Abstract—At the present time, digital signal processing algorithms use elementary operations such as addition, subtraction, multiplication and division. Using the elementary operations more complex algorithms can be implemented. In the case of inverse square root operation ( a^-1/ 2) there are direct instructions to calculate it in “C” language, however, the processing time of these instructions is very large compared with the processing time of basic instructions, because their algorithms are complicated. Another aspect to consider is the used hardware; in particular, the memory is consumed very much, for this reason it is necessary to design faster firmware to obtain optimal performance in digital signal processing algorithms. In this paper, an algorithm to calculate the inverse square root operation in Fixed-Point arithmetic is implemented in a microcontroller using Newton-Raphson Method and Least Squares Method. The goal is to reduce the processing time compared with the required processing time used in Floating-Point arithmetic.

Index Terms—Firmware, fixed-point, inverse square root algorithm, microcontroller.

Leonardo Orozco, Miguel Rocha, César A. Calva, Ma. Del Rosario Osnaya and Rafael Navarrete are with the Escuela Superior de Ingeniería Mecánica y Eléctrica, Instituto Politécnico Nacional, México (e-mail:leo_4_oro@hotmail.com; mrocha@ipn.mx).
M. Isabel Rocha is with the Department of G. F. O., D- I. E, Universidad Politécnica de Valencia, España (e-mail: marocga@doctor.upv.es).
E. Andrade and C. Solis are with the Department of Physics, Universidad Nacional Autónoma de México.

Cite: L. Orozco, M. F. Rocha, C. A. Calva, M. R. Osnaya, M. I. Rocha, R. Navarrete, E. Andrade, and C. Solis, "Implementation of an Algorithm to Calculate the Inverse Square Root Operation in a Microcontroller," International Journal of Computer and Communication Engineering vol. 1, no. 4, pp. 301-304 , 2012.