/**
* Calculate the quotient and remainder from a +ve numerator/denominator with no decimals.
* This function is used when the denominators is smaller than self::BIGNUMBER_MAX_NUM_LEN.
* @param BigNumber $numerator the numerator to use.
* @param BigNumber $denominator the denominator.
* @param BigNumber $quotient the return quotient value.
* @param BigNumber $remainder the remainder value.
* @return boolean success or not.
*/
protected static function AbsQuotientAndRemainderWithSmallDenominator($numerator, $denominator, &$quotient, &$remainder)
{
// is it too long?
$denominatorLen = count($denominator->_numbers);
if ($denominatorLen > self::BIGNUMBER_MAX_NUM_LEN) {
return false;
}
if ($denominatorLen == self::BIGNUMBER_MAX_NUM_LEN) {
// because the numerator is the same len as BIGNUMBER_MAX_NUM_LEN
// we have to make sure that the first 'BIGNUMBER_MAX_NUM_LEN' digits of the numerator are not bigger than the denominator.
//
$numberNumerator = $numerator->_MakeNumberAtIndexForward(0, self::BIGNUMBER_MAX_NUM_LEN);
$numberDenominator = $denominator->ToInt();
if ($numberNumerator < $numberDenominator) {
// this will never work as the first 'BIGNUMBER_MAX_NUM_LEN' digits are too small.
return false;
}
}
// assume that the remainder is the full amount.
$remainder = clone $numerator;
// get the positive denominator.
$intDenominator = $denominator->Abs()->ToInt();
// convert to integer.
$numerator->Abs()->Integer();
// the offset is just one more than the total len of our number.
$offset = count($denominator->_numbers) + 1;
$length = count($numerator->_numbers);
// do a fast division.
// @see http://codereview.stackexchange.com/questions/6331/very-large-a-divide-at-a-very-large-b
// get the first 'x' numbers, as we are in reverse, we get the last x numbers.
// we then work one number at at a time.
$numbers = [];
// get the first 'x' numbers.
// after that we will be getting one number at a time.
$number = $numerator->_MakeNumberAtIndexForward(0, $offset);
// now create an array of our remaining numbers.
// we will use them all one by one to calculate the 'final' denominator.
$array = array_slice($numerator->_numbers, 0, $length - $offset);
$oneOverIntDenominator = 1 / (double) $intDenominator;
$length -= $offset;
for (;;) {
// the div of that number, (we use 1/x as it is a shade faster).
$div = (int) ($number * $oneOverIntDenominator);
// if the number is 0 it means that the section we just did
// (the '$number'), was itself == to zero.
if (0 == $div) {
// if the number is zero, no need to waste time working things out
$numbers[] = 0;
} else {
// add the numbers, in reverse to our final array.
$tnumber = [];
while ($div > 0) {
$s = $div % self::BIGNUMBER_BASE;
$div = (int) ((int) $div / (int) self::BIGNUMBER_BASE);
$tnumber[] = $s;
}
$numbers = array_merge($numbers, array_reverse($tnumber));
}
// are we done?
if ($length <= 0) {
$quotient = static::_FromSafeValues($quotient, array_reverse($numbers), 0, false);
break;
}
// the mod of that number.
$mod = $number % $intDenominator;
$numerator = new BigNumber($mod);
// add the number in front
array_unshift($numerator->_numbers, $array[--$length]);
// get that section number.
$number = $numerator->ToInt();
}
// clean up the quotient and the remainder.
$quotient->PerformPostOperations($quotient->_decimals);
// we know that the remainder is currently equal to the numerator, (see clone above).
$remainder = static::AbsSub($remainder, static::AbsMul($quotient, $denominator, 0));
// success
return true;
}