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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Constant Coefficient Multipliers Using Self-Similarity-Based Hybrid Binary-Unary Computing
Constant coefficient multipliers are widely used in digital signal processing and machine learning architectures. Researchers have proposed HBU-CCM (hybrid binary-unary constant coefficient multiplier), which is an approximate method that outperforms conventional binary and FloPoCo-KCM (table-based real multiplier) methods in terms of hardware cost at the expense of accuracy due to aliasing issues. SimBU (self-similarity-based hybrid binary-unary) is another method that was recently proposed to implement general nonlinear functions using self-similarities leading to few hardware resources. In this work, we use a simplified version of the SimBU algorithm to address the aliasing issues of HBU-CCM and improve accuracy. We also implement a convolution kernel for a Gaussian blurring filter to evaluate our method and compare it to previous works. Our method outperforms conventional binary and FloPoCo-KCM methods in terms of hardware cost with desired accuracy and with no aliasing error as opposed to HBU-CCM.
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- Award ID(s):
- 2016390
- PAR ID:
- 10478288
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- 2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)
- ISSN:
- 1558-2434
- ISBN:
- 979-8-3503-2225-5
- Page Range / eLocation ID:
- 1 to 7
- Format(s):
- Medium: X
- Location:
- San Francisco, CA, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICCAD57390.2023.10323844
