ML-PLAC: Multiplierless Piecewise Linear Approximation for Nonlinear Function Evaluation

Fei Lyu

doi:10.1109/TCSI.2021.3133931

ML-PLAC: Multiplierless Piecewise Linear Approximation for Nonlinear Function Evaluation

2022-04-01

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DOI：10.1109/TCSI.2021.3133931

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In this article, we propose a multiplierless piecewise linear (PWL) approximation computation (ML-PLAC) method for nonlinear unary functions. ML-PLAC seeks the minimum number of segments with the predefined fractional bit width and number of adders to satisfy the restriction on the maximum absolute error (MAE). Compared with the previous universal PWL approximation method, multiplication operations in the segmentor are replaced by a simulation of shift-and-add operations by reducing the fractional bit width of the slope of linear functions. Various numbers of segments are obtained by different predefined numbers of adders to balance the two numbers. In addition, adders are used to replace the multiplier in hardware architecture. The synthesized results prove that ML-PLAC has increased performance without any compromises. Compared with state-of-the-art methods, ML-PLAC saves 58.82% area, 38.16% delay, 60.31% power and 6.10% MAE when computing logarithmic functions; 51.51% area, 46.49% delay, and 46.95% power while maintaining the comparable MAE when computing antilogarithmic functions; 55.21% area, 25% delay, 61.21% power, and 37.30% MAE when computing hyperbolic tangent functions; 82.47% area, 60% delay, 77.51% power and 12.74% MAE when computing sigmoid functions; and 46.43% area, 31.43% delay, and 61.16% power while maintaining the same MAE when computing softsign functions.

Keywords:

Hardware

Delays

Adders

Computer architecture

Table lookup

Approximation methods

Speech recognition

Piecewise linear (PWL) approximation method

maximum absolute error (MAE)

logarithmic function

antilogarithmic function

hyperbolic tangent function

sigmoid function

softsign function

ML-PLAC: Multiplierless Piecewise Linear Approximation for Nonlinear Function Evaluation

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