProgress(0, "Prime P:");
Worker.ReportProgress(0, IntMath.ToString10(PrimeP));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Prime Q:");
Worker.ReportProgress(0, IntMath.ToString10(PrimeQ));
Worker.ReportProgress(0, " ");
PubKeyN.Copy(PrimeP);
IntMath.Multiply(PubKeyN, PrimeQ);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PubKeyN:");
Worker.ReportProgress(0, IntMath.ToString10(PubKeyN));
Worker.ReportProgress(0, " ");
// Test Division:
Integer QuotientTest = new Integer();
Integer RemainderTest = new Integer();
IntMath.Divider.Divide(PubKeyN, PrimeP, QuotientTest, RemainderTest);
if (!RemainderTest.IsZero())
{
throw(new Exception("RemainderTest should be zero after divide by PrimeP."));
}
IntMath.Multiply(QuotientTest, PrimeP);
if (!QuotientTest.IsEqual(PubKeyN))
{
throw(new Exception("QuotientTest didn't come out right."));
}
// Euler's Theorem:
// https://en.wikipedia.org/wiki/Euler's_theorem
// ==========
// Work on the Least Common Multiple thing for
// P - 1 and Q - 1.
// =====
IntMath.GreatestCommonDivisor(PrimePMinus1, PrimeQMinus1, Gcd);
Worker.ReportProgress(0, "GCD of PrimePMinus1, PrimeQMinus1 is: " + IntMath.ToString10(Gcd));
if (!Gcd.IsULong())
{
Worker.ReportProgress(0, "This GCD number is too big: " + IntMath.ToString10(Gcd));
continue;
}
else
{
ulong TooBig = Gcd.GetAsULong();
// How big of a GCD is too big?
// ==============
if (TooBig > 1234567)
{
// (P - 1)(Q - 1) + (P - 1) + (Q - 1) = PQ - 1
Worker.ReportProgress(0, "This GCD number is bigger than 1234567: " + IntMath.ToString10(Gcd));
continue;
}
}
Integer Temp1 = new Integer();
PhiN.Copy(PrimePMinus1);
Temp1.Copy(PrimeQMinus1);
IntMath.Multiply(PhiN, Temp1);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PhiN:");
Worker.ReportProgress(0, IntMath.ToString10(PhiN));
Worker.ReportProgress(0, " ");
if (Worker.CancellationPending)
{
return;
}
// In RFC 2437 there are commonly used letters/symbols to represent
// the numbers used. So the number e is the public exponent.
// The number e that is used here is called PubKeyExponentUint = 65537.
// In the RFC the private key d is the multiplicative inverse of
// e mod PhiN. Which is mod (P - 1)(Q - 1). It's called
// PrivKInverseExponent here.
if (!IntMath.FindMultiplicativeInverseSmall(PrivKInverseExponent, PubKeyExponent, PhiN, Worker))
{
return;
}
if (PrivKInverseExponent.IsZero())
{
continue;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PrivKInverseExponent: " + IntMath.ToString10(PrivKInverseExponent));
if (Worker.CancellationPending)
{
return;
}
// In RFC 2437 it defines a number dP which is the multiplicative
// inverse, mod (P - 1) of e. That dP is named PrivKInverseExponentDP here.
Worker.ReportProgress(0, " ");
if (!IntMath.FindMultiplicativeInverseSmall(PrivKInverseExponentDP, PubKeyExponent, PrimePMinus1, Worker))
{
return;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PrivKInverseExponentDP: " + IntMath.ToString10(PrivKInverseExponentDP));
if (PrivKInverseExponentDP.IsZero())
{
continue;
}
// PrivKInverseExponentDP is PrivKInverseExponent mod PrimePMinus1.
Integer Test1 = new Integer();
Test1.Copy(PrivKInverseExponent);
IntMath.Divider.Divide(Test1, PrimePMinus1, Quotient, Remainder);
Test1.Copy(Remainder);
if (!Test1.IsEqual(PrivKInverseExponentDP))
{
throw(new Exception("This does not match the definition of PrivKInverseExponentDP."));
}
if (Worker.CancellationPending)
{
return;
}
// In RFC 2437 it defines a number dQ which is the multiplicative
// inverse, mod (Q - 1) of e. That dQ is named PrivKInverseExponentDQ here.
