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2013-05-29

The beginning of infinity in JavaScript

Infinity begins relatively early in JavaScript:
    > Math.pow(2, 1024)
    Infinity
    > Math.pow(2, 1023)
    8.98846567431158e+307
What is going on here?

All numbers in JavaScript are floating point numbers and (roughly) encoded internally [1] as

1.f × 2p
This is the most common way of representing floating point numbers. The left-hand side of the multiplication comprises the digits, the right-hand side moves the dot to the correct position (to the left if it is negative, to the right if it is positive).

The mantissa is a binary 1, followed by a binary dot, followed by a 52 bit fraction f. The 11 bit exponent p has to be in the range

−1023 < p < 1024
Thus, the exponent of Math.pow(2, 1024) is out of range and Infinity is an error result.

Consult [1] if you want to know more about how numbers are encoded in JavaScript.

Reference

  1. How numbers are encoded in JavaScript

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