Synthesis of space optimal systolic arrays for band matrix-vector multiplication.
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| Title: | Synthesis of space optimal systolic arrays for band matrix-vector multiplication. |
|---|---|
| Authors: | Milovanović, E.1 ema@elfak.ni.ac.yu, Bekakos, M.2, Milovanović, I.1 |
| Source: | Journal of Supercomputing. Sep2009, Vol. 49 Issue 3, p269-290. 22p. 10 Diagrams, 2 Charts, 2 Graphs. |
| Subjects: | Systolic array circuits, Matrices (Mathematics), Mathematical transformations, Graphic methods, Integrated circuits |
| Abstract: | In this paper, we consider the implementation of a product c= A b, where A is N1× N3 band matrix with bandwidth ω and b is a vector of size N3×1, on bidirectional and unidirectional linear systolic arrays (BLSA and ULSA, respectively). We distinguish the cases when the matrix bandwidth ω is 1≤ ω≤ N3 and N3≤ ω≤ N1+ N3−1. A modification of the systolic array synthesis procedure based on data dependencies and space-time transformations of data dependency graph is proposed. The modification enables obtaining both BLSA and ULSA with an optimal number of processing elements (PEs) regardless of the matrix bandwidth. The execution time of the synthesized arrays has been minimized. We derive explicit formulas for the synthesis of these arrays. The performances of the designed arrays are discussed and compared to the performances of the arrays obtained by the standard design procedure. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Supercomputing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 44096872 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Synthesis of space optimal systolic arrays for band matrix-vector multiplication. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Milovanović%2C+E%2E%22">Milovanović, E.</searchLink><relatesTo>1</relatesTo><i> ema@elfak.ni.ac.yu</i><br /><searchLink fieldCode="AR" term="%22Bekakos%2C+M%2E%22">Bekakos, M.</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Milovanović%2C+I%2E%22">Milovanović, I.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Supercomputing%22">Journal of Supercomputing</searchLink>. Sep2009, Vol. 49 Issue 3, p269-290. 22p. 10 Diagrams, 2 Charts, 2 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Systolic+array+circuits%22">Systolic array circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Graphic+methods%22">Graphic methods</searchLink><br /><searchLink fieldCode="DE" term="%22Integrated+circuits%22">Integrated circuits</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we consider the implementation of a product c= A b, where A is N1× N3 band matrix with bandwidth ω and b is a vector of size N3×1, on bidirectional and unidirectional linear systolic arrays (BLSA and ULSA, respectively). We distinguish the cases when the matrix bandwidth ω is 1≤ ω≤ N3 and N3≤ ω≤ N1+ N3−1. A modification of the systolic array synthesis procedure based on data dependencies and space-time transformations of data dependency graph is proposed. The modification enables obtaining both BLSA and ULSA with an optimal number of processing elements (PEs) regardless of the matrix bandwidth. The execution time of the synthesized arrays has been minimized. We derive explicit formulas for the synthesis of these arrays. The performances of the designed arrays are discussed and compared to the performances of the arrays obtained by the standard design procedure. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Supercomputing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11227-008-0241-x Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 269 Subjects: – SubjectFull: Systolic array circuits Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Mathematical transformations Type: general – SubjectFull: Graphic methods Type: general – SubjectFull: Integrated circuits Type: general Titles: – TitleFull: Synthesis of space optimal systolic arrays for band matrix-vector multiplication. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Milovanović, E. – PersonEntity: Name: NameFull: Bekakos, M. – PersonEntity: Name: NameFull: Milovanović, I. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2009 Type: published Y: 2009 Identifiers: – Type: issn-print Value: 09208542 Numbering: – Type: volume Value: 49 – Type: issue Value: 3 Titles: – TitleFull: Journal of Supercomputing Type: main |
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