Worker.ReportProgress(0, " ");
if (!IntMath.FindMultiplicativeInverseSmall(PrivKInverseExponentDQ, PubKeyExponent, PrimeQMinus1, Worker))
{
return;
}
if (PrivKInverseExponentDQ.IsZero())
{
continue;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "PrivKInverseExponentDQ: " + IntMath.ToString10(PrivKInverseExponentDQ));
if (Worker.CancellationPending)
{
return;
}
Test1.Copy(PrivKInverseExponent);
IntMath.Divider.Divide(Test1, PrimeQMinus1, Quotient, Remainder);
Test1.Copy(Remainder);
if (!Test1.IsEqual(PrivKInverseExponentDQ))
{
throw(new Exception("This does not match the definition of PrivKInverseExponentDQ."));
}
// Make a random number to test encryption/decryption.
Integer ToEncrypt = new Integer();
int HowManyBytes = PrimeIndex * 4;
byte[] RandBytes = MakeRandomBytes(HowManyBytes);
if (RandBytes == null)
{
Worker.ReportProgress(0, "Error making random bytes in MakeRSAKeys().");
return;
}
if (!ToEncrypt.MakeRandomOdd(PrimeIndex - 1, RandBytes))
{
Worker.ReportProgress(0, "Error making random number ToEncrypt.");
return;
}
Integer PlainTextNumber = new Integer();
PlainTextNumber.Copy(ToEncrypt);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Before encrypting number: " + IntMath.ToString10(ToEncrypt));
Worker.ReportProgress(0, " ");
IntMath.ModReduction.ModularPower(ToEncrypt, PubKeyExponent, PubKeyN, false);
if (Worker.CancellationPending)
{
return;
}
// Worker.ReportProgress( 0, IntMath.GetStatusString() );
Integer CipherTextNumber = new Integer();
CipherTextNumber.Copy(ToEncrypt);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Encrypted number: " + IntMath.ToString10(CipherTextNumber));
Worker.ReportProgress(0, " ");
ECTime DecryptTime = new ECTime();
DecryptTime.SetToNow();
IntMath.ModReduction.ModularPower(ToEncrypt, PrivKInverseExponent, PubKeyN, false);
Worker.ReportProgress(0, "Decrypted number: " + IntMath.ToString10(ToEncrypt));
if (!PlainTextNumber.IsEqual(ToEncrypt))
{
throw(new Exception("PlainTextNumber not equal to unencrypted value."));
// Because P or Q wasn't really a prime?
// Worker.ReportProgress( 0, "PlainTextNumber not equal to unencrypted value." );
// continue;
}
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Decrypt time seconds: " + DecryptTime.GetSecondsToNow().ToString("N2"));
Worker.ReportProgress(0, " ");
if (Worker.CancellationPending)
{
return;
}
// Test the standard optimized way of decrypting:
if (!ToEncrypt.MakeRandomOdd(PrimeIndex - 1, RandBytes))
{
Worker.ReportProgress(0, "Error making random number in MakeRSAKeys().");
return;
}
PlainTextNumber.Copy(ToEncrypt);
IntMath.ModReduction.ModularPower(ToEncrypt, PubKeyExponent, PubKeyN, false);
if (Worker.CancellationPending)
{
return;
}
CipherTextNumber.Copy(ToEncrypt);
// QInv is the multiplicative inverse of PrimeQ mod PrimeP.
if (!IntMath.MultiplicativeInverse(PrimeQ, PrimeP, QInv, Worker))
{
throw(new Exception("MultiplicativeInverse() returned false."));
}
if (QInv.IsNegative)
{
throw(new Exception("QInv is negative."));
}
Worker.ReportProgress(0, "QInv is: " + IntMath.ToString10(QInv));
DecryptWithQInverse(CipherTextNumber,
ToEncrypt, // Decrypt it to this.
PlainTextNumber, // Test it against this.
PubKeyN,
PrivKInverseExponentDP,
PrivKInverseExponentDQ,
PrimeP,
PrimeQ,
Worker);
Worker.ReportProgress(0, " ");
Worker.ReportProgress(0, "Found the values:");
Worker.ReportProgress(0, "Seconds: " + StartTime.GetSecondsToNow().ToString("N0"));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "Prime1: " + IntMath.ToString10(PrimeP));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "Prime2: " + IntMath.ToString10(PrimeQ));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "PubKeyN: " + IntMath.ToString10(PubKeyN));
Worker.ReportProgress(0, " ");
Worker.ReportProgress(1, "PrivKInverseExponent: " + IntMath.ToString10(PrivKInverseExponent));
// return; // Comment this out to just leave it while( true ) for testing.
}
}
internal void Divide(Integer ToDivideOriginal,
Integer DivideByOriginal,
Integer Quotient,
Integer Remainder)
{
if (ToDivideOriginal.IsNegative)
{
throw(new Exception("Divide() can't be called with negative numbers."));
}
if (DivideByOriginal.IsNegative)
{
throw(new Exception("Divide() can't be called with negative numbers."));
}
// Returns true if it divides exactly with zero remainder.
