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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