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2. Karatsuba algorithm - Wikipedia

   en.wikipedia.org/wiki/Karatsuba_algorithm

   Since the additions, subtractions, and digit shifts (multiplications by powers of B) in Karatsuba's basic step take time proportional to n, their cost becomes negligible as n increases. More precisely, if T(n) denotes the total number of elementary operations that the algorithm performs when multiplying two n-digit numbers, then

3. Multiplication algorithm - Wikipedia

   en.wikipedia.org/wiki/Multiplication_algorithm

   More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications). When implemented in software, long multiplication algorithms must deal with overflow during additions, which can be expensive.

4. Maths Mansion - Wikipedia

   en.wikipedia.org/wiki/Maths_Mansion

   Multiplication 4: 14 "You Ain't Nothing but a Houndred" Multiplication of 3-digit numbers by single digits 5: 15 "Dividing we Stand" Dividing 3-digit numbers by 2-digit numbers 6: 16 "Double Digit Dating" Multiplying double digit numbers 7: 17 "Six Flat Worms" Area 8: 18 "Learn your Lines" Parallel and Perpendicular lines 9: 19 "Rectangle Delight"

5. Schönhage–Strassen algorithm - Wikipedia

   en.wikipedia.org/wiki/Schönhage–Strassen...

   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.

6. Trachtenberg system - Wikipedia

   en.wikipedia.org/wiki/Trachtenberg_system

   Starting from the rightmost digit, double each digit and add the neighbor. (The "neighbor" is the digit on the right.) If the answer is greater than a single digit, simply carry over the extra digit (which will be a 1 or 2) to the next operation. The remaining digit is one digit of the final result. Example:

7. Napier's bones - Wikipedia

   en.wikipedia.org/wiki/Napier's_bones

   Single-digit numbers are written in the bottom right triangle leaving the other triangle blank, while double-digit numbers are written with a digit on either side of the diagonal. If the tables are held on single-sided rods, 40 rods are needed in order to multiply 4-digit numbers – since numbers may have repeated digits, four copies of the ...