From 23957cb8fb4289a11f55d46c3fa01938ff01dbea Mon Sep 17 00:00:00 2001 From: Mark Dickinson Date: Wed, 30 Jul 2008 20:23:15 +0000 Subject: Add note about problems with math.fsum on x86 hardware. --- Doc/library/math.rst | 26 ++++++++++++++++++++++++++ 1 file changed, 26 insertions(+) diff --git a/Doc/library/math.rst b/Doc/library/math.rst index 5740759..6f8d3c8 100644 --- a/Doc/library/math.rst +++ b/Doc/library/math.rst @@ -90,6 +90,32 @@ Number-theoretic and representation functions: 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 -- cgit v0.12