import { eRemoveLeadingZeros } from "./e-remove-leading-zeros.js";
import { fastExpansionSum } from "big-float-ts";


/**
 * Returns the exact result (bar underflow / overflow) of adding two 
 * polynomials with coefficients given as Shewchuk floating point expansions.
 * 
 * @param p1 a polynomial with coefficients given densely as an array of Shewchuk
 * floating point expansions from highest to lowest power, e.g. `[[5],[-3],[0]]`
 * represents the polynomial `5x^2 - 3x`
 * @param p2 another polynomial
 * 
 * @example
 * ```typescript
 * eAdd([[1],[2],[3]],[[3],[4]]); //=> [[1],[5],[7]]
 * ```
 * 
 * @doc
 */
function eAdd(p1: number[][], p2: number[][]): number[][] {
    // 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 = Math.max(d1, d2);
    
    // Add coefficients
    const result = new Array<number[]>(d+1);
    for (let i=0; i<d+1; i++) {
        const c1 = p1[i+Δd1] || [0];
        const c2 = p2[i+Δd2] || [0];
        result[i] = fastExpansionSum(c1, c2);
    }
    
    // Ensure the result is a valid polynomial representation
    return eRemoveLeadingZeros(result);
}


export { eAdd }