/// <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>
/// 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>
/// Adds n1 and n2 and puts result in dest, without intermediate memory allocation
/// (unsafe if n1 and n2 disagree in precision, safe even if dest is n1 or n2)
/// </summary>
/// <param name="dest"></param>
/// <param name="n1"></param>
/// <param name="n2"></param>
public static void SubFast(BigInt dest, BigInt n1, BigInt n2)
{
//We cast to the highest input precision...
if (n1.digitArray.Length != n2.digitArray.Length) MakeSafe(ref n1, ref n2);
//Then we up the output precision if less than the input precision.
if (dest.digitArray.Length < n1.digitArray.Length) n1.MakeSafe(ref dest);
int Length = n1.digitArray.Length;
if (n1.sign != n2.sign)
{
//Copies sources into digit array and working set for all cases, to avoid
//problems when dest is n1 or n2
for (int i = 0; i < Length; i++)
{
dest.workingSet[i] = n2.digitArray[i];
dest.digitArray[i] = n1.digitArray[i];
}
dest.AddInternalBits(dest.workingSet);
dest.sign = n1.sign;
}
else
{
bool lessThan = LtInt(n1, n2);
if (lessThan)
{
for (int i = 0; i < Length; i++)
{
dest.workingSet[i] = n1.digitArray[i];
dest.digitArray[i] = n2.digitArray[i];
}
dest.SubInternalBits(dest.workingSet);
dest.sign = !n1.sign;
}
else
{
for (int i = 0; i < Length; i++)
{
dest.workingSet[i] = n2.digitArray[i];
dest.digitArray[i] = n1.digitArray[i];
}
dest.SubInternalBits(dest.workingSet);
dest.sign = n1.sign;
}
}
}