This report presents a methodology for measuring the performance of supercomputers. It includes 13 Fortran programs that total over 50,000 lines of source code. They represent applications in several areas of engi neering and scientific computing, and in many cases the codes are currently being used by computational re search and development groups. We also present the PERFECT Fortran standard, a set of guidelines that allow portability to several types of machines. Furthermore, we present some performance measures and a method ology for recording and sharing results among diverse users on different machines. The results presented in this paper should not be used to compare machines, except in a preliminary sense. Rather, they are presented to show how the methodology has been applied, and to encourage others to join us in this effort. The results should be regarded as the first step toward our objec tive, which is to develop a publicly accessible data base of performance information of this type.

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Paper-T h o masons for the creation of llliac IV a n described and Wn history of tho liiiac IV p t + c t is mwntod. The archihchrn or hardware struetun of * llliac IV is di scuss-llllac IV array is an army processor with a rp.dalied control unit (CUI that urn be vkwed as a small stand-alone comput er. The llliac IV sohare strategy is described in k r m s of current user habits and needs. Brief descriptions are given of the systems software itself, i t s history, and the maior lessons l e a d during its development. Some i d e a s for future development are suggested. Applications of lliiac N are discussed in terms of evaluating the fundon ffxJ rimultanoously on up to 64 distinct argument sets x<. Many of the timeconsuming probkms In scientiAc computation invoke repeated evaludon of the same function on dihrenl agument s o h. The agumenl sets which compose the problem data base must be structured in such a fashion tho+ they can bo dimtbuted omong 64 separate memories. Two matrix a p plications: Jacobi's algorithm for Anding the eigenvalues and eigenvectors of mal symmetric matrices, and reducing a mal nonsymmetric matrix to the uppor-Hawnberg form using Householder's transformotions are discussed in detail. The ARPA networlr, a highly sophisticated and wide ranging experiment in the remote access and sharing of computer n-SOUKOS, is brieAy described and its current status discussed. Many remarchers located about the country who will use Illiac IV in solving problems will do so via the network. The various systems, hardware, and procedures they will use is discussed. I. INTRODUCI-ION 1 T ALL BEGAN in the early 1950's shortly after EDVAC [l] became operational. Hundreds, then thousands of computers were manufactured, and they were generally organized on Von Neumann's concepts, as shown and described in Fig. 1. In the decade betwetm 1950 and 190, memories became cheaper and faster, and the concept of archival storage was evolved; control-and-arithmetic and logic units became more sophisticated:

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Linear algebra algorithms based on the BLAS or ex tended BLAS do not achieve high performance on mul tivector processors with a hierarchical memory system because of a lack of data locality. For such machines, block linear algebra algorithms must be implemented in terms of matrix-matrix primitives (BLAS3). Designing ef ficient linear algebra algorithms for these architectures requires analysis of the behavior of the matrix-matrix primitives and the resulting block algorithms as a func tion of certain system parameters. The analysis must identify the limits of performance improvement possible via blocking and any contradictory trends that require trade-off consideration. We propose a methodology that facilitates such an analysis and use it to analyze the per formance of the BLAS3 primitives used in block methods. A similar analysis of the block size-perfor mance relationship is also performed at the algorithm level for block versions of the LU decomposition and the Gram-Schmidt orthogonalization procedures.

SystemA new parallel algorithm for the solution of trmngular banded systems of hnear equations is presented The algorithm Is most statable when the number of available processors is much less than the order of the system. Numerical results obtained for some typical examples are also presented

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