const { abs } = Math;


/**
 * * used in algorithms within [2] below, see e.g. eq. (7) and (8) in that paper.
 * 
 * 
 * @param p1 a polynomial with coefficients given densely as an array of double
 * floating point numbers from highest to lowest power, e.g. `[5,-3,0]` 
 * represents the polynomial `5x^2 - 3x`
 * @param p2 another polynomial
 * 
 * * see [[1] Algorithms for Accurate, Validated and Fast Polynomial Evaluation, *Stef Graillat, Philippe Langlois and Nicolas Louvet*](https://projecteuclid.org/download/pdf_1/euclid.jjiam/1265033778)
 * * see also [[2] *Philippe Langlois, Nicolas Louvet.* Faithful Polynomial Evaluation with Compensated Horner Algorithm. ARITH18: 18th IEEE International Symposium on Computer Arithmetic, Jun 2007, Montpellier, France. pp.141–149. ffhal-00107222f](https://hal.archives-ouvertes.fr/hal-00107222/document)
 * * see also [[3] Horner's Method](https://en.wikipedia.org/wiki/Horner%27s_method)
 * 
 * @internal
 */
function HornerAbsSum(
        p1: number[],
        p2: number[],
        x: number): number {

    //--------------------------------------------------------------------------
    // This is used in algorithms in [2] above
    //--------------------------------------------------------------------------
    let q = 0;
    for (let i=0; i<p1.length; i++) {
        // NOTE: The line below should **NOT** be `abs(p1[i]) + abs(p2[i])` as
        // one would expect, see [2] above eq. (7).
        q = abs(p1[i] + p2[i]) + q*x;
    }

    return q;
}


export { HornerAbsSum }