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基于多项式逼近算法的精确浮点除法器的设计 被引量:2

Design of an exact floating-point divider based on polynomial approximation algorithm
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摘要 单精度浮点除法运算在图像处理、科学计算、人工智能等领域有极其广泛的应用.基于泰勒级数展开式对多项式逼近算法进行改进,设计了一个符合IEEE-754标准的精确浮点除法器.为了得到满足忠实舍入的运算结果,对运算过程中的所有误差进行分析,完成了对系数和中间结果位宽的设计.为了得到精确舍入的结果,提出一种校准方法对有误差的结果进行校准.为了降低硬件成本,使用均匀分段的方式对运算区间进行分段,控制了系数的数量与查找表的大小.为了提高除法器的工作频率与吞吐量,对设计的除法器提出一种流水线划分方式.后仿真结果表明,精确除法器的误差小于0.5 ulp,延时为2.35 ns,面积为0.185 mm^(2),功耗为69.93 mW. Single-precision floating-point division is commonly used in the fields of image processing,artificial intelligence scientific computing.An exact floating-point divider conforming to the IEEE-754 standard is designed based on the Taylor series expansion for polynomial approximation algorithm.To obtain the results of faithful rounding,all errors in the calculation process are analyzed,and the signal bit width of coefficients and intermediate result is designed.To get exact results,a calibration method is proposed to calibrate the results with error.To reduce hardware costs,the number of coefficients and the size of the lookup table are controlled by using uniform segmentation.To improve the operating frequency and throughput of the divider,a pipelining method is proposed to implement a five-stage pipeline divider.The post-simulation results show that the maximum delay is 2.35 ns,the area is 0.185 mm^(2),and the power is 69.93 mW.
作者 李旭军 石娜 龙科莅 彭祥 LI Xujun;SHI Na;LONG Keli;PENG Xiang(School of Physics and Optoelectronics,Xiangtan University,Xiangtan 411000,China;School of Astronautics,Harbin Institute of Technology,Harbin 150006,China;Hunan Great-Leo Microelectronics CO.LTD,Changsha 410000,China)
出处 《微电子学与计算机》 2023年第5期90-96,共7页 Microelectronics & Computer
基金 湖南省教育厅项目(21C0668)。
关键词 除法运算 均匀分段 误差分析 精确舍入 流水线 division operation uniform segmentation error analysis exact rounding pipelining
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