[WP34s] Regularized incomplete Beta function

[Paul Dale]

(05-02-2014 09:03 PM)Dieter Wrote:  While we're at it: I did some tests with the Student and Chi² quantile functions and found some cases that IMHO require too much time before they return a result. 15 seconds (or more than a minute in single cases) can be vastly improved. For instance with a Halley-solver (at least for these two distributions, the second derivative can be easily obtained) and a shorter (yet accurate) way of estimating a first guess for the Student quantile (even without slow logs ;-)). All in all, usually not more than three iterations or 2 to 5 seconds are required for 30+ digit accuracy. In user code, that is. Now imagine how fast this would run in compiled C code.

I can only agree with you here. I'm using a fairly generic Newton based solver for all the quantile functions except the normal QF. I know it can be very slow, that is the price for having a single general solver.

The 34S certainly doesn't have space for a C implementation of these. I originally implemented all the distribution functions in C but had to rewrite them as keystroke programs for space reasons. Adding additional custom solvers is likewise going to consume precious bytes. Thus, the 34S is unlikely to see any distribution speed ups. However, the 31S quite possibly will. I'd like to rewrite the distribution code there in native C -- I can't just drop in the original distribution code, we moved on algorithmically.

So, yes I'd love to hear your thoughts on improving these functions.


- Pauli