Follow up to algebraically tracing carries in base 2 multiplication
- I now have found a way to simplify the calculations somewhat.
Setting z = x y
where z = 1 + 2 z1 + 4 z2 + . . .
x = 1 + 2 x1 + 4 x2 + . . .
y = 1 + 2 y1 + 4 y2 + . . .
If w = a1 s1 + a2 s2
parity(w) = parity( parity(a1) s1 + parity(a2) s2 )
Applying this results in y1, y2, etc having the forms
y1 = t10 + t11 x1
y2 = t20 + t21 x1 + t22 x2 + t23 x2 x1
y3 = t30 + t31 x1 + t32 x2 + t33 x2 x1 + t34 x3 + t35 x3 x1 + t36 x3 x2
+ t37 x3 x2 x1
where all the t parameters depend only on the z's.
Kermit < kermit@... >