((2x&*) &1) 3 8 ((2x&*)^:3) 1 8 ((3x&*) &1) 2 9 ((3x&*)^:2) 1 9
Does dissect http://www.jsoftware.com/jwiki/action/show/Vocabulary/Dissect?action=show&redirect=Addons%2Fdebug%2Fdissect help to follow the execution of the sentences? On Wed, Feb 18, 2015 at 4:14 PM, 'Pascal Jasmin' via Programming < [email protected]> wrote: > I don't follow this completely either. Though I am pretty sure the answer > is rooted in applying a bonded verb dyadically. > > see right and bottom of: > > http://www.jsoftware.com/help/dictionary/d630n.htm > > > > > > ----- Original Message ----- > From: Fausto Saporito <[email protected]> > To: programming <[email protected]> > Cc: > Sent: Wednesday, February 18, 2015 1:00 PM > Subject: Re: [Jprogramming] Fwd: Hello all! > > Hello, > > just a clarification about the "up" verb defined above. > I know "&" is a conjuction bond, used for example in expressions like > "10^&"... but I don't understand the "&1" format ... > > Please could you explain this ? > > thanks > Fausto > > > > 2015-02-18 18:29 GMT+01:00 Fausto Saporito <[email protected]>: > > yes... there's also another definition (recursive) called hyperoperation. > > > > https://en.wikipedia.org/wiki/Hyperoperation > > > > > > > > 2015-02-18 18:20 GMT+01:00 R.E. Boss <[email protected]>: > >> Link? > >> > >> Notice that Conway (who else?) in The Book of Numbers wrote a > generalization > >> of Knuth's up-notation (actually the Ackermann notation), his chained > arrow > >> notation. > >> > >> > >> R.E. Boss > >> > >> > >>> -----Original Message----- > >>> From: [email protected] [mailto:programming- > >>> [email protected]] On Behalf Of John Baker > >>> Sent: woensdag 18 februari 2015 16:15 > >>> To: [email protected] > >>> Subject: Re: [Jprogramming] Fwd: Hello all! > >>> > >>> Very slick. I was just reading Scott Aronson's fine blog post about the > >> Busy > >>> Beaver problem and he commented on Knuth's up up notation. If anyone's > >>> interested in very large numbers Aronson's post is a superb overview. > >>> > >>> Sent from my iPhone > >>> > >>> > On Feb 17, 2015, at 3:05 PM, Jose Mario Quintana > >>> <[email protected]> wrote: > >>> > > >>> > 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 > >>> > > >>> 2003529930406846464979072351560255750447825475569751419265016973710 > >>> 8940595563114530895061308809333481010382343429072631818229493821188 > >>> 1266886950636476154702916504187191635158796634721944293092798208430 > >>> 9104855990570159318959639524863372367203002916969... > >>> > > >>> > # @: ": 2x Knuth up up 5 > >>> > 19729 > >>> > > >>> > 6x Knuth up up 3 > >>> > > >>> 2659119772153226779682489404387918594905342200269924300660432789497 > >>> 0735598738829091213422929061755830324406828265067234256016357755902 > >>> 7938964261261109302039893034777446061389442537960087466214788422902 > >>> 2133853819192905427915750759274952935109319020362271989... > >>> > #@: ": 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) > >>> >> > >>> >> > >>> >> > >>> 2003529930406846464979072351560255750447825475569751419265016973710 > >>> 8940595563114530895061308809333481010382343429072631818229493821188 > >>> 1266886950636476154702916504187191635158796634721944293092798208430 > >>> 9104855990570159318959639524863372367203002916969592156... > >>> >> > >>> >> ^/ 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 > >>> ---------------------------------------------------------------------- > >>> 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
