\\ (C) 2007 Marco Bodrato <http://marco.bodrato.it/>
\\ This code is released under GNU-GPL 2.0 licence.

U = U3*x^3 + U2*x^2*y + U1*x*y^2 + U0*y^3
V = V1*x   + V0*y

\\ P(x,y)[1]: P0=(0,1); P1=(-2,1); P2=(1,1); P3=(-1,1); P4=(1,0)
\\ Evaluation[1]: 7+3 add/sub, 3 shift; 5mul (n)
W3 = U0 + U2         ; W2 = V0 + V1
W1 = U1 + U3         ; W4 = V0 - V1
W0 = W3 - W1
W3 = W3 + W1       

W1 = W3 * W2         ; W2 = W0 * W4

W0 = U0 -(U1 -(U2 -U3<<1)<<1)<<1
                     W4 = W4 - V1

W3 = W0 * W4
W0 = U0 * V0         ; W4 = U3 * V1
\\ Interpolation[2,3]: 8 add/sub, 3 shift, 1 Sdiv (2n)
W3 =(W3 - W1)/3
W1 =(W1 - W2)>>1
W2 = W2 - W0
W3 =(W2 - W3)>>1 + W4<<1
W2 = W2 + W1 - W4
W1 = W1 - W3
\\ Recomposition:
W  = W4*x^4+ W3*x^3*y+ W2*x^2*y^2+ W1*x*y^3 + W0*y^4
W == U*V

\\ References: http://bodrato.it/papers/#Toom-Cook
\\ [1] Marco BODRATO,"Towards Optimal Toom-Cook Multiplication
\\ for Univariate and Multivariate Polynomials in Characteristic
\\ 2 and 0"; "WAIFI'07 proceedings" (C.Carlet and B.Sunar, eds.)
\\ LNCS#4547, Springer, Madrid, Spain, June 2007, pp. 116-133.

\\ [2] M. BODRATO, A. ZANONI, "Integer and Polynomial
\\ Multiplication: Towards Optimal Toom-Cook Matrices";
\\ "Proceedings of the ISSAC 2007 conference", pp. 17-24
\\ ACM press, Waterloo, Ontario, Canada, July 29-August 1, 2007

\\ [3] M. 'Parerga' BODRATO "Moltiplicazione Toom-Cook" Nov-2006
\\ http://it.wikipedia.org/wiki/Moltiplicazione_Toom-Cook