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A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or remainder, the result of Euclidean division. Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into two main categories: slow ...
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
Caldrini (1491) is the earliest printed example of long division, known as the Danda method in medieval Italy, [4] and it became more practical with the introduction of decimal notation for fractions by Pitiscus (1608). The specific algorithm in modern use was introduced by Henry Briggs c. 1600. [5]
Barrett reduction. In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett. [1] A naive way of computing. would be to use a fast division algorithm. Barrett reduction is an algorithm designed to optimize this operation assuming is constant, and , replacing divisions by multiplications.
Standard algorithms. In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. These methods vary somewhat by nation and time, but generally include exchanging, regrouping, long division, and long multiplication using a standard ...
Toom–Cook multiplication — generalization of Karatsuba multiplication. Schönhage–Strassen algorithm — based on Fourier transform, asymptotically very fast. Fürer's algorithm — asymptotically slightly faster than Schönhage–Strassen. Division algorithm — for computing quotient and/or remainder of two numbers.
Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that. and either R = 0 or the degree of R is lower than the degree of B. These conditions uniquely define Q and R ...
The canonical example is the division of a cake using a knife. [1] The simplest example is a moving-knife equivalent of the "I cut, you choose" scheme, first described by A.K.Austin as a prelude to his own procedure: [2] One player moves the knife across the cake, conventionally from left to right. The cake is cut when either player calls "stop".