Question

Assume you have 2 positive long values a and b which are greater than 2^32 (and smaller than 2^63), and an long integer c.
What is the best way, in java and\or c, to perform operations such as

(a*b)%c

while avoiding arithmetic overflow.

Edit :
c is around 2^34, and sometimes both a and b are just between 2^32 and c…

I finally avoided using BigInteger for the specific situation I was in. Indeed, It was possible to know one divisor of both a and b (not always the case), so I would use the arithmetic properties of modulo to my advantage.

Answer 1

Assuming everything’s positive, then you can use the following mathematical identity:

(a*b)%c == ((a%c) * (b%c)) % c

Of course, this still doesn’t eliminate the possibility of overflow.

The easiest way to completely avoid the issue is to use a big-integer library.