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@Article{Leiserson_2020,

author    = {Charles E. Leiserson and Neil C. Thompson and Joel S. Emer and Bradley C. Kuszmaul and Butler W. Lampson and Daniel Sanchez and Tao B. Schardl},
journal   = {Science},
loc       = {Science},
title     = {There's plenty of room at the Top: What will drive computer performance after Moore's law?},
year      = {2020},
month     = {jun},
number    = {6495},
pages     = {eaam9744},
volume    = {368},
doi       = {10.1126/science.aam9744},
publisher = {American Association for the Advancement of Science ({AAAS})},
url       = {https://www.microsoft.com/en-us/research/uploads/prod/2020/11/Leiserson-et-al-Theres-plenty-of-room-at-the-top.pdf}

}

@inbook{10.1145/3453483.3454079,

author    = {Morihata, Akimasa and Sato, Shigeyuki},
title     = {Reverse Engineering for Reduction Parallelization via Semiring Polynomials},
year      = {2021},
isbn      = {9781450383912},
publisher = {Association for Computing Machinery},
address   = {New York, NY, USA},
url       = {https://doi.org/10.1145/3453483.3454079},
abstract  = {Parallel reduction, which summarizes a given dataset, e.g., the total, average, and maximum, plays a crucial role in parallel programming. This paper presents a new approach, reverse engineering, to automatically discovering nontrivial parallel reductions in sequential programs. The body of the sequential reduction loop is regarded as a black box, and its input-output behaviors are sampled. If the behaviors correspond to a set of linear polynomials over a semiring, a divide-and-conquer parallel reduction is generated. Auxiliary reverse-engineering methods enable a long and nested loop body to be decomposed, which makes our parallelization scheme applicable to various types of reduction loops. This approach is not only simple and efficient but also agnostic to the details of the input program. Its potential is demonstrated through several use case scenarios. A proof-of-concept implementation successfully inferred linear polynomials for nearly all of the 74 benchmarks exhaustively collected from the literature. These characteristics and experimental results demonstrate the promise of the proposed approach, despite its inherent unsoundness.},
booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation},
pages     = {820–834},
numpages  = {15}

}

@inproceedings{10.1145/3243176.3243204,

author    = {Jiang, Peng and Chen, Linchuan and Agrawal, Gagan},
title     = {Revealing Parallel Scans and Reductions in Recurrences through Function Reconstruction},
year      = {2018},
isbn      = {9781450359863},
publisher = {Association for Computing Machinery},
address   = {New York, NY, USA},
url       = {https://doi.org/10.1145/3243176.3243204},
doi       = {10.1145/3243176.3243204},
abstract  = {Many sequential loops are actually recurrences and can be parallelized across iterations as scans or reductions. Many efforts over the past 2+ decades have focused on parallelizing such loops by extracting and exploiting the hidden scan/reduction patterns. These approaches have largely been based on a heuristic search for closed-form composition of computations across loop iterations.While the search-based approaches are successful in parallelizing many recurrences, they have a large search overhead and need extensive program analysis. In this work, we propose a novel approach called sampling-and-reconstruction, which avoids the search for closed-form composition and has the potential to cover more recurrence loops. It is based on an observation that many recurrences can have a point-value representation. The loop iterations are divided across processors, and where the initial value(s) of the recurrence variable(s) are unknown, we execute with several chosen (sampling) initial values. Then, correct final result can be obtained by reconstructing the function from the outputs produced on the chosen initial values. Our approach is effective in parallelizing linear, rectified-linear, finite-state and multivariate recurrences, which cover all of the test cases in previous works. Our evaluation shows that our approach can parallelize a diverse set of sequential loops, including cases that cannot be parallelized by a state-of-the-art static parallelization tool, and achieves linear scalability across multiple cores.},
booktitle = {Proceedings of the 27th International Conference on Parallel Architectures and Compilation Techniques},
articleno = {10},
numpages  = {13},
keywords  = {loop parallelization, recurrence, reduction},
location  = {Limassol, Cyprus},
series    = {PACT '18}

}