And Florian Oswald writes: > I would have never guessed that there could be a fast/slow > issue with such basic functions. Little do I know!
See also Jean-Michel Muller's text on "Elementary Functions, Algorithms and Implementation" and others (including, imho, Markstein's "IA-64 and Elementary Functions: Speed and Precision" for very concrete descriptions of trade-offs on one (possibly odd) architecture). It'd be fantastic if something like the NIST Digital Library of Mathematical Functions (http://dlmf.nist.gov/) discussed more of the computational trade-offs, but there are the dual issues of funding and the slow deterioration of knowledge. There might be a role for a high-performance, high-level, free language like Julia here. A few people have made routines dependable enough that few people worry. While this is good for general use, it creates a difficult position for continuing the knowledge. I know that I don't have it...
