flo-poly/src/basic/expansion/e-add.ts

A practical, root-focused JavaScript polynomial utility library.

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

// We *have* to do the below❗ The assignee is a getter❗ The assigned is a pure function❗ Otherwise code is too slow❗
const fastExpansionSum = fastExpansionSum_;
const eRemoveLeadingZeros = eRemoveLeadingZeros_;


/**
 * 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 = [];
	for (let i=0; i<d+1; i++) {
		const c1 = p1[i+Δd1] || [0];
		const c2 = p2[i+Δd2] || [0];
		result.push(fastExpansionSum(c1, c2));  
	}
	
	// Ensure the result is a valid polynomial representation
	return eRemoveLeadingZeros(result);
}


export { eAdd }