🚀 go-pugleaf

On 2 Oct 2003 18:36:58 GMT, Nick Maclaren <nmm1@cus.cam.ac.uk> wrote:
> What is probably the case is that anyone who relies on absolutely
> consistent floating-point results is living dangerously, and may be
> deluding himself.  I know of at least half a dozen ways where the
> assumption will fail, even on consistent IEEE-like architectures.
> And considerably more on older ones.
> 
> That is part of the basis for my assertion that probabilistic rounding
> is good because it forces programmers to realise that floating-point 
> arithmetic does not give precisely predictable results.

I would like true pseudoprobabilistic rounding, one with the
same statisitics as probabilistic rounding, but determinsitically
repeatable if need be.  Gaussian rounding would be better still.  :) 

In dynamical systems at least there almost always is (in reality)
some kind of tiny probabilistic forces, e.g. thermodynamic fluctuations
on a macroscopic object.

Such rounding in calculations would make numerical results which are
ore like what would "physically happen", in the sense that orbits that
arise are likely to be ones on the "natural" physical measure.

The issue of measure of results is in fact tricky and difficult
in theoretical dynamical systems, but everybody agrees that there
is some kind of "natural" physical measure out there.