Efficient Logarithmic Conversion on an ARM Microcontroller for Real Time Acoustic Monitoring

Measuring instrumentation products incorporating embedded microcontrollers are frequently required to perform logarithmic conversions both accurately and efficiently - in this case the application is a high precision acoustic monitoring system. Many contemporary microcontrollers (such as those based on ARM Cortex M4 or M7 cores), incorporate an optional 'on board' Floating Point Unit (FPU), providing very rapid floating point arithmetic calculations leading some programmers to abandon integer variables in favour floating point types. This paper demonstrates how this facet of the microcontrollers may be employed, in an alternative approach, to efficiently compute logarithms using classical mathematical power series working in radix ten format. This is compared and contrasted with traditional iterative binary algorithms and 'Look up Table' techniques. The paper then develops the mathematical background and subsequently presents an efficient practical algorithm for such computations, which may be simply implemented (and adapted) in a high level language such as 'C'. An accuracy of better than 0.0005% has been attained with mean execution times of 350 nS for the mantissa calculation, and 830 nS for an overall common logarithmic conversion for single precision floating point numbers.