import { ddDivDouble } from 'double-double';


/**  
 * Returns the result of integrating the given polynomial in double-double 
 * precision.
 * 
 * @param p a polynomial with coefficients given densely as an array of 
 * double-double precision floating point numbers from highest to lowest 
 * power, e.g. `[[0,5],[0,-3],[0,0]]` 
 * represents the polynomial `5x^2 - 3x`
 * @param c the constant of intergration
 * 
 * @example
 * ```typescript
 * integrate([[0,3], [0,2], [0,1]]); //=> [[0,1], [0,1], [0,1], [0,c]]
 * ```
 * 
 * @doc
 */
 function ddIntegrate(
        p: number[][], 
        c: number[]): number[][] {

    const d = p.length - 1;
    const r = new Array<number[]>(d+2);
    for (let i=0; i<d+1; i++) {
        r[i] = ddDivDouble(p[i],(d+1-i));
    }

    r[d+1] = c;
    
    return r;
}


export { ddIntegrate }