The Design And Verfication Of A High-performance Floating-point Trigonometric Function Unit

In communications, networks, real-time measurement and control, and other fields,researchers have proposed many signal processing algorithm, and in its geometry processing frame structure need to deal with computing problems of the basic functions such as trigonometric functions. In the case of engineering application, floating point trigonometric function operation is very broad. The design and implementation of high-performance floating-point trigonometric function is of great significance in engineering application.In this paper, the theory of floating point calculation of trigonometric functions have been studied, based on the BKM algorithm a floating-point trigonometric function unit was designed and implemented.The article's main research contents and achievements include the following:1. Based on BKM algorithm, this paper proposed serial and parallel BKM implementation framework, which are used for the core functions of floating-point trigonometric function operation. Through the comparison and analysis on the performance of multiple trigonometric function algorithms, including CORDIC algorithm, chosed the BKM algorithm that has better performance of realizing floating point trigonometric function operation. Based on the research the problems of trigonometric functions calculating process and the BKM algorithm need to deal with constant, designed serial and parallel BKM execution framework. Serial BKM implementation framework is the feature of each iteration cycle iterative calculation using the same set of hardware resources to calculate trigonometric function, the set of iterative hardware resources mainly including adder, shifter. The serial execution framework is the way of getting space by time that can saves the hardware consumption;The feature of parallel BKM implementation framework is that each iteration arithmetic using different iterative hardware resources at the same clock cycle, the parallel execution framework is a way of getting time by space and it can saves the hardware computing time.2. Based on BKM algorithm implementation framework, designed and used Verilog hardware description language to realize the floating point trigonometric function unit. The unit uses 10 levels pipeline structure, including three parts of preprocessing unit, core-processing unit and the post-processing unit. pre-processing unit mainly completes functions of conversion decimal input arc data to hexadecimal data form, detecting abnormal radian value, setting initial input value and preprocessing the input curve value. The core-processing unit mainly adopts serial and parallel BKM execution frameworks to accomplish iterative arithmetic calculation of trigonometric function. It also detectes overflow exception. The core-processing unit uses the twoexecutive framework that can speed up the iterative computation and reduce hardware resources. The post-processing unit mainly outputs trigonometric function calculation results and the exception handling results. And using 10 levels pipeline structure have designed the unit that consists of the three parts, researched and analyzed the critical path and the pipeline stations logic was divided. Finally used Verilog hardware description language to complete the coding work of floating-point trigonometric function operation components.3. Builded functional verification environment, and adopted the method of directional testing and random testing to complete work of functional verification on the trigonometric function computation components. Used simulation technology to build environment of verification to test underlying module of trigonometric function unit,and then integrated underlying module into the overall unit, builded simulation function verification environment to test it on the functional verification feature level. In order to make verification completed, in the process of hierarchical functional verification using the manually generated excitation orientation testing and random testing method. The design had passed verification of the orientation test stimulated datas and large numbers of random test datas including the radian of convergence,convergence range legitimate value and special arc incentives datas.Experimental results showed that the design works correctly. Importing a radian value per cycle, the first input radian value gets the results after calculating that takes 10 clycles and achieved performance of caculating a floating-point double-precision trigonometric function results per clycle. At present, most researchers use CORDIC algorithm to implement the floating point trigonometric function unit, they use pipeline structure to realize unit that uses CORDIC algorithm to calculate trigonometric function,the levels of pipeline structure usually more than 10 series, some use 23 levels pipeline structure, and the floating point trigonometric function unit usually handles32-bits single-precision floating-point data.