/// <summary>
/// Calculates 'this' mod n2 (using the schoolbook division algorithm as above)
/// </summary>
/// <param name="n2"></param>
public void Mod(BigInt n2)
{
if (n2.digitArray.Length != digitArray.Length) MakeSafe(ref n2);
int OldLength = digitArray.Length;
//First, we need to prepare the operands for division using Div_32, which requires
//That the most significant digit of n2 be set. To do this, we need to shift n2 (and therefore n1) up.
//This operation can potentially increase the precision of the operands.
int shift = MakeSafeDiv(this, n2);
BigInt Q = new BigInt(this.pres);
BigInt R = new BigInt(this.pres);
Q.digitArray = new UInt32[this.digitArray.Length];
R.digitArray = new UInt32[this.digitArray.Length];
Div_32(this, n2, Q, R);
//Restore n2 to its pre-shift value
n2.RSH(shift);
R.RSH(shift);
R.sign = (sign != n2.sign);
AssignInt(R);
//Reset the lengths of the operands
SetNumDigits(OldLength);
n2.SetNumDigits(OldLength);
}
/// <summary>
/// Makes sure the numbers have matching precisions
/// </summary>
/// <param name="n2">the number to match to this</param>
private void MakeSafe(ref BigInt n2)
{
n2 = new BigInt(n2, pres);
n2.SetNumDigits(digitArray.Length);
}
/// <summary>
/// This function is used for floating-point division.
/// </summary>
/// <param name="n2"></param>
//Given two numbers:
// In floating point 1 <= a, b < 2, meaning that both numbers have their top bits set.
// To calculate a / b, maintaining precision, we:
// 1. Double the number of digits available to both numbers.
// 2. set a = a * 2^d (where d is the number of digits)
// 3. calculate the quotient a <- q: 2^(d-1) <= q < 2^(d+1)
// 4. if a >= 2^d, s = 1, else s = 0
// 6. shift a down by s, and undo the precision extension
// 7. return 1 - shift (change necessary to exponent)
public int DivAndShift(BigInt n2)
{
if (n2.IsZero()) return -1;
if (digitArray.Length != n2.digitArray.Length) MakeSafe(ref n2);
int oldLength = digitArray.Length;
//Double the number of digits, and shift a into the higher digits.
Pad();
n2.Extend();
//Do the divide (at double precision, ouch!)
Div(n2);
//Shift down if 'this' >= 2^d
int ret = 1;
if (digitArray[oldLength] != 0)
{
RSH(1);
ret--;
}
SetNumDigits(oldLength);
n2.SetNumDigits(oldLength);
return ret;
}
/// <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;
}