On Monday 26 February 2007 7:18 pm, Robert Bradshaw wrote: > Shouldn't the error on a quad double be way smaller than this? I'm > not sure what specific numbers you're operating on, but if your > answers are on the order of 10^0, then shouldn't you have around 63 > decimal digits of accuracy, rather than just 4 more orders of > magnitude? Wouldn't an error of 1e-17 be like using mpfr with ~60+ bits?
Yeah, I really don't get it. Quad double should give results correct to (nearly) 212 bits, or what is the point of using quad double at all? Something really funny is going on. > I guess what I'd like to see to understand this better is the > absolute magnitude of cos(1) between rdf, qr, mpfr(212), and mpfr(1000). > > On Feb 26, 2007, at 7:07 PM, didier deshommes wrote: > > How accurate are these results? The error is quite small and more > > accurate than computing with ieee doubles (most of the time, about 4 > > orders of magnitude). Here: > > -- "mpfr vs qd " is the absolute error between a quad double and mpfr > > real, and > > -- "mpfr vs rd" is the absolute error in between a real double and > > mpfr real: > > > > cos: > > mpfr vs qd: 5.4180459105735642433E-17 > > mpfr vs rd: 3.57935903139e-13 > > > > sin: > > mpfr vs qd : 4.9262450620608075647E-17 > > mpfr vs rd :4.22384349719e-13 > > > > tan: > > mpfr vs qd : 1.0996009735470526760E-16 > > mpfr vs rd : 1.37401201528e-12 > > > > acos: > > mpfr vs qd : 1.0587913940429450042E-16 > > mpfr vs rd : 1.95518601309e-12 > > > > asin: > > mpfr vs qd : 8.8793698896573320837E-17 > > mpfr vs rd : 1.95532479097e-12 > > > > atan: > > mpfr vs qd : 4.2348407244178416828E-17 > > mpfr vs rd : 4.09228206877e-13 > > > > cosh: > > mpfr vs qd : 1.1001972366209892607E-16 > > mpfr vs rd : 4.91606755304e-13 > > > > sinh: > > mpfr vs qd : 7.7307263905133232438E-17 > > mpfr vs rd : 6.54809539924e-13 > > > > tanh: > > mpfr vs qd : 5.0901691104837936913E-17 > > mpfr vs rd : 4.08617584213e-13 > > > > cosh: > > mpfr vs qd NAN > > mpfr vs rd nan > > > > sinh: > > mpfr vs qd : 5.0731042379144584142E-17 > > mpfr vs rd : 4.23105994685e-13 > > > > tanh: > > mpfr vs qd : 1.9007614867237325552E-16 > > mpfr vs rd : 8.84181616811e-12 > > ###################### > > > > In conclusion: > > In most cases it is faster to compute with quad double reals instead > > of using mpfr reals at 212 bits. In all cases quad doubles are more > > accurate than simple ieee doubles. > > > > didier > > -- William Stein Associate Professor of Mathematics University of Washington --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
