If you search for something like "GCD non-integer", you will probably get
ten or more pages of integer-only results. The one non-integer result I
found was a query about using Excel to do this that was closed for lack of
response.
Not that should deter us who seek to extend the concept but we are on new
ground in doing so.
On Sat, May 16, 2020 at 5:30 AM bill lam <bbill....@gmail.com> wrote:
> Do you have any reference that gcd is applicable beyond the context of
> inregers?
>
> On Sat, May 16, 2020 at 5:19 PM Hauke Rehr <hauke.r...@uni-jena.de> wrote:
>
> > wrong.
> >
> > first, gcd is a general concept, it’s nothing crafted but found
> > it was always there and not meant for anything in the first place
> > it applies to rational numbers just as fine and to any scaling
> > thereof. Mathematically, you get sane results working with gcd
> > on √2*ℚ, for example.
> >
> > second, the only if part is badly wrong, too.
> > +./ (, -) a
> > will work no matter a’s representation and not give an epsilon
> > (unless a an epsilon :-) to start with)
> >
> > Am 16.05.20 um 08:26 schrieb Raul Miller:
> > > GCD is meant for exact numbers.
> > >
> > > It works fine with fractions, IF (and only if) the numbers you are
> > > working with exactly represent the numbers you intend to manipulate.
> > > For binary floating point numbers this would be sums of powers of 2
> > > which do not exceed the precision of the representation (for current J
> > > on 64 bit machines: all divisors have to be powers of 2, you have 53
> > > bits of mantissa to work with and a limited range of exponents).
> > >
> > > 5r2 +. 7r2
> > > 1r2
> > > 2.5 +. 3.5
> > > 0.5
> > >
> > > Thanks,
> > >
> > >
> > > --
> > > Raul
> > >
> > > On Fri, May 15, 2020 at 11:17 PM bill lam <bbill....@gmail.com> wrote:
> > >>
> > >> Yes I agree GCD meant for whole numbers, so that +. on floating points
> > can
> > >> first convert to rational first and convert back to float afterwards
> > >> +./&.x: 4.57 4.34 4.44
> > >> 0.01
> > >> x: is clever enough to find the shortest form of rational equal to the
> > >> original floating number range
> > >> (3!:3) 4.5700000000000003
> > >>
> > >> e300000000000000
> > >> 0800000000000000
> > >> 0100000000000000
> > >> 0000000000000000
> > >> 48e17a14ae471240
> > >> (3!:3) 4.57
> > >> e300000000000000
> > >> 0800000000000000
> > >> 0100000000000000
> > >> 0000000000000000
> > >> 48e17a14ae471240
> > >> x: 4.5700000000000003
> > >> 457r100
> > >> x: 4.57
> > >> 457r100
> > >>
> > >> That said, I don't see any real benefit for change, if a user want
> > rational
> > >> number behavior, he/she can use the form
> > >> +./&.x:
> > >>
> > >>
> > >>
> > >> On Sat, May 16, 2020 at 7:18 AM Devon McCormick <devon...@gmail.com>
> > wrote:
> > >>
> > >>> Since, AFAIK, GCD was originally defined in the context of whole
> > numbers,
> > >>> you probably get what you deserve using it with non-integers.
> > >>>
> > >>> On Fri, May 15, 2020 at 7:04 PM Raul Miller <rauldmil...@gmail.com>
> > wrote:
> > >>>
> > >>>> It is odd, though, that even with comparison tolerance set to zero,
> +.
> > >>>> is not associative on fractional floating point values:
> > >>>>
> > >>>> 9!:19]0
> > >>>>
> > >>>> 0j16":,.+./4.57 4.34 4.44
> > >>>> 0.0000000000000036
> > >>>> 0j16":,.+./|.4.57 4.34 4.44
> > >>>> 0.0000000000290870
> > >>>>
> > >>>> It is commutative though:
> > >>>> (-:|:)+./@>{;~4.57 4.34 4.44
> > >>>> 1
> > >>>> 0j16":+./@>{;~4.57 4.34 4.44
> > >>>> 4.5700000000000003 0.0100000000000655 0.0099999999999758
> > >>>> 0.0100000000000655 4.3399999999999999 0.0200000000000466
> > >>>> 0.0099999999999758 0.0200000000000466 4.4400000000000004
> > >>>>
> > >>>> I'm not quite sure what's going on here... maybe a built in epsilon
> > >>>> which is independent of comparison tolerance?
