What is the internal representation of integers larger than Number.MAX_SAFE_INTEGER in javascript?

When it comes to javascript, numbers are stored as double-precision floats internally, with 53 bits dedicated to representing integer values. An example of this is the Number.MAX_SAFE_INTEGER constant, calculated as Math.pow(2, 53) - 1. Surprisingly, when I input Number.MAX_SAFE_INTEGER + 20 in the javascript console, it still provides the correct integer value output.

The question that arises is: How does javascript manage to handle numbers exceeding the limitations set by Number.MAX_SAFE_INTEGER?

javascript

Answer №1

Basically, when it comes to floating point numbers, they are represented as:

 digits * 2 ** movement

The digits portion consists of 52 bits, while the movement portion has 11 bits. Together, they make up a 64-bit number (including one sign bit). For integers, you can represent them by setting movement to 0. In this case, the 52-bit number in digits can hold values up to 2 ** 53 - 1. However, for larger numbers, you need to adjust the value in movement. This adjustment involves shifting the position of the binary digits in digits, leading to a loss in accuracy.

Let's consider what would happen if digits only contained 8 bits:

  number     >     digits | movement > result
   // accurately represented
  11111111   >  111111111 | 0        > 11111111
  // loses the last 1
  111111111  >  111111111 | 1        > 111111110
   // loses the two last 1s
  1111111111 >  11111111  | 10       > 1111111100

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