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 > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
