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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 t
The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.
[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 multiplications.
Operation Input Output Algorithm Complexity Addition: Two -digit numbers : One +-digit number : Schoolbook addition with carry ()Subtraction: Two -digit numbers : One +-digit number
Using the second formula above, the technique for multiplication of two numbers works as follows: Scale down : By shifting the decimal point to the left or right, scale both numbers to values between − 1 {\displaystyle -1} and 1 {\displaystyle 1} , to be referred to as cos α {\displaystyle \cos \alpha } and cos β {\displaystyle \cos ...
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.
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