Fast computation of arctangent functions for embedded applications: A comparative analysis
Fast computation of arctangent functions for embedded applications: A comparative analysis
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DOI：
10.1109/isie.2011.5984330
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
A. Ukil;V. H. Shah;B. Deck
中科院分区：
文献类型：
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作者：
A. Ukil;V. H. Shah;B. Deck
逆切函数或反正切函数在电力交流电路分析、电力系统分析等复数相角估计中有着广泛的应用，因此，快速、准确地计算出逆切函数具有重要意义。当计算成本不是问题时，使用级数展开实现arctan或atan2是准确的。但是，对于嵌入式应用程序，不能使用这样的实现。作为替代，提出了不同的近似。在本文中，我们提出了一种使用101点查找表的高效实现。然后，通过线性内插来提高精度。利用反正切函数的特殊性质，将反正切函数的计算扩展到四象限运算。该方案在一个典型的嵌入式应用的60 MHz微控制器平台上实现。对比评估表明，该方法的精度优于已有的近似方法。与相同微控制器平台的库函数相比，该方法的时间消耗明显减少。
Inverse tangent or arctangent function has many applications, for example, in estimating the phase angle of complex number utilized in electrical ac circuit analysis, power systems analysis, etc. Therefore, fast and accurate computation of the arctangent function is of great importance. Implementation of the arctan or atan2 using series expansions is accurate when computational cost is not an issue. However, for embedded applications such implementations cannot be used. As alternative, different approximations are proposed. In this paper, we present an efficient implementation using look-up table with 101-points. The accuracy is then increased by linear interpolation. The arctangent computation is extended to four quadrant operation using particular properties of arctan. The proposed scheme is implemented in a 60MHz microcontroller platform, typical for embedded applications. Comparative evaluations show that the accuracy of the proposed method is better than the reported approximation techniques. The time consumption of the proposed method is significantly less than that of the library function of the same microcontroller platform.