// The ShortDivide() algorithm works like dividing a polynomial which
// looks like:
// (ax3 + bx2 + cx + d) / N = (ax3 + bx2 + cx + d) * (1/N)
// The 1/N distributes over the polynomial:
// (ax3 * (1/N)) + (bx2 * (1/N)) + (cx * (1/N)) + (d * (1/N))
// (ax3/N) + (bx2/N) + (cx/N) + (d/N)
// The algorithm goes from left to right and reduces that polynomial
// expression. So it starts with Quotient being a copy of ToDivide
// and then it reduces Quotient from left to right.
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;
}
private void LongDivide3( Integer ToDivide,
Integer DivideBy,
Integer Quotient,
Integer Remainder )
{
int TestIndex = ToDivide.GetIndex() - DivideBy.GetIndex();
if( TestIndex < 0 )
throw( new Exception( "TestIndex < 0 in Divide3." ));
if( TestIndex != 0 )
{
// Is 1 too high?
TestForDivide1.SetDigitAndClear( TestIndex, 1 );
MultiplyTopOne( TestForDivide1, DivideBy );
if( ToDivide.ParamIsGreater( TestForDivide1 ))
TestIndex--;
}
// Keep a copy of the originals.
ToDivideKeep.Copy( ToDivide );
DivideByKeep.Copy( DivideBy );
ulong TestBits = DivideBy.GetD( DivideBy.GetIndex());
int ShiftBy = FindShiftBy( TestBits );
ToDivide.ShiftLeft( ShiftBy ); // Multiply the numerator and the denominator
DivideBy.ShiftLeft( ShiftBy ); // by the same amount.
ulong MaxValue;
if( (ToDivide.GetIndex() - 1) > (DivideBy.GetIndex() + TestIndex) )
{
MaxValue = ToDivide.GetD( ToDivide.GetIndex());
}
else
{
MaxValue = ToDivide.GetD( ToDivide.GetIndex()) << 32;
MaxValue |= ToDivide.GetD( ToDivide.GetIndex() - 1 );
}
ulong Denom = DivideBy.GetD( DivideBy.GetIndex());
if( Denom != 0 )
MaxValue = MaxValue / Denom;
else
MaxValue = 0xFFFFFFFF;
if( MaxValue > 0xFFFFFFFF )
MaxValue = 0xFFFFFFFF;
if( MaxValue == 0 )
throw( new Exception( "MaxValue is zero at the top in LongDivide3()." ));
Quotient.SetDigitAndClear( TestIndex, 1 );
Quotient.SetD( TestIndex, 0 );
TestForDivide1.Copy( Quotient );
TestForDivide1.SetD( TestIndex, MaxValue );
MultiplyTop( TestForDivide1, DivideBy );
/*
Test2.Copy( Quotient );
Test2.SetD( TestIndex, MaxValue );
Multiply( Test2, DivideBy );
if( !Test2.IsEqual( TestForDivide1 ))
throw( new Exception( "In Divide3() !IsEqual( Test2, TestForDivide1 )" ));
*/
if( TestForDivide1.ParamIsGreaterOrEq( ToDivide ))
{
// ToMatchExactCount++;
// Most of the time (roughly 5 out of every 6 times)
// this MaxValue estimate is exactly right:
Quotient.SetD( TestIndex, MaxValue );
}
else
{
// MaxValue can't be zero here. If it was it would
// already be low enough before it got here.
MaxValue--;
if( MaxValue == 0 )
throw( new Exception( "After decrement: MaxValue is zero in LongDivide3()." ));
TestForDivide1.Copy( Quotient );
TestForDivide1.SetD( TestIndex, MaxValue );
MultiplyTop( TestForDivide1, DivideBy );
/*
Test2.Copy( Quotient );
Test2.SetD( TestIndex, MaxValue );
Multiply( Test2, DivideBy );
if( !Test2.IsEqual( Test1 ))
throw( new Exception( "Top one. !Test2.IsEqual( Test1 ) in LongDivide3()" ));
*/
if( TestForDivide1.ParamIsGreaterOrEq( ToDivide ))
{
// ToMatchDecCount++;
Quotient.SetD( TestIndex, MaxValue );
}
else
{
// TestDivideBits is done as a last resort, but it's rare.
