# ES proposal: arbitrary precision integers

[2017-03-19] dev, javascript, esnext, es proposal, numbers

Update 2017-03-21: New section “FAQ”.

The ECMAScript proposal “Integer: Arbitrary precision integers in JavaScript” by TC39 member Daniel Ehrenberg is not currently at any stage. This blog post gives an overview.

## Rationale  #

Given that the ECMAScript standard only has a single type for numbers (64-bit floating point numbers) it’s amazing how far JavaScript engines were able to go in their support for integers: fractionless numbers that are small enough are stored as integers (usually within 32 bits, possibly minus bookkeeping information).

However, JavaScript can only safely represent integers with up to 53 bits plus a sign. Sometimes, you need more bits. For example:

• Twitter uses 64-bit integers as IDs for tweets (source). In JavaScript, these IDs have to be stored in strings.
• Financial technology uses so-called big ints (integers with arbitrary precision) to represent sums of money.

## Core parts of the proposal  #

The proposal is about adding a new primitive type for big ints to JavaScript. Given that they will be the only type for integers, the type will simply be called Integer.

Core parts of the proposal are:

• Literals for integers: Each literal is a series of digits, suffixed with an `n`. For example: `123n`
• `typeof` returns `'integer'` for Integer values:
``````> typeof 123n
'integer'
``````
• Operators such as `+` and `*` are overloaded and work with Integers. The number of bits used to store values is increased as necessary, automatically.
• There is a wrapper constructor `Integer` for Integers, which is similar to `Number` for Numbers and other wrapper constructors.

Next, we will look at a first example and then will examine all aspects of the proposal in detail.

### A first example  #

This is what using Integers looks like (example taken from the proposal’s readme):

``````/**
* Takes an Integer as an argument and returns an Integer
*/
function nthPrime(nth) {
function isPrime(p) {
for (let i = 2n; i < p; i++) {
if (p % i === 0n) return false;
}
return true;
}
for (let i = 2n; ; i++) {
if (isPrime(i)) {
if (--nth === 0n) return i;
}
}
}
``````

## Integer literals  #

Like Number literals, Integer literals support several bases:

• Decimal: `123n`
• Hexadecimal: `0xFFn`
• Binary: `0b1101n`
• Octal: `0o777n`

Negative integers are produced by prefix the unary minus operator: `-0123n`

The general rule for binary operators is:

You can’t mix Numbers and Integers: If one operand is an Integer, the other one can’t be a Number.

If you do mix them, a `TypeError` is thrown:

``````> 2n + 1
TypeError
``````

The reason for this rule is that there is no general way of coercing a Number and an Integer to a common type: Numbers can’t represent Integers beyond 53 bits, Integers can’t represent fractions. Therefore, the exceptions warn you about typos that could change the results of computations in unexpected ways.

To see why, let’s look at an example: 9007199254740991 is the highest integer that Numbers can represent safely. You can see that if you try adding 1 to the “unsafe” 9007199254740992

``````> 9007199254740992 + 1
9007199254740992
``````

If `9007199254740992n + 1` were interpreted as a Number (due to coercion), you would get wrong results.

The following sections explain what operators are available for Integers.

### Arithmetic and ordering  #

• Binary `+`, binary `-`, `*`, `**` work as expected.

• `/`, `%` round towards zero (think `Math.trunc()`).

``````> 1n / 2n
0n
``````
• Ordering operators `<`, `>`, `>=`, `<=` work as expected.

• Unary `-` works as expected. Unary `+` is not supported for Integers, because much code (incl. asm.js) relies on it coercing its operand to Number.

### Bit operators  #

For bit operators, A negative sign is interpreted as an infinite two’s complement. E.g.:

• `-1` is `...111` (ones extend infinitely to the left)
• `-2` is `...110` (ones extend infinitely to the left)

That is, a negative sign is more of an external flag and not represented as an actual bit.

The following bit operators exist:

• Bitwise operators `|`, `&`, `^` for Integer work analogously to their Number versions.

• Signed shift operators `<<`, `>>` for Integers work analogously to their Number versions. Note that here, too, both operands need to be Integers.

Bit operators for Numbers limit their operands to 32 bits. All operators (except for unsigned right shift `>>>`) interpret the highest (31st) bit as a sign:

``````> Math.pow(2,30) | 0
1073741824
> Math.pow(2,31) | 0
-2147483648
> (Math.pow(2,32)-1) | 0
-1
``````

You can shift a positive Number left so that the highest (31st) bit is set and it becomes negative:

``````> Math.pow(2,30) << 1
-2147483648
``````

With Integers, that can never happen, because they are not limited to specific number of bits and there is therefore no sign bit.

There is no unsigned right shift operator `>>>` for Integers, because its semantics are: “shift in” a zero, replace the highest bit with a zero. First, there is no highest bit. Second, with the infinite sequence of ones prefixing negative values, you’d have to insert a zero somewhere, which makes no sense. Thus, preserving the sign is the natural (and only) thing to do for Integers and there is no `>>>` operator.

