/**
* Performs long multiplication up to $stop digits
*
* If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved.
*
* @see _barrett()
* @param Math_BigInteger $x
* @return Math_BigInteger
* @access private
*/
function _multiplyLower($x, $stop)
{
$this_length = count($this->value);
$x_length = count($x->value);
if (!$this_length || !$x_length) {
// a 0 is being multiplied
return new Math_BigInteger();
}
if ($this_length < $x_length) {
return $x->_multiplyLower($this, $stop);
}
$product = new Math_BigInteger();
$product->value = $this->_array_repeat(0, $this_length + $x_length);
// the following for loop could be removed if the for loop following it
// (the one with nested for loops) initially set $i to 0, but
// doing so would also make the result in one set of unnecessary adds,
// since on the outermost loops first pass, $product->value[$k] is going
// to always be 0
$carry = 0;
for ($j = 0; $j < $this_length; $j++) {
// ie. $i = 0, $k = $i
$temp = $this->value[$j] * $x->value[0] + $carry;
// $product->value[$k] == 0
$carry = floor($temp / 0x4000000);
$product->value[$j] = $temp - 0x4000000 * $carry;
}
if ($j < $stop) {
$product->value[$j] = $carry;
}
// the above for loop is what the previous comment was talking about. the
// following for loop is the "one with nested for loops"
for ($i = 1; $i < $x_length; $i++) {
$carry = 0;
for ($j = 0, $k = $i; $j < $this_length && $k < $stop; $j++, $k++) {
$temp = $product->value[$k] + $this->value[$j] * $x->value[$i] + $carry;
$carry = floor($temp / 0x4000000);
$product->value[$k] = $temp - 0x4000000 * $carry;
}
if ($k < $stop) {
$product->value[$k] = $carry;
}
}
$product->is_negative = $this->is_negative != $x->is_negative;
return $product;
}