Quantum chromodynamics (QCD) is the theory of subnuclear physics, aiming at mod- eling the strong nuclear force, which is responsible for the interactions of nuclear particles. Lattice QCD (LQCD) is the corresponding discrete formulation, widely used for simula- tions. The computational demand for the LQCD is tremendous. It has played a role in the history of supercomputers, and has also helped defining their future. Designing efficient LQCD codes that scale well on large (probably hybrid) supercomputers requires to express many levels of parallelism, and then to explore different algorithmic solutions. While al- gorithmic exploration is the key for efficient parallel codes, the process is hampered by the necessary coding effort. We present in this paper a domain-specific language, QIRAL, for a high level expression of parallel algorithms in LQCD. Parallelism is expressed through the mathematical struc- ture of the sparse matrices defining the problem. We show that from these expressions and from algorithmic and preconditioning formulations, a parallel code can be automatically generated. This separates algorithms and mathematical formulations for LQCD (that be- long to the field of physics) from the effective orchestration of parallelism, mainly related to compilation and optimization for parallel architectures.
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