I wrote:
> >:@<.@^. 1 >. >./@:|@,
Raul responded:
> Personally, I prefer the fork 1 + u over the perhaps more obvious >:@u
In general I agree with you, but in this case I like the sequence of inflected
arrows*:
>: @ <. @ ^.
It’d be cuter if >: happened to be spelled >. but I still like it.
Also, this particular form is closer to the source material I quoted earlier:
2&#. b. _1
($&2@>:@(2&(<.@^.))@(1&>.)@(>./)@:|@, #: ]) :.(2&#.)
-----^
There is one hypothetical drawback, however. The sequence <.@^. (as well as
<.@:^. , though that’s still undocumented) has the potential to be supported by
special code [1], as many similar sequences already are; prepending >:@ would
interfere with that.
Because conjunctions are left-associative, >:@<.@^. is parsed as (>:@<.)@^.
instead of >:@(<.@^.) and so the interpreter never sees the sequence <.@^. in
isolation, and therefore could never recognize an opportunity for optimization.
But, currently, that pitfall is academic; the sequence <.@f is optimized for
many f, but ^. is not among them, and it’s unlikely to be included any time
soon.
Because, as Roger once pointed out to me [2]:
> The problem is not as easy as you imply. To replace the nonce
> error, the implementation has to handle cases like the following:
>
> a=: 11^309x
> a ^. a^100 NB. should be 100x
> a ^. 1+a^100 NB. should return a float at or near 100
> a ^. _1+a^100 NB. should return a float at or near 100
> a <.@^. _1+a^100 NB. should be 99x
> a >.@^. 1+a^100 NB. should be 101x
-Dan
* I’d call it “alliteration” but the initial arrow in each digraph is
different, so, “assonance”?
[1] Appendix B, “Special Code”:
http://www.jsoftware.com/help/dictionary/special.htm
<http://www.jsoftware.com/help/dictionary/special.htm>
<.@f … avoids non-integer intermediate results on extended precision
integers
<.@% (dyad) … special code on integer arguments; see the J6.02 release
notes
And §II.G, "G. Extended and Rational Arithmetic” goes into more detail.
http://www.jsoftware.com/help/dictionary/dictg.htm
<http://www.jsoftware.com/help/dictionary/dictg.htm>
Neither mention ^. as an optimized primitive
[2] J General Forum, Nov, 2005, "Nonce error with #.”:
http://www.jsoftware.com/pipermail/general/2005-November/025859.html
The nonce error raised by <.@^. (implicitly via #:) bit me. I asked Roger
to lift it. He pointed out (in the quote above) why that wouldn’t be as easy as
I thought.
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