Separable projection integrals for higher-order correlators of the cosmic microwave sky: Acceleration by factors exceeding 100
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© 2016. We present a case study describing efforts to optimise and modernise "Modal", the simulation and analysis pipeline used by the Planck satellite experiment for constraining general non-Gaussian models of the early universe via the bispectrum (or three-point correlator) of the cosmic microwave background radiation. We focus on one particular element of the code: the projection of bispectra from the end of inflation to the spherical shell at decoupling, which defines the CMB we observe today. This code involves a three-dimensional inner product between two functions, one of which requires an integral, on a non-rectangular domain containing a sparse grid. We show that by employing separable methods this calculation can be reduced to a one-dimensional summation plus two integrations, reducing the overall dimensionality from four to three. The introduction of separable functions also solves the issue of the non-rectangular sparse grid. This separable method can become unstable in certain scenarios and so the slower non-separable integral must be calculated instead. We present a discussion of the optimisation of both approaches.We demonstrate significant speed-ups of ≈100×, arising from a combination of algorithmic improvements and architecture-aware optimisations targeted at improving thread and vectorisation behaviour. The resulting MPI/OpenMP hybrid code is capable of executing on clusters containing processors and/or coprocessors, with strong-scaling efficiency of 98.6% on up to 16 nodes. We find that a single coprocessor outperforms two processor sockets by a factor of 1.3× and that running the same code across a combination of both microarchitectures improves performance-per-node by a factor of 3.38×. By making bispectrum calculations competitive with those for the power spectrum (or two-point correlator) we are now able to consider joint analysis for cosmological science exploitation of new data.
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1090-2716
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Science and Technology Facilities Council (ST/J005673/1)
Science and Technology Facilities Council (ST/K00333X/1)
Science and Technology Facilities Council (ST/M00418X/1)
Science and Technology Facilities Council (ST/M007065/1)
Science and Technology Facilities Council (ST/H008586/1)