matrices for various k Here we give common interpolation matrices for a few different common small values of km and kn. Toom-1 Toom-1 (km = kn = 1) requires 1 evaluation point, here chosen to be 0. It degenerates to long multiplication, with an interpolation matrix of the identity matrix: Toom-1.5 Toom-1.5 (km = 2, kn = 1) requires 2 evaluation points, here chosen to be 0 and ∞. Its interpolation matrix is then the identity matrix: This also degenerates to long multiplication: both coefficients of one factor are multipled by the sole coefficient of the other factor. Toom-2 Toom-2 (km = 2, kn = 2) requires 3 evaluation points, here chosen to be 0, 1, and ∞. It is the same as Karatsuba multiplication, with an interpolation matrix of: Toom-2.5 Toom-2.5 (km = 3, kn = 2) requires 4 evaluation points, here chosen to be 0, 1, −1, and ∞. It then has an interpolation matrix of: Notes References D. Knuth. The Art of Computer Programming, Volume 2. Third Edition, Addison-Wesley, 1997. Section 4.3.3.A: Digital methods, pg.294. R. Crandall & C. Pomerance. Prime Numbers – A Computational Perspective. Second Edition, Springer, 2005. Section 9.5.1: Karatsuba and Toom–Cook methods, pg.473. M. Bodrato. Toward Optimal Toom–Cook Multiplication.... In WAIFI'07, Springer, 2007. External links Toom–Cook 3-way multiplication from GMP documentation Computer arithmetic algorithms Multiplication