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A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of division. Some are applied by hand, while others are employed by digital circuit designs and software.Division algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring, non-restoring, and SRT division. Fast division methods start with a close approximation to the final quotient and produce twice as many digits of the final quotient on each iteration. NewtonRaphson and Goldschmidt fall into this category.Discussion will refer to the form, whereis the input, andis the output.The simplest division algorithm, historically incorporated into a greatest common divisor algorithm presented in Euclid's Elements, Book VII, Proposition 1, finds the remainder given two positive integers using only subtractions and comparisons:

mathematics, numerical analysis