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


/** 
 * Returns the exact result (bar underflow / overflow) of subtracting the 
 * second polynomial from the first (both with coefficients given as Shewchuk 
 * floating point expansions); (p1 - p2).
 * 
 * @param p1 minuend; the polynomial from which will be subtracted; a polynomial 
 * with coefficients given densely as Shewchuk floating point expansions
 * from highest to lowest power, e.g. `[[5],[-3],[0]]` represents the 
 * polynomial `5x^2 - 3x`
 * @param p2 subtrahend; the polynomial that will be subtracted
 * 
 * @example
 * ```typescript
 * eSubtract([[2],[3]],[[4],[4]]); //=> [[-2], [-1]]
 * ```
 * 
 * @doc
 */
function eSubtract(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] = eDiff(c1, c2);
    }
    
    // Ensure the result is a valid polynomial representation
    return eRemoveLeadingZeros(result);
}


export { eSubtract }