BETTER TO PRESCRIBE ARITHMETIC THAN DESCRIBE IT

[David Hough]

*DAY     February 5, 1990
*EVENT   Numerical Analysis/Scientific Computing Seminar
*PLACE   MJH 352
*TIME    4:15 pm
*PERSON  Professor W. "Velvel" Kahan
*FROM    University of California at Berkeley
*TITLE   BETTER TO PRESCRIBE ARITHMETIC THAN DESCRIBE IT
            (Preview of Turing Lecture)
*ABSTRACT

We do have standards for computing: languages, communication,
interfaces, magnetic media, hardware components, . . . , and now
floating-point arithmetic too.  They must be good things, or we should
not have so many.  Some are better than others; the IEEE standards for
floating-point arithmetic are among the better ones, we shall argue,
because they prescribe so tightly what arithmetic must do.  Earlier
attempts to make sense of approximate arithmetic have been DESCRIPTIVE
instead, relying upon sets of axioms or upon linguistic rules from
which a programmer might hope to deduce something about what computers
will do with his program.  Counter-examples reveal that, though
well-intentioned and even ingenious, the descriptive approach is not
categorical enough to sustain the kind of program verification and
portability we need.  Nor are the IEEE standards categorical enough;
they leave too much about the handling of floating-point exceptions to
the imagination.  We need something more than waving an unnamed flag
when 0/0 occurs, yet something far less brutal than abortion.  What is
proposed herein requires no precise interrupts; it insinuates no new
or invisible spaghetti-like control structures; yet it helps
programmers avoid hordes of precautionary tests for events that hardly
ever happen.

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