Here's the link to Aronson's essay http://www.scottaaronson.com/writings/bignumbers.html
Sent from my iPhone > On Feb 18, 2015, at 12:20 PM, "R.E. Boss" <[email protected]> wrote: > > 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
