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Kirill Smelkov
cpython
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4af36290
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4af36290
authored
Apr 26, 2009
by
Raymond Hettinger
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Improve the rounding and summing examples.
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cc32a119
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Doc/tutorial/floatingpoint.rst
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Doc/tutorial/floatingpoint.rst
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4af36290
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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.
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::
>>> sum = 0.0
>>> for i in range(10):
... sum += 0.1
...
>>> sum
0.9999999999999999
summing three values of 0.1 may not yield exactly 0.3, either::
>>> .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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