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Function LOGAND, LOGANDC1, LOGANDC2, LOGEQV, LOGIOR, LOGNAND, LOGNOR, LOGNOT, LOGORC1, LOGORC2, LOGXOR

Syntax:

logand &rest integers => result-integer

logandc1 integer-1 integer-2 => result-integer

logandc2 integer-1 integer-2 => result-integer

logeqv &rest integers => result-integer

logior &rest integers => result-integer

lognand integer-1 integer-2 => result-integer

lognor integer-1 integer-2 => result-integer

lognot integer => result-integer

logorc1 integer-1 integer-2 => result-integer

logorc2 integer-1 integer-2 => result-integer

logxor &rest integers => result-integer

Arguments and Values:

integers---integers.

integer---an integer.

integer-1---an integer.

integer-2---an integer.

result-integer---an integer.

Description:

The functions logandc1, logandc2, logand, logeqv, logior, lognand, lognor, lognot, logorc1, logorc2, and logxor perform bit-wise logical operations on their arguments, that are treated as if they were binary.

The next figure lists the meaning of each of the functions. Where an `identity' is shown, it indicates the value yielded by the function when no arguments are supplied.

Function Identity Operation performed 
logandc1 --- and complement of integer-1 with integer-2 
logandc2 --- and integer-1 with complement of integer-2 
logand -1 and 
logeqv -1 equivalence (exclusive nor) 
logior 0 inclusive or 
lognand --- complement of integer-1 and integer-2 
lognor --- complement of integer-1 or integer-2 
lognot --- complement 
logorc1 --- or complement of integer-1 with integer-2 
logorc2 --- or integer-1 with complement of integer-2 
logxor 0 exclusive or

Figure 12-18. Bit-wise Logical Operations on Integers

Negative integers are treated as if they were in two's-complement notation.

Examples:

 (logior 1 2 4 8) => 15
 (logxor 1 3 7 15) => 10
 (logeqv) => -1
 (logand 16 31) => 16
 (lognot 0) => -1
 (lognot 1) => -2
 (lognot -1) => 0
 (lognot (1+ (lognot 1000))) => 999
;;; In the following example, m is a mask. For each bit in
;;; the mask that is a 1, the corresponding bits in x and y are
;;; exchanged. For each bit in the mask that is a 0, the 
;;; corresponding bits of x and y are left unchanged.
 (flet ((show (m x y)
 (format t "~%m = #o~6,'0O~%x = #o~6,'0O~%y = #o~6,'0O~%"
 m x y)))
 (let ((m #o007750)
 (x #o452576)
 (y #o317407))
 (show m x y)
 (let ((z (logand (logxor x y) m)))
 (setq x (logxor z x))
 (setq y (logxor z y))
 (show m x y))))
>> m = #o007750
>> x = #o452576
>> y = #o317407
>> 
>> m = #o007750
>> x = #o457426
>> y = #o312557
=> NIL

Side Effects: None.

Affected By: None.

Exceptional Situations:

Should signal type-error if any argument is not an integer.

See Also:

boole

Notes:

(logbitp k -1) returns true for all values of k.

Because the following functions are not associative, they take exactly two arguments rather than any number of arguments.

 (lognand n1 n2) == (lognot (logand n1 n2))
 (lognor n1 n2) == (lognot (logior n1 n2))
 (logandc1 n1 n2) == (logand (lognot n1) n2)
 (logandc2 n1 n2) == (logand n1 (lognot n2))
 (logiorc1 n1 n2) == (logior (lognot n1) n2)
 (logiorc2 n1 n2) == (logior n1 (lognot n2))
 (logbitp j (lognot x)) == (not (logbitp j x))