const { sqrt } = Math;


/**
 * Floating-point-stably calculates and returns the ordered quadratic roots of 
 * the given quadratic polynomial.
 * 
 * * **precondition:** the input polynomial must be quadratic (given as an array
 * of exactly 3 values with the first value *unequal* to zero)
 * * **non-exact:** it is important to note that even though the roots are
 * calculated in a stable way they are still subject to round-off
 * * might be slightly faster than calling [[allRoots]].
 * 
 * @param p a quadratic polynomial with coefficients given as an array 
 * of double floating point numbers from highest to lowest power, e.g. `[5,-3,0]` 
 * represents the quadratic `5x^2 - 3x`
 * 
 * @example
 * ```typescript 
 * quadraticRoots([1, -3, 2]); //=> [1,2]
 * ```
 * 
 * @doc
 */
function quadraticRoots(p: number[]): number[] {
    const [a,b,c] = p;
    
    const _D = b*b - 4*a*c;
    
    if (_D < 0) {
        // No real roots;
        return []; 
    }
    
    if (_D === 0) {
        return [-b / (2*a)];
    }
    
    const D = sqrt(_D);
    
    if (b >= 0) {
        const root1 = (-b - D) / (2*a);
        const root2 = (2*c) / (-b - D);

        return root1 < root2
            ? [root1, root2]
            : [root2, root1];
    }

    const root1 = (2*c) / (-b + D);
    const root2 = (-b + D) / (2*a);

    return root1 < root2
        ? [root1, root2]
        : [root2, root1];
}


export { quadraticRoots }