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A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic. The oldest and simplest method, known since antiquity as long multiplication or grade-school ...
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [ 1][ 2][ 3] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most single-digit ...
Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...
Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. [1] Booth's algorithm is of interest in the study of computer ...
In computing, row-major order and column-major order are methods for storing multidimensional arrays in linear storage such as random access memory . The difference between the orders lies in which elements of an array are contiguous in memory. In row-major order, the consecutive elements of a row reside next to each other, whereas the same ...
Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
In binary encoding each long number is multiplied by one digit (either 0 or 1), and that is much easier than in decimal, as the product by 0 or 1 is just 0 or the same number. Therefore, the multiplication of two binary numbers comes down to calculating partial products (which are 0 or the first number), shifting them left, and then adding them ...
Array (data structure) In computer science, an array is a data structure consisting of a collection of elements ( values or variables ), of same memory size, each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula.