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Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from

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  r65258 | mark.dickinson | 2008-07-27 08:15:29 +0100 (Sun, 27 Jul 2008) | 4 lines

  Remove math.sum tests related to overflow, special values, and behaviour
  near the extremes of the floating-point range.  (The behaviour of math.sum
  should be regarded as undefined in these cases.)
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  r65292 | mark.dickinson | 2008-07-29 19:45:38 +0100 (Tue, 29 Jul 2008) | 4 lines

  More modifications to tests for math.sum:  replace the Python
  version of msum by a version using a different algorithm, and
  use the new float.fromhex method to specify test results exactly.
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  r65299 | mark.dickinson | 2008-07-30 13:01:41 +0100 (Wed, 30 Jul 2008) | 5 lines

  Fix special-value handling for math.sum.
  Also minor cleanups to the code: fix tabbing, remove
  trailing whitespace, and reformat to fit into 80
  columns.
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  r65308 | mark.dickinson | 2008-07-30 17:20:10 +0100 (Wed, 30 Jul 2008) | 2 lines

  Rename math.sum to math.fsum
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  r65309 | mark.dickinson | 2008-07-30 17:25:16 +0100 (Wed, 30 Jul 2008) | 3 lines

  Replace math.sum with math.fsum in a couple of comments
  that were missed by r65308
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  r65315 | mark.dickinson | 2008-07-30 21:23:15 +0100 (Wed, 30 Jul 2008) | 2 lines

  Add note about problems with math.fsum on x86 hardware.
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  r65326 | mark.dickinson | 2008-07-31 15:48:32 +0100 (Thu, 31 Jul 2008) | 2 lines

  Rename testSum to testFsum and move it to proper place in test_math.py
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This commit is contained in:
Mark Dickinson 2008-08-01 08:16:13 +00:00
parent c57df32319
commit aa7633ab94
5 changed files with 201 additions and 211 deletions
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42
Doc/library/math.rst
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@ -76,6 +76,42 @@ Number-theoretic and representation functions:
apart" the internal representation of a float in a portable way.
.. function:: fsum(iterable)
Return an accurate floating point sum of values in the iterable. Avoids
loss of precision by tracking multiple intermediate partial sums. The
algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the
typical case where the rounding mode is half-even.
.. note::
On platforms where arithmetic results are not correctly rounded,
:func:`fsum` may occasionally produce incorrect results; these
results should be no less accurate than those from the builtin
:func:`sum` function, but nevertheless may have arbitrarily
large relative error.
In particular, this affects some older Intel hardware (for
example Pentium and earlier x86 processors) that makes use of
'extended precision' floating-point registers with 64 bits of
precision instead of the 53 bits of precision provided by a C
double. Arithmetic operations using these registers may be
doubly rounded (rounded first to 64 bits, and then rerounded to
53 bits), leading to incorrectly rounded results. To test
whether your machine is one of those affected, try the following
at a Python prompt::
>>> 1e16 + 2.9999
10000000000000002.0
Machines subject to the double-rounding problem described above
are likely to print ``10000000000000004.0`` instead of
``10000000000000002.0``.
.. versionadded:: 2.6
.. function:: isinf(x)
Checks if the float *x* is positive or negative infinite.
@ -100,12 +136,6 @@ Number-theoretic and representation functions:
Return the fractional and integer parts of *x*. Both results carry the sign of
*x*, and both are floats.
.. function:: sum(iterable)
Return an accurate floating point sum of values in the iterable. Avoids
loss of precision by tracking multiple intermediate partial sums. The
algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the
typical case where the rounding mode is half-even.
.. function:: trunc(x)