Kahan on LIA via NCEG

[Ed Barkmeyer]

It strikes me as significant that one of the world's foremost authorities
on floating-point arithmetic, when confronted with the most recent draft
of the Language-Independent Arithmetic standard, is reduced to replying
with empty polemics.  Could it be that there is no longer any technical
facade behind which he can hide his fundamentally religious opposition?

While I am prepared to believe that the IEEE 754 standard was originally
a crusade founded on technical virtue, the assumption that the LIA is a 
counter-crusade marshalled by the forces of DEC-the-Infidel is not only 
unwarranted, it is simply false.  It was the perception of the UK National 
Physical Laboratory, supported by similar views at NIST and several major 
computer manufacturers, that the specification of the required characteristics
of arithmetic in programming language standards is execrable.  The adoption 
of IEEE 754, in various precisions and implementations, by a segment of the 
computer producer community has improved the predictability of numerical 
results, but not in two important ways:
    1.  There is no standard which permits the programmer to obtain
the values of parameters which meaningfully describe the characteristics
of a given arithmetic implementation, whether or not it conforms to 
IEEE 754.  This lack of specification has led to trick software which attempts
to determine those values by curious expressions whose utility is dependent
on the compiler performing exactly the floating arithmetic operations the
author had in mind.  This in turn has led to countless meaningless
debates in the numerical analysis community over what expressions can be
optimized or reordered by compilers and whether computation at precisions
greater than that apparently specified is permitted.
    2.  The average user, which includes most scientists and engineers, is
often unable to obtain any indication that an arithmetic error has occurred
during a computation, without sophisticated use of the exceptional-values
provided by IEEE 754 or their equivalents, supported, if at all, by extensions
to the standard programming languages.  This lack of notification has
resulted in the publication of erroneous scientific results, through no
obvious fault of the scientist involved.  (While one may want to argue that
all numerical programming ought to be performed by experts, good standards
are designed to support a user of average competence with the intent to
produce competent work.  Many of us would be very annoyed if ability to
perform mechanical diagnosis and repair were a prerequisite for a license to 
drive an automobile.)

We are grateful to DEC for providing an honest editorial group which has 
endeavoured to meet the needs above, taken technical criticism and made
the appropriate technical repairs, and taken international guidance on the
necessary restructuring of the approach to avoid even the appearance of
conflict with IEEE 754, in an effort to produce a document which can, by
consensus, become a standard.  This document has been circulated in SIGNUM,
in the IEEE Computer Society, and in the NCEG.  The U.S. committee X3T2
went to some length and international embarassment to prevent the adoption
of the previous draft in the light of comments from the IEEE 754 community.

No one has yet presented evidence that the promulgation of the IEEE 754 
standard has improved the quality of numerical SOFTWARE, in programs 
conforming strictly to ISO programming language standards.  What it has
done is to improve the quality of numerical RESULTS!  The objective of
the LIA IS to improve the quality of numerical software by improving the
programming language standards, and the compiler/library implementations 
thereof, with respect to arithmetic.

Dr. Kahan tells us that the current draft of the LIA fails to support this
objective, but he declines to provide the least inkling of the basis for this
statement.  Instead, he informs us that LIA is a plot by a secret organization
led by Digital Equipment Corporation to control the arithmetic and thus the
computers of this great nation, and that this treason is a cancer on the
body politic and he will have it out.  For shame, sir!  What is it you so
fear that you would corrupt an intellectual forum with inflamatory rhetoric?

-Ed Barkmeyer