一种改进的模乘逆（模$2^w$）
An Improved Integer Modular Multiplicative Inverse (modulo $2^w$)
摘要：
本文提出了一种整数乘逆运算（mod $2^w$）的算法，当使用本机位宽$w$作为模$2^w$时，该算法在现代微处理器已知的最少周期内完成。该算法是对Dumas方法的修改，对于计算机来说，它稍微增加了通用性和效率。给出了一个证明，该算法被证明是密切相关的更好地了解牛顿法算法的逆。简单的直接公式，这是需要由该算法和牛顿的方法，审查和证明的整数逆模$2^k$与$k$ = 1，2，3，4，或5，提供了第一个证明的首选公式与$k$ =4或5。
英文摘要：
This paper presents an algorithm for the integer multiplicative inverse (mod $2^w$) which completes in the fewest cycles known for modern microprocessors, when using the native bit width $w$ for the modulus $2^w$. The algorithm is a modification of a method by Dumas, and for computers it slightly increases generality and efficiency. A proof is given, and the algorithm is shown to be closely related to the better known Newton's method algorithm for the inverse. Simple direct formulas, which are needed by this algorithm and by Newton's method, are reviewed and proven for the integer inverse modulo $2^k$ with $k$ = 1, 2, 3, 4, or 5, providing the first proof of the preferred formula with $k$=4 or 5.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
