gmp_gcdext

Calculate GCD and multipliers (PHP 4 >= 4.0.4, PHP 5)
array gmp_gcdext ( resource a, resource b )

Example 792. Solving a linear Diophantine equation

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<?php
// Solve the equation a*s + b*t = g

// where a = 12, b = 21, g = gcd(12, 21) = 3
$a = gmp_init(12);
$b = gmp_init(21);
$g = gmp_gcd($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 while solving the equation\n";

}

// output: Solution: 12*2 + 21*-1 = 3
?>

Code Examples / Notes » gmp_gcdext

fatphil

The extended GCD can be used to calculate mutual modular inverses of two coprime numbers. Internally gmp_invert uses this extended GCD routine, but effectively throws away one of the inverses. If gcd(a,b)=1, then r.a+s.b=1 Therefore r.a == 1 (mod s) and s.b == 1 (mod r) Note that one of r and s will be negative, and so you'll want to canonicalise it.

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gmp_abs
gmp_add
gmp_and
gmp_clrbit
gmp_cmp
gmp_com
gmp_div_q
gmp_div_qr
gmp_div_r
gmp_div
gmp_divexact
gmp_fact
gmp_gcd
gmp_gcdext
gmp_hamdist
gmp_init
gmp_intval
gmp_invert
gmp_jacobi
gmp_legendre
gmp_mod
gmp_mul
gmp_neg
gmp_nextprime
gmp_or
gmp_perfect_square
gmp_popcount
gmp_pow
gmp_powm
gmp_prob_prime
gmp_random
gmp_scan0
gmp_scan1
gmp_setbit
gmp_sign
gmp_sqrt
gmp_sqrtrem
gmp_strval
gmp_sub
gmp_testbit
gmp_xor

gmp_gcdext

Calculate GCD and multipliers (PHP 4 >= 4.0.4, PHP 5) array gmp_gcdext ( resource a, resource b )

Example 792. Solving a linear Diophantine equation

Code Examples / Notes » gmp_gcdext

Change Language

Calculate GCD and multipliers (PHP 4 >= 4.0.4, PHP 5)
array gmp_gcdext ( resource a, resource b )