计算机科学 ›› 2021, Vol. 48 ›› Issue (12): 29-35.doi: 10.11896/jsjkx.201200135
姚建宇1,2, 张祎维3, 张广婷1, 贾海鹏1
YAO Jian-yu1,2, ZHANG Yi-wei3, ZHANG Guang-ting1, JIA Hai-peng1
摘要： 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_M 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_M算法库有1.34～1.5倍的时间性能提升。
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