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Quantum chromodynamics (QCD) is the theory of subnuclear physics, aiming atmod- eling the strong nuclear force, which is responsible for the interactionsof nuclear particles. Lattice QCD (LQCD) is the corresponding discreteformulation, widely used for simula- tions. The computational demand for theLQCD is tremendous. It has played a role in the history of supercomputers, andhas also helped defining their future. Designing efficient LQCD codes thatscale well on large (probably hybrid) supercomputers requires to express manylevels of parallelism, and then to explore different algorithmic solutions.While al- gorithmic exploration is the key for efficient parallel codes, theprocess is hampered by the necessary coding effort. We present in this paper adomain-specific language, QIRAL, for a high level expression of parallelalgorithms in LQCD. Parallelism is expressed through the mathematical struc-ture of the sparse matrices defining the problem. We show that from theseexpressions and from algorithmic and preconditioning formulations, a parallelcode can be automatically generated. This separates algorithms and mathematicalformulations for LQCD (that be- long to the field of physics) from theeffective orchestration of parallelism, mainly related to compilation andoptimization for parallel architectures.

QIRAL: A High Level Language for Lattice QCD Code Generation