source 2009.04.27 Bernstein
assume Z1 = 1
compute SS1 = S1^2
compute CC1 = 1-SS1
compute SC1 = (S1+C1)^2-SS1-CC1
compute E = D1^2
compute F = SC1^2
compute G = a F
compute Z3 = 4 E+G
compute D3 = 4 E-G
compute C3 = 2(F+4 CC1^2)-Z3
compute S3 = 2((SC1+D1)^2-E-F)