Unary computing is a relatively new method for implementing non-linear functions using few hardware resources compared to binary computing. In its original form, unary computing provides no trade-off between accuracy and hardware cost. In this work, we propose a novel self-similarity-based method to optimize the previous hybrid binary-unary method and provide it with the trade-off between accuracy and hardware cost by introducing controlled levels of approximation. Given a target maximum error, our method breaks a function into sub-functions and tries to find the minimum set of unique sub-functions that can derive all the other ones through trivial bit-wise transformations. We compare our method to previous works such as HBU (hybrid binary-unary) and FloPoCo-PPA (piece-wise polynomial approximation) on a number of non-linear functions including Log, Exp, Sigmoid, GELU, Sin, and Sqr, which are used in neural networks and image processing applications. Without any loss of accuracy, our method can improve the area-delay-product hardware cost of HBU on average by 7% at 8-bit, 20% at 10-bit, and 35% at 12-bit resolutions. Given the approximation of the least significant bit, our method reduces the hardware cost of HBU on average by 21% at 8-bit, 49% at 10-bit, and 60% at 12-bit resolutions, and using the same error budget as given to FloPoCo-PPA, it reduces the hardware cost of FloPoCo-PPA on average by 79% at 8-bit, 58% at 10-bit, and 9% at 12-bit resolutions. We finally show the benefits of our method by implementing a 10-bit homomorphic filter, which is used in image processing applications. Our method can implement the filter with no quality loss at lower hardware cost than what the previous approximate and exact methods can achieve.
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This content will become publicly available on September 1, 2025
SimBU: Self-Similarity-Based Hybrid Binary-Unary Computing for Nonlinear Functions
Unary computing is a relatively new method for implementing arbitrary nonlinear functions that uses unpacked thermometer number encoding, enabling much lower hardware costs. In its original form, unary computing provides no trade-off between accuracy and hardware cost. In this work, we propose a novel self-similarity-based method to optimize the previous hybrid binary-unary work and provide it with the trade-off between accuracy and hardware cost by introducing controlled levels of approximation. Looking for self-similarity between different parts of a function allows us to implement a very small subset of core unique subfunctions and derive the rest of the subfunctions from this core using simple linear transformations. We compare our method to previous works such as FloPoCo-LUT (lookup table), HBU (hybrid binary-unary) and FloPoCo-PPA (piecewise polynomial approximation) on several 8–12-bit nonlinear functions including Log, Exp, Sigmoid, GELU, Sin, and Sqr, which are frequently used in neural networks and image processing applications. The area × delay hardware cost of our method is on average 32%–60% better than previous methods in both exact and approximate implementations. We also extend our method to multivariate nonlinear functions and show on average 78%–92% improvement over previous work.
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- Award ID(s):
- 2016390
- PAR ID:
- 10533919
- Publisher / Repository:
- IEEE Transactions on Computers
- Date Published:
- Journal Name:
- IEEE Transactions on Computers
- Volume:
- 73
- Issue:
- 9
- ISSN:
- 0018-9340
- Page Range / eLocation ID:
- 2192 to 2205
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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