Wednesday, 31 December 2014

Bit Hacks You Must Know

it hacks are ingenious little programming tricks that manipulate integers in a smart and efficient manner. Instead of performing some operation (such as counting the 1 bits in an integer) by looping over individual bits, these programming hacks do the same but in a tricky way.
This post assumes that you know about the following bitwise operations and some C/C++ language.
1. & : Bitwise AND
2. ||   : Bitwise OR
3. ^  : Bitwise XOR
4. ~  : Bitwise NOT
5. <<: Bitwise Shift Left
6. >> : Bitwise Shift Right
I’m taking the size of each variable as 8 bit, where the first bit is b0 and last bit (MSB) is b7.

Let’s go ahead with some bit hacks.

Check if the integer is even or odd

 1 2 3 4 5 6 `if` `((a & 1) == 0) {` `a is even` `}` `else` `{` `a is odd` `}`
The righmost or zeroth bit of odd number is always set. Checking the rightmost bit only will do if we want to find out that a is even or odd.

Turn off the rightmost 1-bit

 1 `b = a & (a - 1)`
If x is even, then x – 1 will be odd and vice versa too. This is gonna unset the zeroth bit. Why? The rightmost bit of odd number is always set.

Test if the n-th bit is set

 1 2 3 4 5 6 `if` `(a & (1 << n)) {` `n-th bit is set` `}` `else` `{` `n-th bit is not set` `}`
1 is left shifted n times and then anded with a, do a example paper run, and you will get it better.

Set the n-th bit

 1 `b = a | (1 << n)`
Shift left 1 n times or it with a and then put it into a new variable b.

Unset the nth bit

 1 `b = a | ~(1 << n)`
Shift 1 n times left, complement it or it with a and then put it into a new variable b.

Toggle the n-th bit

 1 `b = a ^ (1 << n)`
Shift left 1 n times, xor it with a and assign it to a new variable.

Uppercase to lower case letter

 1 `"CAPITAL LETTER"` `XOR ``" "` `= small letter`
Xoring with space i.e., ” “, will give you lowercase letter.

If a integer is power of 2

 1 `b = a && !(a & (a - 1));`
Check a and a – 1 is 0, and AND the result with a, to check that a is not zero and some power of 2.