import { scaleExpansion } from "big-float-ts";


/**
 * Returns the exact result (bar underflow / overflow) of differentiating the 
 * given polynomial (with Shewchuk expansion coefficients).
 * 
 * @param p 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`
 * 
 * @example
 * ```typescript
 * eDifferentiate([[5], [4], [3], [2], [1]]); //=> [[20], [12], [6], [2]]
 * ```
 * 
 * @doc
 */
function eDifferentiate(p: number[][]): number[][] {
    const d = p.length - 1;
    if (d <= 0) { return []; }
    const result = new Array<number[]>(d);
    for (let i=0; i<d; i++) {
        result[i] = scaleExpansion(p[i], d-i);
    }

    return result;
}


export { eDifferentiate }