on floating-point numbers

[Hope Rouselle]

Hope Rouselle <hrouselle at jevedi.com> writes:

> Just sharing a case of floating-point numbers.  Nothing needed to be
> solved or to be figured out.  Just bringing up conversation.
>
> (*) An introduction to me
>
> I don't understand floating-point numbers from the inside out, but I do
> know how to work with base 2 and scientific notation.  So the idea of
> expressing a number as 
>
>   mantissa * base^{power}
>
> is not foreign to me. (If that helps you to perhaps instruct me on
> what's going on here.)
>
> (*) A presentation of the behavior
>
>>>> import sys
>>>> sys.version
> '3.8.10 (tags/v3.8.10:3d8993a, May 3 2021, 11:48:03) [MSC v.1928 64
> bit (AMD64)]'
>
>>>> ls = [7.23, 8.41, 6.15, 2.31, 7.73, 7.77]
>>>> sum(ls)
> 39.599999999999994
>
>>>> ls = [8.41, 6.15, 2.31, 7.73, 7.77, 7.23]
>>>> sum(ls)
> 39.60000000000001
>
> All I did was to take the first number, 7.23, and move it to the last
> position in the list.  (So we have a violation of the commutativity of
> addition.)

Suppose these numbers are prices in dollar, never going beyond cents.
Would it be safe to multiply each one of them by 100 and therefore work
with cents only?  For instance

--8<---------------cut here---------------start------------->8---
>>> ls = [7.23, 8.41, 6.15, 2.31, 7.73, 7.77]
>>> sum(map(lambda x: int(x*100), ls)) / 100
39.6

>>> ls = [8.41, 6.15, 2.31, 7.73, 7.77, 7.23]
>>> sum(map(lambda x: int(x*100), ls)) / 100
39.6
--8<---------------cut here---------------end--------------->8---

Or multiplication by 100 isn't quite ``safe'' to do with floating-point
numbers either?  (It worked in this case.)

I suppose that if I multiply it by a power of two, that would be an
operation that I can be sure will not bring about any precision loss
with floating-point numbers.  Do you agree?