Article

Article title ALGORITHM OF INTEGRATION OF THE GENERATING EQUATIONS FOR THE CALCULATION OF ELEMENTARY FUNCTIONS
Authors M.I. Ledovskoy, E.S. Sinyutin
Section SECTION II. METHODS, MODELS AND ALGORITHMS OF INFORMATION PROCESSING
Month, Year 03, 2015 @en
Index UDC 519.6:004.383
DOI
Abstract In the present paper the task of creation of algorithm with low consumption of energy for a calculation of elementary functions in wireless touch systems where energy consumption is ensured at the expense of accumulation of energy from environment is considered. In an algorithm basis the tabular-algorithmic method of functions evaluation and a mode of definition of the correction is supposed by a path of integration of the generating equations describing behavior of function between the nearest tabular value and a preset value of argument. Original implementation of a mode of integration of the generating equations is offered. Integration process is unrolled on argument bits, and also the variable step equal to weight of current bit of argument is used. On an example of functions sin(x), cos(x) the possibility of use of suitable methods of integration is investigated: Euler"s methods of 1st and 2nd order, a Runge-Kutta method of 4th order from which Euler"s method of 2nd order is chosen. Association of a methodical error of algorithm from order of a method of integration and number of bit of argument is received. The step of the table of values of functions for the considered methods of integration is defined. Matching of offered algorithm with a method of linear interpolation and algorithm CORDIC is reduced. In comparison with algorithm CORDIC the number of executable cycles on the average decreases in 2 times. In comparison with a method of linear interpolation the amount of tabular values of functions several times decreases. For example, for function cos(x) the amount of tabular values decreases in 16 times. Thus the gang of operations of algorithm is limited to simple operations of addition (sub-traction) and shift. Outcomes of the experimental analysis of a methodical, tool and full error of algorithm in system MATLAB are reduced. In the conditions of the limited digit capacity of the microcontroller and calculations with the fixed point the algorithm error accepts admissible values, commensurable with a margin error roundoffs of data. Outcomes of the present paper can find application in development algorithmic and the software for wireless touch units on the basis of microcontrollers, and also other sorts of embedded systems with low consumption of energy.

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Keywords Embedded systems; functions calculation; table-algorithmic method; algorithm CORDIC; algorithm of numerical integration.
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