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• W2024908082 abstract "Multiprecision modular exponentiation has a variety of uses, including cryptography, prime testing and computational number theory. It is also a very costly operation to compute. GPU parallelism can be used to accelerate these computations, but to use the GPU efficiently, a problem must involve many simultaneous exponentiation operations. Handling a large number of TLS/SSL encrypted sessions in a data center is an important problem that fits this profile. We are developing a framework that enables generation of highly efficient implementations of exponentiation operations for different NVIDIA GPU architectures and problem instances. One of the challenges in generating such code is that NVIDIA's PTX is not a true assembly language, but is instead a virtual instruction set that is compiled and optimized in different ways for different generations of GPU hardware. Thus, the same PTX code runs with different levels of efficiency on different machines. And as the precision of the computations changes, each architecture has its own break-even points where a different algorithm or parallelization strategy must be employed. To make the code efficient for a given problem instance and architecture thus requires searching a multidimensional space of algorithms and configurations, by generating PTX code for each combination, executing it, validating the numerical result, and evaluating its performance. Our framework automates much of this process, and produces exponentiation code that is up to six times faster than the best known hand-coded implementations for the NVIDIA GTX 580. Our goal for the framework is to enable users to relatively quickly find the best configuration for each new GPU architecture. However, in migrating to the GTX 680, which has three times as many cores as the GTX 580, we found that the best performance our system could achieve was significantly less than for the GTX 580. The decrease was traced to a radical shift in the NVIDIA architecture that greatly reduces the storage resources for each core. Further analysis and feasibility simulations indicate that it should be possible, through changes in our code generators to adapt for different storage models, to take greater advantage of the parallelism on the GTX 680. That will add a new dimension to our search space, but will also give our framework greater flexibility for dealing with future architectures." @default.
• W2024908082 created "2016-06-24" @default.
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• W2024908082 date "2013-12-01" @default.
• W2024908082 modified "2023-09-23" @default.
• W2024908082 title "SEARCH-BASED AUTOMATIC CODE GENERATION FOR MULTIPRECISION MODULAR EXPONENTIATION ON MULTIPLE GENERATIONS OF GPU" @default.
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• W2024908082 doi "https://doi.org/10.1142/s0129626413400094" @default.
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