Comment by colejohnson66

4 years ago

It also explains why 0.1+0.2 is not 0.3. With binary IEEE-754 floats, none of those can be represented exactly[a]. With decimal IEEE-754 floats, it's possible, but the majority of hardware people interact with works on binary floats.

[a]: Sure, if you `console.log(0.1)`, you'll get 0.1, but it's not possible to express it in binary exactly; only after rounding. 0.5, however, is exactly representable.

3 comments

colejohnson66

jacobolus 4 years ago

    Python 3.9.5
    >>> 0.1.hex()
    '0x1.999999999999ap-4'
    >>> 0.2.hex()
    '0x1.999999999999ap-3'
    >>> (0.1 + 0.2).hex()
    '0x1.3333333333334p-2'
    >>> 0.3.hex()
    '0x1.3333333333333p-2'

colejohnson66 4 years ago
But they are repeating. So, by definition, they are not exactly representable in a (binary) floating point system. Again, that’s why 0.1 + 0.2 is not 0.3 in binary floating point.
- jacobolus 4 years ago
  
  These are not "repeating". This is showing the exact binary representation of the nearest double precision value in each case.