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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
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24
Doc/tutorial/floatingpoint.rst
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@ -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. simply rounding the *display* of the true machine value.
One illusion may beget another. For example, since 0.1 is not exactly 1/10, 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 >>> .1 + .1 + .1 == .3
>>> for i in range(10): False
... sum += 0.1
... Also, since the 0.1 cannot get any closer to the exact value of 1/10 and
>>> sum 0.3 cannot get any closer to the exact value of 3/10, then pre-rounding with
0.9999999999999999 :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 Binary floating-point arithmetic holds many surprises like this. The problem
with "0.1" is explained in precise detail below, in the "Representation Error" with "0.1" is explained in precise detail below, in the "Representation Error"