On 02/17/2010 02:30 PM, Vincent Lefevre wrote: > On 2010-02-16 09:14:58 +0100, Christoph Groth wrote: >> I am aware of the limited precision of floating point calculations. >> However, I assumed that on the processors in question these calculations >> are done according to IEEE standards, i.e. the results of are defined >> unambiguously. > > Note that the old IEEE 754-1985 standard didn't consider elementary > functions such as sin and cos (only +, -, *, / and square root). > The current IEEE 754-2008 standard recommends that (some) elementary > functions be correctly rounded, but that's only a recommendation. Aha, Vincent Lefèvre from Lyon! Thanks for posting. What is the current state of libraries for correctly rounded functions? The main paper I see on making this faster dates from November 1998, although there is [2], not online. Are we in a position where we can use something faster than the IBM Accurate Mathematical Library? Thanks, Andrew. [1] V. Lefevre, J.M. Muller and A. Tisserand, Toward Correctly Rounded Transcendentals, IEEE Transactions on Computers, Vol. 47 No 11, Nov. 1998. http://perso.ens-lyon.fr/jean-michel.muller/Nov98.pdf [2] C. Daramy, D. Defour, F. de Dinechin and J.M. Muller, CR-LIBM: a correctly rounded elementary function library, SPIE 48th Annual Meeting International Symposium on Optical Science and Technology, San Diego, USA, Aug 3-8, 2003.
