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The standard procedure for multiplication of two n-digit numbers requires a number of elementary operations proportional to , or () in big-O notation. Andrey Kolmogorov conjectured that the traditional algorithm was asymptotically optimal, meaning that any algorithm for that task would require () elementary operations.
The run-time bit complexity to multiply two n-digit numbers using the algorithm is ( ) in big O notation. The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007.
The oldest and simplest method, known since antiquity as long multiplication or grade-school multiplication, consists of multiplying every digit in the first number by every digit in the second and adding the results. This has a time complexity of (), where n is the number of digits.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
The classical method of multiplying two n-digit numbers requires n 2 digit multiplications. Multiplication algorithms have been designed that reduce the computation time considerably when multiplying large numbers. Methods based on the discrete Fourier transform reduce the computational complexity to O(n log n log log n).
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The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. . This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplic
The Chisanbop system. When a finger is touching the table, it contributes its corresponding number to a total. Chisanbop or chisenbop (from Korean chi (ji) finger + sanpŏp (sanbeop) calculation [1] 지산법/指算法), sometimes called Fingermath, [2] is a finger counting method used to perform basic mathematical operations.
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