double-double/src/double-mixed-double-double/dd-add-double.ts

Pure double-double precision functions *with strict error bounds*.

/**
 * Returns the result of adding a double to a double-double precision floating 
 * point number.
 * 
 * * relative error bound: 2u^2, i.e. fl(a+b) = (a+b)(1+ϵ), 
 * where ϵ <= 2u^2, u = 0.5 * Number.EPSILON
 * * the error bound is sharp
 * 
 * ALGORITHM 4 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
 * @param x a double-double precision floating point number
 * @param y a double precision floating point number
 */
function ddAddDouble(x: number[], y: number): number[] {
    const xl = x[0];
    const xh = x[1];

    //const [sl,sh] = twoSum(xh, y);
    const sh = xh + y; const c = sh - xh; const sl = (xh - (sh - c)) + (y - c);
    const v = xl + sl;
    //const [zl,zh] = fastTwoSum(sh,v);
    const zh = sh + v; const zl = v - (zh - sh); 
    
    return [zl, zh];
}


export { ddAddDouble }