import { bPremSequenceSubresultant } from "../../euclidean-division-related/bigint/b-prem-sequence-subresultant.js";
import { scaleFloatsToBigints } from "../../scale-to-int/scale-floats-to-bigints.js";
import { scaleFloatssToBigintss } from "../../scale-to-int/scale-floatss-to-bigintss.js";


/**
 * Returns the GCD (Greatest Common Divisor) of the two given polynomials using 
 * Pseudo Remainder Sequences (PRSs) as `bigint`s.
 * 
 * * the modular GCD algorithm, [[gcdModular]], can also be used; it should
 *   be faster for high degree polynomials or when `gcdPrs` encounters pathological
 *   cases. However, `gcdPrs` is faster in general.
 * 
 * * since the final polynomial coefficients can be too large and overflow can
 *   occur in the **final** result is returned as a `bigint` coefficient polynomial
 *   (see `bLandauMignotteBound`).
 * 
 * @param a a polynomial with coefficients given densely as an array of
 * double precision floating point numbers from highest to lowest power, 
 * e.g. `[5,-3,0]` represents the polynomial `5x^2 - 3x`
 * @param b another polynomial
 * 
 * @internal
 */
function gcdPrs(
        a: number[],
        b: number[]): bigint[] {

    if (a.length === 0) {
        return scaleFloatsToBigints(b);
    } else if (b.length === 0) {
        return scaleFloatsToBigints(a);
    }

    const [A,B] = scaleFloatssToBigintss([a,b]);

    const seq = bPremSequenceSubresultant(A,B,false);

    return seq[seq.length-1];
}


export { gcdPrs }