One method to compute multiple precision integer quotients is to use a Newton iteration with multiple precision fixed point or floating point values. On one hand, this allows quotients to be calculated efficiently by employing an efficient multiplication method. On the other hand, this leads to a library structure where exact and approximate arithmetic are interdependent. This paper develops the concept of a shifted inverse and modified Newton iteration to compute quotients efficiently using whole numbers only. The method is equally applicable to computing polynomial quotients efficiently.

翻译：计算多精度整数商的一种方法是使用牛顿迭代法结合多精度定点数或浮点数。一方面，这通过采用高效的乘法方法实现了商的高效计算；另一方面，这导致了精确算术与近似算术相互依赖的库结构。本文提出了移位逆的概念，并改进了牛顿迭代法，使得仅使用整数即可高效计算商。该方法同样适用于高效计算多项式商。