On Sat, 2007-11-10 at 01:29 +0100, Daniel Fischer wrote:
The above essay was written after much experimentation using the MPFR library for correctly-rounded arbitrary-precision floating point, as exposed in the Sage computer algebra system.
Carl Witty
Thanks a lot.
Since you seem to know a lot about these things, out of curiosity, do you know how these functions are actually implemented? Do they use Taylor series or other techniques?
I don't really know that much about it; I just understand that the floating-point numbers are really rational numbers of a particular form, and I know how to use MPFR (via Sage) to play with these rational numbers. The idea to try higher-precision approximations of pi as approx_pi came from the link Dan Piponi posted, to http://blogs.sun.com/jag/entry/transcendental_meditation . Given that our numbers match the "bad" number from that blog post, I assume that sin is actually implemented as the fsin machine instruction. :) It seems likely that this instruction (and library implementations on architectures where sin is not built into the processor) use Taylor series, but I don't know for sure. Carl Witty