/**
* Compute the parity of a number using a technique to erase the LSB.
*
* i.e.
* 64 = 1000000
* 1000000 / result = 1
* parity of 64 is 1
* This works because 64 is &'d with 63 = 1000000 is &'d with 0111111. As we can see that operation will return 0
* which evaluates to false so the while loop terminates.
*
* 65 = 1000001
* 1000001 / result = 1
* 1000000 / result = 0
* parity of 65 is 0
*
* This improves performance in the best and average cases but can still be as slow as brute force. For example if run
* on 9223372036854775807 it will take 63 iterations which matches brute force.
*
* @param int $number
* @return int
* @throws \InvalidArgumentException
*/
function computeParityEraseLowestSetBit($number)
{
if (!is_int($number)) {
throw new \InvalidArgumentException('$number must be an integer');
}
$bitwiseHelper = new BitwiseHelper();
$number = $bitwiseHelper->eraseSignBit($number);
$result = 0;
while ($number) {
$result ^= 1;
$number &= $number - 1;
}
return $result;
}
/**
* Get an array of the pre-computed reverse of all 8-bit words
*
* @return array
*/
function getReverseOf8BitWords()
{
static $cachedReverses = [];
if (empty($cachedReverses)) {
if (!file_exists('computed_reverses.txt')) {
$bitwiseHelper = new BitwiseHelper();
$cachedReverses = $bitwiseHelper->computeReverseOf8BitWords(0b11111111);
$fp = fopen('computed_reverses.txt', 'w');
fwrite($fp, serialize($cachedReverses));
fclose($fp);
} else {
$cachedReverses = unserialize(file_get_contents('computed_reverses.txt'));
}
}
return $cachedReverses;
}
/**
* Compute the parity of a number by comparing the number to smaller halves of itself over and over. Because XOR is
* commutative we can do this until we are down to 4 bits and then use a pre-computed lookup table to compute the final
* parity.
* i.e.
* 64 = 0000000000000000000000000000000000000000000000000000000001000000
*
* 0000000000000000000000000000000000000000000000000000000001000000
* ^ 00000000000000000000000000000000 / Shift 32 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000000
* ^ 000000000000000000000000000000000000000000000000 / Shift 16 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000000
* ^ 00000000000000000000000000000000000000000000000000000000 / Shift 8 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000000
* ^ 000000000000000000000000000000000000000000000000000000000100 / Shift 4 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000100
* 0100 / Last 4 bits
* 0110100110010110 >> 4 & 1 = 011010011001 & 1 = 1 / Parity
*
* 65 = 0000000000000000000000000000000000000000000000000000000001000001
*
* 0000000000000000000000000000000000000000000000000000000001000001
* ^ 00000000000000000000000000000000 / Shift 32 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000001
* ^ 000000000000000000000000000000000000000000000000 / Shift 16 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000001
* ^ 00000000000000000000000000000000000000000000000000000000 / Shift 8 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000001
* ^ 000000000000000000000000000000000000000000000000000000000100 / Shift 4 bits
* --------------------------------------------------------------------
* 0000000000000000000000000000000000000000000000000000000001000101
* 0101 / Last 4 bits
* 0110100110010110 >> 5 & 1 = 01101001100 & 1 = 0 / Parity
*
* @param $number
* @return int
* @throws \InvalidArgumentException
*/
function computeParityShifting($number)
{
if (!is_int($number)) {
throw new \InvalidArgumentException('$number must be an integer');
}
$bitwiseHelper = new BitwiseHelper();
$number = $bitwiseHelper->eraseSignBit($number);
// This contains the parity of 0, 1, 2 ... starting from the LSB
static $fourBitLookupTable = 0b110100110010110;
if (PHP_INT_SIZE == 8) {
$number ^= $number >> BitwiseHelper::WORD_SIZE * 4;
}
$number ^= $number >> BitwiseHelper::WORD_SIZE * 2;
$number ^= $number >> BitwiseHelper::WORD_SIZE;
$number ^= $number >> BitwiseHelper::WORD_SIZE / 2;
$number &= 0b1111;
return $fourBitLookupTable >> $number & 1;
}
