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);
}
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 MultiplyULong(Integer Result, ulong ToMul)
{
// Using compile-time checks, this one overflows:
// const ulong Test = ((ulong)0xFFFFFFFF + 1) * ((ulong)0xFFFFFFFF + 1);
// This one doesn't:
// const ulong Test = (ulong)0xFFFFFFFF * ((ulong)0xFFFFFFFF + 1);
if (Result.IsZero())
{
return; // Then the answer is zero, which it already is.
}
if (ToMul == 0)
{
Result.SetToZero();
return;
}
ulong B0 = ToMul & 0xFFFFFFFF;
ulong B1 = ToMul >> 32;
if (B1 == 0)
{
MultiplyUInt(Result, (uint)B0);
return;
}
// Since B1 is not zero:
if ((Result.GetIndex() + 1) >= Integer.DigitArraySize)
{
throw(new Exception("Overflow in MultiplyULong."));
}
int CountTo = Result.GetIndex();
for (int Column = 0; Column <= CountTo; Column++)
{
ulong Digit = Result.GetD(Column);
M[Column, 0] = B0 * Digit;
// Column + 1 and Row is 1, so it's just like pen and paper.
M[Column + 1, 1] = B1 * Digit;
}
// Since B1 is not zero, the index is set one higher.
Result.IncrementIndex(); // Might throw an exception if it goes out of range.
M[Result.GetIndex(), 0] = 0; // Otherwise it would be undefined
// when it's added up below.
// Add these up with a carry.
Result.SetD(0, M[0, 0] & 0xFFFFFFFF);
ulong Carry = M[0, 0] >> 32;
CountTo = Result.GetIndex();
for (int Column = 1; Column <= CountTo; Column++)
{
// This does overflow:
// const ulong Test = ((ulong)0xFFFFFFFF * (ulong)(0xFFFFFFFF))
// + ((ulong)0xFFFFFFFF * (ulong)(0xFFFFFFFF));
// Split the ulongs into right and left sides
// so that they don't overflow.
ulong TotalLeft = 0;
ulong TotalRight = 0;
// There's only the two rows for this.
for (int Row = 0; Row <= 1; Row++)
{
ulong MValue = M[Column, Row];
TotalRight += MValue & 0xFFFFFFFF;
TotalLeft += MValue >> 32;
}
TotalRight += Carry;
Result.SetD(Column, TotalRight & 0xFFFFFFFF);
Carry = TotalRight >> 32;
Carry += TotalLeft;
}
if (Carry != 0)
{
Result.IncrementIndex(); // This can throw an exception.
Result.SetD(Result.GetIndex(), Carry);
}
}
