In these slides (Ulrich) Kulisch was mentioned from which I downloaded a recent paper "Up-to-date Interval Arithmetic: From Closed Intervals to Connected Sets of Real Numbers" (2016). Anyone interested for a digital copy, contact me off-forum.
R.E. Boss > -----Original Message----- > From: Chat [mailto:[email protected]] On Behalf Of Jo > van Schalkwyk > Sent: donderdag 28 april 2016 9:50 > To: [email protected] > Subject: Re: [Jchat] Unum, new number format > > Umm, Raul, I've had a glance at some of the documentation and I'm not sure > you're right here. Check out: > > http://arith22.gforge.inria.fr/slides/06-gustafson.pdf > > The bit on "The Wrath of Kahan" struck me as fairly convincing. > > My 2c, Jo. > > On 28 April 2016 at 16:58, Raul Miller <[email protected]> wrote: > > > When I run through my head examples of how that would work in > > algorithms I have worked on, it seems to me that it (a) it starts out > > with less precision than floating point (because of the extra bits > > being used for representing an estimate of accuracy), and (b) that it > > would tend to also lose precision faster (because it started out with > > less, so the fractional bits being lost are more significant). > > > > Put differently: as long as (a) this representation stays close to > > original data, and (b) the people using it understand in detail how it > > works, it will probably be ok. But run this through a lengthy sequence > > of calculations and it'll mess up faster than floating point. > > > > Put differently: I prefer J's approach of providing ":!.precision (or > > 9!:11) over these things. > > > > That said, running through the calculation once using unums (to get a > > precision estimate) and then running through it again using floating > > point (to get a more precise result) might be a useful approach (for > > applications where the factor of 2 time and space cost is acceptable). > > > > That said, it is fun reading about how other people think about these > > things. > > > > Then again, there presumably must be applications where unums are a > > better fit than floating point? (I just don't know much about what > > those might be, off the top of my head.) > > > > -- > > Raul > > > > > > > > On Wed, Apr 27, 2016 at 11:36 PM, 'Jon Hough' via Chat > > <[email protected]> wrote: > > > This interview is pretty interesting, about a new number format that > > will solve floating point related errors: > > > http://ubiquity.acm.org/article.cfm?id=2913029 > > > > > > see also: > > http://motherboard.vice.com/read/a-new-number-format-for- > computers-could-nuke-approximation-errors-for-good > > > > > > I wonder about a J implementation of unums... ...it seems Julia (among > > others) has one > > > https://github.com/REX-Computing/unumjl > > > > > > ---------------------------------------------------------------------- > > > For information about J forums see > http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see > http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
