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
