(octave.info)Bit Manipulations

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4.5 Bit Manipulations
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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’.

 -- : C = bitset (A, N)
 -- : C = bitset (A, N, VAL)
     Set or reset bit(s) N of the unsigned integers in A.

     VAL = 0 resets and VAL = 1 sets the bits.  The least significant
     bit is N = 1.  All variables must be the same size or scalars.

          dec2bin (bitset (10, 1))
            ⇒ 1011

     See also: Note: bitand, Note: bitor, Note:
     bitxor, Note: bitget, *note bitcmp:
     XREFbitcmp, Note: bitshift, Note: intmax,
     Note: flintmax.

 -- : C = bitget (A, N)
     Return the status of bit(s) N of the unsigned integers in A.

     The least significant bit is N = 1.

          bitget (100, 8:-1:1)
          ⇒ 0  1  1  0  0  1  0  0

     See also: Note: bitand, Note: bitor, Note:
     bitxor, Note: bitset, *note bitcmp:
     XREFbitcmp, Note: bitshift, Note: intmax,
     Note: flintmax.

   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
two utility functions: ‘flintmax’ for floating point integers, and
‘intmax’ for integer objects (‘uint8’, ‘int64’, etc.).

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

 -- : bitand (X, Y)
     Return the bitwise AND of non-negative integers.

     X, Y must be in the range [0,intmax]

     See also: Note: bitor, Note: bitxor, Note:
     bitset, Note: bitget, *note bitcmp:
     XREFbitcmp, Note: bitshift, Note: intmax,
     Note: flintmax.

 -- : bitor (X, Y)
     Return the bitwise OR of non-negative integers X and Y.

     See also: Note: bitor, Note: bitxor, Note:
     bitset, Note: bitget, *note bitcmp:
     XREFbitcmp, Note: bitshift, Note: intmax,
     Note: flintmax.

 -- : bitxor (X, Y)
     Return the bitwise XOR of non-negative integers X and Y.

     See also: Note: bitand, Note: bitor, Note:
     bitset, Note: bitget, *note bitcmp:
     XREFbitcmp, Note: bitshift, Note: intmax,
     Note: flintmax.

   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’.

 -- : bitcmp (A, K)
     Return the K-bit complement of integers in A.

     If K is omitted ‘k = log2 (flintmax) + 1’ is assumed.

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

     See also: Note: bitand, Note: bitor, Note:
     bitxor, Note: bitset, *note bitget:
     XREFbitget, Note: bitcmp, Note: bitshift,
     Note: flintmax.

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

 -- : bitshift (A, K)
 -- : 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 64.  N must be in the range [1,64].

          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: Note: bitand, Note: bitor, Note:
     bitxor, Note: bitset, *note bitget:
     XREFbitget, Note: bitcmp, Note: intmax,
     Note: flintmax.

   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]’.