Since all of this is also directed at users
trying to figure out how rank works, I want
to further clarify two things:
“3 items in left, 3 rows in right”
yes, but in J lingo, these rows are items
as well. And the IE does just that: match
the number of items (generally: prefixes
of noun ranks) against each other.
The last example doesn’t need the explicitely
stated rank, either, thanks to this very matching.
100 200 300 400 +&.|: a
100 201 302 403
104 205 306 407
108 209 310 411
I attach my effort at explaining ranks stemming
from the discussions about conjunctions back in
May.
Am 17.01.21 um 04:33 schrieb 'Rob Hodgkinson' via Programming:
> Arnab, Henry’s explanation below should be really helpful. When I learnt
> rank it also helped me to see what happens with rank slicing up the left and
> right arguments.
>
> I add some (hopeful) clarity here that may help using the + primitive again
> to show how rank can provide looping constructs between the arguments …
>
> ]a=. i.3 4
> 0 1 2 3
> 4 5 6 7
> 8 9 10 11
>
> 100+a NB. Add 100 to every element of a (+ does
> this natively)
> 100 101 102 103
> 104 105 106 107
> 108 109 110 111
>
> 100 200 300 + a NB. But ‘frames’ are also used to line up to slice
> arguments so the “3 frames” in each argument (3 items in left, 3 rows in
> right) produce this result
> 100 101 102 103
> 204 205 206 207
> 308 309 310 311
>
> 100 200 300 +"0 _ a NB. Rank allows us to now explicitly along a cell in
> the left argument (using rank 0) with the *whole* of the right argument <a>
> (using rank _ infinity)
> 100 101 102 103
> 104 105 106 107
> 108 109 110 111
>
> 200 201 202 203
> 204 205 206 207
> 208 209 210 211
>
> 300 301 302 303
> 304 305 306 307
> 308 309 310 311
>
> 100 200 300 +"0 1 a NB. This case mirrors the second example above (that
> was done within frames by the engine) … each cell is added to each row (3
> frames) using expect rank
> 100 101 102 103
> 204 205 206 207
> 308 309 310 311
>
> 100 200 300 400 +"0 1 &. |: a NB. This shows how we might now add
> cells to columns, by transposing, applying row-wise, then transposing back
> 100 201 302 403
> 104 205 306 407
> 108 209 310 411
>
> I hope this does not confuse, but playing with examples as per above should
> help you understand the rank operator more clearly (and how it slices the
> data, potentially in both arguments in the dyadic case).
>
> HTH, Rob
>
>> On 17 Jan 2021, at 1:52 pm, Henry Rich <[email protected]> wrote:
>>
>> Well explained! What you say makes perfect sense. Now, what can we do to
>> help people stop doing that?
>>
>> Abstractly, specifying rank u"n is simply an instruction to JE to chop up
>> the arguments into pieces of rank(s) n before applying u. For general u, JE
>> does exactly that. Thus "n is a directive to execute a certain loop. It is
>> not merely informational.
>>
>> [Implicitly, every verb has a rank. Presented with an argument larger than
>> its verb rank, the verb will chop up its arguments.]
>>
>> The implementation problem is that executing a verb u has a certain overhead
>> because of the nature of interpreters: arguments have different types,
>> results have types and shapes, they all have to coexist: starting u and
>> assimilating its result takes a few dozen clock cycles. If u executes on
>> one lousy atom, it's finished in 1 clock cycle, and almost all the CPU time
>> is spent in overhead.
>>
>> The solution to this problem is Integrated Rank Support (IRS). When a verb
>> supports IRS, it warrants to JE that it will take care of a rank if given.
>> JE will skip the chopping-up step, trusting the verb to create the right
>> result. All the usual arithmetic verbs, and several others, have IRS.
>>
>> When you write a + b, JE passes a and b to the + verb. Even though its rank
>> is 0, + knows better than to chop up the arguments into atoms: instead it
>> processes them as vectors, repeating a short-frame argument if needed.
>> That's IRS for you: even though the verb has nominal rank 0, it can use the
>> SIMD instructions. The result is AS IF the processing were at rank 0.
>>
>> When you write a +"1 b or a +/ b, JE does even more for you. JE notes that
>> + supports IRS, so it avoids the explicit chopping-up step and passes a and
>> b to + . + now has more work to do: rather than just repeating a short
>> argument, it must also repeat over inner cells, with 4 nested loops. If you
>> perversely write +"0, JE will set up the 4 loops, then see that two are
>> nugatory, and revert to just one or two loops.
>>
>>
>>
>> What's the practical effect of all this? You provided a great example by
>> pointing out that it makes perfect sense to think of scalar and vector
>> addition as different operations. What the beginner needs to do is note
>> that the rank of + is 0, which means that if you want scalar addition you
>> don't need to write +"0: + means the same thing. The added "0 might seem
>> harmless, or even useful for documentation, but it does add to the
>> interpreter's work. If you are adding vectors, write +"1 only when it would
>> give different results from +"0, that is, when you have one vector to add to
>> an array of vectors.
>>
>> The apparent anomaly of sin is because of the details of the & and o.
>> primitives. o. has rank 0 with IRS, but m&o. is defined as having infinite
>> rank (with IRS). So yes, sin has infinite rank. But because it's a monad,
>> it produces the same results no matter what its rank: there is no extension
>> of a short argument.
>>
>> Henry Rich
>>
>>
>>
>>
>>
>> which knows to repeat an argument that
>>
>>
>>
>> On 1/16/2021 8:59 PM, Arnab Chakraborty wrote:
>>> Thanks for the lively discussion, much of which I could not follow, though,
>>> owing to my ignorance about rank integration.
