/**
 * Problem statement and explanation: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
 * 
 * This algorithm plays an important role for modular arithmetic, and by extension for cyptography algorithms
 * 
 * This implementation uses an iterative approach to calculate
 */

/**
 * 
 * @param {Number} arg1 first argument
 * @param {Number} arg2 second argument
 * @returns Array with GCD and first and second Bézout coefficients
 */
const extendedEuclideanGCD = (arg1, arg2) => {
    if(typeof arg1 != 'number' || typeof arg2 != 'number') throw new TypeError('Not a Number');
    if(arg1 < 1 || arg2 < 1) throw new TypeError('Must be positive numbers');

    // Make the order of coefficients correct, as the algorithm assumes r0 > r1
    if (arg1 < arg2) {
        const res = extendedEuclideanGCD(arg2,arg1)
        const temp = res[1]
        res[1] = res[2]
        res[2] = temp
        return res;
    }

    // At this point arg1 > arg2

    // Remainder values
    let r0 = arg1
    let r1 = arg2

    // Coefficient1 values
    let s0 = 1
    let s1 = 0

    // Coefficient 2 values
    let t0 = 0
    let t1 = 1
    
    while(r1 != 0) {
        const q = Math.floor(r0 / r1);

        const r2 = r0 - r1*q;
        const s2 = s0 - s1*q;
        const t2 = t0 - t1*q;
        
        r0 = r1
        r1 = r2
        s0 = s1
        s1 = s2
        t0 = t1
        t1 = t2
    }
    return [r0,s0,t0];
}

export { extendedEuclideanGCD };
// ex