Physics Projects on APEmille

This document represents the effort of several physicists, presently engaged in numerical simulations on computers of the APE100 family. The document intends to present a wide spectrum of projects, that will become possible with the realization of a parallel computer in the one TeraFlops range. Based on previous experience, several common demands have emerged. Besides computer power, good performances can be achieved if the new machine will have: 1. a compact structure, with a small number of nodes per direction and the minimum possible total number of nodes; 2. more than 120 data registers per node; 3. a local memory of 20--30 GigaWords; 4. I/O performances of at least 60 MegaBytes/sec; 5. availability of double precision floating point operations; 6. integer, arithmetic and logical operations on MADmille; 7. local addressing capability, i.e. the processing nodes may access their own memories using different local addresses. The reasons for the above requirements will be clearer from the discussion in secs. 2--9 and will be summarized in the conclusion. Here, we only want to add a few words about 7., which will not be discussed any more in the following. Many physical studies require processing of large matrices both by rows and columns. A typical example is a multi-dimensional Fourier transform, which finds many applications, such as Fourier acceleration in lattice gauge theories, proposed by R.K. Wilson and collaborators, metereology, climatology, signal analysis, etc. In these cases, one requires a "data transposition phase", that reshuffles the data among the nodes of the machine from a "cut along the row" distribution toward a "cut along the column" one. A local addressing capability allows a high efficiency implementation for matrix transposition on a 3D intercon..