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 an optimization for multiplying when
// only the top digit of a number has been set and
// all of the other digits are zero.
internal void MultiplyTop(Integer Result, Integer ToMul)
{
// try
// {
int TotalIndex = Result.GetIndex() + ToMul.GetIndex();
if (TotalIndex >= Integer.DigitArraySize)
{
throw(new Exception("MultiplyTop() overflow."));
}
// Just like Multiply() except that all the other
// rows are zero:
int ToMulIndex = ToMul.GetIndex();
int ResultIndex = Result.GetIndex();
for (int Column = 0; Column <= ToMulIndex; Column++)
{
M[Column + ResultIndex, ResultIndex] = Result.GetD(ResultIndex) * ToMul.GetD(Column);
}
for (int Column = 0; Column < ResultIndex; Column++)
{
Result.SetD(Column, 0);
}
ulong Carry = 0;
for (int Column = 0; Column <= ToMulIndex; Column++)
{
ulong Total = M[Column + ResultIndex, ResultIndex] + Carry;
Result.SetD(Column + ResultIndex, Total & 0xFFFFFFFF);
Carry = Total >> 32;
}
Result.SetIndex(TotalIndex);
if (Carry != 0)
{
Result.SetIndex(Result.GetIndex() + 1);
if (Result.GetIndex() >= Integer.DigitArraySize)
{
throw(new Exception("MultiplyTop() overflow."));
}
Result.SetD(Result.GetIndex(), Carry);
}
/*
* }
* catch( Exception ) // Except )
* {
* // "Exception in MultiplyTop: " + Except.Message
* }
*/
}
internal int MultiplyUIntFromCopy(Integer Result, Integer FromCopy, ulong ToMul)
{
int FromCopyIndex = FromCopy.GetIndex();
Result.SetIndex(FromCopyIndex);
for (int Column = 0; Column <= FromCopyIndex; Column++)
{
Scratch[Column] = ToMul * FromCopy.GetD(Column);
}
// Add these up with a carry.
Result.SetD(0, Scratch[0] & 0xFFFFFFFF);
ulong Carry = Scratch[0] >> 32;
for (int Column = 1; Column <= FromCopyIndex; Column++)
{
ulong Total = Scratch[Column] + Carry;
Result.SetD(Column, Total & 0xFFFFFFFF);
Carry = Total >> 32;
}
if (Carry != 0)
{
Result.IncrementIndex(); // This might throw an exception if it overflows.
Result.SetD(FromCopyIndex + 1, Carry);
}
return(Result.GetIndex());
}
// This is another optimization. This is used
// when the top digit is 1 and all of the other
// digits are zero. This is effectively just a
// shift-left operation.
internal void MultiplyTopOne(Integer Result, Integer ToMul)
{
// try
// {
int TotalIndex = Result.GetIndex() + ToMul.GetIndex();
if (TotalIndex >= Integer.DigitArraySize)
{
throw(new Exception("MultiplyTopOne() overflow."));
}
int ToMulIndex = ToMul.GetIndex();
int ResultIndex = Result.GetIndex();
for (int Column = 0; Column <= ToMulIndex; Column++)
{
Result.SetD(Column + ResultIndex, ToMul.GetD(Column));
}
for (int Column = 0; Column < ResultIndex; Column++)
{
Result.SetD(Column, 0);
}
// No Carrys need to be done.
Result.SetIndex(TotalIndex);
/*
* }
* catch( Exception ) // Except )
* {
* // "Exception in MultiplyTopOne: " + Except.Message
* }
*/
}
private bool ShortDivide(Integer ToDivide,
Integer DivideBy,
Integer Quotient,
Integer Remainder)
{
Quotient.Copy(ToDivide);
// DivideBy has an Index of zero:
ulong DivideByU = DivideBy.GetD(0);
ulong RemainderU = 0;
// Get the first one set up.
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);
}
// Now do the rest.
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); // What's left to divide.
}
// Set the index for the quotient.
// The quotient would have to be at least 1 here,
// so it will find where to set the index.
for (int Count = Quotient.GetIndex(); Count >= 0; Count--)
{
if (Quotient.GetD(Count) != 0)
{
Quotient.SetIndex(Count);
break;
}
}
Remainder.SetD(0, RemainderU);
Remainder.SetIndex(0);
if (RemainderU == 0)
{
return(true);
}
else
{
return(false);
}
}
// 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 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 DoSquare(Integer ToSquare)
{
if (ToSquare.GetIndex() == 0)
{
ToSquare.Square0();
return;
}
if (ToSquare.GetIndex() == 1)
{
ToSquare.Square1();
return;
}
if (ToSquare.GetIndex() == 2)
{
ToSquare.Square2();
return;
}
// Now Index is at least 3:
int DoubleIndex = ToSquare.GetIndex() << 1;
if (DoubleIndex >= Integer.DigitArraySize)
{
throw(new Exception("Square() overflowed."));
}
for (int Row = 0; Row <= ToSquare.GetIndex(); Row++)
{
if (ToSquare.GetD(Row) == 0)
{
for (int Column = 0; Column <= ToSquare.GetIndex(); Column++)
{
M[Column + Row, Row] = 0;
}
}
else
{
for (int Column = 0; Column <= ToSquare.GetIndex(); Column++)
{
M[Column + Row, Row] = ToSquare.GetD(Row) * ToSquare.GetD(Column);
}
}
}
// Add the columns up with a carry.
ToSquare.SetD(0, M[0, 0] & 0xFFFFFFFF);
ulong Carry = M[0, 0] >> 32;
for (int Column = 1; Column <= DoubleIndex; Column++)
{
ulong TotalLeft = 0;
ulong TotalRight = 0;
for (int Row = 0; Row <= Column; Row++)
{
if (Row > ToSquare.GetIndex())
{
break;
}
if (Column > (ToSquare.GetIndex() + Row))
{
continue;
}
TotalRight += M[Column, Row] & 0xFFFFFFFF;
TotalLeft += M[Column, Row] >> 32;
}
TotalRight += Carry;
ToSquare.SetD(Column, TotalRight & 0xFFFFFFFF);
Carry = TotalRight >> 32;
Carry += TotalLeft;
}
ToSquare.SetIndex(DoubleIndex);
if (Carry != 0)
{
ToSquare.SetIndex(ToSquare.GetIndex() + 1);
if (ToSquare.GetIndex() >= Integer.DigitArraySize)
{
throw(new Exception("Square() overflow."));
}
ToSquare.SetD(ToSquare.GetIndex(), 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);
}