宇宙微波天空的高阶散射子的可分离投影积分：超过100倍的加速
Separable projection integrals for higher-order correlators of the cosmic microwave sky: Acceleration by factors exceeding 100
摘要：
我们提出了一个案例研究，描述了努力优化和现代化的“模态”，模拟和分析管道所使用的普朗克卫星实验约束一般非高斯模型的早期宇宙通过双谱（或三点相关）的宇宙微波背景辐射。我们专注于一个特定的元素的代码：双谱的投影从年底的通货膨胀的球壳去耦，这定义了我们今天观察到的CMB。这段代码涉及两个函数之间的三维内积，其中一个需要积分，在包含稀疏网格的非矩形域上。我们表明，通过采用可分离的方法，这种计算可以减少到一个一维的总和加上两个积分，减少整体维数从四到三。可分离函数的引入也解决了非矩形稀疏网格的问题。这种可分离的方法在某些情况下可能变得不稳定，因此必须计算较慢的不可分离积分。我们提出了两种方法的优化讨论。我们展示了约100倍的显着速度提升，这是由于算法改进和架构感知优化的结合，旨在改善线程和向量化行为。由此产生的MPI/OpenMP混合代码能够在包含处理器和/或协处理器的集群上执行，在多达16个节点上具有98.6%的强大扩展效率。我们发现，单个协处理器的性能优于两个处理器插槽的1.3倍，在两个微架构的组合中运行相同的代码，可将每个节点的性能提高3.38倍。通过使双谱计算与功率谱（或两点相关器）的计算竞争，我们现在能够考虑联合分析宇宙科学开发的新数据。
英文摘要：
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 cases and so the slower non-separable integral must be calculated instead. We present a discussion of the optimisation of both approaches. We show significant speed-ups of ~100x, 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 1.3x and that running the same code across a combination of both microarchitectures improves performance-per-node by a factor of 3.38x. 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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