# 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

### 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:**

```
A = INPUT >> 31 => 0x00000000 => 0
B = -A => -0x00000000 => 0
```

**While if A is a Negative number, then:**

```
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:

```
#include <stdio.h>
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[1]); else return (1);
printf("abs(%d) = %d\n\n", input, abs(input));
}
```

Who showed me this hack? eh eh eh! ;)