Question about floating point

[Chris Angelico]

On Wed, Aug 29, 2018 at 12:11 AM, Frank Millman <frank at chagford.com> wrote:
> Hi all
>
> I know about this gotcha -
>
>>>> x = 1.1 + 2.2
>>>> x
>
> 3.3000000000000003
>
> According to the docs, the reason is that "numbers like 1.1 and 2.2 do not
> have exact representations in binary floating point."
>
> So when I do this -
>
>>>> y = 3.3
>>>> y
>
> 3.3
>
> what exactly is happening? What is 'y' at this point?
>
> Or if I do this -
>
>>>> z = (1.1 + 2.2) * 10 / 10
>>>> z
>
> 3.3
>
> What makes it different from the first example?
>

Here's how you can find out *exactly* what a Python float is:

>>> y = 3.3
>>> y.as_integer_ratio()
(3715469692580659, 1125899906842624)
>>> x = 1.1 + 2.2
>>> x
3.3000000000000003
>>> x.as_integer_ratio()
(7430939385161319, 2251799813685248)
>>> z = (1.1 + 2.2) * 10 / 10
>>> z
3.3
>>> z.as_integer_ratio()
(3715469692580659, 1125899906842624)
>>> (1.1).as_integer_ratio()
(2476979795053773, 2251799813685248)
>>> (2.2).as_integer_ratio()
(2476979795053773, 1125899906842624)

The value of y is exactly (3715469692580659 / 1125899906842624) which
is 3.299999999999999822364316060. But x is a teeny bit higher.

You can explore these with the help of decimal.Decimal, too. The
values given by as_integer_ratio() are possibly more interesting in
hex than in decimal, with values like these.