BIT_Tricks.md

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#17202A

Integers

Set n^th bit

x | (1<<n)

Unset n^th bit

x & ~(1<<n)

Toggle n^th bit

x ^ (1<<n)

Round up to the next power of two

unsigned int v; //only works if v is 32 bit
v--;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v++;

Round down / floor a number

n >> 0

5.7812 >> 0 // 5

Get the maximum integer

int maxInt = ~(1 << 31);
int maxInt = (1 << 31) - 1;
int maxInt = (1 << -1) - 1;
int maxInt = -1u >> 1;

Get the minimum integer

int minInt = 1 << 31;
int minInt = 1 << -1;

Get the maximum long

long maxLong = ((long)1 << 127) - 1;

Multiply by 2

n << 1; // n*2

Divide by 2

n >> 1; // n/2

Multiply by the m^th power of 2

n << m;

Divide by the m^th power of 2

n >> m;

Check Equality

_{This is 35% faster in Javascript}

(a^b) == 0; // a == b
!(a^b) // use in an if

Check if a number is odd

(n & 1) == 1;

Exchange (swap) two values

//version 1
a ^= b;
b ^= a;
a ^= b;

//version 2
a = a ^ b ^ (b = a)

Get the absolute value

//version 1
x < 0 ? -x : x;

//version 2
(x ^ (x >> 31)) - (x >> 31);

Get the max of two values

b & ((a-b) >> 31) | a & (~(a-b) >> 31);

Get the min of two values

a & ((a-b) >> 31) | b & (~(a-b) >> 31);

Check whether both numbers have the same sign

(x ^ y) >= 0;

Flip the sign

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

Calculate 2ⁿ

1 << n;

Whether a number is power of 2

n > 0 && (n & (n - 1)) == 0;

Modulo 2ⁿ against m

m & ((1 << n) - 1);

Get the average

(x + y) >> 1;
((x ^ y) >> 1) + (x & y);

Get the m^th bit of n (from low to high)

(n >> (m-1)) & 1;

Set the m^th bit of n to 0 (from low to high)

n & ~(1 << (m-1));

Check if n^th bit is set

if (x & (1<<n)) {
  n-th bit is set
} else {
  n-th bit is not set
}

Isolate (extract) the right-most 1 bit

x & (-x)

Isolate (extract) the right-most 0 bit

~x & (x+1)

Set the right-most 0 bit to 1

x | (x+1)

Set the right-most 1 bit to 0

x & (x-1)

n + 1

-~n

n - 1

~-n

Get the negative value of a number

~n + 1;
(n ^ -1) + 1;

if (x == a) x = b; if (x == b) x = a;

x = a ^ b ^ x;

Swap Adjacent bits

((n & 10101010) >> 1) | ((n & 01010101) << 1)

Different rightmost bit of numbers m & n

(n^m)&-(n^m) // returns 2^x where x is the position of the different bit (0 based)

Common rightmost bit of numbers m & n

~(n^m)&(n^m)+1 // returns 2^x where x is the position of the common bit (0 based)

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Strings

Convert letter to lowercase:

OR by space => (x | ' ')
Result is always lowercase even if letter is already lowercase
eg. ('a' | ' ') => 'a' ; ('A' | ' ') => 'a'

Convert letter to uppercase:

AND by underline => (x & '_')
Result is always uppercase even if letter is already uppercase
eg. ('a' & '_') => 'A' ; ('A' & '_') => 'A'

Invert letter's case:

XOR by space => (x ^ ' ')
eg. ('a' ^ ' ') => 'A' ; ('A' ^ ' ') => 'a'

Letter's position in alphabet:

AND by chr(31)/binary('11111')/(hex('1F') => (x & "\x1F")
Result is in 1..26 range, letter case is not important
eg. ('a' & "\x1F") => 1 ; ('B' & "\x1F") => 2

Get letter's position in alphabet (for Uppercase letters only):

AND by ? => (x & '?') or XOR by @ => (x ^ '@')
eg. ('C' & '?') => 3 ; ('Z' ^ '@') => 26

Get letter's position in alphabet (for lowercase letters only):

XOR by backtick/chr(96)/binary('1100000')/hex('60') => (x ^ '`')
eg. ('d' ^ '`') => 4 ; ('x' ^ '`') => 24