import { γγ } from '../../error-analysis/gamma.js';
import { ddMultDouble2 } from "double-double";
import { eEstimate } from "big-float-ts";


const γγ3 = γγ(3);


/**
 * Returns the result (and resulting coefficient-wise error bound) of 
 * differentiating the given polynomial (with coefficients given in 
 * double-double precision) in double-double precision.
 * 
 * @param pWithErr an object with 2 properties: `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` **and** `pE`: the coefficient-wise error bound of 
 * the input polynomial
 * 
 * @doc
 */
function ddDifferentiateWithError(
        pWithErr: { p: number[][], pE: number[] }): { p: number[][], pE: number[] } {

    const { p, pE } = pWithErr;

    const d = p.length - 1;
    if (d <= 0) { return { p: [], pE: [] }; }

    const dp = new Array<number[]>(d);
    const dpE = new Array<number>(d);

    for (let i=0; i<d; i++) {
        const deg = d-i;
        const c = ddMultDouble2(deg, p[i]);
        dp[i] = c;

        // if 1,2,4 or 8, etc. then no additional error occurs on multiply
        // if 3,5,7 or 9, etc. then additional error occurs
        // deg is a power of 2 <=> (deg & deg-1) === 0
        const extraErr = (deg & deg-1) === 0 ? 0 : γγ3;
        
        const $c = eEstimate(c);
        dpE[i] = deg*pE[i] + Math.abs($c)*extraErr;
    }

    return { p: dp, pE: dpE };
}


export { ddDifferentiateWithError }