I've tried to clean up the code to be more explanatory. All we really care about is generating L2 given an arbitrary Y. Rewriting this has also helped me catch a subtle bug with arrays going left-to-right but #. and #: interpreting numbers right-to-left.

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NB. X and Y are completely arbitary and are chosen to be NB. easy to trace. ] X =. 0 1 1 0 1 0 1 1 0 1 ] Y =. |.=/~i.5 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 NB. This is the final result but we are actually trying to NB. generate lookup tables for highly optimized C++ code. X (+./@:*.) Y 1 0 1 1 0 NB. Break up x into 2-bit chunks. NB. Note: reversed with |. because #. below interprets right-most NB. digit as most significant but J's array has first NB. item as left-most. X 0 1 1 0 1 _2<@|.\X ┌───┬───┬─┐ │1 0│0 1│1│ └───┴───┴─┘ NB. We convert 2-bit chunks of x into indices. _2#.@|.\X 2 1 1 ]L2=. _2((|."1@:#:@:i.@:(2^#)) (+./"2 @: (*."0 1"1 _)) ])\Y 0 0 0 0 0 NB. zero 0 0 0 0 1 NB. 0 { y 0 0 0 1 0 NB. 1 { y 0 0 0 1 1 NB. +./ 0 1 { y 0 0 0 0 0 NB. zero 0 0 1 0 0 NB. 2 { y 0 1 0 0 0 NB. 3 { y 0 1 1 0 0 NB. +./ 2 3 { y 0 0 0 0 0 NB. zero 1 0 0 0 0 NB. 4 { y 0 0 0 0 0 0 0 0 0 0 NB. Compute by 2-bit lookups (same result as +./@:*. above). NB. We don't really care, this just demonstrates that the LUT works. +./ (_2#.@|.\x) {"0 2 L2 1 0 1 1 0 Cheers, Mike On Wed, Oct 12, 2016 at 7:00 PM, Michal Dobrogost < michal.dobrog...@gmail.com> wrote: > Hi Raul, > > What is the definition of *inds*? > > I would describe the higher level operation as: select the rows of Y where > X is 1. Then take the column-wise OR of them. > > However the real thing I'm interested in is generating the lookup tables > which serve as an intermediate step in the higher level operation. > > On Wed, Oct 12, 2016 at 9:35 AM, Raul Miller <rauldmil...@gmail.com> > wrote: > >> I'm not quite sure I understand what you are doing here. >> >> Here's what I understand from your description: >> >> You're looking for rows where a bit set in X has a bit set in Y, and >> you want to split up X and Y into smaller pieces for your intermediate >> result, and you want to use indices rather than bit operations for >> your final operation. >> >> That gives me something like this. >> >> X =: ? 5 $ 2 >> Y =: 30 > ? 5 6 $ 100 >> X >> 0 1 1 1 1 >> Y >> 0 0 0 0 0 0 >> 1 0 0 0 0 0 >> 1 1 1 0 0 1 >> 1 0 0 1 0 0 >> 0 0 0 0 0 1 >> (_2 {. X) inds _2 {. Y >> 0 3 5 >> (3 {. X) inds 3 {. Y >> 0 1 2 5 >> 0 3 5 ([ -. -.) 0 1 2 5 >> 0 5 >> >> So maybe you would be looking at making an adverb along the lines of: >> >> L=: adverb define >> : >> (m {. x) inds m {. y >> ) >> >> Or, more concisely: >> >> L=: adverb define >> inds&(m&{.) >> ) >> >> But when I look at your calculations, I don't see anything like this. >> >> If I am off base here, could you describe how what you are looking for >> differs from what I am understanding? >> >> Thanks, >> >> -- >> Raul >> >> >> On Wed, Oct 12, 2016 at 12:14 PM, Michal Dobrogost >> <michal.dobrog...@gmail.com> wrote: >> > Hi All, >> > >> > I've been mucking around generating look up tables in C++. Getting >> > frustrated, I wrote up this J single liner. Can you think of ways to >> > simplify the LUT computation (the expression we assign to L2 and L3 >> below)? >> > >> > *Original Operator (no LUT)* >> > >> > ] x =. ? 5 $ 2 >> > 1 0 1 1 0 >> > ] y =. 30 > ? 5 6 $ 100 >> > 1 0 0 0 0 0 >> > 0 1 0 1 1 0 >> > 0 1 0 0 0 1 >> > 0 0 0 0 1 1 >> > 0 1 1 1 0 1 >> > x (+./@:*.) y >> > 1 1 0 0 1 1 >> > >> > *LUT Explanation* >> > >> > The idea is to break up x into smaller chunks (2-bits, 3-bits, etc) and >> > precompute the operation for the corresponding chunks of y. Then we just >> > convert the chunks into indices and look them up in the LUT. >> > >> > _2<\x >> > ┌───┬───┬─┐ >> > │1 0│1 1│0│ >> > └───┴───┴─┘ >> > _2#.\x >> > 2 3 0 >> > >> > *2-bit LUT* >> > >> > ]L2=. _2((#:@:i.@:(2&^)@:#) (+./"2 @: (*."0 1"1 _)) ])\y >> > 0 0 0 0 0 0 >> > 0 1 0 1 1 0 >> > 1 0 0 0 0 0 >> > 1 1 0 1 1 0 >> > >> > 0 0 0 0 0 0 >> > 0 0 0 0 1 1 >> > 0 1 0 0 0 1 >> > 0 1 0 0 1 1 >> > >> > 0 0 0 0 0 0 >> > 0 1 1 1 0 1 >> > 0 0 0 0 0 0 >> > 0 0 0 0 0 0 >> > >> > +./ (_2#.\x) {"0 2 L2 NB. Compute by 2-bit lookups >> > 1 1 0 0 1 1 >> > >> > *3-Bit LUT* >> > >> > ]L3=. _3((#:@:i.@:(2&^)@:#) (+./"2 @: (*."0 1"1 _)) ])\y >> > 0 0 0 0 0 0 >> > 0 1 0 0 0 1 >> > 0 1 0 1 1 0 >> > 0 1 0 1 1 1 >> > 1 0 0 0 0 0 >> > 1 1 0 0 0 1 >> > 1 1 0 1 1 0 >> > 1 1 0 1 1 1 >> > >> > 0 0 0 0 0 0 >> > 0 1 1 1 0 1 >> > 0 0 0 0 1 1 >> > 0 1 1 1 1 1 >> > 0 0 0 0 0 0 >> > 0 0 0 0 0 0 >> > 0 0 0 0 0 0 >> > 0 0 0 0 0 0 >> > >> > +./ (_3#.\x) {"0 2 L3 NB. Compute by 3-bit lookups >> > 1 1 0 0 1 1 >> > ---------------------------------------------------------------------- >> > 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