This a way to produce numbers using the Knuth up arrow notation in J: Knuth=. &* NB. (adv) up=. &1 NB. (adv)
2x Knuth up up 4 5 65536 2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348101038234342907263181822949382118812668869506364761547029165041871916351587966347219442930927982084309104855990570159318959639524863372367203002916969... # @: ": 2x Knuth up up 5 19729 6x Knuth up up 3 2659119772153226779682489404387918594905342200269924300660432789497073559873882909121342292906175583032440682826506723425601635775590279389642612611093020398930347774460613894425379600874662147884229022133853819192905427915750759274952935109319020362271989... #@: ": 6x Knuth up up 3 36306 3x Knuth up up up 0 1 2 1 3 7625597484987 2x Knuth up up 6 NB. It is toooooooooooo big! On Tue, Feb 17, 2015 at 2:23 PM, Fausto Saporito <[email protected]> wrote: > Hello, > > yes the number is very big, but why if I don't use the extended > precision I have "infinity" as result, and if I use it I got an error > ? > > I should get infinity anyways. > > this is my J session: > > ^/ 2 2 2 2 > > 65536 > > ^/ 2 2 2 2 2 NB. do not use extended precision and I have "+inf" > > _ > > ^/ 2 2 2 2 2 2 NB. do not use extended precision and I have "+inf" > > _ > > ^/ x: 2 2 2 2 2 NB. using extended precision I have the result (part of > it) > > > 2003529930406846464979072351560255750447825475569751419265016973710894059556311453089506130880933348101038234342907263181822949382118812668869506364761547029165041871916351587966347219442930927982084309104855990570159318959639524863372367203002916969592156... > > ^/ x: 2 2 2 2 2 2 NB. using extended precision I have error... not "+inf" > > |limit error > > | ^/x:2 2 2 2 2 2 > > https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation > > thanks, > Fausto > > 2015-02-17 18:55 GMT+01:00 'Pascal Jasmin' via Programming > <[email protected]>: > > 2 ^. ^/ 5 # 2x > > 65536 > > > > so at just 5, it is a 65k bit number > > > > at 6, the 2log of that number would be that 65kbit number. The number > of atoms in the universe is an 80 bit number. > > > > > > > > > > > > ----- Original Message ----- > > From: Raul Miller <[email protected]> > > To: Programming forum <[email protected]> > > Cc: > > Sent: Tuesday, February 17, 2015 12:32 PM > > Subject: Re: [Jprogramming] Fwd: Hello all! > > > > I would guess that the number you are generating is too big to be > > represented using J's data structures (which would also suggest that > > it would be too big to fit into memory). > > > > Thanks, > > > > -- > > Raul > > > > On Tue, Feb 17, 2015 at 12:12 PM, Fausto Saporito > > <[email protected]> wrote: > >> HI! > >> > >> I'm a new J user with a little experience of APL and LISP. > >> > >> In these days I'm playing with big numbers... very big indeed, and I > >> found a bug (?) in the exteded precision implementation of J. > >> > >> I'm not sure if I can call it a bug, but if I use the standard > >> precision number I got a "infinity" as result... as should be. > >> > >> I'm talking about knuth-up-arrow notation, to build the "tower of > >> power". In J the syntax is amazingly simple : ^/ 2 2 2 2 > >> > >> 2^^4 is 2 * (2* (2* 2)) = 65536 > >> > >> Now 2^^5 is _ with standard precision... but if I use x: (i.e. ^/ x: > >> 2 2 2 2 2) can get most of number... it's quite big indeed. > >> > >> The problem arises with 2^^6 or 3^^4 I get "limit error" instead of _ > ... why ? > >> > >> Is it an expected behaviour ? > >> > >> thanks in advance, > >> Fausto > >> ---------------------------------------------------------------------- > >> 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
