A Fast Fixed-Point Logarithmic Functions Based on ARM Microprocessor

Abstract

The fixed-point mathematical library refers to a highly optimized collection of high-precision mathematical functions primarily used for fast and high-precision real-time calculations. It can execute equivalent code written in the C language with floating-point format faster, while maintaining considerable accuracy. Current mainstream fixed-point mathematical libraries face issues such as being non-open source, having unknown models, incomplete basic mathematical operation functions, and insufficient precision. Therefore, designing an open-source, fast, more optimized, and high-precision fixed-point mathematical library will have a groundbreaking impact. It can not only play a crucial role in industrial control algorithms but also eliminate the dependency of domestic fixed-point MCUs on foreign library functions.This paper conducts research on fixed-point arithmetic for logarithmic functions, designs, and improves the implementation of fast logarithmic functions.Taking Q12 as an example, Simulation experiments and MCU experiments show that, in the Q12 format, the highest precision that can be represented by a 32-bit fixed-point number is 0.000244141. From the test results, it can be observed that for 98.15% of the test data, the computational errors of the two mathematical libraries are both smaller than the highest precision value. Both two logarithmic function computations can maintain good computational accuracy within the ARM microprocessor. In terms of computational speeds, the average computation cycle of the fixed-point logarithmic function designed in this paper is reduced by 31.88% compared to the counterpart. This substantial improvement in computational speed, while ensuring computational accuracy, enhances the performance of fixed-point logarithmic operations based on ARM microprocessors.

Keywords

Logarithm Function / Fast Algorithm / Fixed-point Processors

Author Contributions

Conceptualization: Li Ziyun; Methodology: Li Ziyun; Software: Li Ziyun; Validation: Li Ziyun; Formal analysis: Yang Huifang; Investigation: Yang Huifang; Resources: Yang Huifang; Data Curation: Li Ziyun; Writing - original draft preparation: Li Ziyun; Writing - review and editing: Zhang Qiang; Visualization: Li Ziyun; Supervision: Zhang Qiang; Project administration: Zhang Qiang; Funding acquisition: Zhang Qiang.

Funding

This work was supported by Songshan Laboratory, Spatial Fusion Intelligent Perception Technology and Precision Reconstruction System (221100211000).

Acknowledgements

The author would like to acknowledge financial support from the Songshan Laboratory and equipment support from Geehy Semiconductor.

References

[1] Yang K.R., Yan C.L., & Shi K.(2023). Analysis of Chip Industry Policies between China and Americain a Cross-National Comparative Perspective - Based on Text Quantification. Information Technology and Management Application, 2(5),23-39.

[2] Song W.N., Xu D.J.,& Chen L. (2023). Overview of DSP architecture development. Microelectronics & Computer, 40(4),1-7.

[3] Ding Y.,& Ji P.F.(2023). Technical and Market Analysis of MCU Industry at Home and Abroad. China Integrated Circuit, 32(11),22-27

[4] Hou L.Z.(2020). Floating Point and Fixed Point Comparison in DSP. Telecom Power Technology, 37(1),105-106.

[5] Mopuri S., Acharyya A.(2020). Configurable Rotation Matrix of Hyperbolic CORDIC for Any Logarithm and Its Inverse computation. Circuits, systems, and signal processing: CSSP, 39(5),2551-2573

[6] Turner C.S.(2010). A Fast Binary Logarithm Algorithm. IEEE Signal Processing Magazine, 27(5),124-140.

[7] Li G., Wan L.,& Lin L.(2008). Design and Implementation of FPGA-Based Logarithmic Converter. Electronic Engineering & Product World, (08),86-88+91.

[8] Wang Y.Q.; Lei Y.W.; Peng Y.X. Logarithmic algorithm and hardware implementation based on two-level lookup table polynomial,Computer software and computer applications,The 21st Annual Conference on Computer Engineering and Technology and the 7th Microprocessor Technology Forum, Xiamen, China,2017-08-17; Computer Engineering and Techniques.

[9] Yiu J., & Paul B.(2014). The Definitive Guide to ARM Cortex-M3 and Cortex-M4 Processors 3th ed., Waltham: Newnes.