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Arbitrary precision integers in JavaScript

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# BigInt: Arbitrary precision integers in JavaScript

Daniel Ehrenberg, Igalia. Stage 4

This proposal is complete and already merged into ECMA262 specification. See the specification text here.

Thanks for help and feedback on this effort from Brendan Eich, Waldemar Horwat, Jaro Sevcik, Benedikt Meurer, Michael Saboff, Adam Klein, Sarah Groff-Palermo and others.

## What Is It?

BigInt is a new primitive that provides a way to represent whole numbers larger than 253, which is the largest number Javascript can reliably represent with the Number primitive.

const x = Number.MAX_SAFE_INTEGER;
// ↪ 9007199254740991, this is 1 less than 2^53

const y = x + 1;
// ↪ 9007199254740992, ok, checks out

const z = x + 2
// ↪ 9007199254740992, wait, that’s the same as above!

Learn more about how numbers are represented in Javascript in the slides from Daniel's talk at JSConfEU.

## How Does It Work?

The following sections show BigInt in action. A number have been influenced by or taken outright from Mathias Bynens's BigInt v8 update, which includes more details than this page.

### Syntax

A BigInt is created by appending n to the end of the integer or by calling the constructor.

const theBiggestInt = 9007199254740991n;

const alsoHuge = BigInt(9007199254740991);
// ↪ 9007199254740991n

const hugeButString = BigInt('9007199254740991');
// ↪ 9007199254740991n

### Example: Calculating Primes

function isPrime(p) {
for (let i = 2n; i * i <= p; i++) {
if (p % i === 0n) return false;
}
return true;
}

// Takes a BigInt as an argument and returns a BigInt
function nthPrime(nth) {
let maybePrime = 2n;
let prime = 0n;

while (nth >= 0n) {
if (isPrime(maybePrime)) {
nth -= 1n;
prime = maybePrime;
}
maybePrime += 1n;
}

return prime;
}

### Operators

You can use +, *, -, ** and % with BigInts, just like with Numbers.

const previousMaxSafe = BigInt(Number.MAX_SAFE_INTEGER);
// ↪ 9007199254740991

const maxPlusOne = previousMaxSafe + 1n;
// ↪ 9007199254740992n

const theFuture = previousMaxSafe + 2n;
// ↪ 9007199254740993n, this works now!

const multi = previousMaxSafe * 2n;
// ↪ 18014398509481982n

const subtr = multi  10n;
// ↪ 18014398509481972n

const mod = multi % 10n;
// ↪ 2n

const bigN = 2n ** 54n;
// ↪ 18014398509481984n

bigN * -1n
// ↪ –18014398509481984n

The / operator also work as expected with whole numbers. However, since these are BigInts and not BigDecimals, this operation will round towards 0, which is to say, it will not return any fractional digits.

const expected = 4n / 2n;
// ↪ 2n

const rounded = 5n / 2n;
// ↪ 2n, not 2.5n

See the advanced documentation for use with bitwise operators.

### Comparisons

A BigInt is not strictly equal to a Number, but it is loosely so.

0n === 0
// ↪ false

0n == 0
// ↪ true

Numbers and BigInts may be compared as usual.

1n < 2
// ↪ true

2n > 1
// ↪ true

2 > 2
// ↪ false

2n > 2
// ↪ false

2n >= 2
// ↪ true

They may be mixed in arrays and sorted.

const mixed = [4n, 6, -12n, 10, 4, 0, 0n];
// ↪  [4n, 6, -12n, 10, 4, 0, 0n]

mixed.sort();
// ↪ [-12n, 0, 0n, 10, 4n, 4, 6]

### Conditionals

A BigInt behaves like a Number in cases where it is converted to a Boolean: if, ||, &&, Boolean, !.

if (0n) {
console.log('Hello from the if!');
} else {
console.log('Hello from the else!');
}

// ↪ "Hello from the else!"

