Is there anything special about the number 308?

Question

So one day I was experimenting (like any other good coder does), and I came up across this:

>>> 1e308
1e+308
>>> 1e309
inf

What is going on? First of all, 308’s factors are 2, 2, 7, and 11.

Farther investigation yields:

>>> 1.7976931348623158075e308 # No, I didn’t copy it incorrectly
1.797693134862315e+308
>>> 1.79769313486231581+308
inf

So what is going on? There doesn’t seem any relationship between an absurdly big number and an equally weird number with over 10 decimal places.

Also, all of this was using the repl python console, so others might be different.

Answer 1

A double-precision floating point number in IEEE-754 has an 11-bit exponent and a 53-bit mantissa. The 11-bit exponent means we get from 2**(-1023) to 2**+1023. 2**1023 happens to be 10**308.

You get about 3.23 bits per decimal digit. A 53-bit mantissa gives you about 17 digits of precision.

The largest number that fits in a double is, as you noticed, 1.7976931348623158075E+308.

I recommend https://en.wikipedia.org/wiki/IEEE_754 .