FOM: RE: Re: Re: Godel, f.o.m.
Martin Davis
martin at eipye.com
Fri Jan 28 16:20:21 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?
Martin
Martin Davis
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
(Add 1 and get 0)
http://www.eipye.com
More information about the FOM
mailing list