Add note about problems with math.fsum on x86 hardware.
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 @@
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