BigInt: arbitrary-precision integers in JavaScript

Published · tagged with ECMAScript ES2020

BigInts are a new numeric primitive in JavaScript that can represent integers with arbitrary precision. With BigInts, you can safely store and operate on large integers even beyond the safe integer limit for Numbers. This article walks through some use cases and explains the new functionality in Chrome 67 by comparing BigInts to Numbers in JavaScript.

Use cases

Arbitrary-precision integers unlock lots of new use cases for JavaScript.

BigInts make it possible to correctly perform integer arithmetic without overflowing. That by itself enables countless new possibilities. Mathematical operations on large numbers are commonly used in financial technology, for example.

Large integer IDs and high-accuracy timestamps cannot safely be represented as Numbers in JavaScript. This often leads to real-world bugs, and causes JavaScript developers to represent them as strings instead. With BigInt, this data can now be represented as numeric values.

BigInt could form the basis of an eventual BigDecimal implementation. This would be useful to represent sums of money with decimal precision, and to accurately operate on them (a.k.a. the 0.10 + 0.20 !== 0.30 problem).

Previously, JavaScript applications with any of these use cases had to resort to userland libraries that emulate BigInt-like functionality. When BigInt becomes widely available, such applications can drop these run-time dependencies in favor of native BigInts. This helps reduce load time, parse time, and compile time, and on top of all that offers significant run-time performance improvements.

The native BigInt implementation in Chrome performs better than popular userland libraries.

The status quo: Number

Numbers in JavaScript are represented as double-precision floats. This means they have limited precision. The Number.MAX_SAFE_INTEGER constant gives the greatest possible integer that can safely be incremented. Its value is 2**53-1.

const max = Number.MAX_SAFE_INTEGER;
// → 9_007_199_254_740_991

Note: For readability, I’m grouping the digits in this large number per thousand, using underscores as separators. The numeric literal separators proposal enables exactly that for common JavaScript numeric literals.

Incrementing it once gives the expected result:

max + 1;
// → 9_007_199_254_740_992 ✅

But if we increment it a second time, the result is no longer exactly representable as a JavaScript Number:

max + 2;
// → 9_007_199_254_740_992 ❌

Note how max + 1 produces the same result as max + 2. Whenever we get this particular value in JavaScript, there is no way to tell whether it’s accurate or not. Any calculation on integers outside the safe integer range (i.e. from Number.MIN_SAFE_INTEGER to Number.MAX_SAFE_INTEGER) potentially loses precision. For this reason, we can only rely on numeric integer values within the safe range.

The new hotness: BigInt

BigInts are a new numeric primitive in JavaScript that can represent integers with arbitrary precision. With BigInts, you can safely store and operate on large integers even beyond the safe integer limit for Numbers.

To create a BigInt, add the n suffix to any integer literal. For example, 123 becomes 123n. The global BigInt(number) function can be used to convert a Number into a BigInt. In other words, BigInt(123) === 123n. Let’s use these two techniques to solve the problem we were having earlier:

BigInt(Number.MAX_SAFE_INTEGER) + 2n;
// → 9_007_199_254_740_993n ✅

Here’s another example, where we’re multiplying two Numbers:

1234567890123456789 * 123;
// → 151851850485185200000 ❌

Looking at the least significant digits, 9 and 3, we know that the result of the multiplication should end in 7 (because 9 * 3 === 27). However, the result ends in a bunch of zeroes. That can’t be right! Let’s try again with BigInts instead:

1234567890123456789n * 123n;
// → 151851850485185185047n ✅

This time we get the correct result.

The safe integer limits for Numbers don’t apply to BigInts. Therefore, with BigInt we can perform correct integer arithmetic without having to worry about losing precision.

A new primitive

BigInts are a new primitive in the JavaScript language. As such, they get their own type that can be detected using the typeof operator:

typeof 123;
// → 'number'
typeof 123n;
// → 'bigint'

Because BigInts are a separate type, a BigInt is never strictly equal to a Number, e.g. 42n !== 42. To compare a BigInt to a Number, convert one of them into the other’s type before doing the comparison or use abstract equality (==):

42n === BigInt(42);
// → true
42n == 42;
// → true

When coerced into a boolean (which happens when using if, &&, ||, or Boolean(int), for example), BigInts follow the same logic as Numbers.

if (0n) {
console.log('if');
} else {
console.log('else');
}
// → logs 'else', because `0n` is falsy.

Operators

BigInts support the most common operators. Binary +, -, *, and ** all work as expected. / and % work, and round towards zero as needed. Bitwise operations |, &, <<, >>, and ^ perform bitwise arithmetic assuming a two’s complement representation for negative values, just like they do for Numbers.

(7 + 6 - 5) * 4 ** 3 / 2 % 3;
// → 1
(7n + 6n - 5n) * 4n ** 3n / 2n % 3n;
// → 1n

Unary - can be used to denote a negative BigInt value, e.g. -42n. Unary + is not supported because it would break asm.js code which expects +x to always produce either a Number or an exception.

