Goodness! I don't know whether to be pleased that I wrote it (I mean, the code is pretty good), or sad that I forgot that I wrote it.
On Tue, Dec 22, 2020 at 4:52 PM chris burke <cbu...@jsoftware.com> wrote: > See also Roger's essay: > > https://code.jsoftware.com/wiki/Essays/Chudnovsky_Algorithm > > On Tue, Dec 22, 2020 at 3:22 PM Hauke Rehr <hauke.r...@uni-jena.de> wrote: > > > > a worthy read, thanks > > > > I think I fell in love with J in part > > due to its notationally pleasant guise > > There are so many debates in notation. > > I personally prefer τ over π but I’m > > okay with o.1 and 1p1 meaning πª > > (I’d like to have 1t1 at my disposal); > > and I’m unsure about the Triangle of Power > > but I think it’s worth considering, > > at least in education; > > etc. etc. > > > > As for parethesesº, I’m amoung those trying to avoid paren-noise as much > > as possible (in tex, for example, I build mostly commands taking single > > letters, symbols or commands as input so I may omit braces – but I agree > > this can render texts unreadable if applied excessively). > > > > This personal taste notwithstanding, I do appreciate your > > aesthetics-based plea for expressions like (x>0)-(x<0), > > but I’d rather say x (> - <) 0 instead. (DRY principle) > > > > And I forgot to mention I also think 3. is another important argument. > > When I taught J to pupils recently, they were overwhelmed by the way > > this actually is more readable and intuitive, e. g. > > append =: , > > product_of_items =: */ > > append_its_product =: append product_of_items > > when I had been talking about forks. > > > > > > ª now we’re back with this thread’s topic – in some way > > º in German, “Klammern” are any of ()[]{} > > > > > > Am 22.12.20 um 22:00 schrieb Roger Hui: > > > May I suggest that you read Conventions Governing Order of Evaluation > > > <https://www.jsoftware.com/papers/EvalOrder.htm> [Iverson 1966]. > > > > > > > > > On Tue, Dec 22, 2020 at 12:46 PM Hauke Rehr <hauke.r...@uni-jena.de> > wrote: > > > > > >> IMO the value of right-to-left data flow is > > >> that it reflects the way math notation works. > > >> operatorD operatorC operatorB operatorA data > > >> is “evaluated” from right to left. > > >> -/ I used to consider merely a convenience. > > >> Having read Roger’s answers, I guess I might > > >> have been wrong. > > >> > > >> !warning: opinions/ranting ahead! > > >> Anyone objecting against this doesn’t know > > >> or doesn’t like maths. > > >> Sadly, even methematicians often don’t know > > >> their grammar, writing incomprehensible nonsense > > >> like (ℚ is dense in ℝ) > > >> ∃q∈ℚ: d(q,r)<ε ∀r∈ℝ, ε>0 > > >> instead of (my preferred way) > > >> ∀(r,R)∈ℝ²∩<: ∃q∈ℚ: ((r,q),(q,R))∈<² > > >> One might argue for “r<q<R” to be an okay alternative > > >> for the part after the last colon. I’d disagree still. > > >> What would “true<R” or “r<false” mean? > > >> > > >> Am 22.12.20 um 19:44 schrieb Devon McCormick: > > >>> Thanks everyone for the tips! > > >>> > > >>> Bob - your suggestions still stalls: > > >>> 20j18":%12x*-/chudSeriesa i.2 > > >>> 3.141592653589788641 > > >>> 20j18":%12x*-/chudSeriesa i.3 > > >>> 3.141592653589788641 > > >>> (Should be > > >>> 3.14159265358979323846... > > >>> as we all know :) ) > > >>> > > >>> Roger's suggestion will take me longer to translate. > > >>> > > >>> I got into this diversion from thinking about the array languages > FAQ I > > >>> mentioned in the KEI Centenary discussion last Thursday. One of the > > >> first > > >>> objections a lot of people have is the right-to-left order of > evaluation > > >>> and I wanted a good illustration of how this gives you alternating > sum > > >> with > > >>> -/ . I found it discouraging to read a recent missive from Niklaus > > >> Wirth > > >>> where he takes a jab at this useful simplification as an example of > an > > >>> unwarranted complication. It's sad that an eminent luminary like > this > > >> has > > >>> failed to grasp, after all these years, how useful this convention > is. > > >>> > > >>> The Chudnovsky formula is a good illustration because it includes a > > >> "_1^k" > > >>> term to force the alternating sum. > > >>> > > >>> > > >>> > > >>> > > >>> On Tue, Dec 22, 2020 at 12:56 PM Roger Hui < > rogerhui.can...