// But it does at least limit it to a worst case scenario
// of trying 32 bits, rather than 4 billion or so decrements.
TestDivideBits( MaxValue,
true,
TestIndex,
ToDivide,
DivideBy,
Quotient,
Remainder );
}
// TestGap = MaxValue - LgQuotient.D[TestIndex];
// if( TestGap > HighestToMatchGap )
// HighestToMatchGap = TestGap;
// HighestToMatchGap: 4,294,967,293
// uint size: 4,294,967,295 uint
}
// If it's done.
if( TestIndex == 0 )
{
TestForDivide1.Copy( Quotient );
Multiply( TestForDivide1, DivideByKeep );
Remainder.Copy( ToDivideKeep );
Subtract( Remainder, TestForDivide1 );
//if( DivideByKeep.ParamIsGreater( Remainder ))
// throw( new Exception( "Remainder > DivideBy in LongDivide3()." ));
return;
}
// Now do the rest of the digits.
TestIndex--;
while( true )
{
TestForDivide1.Copy( Quotient );
// First Multiply() for each digit.
Multiply( TestForDivide1, DivideBy );
// if( ToDivide.ParamIsGreater( TestForDivide1 ))
// throw( new Exception( "Bug here in LongDivide3()." ));
Remainder.Copy( ToDivide );
Subtract( Remainder, TestForDivide1 );
MaxValue = Remainder.GetD( Remainder.GetIndex()) << 32;
int CheckIndex = Remainder.GetIndex() - 1;
if( CheckIndex > 0 )
MaxValue |= Remainder.GetD( CheckIndex );
Denom = DivideBy.GetD( DivideBy.GetIndex());
if( Denom != 0 )
MaxValue = MaxValue / Denom;
else
MaxValue = 0xFFFFFFFF;
if( MaxValue > 0xFFFFFFFF )
MaxValue = 0xFFFFFFFF;
TestForDivide1.Copy( Quotient );
TestForDivide1.SetD( TestIndex, MaxValue );
// There's a minimum of two full Multiply() operations per digit.
Multiply( TestForDivide1, DivideBy );
if( TestForDivide1.ParamIsGreaterOrEq( ToDivide ))
{
// Most of the time this MaxValue estimate is exactly right:
// ToMatchExactCount++;
Quotient.SetD( TestIndex, MaxValue );
}
else
{
MaxValue--;
TestForDivide1.Copy( Quotient );
TestForDivide1.SetD( TestIndex, MaxValue );
Multiply( TestForDivide1, DivideBy );
if( TestForDivide1.ParamIsGreaterOrEq( ToDivide ))
{
// ToMatchDecCount++;
Quotient.SetD( TestIndex, MaxValue );
}
else
{
TestDivideBits( MaxValue,
false,
TestIndex,
ToDivide,
DivideBy,
Quotient,
Remainder );
// TestGap = MaxValue - LgQuotient.D[TestIndex];
// if( TestGap > HighestToMatchGap )
// HighestToMatchGap = TestGap;
}
}
if( TestIndex == 0 )
break;
TestIndex--;
}
TestForDivide1.Copy( Quotient );
Multiply( TestForDivide1, DivideByKeep );
Remainder.Copy( ToDivideKeep );
Subtract( Remainder, TestForDivide1 );
// if( DivideByKeep.ParamIsGreater( Remainder ))
// throw( new Exception( "Remainder > DivideBy in LongDivide3()." ));
}
private void SearchSqrtXPart( int TestIndex, Integer Square, Integer SqrRoot )
{
// B is the Big part of the number that has already been found.
// S = (B + x)^2
// S = B^2 + 2Bx + x^2
// S - B^2 = 2Bx + x^2
// R = S - B^2
// R = 2Bx + x^2
// R = x(2B + x)
SqrtXPartTest1.Copy( SqrRoot ); // B
DoSquare( SqrtXPartTest1 ); // B^2
SqrtXPartDiff.Copy( Square );
Subtract( SqrtXPartDiff, SqrtXPartTest1 ); // S - B^2
SqrtXPartTwoB.Copy( SqrRoot ); // B
SqrtXPartTwoB.ShiftLeft( 1 ); // Times 2 for 2B.
