Analytical Method for Efficient Development of Optimal Fixed-Point Software and its Application

The analytical method is presented for the development of software using fixed-point arithmetic. The proposed method uses data range and the required precision of signals and parameters to determine their best data type that is, word length and resolution, while ensuring that numerical errors do not occur. Interval arithmetic operations (addition, subtraction, multiplication and division) on closed and connected real intervals are presented to determine the data range of signals. Application of this method to the math-intensive algorithms - (1) temperature estimator of the automotive passenger compartment and (2) GPS data-based calculation of sun position with respect to the vehicle driving direction, demonstrates the applicability of the proposed method. Particularly, comparable numerical accuracy of fixed-point arithmetic to that of floating-point arithmetic while giving optimal software in terms of its memory requirements and running time are presented. The design method also eliminates time consuming and laborious simulation iterations, therefore making software development more efficient. The proposed design method that offers these advantages along with relatively cheaper hardware makes the fixed-point software a favorable choice than the floating-point software, especially for the products of a large production volume such as automobiles.