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

Installation

npm install double-double

❗Important❗

Use

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 will not be an issue if code is not bundled, e.g. when using Node.js.

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, <, >, ===, etc.
• 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

Research

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

1. Mioara Joldes, Jean-Michel Muller, Valentina Popescu, Tight and rigourous error bounds for basic building blocks of double-word arithmetic
2. T. J. Dekker, A Floating-Point Technique for Extending the Available Precision
3. Yozo Hida, Xiaoye S. Li, David H. Bailey, Library for Double-Double and Quad-Double Arithmetic
4. Nicholas J. Higham, Accuracy and Stability of Numerical Algorithms

Benchmark

Documentation

License

MIT