public static BigInteger ShiftLeft(BigInteger value, int n)
{
if ((n == 0) || (value.Sign == 0))
{
return(value);
}
return((n > 0) ? BitLevel.ShiftLeft(value, n) : BitLevel.ShiftRight(value, -n));
}
/**
* Divides the array 'a' by the array 'b' and gets the quotient and the
* remainder. Implements the Knuth's division algorithm. See D. Knuth, The
* Art of Computer Programming, vol. 2. Steps D1-D8 correspond the steps in
* the algorithm description.
*
* @param quot the quotient
* @param quotLength the quotient's length
* @param a the dividend
* @param aLength the dividend's length
* @param b the divisor
* @param bLength the divisor's length
* @return the remainder
*/
public static int[] Divide(int[] quot, int quotLength, int[] a, int aLength, int[] b, int bLength)
{
int[] normA = new int[aLength + 1]; // the normalized dividend
// an extra byte is needed for correct shift
int[] normB = new int[bLength + 1]; // the normalized divisor;
int normBLength = bLength;
/*
* Step D1: normalize a and b and put the results to a1 and b1 the
* normalized divisor's first digit must be >= 2^31
*/
int divisorShift = Utils.NumberOfLeadingZeros(b[bLength - 1]);
if (divisorShift != 0)
{
BitLevel.ShiftLeft(normB, b, 0, divisorShift);
BitLevel.ShiftLeft(normA, a, 0, divisorShift);
}
else
{
Array.Copy(a, 0, normA, 0, aLength);
Array.Copy(b, 0, normB, 0, bLength);
}
int firstDivisorDigit = normB[normBLength - 1];
// Step D2: set the quotient index
int i = quotLength - 1;
int j = aLength;
while (i >= 0)
{
// Step D3: calculate a guess digit guessDigit
int guessDigit = 0;
if (normA[j] == firstDivisorDigit)
{
// set guessDigit to the largest unsigned int value
guessDigit = -1;
}
else
{
long product = (((normA[j] & 0xffffffffL) << 32) + (normA[j - 1] & 0xffffffffL));
long res = Division.DivideLongByInt(product, firstDivisorDigit);
guessDigit = (int)res; // the quotient of divideLongByInt
int rem = (int)(res >> 32); // the remainder of
// divideLongByInt
// decrease guessDigit by 1 while leftHand > rightHand
if (guessDigit != 0)
{
long leftHand = 0;
long rightHand = 0;
bool rOverflowed = false;
guessDigit++; // to have the proper value in the loop
// below
do
{
guessDigit--;
if (rOverflowed)
{
break;
}
// leftHand always fits in an unsigned long
leftHand = (guessDigit & 0xffffffffL)
* (normB[normBLength - 2] & 0xffffffffL);
/*
* rightHand can overflow; in this case the loop
* condition will be true in the next step of the loop
*/
rightHand = ((long)rem << 32)
+ (normA[j - 2] & 0xffffffffL);
long longR = (rem & 0xffffffffL)
+ (firstDivisorDigit & 0xffffffffL);
/*
* checks that longR does not fit in an unsigned int;
* this ensures that rightHand will overflow unsigned
* long in the next step
*/
if (Utils.NumberOfLeadingZeros((int)Utils.URShift(longR, 32)) < 32)
{
rOverflowed = true;
}
else
{
rem = (int)longR;
}
} while ((leftHand ^ Int64.MinValue) > (rightHand ^ Int64.MinValue));
//} while ((leftHand ^ Int64.MaxValue) > (rightHand ^ Int64.MaxValue));
// while (((leftHand ^ 0x8000000000000000L) > (rightHand ^ 0x8000000000000000L))) ;
}
}
// Step D4: multiply normB by guessDigit and subtract the production
// from normA.
if (guessDigit != 0)
{
int borrow = Division.MultiplyAndSubtract(normA, j - normBLength, normB, normBLength, guessDigit);
// Step D5: check the borrow
if (borrow != 0)
{
// Step D6: compensating addition
guessDigit--;
long carry = 0;
for (int k = 0; k < normBLength; k++)
{
carry += (normA[j - normBLength + k] & 0xffffffffL)
+ (normB[k] & 0xffffffffL);
normA[j - normBLength + k] = (int)carry;
carry = Utils.URShift(carry, 32);
}
}
}
if (quot != null)
{
quot[i] = guessDigit;
}
// Step D7
j--;
i--;
}
/*
* Step D8: we got the remainder in normA. Denormalize it id needed
*/
if (divisorShift != 0)
{
// reuse normB
BitLevel.ShiftRight(normB, normBLength, normA, 0, divisorShift);
return(normB);
}
Array.Copy(normA, 0, normB, 0, bLength);
return(normA);
}