SqrtXPartTest1.Copy( SqrtXPartTwoB );
ulong TestBits = SqrtXPartTest1.GetD( SqrtXPartTest1.GetIndex());
int ShiftBy = FindShiftBy( TestBits );
SqrtXPartR2.Copy( SqrtXPartDiff );
SqrtXPartR2.ShiftLeft( ShiftBy ); // Multiply the numerator and the denominator
SqrtXPartTest1.ShiftLeft( ShiftBy ); // by the same amount.
ulong Highest;
if( SqrtXPartR2.GetIndex() == 0 )
{
Highest = SqrtXPartR2.GetD( SqrtXPartR2.GetIndex());
}
else
{
Highest = SqrtXPartR2.GetD( SqrtXPartR2.GetIndex()) << 32;
Highest |= SqrtXPartR2.GetD( SqrtXPartR2.GetIndex() - 1 );
}
ulong Denom = SqrtXPartTest1.GetD( SqrtXPartTest1.GetIndex());
if( Denom == 0 )
Highest = 0xFFFFFFFF;
else
Highest = Highest / Denom;
if( Highest == 0 )
{
SqrRoot.SetD( TestIndex, 0 );
return;
}
if( Highest > 0xFFFFFFFF )
Highest = 0xFFFFFFFF;
uint BitTest = 0x80000000;
ulong XDigit = 0;
ulong TempXDigit = 0;
for( int BitCount = 0; BitCount < 32; BitCount++ )
{
TempXDigit = XDigit | BitTest;
if( TempXDigit > Highest )
{
BitTest >>= 1;
continue;
}
SqrtXPartTest1.Copy( SqrtXPartTwoB );
SqrtXPartTest1.SetD( TestIndex, TempXDigit ); // 2B + x
SqrtXPartTest2.SetDigitAndClear( TestIndex, TempXDigit ); // Set X.
MultiplyTop( SqrtXPartTest2, SqrtXPartTest1 );
if( SqrtXPartTest2.ParamIsGreaterOrEq( SqrtXPartDiff ))
XDigit |= BitTest; // Then keep the bit.
BitTest >>= 1;
}
SqrRoot.SetD( TestIndex, XDigit );
}
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;
}
for( int Count = 2; Count <= Result.GetIndex(); Count++ )
SignedD[Count] = (long)Result.GetD( Count );
for( int Count = 0; Count < Result.GetIndex(); 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." ));
for( int Count = 0; Count <= Result.GetIndex(); 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 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 );
}
// Finding the square root of a number is similar to division since
// it is a search algorithm. The TestSqrtBits method shown next is
// very much like TestDivideBits(). It works the same as
// FindULSqrRoot(), but on a bigger scale.
/*
private void TestSqrtBits( int TestIndex, Integer Square, Integer SqrRoot )
{
Integer Test1 = new Integer();
uint BitTest = 0x80000000;
for( int BitCount = 31; BitCount >= 0; BitCount-- )
{
Test1.Copy( SqrRoot );
Test1.D[TestIndex] |= BitTest;
Test1.Square();
if( !Square.ParamIsGreater( Test1 ) )
SqrRoot.D[TestIndex] |= BitTest; // Use the bit.
BitTest >>= 1;
}
}
*/
// In the SquareRoot() method SqrRoot.Index is half of Square.Index.
// Compare this to the Square() method where the Carry might or
// might not increment the index to an odd number. (So if the Index
// was 5 its square root would have an Index of 5 / 2 = 2.)
// The SquareRoot1() method uses FindULSqrRoot() either to find the
// whole answer, if it's a small number, or it uses it to find the
// top part. Then from there it goes on to a bit by bit search
// with TestSqrtBits().
public bool SquareRoot( Integer Square, Integer SqrRoot )
{
ulong ToMatch;
if( Square.IsULong() )
{
ToMatch = Square.GetAsULong();
SqrRoot.SetD( 0, FindULSqrRoot( ToMatch ));
SqrRoot.SetIndex( 0 );
if( (SqrRoot.GetD(0 ) * SqrRoot.GetD( 0 )) == ToMatch )
return true;
else
return false;
}
int TestIndex = Square.GetIndex() >> 1; // LgSquare.Index / 2;
SqrRoot.SetDigitAndClear( TestIndex, 1 );
// if( (TestIndex * 2) > (LgSquare.Index - 1) )
if( (TestIndex << 1) > (Square.GetIndex() - 1) )
{
ToMatch = Square.GetD( Square.GetIndex());
}
else
{
// LgSquare.Index is at least 2 here.
