The Tensor Contraction Engine
The majority of software for scientific computations is written in the
lowlevel languages FORTRAN and C. The computational structure of
some of this software, however, has sufficient underlying structure
that it could benefit from specialpurpose software engineering tools
or domainspecific programming languages. E.g., electronic structure
calculations in quantum chemistry and in physics involve large
collections of tensor contractions (generalized matrix
multiplications). Currently, chemists spend weeks or months
manipulating formulas containing dozens or hundreds of terms with
Mathematica, handoptimizing the computation, and writing FORTRAN code
by hand. The computation can take on the order of 1 TFLOP week or
more and can require multiple TBs of storage.
We have developed a domainspecific language that allows chemists to
specify the computation in a highlevel Mathematicastyle language.
The compiler for this language, the Tensor Contraction Engine (TCE),
searches for an optimal implementation and generates FORTRAN code.
First, algebraic transformations are used to reduce the number
of operations. We then minimize the storage requirements to fit the
computation within the disk limits by fusing loops. We have
designed an algorithm that finds the optimal evaluation order if
intermediate arrays are allocated dynamically and are
working on combining loop fusion with dynamic memory allocation. If
the computation does not fit within the disk limits, recomputation
must be traded off for a reduction in storage requirements. If
the target machine is a multiprocessor machine, we optimize the
communication cost together with finding a fusion configuration for
minimizing storage. Finally, we minimize the data access times by
minimizing disktomemory and memorytocache traffic and
generate FORTRAN code. We have completed a first prototype of the TCE
and are working on implementing the communication minimization and
data access optimization algorithms. In future research, we will
extend this approach to handle common subexpressions, symmetric
matrices, and sparse matrices.
The Tensor Contraction Engine (TCE) is the application of compiler
optimization and sourcetosource translation technology to craft a
domain specific language for manybody theories in chemistry and
physics. The underlying equations of these theories are all expressed
as contractions of manydimensional arrays or tensors There may be
many thousands of such terms in any one problem but their regularity
means that they can be translated into efficient massively parallel
code that respects the boundedness of each level of the memory
hierarchy and minimizes overall runtime with effective tradeoff of
increased computation for reduced memory consumption. The approach has
been overwhelming successful and now NWChem contains about 1M lines of
humangenerated code and over 2M lines of machine generated code. The
resulting scientific capabilities would have taken many mandecades of
effort and new theories/models can be tested in a morning on
physically relevant systems instead of on small test systems after
months of effort. In combination with the OCE (operator contraction
engine) that turns Feynmanlike diagrams into tensor expressions the
TCE represents perhaps the first endtoend production quality example
of a solution to the semantic gap.
For an overview of the project, see our
Proceedings of the IEEE paper.
For more information about version 1.0 of the TCE (the "prototype"
TCE), please see our Getting and Using the
TCE page.
Investigators

P. Sadayappan
(Overall PI), Dept. of Computer Sci. and Engr., Ohio State

J. Ramanujam,
(PI from LSU) Dept. of Electrical and Computer Eng., Lousiana State

Gerald Baumgartner,
Dept. of Computer Sci., Louisiana State

David E. Bernholdt,
Oak Ridge National Lab.

Robert J. Harrison,
Oak Ridge National Lab.

Russell M. Pitzer,
Dept. of Chemistry, Ohio State

So Hirata,
University of Florida.

Marcel Nooijen,
Dept. of Chemistry, University of Waterloo
Senior Personnel
 Alexander Auer,
Dept. of Chemistry, University of Waterloo
 Daniel Cociorva,
Dept. of Computer Sci. & Engr., Ohio State
 Venkatesh Choppella,
Indian Institute for Information Technology and Management,
Kerala Technopark, India
 ChiChung Lam,
Dept. of Computer Sci. & Engr., Ohio State
Students
 Ankush Agarwal
 Atef Allam
 Alina Bibireata
 Xiaoyang Gao

