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Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, [1] sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers.
To multiply two numbers with n digits using this method, one needs about n 2 operations. More formally, multiplying two n-digit numbers using long multiplication requires Θ(n 2) single-digit operations (additions and multiplications).
In particular, if n is 2 k, for some integer k, and the recursion stops only when n is 1, then the number of single-digit multiplications is 3 k, which is n c where c = log 2 3. Since one can extend any inputs with zero digits until their length is a power of two, it follows that the number of elementary multiplications, for any n, is at most
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Matraki's triangular lattice multiplication. Multiplication begins by multiplying two numbers in the same column from the far right of the row. Since the 4x5 product (20) is a two-digit number, the number in the theirs digit (2) is written above the mesh, and the number (0) in the ones digit is written below the mesh.