Torture tests: what do they mean?

[DavidM]

(05-14-2014 06:19 AM)HP67 Wrote:  Where can one learn about this? Some of you guys seem to really understand this well and it is an interesting topic I would like to know more about.

By no means would I consider myself in the category of those who understand this well, but I'm at least aware enough of it to be suspicious whenever discussions about disparate results from different platforms come up. It's no small coincidence that the "targeted values" of these functions are almost always chosen to be near points of inflection, infinity, discontinuities, extremes, etc., because differences in implementation will more often be magnified in those areas.

To me, the more subtle and somewhat philosophical issue is that of how "internal" numbers are displayed when not in an exact/CAS mode. If you divide 1 by 3 on your favorite calculator, then multiply that result by 3 again, what should the result be? There are valid arguments for and against implementations with different answers to that question. Knowing how your chosen platform responds to that type of sequence can make a difference in how you approach a solution in some cases.

(05-14-2014 06:30 AM)Paul Dale Wrote:  The difference for fifteen digits from the above is that 1.57079632679489 isn't correctly rounded

Indeed! Interesting (though contrived) example of how small differences in implementation can sometimes result in large numerical differences.

(05-14-2014 06:30 AM)Paul Dale Wrote:  As Deiter wrote, we're really in a steep part of the tan function here.

Which is no accident. We were intentionally taken there by the designer of the test.