# Re: [Jprogramming] Generating Lookup Tables (LUTs)

```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

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:

:
(m {. x) inds m {. y
)

Or, more concisely:

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```