A Low Latency Floating-Point Sine and Cosine Function Hardware Implementation Algorithm

被引：0

作者：

Liang F. ^{[1
]}

Liu C. ^{[2
]}

Li X. ^{[1
]}

Qiu G. ^{[2
]}

Zhang J. ^{[2
]}

Chen Z. ^{[2
]}

Li W. ^{[2
]}

Cao Q. ^{[1
]}

Lei S. ^{[1
]}

机构：

[1] School of Microelectronics, Xi'an Jiaotong University, Xi'an

[2] The 58th Research Institute of China Electronics Technology Group Corporation, Wuxi

来源：

Hsi-An Chiao Tung Ta Hsueh/Journal of Xi'an Jiaotong University | 2021年 / 55卷 / 11期

关键词：

Coordinate rotation digital computer algorithm; Hardware implementation; Sine and cosine function; Taylor first-order approximation;

D O I：

10.7652/xjtuxb202111012

中图分类号：

学科分类号：

摘要：

In order to solve the problem that coordinate rotation digital computer(CORDIC)algorithm is difficult to meet the requirement of low latency and high accuracy in hardware implementation, a low latency floating-point sine and cosine function hardware implementation algorithm is proposed. This algorithm divides the range of the input floating-point number's exponent into 3 regions of [-126, -16], [-15, 21] and [22, 126] based on the mathematical properties of sine and cosine. In the three regions, Taylor 0-order approximation, Taylor 1st-order approximation, and direct calculation methods are used, respectively. Taylor 1st-order approximation method is optimized by converting to fixed-point, induction formula reduction, and precomputing output exponent to reduce calculation complexity and improve parallelism. A 4-stage pipeline hardware implementation of the optimized Taylor 1st-order approximation is provided. By the way of traversal test, the accuracy of the proposed algorithm is only 1 ulp (unit in the last place) away from that of the C-language math library at most. In UMC55nm process, the circuit can reach 250 MHz clock frequency and the total latency per operation is only 4 clock cycle, which means the property of low latency. © 2021, Editorial Office of Journal of Xi'an Jiaotong University. All right reserved.

引用

页码：106 / 114

页数：8

共 21 条

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