基于SIMD的三角函数高性能实现与优化

High Performance Implementation and Optimization of Trigonometric Functions Based on SIMD

作为基本的数学运算,三角函数的高性能实现对构建处理器的基础软件生态具有重要意义,特别是当前处理器都采用了SIMD架构,基于SIMD实现高性能三角函数具有重要的研究意义和应用价值。对此,文中采用数值分析的方法,对5个常用的三角函数sin,cos,tan,atan,atan2进行了高性能的实现与优化。首先通过分析浮点数IEEE754标准,设计了高效的三角函数算法;然后通过多项式逼近算法中的泰勒公式、帕德近似及雷米兹算法提升了算法精度;最后利用指令流水线与SIMD优化进一步提升了算法性能。实验结果表明,在满足精度的前提下,所实现的三角函数,相较于libm算法库和ARM;算法库,在ARM V8计算平台上都获得了较大的性能提升,其中相比libm算法库有1.77~6.26倍的时间性能提升,相比ARM;算法库有1.34~1.5倍的时间性能提升。

As a basic mathematical operation,the high-performance implementation of trigonometric functions is of great significance to the construction of the basic software ecology of the processor.Especially,the current processors have adopted the SIMD architecture,and the implementation of high-performance trigonometric functions based on SIMD has important research significance and application value.In this regard,this paper uses numerical analysis method to implement and optimize the five commonly used trigonometric functions sin,cos,tan,atan,atan2 with high performance.Based on the analysis of floating-point IEEE754 standard,an efficient trigonometric function algorithm is designed.Then,the algorithm accuracy is further improved by the application of Taylor formula,Pade approximation and Remez algorithm in polynomial approximation algorithm.Finally,the perfor-mance of the algorithm is further improved by using instruction pipeline and SIMD optimization.The experimental results show that,on the premise of satisfying the accuracy,the trigonometric function implemented is compared with libm algorithm library and ARM;algorithm library,on the ARM V8 computing platform,has achieved great performance improvement,whose time performance is 1.77~6.26 times higher than libm algorithm library,and compared with ARM;,its times performance is 1.34~1.5 times higher.