One last illustration of how negative bit operands work: For both Numbers and Integers, however often you signed-shift `-1` to the right, the result is always `-1`:

``````> -1 >> 20
-1
> -1n >> 20n
-1n
``````

### Equality  #

Lenient equality (`==`) and inequality (`!=`) are coercing operators, which makes them difficult to adapt to Integers. At the moment, comparing Numbers and Integers throws an exception:

``````> 0n == 0
TypeError
``````

Alas, lenient equality coerces booleans to Numbers, meaning that exceptions are thrown, too:

``````> 0n == false
TypeError
``````

Strict equality (`===`) and inequality (`!==`) only consider values to be equal if they have the same type. Therefore, adapting them to Integers is simple:

``````> 0n === 0
false
``````

## The wrapper constructor `Integer`#

Similar to Numbers, Integers have the associated wrapper constructor `Integer()`. It works as follows:

• `Integer(x)`: convert arbitrary values `x` to Integer. This works similarly to `Number()`, but:

• A `TypeError` is thrown if `x` is either `null` or `undefined`.
• Instead of returning `NaN` for Strings that don’t represent Integers, a `SyntaxError` is thrown.
• `new Integer()`: throws a `TypeError`.

This is what using `Integer()` looks like:

``````> Integer(undefined)
TypeError
> Integer(null)
TypeError

> Integer(false)
0n
> Integer(true)
1n

> Integer(123)
123n

> Integer('123')
123n
> Integer('123n')
SyntaxError
> Integer('abc')
SyntaxError
``````

### `Integer` methods  #

`Integer.prototype` holds the methods “inherited” by primitive Integers:

• `Integer.prototype.toLocaleString(reserved1?, reserved2?)`
• `Integer.prototype.toString(radix?)`
• `Integer.prototype.valueOf()`

### Utility functions  #

• `Integer.asUintN(width, theInt)`
Casts `theInt` to `width` bits (unsigned). This influences how the value is represented internally.

• `Integer.asIntN(width, theInt)`
Casts `theInt` to `width` bits (signed).

• `Integer.parseInt(string, radix?)`
Works similarly to `Number.parseInt()`, but throws a `SyntaxError` instead of returning `NaN`:

``````> Integer.parseInt('9007199254740993', 10)
9007199254740993n
> Integer.parseInt('abc', 10)
SyntaxError
``````

For comparison, this is what `Number.parseInt()` does:

``````> Number.parseInt('9007199254740993', 10)
9007199254740992
> Number.parseInt('abc', 10)
NaN
``````

### Casting and 64-bit integers  #

Casting allows you to create integer values with a specific number of bits. If you want to restrict yourself to just 64-bit integers, you have to always cast:

``````const int64a = Integer.asUintN(64, 12345n);
const int64b = Integer.asUintN(64, 67890n);
const result = Integer.asUintN(64, int64a * int64b);
``````

## Coercing Integers to other primitive types  #

This table show what happens if you convert Integers to other primitive types:

Convert to Explicit conversion Coercion (implicit conversion)
boolean `Boolean(0n)``false` `!0n``true`
`Boolean(int)``true` `!int``false`
number `Number(int)` → OK `+int``TypeError`
string `String(int)` → OK `''+int` → OK

Still under discussion: Should the result of `String()` applied to an Integer should have the suffix `'n'`? At the moment, it works like this:

``````> String(123n)
'123'
``````

## TypedArrays and DataView operations for 64-bit values  #

Integers make it possible to add 64 bit support to Typed Arrays and DataViews:

• New Typed Array constructors:
• `Uint64Array`
• `Int64Array`
• New DataView methods:
• `DataView.prototype.getInt64()`
• `DataView.prototype.getUint64()`

## Integers and JSON  #

Integers in JSON data will probably be handled similarly to other unsupported data such as symbols:

``````> JSON.stringify(123n)
undefined
> JSON.stringify([123n])
'[null]'
``````

## Future  #

There’ll probably be a library with functions and constants for Integers (think `Math`, but for Integers instead of Numbers).

It’s likely that a single type for Integers will be enough. If not, subtypes could be introduced (`Uint64`, `Uint8`, etc.). Implementers currently expect that performance will be good for Integers, even without introducing subtypes.

### Beyond Integers  #

We’ll probably eventually see support for:

• Custom value types (compared by value; think: primitive types user-defined via classes)
• Custom number literal syntax

The following features may be added to JavaScript and could be based on these mechanisms.

• Decimal data type: for base-10 arithmetic, which is useful for representing sums of money and results of scientific measurements.
• Rational data type: representing fractions (1/3 etc.) without rounding.
• Complex numbers
• Vectors and matrices
• And more

## FAQ: Integers  #

### How do I decide when to use Numbers and when to use Integers?  #

My recommendations:

• Use Numbers for up to 53 bits and for Array indices. Rationale: They already appear everywhere and are handled efficiently by most engines (especially if they fit into 31 bits). Appearances include:
• `Array.prototype.forEach()`
• `Array.prototype.entries()`
• Use Integers for large numeric values: If your fraction-less values don’t fit into 53 bits, you have the option to move to Integers.

### Why not just increase the precision of Numbers in the same manner as is done for Integers?  #

That would probably break existing code that may depend, possibly in subtle ways on Numbers being doubles (64-bit floating point numbers).

## Conclusions  #

It is great to see support for integers beyond 53 bits being planned for JavaScript. Using a single type for integers is an interesting experiment. It’d be great if it worked out. Once again, JavaScript engines would do “the right thing” for programmers. Just like already do for smaller integers, Arrays, constructors (hidden classes...), etc.

With Integers, we get a glimpse at what JavaScript would be like if it had had exceptions from the start (they were introduced in ES3): using the wrong operands for some of the operators throws exceptions now.

Feedback to the proposal is best given by filing an issue on GitHub.