Elementary linear algebra breaks down for so-called ill-conditioned problems
needing more precision than is provided by standard floating point numbers.
Condition number
|
| |
Condition number
The condition number is an application of the derivative, and is formally
defined as the value of the asymptotic... | |
|
Den 18:35 torsdag den 7. september 2017 skrev Marshall Lochbaum
<[email protected]>:
Primality testing is a much less common use case than you think, and in
fact I'm not aware of any use for extended-precision integers outside of
recreational mathematics (I guess you can count cryptography, but anyone
using extended-precision integers instead of large fixed-width integers
for that falls squarely on the recreational side as well). It would be a
poor choice to severely degrade J's performance to help out people doing
Project Euler problems.
Marshall
On Thu, Sep 07, 2017 at 12:54:58PM +0100, Rob B wrote:
> Thanks Raul, I am familiar with these ideas, and using x: is almost a reflex
> now.
>
> I feel that to protect the new J user, mod should convert to extended
> precision automatically or issue an warning message. Giving tha answer zero
> is very misleading.
>
> PS I am not so concerned with small numbers and measurability as with large
> numbers and primality. Heisenberg's Uncertainty Principle is not usually an
> issue for me :)
>
> Ragards, Rob.
>
> > On 7 Sep 2017, at 11:32, Raul Miller <[email protected]> wrote:
> >
> > The answer, oddly enough, is: yes.
> >
> > The philosophical arguments are buried here:
> >
> > https://en.wikipedia.org/wiki/Accuracy_and_precision
> >
> > The technical issues are buried here:
> >
> > https://en.wikipedia.org/wiki/IEEE_754
> >
> > That said, if you have reason to be using numbers which are precise
> > beyond anyone's ability to measure (and keep in mind Heisenberg
> > Uncertainty as one of the practical limits on measurability), you
> > should probably be using extended precision numbers (123x instead of
> > 123). This will give you exact results in exchange for a performance
> > penalty.
> >
> > Thanks,
> >
> > --
> > Raul
> >
> >
> >> On Thu, Sep 7, 2017 at 4:42 AM, Rob B <[email protected]> wrote:
> >> On reflection my real question is; should mod suddenly and without warning
> >> give the wrong answer when a number gets suffiently large? I have been
> >> caught by this many times. The incorrect answer zero is problematic as it
> >> suggests divisibility.
> >>
> >> Apologies if this has all been discussed before.
> >>
> >> Regards, Rob Burns.
> >>
> >>
> >>
> >>> On 6 Sep 2017, at 09:11, Rob B <[email protected]> wrote:
> >>>
> >>> Thanks,
> >>>
> >>> I now see it's reasonable for ^ to convert to flost and *: to remain
> >>> exact.
> >>>
> >>> The other discrepancy is probably due to my old version, iPad 701.
> >>>
> >>> Regards, Rob Burns.
> >>>
> >>>> On 5 Sep 2017, at 17:48, HenryRich <[email protected]> wrote:
> >>>>
> >>>> datatype 47^2
> >>>>
> >>>> floating
> >>>>
> >>>>
> >>>> So
> >>>>
> >>>> (n^2) | 5729082486784839
> >>>>
> >>>> is promoted to float, and loses precision. Same when the big number is
> >>>> extended - it's converted to float.
> >>>>
> >>>> For
> >>>>
> >>>> (x: n^2) | 5729082486784839
> >>>>
> >>>> I get 147 as the result.
> >>>>
> >>>> Henry Rich
> >>>>
> >>>>> On 9/5/2017 12:41 PM, Rob B wrote:
> >>>>> Could someone explain this please?
> >>>>>
> >>>>> n=.14
> >>>>> n
> >>>>> 14
> >>>>> (*: n) | 5729082486784839
> >>>>> 147
> >>>>> 196 | 5729082486784839
> >>>>> 147
> >>>>> (n^2) | 5729082486784839
> >>>>> 0
> >>>>> (n^2) | 5729082486784839x
> >>>>> 0
> >>>>> (x: n^2) | 5729082486784839
> >>>>> 0
> >>>>> (x: n^2) | 5729082486784839x
> >>>>> 147
> >>>>>
> >>>>>
> >>>>> Regards, Rob Burns
> >>>>> ----------------------------------------------------------------------
> >>>>> 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
> ----------------------------------------------------------------------
> 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