ToMatch = Square.GetD( Square.GetIndex()) << 32;
ToMatch |= Square.GetD( Square.GetIndex() - 1 );
}
SqrRoot.SetD( TestIndex, FindULSqrRoot( ToMatch ));
TestIndex--;
while( true )
{
// TestSqrtBits( TestIndex, LgSquare, LgSqrRoot );
SearchSqrtXPart( TestIndex, Square, SqrRoot );
if( TestIndex == 0 )
break;
TestIndex--;
}
// Avoid squaring the whole thing to see if it's an exact square root:
if( ((SqrRoot.GetD( 0 ) * SqrRoot.GetD( 0 )) & 0xFFFFFFFF) != Square.GetD( 0 ))
return false;
TestForSquareRoot.Copy( SqrRoot );
DoSquare( TestForSquareRoot );
if( Square.IsEqual( TestForSquareRoot ))
return true;
else
return false;
}
private void AddUpAccumulateArray( Integer Result, int HowManyToAdd, int BiggestIndex )
{
try
{
for( int Count = 0; Count <= (BiggestIndex + 1); Count++ )
Result.SetD( Count, 0 );
Result.SetIndex( BiggestIndex );
for( int Count = 0; Count < HowManyToAdd; Count++ )
{
int HowManyDigits = AccumulateArray[Count].GetIndex() + 1;
for( int CountDigits = 0; CountDigits < HowManyDigits; CountDigits++ )
{
ulong Sum = AccumulateArray[Count].GetD( CountDigits ) + Result.GetD( CountDigits );
Result.SetD( CountDigits, Sum );
}
}
// This is like ax + by + cz + ... = Result.
// You know what a, b, c... are.
// But you don't know what x, y, and z are.
// So how do you reverse this and get x, y and z?
// Is this reversible?
Result.OrganizeDigits();
}
catch( Exception Except )
{
throw( new Exception( "Exception in AddUpAccumulateArray(): " + Except.Message ));
}
}
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." ));
for( int Count = 0; Count <= ToSub.GetIndex(); Count++ )
SignedD[Count] = (long)Result.GetD( Count ) - (long)ToSub.GetD( Count );
for( int Count = ToSub.GetIndex() + 1; Count <= Result.GetIndex(); Count++ )
SignedD[Count] = (long)Result.GetD( Count );
for( int Count = 0; Count < Result.GetIndex(); 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." ));
for( int Count = 0; Count <= Result.GetIndex(); 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 );
}
internal int MultiplyUIntFromCopy( Integer Result, Integer FromCopy, ulong ToMul )
{
int FromCopyIndex = FromCopy.GetIndex();
// The compiler knows that FromCopyIndex doesn't change here so
// it can do its range checking on the for-loop before it starts.
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();
}
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." ));
for( int Column = 0; Column <= Result.GetIndex(); Column++ )
{
M[Column, 0] = B0 * Result.GetD( Column );
// Column + 1 and Row is 1, so it's just like pen and paper.
M[Column + 1, 1] = B1 * Result.GetD( Column );
}
// 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;
for( int Column = 1; Column <= Result.GetIndex(); 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++ )
{
TotalRight += M[Column, Row] & 0xFFFFFFFF;
TotalLeft += M[Column, Row] >> 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 );
}
}
// 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." ));
for( int Column = 0; Column <= ToMul.GetIndex(); Column++ )
Result.SetD( Column + Result.GetIndex(), ToMul.GetD( Column ));
for( int Column = 0; Column < Result.GetIndex(); Column++ )
Result.SetD( Column, 0 );
// No Carrys need to be done.
