[issue2819] Full precision summation
report at bugs.python.org
Sat Jul 26 12:38:41 CEST 2008
Mark Dickinson <dickinsm at gmail.com> added the comment:
Here's a patch giving an alternative implementation of math.fsum; it's
based on Tim Peter's suggestions, works mostly with integer arithmetic,
and so bypasses problems with double rounding and extended precision
The patch is experimental: it doesn't have sufficient tests, has no
documentation, and it adds math.fsum alongside the current math.sum, to
make it easy to compare the two implementations.
On my MacBook, math.fsum is a factor of 2-3 times slower than math.sum.
It's also longer and distinctly less elegant. So its only real
advantage is that it should fix the difficulties on x86 hardware.
We *really* need to sort math.sum out, one way or another, before the
next beta. Georg recently discovered another problem on x86/Linux: see
(1) leave math.sum as it is, skip all tests on x86/Linux, and document
the current behaviour.
(2) investigate a version of math.sum that plays with the FPU control
word to force 53-bit rounding (and round-half-even)
(3) replace math.sum with the slower but (presumably) less erratic
math.fsum, possibly just as a temporary measure. This would at least
get all tests passing.
Jean, Raymond: what do you think?
Added file: http://bugs.python.org/file10988/fsum7.patch
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