# Calculate abs(int) without branching

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)

`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 #includeint 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[1]); else return (1); printf("abs(%d) = %d\n\n", input, abs(input)); } ``` Who showed me this hack? eh eh eh! ;)