[34S] Time diff. STO.00 vs. STO 00 ?

[Sikuq]

(03-13-2014 09:53 PM)Paul Dale Wrote:  

(03-13-2014 09:20 PM)Sikuq Wrote:  However I always wondered just how the 34S actually calculates say a square root or the Gamma function. Does it use a power series, other basic functions, or say Fourier? And did you get those functions from somewhere else and just compiled them in there?

Square root, the four arithmetic operations, natural logarithm and exponential are included in the decNumber library we used. I replaced the natural logarithm (twice) because the supplied version was unacceptably slow, I'm still not entirely happy with its performance. For reference, square root uses Newton's method after an initial guess -- this is a fairly standard technique.

Pretty much everything else I wrote after finding suitable standard algorithms or in a couple of cases doing my own expansions. As an example of the former, the gamma function uses a rapidly converging series -- unfortunately I don't remember the source I used, but I will have the original paper stored away somewhere. I ended up purchasing a not-insignificant number of books about numeric analysis and transcendental function implementation and spent lots of time searching the Internet for suitable algorithms.

If you look in doc/formulas there are some erratic notes about what I used where and doc/distribution-formulas contains a longish exchange between Dieter and others giving incremental improvements to the statistical distributions. These documents were primarily for my use and aren't well organised but I figured some record was better than none.

Finally, a few of the functions have been examined in detail by members of this forum and sometimes, changes and improvements have been added. For example, Dieter's work on getting the Lambert W function accurate.


- Pauli

Pauli,

Despite Walter's possible consternation I allow myself to re-quote you fully. Your post is so profoundly interesting to me and I am sure most other 34S users that it would be a shame to truncate it. I wish I had had the knowledge and involvement at that time to experience what I can only describe and imagine as a transcontinental total brainstorming which at times lead to Nobel Prizes. I can vividly imagine your discussions as to size, accuracy, speed, convergence, etc. I never did know that you guys were so involved at that fundamental level. My interest in this topic has boosted and I must look into your sources and elsewhere.

Years ago I did my own simple Newton-Raphson and secant method solve routine on my HP41C and I remember it was sometimes calculating overnight before it printed out on my small HP thermal printer. I did have two of the HP 41C IL-Loop tape drives but I can't remember if I involved those. I was solving some huge complicated Gamma functions. One of my problems was to discern which of the multiple solutions were legitimate. I still have problems with those issues; I can never make up my mind as I have often been unable to establish a delimiting criteria for solution detection. Thus I often worry about the consequences of the solution I let go of coming home to roost.

I'm going to have a sleepless night thinking about your exciting endeavors.

- Sikuq