## DEV Community # Working with extremely large numbers in JavaScript ## The problem

JavaScript has a limitation it only allows precision of about 16 digits for the number format.

Minimum & maximum value that a number can go to without losing precision is `-2^53<= x <=2^53`, where 2^53 = 9007199254740992.

If we go beyond this limit then we'll lose precision.

``````console.log(1000000000000011112); // => 1000000000000011100
``````

This impreciseness affect arithmetic operations as well.

``````console.log(10000000000000001+1) // => 10000000000000000
console.log(10000000000000002-1) // => 10000000000000000
console.log(10000000000000002*3) // => 30000000000000010
console.log(10000000000000001==10000000000000000) // => true
``````

It is difficult to get answers from arithmetic operations of large integers.

## The Solution

To solve this impreciseness, We have created a library called sateek.js

The word sateek means exact or precise in hindi language.

To use this library, Encode your large integer in a string format & call the functions provided by sateek.js

``````sateek.add("10000000000000001", "1"); // => 10000000000000002
sateek.subtract("10000000000000002", "1"); // => 10000000000000001
sateek.multiply("10000000000000002", "3"); // => 30000000000000006
``````

It returns output in string format.

## Installation

Sateek.js is available on github & npm or you can simply add it's CDN to your JavaScript file.

##### Node.js

1) To use this library, You need to install Node.js & npm.
2) Now run the following command in your project directory.

``````npm install --save sateek
``````

3) Import sateek.js library in your project.

``````var sateek = require('sateek')();
``````
##### JavaScript

1) Create a HTML file & write some code in it.

``````<html>
<body>

</body>
<script type="module">
import sateekModule from 'https://cdn.skypack.dev/sateek';
const sateek = sateekModule();
</script>
</html>
``````

## Usage

Sateek.js offers 5 functions.
2) subtract(n1,n2);
3) divide(n1,n2);
4) compare(n1,n2);

Where n1 & n2 are two numbers encoded in string format.

``````sateek.add("10000000000000001", "1"); // => 10000000000000002
``````
##### Subtract
``````sateek.subtract("10000000000000002", "1"); // => 10000000000000001
``````
##### Multiply
``````sateek.multiply("10000000000000002", "3"); // => 30000000000000006
``````
##### Divide
``````sateek.divide("20000000000000022", "2"); // => 10000000000000011
``````
##### Compare
``````sateek.compare("10000000000000001", "10000000000000000"); // => 1

sateek.compare("10000000000000000", "10000000000000001"); // => -1

sateek.compare("10000000000000001", "10000000000000001"); // => 0
``````

if n1>n2, it returns 1
if n1<n2, it returns -1
if n1==n2, it returns 0

## The Conclusion

Every library has it's own advantages & limitations. Here are some limitations of sateek.js library.

1) Sateek.js focuses more on precision as compare to efficiency.
2) It only work with integers.
3) Division operation only work when dividend is greater than divisor.
4) Division operation only returns quotient.

We have tested this library with large test cases, Still if you found any issue feel free to report it on github/npm or mail me at kalpitrathore@gmail.com. What is wrong with BigInt? Available since Node.js 10.4.0 (2018) and caniuse.

``````console.assert((10000000000000001n + 1n).toString(), '10000000000000002');
console.assert((10000000000000002n - 1n).toString(), '10000000000000001');
console.assert((10000000000000002n * BigInt(3)).toString(), '30000000000000006');
`````` When I tried to compute the below it gives me two different "k" constant values when they should be identical. See below results.
I´ve also tried all bignumber libraries with the exact two differing results each time.

``````    // transaction
const tx0 = 2755738843649989653057n; // amount0Out BMON
const tx1 = 113747760332474227520n; // amount1In BUSD

// reserve after transaction
const x = 466822693713887341798087n; // reserve0 BMON
const y = 19334468154310748213608n; // reserve1 BUSD

// BigInt method
console.log("BigInt method...");
const k = x * y;
console.log("xy ", k); // 9025768505320715115682091222146517245881767896n

const newX = x + tx0;
const newY = y - tx1;
const newK = newX * newY;
console.log("xy ", newK); // 9025635755231009297480820885627169090307684672n
``````

Any ideas on how to resolve this issue in JavaScript would be greatly appreciated!