romberg-- replacement for bigfloat romberg

Richard Fateman wrote:
> I looked at Sherry Li's papers again, and there are 2 things worth noting.
>  
> 1. There is a version of ARPREC, which is comparable to MPFR (that is,
> arbitrary precision floats) implemented in Fortran 90. So maybe it can be
> run through f2cl.  (I have used ARPREC and its predecessor MPFUN in the
>   
Unless the code uses only a small part of Fortran 90, it's unlikely f2cl
can convert it.  At least not without adding a ton of new parsers and
such.  MPFUN, as you know, can be converted fairly easily.

> past; MPFR seems to have more of a following and in some timing tests is
> faster. In favor of ARPREC (and QD), it is locally produced by friends and I
> can sometimes get help :)  )
>   
FWIW, I have (had) an implementation of double-double in pure portable
Lisp.  I also have a partial implementation of QD in Lisp but it
currently depends on a (complex double-double) type.  Without such
support, there would be a lot of consing going on for each operation,
but perhaps that's not so bad, since, I think a quad-double add is some
500 (or more) machine instructions.
> Is there anyone who cares about
>  making this (a: arprec; b: Li's integration) work in Maxima? I believe that
> part b can be done using existing bigfloats.
>
>   
Although not directly applicable to either a or b, I've wanted to add
some classes to support double, bfloat, and complex bfloat operations. 
Right now, I find it a pain to do bfloat stuff in Lisp, especially if
you want to operate on complex numbers.

Ray