One gotcha is that it’s not allowed to mix operations between BigInts and Numbers. This is a good thing, because any implicit coercion could lose information. Consider this example:

BigInt(Number.MAX_SAFE_INTEGER) + 2.5;
// → ?? 🤔

What should the result be? There is no good answer here. BigInts can’t represent fractions, and Numbers can’t represent BigInts beyond the safe integer limit. For that reason, mixing operations between BigInts and Numbers results in a TypeError exception.

The only exception to this rule are comparison operators such as === (as discussed earlier), <, and >= – because they return booleans, there is no risk of precision loss.

1 + 1n;
// → TypeError
123 < 124n;
// → true

Because BigInts and Numbers generally don’t mix, please avoid overloading or magically “upgrading” your existing code to use BigInts instead of Numbers. Decide which of these two domains to operate in, and then stick to it. For new APIs that operate on potentially large integers, BigInt is the best choice. Numbers still make sense for integer values that are known to be in the safe integer range.

Another thing to note is that the >>> operator, which performs an unsigned right shift, does not make sense for BigInts since they’re always signed. For this reason, >>> does not work for BigInts.

API

Several new BigInt-specific APIs are available.

The global BigInt constructor is similar to the Number constructor: it converts its argument into a BigInt (as mentioned earlier). If the conversion fails, it throws a SyntaxError or RangeError exception.

BigInt(123);
// → 123n
BigInt(1.5);
// → RangeError
BigInt('1.5');
// → SyntaxError

Two library functions enable wrapping BigInt values as either signed or unsigned integers, limited to a specific number of bits. BigInt.asIntN(width, value) wraps a BigInt value to a width-digit binary signed integer, and BigInt.asUintN(width, value) wraps a BigInt value to a width-digit binary unsigned integer. If you’re doing 64-bit arithmetic for example, you can use these APIs to stay within the appropriate range:

// Highest possible BigInt value that can be represented as a
// signed 64-bit integer.
const max = 2n ** (64n - 1n) - 1n;
BigInt.asIntN(64, max);
9223372036854775807n
BigInt.asIntN(64, max + 1n);
// → -9223372036854775808n
// ^ negative because of overflow

Note how overflow occurs as soon as we pass a BigInt value exceeding the 64-bit integer range (i.e. 63 bits for the absolute numeric value + 1 bit for the sign).

BigInts make it possible to accurately represent 64-bit signed and unsigned integers, which are commonly used in other programming languages. Two new typed array flavors, BigInt64Array and BigUint64Array, make it easier to efficiently represent and operate on lists of such values:

const view = new BigInt64Array(4);
// → [0n, 0n, 0n, 0n]
view.length;
// → 4
view[0];
// → 0n
view[0] = 42n;
view[0];
// → 42n

The BigInt64Array flavor ensures that its values remain within the signed 64-bit limit.

// Highest possible BigInt value that can be represented as a
// signed 64-bit integer.
const max = 2n ** (64n - 1n) - 1n;
view[0] = max;
view[0];
// → 9_223_372_036_854_775_807n
view[0] = max + 1n;
view[0];
// → -9_223_372_036_854_775_808n
// ^ negative because of overflow

The BigUint64Array flavor does the same using the unsigned 64-bit limit instead.

Polyfilling and transpiling BigInts

At the time of writing, BigInts are only supported in Chrome. Other browsers are actively working on implementing them. But what if you want to use BigInt functionality today without sacrificing browser compatibility? I’m glad you asked! The answer is… interesting, to say the least.

Unlike most other modern JavaScript features, BigInts cannot reasonably be transpiled down to ES5.

The BigInt proposal changes the behavior of operators (like +, >=, etc.) to work on BigInts. These changes are impossible to polyfill directly, and they are also making it infeasible (in most cases) to transpile BigInt code to fallback code using Babel or similar tools. The reason is that such a transpilation would have to replace every single operator in the program with a call to some function that performs type checks on its inputs, which would incur an unacceptable run-time performance penalty. In addition, it would greatly increase the file size of any transpiled bundle, negatively impacting download, parse, and compile times.

A more feasible and future-proof solution is to write your code using the JSBI library for now. JSBI is a JavaScript port of the BigInt implementation in V8 and Chrome — by design, it behaves exactly like the native BigInt functionality. The difference is that instead of relying on syntax, it exposes an API:

import JSBI from './jsbi.mjs';

const max = JSBI.BigInt(Number.MAX_SAFE_INTEGER);
const two = JSBI.BigInt('2');
const result = JSBI.add(max, two);
console.log(result.toString());
// → '9007199254740993'

Once BigInts are natively supported in all browsers you care about, you can use babel-plugin-transform-jsbi-to-bigint to transpile your code to native BigInt code and drop the JSBI dependency. For example, the above example transpiles to:

const max = BigInt(Number.MAX_SAFE_INTEGER);
const two = 2n;
const result = max + two;
console.log(result);
// → '9007199254740993'

Further reading

If you’re interested in how BigInts work behind the scenes (e.g. how they are represented in memory, and how operations on them are performed), read our V8 blog post with implementation details.

BigInt support