And +./"2@:# can be rewritten as +./@#.
Anything else?
On Wed, Oct 12, 2016 at 11:55 PM, Michal Dobrogost <
michal.dobrog...@gmail.com> wrote:
> You can rewrite *."0 1"1 _ as #
>
> ]L3=. _3((|."1@:#:@:i.@:(2^#)) (+./"2 @: #) ])\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 1 0 0 NB. 2 { y
> 0 0 1 0 1 NB. 0 2 { Y
> 0 0 1 1 0 NB. +./ 0 1 { Y
> 0 0 1 1 1 NB. +./ 0 1 2 { Y
>
> 0 0 0 0 0 NB. zero
> 0 1 0 0 0 NB. 3 { Y
> 1 0 0 0 0 NB. 4 { Y
> 1 1 0 0 0 NB. +./ 3 4 { Y
> 0 0 0 0 0
> 0 0 0 0 0
> 0 0 0 0 0
> 0 0 0 0 0
>
> On Wed, Oct 12, 2016 at 11:34 PM, Michal Dobrogost <
> michal.dobrog...@gmail.com> wrote:
>
>> 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.
>>
>> 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/forum
>>>> s.htm
>>>> ----------------------------------------------------------------------
>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>
>>>
>>>
>>
>
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