import { bRemoveLeadingZeros } from "./b-remove-leading-zeros.js";

const { max } = Math;


/** 
 * Returns the result of subtracting the second polynomial from the first with
 * coefficients given as bigints; (p1 - p2).
 * 
 * @param a minuend; the polynomial from which will be subtracted; a polynomial 
 * with coefficients given densely as an array of bigints 
 * from highest to lowest power, e.g. `[5,-3,0]` represents the 
 * polynomial `5x^2 - 3x`
 * @param b subtrahend; the polynomial that will be subtracted
 * 
 * @example
 * ```typescript
 * bSubtract([2n,3n],[4n,4n]); //=> [-2n, -1n]
 * ```
 * 
 * @doc
 */
function bSubtract(a: bigint[], b: bigint[]): bigint[] {
    // Initialize result array  
    const da = a.length - 1;
    const db = b.length - 1;
    const Δd = da - db;
    
    const Δd2 = Δd > 0 ? -Δd : 0;
    const Δd1 = Δd < 0 ? +Δd : 0;

    const d = max(da, db);
    
    // Add coefficients
    const result = new Array<bigint>(d+1);
    for (let i=0; i<d+1; i++) {
        const c1 = a[i+Δd1] || 0n;
        const c2 = b[i+Δd2] || 0n;
        result[i] = c1 - c2;
    }

    // Ensure the result is a valid polynomial representation
    return bRemoveLeadingZeros(result);
}


export { bSubtract }