import { ddMultDouble2 } from "double-double";


/**
 * Returns the result of differentiating the given polynomial (with coefficients 
 * given in double-double precision) in double-double precision.
 * 
 * @param p a polynomial with coefficients given densely as an array of 
 * double-double precision floating point numbers from highest to lowest power, 
 * e.g. `[[5],[-3],[0]]` represents the polynomial `5x^2 - 3x`
 * 
 * @example
 * ```typescript
 * ddDifferentiate([[0,5], [0,4], [0,3], [0,2], [0,1]]); //=> [[0,20], [0,12], [0,6], [0,2]]
 * ```
 * 
 * @doc
 */
function ddDifferentiate(p: number[][]): number[][] {
    const d = p.length - 1;
    if (d <= 0) { return []; }
    const r = new Array<number[]>(d);
    for (let i=0; i<d; i++) {
        r[i] = ddMultDouble2((d-i), p[i]);
    }
    
    return r;
}


export { ddDifferentiate }