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

Oren Tirosh oren-py-d@hishome.net
Thu, 3 Oct 2002 13:43:38 -0400

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