/// <summary>
/// Schoolbook division algorithm
/// </summary>
/// <param name="n1"></param>
/// <param name="n2"></param>
/// <param name="Q"></param>
/// <param name="R"></param>
private static void Div_32(BigInt n1, BigInt n2, BigInt Q, BigInt R)
{
int digitsN1 = n1.GetMSD() + 1;
int digitsN2 = n2.GetMSD() + 1;
//n2 is bigger than n1
if (digitsN1 < digitsN2)
{
R.AssignInt(n1);
Q.Zero();
return;
}
if (digitsN1 == digitsN2)
{
//n2 is bigger than n1
if (LtInt(n1, n2))
{
R.AssignInt(n1);
Q.Zero();
return;
}
//n2 >= n1, but less the 2x n1 (initial conditions make this certain)
Q.Zero();
Q.digitArray[0] = 1;
R.Assign(n1);
R.SubInternalBits(n2.digitArray);
return;
}
int digits = digitsN1 - (digitsN2 + 1);
//Algorithm Div_31 can be used to get the answer in O(n) time.
if (digits == 0)
{
Div_31(n1, n2, Q, R);
return;
}
BigInt n1New = DigitShiftRight(n1, digits);
BigInt s = DigitTruncate(n1, digits);
BigInt Q2 = new BigInt(n1, n1.pres, true);
BigInt R2 = new BigInt(n1, n1.pres, true);
Div_31(n1New, n2, Q2, R2);
R2.DigitShiftSelfLeft(digits);
R2.Add(s);
Div_32(R2, n2, Q, R);
Q2.DigitShiftSelfLeft(digits);
Q.Add(Q2);
}
/// <summary>
/// Shifts and optionally precision-extends the arguments to prepare for Div_32
/// </summary>
/// <param name="n1"></param>
/// <param name="n2"></param>
private static int MakeSafeDiv(BigInt n1, BigInt n2)
{
int shift = n2.GetDivBitshift();
int n1MSD = n1.GetMSD();
uint temp = n1.digitArray[n1MSD];
if (n1MSD == n1.digitArray.Length - 1 && ((temp << shift) >> shift) != n1.digitArray[n1MSD])
{
//Precision-extend n1 and n2 if necessary
int digits = n1.digitArray.Length;
n1.SetNumDigits(digits + 1);
n2.SetNumDigits(digits + 1);
}
//Logical left-shift n1 and n2
n1.LSH(shift);
n2.LSH(shift);
return shift;
}
/// <summary>
/// Schoolbook division helper function.
/// </summary>
/// <param name="n1"></param>
/// <param name="n2"></param>
/// <param name="Q">Quotient output value</param>
/// <param name="R">Remainder output value</param>
private static void Div_31(BigInt n1, BigInt n2, BigInt Q, BigInt R)
{
int digitsN1 = n1.GetMSD() + 1;
int digitsN2 = n2.GetMSD() + 1;
if ((digitsN1 > digitsN2))
{
BigInt n1New = new BigInt(n2);
n1New.DigitShiftSelfLeft(1);
//If n1 >= n2 * 2^32
if (!LtInt(n1, n1New))
{
n1New.sign = n1.sign;
SubFast(n1New, n1, n1New);
Div_32(n1New, n2, Q, R);
//Q = (A - B*2^32)/B + 2^32
Q.Add2Pow32Self();
return;
}
}
UInt32 q = 0;
if (digitsN1 >= 2)
{
UInt64 q64 = ((((UInt64)n1.digitArray[digitsN1 - 1]) << 32) + n1.digitArray[digitsN1 - 2]) / (UInt64)n2.digitArray[digitsN2 - 1];
if (q64 > 0xfffffffful)
{
q = 0xffffffff;
}
else
{
q = (UInt32)q64;
}
}
BigInt temp = Mul(n2, q);
if (GtInt(temp, n1))
{
temp.SubInternalBits(n2.digitArray);
q--;
if (GtInt(temp, n1))
{
temp.SubInternalBits(n2.digitArray);
q--;
}
}
Q.Zero();
Q.digitArray[0] = q;
R.Assign(n1);
R.SubInternalBits(temp.digitArray);
}
/// <summary>
/// Gets the most significant bit
/// </summary>
/// <param name="value">the input to search for the MSB in</param>
/// <returns>-1 if the input was zero, the position of the MSB otherwise</returns>
public static int GetMSB(BigInt value)
{
int digit = value.GetMSD();
int bit = GetMSB(value.digitArray[digit]);
return (digit << 5) + bit;
}