I can explain it for you, but I can’t understand it for you.

— *Anonymous*

Many languages provide the ability to perform *bitwise* operations
on two integer numbers. In other words, the operation is performed on
each successive pair of bits in the operands.
Three common operations are bitwise AND, OR, and XOR.
The operations are described in Table 9.6.

Bit operator | AND | OR | XOR |---+---+---+---+---+--- Operands | 0 | 1 | 0 | 1 | 0 | 1 ----------+---+---+---+---+---+--- 0 | 0 0 | 0 1 | 0 1 1 | 0 1 | 1 1 | 1 0

As you can see, the result of an AND operation is 1 only when *both*
bits are 1.
The result of an OR operation is 1 if *either* bit is 1.
The result of an XOR operation is 1 if either bit is 1,
but not both.
The next operation is the *complement*; the complement of 1 is 0 and
the complement of 0 is 1. Thus, this operation “flips” all the bits
of a given value.

Finally, two other common operations are to shift the bits left or right.
For example, if you have a bit string ‘`10111001`’ and you shift it
right by three bits, you end up with ‘`00010111`’.^{62}
If you start over again with ‘`10111001`’ and shift it left by three
bits, you end up with ‘`11001000`’. The following list describes
`gawk`

’s built-in functions that implement the bitwise operations.
Optional parameters are enclosed in square brackets ([ ]):

`and(`

`v1``,`

`v2`[`,`

…]`)`

Return the bitwise AND of the arguments. There must be at least two.

`compl(`

`val`)Return the bitwise complement of

`val`.`lshift(`

¶`val`,`count`)Return the value of

`val`, shifted left by`count`bits.`or(`

`v1``,`

`v2`[`,`

…]`)`

Return the bitwise OR of the arguments. There must be at least two.

`rshift(`

¶`val`,`count`)Return the value of

`val`, shifted right by`count`bits.`xor(`

`v1``,`

`v2`[`,`

…]`)`

Return the bitwise XOR of the arguments. There must be at least two.

CAUTION:Beginning with`gawk`

version 4.2, negative operands are not allowed for any of these functions. A negative operand produces a fatal error. See the sidebar “Beware The Smoke and Mirrors!” for more information as to why.

Here is a user-defined function (see User-Defined Functions) that illustrates the use of these functions:

# bits2str --- turn an integer into readable ones and zeros function bits2str(bits, data, mask) { if (bits == 0) return "0" mask = 1 for (; bits != 0; bits = rshift(bits, 1)) data = (and(bits, mask) ? "1" : "0") data while ((length(data) % 8) != 0) data = "0" data return data }

BEGIN { printf "123 = %s\n", bits2str(123) printf "0123 = %s\n", bits2str(0123) printf "0x99 = %s\n", bits2str(0x99) comp = compl(0x99) printf "compl(0x99) = %#x = %s\n", comp, bits2str(comp) shift = lshift(0x99, 2) printf "lshift(0x99, 2) = %#x = %s\n", shift, bits2str(shift) shift = rshift(0x99, 2) printf "rshift(0x99, 2) = %#x = %s\n", shift, bits2str(shift) }

This program produces the following output when run:

$gawk -f testbits.awk-| 123 = 01111011 -| 0123 = 01010011 -| 0x99 = 10011001 -| compl(0x99) = 0x3fffffffffff66 = -| 00111111111111111111111111111111111111111111111101100110 -| lshift(0x99, 2) = 0x264 = 0000001001100100 -| rshift(0x99, 2) = 0x26 = 00100110

The `bits2str()`

function turns a binary number into a string.
Initializing `mask`

to one creates
a binary value where the rightmost bit
is set to one. Using this mask,
the function repeatedly checks the rightmost bit.
ANDing the mask with the value indicates whether the
rightmost bit is one or not. If so, a `"1"`

is concatenated onto the front
of the string.
Otherwise, a `"0"`

is added.
The value is then shifted right by one bit and the loop continues
until there are no more one bits.

If the initial value is zero, it returns a simple `"0"`

.
Otherwise, at the end, it pads the value with zeros to represent multiples
of 8-bit quantities. This is typical in modern computers.

The main code in the `BEGIN`

rule shows the difference between the
decimal and octal values for the same numbers
(see Octal and Hexadecimal Numbers),
and then demonstrates the
results of the `compl()`

, `lshift()`

, and `rshift()`

functions.

Beware The Smoke and Mirrors! |
---|

It other languages, bitwise operations are performed on integer values, not floating-point values. As a general statement, such operations work best when performed on unsigned integers.
In normal operation, for all of these functions, first the
double-precision floating-point value is converted to the widest C
unsigned integer type, then the bitwise operation is performed. If the
result cannot be represented exactly as a C However, when using arbitrary precision arithmetic with the $ What’s going on becomes clear when printing the results in hexadecimal: $ When using the In short, using |

This example
shows that zeros come in on the left side. For `gawk`

, this is
always true, but in some languages, it’s possible to have the left side
fill with ones.

If you don’t
understand this paragraph, the upshot is that `gawk`

can only
store a particular range of integer values; numbers outside that range
are reduced to fit within the range.