Extended Euclidean algorithm

The objective of the extended Euclidean algorithm is to compute the greatest common divisor of two natural numbers and solve Bézout’s identity

$ax+by=d$.

Given two positive integers a and b, this Diophantine equation is solved for integers x, y, which will not both be positive, and $d=\gcd(a,b)$.

If $d=1$, the algorithm yields the modular multiplicative inverses of a mod b and b mod a since in this case the congruences

$ax\equiv 1\mod b$

and

$by\equiv 1\mod a$

are solved. Here is a naïve C++ implementation of pseudocode found on Wikipedia.

#include <iostream>
#include <cassert>

int main(int argc, char **argv) {
    long int a, b, q, r0, r1, r,
        s0 = 1, s1, s = 0, t0 = 0, t1, t = 1;
    std::cout << "Enter two positive integers: ";
    std::cin >> a >> b;
    assert(a > 0 && b > 0); r0=a; r=b;
    while(r != 0) {
        q = r0 / r;
        r1 = r0 - q * r; r0 = r; r = r1;
        s1 = s0 - q * s; s0 = s; s = s1;
        t1 = t0 - q * t; t0 = t; t = t1;
    }
    std::cout
        << "Bézout coefficients: "
            << s0 << ", " << t0 << std::endl
        << "greatest common divisor: "
            << r0 << std::endl
        << "quotients by the gcd: "
            << t << ", "<< s << std::endl;
    return 0;
}