An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation
In this paper, we propose an optimized method for nonlinear function approximation based on multiplierless piecewise linear approximation computation (ML-PLAC), which we call OML-PLAC. OML-PLAC finds the minimum number of segments with the predefined fractional bit width of input/output, maximum num...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/20/10616 |
| _version_ | 1827651801538625536 |
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| author | Hongjiang Yu Guoshun Yuan Dewei Kong Lei Lei Yuefeng He |
| author_facet | Hongjiang Yu Guoshun Yuan Dewei Kong Lei Lei Yuefeng He |
| author_sort | Hongjiang Yu |
| collection | DOAJ |
| description | In this paper, we propose an optimized method for nonlinear function approximation based on multiplierless piecewise linear approximation computation (ML-PLAC), which we call OML-PLAC. OML-PLAC finds the minimum number of segments with the predefined fractional bit width of input/output, maximum number of shift-and-add operations, user-defined widths of intermediate data, and maximum absolute error (MAE). In addition, OML-PLAC minimizes the actual MAE as much as possible by iterating. As a result, under the condition of satisfying the maximum number of segments, the MAE can be minimized. Tree-cascaded 2-input and 3-input multiplexers are used to replace multi-input multiplexers in hardware architecture as well, reducing the depth of the critical path. The optimized method is applied to logarithmic, antilogarithmic, hyperbolic tangent, sigmoid and softsign functions. The results of the implementation prove that OML-PLAC has better performance than the current state-of-the-art method. |
| first_indexed | 2024-03-09T20:45:39Z |
| format | Article |
| id | doaj.art-663e434ee58a4037b8a6c7cde7c35295 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T20:45:39Z |
| publishDate | 2022-10-01 |
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| series | Applied Sciences |
| spelling | doaj.art-663e434ee58a4037b8a6c7cde7c352952023-11-23T22:47:35ZengMDPI AGApplied Sciences2076-34172022-10-0112201061610.3390/app122010616An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear ApproximationHongjiang Yu0Guoshun Yuan1Dewei Kong2Lei Lei3Yuefeng He4Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, ChinaInstitute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, ChinaInstitute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, ChinaInstitute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, ChinaInstitute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, ChinaIn this paper, we propose an optimized method for nonlinear function approximation based on multiplierless piecewise linear approximation computation (ML-PLAC), which we call OML-PLAC. OML-PLAC finds the minimum number of segments with the predefined fractional bit width of input/output, maximum number of shift-and-add operations, user-defined widths of intermediate data, and maximum absolute error (MAE). In addition, OML-PLAC minimizes the actual MAE as much as possible by iterating. As a result, under the condition of satisfying the maximum number of segments, the MAE can be minimized. Tree-cascaded 2-input and 3-input multiplexers are used to replace multi-input multiplexers in hardware architecture as well, reducing the depth of the critical path. The optimized method is applied to logarithmic, antilogarithmic, hyperbolic tangent, sigmoid and softsign functions. The results of the implementation prove that OML-PLAC has better performance than the current state-of-the-art method.https://www.mdpi.com/2076-3417/12/20/10616nonlinear function approximationmaximum absolute error (MAE)iteratingtree-cascaded multiplexerlogarithmic functionantilogarithmic function |
| spellingShingle | Hongjiang Yu Guoshun Yuan Dewei Kong Lei Lei Yuefeng He An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation Applied Sciences nonlinear function approximation maximum absolute error (MAE) iterating tree-cascaded multiplexer logarithmic function antilogarithmic function |
| title | An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation |
| title_full | An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation |
| title_fullStr | An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation |
| title_full_unstemmed | An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation |
| title_short | An Optimized Method for Nonlinear Function Approximation Based on Multiplierless Piecewise Linear Approximation |
| title_sort | optimized method for nonlinear function approximation based on multiplierless piecewise linear approximation |
| topic | nonlinear function approximation maximum absolute error (MAE) iterating tree-cascaded multiplexer logarithmic function antilogarithmic function |
| url | https://www.mdpi.com/2076-3417/12/20/10616 |
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