On Apr 30, 3:03 am, Bill Hart <[EMAIL PROTECTED]> wrote: > Paul Zimmermann commented to me that he doubts qd has proofs of > correctness associated with it, as mpfr does. > > The main advantage of qd is that it is a fixed precision package, > which is faster than multiprecision but subject to overflow if not > used correctly. > > If a port of mpfr were created to be built on the new fmpz type in the > mpir package we want to create to replace GMP, arithmetic for small > floats may be considerably faster, but in general you will never beat > a fixed precision package for small precision. Someone ought to figure/ > find out which parts of qd have proofs available and write them for > the cases where they are not. Writing proofs for the transcendental > functions may be quite hard, but it should be straightforward to > produce them for the basic arithmetic operations, and indeed this is > what we should be using qd for in SAGE in my opinion. > > Often getting a few extra bits of precision can add nearly a factor of > two in time since the number of branches and floating point operations > essentially doubles. This also happens in the use of floating point to > do precomputed inverses, as happens in FLINT. Packages can offer both > options if this is practical, but this is not a matter of errors vs > speed. It is a matter of required precision vs speed. > > Bill. > > On 29 Apr, 15:41, "William Stein" <[EMAIL PROTECTED]> wrote: > > > On Tue, Apr 29, 2008 at 1:46 AM, mabshoff > > > <[EMAIL PROTECTED]> wrote: > > > > On Apr 29, 10:33 am, Francois <[EMAIL PROTECTED]> wrote: > > > <SNIP> > > > > Hi Francois, > > > > > > Once you get some answer from upstream please open a ticket. I find > > > it > > > > > odd that the defaults are this way to say the least. > > > > > I did email the author about the precision here is what he has to say: > > > > > For ieee-add, it all depends on what kind of error bound you need. > > > > If enabled, the error satisfies > > > > > |e| <= |a+b| * epsilon > > > > > It not enabled, the error satisfies > > > > > |e| <= epsilon * max (|a|, |b|) > > > > > For most uses the second one is just fine, but some times one needs > > > > the > > > > first one. > > > > > Sloppy-mul and sloppy div usually degrades by few bits, so maybe you > > > > lose a digit of accuracy. For double-double, the degredation is > > > > smaller. > > > > Ok. Thanks for finding out. > > > > > ================ > > > > The answer is not qualified by processors. He didn't say anything > > > > about performance (I asked). > > > > Ok. Is there anybody out there who can run some quick test with a > > > decent runtime using quaddouble only in a tight loop, preferably in > > > pure C? We can pay in credit ;) > > > By the way, my understanding is that by far the main advantage of > > quaddouble over mpfr is that it uses a very simple data structure, > > which makes quaddouble more suitable for numerical linear algebra and > > applications that involve supercomputing. > > > -- William
If you read the pdf document that comes with qd it states in chapter 9, that they don't have a proof of correctness for the basic routines. They rely on an assumption that has apparently not been proved to be valid. The document includes a proof on the error bound of the quad-double addition. Francois --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
