On 02/16/2010 02:39 PM, Christoph Groth wrote: > Andrew Haley <aph@xxxxxxxxxx> writes: > >> I've just checked, and the 64-bit glibc version of sincos does indeed >> do >> >> ENTRY (BP_SYM (__sincos)) >> ENTER >> >> movsd %xmm0, -8(%rsp) >> fldl -8(%rsp) >> fsincos >> ... > > Thank you all very much for clarifying this issue. I am very much > surprised that x87 instructions behave differently on AMD and Intel > processors but this seems indeed to be the case. I don't know why you're surprised; I'm not. ;-) AMD and Intel processors use different algorithms for transcendental functions, and different Intel processors may not return the same results. The usual guarantee is not correctly rounded results, but to specify some accuracy, often 1ulp (Unit in the Last Place). Correctly rounded sines and cosines require extended intermediate precision, and in a few cases enormously extended intermediate precision. So, accurate routines can be slow. There is active research in this area, in particular Jean-Michel Muller's group at Lyon (http://perso.ens-lyon.fr/jean-michel.muller/publications.html) They have been working on making correctly-rounded algorithms that are fast enough to be used everywhere, so in the future correct rounding may be the norm. > I found the following article (especially section 4.1) helpful: > > D. Monniaux, "The Pitfalls of Verifying Floating-Point Computations", > http://dx.doi.org/10.1145/1353445%2E1353446 cf. http://docs.sun.com/source/806-3568/ncg_goldberg.html BTW, if your Monte Carlo simulation is affected by such tiny differences in transcendentals, then your simulation really is broken! Andrew.
