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Small doc fix-ups to floatingpoint.rst. More are forthcoming.
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Doc/tutorial/floatingpoint.rst

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@@ -82,7 +82,7 @@ values share the same approximation, any one of them could be displayed
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while still preserving the invariant ``eval(repr(x)) == x``.
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Historically, the Python prompt and built-in :func:`repr` function would chose
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the one with 17 significant digits, ``0.10000000000000001``, Starting with
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the one with 17 significant digits, ``0.10000000000000001``. Starting with
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Python 3.1, Python (on most systems) is now able to choose the shortest of
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these and simply display ``0.1``.
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@@ -123,9 +123,9 @@ Also, since the 0.1 cannot get any closer to the exact value of 1/10 and
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Though the numbers cannot be made closer to their intended exact values,
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the :func:`round` function can be useful for post-rounding so that results
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have inexact values that are comparable to one another::
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with inexact values become comparable to one another::
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>>> round(.1 + .1 + .1, 1) == round(.3, 1)
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>>> round(.1 + .1 + .1, 10) == round(.3, 10)
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True
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Binary floating-point arithmetic holds many surprises like this. The problem
@@ -137,7 +137,7 @@ As that says near the end, "there are no easy answers." Still, don't be unduly
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wary of floating-point! The errors in Python float operations are inherited
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from the floating-point hardware, and on most machines are on the order of no
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more than 1 part in 2\*\*53 per operation. That's more than adequate for most
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tasks, but you do need to keep in mind that it's not decimal arithmetic, and
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tasks, but you do need to keep in mind that it's not decimal arithmetic and
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that every float operation can suffer a new rounding error.
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While pathological cases do exist, for most casual use of floating-point
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>>> x = 3.14159
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>>> x.as_integer_ratio()
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(3537115888337719L, 1125899906842624L)
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(3537115888337719, 1125899906842624)
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Since the ratio is exact, it can be used to losslessly recreate the
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original value::

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