12571
Ichitaro Yamazaki, Stanimire Tomov, Tingxing Dong, Jack Dongarra
We propose a mixed-precision orthogonalization scheme that takes the input matrix in a standard 32 or 64-bit floating-point precision, but uses higher-precision arithmetics to accumulate its intermediate results. For the 64-bit precision, our scheme uses software emulation for the higher-precision arithmetics, and requires about 20x more computation but about the same amount of communication as […]
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Jacques du Toit, Johannes Lotz, Uwe Naumann
We consider a GPU accelerated program using Monte Carlo simulation to price a basket call option on 10 FX rates driven by a 10 factor local volatility model. We develop an adjoint version of this program using algorithmic differentiation. The code uses mixed precision. For our test problem of 10,000 sample paths with 360 Euler […]
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Jianfei Zhang, Lei Zhang
Graphics Processing Unit (GPU) has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using Compute Unified Device Architecture (CUDA). Sliced Block ELLPACK (SBELL) format […]
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Jacques du Toit, Isabel Ehrlich
We present high performance implementations on a CPU and an NVIDIA GPU of a Monte Carlo pricer for a simple FX basket option driven by a multi-factor local volatility model. Basket options such as these are typically considered too complicated to tackle analytically in a market-consistent manner, and are too high dimensional for PDE methods. […]
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Mario Schrock, Hannes Vogt
A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA’s CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional […]
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Hartwig Anzt, Maribel Castillo, Juan C. Fernandez, Vincent Heuveline, Francisco D. Igual, Rafael Mayo and Enrique S. Quintana-Orti
In this paper, we analyze the power consumption of different GPU-accelerated iterative solver implementations enhanced with energy-saving techniques. Specifically, while conducting kernel calls on the graphics accelerator, we manually set the host system to a power-efficient idle-wait status so as to leverage dynamic voltage and frequency control. While the usage of iterative refinement combined with […]
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Hartwig Anzt, Piotr Luszczek, Jack Dongarra, Vincent Heuveline
In hardware-aware high performance computing, block- asynchronous iteration and mixed precision iterative refinement are two techniques that are applied to leverage the computing power of SIMD accelerators like GPUs. Although they use a very different approach for this purpose, they share the basic idea of compensating the convergence behaviour of an inferior numerical algorithm by […]
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Hartwig Anzt, Vincent Heuveline, Bjorn Rocker, Maribel Castillo, Juan C. Fernandez, Rafael Mayo, Enrique S. Quintana-Orti
This paper presents a detailed analysis of a mixed precision iterative refinement solver applied to a linear system obtained from the 2D discretization of a fluid flow problem. The total execution time and energy need of different soft- and hardware implementations are measured and compared with those of a plain GMRES-based solver in double precision. […]
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Hartwig Anzt, Vincent Heuveline, Bjorn Rocker
This paper proposes an error correction method for solving linear systems of equations and the evaluation of an implementation using mixed precision techniques. While different technologies are available, graphic processing units (GPUs) have been established as particularly powerful coprocessors in recent years. For this reason, our error correction approach is focused on a CUDA implementation […]
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Jack J. Dongarra
Summary form only given. In this talk we examine how high performance computing has changed over the last 10-years and look toward the future in terms of trends. These changes have had and will continue to have a major impact on our software. Some of the software and algorithm challenges have already been encountered, such […]
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Yong-Chull Jang, Hyung-Jin Kim, Weonjong Lee
GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have implemented mixed precision algorithm to our multi GPU conjugate gradient solver. The single precision calculation use half […]
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Wang Lei, Zhang Yunquan, Zhang Xianyi, Liu Fangfang
In this paper, the mixed precision algorithm to solve the linear system of equations and the implementation of HPL package are introduced. We use this mixed precision algorithm to improve HPL package on CPU + GPGPU heterogeneous clusters, which is named for GHPL, and give the implementation mechanisms in detail. The experimental results are measured […]
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