A different issue - ": ignores the imaginary part of a number. 33j30":1j1
1.000000000000000000000000000000 On Sun, Feb 21, 2021 at 3:55 AM Raul Miller <[email protected]> wrote: > Ok, let's walk through this. > > First, let's extract the J's binary representation of pi: > ' '-.~":(64#2)#:256x#.|.a.i.2(3!:5) o.1 > 0100000000001001001000011111101101010100010001000010110100011000 > > To interpret this, let's refer to the wikipedia page on this numeric > format: > https://en.wikipedia.org/wiki/Double-precision_floating-point_format > > (];.1~0 1 12 e.~i.@#)' '-.~":#:256x#.|.a.i.2(3!:5) o.1 > (];.1~0 1 12 e.~i.@#)' '-.~":(64#2)#:256x#.|.a.i.2(3!:5) o.1 > 0 > 10000000000 > 1001001000011111101101010100010001000010110100011000 > > The sign flag is zero, which means it's a positive number. Negative > numbers have a sign flag of 1. > > The binary exponent is > 2b10000000000-1023 > 1 > > Or, we've got a binary fraction which we'll be multiplying by 2. > > The binary fraction is > 2b1.1001001000011111101101010100010001000010110100011000 > 1.5708 > > Or, the actual value is: > 2*2b1.1001001000011111101101010100010001000010110100011000 > 3.14159 > > Our problem is that this is not the actual value of pi, it's just an > approximation. > > If we want to work with a better approximation, we might do something like > this: > pistring=:{{)n > 3.14159265358979323846264338327950288419716939937510582097494459 > 2307816406286208998628034825342117067982148086513282306647093844 > 6095505822317253594081284811174502841027019385211055596446229489 > 5493038196442881097566593344612847564823378678316527120190914564 > 8566923460348610454326648213393607260249141273724587006606315588 > 1748815209209628292540917153643678925903600113305305488204665213 > 8414695194151160943305727036575959195309218611738193261179310511 > 8548074462379962749567351885752724891227938183011949129833673362 > }}-.LF > > pirat=: (".(pistring,'x')-.'.')%_10x^_2+#pistring > > 60{.' '-.~":#:(2^64x)*pirat > 110010010000111111011010101000100010000101101000110000100011 > > There's a trailing 0100011 on that binary fraction which would make > our representation just a bit more accurate (but which would also make > J slower, because we would no longer be taking advantage of the > specialized hardware supporting the number format). > > This would crop up if we're subtracting something from pi (or adding a > negative number), in a fashion which lops off leading digits from the > representation. > > Short form: if we're going to be using + or - on values which are > non-zero multiples of pi, this might matter. > > I hope this made sense. > > -- > Raul > > On Sun, Feb 21, 2021 at 2:14 AM 'Bo Jacoby' via Programming > <[email protected]> wrote: > > > > Thank you all for the comments! > > Raul wrote: "A cost, though, of that kind of approach, is that it would > lure us into a false sense of security, leaving us even more upset in other > circumstances." > > Which circumstances are you thinking of? > > The rounding to zero is beneficial in all the cases mentioned in the > comments, and I fail to construct examples where it is not. > > > > (^ j. 1p1) NB. confusing > > > > _1j1.22465e_16 > > f0(^ j. 1p1) NB. clear > > _1 > > > > > > > > f0 9e99j1e6 > > > > 9e99 > > > > > > Thanks. > > Bo. > > > > Den søndag den 21. februar 2021 07.32.51 CET skrev Joey K Tuttle < > [email protected]>: > > > > Ahh for the good ole days ;-) > > > > JVERSION > > Binary: j601binc_linux32 > > Library: j601libc > > Help: j601hlpc > > Engine: j601/2006-11-17/17:05 > > ^ o.0j1 > > _1 > > ^j.1p1 > > _1 > > > > But time marches on and things change ... > > > > JVERSION > > Installer: j602a_linux32.sh > > Engine: j602/2008-03-03/16:45 > > Library: 6.02.023 > > ^ o. 0j1 > > _1j1.22461e_16 > > (^j.1p1) > > _1j1.22461e_16 > > > > > > JVERSION > > Engine: j903/j64avx2/darwin > > Beta-e: commercial/2021-02-16T18:34:19 > > Library: 9.03.01 > > Platform: Darwin 64 > > Installer: J903 install > > InstallPath: /applications/j903 > > Contact: www.jsoftware.com > > ^j.1p1 > > _1j1.224646799e_16 > > NB. but even today the formatted result is satisfying. > > 33j30 ": ^ o. 0j1 > > _1.000000000000000000000000000000 > > > > > > > On 2021Feb 20, at 11:12, Henry Rich <[email protected]> wrote: > > > > > > No, the code is still there, but it doesn't do much - gives a little > bit better precision on large arguments IIRC. > > > > > > Henry Rich > > > > > > On 2/20/2021 2:10 PM, Roger Hui wrote: > > >> https://www.jsoftware.com/papers/APLQA.htm#worldmathsday > > >> > > >> * ○ 0j1 × 2e9 + a ÷ 2 > > >> 1 0J1 ¯1 0J¯1 > > >> 1 0J1 ¯1 0J¯1 > > >> 1 0J1 ¯1 0J¯1 > > >> > > >> (Basically, ^ o. 0j1 * 2e9 + a % 2 where a=: 3 4$i.12) > > >> > > >> I thought I did the same in J, predating what's done in Dyalog APL. > > >> According to https://www.jsoftware.com/help/dictionary/special.htm, > there > > >> is supposed to be special code for ^@o., but apparently it got lost > > >> somewhere, sometime. > > >> > > >> > > >> > > >> > > >> On Sat, Feb 20, 2021 at 9:45 AM Raul Miller <[email protected]> > wrote: > > >> > > >>> On Sat, Feb 20, 2021 at 12:46 AM María Magdalena Mixuhca > > >>> <[email protected]> wrote: > > >>>> I find this lack of beauty surprisingly disturbing: > > >>>> > > >>>> (^ j. 1p1) > > >>>> _1j1.22465e_16 > > >>> Ok... so... > > >>> > > >>> I think what we want here is a handling of > > >>> exponentials/transcendentals so that necessarily minimal deviations > > >>> from pi are smoothly handled so that we get zeros when we expect > them. > > >>> > > >>> A cost, though, of that kind of approach, is that it would lure us > > >>> into a false sense of security, leaving us even more upset in other > > >>> circumstances. > > >>> > > >>> Still... it's an interesting challenge. > > >>> > > >>> Thanks, > > >>> > > >>> -- > > >>> Raul > > >>> > ---------------------------------------------------------------------- > > >>> For information about J forums see > http://www.jsoftware.com/forums.htm > > >>> > > >> ---------------------------------------------------------------------- > > >> For information about J forums see > http://www.jsoftware.com/forums.htm > > > > > > > > > -- > > > This email has been checked for viruses by AVG. > > > https://www.avg.com > > > > > > ---------------------------------------------------------------------- > > > 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
