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.