Question

I am writing a function that is supposed to do powers, but only display the last n digits specified. It is working great… mostly. For some reason when I specify how many of the last digits I want, it works fine all the way up to and including the number 12. Any digit amount above 12 seems to give me a very strange number. I know I must be missing something obvious, but I really don’t see it.

Here is the code:

function power(base, exponent, digits) {
total = base;
for(i = 1; i < exponent; i++) {
    total =  total * base;

    if(total.toString().length > digits)  {
        total = total.toString().substr(total.toString().length - digits, digits);
        }
    }

return total;
}

So, for some examples (displaying 12 digits and lower works fine):

If I do power(999, 999, 1) I end up with => 9

If I do power(999, 999, 5) I end up with => 98999

If I do power(999, 999, 12) I end up with => 000499998999

Here is where it starts messing up:

If I do power(999, 999, 13) I end up with => 5710054009000

If I do power(999, 999, 14) I end up with => ‘79077027006000’

At first I thought I was hitting some kind of integer limit and scientific notation was screwing things up, but I don’t think that is the case, because it should work up to 20 digits.

I suspect it is something wrong with the way I am reducing the string in the if statement. But I am not sure why it wouldn’t mess up for calculations below 13 digits.

Thanks!

Answer 1

You need a function to compute b^e (mod m). A good algorithm is known as square and multiply:

Algorithm PowerMod: Compute b^e (mod m) with b, e and m all positive integers.
1. [Initialize] Set r := 1.
2. [Terminate when finished] If e == 0, return r and stop.
3. [Multiply if odd] If e is odd, set r := r * b (mod n).
4. [Square and iterate] Set e := floor(e / 2). Set b := b * b (mod n). Go to Step 2.

Then to make your computation, say PowerMod(999, 999, 10^14); you should get 17000499998999.