为什么这个函数会导致段错误？

Question

I wrote the following simple function to perform modular exponentiation. However, it segfaults when the exponent parameter is greater than about 261,000. Why is this? And how can I fix it?

I'm compiling with gcc on 64-bit Ubuntu.

Thanks

unsigned int modex(unsigned int base, unsigned int exponent, unsigned int modulus)
{
   if(exponent == 1)
      return base;

   base = base % modulus;

   if(exponent == 0 || base == 1)
      return 1;

   return (modex(base, exponent - 1, modulus) * base) % modulus;
}

Answer 1

@ouah already posted the answer in a comment, so if he wants to post an answer I'll delete this.

You have a stack overflow. You are recursing too many times and blowing your stack space. C++ does not guarantee tail call optimization (even if you didn't have that operation on the return value of the recursive call at the end), so you're better off implementing this using a loop.

If you want to stick with the recursive route, try making it truly tail recursive via the explanation here and see if the compiler helps you out.

Answer 2

You're creating a enormous recursion chain. You should try to save memory and processing by doing it iterative.

unsigned modex(unsigned base, unsigned exponent, unsigned modulus){

    unsigned
        result = 1;

    while(expoent--){
        result *= base;
        result %= modulus;

    }

    return result;

}

Still, you can do it even faster.

Answer 3

Your recursion becomes so deep that it takes up the entire sack. Consider using a while loop instead.