Toom-Cook 8-way for Long Integers Multiplication

Toom-Cook algorithms are efficient subquadratic polynomial/long integers multiplication methods. In general, only the degree 2 (Karatsuba), 3 and 4 version are used in practice. In this paper we analyse a high (8-way - degree 7) version, showing it can be effective for long integers whose digits number lies in a certain range. Comparison with GMP 4.3.0 library shows that the gain for multiplication and squaring can be quite considerable.