const abs = Math.abs;


/** 
 * Returns the result of evaluating a univariate polynomial using 
 * Horner's method and where:
 *  1. the absolute value of each coefficient is taken
 *  2. the absolute value of `x` is taken
 * 
 * * i.e. P(x) = ∑ᵢ₌₀ⁿ |aᵢ| |x|ⁱ
 * 
 * * intermediate calculations are done in double precision
 * 
 * @param p 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 x the value at which `p` should be evaluated
 * 
 * @doc
 */
function AbsHorner(
        p: number[],
        x: number): number {

    const _x = abs(x);
    let q = 0;
    for (let i=0; i<p.length; i++) {
        q = q*_x + abs(p[i]);
    }

    return q;
}
// inlined (with q => e2, p => p0)
//let e2 = abs(p0[0]); for (let i=1; i<p0.length; i++) { e2 = e2*x + abs(p0[i]); }


export { AbsHorner }