Stencil computations represent a very common class of nested loops in scientific and engineering applications. Exploiting vector units in modern CPUs is crucial to achieving peak performance. Previous vectorization approaches often consider the data space, in particular the innermost unit-strided loop. It leads to the well-known data alignment conflict problem that vector loads are overlapped due to the data sharing between continuous stencil computations. This paper proposes a novel temporal vectorization scheme for stencils. It vectorizes the stencil computation in the iteration space and assembles points with different time coordinates in one vector. The temporal vectorization leads to a small fixed number of vector reorganizations that is irrelevant to the vector length, stencil order, and dimension. Furthermore, it is also applicable to Gauss-Seidel stencils, whose vectorization is not well-studied. The effectiveness of the temporal vectorization is demonstrated by various Jacobi and Gauss-Seidel stencils.

中文翻译：

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模板的时间矢量化

模板计算代表了科学和工程应用中非常常见的一类嵌套循环。利用现代 CPU 中的向量单元对于实现峰值性能至关重要。以前的矢量化方法通常会考虑数据空间，尤其是最内层的单位步长循环。由于连续模板计算之间的数据共享，这导致了众所周知的数据对齐冲突问题，即矢量加载重叠。本文提出了一种新的模板时间矢量化方案。它将迭代空间中的模板计算向量化，并将具有不同时间坐标的点组装在一个向量中。时间向量化导致少量固定的向量重组，这些重组与向量长度、模板顺序和维度无关。此外，它也适用于 Gauss-Seidel 模板，其矢量化没有得到很好的研究。各种 Jacobi 和 Gauss-Seidel 模板证明了时间矢量化的有效性。