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Can someone explain where and how Halide applies interval analysis internally? Does Halide use interval analysis on an array-based data dependence test?

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It may be "extreme value test" which can be found in the textbook "High-Performance Compilers for Parallel Computing". https://www.amazon.com/dp/0805327304

It may be "interval analysis" written in another textbook "Introduction to Interval Analysis". http://www-sbras.nsc.ru/interval/Library/InteBooks/IntroIntervAn.pdf

Both the above two are the same.