| Given A1A0 * B1B0 == S3S2S1S0 | |
| S0= low(A0*B0) | |
| S1= low( (A1-A0)*(B0-B1)) +low( A1*B1) +high(A0*B0) | |
| S2= high((A1-A0)*(B0-B1)) +high(A1*B1) +low( A1*B1) | |
| S3= high(A1*B1); | |
| Assume we know S1 and S0, and can calulate A1*B1 and high((A1-A0)*(B0-B1)) | |
| k0= S0 == low(A0*B0) | |
| k1= S1 | |
| k2= low( A1*B1) | |
| k3= high(A1*B1) | |
| k4= high((A1-A0)*(B0-B1)) | |
| k1= low((A1-A0)*(B0-B1)) +k2 +high(A0*B0) | |
| S2= k4 +k3 +k2 | |
| S3= k3 | |
| S1-k2= low((A1-A0)*(B0-B1)) +high(A0*B0) | |
| We potentially have a carry or a borrow from S1 |