We consider the requirements for uniform pseudo-random number generators on modern vector and parallel supercomputers, consider the pros and cons of various classes of methods, and outline what is currently available. We propose a class of random number generators which have good statistical properties and can be implemented efficiently on vector processors and parallel machines. A good method for initialization of these generators is described, and an implementation on a Fujitsu VP 2200/10 vector processor is discussed. 1

Abstract: In biological systems formed by living cells, the small populations of some reactant species can result in inherent randomness which cannot be captured by traditional deterministic approaches. In that case, a more accurate simulation can be obtained by using the Stochastic Simulation Algorithm (SSA). Many stochastic realizations are required to capture accurate statistical information of the solution. This carries a very high computational cost. The current generation of graphics processing units (GPU) is well-suited to this task. We describe our implementation, and present some computational experiments illustrating the power of this technology for this important and challenging class of problems.

We consider an individual-based model for fish schooling which incorporates a tendency for each fish to align its position and orientation with an appropriate average of its neighbors ’ positions and orientations, plus a tendency for each fish to avoid collisions. To accurately determine statistical properties of the collective motion of fish whose dynamics are described by such a model, many realizations are typically required. This carries a very high computational cost. The current generation of graphics processing units is well-suited to this task. We describe our implementation, and present computational experiments illustrating the power of this technology for this important and challenging class of problems. 1.

Since 1991 the Australian National University and Fujitsu Ltd. Japan have been involved in a collaboration to develop new algorithms and mathematical software for the Fujitsu supercomputers. Software which has been released for the Fujitsu VPP 500 includes routines for the direct and iterative solution of linear systems of equations, random number generators and fast Fourier transforms. Other software under development is for eigenvalue problems and nonlinear problems. The software developed at the ANU lets the user enjoy the high performance of the VPP 500 while not having to deal with the implementational details and the choice of the best algorithms. The talk will discuss some of the projects and problems, solutions and experiences encountered while developing the mathematical software on the VPP 500. 1 Introduction Since the end of 1993 a team of researchers at ANU has been actively involved in the development of algorithms and software for the Fujitsu VPP 500. This followed almos...

this article, the general design of RANEXP is outlined and the generators included are briefly described. The theoretical background for these generators is not discussed here, since various textbooks and review articles cover this field. For details on the algorithms, chapter 3 of Knuth[5], chapter 6 of Bratley/Fox/Schrage[2], chapter 7 of Press et.al[11, 12] and the review articles by James[4] and Marsaglia[7] may be referenced. The bibliography of the separate RANEXP manual contains further references. The generators are implemented in ANSI C[1], which is well-suited to efficiently implement those algorithms in a way fully conforming to the language standard, thus enhancing portability. A separate Fortran interface is provided which enables Fortran application programs to use the generators.