Section: Software

Exhaustive Tests for the Correct Rounding of Mathematical Functions

Participant : Vincent Lefèvre.

The search for the worst cases for the correct rounding (hardest-to-round cases) of mathematical functions ($exp$, $log$, $sin$, $cos$, etc.) in a fixed precision (mainly double precision) using Lefèvre's algorithm is implemented by a set of utilities written in Perl, with calls to Maple/intpakX for computations on intervals and with C code generation for fast computations. It also includes a client-server system for the distribution of intervals to be tested and for tracking the status of intervals (fully tested, being tested, aborted).

These programs are run on the LIP network via Grid Engine (SGE). In June 2011, the SGE configuration was changed by the system administrator so that SIGSTOP/SIGCONT signals are sent to the jobs, allowing several users to use SGE at the same time. These signals make Maple crash (segmentation fault), and the Perl scripts needed to be improved to handle these crashes gracefully (by restarting the computations when need be, etc.). This SGE change made other problems appear, such as when the client is first stopped by SGE and is then killed by SGE (without being woke up by SGE), it cannot do its usual clean-up; workarounds were tried, but without success.

The above problems also made an inconsistency in the client-server protocol appear. The validity of the results was not affected, but the protocol had to be redesigned.