gcc "overflow in expression" while equivalent equivalent expression works fine

Question

Here is my code

#include <iostream>
static const unsigned long long int xx = (36 * 36 * 36 * 36) * (36 * 36 * 36 * 36);
static const unsigned long long int y = 36 * 36 * 36 * 36;
static const unsigned long long int yy = y * y;

int main()
{
  std::cout << xx << std::endl;
  std::cout << yy << std::endl;
  return 0;
}

This the compilation output

# g++ -std=c++11 test.cpp -o test
test.cpp:2:62: warning: integer overflow in expression [-Woverflow]
 static const unsigned long long int xx = (36 * 36 * 36 * 36) * (36 * 36 * 36 * 36);

This is the execution output

# ./test
18446744073025945600
2821109907456

Can you explain why do I see this warning and different results? if 36 can fit into char then 36^8 can fit in unsigned long long int so I'm not sure what is problem here, please advise. (I'm using gcc 4.9.2)

Answer 1

static const unsigned long long int xx = (36 * 36 * 36 * 36) * (36 * 36 * 36 * 36);

36 has type int

∴ 36 * 36 has type int

∴ (36 * 36 * 36 * 36) has type int

∴ (36 * 36 * 36 * 36) * (36 * 36 * 36 * 36) has type int and overflows, which is actually undefined behavior for signed types.

You probably wanted

static const unsigned long long int xx = (36ull * 36 * 36 * 36) * (36 * 36 * 36 * 36);

As for the second case:

static const unsigned long long int yy = y * y;

y has type unsigned long long

∴ y * y has type unsigned long long so there's no overflow.