Don, It's not just that giving an answer of zero instead of 147 is 'imprecise'. It is horribly wrong, as it implies divisibility where none exists.
Regards, Rob. > On 7 Sep 2017, at 18:40, Don Guinn <[email protected]> wrote: > > Never assume that floating point numbers are exact. > > On Sep 7, 2017 10:50 AM, "'Bo Jacoby' via Programming" < > [email protected]> 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 < >> [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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
