Loop transformations are critical for compiling high-performance code for modern computers. Existing work has focused on transformations for perfectly nested loops (that is, loops in which all assignment statements are contained within the innermost loop of a loop nest). In practice, most loop nests, such as those in matrix factorization codes, are imperfectly nested. In some programs, imperfectly nested loops can be transformed into perfectly nested loops by loop distribution, but this is not always legal. In this paper, we present an approach to transforming imperfectly nested loops directly. Our approach is an extension of the linear loop transformation framework for perfectly nested loops, and it models permutation, reversal, skewing, scaling, alignment, distribution and jamming. We also give a completion procedure which generates a complete transformation from a partial transformation.
循环转换对于编译现代计算机的高性能代码至关重要。现有工作集中在完美嵌套循环(即其中所有赋值语句都包含在循环嵌套的最内部循环中的循环)的转换上。实际上,大多数循环嵌套(例如矩阵分解代码中的那些嵌套)是不完美的嵌套。在某些程序中,不完全嵌套的循环可以通过循环分布转换为完全嵌套的循环,但这并不总是合法的。在本文中,我们提出了一种直接转换不完美嵌套循环的方法。我们的方法是针对完美嵌套循环的线性循环转换框架的扩展,并且它对置换,反转,倾斜,缩放,对齐,分布,干扰进行建模。我们还给出了一个完成过程,该过程可以从部分转换中生成完整的转换。 P>
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机译:具有仿射依赖关系的嵌套循环的On循环转换
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机译:合成变换以增强不完美嵌套的循环嵌套的位置