仅使用按位运算符复制for循环的功能

Question

I'm trying to replicate the function of a loop using only bitwise and certain operators including ! ~ & ^ | + << >>

int loop(int x) {
   for (int i = 1; i < 32; i += 2)
     if ((x & (1 << i)) == 0)
       return 0;
   return 1; 
}

Im unsure however how to replicate the accumulating nature of a loop using just these operators. I understand shifting << >> will allow me to multiply and divide. However manipulation using ! ~ & ^ ~ has proven more difficult. Any Tips?

http://www.tutorialspoint.com/cprogramming/c_operators.htm

Edit: I understand how the addition of bits can be achieved, however not how such an output can be achieved without first calling a while or for loop.

Answer 1

Maybe this can help:

int loop(int x) {
    x = x & 0xaaaaaaaa; // Set all even numbered bits in x to zero
    x = x ^ 0xaaaaaaaa; // If all odd numbered bits in x are 1, x becomes zero
    x = !x;             // The operation returns 1 if x is zero - otherwise 0
    return x;
}

Answer 2

Your code tests all odd bits and returns 1 if all of them are set. You can use this bitmask: ...0101 0101 0101 Which, for 32 bits is 0xAAAAAAAA. Then you take your value und bitwise-and it. If the result is the same as your mask, it means all bits are set.

int testOddBits(int x) {
    return (x & 0xAAAAAAAA) == 0xAAAAAAAA;
}