double-double/src/double-double/multi/dd-sum.ts

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

import { ddAddDd } from "../binary/dd-add-dd.js";


/**
 * Returns the result of summing an array of double-double-precision floating 
 * point numbers naively (i.e. not using pairwise addition to reduce error a bit).
 * 
 * * an error bound is given by: (n-1)(1+ϵ), 
 * where ϵ <= 3u^2 + 13u^3, u = 0.5 * Number.EPSILON
 */
function ddSum(qs: number[][]) {
    let q = qs[0];
    for (let i=1; i<qs.length; i++) {
        q = ddAddDd(q, qs[i]);
    }

    return q;
}


export { ddSum }