how can I speed up bromberg

On Nov. 24, 2012, Robert Dodier wrote:

>
> Where is the new bromberg?

Raymond Toy, on the thread 'how can I speed up bromberg?',
on Nov. 6,  provided a link to his "improved" version:

http://common-lisp.net/~rtoy/maxima/bromberg.lisp

which is what I have been testing on the rest of
the thread.

>
>We could obviate the lack of documentation by implementing
>something more sophisticated than Romberg's method for bigfloats so then
>we could just nuke bromberg.
>

On Nov 21, 2012, responding to Raymond Toy's remark:

-------------------------------
>Don't know if this will help or not, but it might be worthwhile to
>implement tanh-sinh quadrature
>(http://en.wikipedia.org/wiki/Tanh-sinh_quadrature).  (I think Richard
>has mentioned this before.)
------------------------------------------------

I answered:

---------------------------------------
However in reference to your last remarks, I would like to emphasize
 that the famous tanh-sinh quadrature method has been
available to Maxima users for a "long time".

 I posted the Ch.9, Maxima by Example, mbe9bfloat.pdf (see pp. 21-26),
in April, 2009, (with a long message to the mailing list) which is
 titled: "Bigfloats and Arbitrary Precision Quadrature", and section 9.3.3
 has a detailed discussion of the ideas behind the tanh-sinh method,
 and the Maxima implementation, with the Ch.9 file quad_ts.mac
 allowing Maxima users to try out this method with their integrals.

When posting recently the latest version of Ch. 8 and its new software
 files (as used below), I should have mentioned that the arbitrary precision
 functions apnint and apquad make use of the tanh-sinh method for
a finite domain, and the double exponential method (also available in
 Ch. 9 since 2009) for a non-finite domain.

An additional bigfloat quadrature method for a finite domain is
implemented in Ch 9: the bigfloat Gauss-Legendre method, see the
file quad_gs.mac and examples in the pdf file.
--------------------------------------------------------

Thanks for your feedback.

 I am going forward with a comparison of
the tanh-sinh bigfloat method, the Gauss-Legendre bigfloat method,
and the new bromberg method

Ted