0n || 12n
// ↪ 12n

0n && 12n
// ↪ 0n

Boolean(0n)
// ↪ false

Boolean(12n)
// ↪ true

!12n
// ↪ false

!0n
// ↪ true

### Other API Notes

BigInts may also be used in BigInt64Array and BigUint64Array typed arrays for 64-bit integers.

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

// 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

For more about BigInt library functions, see the advanced section.

## Gotchas & Exceptions

### Interoperation with Number and String

The biggest surprise may be that BigInts cannot be operated on interchangeably with Numbers. Instead a TypeError will be thrown. (Read the design philosophy for more about why this decision was made.)

1n + 2
// ↪ TypeError: Cannot mix BigInt and other types, use explicit conversions

1n * 2
// ↪ TypeError: Cannot mix BigInt and other types, use explicit conversions

BigInts also cannot be converted to Numbers using the unary +. Number must be used.

+1n
// ↪ TypeError: Cannot convert a BigInt value to a number

Number(1n)
// ↪ 1

The BigInt can however be concatenated with a String.

1n + '2'
// ↪ "12"

'2' + 1n
// ↪ "21"

For this reason, it is recommended to continue using Number for code which will only encounter values under 253.

Reserve BigInt for cases where large values are expected. Otherwise, by converting back and forth, you may lose the very precision you are hoping to preserve.

const largeFriend = 900719925474099267n;
const alsoLarge = largeFriend + 2n;

const sendMeTheBiggest = (n, m) => Math.max(Number(n), Number(m));

sendMeTheBiggest(largeFriend, alsoLarge)
// ↪900719925474099300  // This is neither argument!

Reserve Number values for cases when they are integers up to 253, for other cases, using a string (or a BigInt literal) would be advisable to not lose precision.

const badPrecision = BigInt(9007199254740993);
// ↪9007199254740992n

const goodPrecision = BigInt('9007199254740993');
// ↪9007199254740993n

const alsoGoodPrecision = 9007199254740993n;
// ↪9007199254740993n

### Rounding

As noted above, the BigInt only represents whole numbers. Number only reliably represents integers up to 253. That means both dividing and converting to a Number can lead to rounding.

5n / 2n
// ↪ 2n

Number(151851850485185185047n)
// ↪ 151851850485185200000

### Cryptography

The operations supported on BigInts are not constant time. BigInt is therefore unsuitable for use in cryptography.

Many platforms provide native support for cryptography, such as webcrypto or node crypto.

### Other Exceptions

Attempting to convert a fractional value to a BigInt throws an exception both when the value is represented as an Number and a String.

BigInt(1.5)
// ↪ RangeError: The number 1.5 is not a safe integer and thus cannot be converted to a BigInt

BigInt('1.5')
// ↪ SyntaxError: Cannot convert 1.5 to a BigInt

Operations in the Math library will throw an error when used with BigInts, as will |.

Math.round(1n)
// ↪ TypeError: Cannot convert a BigInt value to a number

Math.max(1n, 10n)
// ↪ TypeError: Cannot convert a BigInt value to a number

1n|0
// ↪ TypeError: Cannot mix BigInt and other types, use explicit conversions

parseInt and parseFloat will however convert a BigInt to a Number and lose precision in the process. (This is because these functions discard trailing non-numeric values — including n.

parseFloat(1234n)
// ↪1234

parseInt(10n)
// ↪10

// precision lost!
parseInt(900719925474099267n)
// ↪900719925474099300

Finally, BigInts cannot be serialized to JSON. There are, however, libraries — for instance, granola — that can handle this for you.

const bigObj = {a: BigInt(10n)};
JSON.stringify(bigObj)
// ↪TypeError: Do not know how to serialize a BigInt

### Coercion

Because coercing between Number and BigInt can lead to loss of precision, it is recommended to only use BigInt when values greater than 253 are reasonably expected and not to coerce between the two types.

## About the Proposal

### Motivation: Why Do We Need Such Big Numbers?

There are a number of cases in JavaScript coding where integers larger than 253 come up — both instances where signed or unsigned 64-bit integers are needed and times where we may want integers even larger than 64-bits.

#### 64-bit Use Cases

Often, other systems with which Javascript interacts provides data as 64-bit integers, which lose precision when coerced to Javascript Numbers.

