14 June 2011

             DESPERATELY NEEDED REMEDIES FOR THE
                       UNDEBUGGABILITY
                OF LARGE-SCALE FLOATING-POINT
           COMPUTATIONS IN SCIENCE AND ENGINEERING

                        Prof. W. Kahan
                  Univ. of Calif. @ Berkeley

 We could have,  but out of ignorance we lack the software
 tools we need to debug big floating-point computations in
 Science and Engineering.

 These tools are needed by software developers and especially
 users who suspect anomalous computed results.  Overwhelmed
 by  Gigaflops and Terabytes,  we cannot afford the months it
 may cost to track down a merely suspected anomaly to allay
 or confirm our suspicions.  This cost could be reduced by
 orders of magnitude if we had the appropriate tools.  Most
 of these have existed,  but not all in the same place and at
 the same time.  For instance,  ...

 >  48 years ago on the  IBM 7094  at the  Univ. of Toronto,
    I had Retrospective Diagnostics to locate in my programs
    any floating-point exceptions,  like over/underflows and
    divisions-by-zero,  that may have been  "fudged"  badly.

 >  For over  25  years,  my old  68040-based Macintosh with
    the (then)  Standard Apple Numeric Environment,  and my
    old  PC  running an  Intel Fortran  compiler and an old
    MATLAB v. 3.5  under  DOS,  have let me rerun suspected
    subprograms with the same data but redirected roundings
    to help track down roundoff-induced anomalies.

 You too could have such tools added to debuggers,  developed
 to cope with massively parallel computation, but for a state
 of indifference towards floating-point into which  Computer
 Scientists  have drifted.  They perceive no market for the
 tools we need because we don't demand to buy them,  since
 almost none of us know about them.

 Now we risk a return to the general consensus prevalent when
 I was young.  Experts who thought they understood floating-
 point distrusted it then as if it were intrinsically and
 irremediably unreliable,  refractory to error-analysis.  And
 they had  John von Neumann,  who had disparaged floating-
 point,  on their side.  He died in  1957,  before he could
 protest  "No,  that's not what I meant".

 If that belief in intrinsic unreliability becomes accepted
 as technological lore,  you will not like the consequences.

 For more,  see  <www.eecs.berkeley.edu/~wkahan/NeeDebug.pdf>
 and <.../Mindless.pdf>  and  <.../7094II.pdf>.