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

U0=u0*Mod(1,2);U1=u1*Mod(1,2);U2=u2*Mod(1,2);U3=u3*Mod(1,2);
V0=v0*Mod(1,2);V1=v1*Mod(1,2);

U = U3*Y^3 + U2*Y^2*X + U1*Y*X^2 + U0*X^3
V = V1*Y   + V0*X

\\ P(X,Y): P0=(1,0); P1=(1,1); P2=(1,x); P3=(1,1+x); P4=(0,1)
\\ Evaluation: 8+3 add, 3+1 shift, 1 Smul; 5 mul (n)
W3 = U3+U2 + U1+U0; W2 = V1 + V0

W1 = W2 * W3

W0 =(U1 +(U2 + U3*x)*x)*x
W3 = W3 + W0 + U3*(x^2+x)
                    W2 = W2 + V1*x
W0 = W0 + U0      ; W4 = W2 + V1

W3 = W3 * W2      ; W2 = W0 * W4
W4 = U3 * V1      ; W0 = U0 * V0
\\ Interpolation: 9 add, 1 shift, 1 Smul, 2 Sdiv (2n)
W3 = W3 + W2
W1 = W1 + W0
W2 =(W2 + W0)/(x)
W2 =(W2 + W3 + W4*(x^3+1))/(x+1)
W3 =(W3 + W1)/(x*(x+1))
W1 = W1 + W4 + W2
W2 = W2 + W3

\\ Recomposition
W  = W4*Y^4+ W3*Y^3*X+ W2*Y^2*X^2+ W1*Y*X^3 + W0*X^4
W == U*V

\\ Reference: http://bodrato.it/papers/#WAIFI2007
\\ 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.