A Novel Mapping of Arbitrary Precision Integer Operations to the GPU

Matthias Gusenbauer
A Novel Mapping of Arbitrary Precision Integer Operations to the GPU
[Thesis]

Information

Abstract

With modern processing hardware converging on the physical barrier in terms of transistor size and speed per single core, hardware manufacturers have shifted their focus to improve performance from raw clock power towards parallelization. Solutions to utilize the computation power of GPUs are published and supported by graphics card manufacturers. While there exist solutions for arbitrary precision integer arithmetics on the CPU there has been little adoption of these libraries to the GPU. This thesis presents an approach to map arbitrary precision integer operations to single threads on the GPU. This novel computation mapping technique is benchmarked and compared to a library that runs these computations on the CPU. Furthermore the novel parallelization technique is compared to an alternative mapping scheme proposed by Langer et al [Lan15]. It is shown that mapping computations to single threads outperforms both the CPU and the approach by Langer. This thesis also explored the feasibility of rational number operations on the GPU and shows that this is in fact practically usable by providing benchmarks.

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BibTeX

@bachelorsthesis{Gusenbauer_Matthias_2015_ANM,
  title =      "A Novel Mapping of Arbitrary Precision Integer Operations to
               the GPU",
  author =     "Matthias Gusenbauer",
  year =       "2015",
  abstract =   "With modern processing hardware converging on the physical
               barrier in terms of transistor size and speed per single
               core, hardware manufacturers have shifted their focus to
               improve performance from raw clock power towards
               parallelization. Solutions to utilize the computation power
               of GPUs are published and supported by graphics card
               manufacturers.  While there exist solutions for arbitrary
               precision integer arithmetics on the CPU there has been
               little adoption of these libraries to the GPU. This thesis
               presents an approach to map arbitrary precision integer
               operations to single threads on the GPU. This novel
               computation mapping technique is benchmarked and compared to
               a library that runs these computations on the CPU.
               Furthermore the novel parallelization technique is compared
               to an alternative mapping scheme proposed by Langer et al
               [Lan15]. It is shown that mapping computations to single
               threads outperforms both the CPU and the approach by Langer.
               This thesis also explored the feasibility of rational number
               operations on the GPU and shows that this is in fact
               practically usable by providing benchmarks.",
  month =      sep,
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  school =     "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2015/Gusenbauer_Matthias_2015_ANM/",
}