>>>
>>> However, I understand that some sort of efficiency issue is involved.
>>>
>>> BTW, I can answer one question that even Henry could not answer (for a
>>> change): why beginners write things like +"0 and sin"0.
>>>
>>> They (read "we") are confused by ranks, and the closest concept familiar to
>>> them is that of dimension of domain. For instance, scalar addition is
>>> different from vector addition. So +"0 is scalar addition, and +"1 is
>>> vector addition. This habit is further encouraged by the apparently
>>> inconsistent rank system of J, like *: having rank 0 while sin has rank
>>> infinity. But both are functions from IR to IR. Not sure what is happening
>>> internally, they prefer to explicitly "specify the domain."
>>>
>>> Indeed, before this email thread, it never occurred to me that rank is
>>> somehow linked with efficiency. I just considered a function's rank to be a
>>> property that is competely dictated by the math of the function.
>>>
>>>
>>>
>>> On Sun, 17 Jan 2021, 06:46 Henry Rich, <[email protected]> wrote:
>>>
>>>> I can't answer that, but I can assure you that they do.
>>>>
>>>> Henry Rich
>>>>
>>>> On 1/16/2021 7:38 PM, bill lam wrote:
>>>>> I didn't mean to change stdlib sooner or later, but if we do it again,
>>>> rank
>>>>> 0 should be a better option.
>>>>>
>>>>> Why users (beginner or not) would write a+"0 b or sin"0 ?
>>>>>
>>>>>
>>>>>
>>>>> On Sun, Jan 17, 2021, 8:20 AM Henry Rich <[email protected]> wrote:
>>>>>
>>>>>> I would be happy for a user to do that, but changing stdlib might not be
>>>>>> a good idea. Beginning users often write
>>>>>>
>>>>>> a +"0 b
>>>>>>
>>>>>> and it doesn't cost them dearly. If you make the change, sin"0 will be
>>>>>> expensive.
>>>>>>
>>>>>> Henry Rich
>>>>>>
>>>>>> On 1/16/2021 7:17 PM, bill lam wrote:
>>>>>>> Thanks. then defining sine as 1&o."0 should be fine.
>>>>>>>
>>>>>>> On Sun, Jan 17, 2021, 8:07 AM Henry Rich <[email protected]> wrote:
>>>>>>>
>>>>>>>> What makes them efficient is IRS. 1&o. supports IRS; 1&o."0 does not.
>>>>>>>> Is you define sin as 1&o."0, sin will run fast, but sin"0 will not.
>>>>>>>>
>>>>>>>> Henry Rich
>>>>>>>>
>>>>>>>> On 1/16/2021 6:24 PM, bill lam wrote:
>>>>>>>>> IIUC All atomic math functions are rank 0 but support IRS so that
>>>> they
>>>>>>>> are
>>>>>>>>> as efficient as rank infinity on long array arguments.
>>>>>>>>>
>>>>>>>>> The question should be that
>>>>>>>>> is 1&o."0 as efficient as 1&o. on long arrays.
>>>>>>>>>
>>>>>>>>> On Sun, Jan 17, 2021, 12:32 AM Henry Rich <[email protected]>
>>>>>> wrote:
>>>>>>>>>> Terminology. If verb v has IRS, it can handle v"n internally
>>>> without
>>>>>> a
>>>>>>>>>> rank loop.
>>>>>>>>>>
>>>>>>>>>> + has IRS. +"n does not need a rank loop.
>>>>>>>>>>
>>>>>>>>>> +"n does not have IRS. +"n"n2 does need a rank loop.
>>>>>>>>>>
>>>>>>>>>> +/@:*"1 has IRS, but +/@:* does not - that's how they're coded.
>>>>>>>>>>
>>>>>>>>>> 1&o."0 does not have IRS.
>>>>>>>>>>
>>>>>>>>>> Henry Rich
>>>>>>>>>>
>>>>>>>>>> On 1/16/2021 11:27 AM, bill lam wrote:
>>>>>>>>>>> but the verb in this question is
>>>>>>>>>>> (1&o.)"0
>>>>>>>>>>>
>>>>>>>>>>> even if 1&o. has IRS, does (1&o.)"0 also has IRS ?
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> On Sun, Jan 17, 2021, 12:02 AM Henry Rich <[email protected]>
>>>>>>>> wrote:
>>>>>>>>>>>> m&v does have IRS if v does. I didn't know that until I just
>>>>>> checked.
>>>>>>>>>>>> Henry Rich
>>>>>>>>>>>>
>>>>>>>>>>>> On 1/16/2021 7:10 AM, bill lam wrote:
>>>>>>>>>>>>> I'm not sure if 1&o."0 has IRS (integrated rank support) or not.
>>>> If
>>>>>>>> it
>>>>>>>>>>>>> doesn't then I think the phase with infinity rank is fine.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Sat, Jan 16, 2021, 7:02 PM Arnab Chakraborty <
>>>>>> [email protected]>
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>> Dear all,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Just wondering if the correct defn of sin shouldn't be
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> sin=:1&o."0
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> instead of
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> sin=:1&o.
>>>>>>>>>>>>>> which has rank infinity.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> With the rank infinity definition +/@sin behaves just like
>>>> +/@:sin
>>>>>>>>>>>>>> But, ideally, +/@sin 4 5 should be a list of two numbers, while
>>>>>>>>>> +/@:sin
>>>>>>>>>>>>>> should be their sum.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Just like, +/@*: and +/@:*:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks and regards,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Arnab
>>>>>>>>>>>>>>
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