9.1.6 Bit-Manipulation Functions

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

                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

Table 9.4: Bitwise Operations

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’.(51) If you start over again with ‘10111001’ and shift it left by three bits, you end up with ‘11001000’. gawk provides built-in functions that implement the bitwise operations just described. They are:

and(v1, v2)

Return the bitwise AND of the values provided by v1 and v2.

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 values provided by v1 and v2.

rshift(val, count)

Return the value of val, shifted right by count bits.

xor(v1, v2)

Return the bitwise XOR of the values provided by v1 and v2.

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 double, leading nonzero bits are removed one by one until it can be represented exactly. The result is then converted back into a C double. (If you don’t understand this paragraph, don’t worry about it.)

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

# bits2str --- turn a byte into readable 1's and 0's

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) = 0xffffff66 = 11111111111111111111111101100110
-| lshift(0x99, 2) = 0x264 = 0000001001100100
-| rshift(0x99, 2) = 0x26 = 00100110

The bits2str() function turns a binary number into a string. The number 1 represents a binary value where the rightmost bit is set to 1. Using this mask, the function repeatedly checks the rightmost bit. ANDing the mask with the value indicates whether the rightmost bit is 1 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 1 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 section Octal and Hexadecimal Numbers), and then demonstrates the results of the compl(), lshift(), and rshift() functions.