A Design And Fpga Realization For Tangent And Cotangent Function Based On A Cordic Algorithm

Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications, and also have a wide range of uses including computing unknown lengths and angles in triangles. In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics. With the rapid development of VLSI (Very Large Scale Integrated circuits), hardware implementation is often considered as a very well method to realize quickly and accurately trigonometric functions’calculation. Coordinate Rotation Digital Computer (CORDIC) can disassemble complex operations which are hardly achieved by the hardware circuit directly into unified addition and subtraction, which greatly reduces the complexity of the hardware design. Traditional CORDIC algorithm could well achieve trigonometric functions in hardware circuits, yet there is a restriction that the range of radian is too narrow. Further, while there are still quite few researches on tangent and cotangent’s hardware realization.According to these problems, This paper firstly introduces the extended CORDIC algorithm, a detailed description of the extended CORDIC algorithm theory is present here. Then, on the basis of theoretical analysis and experimental Validation of extended CORDIC algorithm, a series of optimization measures are proposed in this article. The theoretical analysis and experimental tests indicate that the optimized arithmetic can increase the operation speed and reduce the hardware resources occupied by the system under unchanged accuracy. According to previous two chapters’ theoretical analysis, Chapter IV has analyzed algorithm structure of tangent and cotangent functions, and proposed a hardware solution which adopts field programmable gate array (Field Programmable Gate Array, FPGA) as the platform. Next, the paper has discussed the system overall framework and internal modules’design at detailed, and ultra-high-speed integrated circuit hardware description language (Verilog HDL) as well as M-Circuit technology are used to complete the design of the whole system; Finally RTL synthesis circuit and Modelsim simulation waveform of tangent-cotangent calculation module are presented. From the synthesized log, the tangent-cotangent module can considerably improve operation speed and meanwhile reduce logic resources occupied.