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[34S] Time diff. STO.00 vs. STO 00 ?
03-13-2014, 09:53 PM
Post: #19
RE: [34S] Time diff. STO.00 vs. STO 00 ?
(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
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RE: [34S] Time diff. STO.00 vs. STO 00 ? - Paul Dale - 03-13-2014 09:53 PM

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