Albert Hartono
 Jinpyo Hong
 Sandhya Krishnan

Sriram Krishnamoorthy
 Qingda Lu
 Hassan Salamy
 Alexander Sibiriakov
 Vaidyanathan Sivaraman
 Tong Wang
Publications
 Q. Lu, X. Gao, S. Krishnamoorthy, G. Baumgartner, J. Ramanujam and P. Sadayappan,
"Empirical Performance ModelDriven Data Layout Optimization and
Library Call Selection for Tensor Contraction Expressions,"
in Journal of Parallel and Distributed Computing,
72(3):338352, March 2012.
 A. Hartono, Q. Lu, T. Henretty, S.
Krishnamoorthy, H. Zhang, G. Baumgartner, D. E. Bernholdt, M. Nooijen,
R. Pitzer, J. Ramanujam, and P. Sadayappan,
"Performance Optimization of Tensor Contraction Expressions for
ManyBody Methods in Quantum Chemistry," The Journal of Physical Chemistry A,
Vol. 113 (45), pp. 1271512723, 2009.
 X. Gao, S. Krishnamoorthy, S. Sahoo, C. Lam, G. Baumgartner, J.
Ramanujam, and P. Sadayappan, "Efficient SearchSpace Pruning for
Integrated Fusion and Tiling Transformations," Concurrency and
Computation: Practice and Experience, 2007.
[pdf]
 S. Krishnan, S. Krishnamoorthy, G. Baumgartner, C. Lam,
J. Ramanujam, P. Sadayappan, and V. Choppella, "Efficient Synthesis of
OutofCore Algorithms Using a Nonlinear Optimization Solver,"
Journal of Parallel and Distributed Computing, vol. 66, no. 5,
pp. 659673, May 2006.
[pdf]
 A. Auer, G. Baumgartner, D. Bernholdt,
A. Bibireata, V. Choppella, D. Cociorva,
X. Gao, R. Harrison, S. Krishnamoorthy,
S. Krishnan, C. Lam, Q. Lu, M. Nooijen,
R. Pitzer, J. Ramanujam, P. Sadayappan, and
A. Sibiryakov, "Automatic Code Generation for ManyBody
Electronic Structure Methods: The Tensor Contraction Engine,"
Molecular Physics, vol. 104, no. 2,
pp. 211228, January 2006.
[pdf]
 A. Hartono, Q. Lu, X. Gao, S. Krishnamoorthy, M. Nooijen,
G. Baumgartner, D. Bernholdt, R. Pitzer, J. Ramanujam, A. Rountev,
and P. Sadayappan, "Identifying CostEffective Common
Subexpressions to Reduce Operation Count in Tensor Contraction
Evaluations," in Proc. International Conference on
Computational Science 2006 (ICCS 2006), Reading, UK, Lecture
Notes in Computer Science, SpringerVerlag, 2006.
[pdf]
 G. Baumgartner, A. Auer, D. Bernholdt, A. Bibireata,
V. Choppella, D. Cociorva, X. Gao, R. Harrison, S. Hirata,
S. Krishnamoorthy, S. Krishnan, C. Lam, Q. Lu, M. Nooijen, R. Pitzer,
J. Ramanujam, P. Sadayappan, and A. Sibiryakov,
"Synthesis of HighPerformance Parallel Programs for a Class of ab
initio Quantum Chemistry Models,"
Proceedings of the IEEE, vol. 93, no. 2, pp. 276292, February 2005.
[pdf]
 X. Gao, S. Sahoo, Q. Lu, G. Baumgartner, C. Lam, J. Ramanujam, and
P. Sadayappan, "Performance Modeling and Optimization of
Parallel OutofCore Tensor Contractions," in Proc. ACM
SIGPLAN 2005 Symposium on Principles and Practice of Parallel
Programming, Chicago, IL, June 2005.
[pdf]
 A. Hartono, A. Sibiryakov, M. Nooijen, G. Baumgartner,
D.E. Bernholdt, S. Hirata, C. Lam, R. Pitzer, J. Ramanujam, and
P. Sadayappan, "Automated Operation Minimization of Tensor
Contraction Expressions in Electronic Structure Calculations," in
Proc. International Conference on Computational Science 2005
(ICCS 2005), Atlanta, GA, May 2005.
[pdf]
 Efficient Synthesis of Outofcore Algorithms Using a
Nonlinear Optimization Solver, Sandhya Krishnan, Sriram
Krishnamoorthy, Gerald Baumgartner, ChiChung Lam, J. Ramanujam, and
P. Sadayappan. In Proceedings of the 18th International
Parallel and Distributed Processing Symposium (2004 IPDPS
Conference), Santa Fe, April 2004. (Best Paper
Award)
[pdf]
 A HighLevel Approach to Synthesis of HighPerformance Codes
for Quantum Chemistry: The Tensor Contraction Engine
G. Baumgartner, D.E. Bernholdt, V. Choppella, J. Ramanujam,
P. Sadayappan.
In Proceedings of the 11th Workshop
on Compilers for Parallel Computers (CPC 2004),
Chiemsee, Germany, 79 July 2004, pp. 281290.

Data Locality Optimization for Synthesis of Efficient
OutofCore Algorithms
S. Krishnan, S. Krishnamoorthy, G. Baumgartner, D. Cociorva,
C. Lam, P. Sadayappan, J. Ramanujam, D.E. Bernholdt, V. Choppella.
In Proceedings of the International Conference on
HighPerformance Computing (HiPC '03),
Hyderabad, India, 1720 December 2003.
In Lecture Notes in Computer Science, Vol. 2913, SpringerVerlag,
pp. 406417. Best paper award.

