PHP | gmp_gcdext() function

The gmp_gcdext() is an inbuilt function in PHP which calculates the GCD ( Greatest Common Divisor ) and multipliers of a given equation such that a * x + b * y = GCD(a, b), where GCD is the greatest common divisor.
This function is used to solve linear Diophantine equation in two variables .

Syntax:

array gmp_gcdext ( GMP $a, GMP $b )

Parameters: The gmp_gcdext() function accepts two parameters as listed above and described below:

• $a: This parameter can be a GMP resource in PHP 5.5 and earlier, a GMP object in PHP 5.6, or we are also allowed to pass a numeric string provided that it is possible to convert that string to a number.
• $b: This parameter can be a GMP resource in PHP 5.5 and earlier, a GMP object in PHP 5.6, or we are also allowed to pass a numeric string provided that it is possible to convert that string to a number.

Return Values: This function will return an array of GMP numbers (GNU Multiple Precision: For large numbers) that is the multipliers (x and y of a given equation ) and the gcd.

Examples:

Input: a = 12  ,  b = 21
       equation = 12 * x + 21 * y = 3
Output:  

Input: a = 5  ,  b = 10
       equation = 5 * x + 10 * y = 5
Output: x = 1  ,  y = 0  ,  GCD(12,21) = 5

Below program illustrate the gmp_gcdext() function:

<?php
// PHP code to solve a Diophantine equation

// Solve the equation a*x + b*y = g
// where a =, b =, g = gcd(5, 6) = 1
$a = gmp_init(5);
$b = gmp_init(6);

// calculates gcd of two gmp numbers
$g = gmp_gcd($a, $b);

$r = gmp_gcdext($a, $b);

$check_gcd = (gmp_strval($g) == gmp_strval($r['g']));
$eq_res = gmp_add(gmp_mul($a, $r['s']), gmp_mul($b, $r['t']));
$check_res = (gmp_strval($g) == gmp_strval($eq_res));

if ($check_gcd && $check_res) {

    $fmt = "Solution: %d * %d + %d * %d = %d\n";
    printf($fmt, gmp_strval($a), gmp_strval($r['s']), gmp_strval($b),
    gmp_strval($r['t']), gmp_strval($r['g']));
}
else
    echo "Error generated\n";
?>

Output:

Solution: 5 * -1 + 6 * 1 = 1

Reference : http://php.net/manual/en/function.gmp-gcdext.php