Why does IEEE 754 reserve so many NaN values?

Question

It seems that the IEEE 754 standard defines 16,777,214 32-bit floating point values as NaNs, or 0.4% of all possible values.

I wonder what is the rationale for reser

Answer 1

There is likewise a payload for 64 bit floating point numbers as well, with ~10^15 possible values. Unfortunately, implementations diverge as to how the payload should be transferred between 32 and 64 bit floating point numbers and back again, i.e. whether you preserve the most significant or least significant bits. Since payload treatment is machine specific, you need different code to deal with payloads on different machines.

I wouldn't worry too much about which NaN payload is propagated after a binary operation. NaNs are exceptional values that occur with low probability, and the probability of getting 2 of them is unlikely.