quaeratin/src/double-expansion/e-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 { growExpansion } from "./grow-expansion.js";
import { fastExpansionSum } from "./fast-expansion-sum.js";


// We *have* to do the below❗ The assignee is a getter❗ The assigned is a pure function❗
const ts = twoSum;
const addDouble = growExpansion;
const add = fastExpansionSum;


/**
 * Returns the result of summing an array of floating point expansions.
 * 
 * * The result is exact in the form of a non-overlapping floating point 
 * expansion.
 * 
 * * see [Shewchuk](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf)
 * 
 * @param terms An array of numbers to be summed; A term is represented by a 
 * floating point expansion.
 */
// The terms parameter were chosen to always be expansions in order to keep the 
// function monomorhic, but whether it's really worth it I am not sure.
function eSum(terms: number[][]) {
    let total = [0];
    for (let i=0; i<terms.length; i++) {
        const term = terms[i];

        // add
        if (term.length === 1) {
            if (total.length === 1) {
                total = ts(total[0], term[0]);
            } else {
                total = addDouble(total, term[0]);
            }
        } else {
            if (total.length === 1) {
                total = addDouble(term, total[0]);
            } else {
                total = add(total, term);
            }
        }
    }

    return total;
}


export { eSum }