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Document Fast Swap Values Between Two Variables in C


by Miroslaw M. Soja
First Published: September 1st, 2002

At the beginning there was a swap() ...
     Most of beginner programmers and computer science students face a simple problem: how to swap two numerical variables? In most cases, course's books and instructors suggest a following solution:

  void swap(int *a, int *b)
{
int temp ;
temp = *a ;
*a = *b ;
*b = temp ;
}

     For the educational purposes, the mentioned function swap() serves well in order to educate future champions in computer science. However, the computer programming industry is not the University - the industry requires that people must think harder.

     In other words, the function swap() has a problem - each time when the function is invoked, it must create (a time expensive process) a temporary variable the int temp. In spite of the fact that today's computers are relatively fast, it still could be a problem - especially, when the real time system requires to invoke the process of swapping in a large scale.

     In reply to the challenge, one could propose a solution: the int temp must be declared as a static variable - it eliminate the time for creating temporary variable in a computer memory. It is great! Yahoo! But... unfortunately, this solution is only good for students who want to get some bonus points on an exam as a reward for their smart suggestion.

Real World Challenges Academic swap()
     Real life is more difficult and full of surprises! Therefore, the real problem is finding answer to the following question: Can we swap two values without any additional variable used as a temporary storage?

     For a small group of industrial programmers the answer is obvious - it means, YES! And the solution is extremely simple -- when I learned about the solution for the first time, I was amazed with its simplicity and beauty.

XOR Logic and its Beauty
     The new code for swap() is following:
  void swap(int *a, int *b)
{
*a ^= *b ;
*b ^= *a ;
*a ^= *b ;
}


XOR -- How Does it Work?
     The entire secret is in a property of XOR - the logical operation. The XOR has following logic:
0 XOR 0 = 0
1 XOR 1 = 0
1 XOR 0 = 1
0 XOR 1 = 1

     In order to illustrate the method used in function swap(), let us consider two integer numbers x and y in binary form:
x = {0011} and
y = {1001}
Let us perform the first operation: x= x XOR y (which is equivalent of *a ^= *b )

x = x XOR y = {0011} XOR {1001} = {1010}
The value {1010}, from the XOR perspective, carries information about two numbers: {0011} and {1001}

Next, y = x XOR y (or *b ^= *a ),
Please note: the current value of x is {1010}!

y = x XOR y = {1010} XOR {1001} = {0011}
At this moment y value became the original value of x !

Finally, x = x XOR y (or *a ^= *b ),
x = x XOR y = {1010} XOR {0011} = {1001}
Therefore x value became the original value of y !

Conclusion
     The logical operation XOR is amazing - it can create a new result number by merging two other initial numbers. At the same time, XOR is capable to restore from the result number one of the initial numbers using another one.

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