ES proposal: arbitrary precision integers

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The ECMAScript proposal “Integer: Arbitrary precision integers in JavaScript” by TC39 member Daniel Ehrenberg is currently at stage 2. This blog post gives an overview.

Update 2017-03-21: New section “FAQ”.

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

Operator overloading  

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.

Additionally, disallowing mixed operand types keeps operator overloading simple, which is helpful should overloading be extended further in the future.

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 !0ntrue
Boolean(int)true !intfalse
number Number(int) → OK +intTypeError
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 will probably be a library with functions and constants for Integers (think Math, but for Integers instead of Numbers).

Implementors of JS engines are confident that we will only need a single type for integers and that it will be fast enough for all use cases. But one could, in principle, introduce subtypes of Integer (Uint64, Uint8, ...).

Beyond Integers  

We’ll probably eventually see support for:

  • Custom value types (compared by value; think: primitive types user-defined via classes)
  • Operator overloading
  • 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.

All existing web APIs return and accept only Numbers and will only upgrade to Integer on a case by case basis

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.

Further reading  

Acknowledgement. Thanks to Daniel Ehrenberg for reviewing this blog post.


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