Accurate Bernoulli numbers on the 41C, or "how close can you get"?

03202014, 09:07 PM
(This post was last modified: 03202014 09:14 PM by Dieter.)
Post: #24




RE: Accurate Bernoulli numbers on the 41C, or "how close can you get"?
(03202014 02:21 PM)Ángel Martin Wrote: Believe it or not I typed the wrong value before. The result from ICPF is as follows: That looks much better. ;) Of course I did not assume that the Sandmath function would return a result with an error as large as in the previous value. BTW my current FOCAL program on a standard V41 runs in about 4,5 seconds. (03202014 02:21 PM)Ángel Martin Wrote: Yes it is a polynomial approximation, two to be precise depending on the region. Polynomials are very nice in compiled computer languages where it does not matter whether a constant has 2 or 15 digits, but on a calculator every single digit requires at least one byte of memory. I remember that some time ago I set up two rational approximations for the HP67/97 where the coefficients were kept in the primary and secondary registers which may be stored on a data card. ;) Multidigit numeric constants in user code tend to slow down program execution, even on a HP41 where every value fits in a single line. On the other hand the method is very straightforward and fast by design. I just found an earlier HP41 program for the Normal quantile that uses two rational approximations. It runs in about 6 seconds (in FOCAL) for any input value on a hardware HP41. BTW, if you are interested in rational approximations for the Normal quantile (or its evaluation in general) I can recommend the papers by W. T. Shaw. Several PDFs are available. Dieter 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)