TY - GEN

T1 - On the synthesis of parallel programs from tensor product formulas for block recursive algorithms

AU - Gupta, S.

AU - Huang, C. H.

AU - Sadayappan, P.

AU - Johnson, R.

N1 - Funding Information:
1This work was supported in part by DARPA,o rder number 7898, monitored by NIST under grant number 60NANB1D1151, DARPA, order number 7899, monitored by NIST under grant number 60NANB1D1150, and Ohio State UniversityS eed Grant, No. 221337.

PY - 1993

Y1 - 1993

N2 - This paper presents a methodology for synthesizing parallel programs for block recursive algorithms such as fast Fourier transforms and Strassen’s matrix multiplication algorithm. A block recursive algorithm is expressed as a tensor product formula which consists of matrix sums, matrix products, direct sums, tensor products, componentwise matrix operations, and stride permutations. These mathematical operations can be mapped to high-level programming language constructs such as iteration, sequential composition, parallel composition, vector operations, and index computation. Translation of a tensor product formula consisting of these primitives into a parallel program involves determination of the proper indexing schemes for the arrays. This paper gives an algorithm to determine the indexing scheme and the code required for the index computation. Various parallel programs can be synthesized by manipulating tensor product formulas to exploit different computational structures. In this paper, we discuss some issues involved in formula manipulation for a particular target machine, the Cray Y-MP.

AB - This paper presents a methodology for synthesizing parallel programs for block recursive algorithms such as fast Fourier transforms and Strassen’s matrix multiplication algorithm. A block recursive algorithm is expressed as a tensor product formula which consists of matrix sums, matrix products, direct sums, tensor products, componentwise matrix operations, and stride permutations. These mathematical operations can be mapped to high-level programming language constructs such as iteration, sequential composition, parallel composition, vector operations, and index computation. Translation of a tensor product formula consisting of these primitives into a parallel program involves determination of the proper indexing schemes for the arrays. This paper gives an algorithm to determine the indexing scheme and the code required for the index computation. Various parallel programs can be synthesized by manipulating tensor product formulas to exploit different computational structures. In this paper, we discuss some issues involved in formula manipulation for a particular target machine, the Cray Y-MP.

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U2 - 10.1007/3-540-57502-2_52

DO - 10.1007/3-540-57502-2_52

M3 - Conference contribution

AN - SCOPUS:84888604621

SN - 9783540575023

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 264

EP - 280

BT - Languages and Compilers for Parallel Computing - 5th International Workshop, Proceedings

A2 - Banerjee, Utpal

A2 - Gelernter, David

A2 - Nicolau, Alex

A2 - Padua, David

PB - Springer Verlag

T2 - IFIP WG 5.7 International Conference on Advances in Production Management Systems, APMS 2017

Y2 - 3 September 2017 through 7 September 2017

ER -