// This first checks for some basics before trying to divide it:
if (DivideByOriginal.IsZero())
{
throw(new Exception("Divide() dividing by zero."));
}
ToDivide.Copy(ToDivideOriginal);
DivideBy.Copy(DivideByOriginal);
if (ToDivide.ParamIsGreater(DivideBy))
{
Quotient.SetToZero();
Remainder.Copy(ToDivide);
return; // false;
}
if (ToDivide.IsEqual(DivideBy))
{
Quotient.SetFromULong(1);
Remainder.SetToZero();
return; // true;
}
// At this point DivideBy is smaller than ToDivide.
if (ToDivide.IsULong())
{
ulong ToDivideU = ToDivide.GetAsULong();
ulong DivideByU = DivideBy.GetAsULong();
ulong QuotientU = ToDivideU / DivideByU;
ulong RemainderU = ToDivideU % DivideByU;
Quotient.SetFromULong(QuotientU);
Remainder.SetFromULong(RemainderU);
// if( RemainderU == 0 )
return; // true;
// else
// return false;
}
if (DivideBy.GetIndex() == 0)
{
ShortDivide(ToDivide, DivideBy, Quotient, Remainder);
return;
}
Integer ToDivideTest2 = new Integer();
Integer DivideByTest2 = new Integer();
Integer QuotientTest2 = new Integer();
Integer RemainderTest2 = new Integer();
Integer ToDivideTest3 = new Integer();
Integer DivideByTest3 = new Integer();
Integer QuotientTest3 = new Integer();
Integer RemainderTest3 = new Integer();
ToDivideTest2.Copy(ToDivide);
ToDivideTest3.Copy(ToDivide);
DivideByTest2.Copy(DivideBy);
DivideByTest3.Copy(DivideBy);
LongDivide1(ToDivideTest2, DivideByTest2, QuotientTest2, RemainderTest2);
LongDivide2(ToDivideTest3, DivideByTest3, QuotientTest3, RemainderTest3);
LongDivide3(ToDivide, DivideBy, Quotient, Remainder);
if (!Quotient.IsEqual(QuotientTest2))
{
throw(new Exception("!Quotient.IsEqual( QuotientTest2 )"));
}
if (!Quotient.IsEqual(QuotientTest3))
{
throw(new Exception("!Quotient.IsEqual( QuotientTest3 )"));
}
if (!Remainder.IsEqual(RemainderTest2))
{
throw(new Exception("!Remainder.IsEqual( RemainderTest2 )"));
}
if (!Remainder.IsEqual(RemainderTest3))
{
throw(new Exception("!Remainder.IsEqual( RemainderTest3 )"));
}
}
internal ulong GetMod64(Integer ToDivideOriginal, ulong DivideBy)
{
if (ToDivideOriginal.IsULong())
{
return(ToDivideOriginal.GetAsULong() % DivideBy);
}
ToDivide.Copy(ToDivideOriginal);
ulong Digit1;
ulong Digit0;
ulong Remainder;
if (ToDivide.GetIndex() == 2)
{
Digit1 = ToDivide.GetD(2);
Digit0 = ToDivide.GetD(1) << 32;
Digit0 |= ToDivide.GetD(0);
return(GetMod64FromTwoULongs(Digit1, Digit0, DivideBy));
}
if (ToDivide.GetIndex() == 3)
{
Digit1 = ToDivide.GetD(3) << 32;
Digit1 |= ToDivide.GetD(2);
Digit0 = ToDivide.GetD(1) << 32;
Digit0 |= ToDivide.GetD(0);
return(GetMod64FromTwoULongs(Digit1, Digit0, DivideBy));
}
int Where = ToDivide.GetIndex();
while (true)
{
if (Where <= 3)
{
if (Where < 2) // This can't happen.
{
throw(new Exception("GetMod64(): Where < 2."));
}
if (Where == 2)
{
Digit1 = ToDivide.GetD(2);
Digit0 = ToDivide.GetD(1) << 32;
Digit0 |= ToDivide.GetD(0);
return(GetMod64FromTwoULongs(Digit1, Digit0, DivideBy));
}
if (Where == 3)
{
Digit1 = ToDivide.GetD(3) << 32;
Digit1 |= ToDivide.GetD(2);
Digit0 = ToDivide.GetD(1) << 32;
Digit0 |= ToDivide.GetD(0);
return(GetMod64FromTwoULongs(Digit1, Digit0, DivideBy));
}
}
else
{
// The index is bigger than 3.
