The IBM APL I first used on mainframes in the 70s had a rank limit of 63 but there was a time when it was implemented improperly, allowing users to create a rank-64 array using "encode". This array's dimensions were a bunch of random numbers that included negatives and zeros (of course or otherwise there would have been not enough memory for it). If you tried to display the array, it crashed APL but you could reduce the dimensionality down to a couple of negative numbers with careful reduction of axes. Since the dimensions were negative, this array accessed "high" (protected) memory and allowed us to see random passwords.
This was eventually fixed. On Sun, Apr 4, 2021 at 11:37 AM John Baker <[email protected]> wrote: > At first I thought this was a tardy April Fools joke. I seem to remember > some APLs had a rank limit in the 60s but like many I’ve never used ranks > beyond 10. > > Sent from my iPhone > > > On Apr 4, 2021, at 09:09, Roger Hui <[email protected]> wrote: > > > > So Henry, can you imagine yourself doing FFT on a sparse hypercube, > sparse > > because many of the entries are 0? For this application not having rank > > restricted to 63 or less would be nice. > > > > > > > > > > On Sun, Apr 4, 2021 at 8:04 AM Roger Hui <[email protected]> > wrote: > > > >>> I haven't used rank beyond 6 that I can recall, if that. > >> > >> FFT uses a high rank array, a hypercube with shape (>.2^.#x)$2 . Of > >> course, a rank-64 hypercube would blow current computers out of the > water. > >> > >> https://code.jsoftware.com/wiki/Essays/FFT > >> > >> > >> > >> On Sun, Apr 4, 2021 at 7:55 AM 'robert therriault' via Programming < > >> [email protected]> wrote: > >> > >>> I haven't used rank beyond 6 that I can recall, if that. > >>> > >>> I suppose that I could get around the limit by boxing items of a higher > >>> rank to reduce them to lower rank and using one verb to manipulate the > >>> boxes and another to manipulate the dimensions within the box. > >>> > >>> What is the performance advantage to setting a boundary? > >>> > >>> > >>>> On Apr 4, 2021, at 07:45, bill lam <[email protected]> wrote: > >>>> > >>>> What's special about 63? Why not 128, say. > >>>> > >>>>> On Sun, Apr 4, 2021, 9:52 PM Henry Rich <[email protected]> > wrote: > >>>>> > >>>>>> I propose that the maximum value for a rank, whether of a verb or a > >>>>>> noun, will be 63. Minimum verb rank will be _63. > >>>>>> > >>>>>> You got a problem with that? > >>>>>> > >>>>>> Henry Rich > >>>>>> > >>>>>> -- > >>>>>> This email has been checked for viruses by AVG. > >>>>>> https://www.avg.com > >>>>>> > >>>>>> > ---------------------------------------------------------------------- > >>>>>> 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 > >>> > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Devon McCormick, CFA Quantitative Consultant ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
