I actually made a video for Pi day showing this technique and the various adjustments you need to make to get pi in an extended form from its original float representation.
https://youtu.be/vyILnD0e2IE Cheers, bob > On May 15, 2022, at 07:12, Jan-Pieter Jacobs <janpieter.jac...@gmail.com> > wrote: > > actually, J lets you approximate pi to as many digits as you'd want, but > you have to know the trick: > > pix =. ([: <.@:o. 10^x:) > > _10 ]\ ": pix 100 > > 3141592653 > 5897932384 > 6264338327 > 9502884197 > 1693993751 > 0582097494 > 4592307816 > 4062862089 > 9862803482 > 5342117067 > 9 > > gives the first 101 digits of pi (including the initial 3). This is so > because it's implemented as special code in J. Somehow, this seems not yet > to be documented in NuVoc, but can be found e.g. here: > https://code.jsoftware.com/wiki/JPhrases/NumbersCounting > > pix gives you an extended integer of pi time 10^y, the _10 ]\ ": just does > conversion to string, and formatting with 10 digits per line. > > Jan-Pieter > > > On Sun, 15 May 2022, 10:49 Elijah Stone, <elro...@elronnd.net> wrote: > >> J has a few different ways of representing numbers, including: >> >> - Machine integers (limited to 64 or 32 bit); this is what you get if you >> type a number like 123 >> >> - Machine floating-point numbers (limited precision, but can have decimal >> points in them); this is what you get if you type a number like 3.45 or 1p1 >> >> - Extended-precision numbers (unlimited precision, but can only represent >> integers and rational numbers); this is what you get if you type a number >> like 123x or 3r4 >> >> You would like an unlimited-precision representation of pi, I assume. But >> the >> present implementation of j is incapable of this; the only things it can >> represent with unlimited precision are integers and rational numbers, and >> pi >> is irrational. >> >> Machine representation of irrational numbers is a very interesting topic, >> but >> it is fraught with tradeoffs and complexities, and the present >> implementation >> of j does not attempt it. As far as I know, all implementations of apl >> have >> the same limitation; there, too, ○1 is a floating-point approximation. And >> I >> do not think most apl implementations even have extended-precision >> integers or >> rational numbers. >> >> You might like to look into computer algebra systems (cas), such as >> mathematica. >> >> On Sun, 15 May 2022, yt wrote: >> >>> >>> Dear All, >>> i come back to start in J >>> >>> in jijx>tour>overview >>> 3p5 NB. Pi (3 * Pi ^ 5) >>> 918.059 >>> >>> may be it is not the better way to find Pi : >>> 1p1 NB. Pi (1 * Pi ^ 1) >>> >>> 1p1 >>> 3.14159 >>> 1p1x >>> |ill-formed number >>> | 1p1x >>> | ^ >>> >>> but this is ok for : >>> ^/ 2 3 4 >>> 2.41785e24 >>> ^/ 2 3 4x >>> 2417851639229258349412352 >>> 3^4 >>> 81 >>> 2^81 >>> 2.41785e24 >>> 2^81x >>> 2417851639229258349412352 >>> >>> why 1p1 is not good ? >>> >>> i have not this problem in APL >>> >>> Sorry for the inconvenience >>> Regards, >>> Yves >>> ---------------------------------------------------------------------- >>> 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
