const { abs } = Math;


/**
 * Returns the value of the polynomial `p` evaluated at `x` along with an
 * error bound on the result that has **NOT** yet been scaled by `γ1`.
 * 
 * @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 to evaluate the polynomial
 * @param p_ an error polynomial that provides a coefficient-wise error bound
 * on the input polynomial **NOT** yet scaled by `γ1`
 */
function HornerWithInpError(
        p: number[],
        x: number,
        p_: number[]): [number, number] {
    
    const _x = abs(x);
    let r̂ = p[0];
    let r̂_ = p_[0];
    for (let i=1; i<p.length; i++) {
        const r̂x = r̂*x;
        r̂ = r̂x + p[i];
        r̂_ = r̂_*_x + abs(r̂x) + p_[i] + abs(r̂);
    }

    return [r̂, r̂_];
}


export { HornerWithInpError }