I am thinking of a memory efficient way of getting modulo from product of multiplication.
I DO NOT want to store product separatly, i want to combine multiplication and division.

Is that possible?

Lets assume that i have a:
AB * CD % EF
each letter is a radix point

i can do first AB * CD = PRODUCT
and then PRODUCT % EF = REMINDER

this requires me to have a memory for PRODUCT

x is a value that makes it go on new row, eg. 49 = 9 + 4*10, x =10.

I can write this as AB * CD % EF = (A + B*x) * (C + D*x) % (EF) =
(A*C + A*D*x + C*B*x + B*D*x*x) % (EF) =
= (A*C % EF) + (A*D*x % EF) + (C*B*x % EF) + (B*D*x*x % EF)

I have no idea what to do now. Or even if thats possible.
I just want to avoid storing memory for product.
Perhaps i should shift left by power of x? 0 = no shift, 1 = single shift, and so on. then compare with entire EF (zero fill mul result) and if greater subtract. If equal advance lower, if less break. I dont know, my math suck.

Is that possible? Or not. Of course modulus is a large number, not fitting into any hardware solutions.

In theory it looks fine, but 'normally' with memory buffer i just do one modulo cycle. Here i dont know. I belive its compare and after that modulo.
Any ideas how to optimize it?