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In this paper, we describe a model-driven compile-time code generator that transforms a class of tensor contraction expressions into highly optimized short-vector SIMD code. We use as a case study a multi-resolution tensor kernel from the MADNESS quantum chemistry application. Performance of a C-based implementation is low, and because the dimensions of the tensors are small, performance using vendor optimized BLAS libraries is also suboptimal. We develop a model-driven code generator that determines the optimal loop permutation and placement of vector load/store, transpose, and splat operations in the generated code, enabling portable performance on short-vector SIMD architectures. Experimental results on an SSE-based platform demonstrate the ef?ciency of the vector-code synthesizer.
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