On Tuesday, October 29, 2013 1:48:55 PM UTC+1, vdelecroix wrote: > > I do not see why RIF might be slower than RR. By construction, RIF is > a pair of real numbers. For arithmetic involving only +,-,*,/ we > should get a ratio of 2 for the execution time because all rounding > are implemented in the CPU (is that true ? perhaps changing the > rounding often makes it slower). Do you have timings ? Having a pair > (value, error) should really be the same timing as RIF except that > your resulting error would be larger. > See http://fredrikj.net/blog/2013/10/tradeoffs-in-ball-arithmetic/ for some jsutification on such a reprensentation.
> > That being said, and if you care about good error bounds and as far as > I understand, RIF is not well suited for polynomial or serie > evaluation. See for example my question in [1]. > > Best, > Vincent > > [1] > http://ask.sagemath.org/question/2415/polynomial-and-interval-arithmetic > > 2013/10/29, Volker Braun <[email protected] <javascript:>>: > > This is called ball arithmetic and was jut implemented in FLINT by > Fredrik > > Johannson, > > e.g. http://fredrikj.net/blog/2012/04/high-precision-ball-arithmetic/. > I > > talked to him at the recent LMFDB workshop in Bristol and he thinks that > it > > > > is ready for production. We should definitely wrap it ;-) > > > > > > > > On Tuesday, October 29, 2013 11:26:50 AM UTC, Jeroen Demeyer wrote: > >> > >> At #15299, we need to compute some series and we also want an error > >> bound on the result. Normally, interval arithmetic should be ideal for > >> this, but unfortunately RealIntervalField() is quite a bit slower than > >> RealField(). So I'm thinking about creating a faster (but more naive) > >> version of RIF, which internally computes with (value,error) pairs. We > >> obviously still want rigorous error bounds, but in the end result, the > >> error might be bigger than what true interval arithmetic would give. > >> > >> Is this desirable or is it a bad idea? > >> > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to [email protected] <javascript:>. > > To post to this group, send email to > > [email protected]<javascript:>. > > > Visit this group at http://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
