Essays/Boolean Array Size

Certain operations on boolean arrays are faster if the product of key axis lengths is a multiple of the number of boolean atoms (bytes) in a machine word. It is simplest to ensure this by making the trailing axis length be a multiple. For example:

   b=: 10000 3 32 ?@$ 2
   c=: 10000 3 31 ?@$ 2

   ts=: 6!:2 , 7!:2@]

   ts '+/b'
0.00534817 1792
   ts '+/c'
0.00654999 1792

   ts '+./b'
0.00549204 1280
   ts '+./c'
0.00769232 1280

In this case */}.$b is 96 and */}.$c is 93; the former is a multiple of 4 (4 bytes in a machine word on 32-bit systems) but the latter is not. Therefore, f/b is faster than f/c even though b has more elements than c .

So if you are doing data design, and it does not matter if the boolean arrays have a few extra columns, then pad them appropriately. At least, do this until the J interpreter is smart enough to do it on its own, in some future release.

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Contributed by Roger Hui.