Sigmoid function fitting hardware circuit based on Remez approximating algorithm

Abstract

The invention discloses a sigmoid function fitting hardware circuit based on a Remez approximating algorithm. A sigmoid function fitting method is characterized by including the following steps that (1), the order of a fitting polynomial is determined; (2), a fitting interval of a sigmoid function is obtained; (3), a piecewise interval is obtained; (4), the fitting polynomial is obtained; (5), a coefficient storing module is designed; (6), a polynomial calculation module is designed; (7), a judgment module is designed; (8), the fitting hardware circuit is obtained; (9), a fitting execution interval where operands are located is judged; (10), a coefficient of the fitting polynomial is read; (11), fitting calculation is carried out in the polynomial calculation module. On the basis of reducing hardware resource consumption, the calculation accuracy is improved, the calculation speed is increased, and the flexibility of a calculation structure is promoted.

Description

technical field [0001] The invention relates to the field of artificial neural networks, in particular to a sigmoid function fitting hardware circuit based on the Lemez approximation algorithm. Background technique [0002] Neural network is the abbreviation of artificial neural network, and the research and application of neural network is also one of the current research hotspots. The advantages of neural networks are mainly reflected in two aspects, one is parallelism, and the other is powerful nonlinear information processing and learning capabilities. At present, the theoretical basis and working principles of several neural network models have reached a mature level, making further research on their application in signal processing, control systems, speech recognition and other related fields a hot topic. Compared with software simulation, the neural network based on hardware has fast processing speed and high parallelism, and it is easier to meet the requirements of ...

AI Technical Summary

Problems solved by technology

Among them, the direct lookup table method (ZhiliangNie, 2012; Alexander Gomperts, 2010) is to store the sigmoid operation results in the storage module, and directly search and read the results according to the input operands. This method requires a lot of storage resources, and hardware implementation The precision is not high; the piecewise linear approximation method (ManishPanicker, 2012) adopts a 3-section piecewise linear approximation in the range of (-5,5), and uses a 32bit fixed-point number format, which has less computing and storage resources, but the computing accuracy is higher Low, the maximum mean square error is 0.00187; CORDIC algorithm (Xi Chen, 2006) uses the combination of CORDIC algorithm and lookup table algorithm, the data format adopts custom 16bit floating-point format input and custom 32bit floating-point format output, large computing resources, computing very low precision

Genetic algorithm (BharatKishore Bharkhada, 2004) in the range of [0,8], using genetic algorithm to fit integer coefficient piecewise cubic polynomial, using 16-bit fixed-point number format, low computing resources, low storage resources, low computing accuracy High, absolute error 2.4376×10 -3 ; The polynomial approximation algorithm is the most common, the traditional Taylor series expansion method needs to consume a lot of computing resources, and the computing accuracy is very low

The more classic piecewise polynomial approximation algorithm (Joao O.P.Pinto, 2006) uses piecewise 5th-order polynomials, which have low storage resources, low computing resources, high computing accuracy, and a maximum error of 8×10 -5 , this fitting accuracy is the optimal accuracy that can be achieved in all existing technologies, but it still cannot meet the high-precision calculation requirements

[0005] And in terms of data format selection, all the above methods are mostly self-defined floating-point formats in order to improve operational accuracy. In the field of real-time high-speed processing, the data format is often the 32bit single-precision floating-point format of the IEEE754 standard. This custom data Format When communicating with other processing modules, data format conversion also needs to be considered, and the communication cost is relatively high

In terms of reducing resource consumption, in order to reduce the consumption of computing resources, the look-up table method is adopted. Although the computing results can be obtained and the computing resource consumption is greatly reduced, the storage resources are greatly increased.

In terms of calculation accuracy, due to the problems of the algorithm itself and the consideration of comprehensive resources, in the current existing technology, the accuracy of hardware implementation is generally not high, and it is far from meeting the requirements of real-time high-precision processing; these are urgently needed to be solved bottleneck problem

Images