Bitwise

Functions for doing bitwise operations.

Bitwise operations only work on 32-bit integers. When an Int is passed to a bitwise operation, only the 32 least significant bits are used.

and : Int -> Int -> Int

Bitwise AND

or : Int -> Int -> Int

Bitwise OR

xor : Int -> Int -> Int

Bitwise XOR

complement : Int -> Int

Flip each bit individually, often called bitwise NOT

countLeadingZeros : Int -> Int

Count the number of leading zero bits in an integer.

countLeadingZeros 0 == 32
countLeadingZeros 1 == 31
countLeadingZeros 0xFFFF == 16

Bit Shifts

Note: Because bitwise operations only work on 32-bit integers, the shift distance is effectively limited to 31. If you shift by n, only the lowest 5 bits of n will be used and the binary will be shifted by modBy 32 n. For example, the following two commands perform the same operation:

Bitwise.shiftLeftBy  1 10
Bitwise.shiftLeftBy 33 10

shiftLeftBy : Int -> Int -> Int

Shift bits to the left by a given offset, filling new bits with zeros. This can be used to multiply numbers by powers of two.

shiftLeftBy 1 5 == 10

shiftLeftBy 5 1 == 32

shiftRightBy : Int -> Int -> Int

Shift bits to the right by a given offset, filling new bits with whatever is the topmost bit. This can be used to divide numbers by powers of two.

shiftRightBy 1 32 == 16

shiftRightBy 2 32 == 8

shiftRightBy 1 -32 == -16

This is called an arithmetic right shift, often written >>, and sometimes called a sign-propagating right shift because it fills empty spots with copies of the highest bit.

shiftRightZfBy : Int -> Int -> Int

Shift bits to the right by a given offset, filling new bits with zeros.

shiftRightZfBy 1 32 == 16

shiftRightZfBy 2 32 == 8

shiftRightZfBy 1 -32 == 2147483632

This is called an logical right shift, often written >>>, and sometimes called a zero-fill right shift because it fills empty spots with zeros.