# Simplifying Multiple-Statement Reductions with the Polyhedral Model

@article{Yang2020SimplifyingMR, title={Simplifying Multiple-Statement Reductions with the Polyhedral Model}, author={Cambridge Yang and Eric Hamilton Atkinson and Michael Carbin}, journal={ArXiv}, year={2020}, volume={abs/2007.11203} }

A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and financial analytics.
Contemporary polyhedral-based compilation techniques make it possible to optimize reductions, such as prefix sum, in which each component of the reduction's output potentially shares computation with another component in the reduction. Therefore…

## 2 Citations

On Simplifying Dependent Polyhedral Reductions

- Computer ScienceArXiv
- 2020

It is shown that simplification of dependent reductions can be formulated as a simple extension of the Gautam-Rajopadhye backtracking search algorithm.

Simplifying Dependent Reductions

- Computer Science
- 2021

This paper shows how to extend the Gautam-Rajopadhye algorithm to optimally simplify such dependent reductions, tackling the case when ( some) input values depend on (some) outputs.

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