You can see how Raul's 2nd example, where he does not add 2, has fewer correct digits than the one where he does not add it because adding 2 gives you two more useful terms, as he mentions.
On Tue, Oct 3, 2023 at 7:35 AM Raul Miller <rauldmil...@gmail.com> wrote: > A couple notes here: > > One is that 0j18":Y will give you 18 places after the decimal point > regardless of the magnitude of Y > > Another is that we can inspect intermediate results in the expression > %-/%!2+x:i.x > > Let's try that here with smaller values for x (and leaving out the x: > so that we're using floating point approximations for more comfortable > display): > > i.4 > 0 1 2 3 > !i.4 > 1 1 2 6 > !2+i.4 > 2 6 24 120 > %!2+i.4 > 0.5 0.166667 0.0416667 0.00833333 > %~/%!2+i.4 > 2.4 > > Inspecting these results (and perhaps playing with a few other > examples), I am reminded that !0 and !1 both have the value 1. And, of > course, the reciprocal of 1 is 1. And, %~ will finish up by dividing > the accumulated result by these values. So, this skips a couple > unnecessary "divide by 1" steps. > > But, also, adding 2 means that we've added another two significant > terms to the initial (right hand side) part of the series, giving us a > more accurate result. > > These correspond to relatively small values in the result, but they do > increase its precision. > > And, I do see a change there, on the right hand side, in the case of > the example you suggested: > > 0j18":%-/%!2+i.x:10 > 2.718281842777827338 > 0j18":%-/%!i.x:10 > 2.718283693893449991 > > I hope this helps, > > -- > Raul > > On Tue, Oct 3, 2023 at 3:26 AM Richard Donovan <rsdono...@hotmail.com> > wrote: > > > > After watching a math video on YouTube I started to investigate the > implementation of alternating sequences in J. > > > > Using the site search function, (alternating sequences site: > jsoftware.com) I discovered an entry in the NYCJUG of 2022-11-08 which > contains an excellent example: > > > > > > calce=: 13 : '%-/%!2+i.x: y' > > calce 10 > > 3991680r1468457 > > 20j18":calce 10 NB. Format rational to 20-digit decimal with 18 > places past the decimal > > 2.718281842777827338 > > > > Using this as a startpoint, I followed the logic thru but couldn't > understand why 2 is added to i. x: y > > > > Removing the 2+ doesn't seem to affect the result in any of the cases I > tried. > > > > > > Thanks in advance, > > > > Richard > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Devon McCormick, CFA Quantitative Consultant ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
