Compute the integer absolute value (abs) without branching | GeeksforGeeks

We need not to do anything if a number is positive. We want to change only negative numbers. Since negative numbers are stored in 2′s complement form, to get the absolute value of a negative number we have to toggle bits of the number and add 1 to the result.

1) Set the mask as right shift of integer by 31 (assuming integers are stored using 32 bits).

 mask = n>>31 

2) For negative numbers, above step sets mask as 1 1 1 1 1 1 1 1 and 0 0 0 0 0 0 0 0 for positive numbers. Add the mask to the given number.

 mask + n 

3) XOR of mask +n and mask gives the absolute value.

 (mask + n)^mask 

-X=~x+1 ==> -(X-1)=~(x-1)+1 => -X=~(X-1)

unsigned int getAbs(int n)

{

  int const mask = n >> (sizeof(int) * CHAR_BIT - 1);//>>31

  return ((n + mask) ^ mask);

}




Alternative Solution
Subtract mask from result of step 2 and return the result.

 (mask^n) - mask 

unsigned int getAbs(int n) {   int const mask = n >> (sizeof(int) * CHAR_BIT - 1);   return ((n ^ mask) - mask); }

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