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When designing an algorithm, one cares about arithmetic/compu- tational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a given I/O model, scheduling strategies such as loop tiling can reduce the required I/O down to a limit, called the I/O complexity, inherent to the algorithm itself. The objective of I/O complexity analysis is to compute, for a given program, its minimal I/O requirement among all valid schedules. We consider a sequential execution model with two memories, an infinite one, and a small one of size 𝑆 on which the computations retrieve and produce data. The I/O is the number of reads and writes between the two memories. We identify a common “hourglass pattern” in the dependency graphs of several common linear algebra kernels. Using the proper- ties of this pattern, we mathematically prove tighter lower bounds on their I/O complexity, which improves the previous state-of-the- art bound by a parametric ratio. This proof was integrated inside the IOLB automatic lower bound derivation tool. 

Python has become one of the most used and taught languages nowadays. Its expressiveness, cross-compatibility and ease of use have made it popular in areas as diverse as finance, bioinformatics or machine learning. However, Python programs are often significantly slower to execute than an equivalent native C implementation, especially for computation-intensive numerical kernels. This work presents PolyBench/Python, implementing the 30 kernels in PolyBench/C, one of the standard benchmark suites for polyhedral optimization, in Python. In addition to the benchmark kernels, a functional wrapper including mechanisms for performance measurement, testing, and execution configuration has been developed. The framework includes support for different ways to translate C-array codes into Python, offering insight into the tradeoffs of Python lists and NumPy arrays. The benchmark performance is thoroughly evaluated on different Python interpreters, and compared against its PolyBench/C counterpart to highlight the profitability (or lack thereof) of using Python for regular numerical codes.