import { eAbs, eSign, eRem } from 'big-float-ts';


/**
 * Computes the greatest common divisor of two integers a and b, using the 
 * Euclidean Algorithm.
 * 
 * **precondition** `a`, `b` must be integers given as Shewchuk expansions
 * 
 * @doc
 */
function eGcdInt(
        a: number[],
        b: number[]): number[] {

    a = eAbs(a);
    b = eAbs(b);

    // The below 2 commented lines represent Euclid's original algorithm.
    //if (a === b) { return a; }
    //return a > b ? gcdInt(a - b, b) : gcdInt(a, b - a);
    
    if (eSign(a) === 0) { return b; }
    if (eSign(b) === 0) { return a; }

    while (eSign(b) !== 0) {
        const t = b;
        b = eRem(a,b);
        a = t;
    }

    return a;
}


/**
 * Naively computes and returns the greatest common divisor of 2 or more 
 * integers by taking each integer in turn and calculating the GCD of that 
 * integer and the previously calculated GCD (where the first GCD is simply
 * taken as the first number).
 * 
 * @param vals the integers (given as Shewchuk expansions) for which the GCD is 
 * to be calculated
 */
function eGcdInts(vals: number[][]): number[] {
    const vals_ = vals.slice();
    const len = vals_.length;

    // make array of numbers all positive
    for (let i=0; i<len; i++) { 
        vals_[i] = eAbs(vals_[i]); 
    }
    
    let a = vals_[0];
    for (let i=1; i<len; i++) {
        a = eGcdInt(a, vals_[i]);
    }
    
    return a;
} 


export { eGcdInt, eGcdInts }