NaN and infinity

NaN stands for “not a number”

It means the result of the calculation is undefined.

0/0 = NaN

sqrt(-1) = NaN

log(-1) = NaN

infinity

“Infinity” just means “this number is too big for floating point to handle.” There are two infinities: one positive, one negative.

2.0**1024 = inf

(2.0**1024 means 2^1024)

-1/0 = -inf

inf 10 = inf

inf - inf = NaN

NaNs spread

As soon as one NaN gets in, it gets everywhere

NaN * 5 = NaN

NaN + 2 = NaN

NaN != NaN

NaN isn’t equal to anything (including itself)

NaN and infinity: the bits

A floating point value is NaN or infinity if the bits in the exponent are all 1. For example, this is a NaN:

01111111 11110001 00000000 00000000 00000000 00000000 00000000 00000000

It’s infinity if the offset bits are all 0, otherwise it’s NaN.

There are 2^52 values like this: 2 of them are ±infinity and the other 2^52-2 are NaN.

We usually treat NaN like a single value though.

a note on byte order

All of the floating point examples in this zine use a big endian byte order, because it’s easier to read. But most computers use a little endian byte order.

You can see this in action at https://memory-spy.wizardzines.com