# Calculate abs(int) without branching

• branching • code • personal • operators • english • it • bitwise • twos-complement • abs • value • hack • absolute • cool
• 417 words

For this you need someone to teach it to you: if you made it yourself, then you are a very good Comp-Sci, and you should send your CV to Google ASAP. ;)

## Without branching O_o?

Yes, without using any “`if ( a < 0 )...`”. To do that, you need to refresh how Two’s Complement works, then come back.

What we really need to focus on is that, given a `signed int A`, the negative of that number is: `B = ~A + 1`. BUT, we are trying to calculate the Absolute Value, not the negative. So, something like:

``````RESULT =
(INPUT, if positive, or NEGATE_INPUT, if negative)
+
(0, if positive, or 1, if negative)
``````

Does it makes sense to you? To me it didn’t for the first 10 minutes.

## What do we need?

We need, given the integer in input, to calculate 2 values:

• A way to "optionally negate" the input
• A variable carrying `0` if the input is positive, `1` otherwise </ul> ### Look what we have here: the `XOR` Properties of XOR are:
• `A ^ 0 = A`
• `A ^ 1 = ~A`
• `A ^ A = 0`
• `A ^ B = B ^ A` (commutative)
The first two properties are key here: if we could only generate a variable from the input that contains `0` if positive and `1` if negative, we would have half hack done. ### Ladies and Gentleman, all shift please Now, let's see some shifting in action. If A is a Positive number, then: ```c A = INPUT >> 31 => 0x00000000 => 0 B = -A => -0x00000000 => 0 ``` While if A is a Negative number, then: ```c A = INPUT >> 31 => 0xFFFFFFFF => -1 B = -A => 0x00000001 => 1 ``` ## Putting all together So, this means that we can calculate the absolute value using the new variables we have produced, A and B. Here is how: ```c #include int abs(const int value) { int A = value >> 31; // 0x00000000 if Positive, 0xFFFFFFFF if Negative int B = -A; // 0x00000000 if Positive, 0x00000001 if Negative return (value ^ A) + B; // value ^ A = value if Positive, value ^ A = ~value if Negative } int main(int argc, char** argv) { int input; // Check the Input if ( argc == 2 ) input = atoi(argv); else return (1); printf("abs(%d) = %d\n\n", input, abs(input)); } ``` Who showed me this hack? eh eh eh! ;)