Result.SetIndex( TotalIndex );
/*
}
catch( Exception ) // Except )
{
// "Bug in MultiplyTopOne: " + Except.Message
}
*/
}
internal void MultiplyUInt( Integer Result, ulong ToMul )
{
try
{
if( ToMul == 0 )
{
Result.SetToZero();
return;
}
if( ToMul == 1 )
return;
for( int Column = 0; Column <= Result.GetIndex(); Column++ )
M[Column, 0] = ToMul * Result.GetD( Column );
// Add these up with a carry.
Result.SetD( 0, M[0, 0] & 0xFFFFFFFF );
ulong Carry = M[0, 0] >> 32;
for( int Column = 1; Column <= Result.GetIndex(); Column++ )
{
// Using a compile-time check on this constant,
// this Test value does not overflow:
// const ulong Test = ((ulong)0xFFFFFFFF * (ulong)(0xFFFFFFFF)) + 0xFFFFFFFF;
// ulong Total = checked( M[Column, 0] + Carry );
ulong Total = M[Column, 0] + Carry;
Result.SetD( Column, Total & 0xFFFFFFFF );
Carry = Total >> 32;
}
if( Carry != 0 )
{
Result.IncrementIndex(); // This might throw an exception if it overflows.
Result.SetD( Result.GetIndex(), Carry );
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in MultiplyUInt(): " + Except.Message ));
}
}
// 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:
for( int Column = 0; Column <= ToMul.GetIndex(); Column++ )
M[Column + Result.GetIndex(), Result.GetIndex()] = Result.GetD( Result.GetIndex() ) * ToMul.GetD( Column );
for( int Column = 0; Column < Result.GetIndex(); Column++ )
Result.SetD( Column, 0 );
ulong Carry = 0;
for( int Column = 0; Column <= ToMul.GetIndex(); Column++ )
{
ulong Total = M[Column + Result.GetIndex(), Result.GetIndex()] + Carry;
Result.SetD( Column + Result.GetIndex(), 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 )
{
// "Bug in MultiplyTop: " + Except.Message
}
*/
}
// See also: http://en.wikipedia.org/wiki/Karatsuba_algorithm
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." ));
for( int Row = 0; Row <= ToMul.GetIndex(); Row++ )
{
if( ToMul.GetD( Row ) == 0 )
{
for( int Column = 0; Column <= Result.GetIndex(); Column++ )
M[Column + Row, Row] = 0;
}
else
{
for( int Column = 0; Column <= Result.GetIndex(); 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;
for( int Column = 1; Column <= TotalIndex; Column++ )
{
ulong TotalLeft = 0;
ulong TotalRight = 0;
for( int Row = 0; Row <= ToMul.GetIndex(); Row++ )
{
if( Row > Column )
break;
if( Column > (Result.GetIndex() + 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 );
}
private void DoCRTTest( Integer StartingNumber )
{
CRTMath CRTMath1 = new CRTMath( Worker );
ECTime CRTTestTime = new ECTime();
ChineseRemainder CRTTest = new ChineseRemainder( IntMath );
ChineseRemainder CRTTest2 = new ChineseRemainder( IntMath );
ChineseRemainder CRTAccumulate = new ChineseRemainder( IntMath );
ChineseRemainder CRTToTest = new ChineseRemainder( IntMath );
ChineseRemainder CRTTempEqual = new ChineseRemainder( IntMath );
ChineseRemainder CRTTestEqual = new ChineseRemainder( IntMath );
Integer BigBase = new Integer();
Integer ToTest = new Integer();
Integer Accumulate = new Integer();
Integer Test1 = new Integer();
Integer Test2 = new Integer();
CRTTest.SetFromTraditionalInteger( StartingNumber );
// If the digit array size isn't set right in relation to
// Integer.DigitArraySize then it can cause an error here.
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( StartingNumber ))
throw( new Exception( " !Accumulate.IsEqual( Result )." ));
CRTTestEqual.SetFromTraditionalInteger( Accumulate );
if( !CRTMath1.IsEqualToInteger( CRTTestEqual, Accumulate ))
throw( new Exception( "IsEqualToInteger() didn't work." ));
// Make sure it works with even numbers too.
