source 1986 Chudnovsky--Chudnovsky "Sequences of numbers generated by addition in formal groups and new primality and factorization tests", formula (4.9i)
compute S3 = Z1 C2 S1 D2+D1 S2 C1 Z2
compute C3 = Z1 C2 C1 Z2-D1 S2 S1 D2
compute D3 = Z1 D1 Z2 D2-a S1 C1 S2 C2
compute Z3 = (Z1 C2)^2+(D1 S2)^2