Pure double & double-double floating point arithmetic functions with strict error bounds

Documentation

Overview

Double-double precision floating point operators (similar to quad precision)
Each function documents a strict error bound (see research [1] below)
Optimized for speed (see benchmark below)
Operators include: +, -, *, /, √, abs, <, >, ===, min, max, etc.
Operators mixing double and double-doubles are also included, e.g. ddAddDouble (for adding a double to a double-double)
Error free double precision operators also included, e.g. twoProduct (for calculating the exact result of multiplying to doubles)
No classes ⇒ a double-double is simply a length 2 Number array, e.g.

import { twoSum } from 'double-double';
// Specified directly (low order double first)
const a = [-4.357806199228875e-10, 11_638_607.274152497];
// ...or more usually from an earlier calculation
const b = twoSum(213.456, 111.111);  // => [-1.4210854715202004e-14, 324.567] (completely error-free)

All functions are pure, e.g.

// using `a` and `b` as defined above (ddAddDd => double-double + double-double)
const c = ddAddDd(a,b);  // => [-2.42072459299969e-10, 11638931.841152497]

No dependencies

Installation

npm install double-double

This package is ESM only and can be used in Node.js (or in a browser when bundled using e.g. Webpack).

Additionally, self-contained ECMAScript Module (ESM) files index.module.js and index.module.min.js in the ./browser folder is provided.

Or, if you need a legacy browser script there is also index.js and index.min.js in the ./browser folder. Either script exposes a global variable called doubleDouble.

See full examples below.

Usage

Node.js

// @filename: `test.mjs` (or `test.js` if { "type": "module" } is specified in your package.json)
import { ddAddDd } from 'double-double';  // `ddAddDd` returns the sum of two double-doubles 

const dd1 = [-4.357806199228875e-10, 11638607.274152497];  // some double-double
const dd2 = [4.511949494578893e-11, -2797357.2918064594];  // another double-double

const r1 = ddAddDd(dd1,dd2);  // sum the two double-doubles
const r2 = [-3.906611249770986e-10, 8841249.982346037];  // the correct result

if (r1[0] === r2[0] && r1[1] === r2[1]) {
    console.log('success! 😁');  // we should get to here!
} else {
    console.log('failure! 😥');  // ...and not here
}

Browsers - ESM - (Chrome 61+, Safari 11+, Firefox 60+, Opera 48+, Edge 16+, Internet Explorer)

<!doctype html>

<html lang="en">
<head>
    <script type="module">
        import { ddAddDd } from "./node_modules/double-double/browser/index.module.min.js";

        const dd1 = [-4.357806199228875e-10, 11638607.274152497];  // some double-double
        const dd2 = [4.511949494578893e-11, -2797357.2918064594];  // another double-double

        const r1 = ddAddDd(dd1,dd2);  // sum the two double-doubles
        const r2 = [-3.906611249770986e-10, 8841249.982346037];  // the correct result

        if (r1[0] === r2[0] && r1[1] === r2[1]) {
            console.log('success! 😁');  // we should get to here!
        } else {
            console.log('failure! 😥');  // ...and not here
        }
    </script>
</head>

<body>Check the console.</body>

</html>

Browsers (older) - Legacy Scripts

<!doctype html>

<html lang="en">
<head>
    <script src="./browser/index.min.js"></script>
    <script>
        const { ddAddDd } = doubleDouble;

        const dd1 = [-4.357806199228875e-10, 11638607.274152497];  // some double-double
        const dd2 = [4.511949494578893e-11, -2797357.2918064594];  // another double-double

        const r1 = ddAddDd(dd1,dd2);  // sum the two double-doubles
        const r2 = [-3.906611249770986e-10, 8841249.982346037];  // the correct result

        if (r1[0] === r2[0] && r1[1] === r2[1]) {
            console.log('success! 😁');  // we should get to here!
        } else {
            console.log('failure! 😥');  // ...and not here
        }
    </script>
</head>

<body>Check the console.</body>

</html>

Bundlers (Webpack, Rollup, ...)

Webpack will be taken as an example here.

Since your webpack config file might still use CommonJS you must rename webpack.config.js to webpack.config.cjs.

If you are using TypeScript:

Since this is an ESM only library you must use resolve-typescript-plugin (at least until webpack catches up with ESM?) in your webpack.config.cjs file.

npm install --save-dev resolve-typescript-plugin

and follow the instructions given at resolve-typescript-plugin.

Additionally, follow this guide.

❗Important❗

When using bundlers:
import { operators } from 'double-double'
and then later in the code get the functions you need, e.g.:
const { ddAddDd as add, twoProduct, /* etc. */ } = operators;
as opposed to importing the operators directly.

This will increase performance roughly 5 times!

Why? Because Webpack (and Rollup) exports functions using getters that gets invoked on every function call adding a big overhead and slowing down each function. This is not an issue if the code is not bundled, e.g. when using Node.js.

Research

The following research / books / lectures have been used or are directly relevant to this library (especially the first two):

Benchmark

benchmark

Similar libraries

double.js

License

MIT