[ericfrederich]

I was looking once at Python and Redis and how numbers get stored. I remember Python would in the end send Redis some strings. I dove pretty deep and found that Python floats when turned into a string and then back are exactly the same float.

I remember even writing a program that tested every possible floating point number (must have only been 32 bit). I think I used ctypes and interpreted every binary combination of 32 bits as a float, turned it into a string, then back and checked equality. A lot of them were NaN.

[mark-r]

Checking equality on NaN doesn't work the way it does for other numbers. Your test might have had a fatal flaw.

[dagw]

A lot of them were NaN.

I seem to recall that ~0.5% of the IEEE 32 bit float space is NaN.

[ekimekim]

A NaN is any value where the 7-bit (for 32-bit floats) exponent is all 1s, except for +/-inf. So a quick approximation is that 1/128 ~= 0.78% of the space is NaN.

That means there's 25 bits that we can change while still being either a NaN or an inf. But two of those values are infs, so we need to remove them. Divide that by the entire range and we have (2^25 - 2) / 2^32 = 16777215/2147483648, or about 0.78124995%.