/** Add an IntNum and an int, yielding a new IntNum. */
public static IntNum add(IntNum x, int y)
{
if (x.words == null)
return IntNum.add (x.ival, y);
IntNum result = new IntNum (0);
result.setAdd (x, y);
return result.canonicalize ();
}
/** Divide two integers, yielding quotient and remainder.
* @param x the numerator in the division
* @param y the denominator in the division
* @param quotient is set to the quotient of the result (iff quotient!=null)
* @param remainder is set to the remainder of the result
* (iff remainder!=null)
* @param rounding_mode one of FLOOR, CEILING, TRUNCATE, or ROUND.
*/
public static void divide(IntNum x, IntNum y,
IntNum quotient, IntNum remainder,
int rounding_mode)
{
if ((x.words == null || x.ival <= 2)
&& (y.words == null || y.ival <= 2))
{
long x_l = x.longValue ();
long y_l = y.longValue ();
if (x_l != long.MinValue && y_l != long.MinValue)
{
divide (x_l, y_l, quotient, remainder, rounding_mode);
return;
}
}
bool xNegative = x.isNegative ();
bool yNegative = y.isNegative ();
bool qNegative = xNegative ^ yNegative;
int ylen = y.words == null ? 1 : y.ival;
int[] ywords = new int[ylen];
y.getAbsolute (ywords);
while (ylen > 1 && ywords[ylen-1] == 0) ylen--;
int xlen = x.words == null ? 1 : x.ival;
int[] xwords = new int[xlen+2];
x.getAbsolute (xwords);
while (xlen > 1 && xwords[xlen-1] == 0) xlen--;
int qlen, rlen;
int cmpval = MPN.cmp (xwords, xlen, ywords, ylen);
if (cmpval < 0) // abs(x) < abs(y)
{ // quotient = 0; remainder = num.
int[] rwords = xwords; xwords = ywords; ywords = rwords;
rlen = xlen; qlen = 1; xwords[0] = 0;
}
else if (cmpval == 0) // abs(x) == abs(y)
{
xwords[0] = 1; qlen = 1; // quotient = 1
ywords[0] = 0; rlen = 1; // remainder = 0;
}
else if (ylen == 1)
{
qlen = xlen;
rlen = 1;
ywords[0] = MPN.divmod_1 (xwords, xwords, xlen, ywords[0]);
}
else // abs(x) > abs(y)
{
// Normalize the denominator, i.e. make its most significant bit set by
// shifting it normalization_steps bits to the left. Also shift the
// numerator the same number of steps (to keep the quotient the same!).
int nshift = MPN.count_leading_zeros (ywords[ylen-1]);
if (nshift != 0)
{
// Shift up the denominator setting the most significant bit of
// the most significant word.
MPN.lshift (ywords, 0, ywords, ylen, nshift);
// Shift up the numerator, possibly introducing a new most
// significant word.
int x_high = MPN.lshift (xwords, 0, xwords, xlen, nshift);
xwords[xlen++] = x_high;
}
if (xlen == ylen)
xwords[xlen++] = 0;
MPN.divide (xwords, xlen, ywords, ylen);
rlen = ylen;
MPN.rshift0 (ywords, xwords, 0, rlen, nshift);
qlen = xlen + 1 - ylen;
if (quotient != null)
{
for (int i = 0; i < qlen; i++)
xwords[i] = xwords[i+ylen];
}
}
while (rlen > 1 && ywords[rlen-1] == 0)
rlen--;
if (ywords[rlen-1] < 0)
{
ywords[rlen] = 0;
rlen++;
}
// Now the quotient is in xwords, and the remainder is in ywords.
bool add_one = false;
if (rlen > 1 || ywords[0] != 0)
{ // Non-zero remainder i.e. in-exact quotient.
switch (rounding_mode)
{
case TRUNCATE:
break;
case CEILING:
if (qNegative == (rounding_mode == FLOOR))
add_one = true;
break;
case FLOOR:
if (qNegative == (rounding_mode == FLOOR))
add_one = true;
break;
case ROUND:
// int cmp = compare (remainder<<1, abs(y));
IntNum tmp = remainder == null ? new IntNum() : remainder;
tmp.set (ywords, rlen);
tmp = shift (tmp, 1);
if (yNegative)
tmp.setNegative();
int cmp = compare (tmp, y);
// Now cmp == compare(sign(y)*(remainder<<1), y)
if (yNegative)
cmp = -cmp;
add_one = (cmp == 1) || (cmp == 0 && (xwords[0]&1) != 0);
break;
}
}
if (quotient != null)
{
if (xwords[qlen-1] < 0)
{
xwords[qlen] = 0;
qlen++;
}
quotient.set (xwords, qlen);
if (qNegative)
{
if (add_one) // -(quotient + 1) == ~(quotient)
quotient.setInvert ();
else
quotient.setNegative ();
}
else if (add_one)
quotient.setAdd (1);
}
if (remainder != null)
{
// The remainder is by definition: X-Q*Y
remainder.set (ywords, rlen);
if (add_one)
{
// Subtract the remainder from Y:
// abs(R) = abs(Y) - abs(orig_rem) = -(abs(orig_rem) - abs(Y)).
IntNum tmp;
if (y.words == null)
{
tmp = remainder;
tmp.set(yNegative ? ywords[0] + y.ival : ywords[0] - y.ival);
}
else
tmp = IntNum.add(remainder, y, yNegative ? 1 : -1);
// Now tmp <= 0.
// In this case, abs(Q) = 1 + floor(abs(X)/abs(Y)).
// Hence, abs(Q*Y) > abs(X).
// So sign(remainder) = -sign(X).
if (xNegative)
remainder.setNegative(tmp);
else
remainder.set(tmp);
}
else
{
// If !add_one, then: abs(Q*Y) <= abs(X).
// So sign(remainder) = sign(X).
if (xNegative)
remainder.setNegative ();
}
}
}