By 1985, the Mark II machine was in constant use and we were beginning to examine software issues that had previously been of little concern. Algorithms, such as the standard FFT, had obvious implementations on a hypercube [Salmon:86b], [Fox:88a]-the ``bit-twiddling'' done by the FFT algorithm could be mapped onto a hypercube by ``twiddling'' the bits in a slightly revised manner. More problematic was the issue of two- or three-dimensional problem solving. A two- or three-dimensional problem could easily be mapped into a small number of nodes. However, one cannot so easily perform the mapping of grids onto 128 nodes connected as a seven-dimensional hypercube.
Another issue that quickly became apparent was that C
P users did
not have a good feel for the ``chan'' argument used by the
primitive communication functions. Users wanted to think of a
collection of processors each labelled by a number, with data exchanged
between them, but unfortunately the software was driven instead by the
hypercube architecture of the machine. Tolerance of the explanation of
``Well, you XOR the processor number with one shifted left by
the 
'' was rapidly exceeded in all but the most stubborn users.
Both problems were effectively removed by the development of whoami [Salmon:84b]. We used the well-known techniques of binary grey codes to automate the process of mapping two, three, or higher dimensional problems to the hypercube. The whoami function took the dimensionality of the physical system being modelled and returned all the necessary ``chan'' values to make everything else work out properly. No longer did the new user have to spend time learning about channel numbers, XORing, and the ``mapping problem''-everything was done by the call to whoami. Even on current hardware, where long-range communication is an accepted fact, the techniques embodied by whoami result in programs that can run up to an order of magnitude faster than those using less convenient mapping techniques (see Figure 5.1).
Figure 5.1: Mapping a Two-dimensional World