2013/10/29, Jean-Pierre Flori <jpfl...@gmail.com>: > > > 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.
Thanks for the pointer. He agrees with me: interval arithmetic is x2. But, as I did not notice, ball arithmetic might be x(1+epsilon) as the precision of the interval might be small compared to the precision of the center. >> 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 <vbrau...@gmail.com <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 sage-devel+...@googlegroups.com <javascript:>. >> > To post to this group, send email to >> > sage-...@googlegroups.com<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 sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > 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 sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
