While I don't have a specific explanation (I have not looked closely enough), I was somewhat bemused by the consequences of executing:
NXT1=: 4 : 'x nxt1 y [ echo x;y' PS1=: 0 +/@:((NXT1 ,^:(0 ~: [) ])^:_)~ ] (PS1 - ^.@>:)"0 % 2^>:i.5 Sums of alternating signed floating point numbers of similar magnitude have a tendency to lose precision. (And, values in the range of 1e_323 also tend to run into issues, if that matters.) Take care, -- Raul On Sat, Sep 11, 2021 at 6:37 AM Hauke Rehr <hauke.r...@uni-jena.de> wrote: > > Hello, > > I just wanted to look at some power series, > here is code for ^.@>: > (quite literal translation from the maths) > > nxt1 =: [ (^ % (* _1 ^ >:)@]) #@] > ps1 =: 0 +/@:((nxt1 ,^:(0~:[) ])^:_)~ ] > > now executing > (ps1 - ^.@>:)"0 % 2^>:i.5 > gives > _1.11022e_16 _5.55112e_17 _1.38778e_17 6.93889e_18 0 > or > _1.11022e_16 0 2.77556e_17 6.93889e_18 0 > depending on J version > not bad > > I thought I made an improvement when I rewrote it thus: > nxt2 =: [ (^ % ]) #@] > ps2 =: 0 -/@:((nxt2 ,^:(0~:[) ])^:_)~ ] > > but now I get > (ps2 - ^.@>:)"0 % 2^>:i.5 > _0.81093 _0.446287 2.77556e_17 _0.121249 0 > ouch! > > … and now I’d have expected > +/@:(* 1 _1 $~ #)@: > instead of -/@: > not to help with that bad result but it did > _0.81093 _0.446287 _1.38778e_17 _0.121249 0 > > Okay, this will be representation/fp issues; > still the difference in accuracy puzzles me > when comparing ps1 and ps2 … > > Does anyone have an explanation? > > -- > ---------------------- > 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
