one day course in arithmetic testing

[David Hough]

                      TESTS for FLOATING-POINT ARITHMETIC

                          A One-Day Impromptu Course

                              by  Prof. W. Kahan
                        Elect. Eng. & Computer Science
                           University of California
                           Berkeley   CA  94720-1776

                         to be held in  405  Soda Hall
                      10 am. - 4 pm,  Friday 14 July 1995
                      ( with a break to forage for lunch )

    Abstract:  Floating-point operations  ( +, -, *, /, ... )  and
               functions  ( cos, exp, ... )  ought ideally to be proved
               correct by their implementors,  but the proofs are longer
               computations by far than the operations they are intended
               to validate,  and consequently more vulnerable to error.
               That is why tests are indispensable.  Random testing is
               necessary but so inefficient that it cannot be expected to
               find designers' errors in time to prevent embarrassments
               like the  Pentium  divide bug of  1994.  Systematic tests
               are necessary too,  and this short course will outline how
               to devise them and how to use those that exist already.

    Topics:    Corroboration is the goal,  not certainty.
               Batteries of tests -  the  IEEE 754 Test Tape.
               Pattern tests -  Norm Schryer's  programs.
               Tests based upon  P-adic Arithmetic  for  *, /, SQRT .
               PARANOIA -  tests for common misconceptions.
               Fast scatter-plots of errors in  log,  exp,  cos,  ... .
               What not to do when an error is discovered too late.


    Who may attend:  Anyone interested;  the course will not be graded.

    How to get there:  Soda Hall  is on the  North-West  corner of
               Hearst  and  Le Roy,  very near a bus stop for a shuttle
               that runs from near the  Berkeley Shattuck BART  station
               to the  UCB  campus.  There are also parking structures
               a block uphill and two blocks downhill on  Hearst,  but
               parking spaces in them usually fill up by  9  am.;  bring
               $3.00  in quarters.