基于泰勒级数近似的浮点开方运算器的设计  

Design of Floating-Point Square Root Operator Based on Taylor Series Approximation

作　　者：谌民迪 万江华 SHEN Mindi;WAN Jianghua(School of Physics and Optoelectronics,Xiangtan University,Xiangtan 411100,China;Hunan Great-Leo Microelectronics Co.,Ltd.,Changsha 410000,China)

机构地区：[1]湘潭大学物理与光电工程学院,湖南湘潭411100 [2]湖南毂梁微电子有限公司,长沙410000

出　　处：《电子与封装》2024年第5期42-47,共6页Electronics & Packaging

摘　　要：基于泰勒级数展开式对浮点开方运算进行优化,设计了1个符合IEEE-754标准的精确浮点开方运算器。为了平衡开方运算器的整体性能,采用泰勒级数的二次展开式。为了解决算法中存在的不能进行精确舍入的问题,引入了1种校准方法,通过对初始近似值进行校准,获得了理想的误差范围。为了提高数据吞吐率和工作频率,对开方运算器进行了5级流水线划分。仿真和综合结果表明,浮点开方运算器的误差小于0.5ulp,关键路径延时为2.23ns,面积为53478.240μm^(2),功耗为12.52mW。Based on the Taylor series expansions,optimization is performed for the floating-point square root operation,resulting in a design of a precise floating-point square root operator compliant with the IEEE-754 standard.To balance the overall performance of the square root operator,a quadratic expansion of the Taylor series is employed.In order to address the issue of not being able to perform precise rounding in the algorithm,a calibration method is introduced,calibrating the initial approximation to achieve an ideal error range.To improve data throughput rate and operating frequency,a 5-stage pipeline division is implemented for the square root operator.Simulation and synthesis results show that the error of the floating-point square root operator is less than 0.5 ulp,with a critical path delay of 2.23 ns,an area of 53478.240μm^(2),and a power consumption of 12.52 mW.

关 键 词：开方运算器 误差分析 精确舍入 流水线 

分 类 号：TN402[电子电信—微电子学与固体电子学]