#### 12.2.62 logand, logandc1, logandc2, logeqv, logior, ¶

#### lognand, lognor, lognot, logorc1, logorc2, ¶

#### logxor ¶

[Function]

`logand` &rest integers ⇒ result-integer

`logandc` 1 ⇒ integer-1 integer-2 result-integer `logandc` 2 ⇒ 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

`logorc` 1 ⇒ integer-1 integer-2 result-integer `logorc` 2 ⇒ 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.

Figure 12–17 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 12–17: 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 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

#### Exceptional Situations:: ¶

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

#### See Also:: ¶

boole [Function]

#### 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))