Which is the fastest way to get the absolute value of a number

For completeness, here's a way to do it for IEEE floats on x86 systems in C++:

*(reinterpret_cast<uint32_t*>(&foo)) &= 0xffffffff >> 1;

Calculating the square root is probably one of the worst things you could do because it is really slow. Usually there is a library function for doing this; something like Math.Abs(). Multiplying with -1 is also unnecessary; just return -x. So a good solution would be the following.

(x >= 0) ? x : -x

The compiler will probably optimize this to a single instructions. Conditions may be quite expensive on modern processors because of the long execution pipelines -the calculations must be thrown away if a branch was misspredicted and the processor started executing the instructions from the wrong code path. But because of the mentioned compiler optimization you need not care in this case.

There is a great trick to calculate the absolute value of a 2s-complement integer without using an if statement. The theory goes, if the value is negative you want to toggle the bits and add one, otherwise you want to pass the bits through as is. A XOR 1 happens to toggle A and A XOR 0 happens to leave A intact. So you want do something like this:

  uint32_t temp = value >> 31;     // make a mask of the sign bit
  value ^= temp;                   // toggle the bits if value is negative
  value += temp & 1;               // add one if value was negative

In principle, you can do it in as few as three assembly instructions (without a branch). And you'd like to think that the abs() function that you get with math.h does it optimally.

No branches == better performance. Contrary to @paxdiablo's response above, this really matters in deep pipelines where the more branches you have in your code, the more likely you are to have your branch predictor get it wrong and have to roll-back, etc. If you avoid branching where possible, things will keep moving along at full throttle in your core :).

Conditionals are slower than plain arithmetic operations, but much, much faster than something as silly as calculating the square root.

Rules of thumb from my assembly days:

• Integer or bitwise op: 1 cycle
• Floating-point add/sub/mul: 4 cycles
• Floating-point div: ~30 cycles
• Floating-point exponentiation: ~200 cycles
• Floating-point sqrt: ~60 cycles depending on implementation
• Conditional branch: avg. 10 cycles, better if well-predicted, much worse if mispredicted