Is the number 9933272057275866 truly magical?

I encountered a strange issue that I cannot quite understand. It has left me quite baffled. When I attempt to increase the number 9933272057275866 by 1, it somehow adds 2 instead!!! Here is the code snippet:

let test = 9933272057275866;
let test2 = test+1;
console.log('Before:', test);
console.log('After:', test2);
console.log('Sub:', test2-test);

Here is the output:

Before: 9933272057275866
After: 9933272057275868
Sub: 2

How is this even possible?

This issue occurred in a JavaScript environment. It first came to my attention when I encountered it on Hackerrank, and I then replicated it in my own node.js environment. The result was the same!

Can anyone explain what is going on here?

javascriptinteger-arithmetic

Answer №1

Essentially, the limitation arises from the fact that 64-bit numbers are insufficient to accurately represent the given number.

  • 4341 A521 1037 32ED: 9.933272057275866 ⨉ 1015
  • 4341 A521 1037 32EE: 9.933272057275868 ⨉ 1015

Notice the gap of one integer between them. With IEEE 754, as the numbers increase, they become more widely spaced along the number line. It's important to remember that floating point numbers are approximations. This explains why the result turns out to be:

0.1 + 0.2 === 0.3    // false

The maximum safe integer in IEEE 754 is 9007199254740991.

Here are some interesting facts about floating point arithmetic:

A + B == B + A              // true, commutative, except when A or B is NaN
(A + B) + C == A + (B + C)  // false, not associative

* It's important to note that numbers in JavaScript (ECMAScript) are stored as 64-bit IEEE 754 doubles. ref

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