Raul, note that this works: (+.&.(*&1p1))/2 3 1
even though the numbers 0j16":(*&1p1)2 3 6.2831853071795862 9.4247779607693793 do not satisfy your demands of being exactly represented. Thanks! Bo Den lørdag den 16. maj 2020 13.03.21 CEST skrev Hauke Rehr <hauke.r...@uni-jena.de>: The answer 3j2 looks sane. 3j2 * 0j1 0j_1 and the only one in the first quadrant. Nice! Am 16.05.20 um 12:32 schrieb Raul Miller: > Oh, I see -- or, I think I see what you were trying to illustrate now. > > That said, this is kind of interesting: > +./(,-)2j_3 > 3j2 > > But I also noticed that +/(,-) seems to bring back associativity (we > already had commutativity with +.): > > (i.6) A."0 1]4.57 4.34 4.44 > 4.57 4.34 4.44 > 4.57 4.44 4.34 > 4.34 4.57 4.44 > 4.34 4.44 4.57 > 4.44 4.57 4.34 > 4.44 4.34 4.57 > +./@(,-)"1 (i.6) A."0 1]4.57 4.34 4.44 > 8.88178e_16 8.88178e_16 8.88178e_16 8.88178e_16 8.88178e_16 8.88178e_16 > > Thanks, > > > -- > Raul > > On Sat, May 16, 2020 at 5:51 AM Hauke Rehr <hauke.r...@uni-jena.de> wrote: >> >> sorry, I was not sufficiently precise about my example >> I meant to talk about atomic a only >> >> if $ a is empty, then >> +./ (, -) a >> will work >> >> Thanks for pointing out the lack of precision. >> >> Am 16.05.20 um 11:46 schrieb Raul Miller: >>> I was talking about the implementation. >>> >>> These are different results: >>> >>> +./@(,-)4.57 4.34 4.44 >>> 8.88178e_16 >>> +./@(,-)&.x:4.57 4.34 4.44 >>> 0.01 >>> +./@(,-)&.:(*&1p1)4.57 4.34 4.44 >>> 5.65432e_16 >>> >>> The reason is that binary floating point cannot represent 5^_1 nor >>> 5^_2 accurately. >>> >>> Thanks, >>> >> >> -- >> ---------------------- >> 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