FOM: What are the FOM issues in this?

Steve Stevenson steve at
Mon Jan 31 13:11:59 EST 2000

At 01:39 PM 1/28/00 -0500, Steve Stevenson wrote:
>>Here's a simple experiment. Take a
>>standard, commercially developed Fortran compiler with its trig
>>routines. You should find that sin^2(x)+cos^2(x) is greater than 1.0
>>about three percent of the time. Is this any *real* problem or do we
>>just widen 1.0 to 1.0+\delta?
>Are there no numerical analysts in your CS department? Because what are 
>called "reals" as data types in programming languages are (of necessity) 
>rational numbers, all computations with real numbers are approximations. 
>For arithmetic operations the IEEE floating point standard is a beautiful 
>accommodation, implemented in most compilers. For transcendental functions, 
>error analysis is crucial.
>What are there foundational issues in any of this?

There are numerical analysts in our department: I'm them. The IEEE
recommendations have have nothing to do with compilers: they're machine
specs. And check William Kahan's website at

to see how big a joke they really are. My own small site at 

has some other information. In short, IEEE is part of the problem, not 
part of the solution.

I believe the foundational issues are related to the problem of
validating models to reality and that in turn is related to reasoning
when simulations are part of the problem. Suppose a physicist gives
you an analytical statement of a system to solve. These are usually
very complex etc etc. During the computation, you regularly violate
something inviolable in the model. Conservation of energy is a common
problem due to cancellation. You now finish and the physicist now
starts drawing conclusions from the output of the simulation.

Are these viable conclusions?

This is the problem facing the simulation community right now and it's
called "validation of simulations" rather than "verification of

Best regards,

Steve (really "D. E.") Stevenson           Assoc Prof
Department of Computer Science, Clemson,   (864)656-5880.mabell
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