Re: [Maxima-discuss] e, pi, gamma, log(2)

[Henry B. <hb...@pi...>]

I don't know whether my problem is connected with e, pi, gamma, log(2), or not, but
when I was recently working with cdf_normal, cdf_logistic & friends, I noticed that
some of the numerical functions weren't terribly accurate in the long tails.  I also
tried bfloat, and that didn't improve matters, so I suspect that some of these
functions need some numerical approximation work.

Two of the functions I was using were quantile_logistic and quantile_normal.

The accuracy was good enough for what I was doing (4-5 decimal places), but
I was getting what looked like non-monotonic results in some lower order digits.

I haven't the slightest idea how these functions are computed in Maxima, but
perhaps a few 20-30 digit spot checks by someone who knows this stuff might be
in order.

At 11:35 AM 9/19/2014, Raymond Toy wrote:
>>>>>> "Volker" == Volker van Nek <vol...@gm...> writes:
>
>    Volker> Greetings.
>    Volker> I attached new implementations of float.lisp/fpe1, fppi1, fpgamma1,
>    Volker> comp-log2 as a proposal.
>
>    Volker> I discovered a paper by Bruno Haible and Thomas Papanikolaou about the
>    Volker> technique of binary splitting to approximate infinite series.
>    Volker> See http://www.ginac.de/CLN/binsplit.pdf for details if you are interested.
>
>    Volker> With this technique I succeeded in implementing fast functions for
>    Volker> computing %e, %pi, %gamma and log(2).
>
>    Volker> [ I also implemented exp(x), log(x), sin(x) and friends for bigfloat x.
>    Volker> In contrast to fpe1, .. these implementions are still some kind of raw
>    Volker> material and need more error analysis. And of course it's a lot more
>    Volker> difficult to merge them into Maxima. My idea is to put them into
>    Volker> /share/contrib for now. ]
>
>Is there something wrong with the current implementations of these functions?
>
>Ray