Raul Miller wrote: > On 4/24/07, John Randall <[EMAIL PROTECTED]> wrote: > >> We could argue endlessly about the details of the example. It >> obviously did not impress you. > > Right -- it did not impress me because it left out so many details > about what is supposed to be going on here, and why I should > expect different behavior. > >> Its intended audience is people doing scientific computation, where >> solutions to differential equations (like streamlines) are commonplace. >> People using complex numbers expect them to work correctly in >> standard scenarios, such as conformal mappings of boundary value >> problems. > > Ok. If you believe this topic should not be approached by a person > without that background, I guess I should not post further on this topic. > (Though I might if I find what I feel is an elegant way of finding these > streamlines without the artifacts you've mentioned here.) >
I am by no means warning you off. I am just trying to explain that this sort of problem is important to people who care about floating-point and complex arithmetic, that they are the audience, and they might be reasonably be expected to appreciate the example with little preamble. I agree that Kahan's does not explain as much as he might, and that his style can come across as ranting. > I am not completely convinced that an alternate representation couldn't > also address the issue of which branch point value is desired from the > function range. > I agree an alternative approach could work. However, the scenario in which a region is transformed so that part of its boundary is a branch cut is both common and the place for maximal error as you approach the boundary. The inclusion of +/-0 in the IEEE standard was inspired by this kind of consideration, and Kahan is apoplectic that it is ignored in many languages used for numerical analysis, despite hardware support. Having language support for this eliminates a lot of work-arounds and naive errors. It is impossible to get a perfect model of the complex numbers on a computer. Kahan's suggestion addresses an important recurring problem. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