@gmail.com> > > >>> wrote: > > >>> > > >>>> In the J source, file vx.c, function jtxpi(), you find an > > >> implementation of > > >>>> the Chudnovsky algorithm using extended precision arithmetic. It > is in > > >> C > > >>>> but it should not be too hard to figure out the J equivalent. > > >>>> > > >>>> static XF1(jtxpi){A e;B p;I i,n,n1,sk;X a,b,c,d,*ev,k,f,m,q,s,s0,t; > > >>>> RZ(w); > > >>>> if(!XDIG(w))R xzero; > > >>>> ASSERT(jt->xmode!=XMEXACT,EVDOMAIN); > > >>>> RZ(a=xc(545140134L)); > > >>>> RZ(b=XCUBE(xc(640320L))); > > >>>> RZ(c=xc(13591409L)); > > >>>> RZ(d=xplus(xc(541681608L),xtymes(xc(10L),xc(600000000L)))); > > >>>> n1=(13+AN(w)*XBASEN)/14; n=1+n1; > > >>>> RZ(e=piev(n,b)); ev=XAV(e); m=ev[n1]; > > >>>> f=xzero; s0=xone; sk=1; > > >>>> for(i=p=0;;++i,p=!p){ > > >>>> s=xtymes(s0,xplus(c,xtymes(a,xc(i)))); > > >>>> t=xdiv(xtymes(s,m),ev[i],XMEXACT); > > >>>> f=p?xminus(f,t):xplus(f,t); > > >>>> if(i==n1)break; > > >>>> DO(6, s0=xtymes(s0,xc(sk++));); RE(s0); /* s0 = ! 6*i */ > > >>>> } > > >>>> f=xtymes(d,f); > > >>>> q=xpow(xc(10L),xc(14*n1)); > > >>>> k=xtymes(xtymes(a,m),xsqrt(xtymes(b,xsq(q)))); > > >>>> R xdiv(xtymes(k,w),xtymes(f,q),jt->xmode); > > >>>> } /* Chudnovsky Bros. */ > > >>>> > > >>>> > > >>>> On Tue, Dec 22, 2020 at 9:30 AM Devon McCormick <devon...@gmail.com > > > > >>>> wrote: > > >>>> > > >>>>> The Chudnovsky algorithm - > > >>>>> https://en.wikipedia.org/wiki/Chudnovsky_algorithm - is supposed > to > > >> have > > >>>>> the fastest convergence for pi (or 1/pi, to be exact). I had tried > > >> this > > >>>>> one which is OK but only seems to add one digit for each power of > 10: > > >>>>> 6!:2 'pi=. 4*-/%>:+:i. 1e6' > > >>>>> 0.0145579 > > >>>>> 20j18":pi > > >>>>> 3.141591653589793420 > > >>>>> 6!:2 'pi=. 4*-/%>:+:i. 1e7' > > >>>>> 0.140673 > > >>>>> 20j18":pi > > >>>>> 3.141592553589793280 > > >>>>> 6!:2 'pi=. 4*-/%>:+:i. 1e8' > > >>>>> 1.44487 > > >>>>> 20j18":pi > > >>>>> 3.141592643589793177 > > >>>>> 6!:2 'pi=. 4*-/%>:+:i. 1e9' > > >>>>> 16.7988 > > >>>>> 20j18":pi > > >>>>> 3.141592652589793477 > > >>>>> > > >>>>> The Chudnovsky series is fast and gives me 15 correct decimal > digits > > >> for > > >>>>> only 2 iterations but fails to improve after that presumably > because of > > >>>>> floating point limitations: > > >>>>> 20j18":%12*-/chudSeries i.2 > > >>>>> 3.141592653589795336 > > >>>>> 20j18":%12*-/chudSeries i.3 > > >>>>> 3.141592653589795336 > > >>>>> 20j18":%12*-/chudSeries i.4 > > >>>>> 3.141592653589795336 > > >>>>> chudSeries i.4 > > >>>>> 0.0265258 4.98422e_16 2.59929e_30 1.45271e_44 > > >>>>> > > >>>>> However, when I try to use extended precision, it does not seem to > give > > >>>> me > > >>>>> extended precision results: > > >>>>> chudSeries=: 13 : '((!6x*x: y)*13591409x+545140134x*x: > y)%(!3x*x: > > >>>>> y)*(3x^~!x: y)*640320x^3r2+3x*x: y' > > >>>>> > > >>>>> I get the same fp values for the "i.4" argument as shown above. > Am I > > >>>> doing > > >>>>> something wrong or overlooking something? > > >>>>> > > >>>>> Thanks, > > >>>>> > > >>>>> Devon > > >>>>> > > >>>>> -- > > >>>>> > > >>>>> Devon McCormick, CFA > > >>>>> > > >>>>> Quantitative Consultant > > >>>>> > ---------------------------------------------------------------------- > > >>>>> For information about J forums see > http://www.jsoftware.com/forums.htm > > >>>>> > > >>>> > ---------------------------------------------------------------------- > > >>>> For information about J forums see > http://www.jsoftware.com/forums.htm > > >>>> > > >>> > > >>> > > >> > > >> -- > > >> ---------------------- > > >> mail written using NEO > > >> neo-layout.org > > >> > > >> ---------------------------------------------------------------------- > > >> For information about J forums see > http://www.jsoftware.com/forums.htm > > >> > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > > -- > > ---------------------- > > mail written using NEO > > neo-layout.org > > > > ---------------------------------------------------------------------- > > 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