> > >>>>
> > >>>> Thanks,
> > >>>>
> > >>>> --
> > >>>> Raul
> > >>>>
> > >>>> On Fri, May 15, 2020 at 6:53 PM Hauke Rehr <hauke.r...@uni-jena.de>
> > >>> wrote:
> > >>>>>
> > >>>>> In case you are willing to accept labelling it a problem.
> > >>>>>
> > >>>>> As I mentioned by altering the thread’s subject, yes,
> > >>>>> this ain’t a bug. But there may be an opportunity for
> > >>>>> improvement without sacrifice. Or so do I think.
> > >>>>>
> > >>>>>
> > >>>>> Am 16.05.20 um 00:49 schrieb 'Michael Day' via Programming:
> > >>>>>> Not a new "bug" - I've still got J503 for some reason - so:
> > >>>>>>
> > >>>>>> +./4.57 4.34 4.44
> > >>>>>> 5.39568e_12
> > >>>>>>
> > >>>>>> ABOUTJ_jijs_ NB. nearest thing to JVERSION???
> > >>>>>> Copyright 1994-2004 Jsoftware Inc.
> > >>>>>> For information about this and related products:
> > >>>>>>
> > >>>>>> Jsoftware Inc.
> > >>>>>> P.O. Box 330
> > >>>>>> Excelsior, MN 55331
> > >>>>>> tel: 952 470-7345 fax: 952 470-9202
> > >>>>>> www.jsoftware.com
> > >>>>>> i...@jsoftware.com
> > >>>>>>
> > >>>>>> As Devon and Henry suggest, it's the usual problem with "exact"
> > >>>>>> representation of reals.
> > >>>>>>
> > >>>>>> Mike
> > >>>>>>
> > >>>>>>
> > >>>>>>
> > >>>>>> On 15/05/2020 15:17, 'Bo Jacoby' via Programming wrote:
> > >>>>>>> +./4.57 4.34 4.44
> > >>>>>>> 5.39568e_12
> > >>>>>>>
> > >>>>>>> NB. this was not the correct answer. A bug?
> > >>>>>>>
> > >>>>>>> +./x:4.57 4.34 4.44
> > >>>>>>>
> > >>>>>>> 1r100
> > >>>>>>>
> > >>>>>>> NB. this was a work-around
> > >>>>>>> Thanks!
> > >>>>>>> Bo.
> > >>>>>>>
> > >>>>>>>
> > >>>>>>>
> > >>>>>>>
> > >>>>>>>
> > >>>
> ----------------------------------------------------------------------
> > >>>>>>> For information about J forums see
> > >>>> http://www.jsoftware.com/forums.htm
> > >>>>>>
> > >>>>>
> > >>>>> --
> > >>>>> ----------------------
> > >>>>> mail written using NEO
> > >>>>> neo-layout.org
> > >>>>>
> > >>>>>
> > ----------------------------------------------------------------------
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> > http://www.jsoftware.com/forums.htm
> > >>>>
> ----------------------------------------------------------------------
> > >>>> For information about J forums see
> > http://www.jsoftware.com/forums.htm
> > >>>>
> > >>>
> > >>>
> > >>> --
> > >>>
> > >>> Devon McCormick, CFA
> > >>>
> > >>> Quantitative Consultant
> > >>>
> ----------------------------------------------------------------------
> > >>> For information about J forums see
> http://www.jsoftware.com/forums.htm
> > >>>
> > >> ----------------------------------------------------------------------
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> > >
> >
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> >
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>
--
Devon McCormick, CFA
Quantitative Consultant
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