Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic
•An algorithm and a software are proposed for floating-point precision auto-tuning.•Input programs are automatically modified taking into account accuracy requirements.•Discrete Stochastic Arithmetic is used to verify the results accuracy.•Performance results are presented on several benchmarks and...
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| Vydané v: | Journal of computational science Ročník 36; s. 101017 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.09.2019
Elsevier |
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| ISSN: | 1877-7503, 1877-7511 |
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| Abstract | •An algorithm and a software are proposed for floating-point precision auto-tuning.•Input programs are automatically modified taking into account accuracy requirements.•Discrete Stochastic Arithmetic is used to verify the results accuracy.•Performance results are presented on several benchmarks and on an industrial code.
The type length chosen for floating-point numbers (e.g. 32 bits or 64 bits) may have an impact on the execution time, especially on SIMD (Single Instruction Multiple Data) units. Furthermore optimizing the types used in a numerical simulation causes a reduction of the data volume that is possibly transferred. In this paper we present PROMISE, a tool that makes it possible to optimize the numerical types in a program by taking into account the requested accuracy on the computed results. With PROMISE the numerical quality of results is verified using DSA (Discrete Stochastic Arithmetic) that enables one to estimate round-off errors. The search for a suitable type configuration is performed with a reasonable complexity thanks to the delta debugging algorithm. The PROMISE tool has been successfully tested on programs implementing several numerical algorithms including linear system solving and also on an industrial code that solves the neutron transport equations. |
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| AbstractList | The type length chosen for floating-point numbers (e.g. 32 bits or 64 bits) may have an impact on the execution time, especially on SIMD (Single Instruction Multiple Data) units. Furthermore optimizing the types used in a numerical simulation causes a reduction of the data volume that is possibly transferred. In this paper we present PROMISE, a tool that makes it possible to optimize the numerical types in a program by taking into account the requested accuracy on the computed results. With PROMISE the numerical quality of results is verified using DSA (Discrete Stochastic Arithmetic) that enables one to estimate round-off errors. The search for a suitable type configuration is performed with a reasonable complexity thanks to the delta debugging algorithm. The PROMISE tool has been successfully tested on programs implementing several numerical algorithms including linear system solving and also on an industrial code that solves the neutron transport equations. •An algorithm and a software are proposed for floating-point precision auto-tuning.•Input programs are automatically modified taking into account accuracy requirements.•Discrete Stochastic Arithmetic is used to verify the results accuracy.•Performance results are presented on several benchmarks and on an industrial code. The type length chosen for floating-point numbers (e.g. 32 bits or 64 bits) may have an impact on the execution time, especially on SIMD (Single Instruction Multiple Data) units. Furthermore optimizing the types used in a numerical simulation causes a reduction of the data volume that is possibly transferred. In this paper we present PROMISE, a tool that makes it possible to optimize the numerical types in a program by taking into account the requested accuracy on the computed results. With PROMISE the numerical quality of results is verified using DSA (Discrete Stochastic Arithmetic) that enables one to estimate round-off errors. The search for a suitable type configuration is performed with a reasonable complexity thanks to the delta debugging algorithm. The PROMISE tool has been successfully tested on programs implementing several numerical algorithms including linear system solving and also on an industrial code that solves the neutron transport equations. |
| ArticleNumber | 101017 |
| Author | Févotte, François Jézéquel, Fabienne Graillat, Stef Picot, Romain Lathuilière, Bruno |
| Author_xml | – sequence: 1 givenname: Stef surname: Graillat fullname: Graillat, Stef email: Stef.Graillat@lip6.fr organization: Sorbonne Université, CNRS, LIP6, F-75005 Paris, France – sequence: 2 givenname: Fabienne surname: Jézéquel fullname: Jézéquel, Fabienne email: Fabienne.Jezequel@lip6.fr organization: Sorbonne Université, CNRS, LIP6, F-75005 Paris, France – sequence: 3 givenname: Romain surname: Picot fullname: Picot, Romain email: Romain.Picot@lip6.fr organization: Sorbonne Université, CNRS, LIP6, F-75005 Paris, France – sequence: 4 givenname: François orcidid: 0000-0003-2402-0535 surname: Févotte fullname: Févotte, François email: Francois.Fevotte@edf.fr organization: EDF R&D, 7 boulevard Gaspard Monge, 91120 Palaiseau, France – sequence: 5 givenname: Bruno surname: Lathuilière fullname: Lathuilière, Bruno email: Bruno.Lathuiliere@edf.fr organization: EDF R&D, 7 boulevard Gaspard Monge, 91120 Palaiseau, France |
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| Keywords | Round-off errors Numerical validation Discrete Stochastic Arithmetic Auto-tuning Floating-point arithmetic floating-point arithmetic round-off errors numerical validation auto-tuning |
| Language | English |
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| Snippet | •An algorithm and a software are proposed for floating-point precision auto-tuning.•Input programs are automatically modified taking into account accuracy... The type length chosen for floating-point numbers (e.g. 32 bits or 64 bits) may have an impact on the execution time, especially on SIMD (Single Instruction... |
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| SubjectTerms | Auto-tuning Computer Science Discrete Stochastic Arithmetic Floating-point arithmetic Numerical validation Round-off errors |
| Title | Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic |
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