Question

Say I have two Python floats a and b, is there an easy way to find out how many representable real numbers are between the two in IEEE-754 representation (or whatever representation the machine used is using)?

Answer 1

I don’tknow what you will be using this for – but, if both floats have the same exponent, it should be possible. As the exponent is kept on the high order bits, loading the float bytes (8 bytes in this case) as an integer and subtracting one from another should give the number you want. I use the struct model to pack the floats to a binary representation, and then unpack those as (C, 8 byte) long ints:

>>> import struct
>>> a = struct.pack("dd", 1.000000,1.000001)
>>> b = struct.unpack("ll",a)
>>> b[1] - b[0]
4503599627
>>> a = struct.pack("dd", 1.000000000,1.000000001)
>>> b = struct.unpack("ll",a)
>>> b[1] - b[0]
4503600
>>>