Piecewise Parabolic Approximate Computation Based on an Error-Flattened Segmenter and a Novel Quantizer

This paper proposes a novel Piecewise Parabolic Approximate Computation method for hardware function evaluation, which mainly incorporates an error-flattened segmenter and an implementation quantizer. Under a required software maximum absolute error (MAE), the segmenter adaptively selects a minimum...

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Bibliographic Details
Published in:Electronics (Basel) 2021-11, Vol.10 (21), p.2704
Main Authors: An, Mengyu, Luo, Yuanyong, Zheng, Muhan, Wang, Yuxuan, Dong, Hongxi, Wang, Zhongfeng, Peng, Chenglei, Pan, Hongbing
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Circuit design
Computation
Design
Errors
Fixed points (mathematics)
Hardware
Iterative methods
Linear programming
Lookup tables
Mathematical analysis
Methods
Parabolas
Segments
Software
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Summary:This paper proposes a novel Piecewise Parabolic Approximate Computation method for hardware function evaluation, which mainly incorporates an error-flattened segmenter and an implementation quantizer. Under a required software maximum absolute error (MAE), the segmenter adaptively selects a minimum number of parabolas to approximate the objective function. By completely imitating the circuit’s behavior before actual implementation, the quantizer calculates the minimum quantization bit width to ensure a non-redundant fixed-point hardware architecture with an MAE of 1 unit of least precision (ulp), eliminating the iterative design time for the circuits. The method causes the number of segments to reach the theoretical limit, and has great advantages in the number of segments and the size of the look-up table (LUT). To prove the superiority of the proposed method, six common functions were implemented by the proposed method under TSMC-90 nm technology. Compared to the state-of-the-art piecewise quadratic approximation methods, the proposed method has advantages in the area with roughly the same delay. Furthermore, a unified function-evaluation unit was also implemented under TSMC-90 nm technology.
ISSN:2079-9292
2079-9292
DOI:10.3390/electronics10212704