These might come when reading certain machine registers or wire protocols or using protobufs or JSON documents that have GUIDs generated by 64-bit systems in them — including things like credit card or account numbers — which currently must remain strings in Javascript. (Note, however, BigInts cannot be serialized to JSON directly. But you can use libraries like granola to serialize and deserialize BigInt and other JS datatypes to JSON.)

In node, fs.stat may give some data as 64-bit integers, which has caused issues already:

fs.lstatSync('one.gif').ino
// ↪ 9851624185071828

fs.lstatSync('two.gif').ino
// ↪ 9851624185071828, duplicate, but different file!

Finally, 64-bit integers enable higher resolution — nanosecond! — timestamps. These will be put to use in the temporal proposal, currently in Stage 1.

#### Bigger Than 64-bit Use Cases

Integers larger than 64-bit values are most likely to arise when doing mathematical calculations with larger integers, such as solving Project Euler problems or exact geometric calculations. Adding BigInt makes it possible to meet a reasonable user expectation of a high-level language that integer arithmetic will be "correct" and not suddenly overflow.

If this seems far-fetched, consider the case of the Pentium FDIV bug. In 1994, a bug in Pentium chips made floating point values rarely —but possibly — imprecise. It was discovered by a mathematics professor who was relying on that precision.

### Design Goals, Or Why Is This Like This?

These principles guided the decisions made with this proposal. Check out ADVANCED.md for more in-depth discussion of each.

#### Find a balance between maintaining user intuition and preserving precision

In general, this proposal has aimed to work in a manner complementary to user intuition about how Javascript works. At the same time, the goal for this proposal is to add further affordances for precision to the language. Sometimes these can conflict.

When a messy situation comes up, this proposal errs on the side of throwing an exception rather than rely on type coercion and risk giving an imprecise answer. This is what's behind throwing a TypeError on adding a BigInt and a Number and other exceptions detailed above: If we don't have a good answer, better to not give one.

For more discussion of these choices, see Axel Rauschmeyer's proposal and further discussion of its effects on Numbers. We ended up concluding that it would be impractical to provide transparent interoperability between Number and BigInt.

#### Don't break math

The semantics of all operators should ideally be based on some mathematical first principles, to match developer expectations. The division and modulo operators are based on conventions from other programming languages for integers.

#### Don't break JavaScript ergonomics

This proposal comes with built-in operator overloading in order to not make BigInts too ugly to be usable. One particular hazard, if BigInts were to be operated on with static methods, is that users may convert the BigInt into a Number in order to use the + operator on it--this would work most of the time, just not with big enough values, so it might pass tests. By including operator overloading, it would be even shorter code to add the BigInts properly than to convert them to Numbers, which minimizes the chance of this bug.

#### Don't break the web

This proposal doesn't change anything about the way Numbers work. The name BigInt was chosen in part to avoid compatibility risks carried by the more general Integer name (and in part to make it clear that they are useful for the "big" cases).

#### Don't break good performance

Design work here has been done in conjunction with prototyping in to ensure that the proposal is efficiently implementable.

#### Don't break potential future value types extensions

When adding new primitives to the language, it is important to avoid giving them superpowers that would be very difficult to generalize. This is another good reason for BigInt to avoid mixed operands.

Mixed comparisons are a one-off exception to this principle, however, taken in support of the intuition design principle.

#### Don't break a consistent model of JavaScript

This proposal adds a new primitive type with wrappers, similar to Symbol. As part of integrating BigInts into the JavaScript specification, a high amount of rigor will be required to differentiate three types floating around in the specification: Mathematical values, BigInts and Numbers.

### State of the Proposal

This proposal is currently in Stage 4.

BigInt has been shipped in Chrome, Node, Firefox, and is underway in Safari.

• V8 by Georg Neis and Jakob Kummerow.
• JSC by Caio Lima and Robin Morisset.
• SpiderMonkey by Robin Templeton and Andy Wingo.

Related specification proposals:

Arbitrary precision integers in JavaScript

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