on floating-point numbers

[Schachner, Joseph]

Actually, Python has an fsum function meant to address this issue.

>>> math.fsum([1e14, 1, -1e14])
1.0
>>>

Wow it works.

--- Joseph S.

Teledyne Confidential; Commercially Sensitive Business Data

-----Original Message-----
From: Hope Rouselle <hrouselle at jevedi.com> 
Sent: Thursday, September 2, 2021 9:51 AM
To: python-list at python.org
Subject: on floating-point numbers

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.)

Let me try to reduce the example.  It's not so easy.  Although I could display the violation of commutativity by moving just a single number in the list, I also see that 7.23 commutes with every other number in the list.

(*) My request

I would like to just get some clarity.  I guess I need to translate all these numbers into base 2 and perform the addition myself to see the situation coming up?