Created
April 23, 2014 20:14
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Binary GCD algorithm php implementation. Iterative version.
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function binary_gcd($a, $b){ | |
/* computes and returns the greatest common divisor between a and b */ | |
/* | |
* Binary GCD Algorithm, according to Wikipedia "binary GCD can be about 60% | |
* more efficient (in terms of the number of bit operations) on average than the Euclidean algorithm". | |
* More about the Binary GCD Algorithm: http://en.wikipedia.org/wiki/Binary_GCD_algorithm | |
* Java Implementation: http://introcs.cs.princeton.edu/java/23recursion/BinaryGCD.java.html | |
* C++ Implementation: https://gist.github.com/cslarsen/1635213 | |
*/ | |
$shiftleft = 0; | |
while( ($a && $b) && ($a != $b) ){ | |
$a_is_even = !($a & 1); // check if a is even | |
$b_is_even = !($b & 1); // check if b is even | |
// if both a and b are even | |
if ($a_is_even && $b_is_even){ | |
$shiftleft++; | |
$a >>= 1; // shift a right by 1 bit (i.e. divide by 2) | |
$b >>= 1; // shift b right by 1 bit (i.e. divide by 2) | |
} | |
// if a is even and b is odd | |
else if ($a_is_even && !$b_is_even) | |
$a >>= 1; | |
// if b is even and a is odd | |
else if (!$a_is_even && $b_is_even) | |
$b >>= 1; | |
// if both a and b are odd and a >= b | |
else if ($a >= $b) | |
$a = ($a-$b) >> 1; | |
// if both a and b are odd and a < b | |
else{ | |
$temp = $a; | |
$a = ($b - $a) >> 1; | |
$b = $temp; | |
} | |
} | |
// if $a is 0, then shift $b left by $shiftleft bits, otherwise, shit $a by $shiftleft bits | |
return !$a ? $b << $shiftleft : $a << $shiftleft; | |
/* | |
* NOTE: Doing (inetger & 1) check if it's even. | |
* Example: 1 --> 0001 | |
* 6 --> 0110 | |
* 0001 & 0110 ---> 0000 (which is 0) | |
* | |
* 1 --> 0001 | |
* 7 --> 0111 | |
* 0001 & 0111 ---> 0001 (which is 1) | |
*/ | |
} |
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