Torture tests: what do they mean?

[HP67]

(05-14-2014 11:55 PM)Paul Dale Wrote:  I've posted this list before but here are some good texts on numeric mathematics:

Thanks, that looks like a great list. Is there not one go-to book that covers the issues of accuracy and precision in implementations? Otherwise it looks like it could take a decade to absorb all this info.

(05-14-2014 08:58 PM)jebem Wrote:  I'm digging the WWW now for calculator algorithms. Starting from the basics: Alan Sultan explain the CORDIC. Nice reading.
http://www.qc.cuny.edu/Academics/Degrees...ultan1.pdf

Thanks for the link. I have heard of this before. I can't remember where.

(05-14-2014 09:39 PM)Jim Horn Wrote:  Alan Sultan's CORDIC article is a fine introduction. It misses one important simplification, though - instead of multiplying the result of the rotations by K, you can start with (K,0) as the initial vector. Then *no* multiplication is needed other than the binary shifts and adds. This was covered in the HP Journal article on the HP35 algorithms. Pretty nifty!

Thank you. I have the HP Journals. It's been a while but I seem to remember I was disappointed but not surprised that they seemed to give a good overview but left out some important details about how things were actually implemented. I'll put this on the list to go over again at some point.

(05-14-2014 10:31 PM)jebem Wrote:  Thanks for all people sharing their knowledge and thoughts here (so far: Paul, Pauli, David, Pauli, Dieter, HP67, Manolo, Jim). I'm learning a lot from you, as I'm not a mathematician by education, but I have the basics to follow what is being said.

I have nothing to share on this topic but I echo your thanks to all the guys on the forum including you, for sharing your knowledge.

(05-14-2014 10:31 PM)jebem Wrote:  What algorithms are in use at hardware and software level, that combined, can support our trigonometric functions?
Do they still maintain secrecy after all this years?

I think hardware implementations of decimal floating point have been a big bang that has been mostly overlooked. This seems to be something targeted at a fairly narrow range of problems but dealing with the important topic of money. There is a lot of good info at Mike Colishaw's Floating Point Decimal Pages. IBM has published a lot of information on this and the implementations are described in an architectural document. But this whole thing does not apply much to general scientific computation as far as I know since there are already binary and hex floating point hardware implementations for those topics and obviously IEEE binary FP is the main target for the majority of software implementations. Still, it's interesting to note all the developments and that things are moving right along in many areas. There is a lot of doc and some important software here like the arbitrary precision decimal reference implementation with full doc on the algorithms. Even IBM seems more open these days.

(05-14-2014 10:31 PM)jebem Wrote:  I know that 50 years is just a time tick in science. Technology is a different matter, however.

That seems to be the issue and we talked about it in other threads. The software and the advances in science behind the software have not kept pace with the advances in technology (hardware). As you alluded to, this is just the way things seem to work and nobody seems to be able to get around it.