### 4.4 Bit Manipulations

Octave provides a number of functions for the manipulation of numeric values on a bit by bit basis. The basic functions to set and obtain the values of individual bits are `bitset` and `bitget`.

— Function File: x = bitset (a, n)
— Function File: x = bitset (a, n, v)

> Set or reset bit(s) n of unsigned integers in a. v = 0 resets and v = 1 sets the bits. The lowest significant bit is: n = 1

>               dec2bin (bitset (10, 1))
>               => 1011

> See also: bitand, bitor, bitxor, bitget, bitcmp, bitshift, bitmax.

— Function File: X = bitget (a,n)

> Return the status of bit(s) n of unsigned integers in a the lowest significant bit is n = 1.

>               bitget (100, 8:-1:1)
>               => 0  1  1  0  0  1  0  0

> See also: bitand, bitor, bitxor, bitset, bitcmp, bitshift, bitmax.

The arguments to all of Octave's bitwise operations can be scalar or arrays, except for `bitcmp`, whose k argument must a scalar. In the case where more than one argument is an array, then all arguments must have the same shape, and the bitwise operator is applied to each of the elements of the argument individually. If at least one argument is a scalar and one an array, then the scalar argument is duplicated. Therefore

         bitget (100, 8:-1:1)

is the same as

         bitget (100 * ones (1, 8), 8:-1:1)

It should be noted that all values passed to the bit manipulation functions of Octave are treated as integers. Therefore, even though the example for `bitset` above passes the floating point value `10`, it is treated as the bits `[1, 0, 1, 0]` rather than the bits of the native floating point format representation of `10`.

As the maximum number that can be represented by a number is important for bit manipulation, particularly when forming masks, Octave supplies the function `bitmax`.

— Built-in Function: bitmax ()

> Return the largest integer that can be represented as a floating point value. On IEEE-754 compatible systems, `bitmax` is `2^53 - 1`.

This is the double precision version of the functions `intmax`, previously discussed.

Octave also include the basic bitwise 'and', 'or' and 'exclusive or' operators.

— Built-in Function: bitand (x, y)

> Return the bitwise AND of nonnegative integers. x, y must be in range [0..bitmax]

> See also: bitor, bitxor, bitset, bitget, bitcmp, bitshift, bitmax.

— Built-in Function: bitor (x, y)

> Return the bitwise OR of nonnegative integers. x, y must be in range [0..bitmax]

> See also: bitor, bitxor, bitset, bitget, bitcmp, bitshift, bitmax.

— Built-in Function: bitxor (x, y)

> Return the bitwise XOR of nonnegative integers. x, y must be in range [0..bitmax]

> See also: bitand, bitor, bitset, bitget, bitcmp, bitshift, bitmax.

The bitwise 'not' operator is unary operator that performs a logical negation of each of the bits of the value. For this to make sense, the mask against which the value is negated must be defined. Octave's bitwise 'not' operator is `bitcmp`.

— Function File: bitcmp (a, k)

> Return the k-bit complement of integers in a. If k is omitted `k = log2 (bitmax) + 1` is assumed.

>               bitcmp(7,4)
>               => 8
>               dec2bin(11)
>               => 1011
>               dec2bin(bitcmp(11, 6))
>               => 110100

> See also: bitand, bitor, bitxor, bitset, bitget, bitcmp, bitshift, bitmax.

Octave also includes the ability to left and right values bitwise.

— Built-in Function: bitshift (a, k)
— Built-in Function: bitshift (a, k, n)

> Return a k bit shift of n- digit unsigned integers in a. A positive k leads to a left shift. A negative value to a right shift. If n is omitted it defaults to log2(bitmax)+1. n must be in range [1,log2(bitmax)+1] usually [1,33]

>               bitshift (eye (3), 1)
>               =>
>               2 0 0
>               0 2 0
>               0 0 2

>               bitshift (10, [-2, -1, 0, 1, 2])
>               => 2   5  10  20  40

> See also: bitand, bitor, bitxor, bitset, bitget, bitcmp, bitmax.

Bits that are shifted out of either end of the value are lost. Octave also uses arithmetic shifts, where the sign bit of the value is keep during a right shift. For example

         bitshift (-10, -1)
         => -5
         bitshift (int8 (-1), -1)
         => -1

Note that `bitshift (int8 (-1), -1)` is `-1` since the bit representation of `-1` in the `int8` data type is `[1, 1, 1, 1, 1, 1, 1, 1]`.