An Efficient Single-Precision Floating-Point Trigonometric Function Calculation Circuit Structure and Implementation

LI Tian-li; YIN Tao; WEI Xing; YANG Hai-gang

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An Efficient Single-Precision Floating-Point Trigonometric Function Calculation Circuit Structure and Implementation

更新时间：2026-09-04

- An Efficient Single-Precision Floating-Point Trigonometric Function Calculation Circuit Structure and Implementation
- Vol. 35, Issue 12, Pages: 33-37(2018)
- 作者机构：
  
  1. 中国科学院机构电子学研究所,北京,100190
  2. 中国科学院大学机构,北京,101408
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2018
- 稿件说明：
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李天立, 尹韬, 魏星, 杨海钢. 高效单精度浮点三角函数计算电路结构与实现[J]. 微电子学与计算机, 2018, 35(12): 33-37.

LI Tian-li, YIN Tao, WEI Xing, et al. An Efficient Single-Precision Floating-Point Trigonometric Function Calculation Circuit Structure and Implementation[J]. 2018, 35(12): 33-37.
李天立, 尹韬, 魏星, 杨海钢. 高效单精度浮点三角函数计算电路结构与实现[J]. 微电子学与计算机, 2018, 35(12): 33-37. DOI：

LI Tian-li, YIN Tao, WEI Xing, et al. An Efficient Single-Precision Floating-Point Trigonometric Function Calculation Circuit Structure and Implementation[J]. 2018, 35(12): 33-37. DOI：

摘要

针对基于浮点加法器的CORDIC(Coordinate Rotation Digital Calculation

坐标旋转数字计算)实现单精度浮点型三角函数的角度收敛范围受限、处理速度低、电路开销大、响应延时长等问题

通过将浮点运算转化为定点运算以及对无缩放因子CORDIC算法的优化

提出一种基于查找表技术和双步迭代技术的高计算效率电路设计结构

解决了无缩放因子CORDIC算法计算三角函数需要引入乘法器和迭代次数过高的问题.在Stratix IV(EP4SGX70DF29C2X型FPGA)上实现了满足IEEE-754标准的单精度浮点正弦、余弦的三角函数运算.实验结果表明该电路工作频率可达282 MHz

对比已有电路结构

响应延时和电路总面积有效降低

计算精度达到10E-7.

Abstract

There are four questions for single-precision floating point trigonometric functions by CORDIC(Coordinate Rotation Digital Calculation)algorithm based on floating point adder

including the range of angles is not enough

large area

low operating frequency and high output delay. In this paper

a high computation circuit structure based on look up table and two-step iterative technology is proposed through converting floating-point operations into fixed-ponit operations and the optimization of scaling free CORDIC.It solves the problem that the CORDIC algorithm needs to use the multiplier and high numbers of iteration. This circuit is implemented on Alteras Stratix IV(EP4SGX70DF29C2X FPGA)and achieves Sin and Cosine in IEEE-754 standard.The synthesis results show the clock frequency can reach 282 MHz. Comparing to existed circuit structure

output delay and area reduced effectively

the calculation accuracy can reach 10E-7.

关键词

Keywords

references

Peng Y, Zhu B, Lei Y, et al. CORDIC and Taylor algorithm based combined full pipeline floating-point trigonometric function device, has post-processing module for calculating cordic algorithm processing result and outputting sine and cosine of calculation result: China, CN106202890-A[P].2016-12-07.

Arun Kumar Singh, Madhav Kumar Singh, Kailash Chandra Ray.Design and implementation of quadruple floating-point CORDIC[C]//IEEE International Symposium on Nanoelectronic and Information Systems, 2015 IEEE. Indore, India, IEEE, 2015: 286-290.

Voldct.The cordic trigonometric computing technique.IRETrans [J].Electronic Computers, 1959, EC-8(3):334-334. DOI: 334

Lei Y, Zhu B, Peng Y, et al. Low overhead iterative trigonometric function device has pretreatment module that judges signal output of trigonometric function and convert output from fixed-point to floating-point format: China, CN106155627-A[P].2016-11-23.

吴庆达, 何书专, 潘红兵, 等.32位定浮点数正余弦函数FPGA实现方法[J].微电子学与计算机, 2012, 29(1):113-116. DOI: 113

Chen Dong, Chen He, Sun Xing, et al. Implementation of single-precision floating-point trigonometric functions with small area[C]// International Conference on Control Engineering and Communication Technology.Washington DC : IEEE, 2012: 589-592.

Kishore Kota Joseph. Numerical accuracy and hardware tradeoffs for cordic arithmetic for special-purpose processors[J]. IEEE Transactions on Computers, 1993, 42(7):769-77. DOI: 769

徐成, 秦云川, 李肯立, 等.免缩放因子双步旋转CORDIC算法[J].电子学报, 2014, 42(7):1441-1445. DOI: 1441

Koushik Maharatna, Swapna Banerjee, Senior Member. Modified virtually scaling-free adaptive cordic rotator algorithm and architecture[J].IEEE Transactions on Circuits and Systems for Video Technology, 2005, 15(11):1463-1474. DOI: 1463

Rodrigues T K, Swartzlander E.Adaptive cordic:using parallel angle recoding to accelerate rotations [J].IEEE Transactions onComputers, 2010, 59(4):522 - 531. DOI: 522

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