This paper presents an integrated compiler framework for tiling a class of nontrivial imperfectly-nested loops such that cache locality is improved. We develop a new memory cost model to analyze data reuse in terms of both the cache and the TLB, based on which we compute the tile size with or without array duplication. We determine whether to duplicate arrays for tiling by comparing the respect...

• Prop. 8. If g imperfectly dominates f, then hβ(f,g) imperfectly dominates f. ... and yield a hierarchy of manipulability and efficiency. • Prop. 9./10. Given f SP, g manipulable and weakly less varying than f, g imperfectly dominates f, 0≤β<β‘≤1, then 1. hβ‘(f,g) is intensely and strongly more manipulable than hβ(f,g) 2. hβ‘(f,g) imperfectly dominates hβ(f,g). ... which preserve PSP, are comp...