BigInt: arbitrary-precision integers in JavaScript
BigInt
s are a new numeric primitive in JavaScript that can represent integers with arbitrary
precision. With BigInt
s, you can safely store and operate on large integers even beyond the safe
integer limit for Number
s. This article walks through some use cases and explains the new
functionality in Chrome 67 by comparing BigInt
s to Number
s in JavaScript.
Use cases
Arbitrary-precision integers unlock lots of new use cases for JavaScript.
BigInt
s 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 Number
s 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 BigInt
s. This helps reduce load time,
parse time, and compile time, and on top of all that offers significant run-time performance
improvements.
“Polyfilling” BigInt
s requires a run-time library that implements similar functionality, as well
as a transpilation step to turn the new syntax into a call to the library’s API. Babel currently
supports parsing BigInt
literals through a plugin, but doesn’t transpile them. As such, we don’t
expect BigInt
s to be used in production sites that require broad cross-browser compatibility just
yet. It’s still early days, but now that the functionality is starting to ship in browsers, you can
start to experiment with BigInt
s. Expect wider BigInt
support soon.
The status quo: Number
Number
s 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
BigInt
s are a new numeric primitive in JavaScript that can represent integers with arbitrary
precision. With BigInt
s, you can
safely store and operate on large integers even beyond the safe integer limit for Number
s.
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 Number
s:
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 BigInt
s instead:
1234567890123456789n * 123n;
// → 151851850485185185047n ✅
This time we get the correct result.
The safe integer limits for Number
s don’t apply to BigInt
s. Therefore, with BigInt
we can
perform correct integer arithmetic without having to worry about losing precision.
A new primitive
BigInt
s 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 BigInt
s 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), BigInt
s follow the same logic as Number
s.
if (0n) {
console.log('if');
} else {
console.log('else');
}
// → logs 'else', because `0n` is falsy.
Operators
BigInt
s 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 Number
s.
(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 BigInt
s and Number
s. 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. BigInt
s can’t represent fractions, and
Number
s can’t represent BigInt
s beyond the safe integer limit. For that reason, mixing
operations between BigInt
s and Number
s 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
Note: Because BigInt
s and Number
s generally don’t mix, please avoid overloading or magically
"upgrading" your existing code to use BigInt
s instead of Number
s. 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. Number
s 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 BigInt
s since they’re always
signed. For this reason, >>>
does not work for BigInt
s.
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).
BigInt
s 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.
Have fun with BigInt
s!
Note: Thanks to Daniel Ehrenberg, the BigInt
proposal champion,
for reviewing this article.