# Bitwise gems – fast integer math

Bitwise operators are very fast in AS3, so here is a small collection of code snippets which can speed up certain computations. I won’t explain what bit operators are and how to use them, rather pointing to an excellent article hosted on gamedev.net: ‘Bitwise Operations in C’.
If you know any good tricks that are not included here, feel free to leave a comment or send me an email. All benchmarks were done in AS3.

### Left bit shifting to multiply by any power of two

Approximately 300% faster.

```x = x * 2;
x = x * 64;

//equals:
x = x << 1;
x = x << 6;
```

### Right bit shifting to divide by any power of two

Approximately 350% faster.

```x = x / 2;
x = x / 64;

//equals:
x = x >> 1;
x = x >> 6;
```

### Number to integer conversion

Using int(x) is 10% faster in AS3. Still the bitwise version works better in AS2.

```x = int(1.232)

//equals:
x = 1.232 >> 0;
```

### Extracting color components

Not really a trick, but the regular way of extracting values using bit masking and shifting.

```//24bit
var color:uint = 0x336699;
var r:uint = color >> 16;
var g:uint = color >> 8 & 0xFF;
var b:uint = color & 0xFF;

//32bit
var color:uint = 0xff336699;
var a:uint = color >>> 24;
var r:uint = color >>> 16 & 0xFF;
var g:uint = color >>>  8 & 0xFF;
var b:uint = color & 0xFF;
```

### Combining color components

‘Shift up’ the values into the correct position and combine them.

```//24bit
var r:uint = 0x33;
var g:uint = 0x66;
var b:uint = 0x99;
var color:uint = r << 16 | g << 8 | b;

//32bit
var a:uint = 0xff;
var r:uint = 0x33;
var g:uint = 0x66;
var b:uint = 0x99;
var color:uint = a << 24 | r << 16 | g << 8 | b;
```

### Swap integers without a temporary variable using XOR

Pretty neat trick, it is explained in detail in the link at the top of the page. This is 20% faster.

```var t:int = a;
a = b;
b = t;

//equals:
a ^= b;
b ^= a;
a ^= b;
```

### Increment/decrement

This is much slower than the pre/post decrement operator, but a nice way to obfuscate your code ;-)

```i = -~i; // i++
i = ~-i; // i--
```

### Sign flipping using NOT or XOR

Strangely enough, this is 300%(!) faster.

```i = -i;

//equals
i = ~i + 1;

//or
i = (i ^ -1) + 1;
```

### Fast modulo operation using bitwise AND

If the divisor is a power of 2, the modulo (%) operation can be done with:
modulus = numerator & (divisor – 1);

```x = 131 % 4;

//equals:
x = 131 & (4 - 1);
```

### Check if an integer is even/uneven using bitwise AND

This is 600% faster.

```isEven = (i % 2) == 0;

//equals:
isEven = (i & 1) == 0;
```

### Absolute value

Forget Math.abs() for time critical code. Version 1 is 2500% faster than Math.abs(), and the funky bitwise version 2 is again 20% faster than version 1.

```//version 1
i = x < 0 ? -x : x;

//version 2
i = (x ^ (x >> 31)) - (x >> 31);
```

### Comparing two integers for equal sign

This is 35% faster.

```eqSign = a * b > 0;

//equals:
eqSign = a ^ b >= 0;
```

### Fast color conversion from R5G5B5 to R8G8B8 pixel format using shifts

```R8 = (R5 << 3) | (R5 >> 2)
G8 = (R5 << 3) | (R5 >> 2)
B8 = (R5 << 3) | (R5 >> 2)
```