Abstract
This chapter considers functional decompositions of index generation functions. A Monte Carlo method to predict column multiplicities of the decomposition charts is presented. With this, we can efficiently find a circuit structure to implement the function. Our goal is not to find a minimum column multiplicity of a given function, but to predict the column multiplicities of random index generation functions. With these results, we can estimate the size of the programmable architecture when we know only the number of inputs and registered vectors.
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Notes
- 1.
For simplicity, readers can assume that LUTs are used to implement the functions.
- 2.
This assumes that k ≤ 2n−s.
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Acknowledgements
This research is partly supported by the Japan Society for the Promotion of Science (JSPS) Grant in Aid for Scientific Research. Discussion with Mr. Kyu Matsuura was useful to improve Sect. 5. Also, the reviewers’ comments improved the presentation of the chapter.
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Sasao, T., Butler, J.T. (2018). Decomposition of Index Generation Functions Using a Monte Carlo Method. In: Reis, A., Drechsler, R. (eds) Advanced Logic Synthesis. Springer, Cham. https://doi.org/10.1007/978-3-319-67295-3_10
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