calculating with bfloats (was: stuff not in 5.13 branch)

Doing almost anything with floats and polynomials of degree 2^1024 is probably giving you nonsense, at least if you are trying to evaluate at a point other than 0.0, or perhaps +-1.0

You may be much better off if you can think of a simplification that reduces the problem to a more manageable size.
RJF

----- Original Message -----
From: sen1 at math.msu.edu
Date: Saturday, August 4, 2007 8:17 pm
Subject: Re: [Maxima] calculating with bfloats (was: stuff not in 5.13	branch)

> On Sat, 4 Aug 2007, Harald Geyer wrote:
> 
> >> One thing I (and I think other users) would very much like to 
> see is a
> >> global key  which transparently turns on and off arbitrary
> >> precision. I realize that this may require redoing some intrinsic
> >> functions, so it may take time to do.  Are any of the current lisps
> >> set up to do this?
> >
> > This is not a matter of the lisp implementation. AFAIK bfloats are
> > implemented entirely within the maxima source.
> >
> > If you don't use floats (use rationals instead) you get exact
> > arithmetic by default.
> Can't use rationals since square roots occur.
> 
> >
> > I think the main change would be to make the parser read floats as
> > bfloats. I don't really see the point of that.
> >
> >> I have tried to work on individual variables and functions (at this
> >> point involving algebraic functions no worse than square roots) by
> >> declaring all variables and functions to be bfloat, but for some
> >> reason it doesn't work. Certain of the operations still come 
> back as
> >> float.  Maybe the square root is the problem. I have been using
> >> cmucl. Is that a potential problem?
> >
> > Do you have example sessions, that show this behaviour? Probably 
> there> are some bugs. I'd fix the bugs rather than inventing a new 
> global> switch.
> >
> > The only problem I'm aware of in this context is the numer flag.
> > But you shouldn't need to use that, if you work with bfloats from
> > the beginning.
> >
> > HTH,
> > Harald
> >
>   My code is long and complicated.  It involves polynomials of degree
>   2^(2^d) with d = 10 or 15.  (They come from composing degree
>   two polynomials 10 or 15 times). Many of the coefficients are
>   exponentially small, but I can't know that in advance.  Trying to
>  work symbolically, the routines take a very long time --probably
>  doing things which are irrelevant like adding and subtracting 
> terms of order
>  10^(-75).  When I hit the terms with float or bfloat, they finish in
>  a reasonable amount of time, but don't seem to be very different.
> 
>   I played with things like    1e-(200)*3^200 and the precision is
>   there, so I don't know why I   don't see a difference with bfloats
>   instead of floats.
> 
> I thought if I could control the bfloat order in everything, then I
> could get more accurate results but which would actually finish in a
> reasonable amount of time.
> 
> I'll play some more and see what I can get.
> Thanks for your answer.
> 
> -sen
> 
> 
> 
> 
> 
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