Question

Can someone please tell me how I can implement the following line of pseudo-code.

c[k]=c[k] (mod M) with |c[k]|<=M/2

I do not understand what the ‘with’ means, does it mean that I have to ensure that after reduction modulo M, c[k] must be less than or equal to M/2. What does ‘with’ usually mean (if anything) in pseudo-code?

Note that M is of type int. I’m implementing this in Java if it helps.

Thanks in advance.

Answer 1

I think it means set c[k] = c[k] + x*M, where -M/2 <= c[k] + x*M <= M/2 (choose the positive or negative integer x such that this is true).

For example, if M = 5, we would have:

       Previous value         New value
          of c[k]              of c[k]
            8                    -2
            9                    -1
           10                     0
           11                     1
           12                     2
           13                    -2