// This part would get called at least once.
Digit1 = ToDivide.GetD(Where) << 32;
Digit1 |= ToDivide.GetD(Where - 1);
Digit0 = ToDivide.GetD(Where - 2) << 32;
Digit0 |= ToDivide.GetD(Where - 3);
Remainder = GetMod64FromTwoULongs(Digit1, Digit0, DivideBy);
ToDivide.SetD(Where, 0);
ToDivide.SetD(Where - 1, 0);
ToDivide.SetD(Where - 2, Remainder >> 32);
ToDivide.SetD(Where - 3, Remainder & 0xFFFFFFFF);
}
Where -= 2;
}
}
internal void Add(Integer ToAdd)
{
// There is a separate IntegerMath.Add() that is a wrapper to handle
// negative numbers too.
// if( IsNegative )
// throw( new Exception( "Integer.Add() is being called when it's negative." ));
// if( ToAdd.IsNegative )
// throw( new Exception( "Integer.Add() is being called when ToAdd is negative." ));
if (ToAdd.IsULong())
{
AddULong(ToAdd.GetAsULong());
return;
}
int LocalIndex = Index;
int LocalToAddIndex = ToAdd.Index;
if (LocalIndex < ToAdd.Index)
{
for (int Count = LocalIndex + 1; Count <= LocalToAddIndex; Count++)
{
D[Count] = ToAdd.D[Count];
}
for (int Count = 0; Count <= LocalIndex; Count++)
{
D[Count] += ToAdd.D[Count];
}
Index = ToAdd.Index;
}
else
{
for (int Count = 0; Count <= LocalToAddIndex; Count++)
{
D[Count] += ToAdd.D[Count];
}
}
// After they've been added, reorganize it.
ulong Carry = D[0] >> 32;
D[0] = D[0] & 0xFFFFFFFF;
LocalIndex = Index;
for (int Count = 1; Count <= LocalIndex; Count++)
{
ulong Total = Carry + D[Count];
D[Count] = Total & 0xFFFFFFFF;
Carry = Total >> 32;
}
if (Carry != 0)
{
Index++;
if (Index >= DigitArraySize)
{
throw(new Exception("Integer.Add() overflow."));
}
D[Index] = Carry;
}
}
internal void Multiply(Integer Result, Integer ToMul)
{
// try
// {
if (Result.IsZero())
{
return;
}
if (ToMul.IsULong())
{
MultiplyULong(Result, ToMul.GetAsULong());
SetMultiplySign(Result, ToMul);
return;
}
// It could never get here if ToMul is zero because GetIsULong()
// would be true for zero.
// if( ToMul.IsZero())
int TotalIndex = Result.GetIndex() + ToMul.GetIndex();
if (TotalIndex >= Integer.DigitArraySize)
{
throw(new Exception("Multiply() overflow."));
}
int CountTo = ToMul.GetIndex();
for (int Row = 0; Row <= CountTo; Row++)
{
if (ToMul.GetD(Row) == 0)
{
int CountZeros = Result.GetIndex();
for (int Column = 0; Column <= CountZeros; Column++)
{
M[Column + Row, Row] = 0;
}
}
else
{
int CountMult = Result.GetIndex();
for (int Column = 0; Column <= CountMult; Column++)
{
M[Column + Row, Row] = ToMul.GetD(Row) * Result.GetD(Column);
}
}
}
// Add the columns up with a carry.
Result.SetD(0, M[0, 0] & 0xFFFFFFFF);
ulong Carry = M[0, 0] >> 32;
int ResultIndex = Result.GetIndex();
int MulIndex = ToMul.GetIndex();
for (int Column = 1; Column <= TotalIndex; Column++)
{
ulong TotalLeft = 0;
ulong TotalRight = 0;
for (int Row = 0; Row <= MulIndex; Row++)
{
if (Row > Column)
{
break;
}
if (Column > (ResultIndex + Row))
{
continue;
}
// Split the ulongs into right and left sides
// so that they don't overflow.
TotalRight += M[Column, Row] & 0xFFFFFFFF;
TotalLeft += M[Column, Row] >> 32;
}
TotalRight += Carry;
Result.SetD(Column, TotalRight & 0xFFFFFFFF);
Carry = TotalRight >> 32;
Carry += TotalLeft;
}
Result.SetIndex(TotalIndex);
if (Carry != 0)
{
Result.IncrementIndex(); // This can throw an exception if it overflowed the index.
Result.SetD(Result.GetIndex(), Carry);
}
SetMultiplySign(Result, ToMul);
}