Test1.Copy( StartingNumber );
Test1.SetD( 0, Test1.GetD( 0 ) & 0xFE );
CRTTest.SetFromTraditionalInteger( Test1 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "For even numbers. !Accumulate.IsEqual( Test )." ));
////////////
// Make sure the size of this works with the Integer size because
// an overflow is hard to find.
CRTTestTime.SetToNow();
Test1.SetToMaxValueForCRT();
CRTTest.SetFromTraditionalInteger( Test1 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "For the max value. !Accumulate.IsEqual( Test1 )." ));
// Worker.ReportProgress( 0, "CRT Max test seconds: " + CRTTestTime.GetSecondsToNow().ToString( "N1" ));
// Worker.ReportProgress( 0, "MaxValue: " + IntMath.ToString10( Accumulate ));
// Worker.ReportProgress( 0, "MaxValue.Index: " + Accumulate.GetIndex().ToString());
// Multiplicative Inverse test:
Integer TestDivideBy = new Integer();
Integer TestProduct = new Integer();
ChineseRemainder CRTTestDivideBy = new ChineseRemainder( IntMath );
ChineseRemainder CRTTestProduct = new ChineseRemainder( IntMath );
TestDivideBy.Copy( StartingNumber );
TestProduct.Copy( StartingNumber );
IntMath.Multiply( TestProduct, TestDivideBy );
CRTTestDivideBy.SetFromTraditionalInteger( TestDivideBy );
CRTTestProduct.SetFromTraditionalInteger( TestDivideBy );
CRTTestProduct.Multiply( CRTTestDivideBy );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTestProduct );
if( !Accumulate.IsEqual( TestProduct ))
throw( new Exception( "Multiply test was bad." ));
IntMath.Divide( TestProduct, TestDivideBy, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "This test won't work unless it divides it exactly." ));
ChineseRemainder CRTTestQuotient = new ChineseRemainder( IntMath );
CRTMath1.MultiplicativeInverse( CRTTestProduct, CRTTestDivideBy, CRTTestQuotient );
// Yes, multiplicative inverse is the same number
// as with regular division.
Integer TestQuotient = new Integer();
CRTMath1.GetTraditionalInteger( TestQuotient, CRTTestQuotient );
if( !TestQuotient.IsEqual( Quotient ))
throw( new Exception( "Modular Inverse in DoCRTTest didn't work." ));
// Subtract
Test1.Copy( StartingNumber );
IntMath.SetFromString( Test2, "12345678901234567890123456789012345" );
CRTTest.SetFromTraditionalInteger( Test1 );
CRTTest2.SetFromTraditionalInteger( Test2 );
CRTTest.Subtract( CRTTest2 );
IntMath.Subtract( Test1, Test2 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "Subtract test was bad." ));
// Add
Test1.Copy( StartingNumber );
IntMath.SetFromString( Test2, "12345678901234567890123456789012345" );
CRTTest.SetFromTraditionalInteger( Test1 );
CRTTest2.SetFromTraditionalInteger( Test2 );
CRTTest.Add( CRTTest2 );
IntMath.Add( Test1, Test2 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "Add test was bad." ));
/////////
CRTBaseMath CBaseMath = new CRTBaseMath( Worker, CRTMath1 );
ChineseRemainder CRTInput = new ChineseRemainder( IntMath );
CRTInput.SetFromTraditionalInteger( StartingNumber );
Test1.Copy( StartingNumber );
IntMath.SetFromString( Test2, "12345678901234567890123456789012345" );
IntMath.Add( Test1, Test2 );
Integer TestModulus = new Integer();
TestModulus.Copy( Test1 );
ChineseRemainder CRTTestModulus = new ChineseRemainder( IntMath );
CRTTestModulus.SetFromTraditionalInteger( TestModulus );
Integer Exponent = new Integer();
Exponent.SetFromULong( PubKeyExponentUint );
CBaseMath.ModularPower( CRTInput, Exponent, CRTTestModulus, false );
IntMath.IntMathNew.ModularPower( StartingNumber, Exponent, TestModulus, false );
if( !CRTMath1.IsEqualToInteger( CRTInput, StartingNumber ))
throw( new Exception( "CRTBase ModularPower() didn't work." ));
CRTBase ExpTest = new CRTBase( IntMath );
CBaseMath.SetFromCRTNumber( ExpTest, CRTInput );
CBaseMath.GetExponentForm( ExpTest, 37 );
// Worker.ReportProgress( 0, "CRT was good." );
}
/*
private bool LongDivide1( Integer ToDivide,
Integer DivideBy,
Integer Quotient,
Integer Remainder )
{
Integer Test1 = new Integer();
int TestIndex = ToDivide.Index - DivideBy.Index;
if( TestIndex != 0 )
{
// Is 1 too high?
