[Python-Dev] Re: PEP239 (Rational Numbers) Reference Implementation and new issues

[Oren Tirosh]

On Thu, Oct 03, 2002 at 12:50:38PM -0400, Tim Peters wrote:
> [Oren Tirosh]
> > Comparisons could produce a third boolean value called 'Undetermined':
> 
> Why?  What real numeric problem are you trying to solve?

I guess the smiley was camouflaged too well as the closing bracket :-)

> It's called interval arithmetic; about 30 years ago I had to implement it
> for a numerical analysis class assignment, in assembler for a Univac 1108;
> the interface to the Fortran compiler indeed tricked it into storing the
> bounds in complex numbrs; *efficient* support for interval arithmetic is why
> the 754 std requires the directed (to-plus-inf, to-minus-inf) rounding
> modes; it hasn't caught on, and the current incarnation of the 754 committee
> is thinking about removing this requirement; in the hands of an expert it
> can be very powerful; in the hands of a non-expert, the usual result is that
> the error bounds grow so large as to render the computation useless.

I was thinking more of estimates based on the assumption that errors are 
normally distributed and track standard deviation. SD grows more slowly
(i.e. realistically) than true error bounds.  Have you ever tried measuring 
noise or bit error rates in a simulation that runs thousands of times 
slower than real time? (change a paremeter, rinse, repeat). Something that 
quickly estimates the error energy could be useful.

I guess that "everything is gaussian" is an approximation only an engineer 
could love and makes mathematicians shake their heads in disgust :-)

	Oren