8000 Misc improvements to the float tutorial by rhettinger · Pull Request #102052 · python/cpython · GitHub
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Misc improvements to the float tutorial #102052

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Merged
merged 10 commits into from
Feb 19, 2023
Merged

Misc improvements to the float tutorial #102052

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1e2ec34
Example is more intelligible without the leading zeros
rhettinger Feb 19, 2023
082d7a8
Leading zeros are easier to read and match the surrounding text.
rhettinger Feb 19, 2023
2ff520d
Compare sum() to straight addition and to math.fsum()
rhettinger Feb 19, 2023
22e1a96
Show math.isclose() for comparing inexact values
rhettinger Feb 19, 2023
cb1f78a
Add doctests throughout
rhettinger Feb 19, 2023
e9e959a
Add a more useful example of round() for comparisons
rhettinger Feb 19, 2023
8f02dc5
Shorter example
rhettinger Feb 19, 2023
d8bcc4c
Fix doctests: Missing import and counterfactual example.
rhettinger Feb 19, 2023
cd8abc5
Compare sum() and fsum() with straight addition
rhettinger Feb 19, 2023
d6a6b6b
Add section author
rhettinger Feb 19, 2023
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Compare sum() to straight addition and to math.fsum()
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@rhettinger
rhettinger committed Feb 19, 2023
commit 2ff520d94823f5bb690785e641dfb4fe68ab3132
29 changes: 23 additions & 6 deletions Doc/tutorial/floatingpoint.rst
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Expand Up @@ -186,17 +186,34 @@ Since the representation is exact, it is useful for reliably porting values
across different versions of Python (platform independence) and exchanging
data with other languages that support the same format (such as Java and C99).

Another helpful tool is the :func:`math.fsum` function which helps mitigate
loss-of-precision during summation. It tracks "lost digits" as values are
added onto a running total. That can make a difference in overall accuracy
so that the errors do not accumulate to the point where they affect the
final total:
Another helpful tool is the :func:`sum` function which helps mitigate
loss-of-precision during summation. It uses extended precision for
intermediate rounding steps as values are added onto a running total.
That can make a difference in overall accuracy so that the errors do not
accumulate to the point where they affect the final total::

>>> 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 == 1.0
False
>>> math.fsum([0.1] * 10) == 1.0
>>> sum([0.1] * 10) == 1.0
True

The :func:`math.fsum()` goes further and tracks all of the "lost digits"
as values are added onto a running total so that the result has only a
single rounding. This is slower than :func:`sum` but will be more
accurate in uncommon cases where large magnitude inputs mostly cancel
each other out leaving a final sum near zero::

>>> arr = [-125546.2071591587, 0.04336622547760194, 18741774.60535662,
... 57.207123035704896, 454267277684011.1, -0.04815896904694777,
... -18741774.600527752, -454267277558522.1]
>>> float(sum(map(Fraction, arr))) # Exact summation with single rounding
5.777552047891987e-12
>>> math.fsum(arr) # Single rounding
5.777552047891987e-12
>>> sum(arr) # Multiple roundings in extended precision
5.777545108998083e-12


.. _tut-fp-error:

Representation Error
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0