[Python-checkins] r71991 - python/branches/py3k/Doc/tutorial/floatingpoint.rst
raymond.hettinger
python-checkins at python.org
Sun Apr 26 23:37:46 CEST 2009
Author: raymond.hettinger
Date: Sun Apr 26 23:37:46 2009
New Revision: 71991
Log:
Improve the rounding and summing examples.
Modified:
python/branches/py3k/Doc/tutorial/floatingpoint.rst
Modified: python/branches/py3k/Doc/tutorial/floatingpoint.rst
==============================================================================
--- python/branches/py3k/Doc/tutorial/floatingpoint.rst (original)
+++ python/branches/py3k/Doc/tutorial/floatingpoint.rst Sun Apr 26 23:37:46 2009
@@ -109,14 +109,24 @@
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"
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