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| 摘要: |
| 针对全波傅氏算法中的开平方运算较耗时影响微机保护瞬动性问题,提出一种选取接近定点数开方真值的牛顿迭代初值的方法,该方法利用数字信号处理器(DSP)的移位指令、256个单元的查表技术和DSP的硬件乘法器,通过1次查表和1￣2次乘法运算,就能快速确定迭代误差小于2-9的迭代初值。在TIDSP集成开发平台上,运行牛顿迭代开平方汇编程序。运算结果表明:该算法对范围在00000004.0000H￣01FFFFFF.FFFFH的定点数抽样开方运算,迭代次数均不大于3次,就达到2-16以上迭代精度,且占用内存小,非常适合带有硬件乘法器的嵌入式微处理器实现。 |
| 关键词: 开平方,迭代,微机保护,DSP |
| DOI： |
| 分类号:TM744 |
| 基金项目: |
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| High-precision and fast square root algorithm based on Newton iteration method |
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ZHANG Xiaoming LI Yongxin
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| Abstract: |
| As the square root calculation of full-wave Fourier algorithm takes longer time,the real-time performance of microcomputer-based protection is seriously influenced. A method based on Newton iteration is proposed. To reduce the iteration times,it can select the initial value very close to the real square root with error less than 2-9 by only executing displacement instruction,referring a 256 - unit table once,and doing once or twice multiply operations with DSP hardware multiplier. The algorithm is programmed with assembly language and tested on TI DSP integrated development platform. The results of sampling tests show that,the iteration time of the square root operation for the fixed-point numbers ranging from 0000 0004.0000 H to 01FF FFFF.FFFF H is not greater than 3 with the iteration precision better than 2-16. This method needs smaller memory,very suitable for the embedded microcomputer with hardware multipliers. |
| Key words: square root,iteration,microcomputer-based protection,DSP |