Test1.SetDigitAndClear( TestIndex, 1 );
Test1.MultiplyTopOne( DivideBy );
if( ToDivide.ParamIsGreater( Test1 ))
TestIndex--;
}
Quotient.SetDigitAndClear( TestIndex, 1 );
Quotient.D[TestIndex] = 0;
uint BitTest = 0x80000000;
while( true )
{
// For-loop to test each bit:
for( int BitCount = 31; BitCount >= 0; BitCount-- )
{
Test1.Copy( Quotient );
Test1.D[TestIndex] |= BitTest;
Test1.Multiply( DivideBy );
if( Test1.ParamIsGreaterOrEq( ToDivide ))
Quotient.D[TestIndex] |= BitTest; // Then keep the bit.
BitTest >>= 1;
}
if( TestIndex == 0 )
break;
TestIndex--;
BitTest = 0x80000000;
}
Test1.Copy( Quotient );
Test1.Multiply( DivideBy );
if( Test1.IsEqual( ToDivide ) )
{
Remainder.SetToZero();
return true; // Divides exactly.
}
Remainder.Copy( ToDivide );
Remainder.Subtract( Test1 );
// Does not divide it exactly.
return false;
}
*/
private void TestDivideBits( ulong MaxValue,
bool IsTop,
int TestIndex,
Integer ToDivide,
Integer DivideBy,
Integer Quotient,
Integer Remainder )
{
// For a particular value of TestIndex, this does the
// for-loop to test each bit.
// When you're not testing you wouldn't want to be creating these
// and allocating the RAM for them each time it's called.
// Integer Test1 = new Integer();
// Integer Test2 = new Integer();
uint BitTest = 0x80000000;
for( int BitCount = 31; BitCount >= 0; BitCount-- )
{
if( (Quotient.GetD( TestIndex ) | BitTest) > MaxValue )
{
// If it's more than the MaxValue then the
// multiplication test can be skipped for
// this bit.
// SkippedMultiplies++;
BitTest >>= 1;
continue;
}
// Is it only doing the multiplication for the top digit?
if( IsTop )
{
TestForBits.Copy( Quotient );
TestForBits.SetD( TestIndex, TestForBits.GetD( TestIndex ) | BitTest );
MultiplyTop( TestForBits, DivideBy );
/*
Test2.Copy( Quotient );
Test2.SetD( TestIndex, Test2.GetD( TestIndex ) | BitTest );
Multiply( Test2, DivideBy );
if( !Test1.IsEqual( Test2 ))
throw( new Exception( "!Test1.IsEqual( Test2 ) in TestDivideBits()." ));
*/
}
else
{
TestForBits.Copy( Quotient );
TestForBits.SetD( TestIndex, TestForBits.GetD( TestIndex ) | BitTest );
Multiply( TestForBits, DivideBy );
}
if( TestForBits.ParamIsGreaterOrEq( ToDivide ))
Quotient.SetD( TestIndex, Quotient.GetD( TestIndex ) | BitTest ); // Keep the bit.
BitTest >>= 1;
}
}
// 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 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 bool GetProduct( Integer BigIntToSet )
{
BigIntToSet.SetToZero();
if( !AllProductBitsAreKnown())
return false;
int Highest = GetHighestProductBitIndex();
for( int Row = Highest; Row >= 0; Row-- )
{
// The first time through it will just shift zero
// to the left, so nothing happens with zero.
BigIntToSet.ShiftLeft( 1 );
uint ToSet = MultArray[Row].OneLine[0];
if( GetAccumOutValue( ToSet ))
{
ulong D = BigIntToSet.GetD( 0 );
D |= 1;
BigIntToSet.SetD( 0, D );
}
}
return true;
}
