xfloat - Arbitrary-precision binary floating point for JavaScript

xfloat is a small (one ES module with ~600 lines of code, ~12KiB minified), dependency-free JavaScript library for representing and computing with arbitrary-precision binary floating-point numbers. It is implemented in pure JavaScript and relies on native bigint for base arithmetic, without the use of limb arrays or external number theory libraries.

Overview

xfloat provides a type BigFloat. A BigFloat represents numbers in the form n × 2^e, where:

• n is a signed bigint (the significand),
• e is a regular JavaScript number (the exponent).

This structure allows exact representation of any finite binary-rational number and supports a wide range of operations: arithmetic, comparison, rounding, transcendental functions (like log, exp, sqrt), and precision-controlled division.

The library closely follows IEEE-754 semantics, including handling of NaN, Infinity, and precision loss in repeating fractions. However, it avoids some of IEEE-754's complexities, such as subnormals and negative zero.

Features

• Pure JavaScript implementation (no WebAssembly, no native code)
• Zero external dependencies
• Uses bigint directly; no "limb" arrays or bignum engines
• Exact representation of binary-rational numbers
• Precise, user-controllable rounding and precision
• IEEE-754-like behavior for infinities, NaN, and division edge cases
• Support for common transcendental functions (log, exp, sqrt, pow)
• Includes a set of physical, mathematical, and statistical constants

Use Cases

xfloat is suitable for applications requiring rational numbers with precision beyond Number.MAX_SAFE_INTEGER or smaller than the machine epsilon.

Anti-cases

xfloat is not suitable for financial calculations requiring decimal precision. xfloat is still fundamentally a binary representation of numbers. Support for decimally-accurate representations may be added in the future in a separate module, but xfloat does not provide this.

Usage

Install xfloat from NPM:

$ npm i --save xfloat

Example

import BigFloat from 'xfloat';

const a = BigFloat(1.5);               // Convert a JS number to a BigFloat.
const b = BigFloat.fromParts(6n, -2);  // Construct a BigFloat from raw `n` and `e` values. This is also `1.5` (not normalized).

const sum = a.add(b);                  // 3F
const sqrt = sum.sqrt(128);            // 1.7320508075688772F with 128 bits of numeric precision.

console.log(sqrt.toNumber());          // 1.7320508075688772
console.log(Math.sqrt(3));             // 1.7320508075688772

Design

Internally, a BigFloat is defined by:

• n: bigint — the significand
• e: number — the binary exponent

You can think of a BigFloat as being an integer n with the radix point moved to the right by e bits. So a significand n value of 3 with an exponent e of 4 is equal to 3 × 2^4, or 48. A significand value of 3 with an exponent of -2 is 3 × 2^-2, or 3/4 = 0.75.

Two BigFloat values with different values of n and e can be equal. For example, given a BigFloat with n = 1 and e = 0 (this is the value 1), and another BigFloat with n = 2 and e = -1 (2 × 2^-1 = 1). However, only one BigFloat of any particular numeric value is normalized. Normalization ensures that n is odd, meaning that the representation is minimal (no trailing zeros in binary). Normalization is optional and can be applied via .normalize(), but is also applied by most operations and numbers are normalized as-needed within operations.

Comparison to Other Libraries

• xfloat is binary-based, not decimal-based.
• No limb arrays: Computations operate directly on bigint, offloading most computation to the JavaScript engine itself rather than requiring them to be performed in software.
• Fully immutable API: All operations return new BigFloat instances.

Constants

A large collection of scientific and mathematical constants is included, such as:

• BigFloat.constants.PI: The ratio of a circle's circumference to its diameter.
• BigFloat.constants.EULER: Euler's constant (e).
• BigFloat.constants.SPEED_OF_LIGHT: The speed of light in a vacuum.
• BigFloat.constants.GOLDEN_RATIO: The golden ratio (φ).
• and many, many others

These are accurate to a reasonable default precision and can be generated with arbitrary precision using BigFloat.constants(precision).

Caveats

• Binary only: xfloat cannot exactly represent decimal fractions like 0.1, just as native JavaScript number cannot. This is not going to solve your gripes about how "0.2 + 0.1 isn't exactly 0.3." It's going to be really really close to 0.3, but this is commonly misunderstood to be a problem with IEEE-754 binary floating-point numbers (or worse, of JavaScript numbers specifically), it is a limitation of any finite binary numeric representation.
• Slow with very large precisions: Division and transcendental functions use iterative algorithms on bigint and may become slow with high precision values (hundreds or thousands of bits).
• No decimal formatting: Currently, there is no .toString() with decimal formatting or support for custom output bases.
• Not IEEE-754 compliant: While behavior is similar, this is not a drop-in IEEE-754 replacement (e.g., no negative zero, no subnormals).
• No trigonometry: These are coming, possibly in a separate module to keep the implementation tiny for users who don't need trig.

Implementation Status

This library is tested with a fuzzing strategy:

100000 Fuzzing iterations.
Passed: 583756
Failed: 27
Crashed: 0

⚠️ WARNING: The implementation is incomplete and is of alpha quality:

• Fuzzing is rather incomplete. The 0.0004% of failing fuzzy tests are due to BigFloat.exp collapsing to zero when the argument is a negative number with high magnitude (<= -50 or so) because the value of arg.log2() is very small and our definition of Euler's constant is too low precision.
• Constants described in the TypeScript API surface are mostly unimplemented, and arbitrary-precision constants are fully unimplemented.
• More thorough testing around edge-cases, rounding modes, etc. is coming.
• Stack traces are a little screwed up right now on account of minification.

License

MIT License