FOM: RE: Re: Re: Godel, f.o.m.

[Martin Davis]

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?

Martin



                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
                          (Add 1 and get 0)
                        http://www.eipye.com