968 research outputs found
Three-dimensional memory vectorization for high bandwidth media memory systems
Vector processors have good performance, cost and adaptability when targeting multimedia applications. However, for a significant number of media programs, conventional memory configurations fail to deliver enough memory references per cycle to feed the SIMD functional units. This paper addresses the problem of the memory bandwidth. We propose a novel mechanism suitable for 2-dimensional vector architectures and targeted at providing high effective bandwidth for SIMD memory instructions. The basis of this mechanism is the extension of the scope of vectorization at the memory level, so that 3-dimensional memory patterns can be fetched into a second-level register file. By fetching long blocks of data and by reusing 2-dimensional memory streams at this second-level register file, we obtain a significant increase in the effective memory bandwidth. As side benefits, the new 3-dimensional load instructions provide a high robustness to memory latency and a significant reduction of the cache activity, thus reducing power and energy requirements. At the investment of a 50% more area than a regular SIMD register file, we have measured and average speed-up of 13% and the potential for power savings in the L2 cache of a 30%.Peer ReviewedPostprint (published version
Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures
Feltor is a modular and free scientific software package. It allows
developing platform independent code that runs on a variety of parallel
computer architectures ranging from laptop CPUs to multi-GPU distributed memory
systems. Feltor consists of both a numerical library and a collection of
application codes built on top of the library. Its main target are two- and
three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin
methods as the main numerical discretization technique. We observe that
numerical simulations of a recently developed gyro-fluid model produce
non-deterministic results in parallel computations. First, we show how we
restore accuracy and bitwise reproducibility algorithmically and
programmatically. In particular, we adopt an implementation of the exactly
rounded dot product based on long accumulators, which avoids accuracy losses
especially in parallel applications. However, reproducibility and accuracy
alone fail to indicate correct simulation behaviour. In fact, in the physical
model slightly different initial conditions lead to vastly different end
states. This behaviour translates to its numerical representation. Pointwise
convergence, even in principle, becomes impossible for long simulation times.
In a second part, we explore important performance tuning considerations. We
identify latency and memory bandwidth as the main performance indicators of our
routines. Based on these, we propose a parallel performance model that predicts
the execution time of algorithms implemented in Feltor and test our model on a
selection of parallel hardware architectures. We are able to predict the
execution time with a relative error of less than 25% for problem sizes between
0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth
gives a minimum array size per compute node to achieve a scaling efficiency
above 50% (both strong and weak)
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
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