quaeratin/src/double-expansion/expansion-sum.ts

An extended precision floating point library (as per Shewchuk) - precision only limited by overflow / underflow

import { twoSum } from "../basic/two-sum.js";
import { eCompress } from "./e-compress.js";


// We *have* to do the below❗ The assignee is a getter❗ The assigned is a pure function❗
const ts = twoSum;
const compress = eCompress;


/**
 * Returns the result of adding two expansions. 
 * * use `fastExpansionSum` instead, `fastExpansionSum` is nearly always 
 * preferred above this function.
 * 
 * Theorem 12: Let e = sum_(i=1)^m(e_i) and f = sum_(i=1)^n(f_i) be
 * nonoverlapping expansions of m and n-bit components respectively, where
 * p >= 3. Suppose that the components of both e and f are sorted in order of
 * increasing magnitude, except that any of the e_i or f_i may be zero. Then the
 * following algorithm will produce a nonoverlapping expansion h such that
 * h = sum_(i=1)^(m+n)(h_i) = e + f, where the components of h are in order of
 * increasing magnitude, except that any of the h_i may be zero. Furthermore, if
 * e and f are nonadjacent and round-to-even tiebreaking is used, then h is 
 * nonadjacent.
 * 
 * See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
 */
function expansionSum(e: number[], f: number[]) {
    for (let i=0; i<f.length; i++) {
        // the below is growExpansion unrolled
        const m = e.length;

        let q = f[i];
        //let h: number[] = new Array(m+1);
        const h: number[] = [];
        for (let i=0; i<m; i++) {
            // Note the use of twoSum and not fastTwoSum.
            //[h[i], q] = ts(q, e[i]);
            // inlined (above line)
            const ei = e[i];
            const x = q + ei;
            const bv = x - q;
            //h[i] = (q - (x - bv)) + (ei - bv);
            const hh = (q - (x - bv)) + (ei - bv);
            if (hh !== 0) { h.push(hh); }
            q = x;
        }
        //h[m] = q;
        h.push(q);

        e = h;
    }

    return compress(e);
    //return e;
}


export { expansionSum }