Never assume that floating point numbers are exact. On Sep 7, 2017 10:50 AM, "'Bo Jacoby' via Programming" < programm...@jsoftware.com> wrote:
> 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 < > mwlochb...@gmail.com>: > > > 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 <rauldmil...@gmail.com> 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 <rb75...@me.com> 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 <rb75...@icloud.com> 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 <henryhr...@gmail.com> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
