Mirror
/
cpython
mirror of https://github.com/python/cpython
4
1
Fork 0
Code Issues Releases Wiki Activity

Improve the rounding and summing examples.

This commit is contained in:
Raymond Hettinger 2009-04-26 21:37:46 +00:00
parent cc32a11976
commit 4af362905c
1 changed files with 17 additions and 7 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

24
Doc/tutorial/floatingpoint.rst
View File

@ -109,14 +109,24 @@ It's important to realize that this is, in a real sense, an illusion: you're
simply rounding the *display* of the true machine value.
One illusion may beget another. For example, since 0.1 is not exactly 1/10,
summing ten values of 0.1 may not yield exactly 1.0, either::
summing three values of 0.1 may not yield exactly 0.3, either::
>>> sum = 0.0
>>> for i in range(10):
... sum += 0.1
...
>>> sum
0.9999999999999999
>>> .1 + .1 + .1 == .3
False
Also, since the 0.1 cannot get any closer to the exact value of 1/10 and
0.3 cannot get any closer to the exact value of 3/10, then pre-rounding with
:func:`round` function cannot help::
>>> round(.1, 1) + round(.1, 1) + round(.1, 1) == round(.3, 1)
False
Though the numbers cannot be made closer to their intended exact values,
the :func:`round` function can be useful for post-rounding so that results
have inexact values that are comparable to one another::
>>> round(.1 + .1 + .1, 1) == round(.3, 1)
True
Binary floating-point arithmetic holds many surprises like this. The problem
with "0.1" is explained in precise detail below, in the "Representation Error"