MemoryConstrained Data Locality Optimization for
Tensor Contractions
A. Bibireata, S. Krishnan, G. Baumgartner, D. Cociorva, C. Lam,
P. Sadayappan, J. Ramanujam, D.E. Bernholdt, V. Choppella.
In L. Rauchwerger (ed.),
Proceedings of the 16th International Workshop on
Languages and Compilers for Parallel Computing (LCPC '03),
College Station, Texas, 24 October 2003, SpringerVerlag,
Lecture Notes in Computer Science, Vol. 2958, 2004, pp. 93108.

Global Communication Optimization for Tensor Contraction
Expressions under Memory Constraints
D. Cociorva, X. Gao, S. Krishnan, G. Baumgartner, C. Lam,
P. Sadayappan, J. Ramanujam.
In Proceedings of the International Parallel and
Distributed Processing Symposium (IPDPS '03),
Nice, France, 2226 April 2003, Abstract p. 37b, 8 pages.
 CompileTime Optimizations for Tensor Contraction Expressions
G. Baumgartner, D. Cociorva, C. Lam, P. Sadayappan, J. Ramanujam.
In Proceedings of Compilers for Parallel Computers
(CPC '03), Amsterdam, The Netherlands, 810 January, 2003.

A HighLevel Approach to Synthesis of HighPerformance Codes for
Quantum Chemistry
G. Baumgartner, D.E. Bernholdt, D. Cociorva, R.J. Harrison, S. Hirata,
C. Lam, M. Nooijen, R.M. Pitzer, J. Ramanujam, P. Sadayappan.
In Proceedings of Supercomputing 2002,
Baltimore, Maryland, 1622 November 2002.
IEEE Computer Society Press, Abstract p. 5, 10 pages.

MemoryConstrained Communication Minimization for a Class of
Array Computations
D. Cociorva, G. Baumgartner, C. Lam, P. Sadayappan, J. Ramanujam.
To appear in B. Pugh, C. Tseng (eds.),
Proceedings of the 15th International Workshop
on Languages and Compilers for Parallel Computing (LCPC '02),
College Park, Maryland, 2527 July 2002.

Automatic Synthesis of HighPerformance Codes for Quantum
Chemistry Applications
G. Baumgartner, D.E. Bernholdt, D. Cociorva, R.J. Harrison,
C. Lam, M. Nooijen, J. Ramanujam, P. Sadayappan.
To appear in Proceedings of the Workshop on Performance
Optimization for HighLevel Languages and Libraries
(POHLL02), New York, New York, 22 June 2002.
 G. Baumgartner, J. Ramanujam, and P. Sadayappan (editors),
Proceedings of the Workshop on Performance Optimization for HighLevel
Languages and Libraries (POHLL02), held in conjunction with the
16th Annual ACM International Conference on Supercomputing (ICS'02),
June 2002, New York, NY.

SpaceTime TradeOff Optimization for a Class of Electronic
Structure Calculations
D. Cociorva, G. Baumgartner, C. Lam, P. Sadayappan,
J. Ramanujam, M. Nooijen, D.E. Bernholdt, R.J. Harrison.
In Proceedings of the ACM SIGPLAN 2002 Conference on
Programming Language Design and Implementation (PLDI '02),
Berlin, Germany, 1719 June 2002, pp. 177186.

A Performance Optimization Framework for Compilation of Tensor
Contraction Expressions into Parallel Programs.
G. Baumgartner, D.E. Bernholdt, D. Cociorva, R.J. Harrison,
C. Lam, M. Nooijen, J. Ramanujam, P. Sadayappan.
7th International Workshop on HighLevel Parallel
Programming Models and Supportive Environments (HIPS '02),
In Proceedings of the International Parallel and Distributed
Processing Symposium (IPDPS '02),
Fort Lauderdale, Florida, 15 April 2002,
IEEE Computer Society, pp. 106114.

Towards Automatic Synthesis of HighPerformance Codes for
Electronic Structure Calculations: Data Locality Optimization
D. Cociorva, J. Wilkins, G. Baumgartner, P. Sadayappan, J. Ramanujam,
M. Nooijen, D.E. Bernholdt, R.J. Harrison.
In Proceedings of the International Conference on
HighPerformance Computing (HiPC '01),
Hyderabad, India, 1721 December 2001, SpringerVerlag, Lecture Nodes
in Computer Science, Vol. 2228, pp. 237248.

Loop Optimizations for a Class of MemoryConstrained
Computations
D. Cociorva, J. Wilkins, C. Lam, G. Baumgartner, P. Sadayappan,
J. Ramanujam.
In Proceedings of the 15th ACM International Conference on
Supercomputing (ICS '01),
Sorrento, Italy, 1621 June 2001, pp. 103113.
Software
Funding
J. Ramanujam
Last modified: Wed Mar 5 06:30:00 CST 2008