double-double/src/double-mixed-double-double/double-sqrt.ts

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

/** @internal */
const f = 134217729;  // 2**27 + 1;


// Taken from https://github.com/munrocket/double.js/blob/master/src/double.ts
// Unfortunately no error bound given
/**
 * Returns the square root of a double as a double-double.
 * * no error bound is returned
 */
// TODO - calculate an error bound and add to function description
function doubleSqrt(x: number): number[] {
    if (x === 0) { return [0,0]; }

    const s = Math.sqrt(x);

    //const [tl,th] = twoSquare(s);
    const th = s*s;
    const c = f * s; const ah = c - (c - s); const al = s - ah;
    const tl = (al*al) - ((th - (ah*ah)) - 2*(ah*al));

    const e = (x - th - tl) * 0.5 / s;
    x = s + e;
    const xl = e - (x - s);

    return [xl,x];
}


export { doubleSqrt }