### 4.5 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: C = bitset (A, n)
Function File: C = bitset (A, n, val)

  Set or reset bit(s) n of unsigned integers in A. val = 0 resets and val = 1 sets the bits. The lowest significant bit is: n = 1. All variables must be the same size or scalars.

      dec2bin (bitset (10, 1))
        ⇒ 1011

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

Function File: c = 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 value 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 ()
Built-in Function: bitmax ("double")
Built-in Function: bitmax ("single")

  Return the largest integer that can be represented within a floating point value. The default class is `"double"`, but `"single"` is a valid option. On IEEE-754 compatible systems, `bitmax` is 2^{53} - 1 for `"double"` and 2^{24} -1 for `"single"`.

  See also: flintmax, intmax, realmax, realmin.

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

Octave also includes the basic bitwise ’and’, ’or’, and ’exclusive or’ operators.

Built-in Function: bitand (x, y)

  Return the bitwise AND of non-negative integers. x, y must be in the range [0,bitmax]

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

Built-in Function: bitor (x, y)

  Return the bitwise OR of non-negative integers. x, y must be in the range [0,bitmax]

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

Built-in Function: bitxor (x, y)

  Return the bitwise XOR of non-negative integers. x, y must be in the range [0,bitmax]

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

The bitwise ’not’ operator is a 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-shift and right-shift 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 the 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 kept 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]`.