基于FPGA的浮点指数函数算法研究与实现

Algorithm Research and Implementation of Float Point Exponential Function Based on FPGA

摘要:

基于FPGA的核电站仪控设备中涉及大量浮点指数运算,而常用的CORDIC算法和线性逼近法等存在计算范围小、计算精度不高等问题,对FPGA硬件实现指数函数的方法进行研究,并提出一种改进的级数近似法;该方法对输入进行预处理,将输入分解后采用查找表和泰勒级数展开结合的方法,在展开很少项数的情况下快速收敛,发挥查找表法和级数近似法的优势,提高算法的运算精度和效率;在Matlab环境下对改进算法的有效性进行仿真验证,且采用Verilog语言进行编程实现,在Microsemi公司的IGLOO2系列FPGA上进行具体算法性能验证;Matlab仿真和FPGA验证结果均表明,改进的级数近似法能够大幅增大指数函数的自变量输入范围,并提高计算精度。

Abstract:

A large number of floating-point exponential calculations are involved in nuclear power plant instrumentation based on FPGA,and the methods for hardware implementation of exponential function are studied, an improved series approximation algorithm is proposed, aiming at solving the problems such as small calculation scale, low precision existing in CORDIC algorithm and linear approximation algorithm. The lookup table and series approximation algorithm are combined in the proposed algorithm, with input data splitting into two part. It takes advantage of the lookup method and the linear approximation, and can work even using a few expansion series. The validity of the improved algorithm is simulated in Matlab, and algorithm is programmed using Verilog and verified on the IGLOO2 series FPGA of Microsemi Corporation. The Matlab simulation result and the implementation result on FPGA demonstrates that this method can expand the calculation capacity and with high accuracy.