\\ (C) 2007-2008 Marco Bodrato <http://marco.bodrato.it/>
\\ This code is released under GNU-GPL 3.0 licence.
\\ 4-way asymmetric squaring,
\\ recurse on both products and squares.

U = U3*x^3 + U2*x^2 + U1*x + U0

\\ P(x)[2]: P0=0; P1=P'(0); P2=; P3=; P4=1; P5=P'(1/0); P6=1/0
\\ Evaluation[1]: 6 add|sub, 1 shift; 4 mul, 3 sqr (n)
W2 = U0 - U2    ; W6= U3 - U1
W1 = W2 - W6    ; W5= W2 + W6
W0 =(U2 + U3)<<1 + W1

W4 =(W1)*(W5)   ; W3 =(W2)*(W6)





W5 = U3 * U2    ; W1 = U0 * U1
W2 =(W0)^2
W6 = U3 ^2      ; W0 = U0 ^2

\\ Interpolation[1,2]: 8 add|sub, 4 shift (2n)
W2  =(W2 - W4)>>1 + W3
W3  =(W3 + W1 + W5)<<1
W2  = W2 - W3
W4  = W4 + W2 - W0
W2  = W2 - W6
W1<<=1          ; W5<<=1

\\ Recomposition: check
U^2 == W6*x^6 + W5*x^5 + W4*x^4 + W3*x^3 + W2*x^2 + W1*x + W0

\\ References: http://bodrato.it/papers/#WAIFI2007
\\ [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] J. CHUNG and M.A. Hasan,"Asymmetric squaring formulae";
\\ Technical Report CACR 2006-24, University of Waterloo,
\\ Ontario, Canada, 2006