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

const { max } = Math;


/**
 * Returns the result of adding two polynomials with bigint coefficients.
 * 
 * @param p1 a polynomial with coefficients given densely as an array of
 * bigints from highest to lowest power, e.g. `[5n,-3n,0n]` represents the 
 * polynomial `5x^2 - 3x`
 * @param p2 another polynomial
 * 
 * @example
 * ```typescript
 * bAdd([1n,2n,3n],[3n,4n]); //=> [1n,5n,7n]
 * ```
 * 
 * @doc
 */
function bAdd(p1: bigint[], p2: bigint[]): bigint[] {
    // Initialize result array  
    const d1 = p1.length-1;
    const d2 = p2.length-1;
    const Δd = d1-d2;
    
    const Δd1 = Δd < 0 ? +Δd : 0;
    const Δd2 = Δd > 0 ? -Δd : 0;
    
    const d = max(d1, d2);
    
    // Add coefficients
    const result = new Array<bigint>(d+1);
    for (let i=0; i<d+1; i++) {
        const c1 = p1[i+Δd1] || 0n;
        const c2 = p2[i+Δd2] || 0n;
        result[i] = c1 + c2;
    }
    
    // Ensure the result is a valid polynomial representation
    return bRemoveLeadingZeros(result);
}


export { bAdd }