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  ANSI Common Lisp   12 Numbers   12.2 Dictionary of Numbers

12.2.60 boole Function

Syntax:
boole op integer-1 integer-2    result-integer

Arguments and Values:
Op - a bit-wise logical operation specifier.

integer-1 - an integer.

integer-2 - an integer.

result-integer - an integer.

Description:
boole performs bit-wise logical operations on integer-1 and integer-2, which are treated as if they were binary and in two's complement representation.

The operation to be performed and the return value are determined by op.

boole returns the values specified for any op in the next figure.

Bit-Wise Logical Operations
Op Result
boole-1 integer-1
boole-2 integer-2
boole-andc1 and complement of integer-1 with integer-2
boole-andc2 and integer-1 with complement of integer-2
boole-and and
boole-c1 complement of integer-1
boole-c2 complement of integer-2
boole-clr always 0 (all zero bits)
boole-eqv equivalence (exclusive nor)
boole-ior inclusive or
boole-nand not-and
boole-nor not-or
boole-orc1 or complement of integer-1 with integer-2
boole-orc2 or integer-1 with complement of integer-2
boole-set always -1 (all one bits)
boole-xor exclusive or

Examples:
 (boole boole-ior 1 16)  17
 (boole boole-and -2 5)  4
 (boole boole-eqv 17 15)  -31

;;; These examples illustrate the result of applying BOOLE and each
;;; of the possible values of OP to each possible combination of bits.
 (progn
   (format t "~&Results of (BOOLE <op> #b0011 #b0101) ...~
           ~% - Op---- - Decimal-- - Binary- - Bits - ~%")
   (dolist (symbol '(boole-1     boole-2    boole-and  boole-andc1
                     boole-andc2 boole-c1   boole-c2   boole-clr
                     boole-eqv   boole-ior  boole-nand boole-nor
                     boole-orc1  boole-orc2 boole-set  boole-xor))
     (let ((result (boole (symbol-value symbol) #b0011 #b0101)))
       (format t "~& ~A~13T~3,' D~23T~:*~5,' B~31T ...~4,'0B~%" 
               symbol result (logand result #b1111)))))
 Results of (BOOLE <op> #b0011 #b0101) ...
 - Op---- - Decimal-- - Binary- - Bits - 
 BOOLE-1       3          11    ...0011
 BOOLE-2       5         101    ...0101
 BOOLE-AND     1           1    ...0001
 BOOLE-ANDC1   4         100    ...0100
 BOOLE-ANDC2   2          10    ...0010
 BOOLE-C1     -4        -100    ...1100
 BOOLE-C2     -6        -110    ...1010
 BOOLE-CLR     0           0    ...0000
 BOOLE-EQV    -7        -111    ...1001
 BOOLE-IOR     7         111    ...0111
 BOOLE-NAND   -2         -10    ...1110
 BOOLE-NOR    -8       -1000    ...1000
 BOOLE-ORC1   -3         -11    ...1101
 BOOLE-ORC2   -5        -101    ...1011
 BOOLE-SET    -1          -1    ...1111
 BOOLE-XOR     6         110    ...0110
  NIL

Exceptional Situations:
Should signal type-error if its first argument is not a bit-wise logical operation specifier or if any subsequent argument is not an integer.

See Also:
logand

Notes:
In general,

 (boole boole-and x y) ==(logand x y)

Programmers who would prefer to use numeric indices rather than bit-wise logical operation specifiers can get an equivalent effect by a technique such as the following:

;; The order of the values in this `table' are such that
;; (logand (boole (elt boole-n-vector n) #b0101 #b0011) #b1111) => n
 (defconstant boole-n-vector
    (vector boole-clr   boole-and  boole-andc1 boole-2
            boole-andc2 boole-1    boole-xor   boole-ior
            boole-nor   boole-eqv  boole-c1    boole-orc1
            boole-c2    boole-orc2 boole-nand  boole-set))
  BOOLE-N-VECTOR
 (proclaim '(inline boole-n))
 implementation-dependent
 (defun boole-n (n integer &rest more-integers)
   (apply #'boole (elt boole-n-vector n) integer more-integers))
  BOOLE-N
 (boole-n #b0111 5 3)  7
 (boole-n #b0001 5 3)  1
 (boole-n #b1101 5 3)  -3
 (loop for n from #b0000 to #b1111 collect (boole-n n 5 3))
 (0 1 2 3 4 5 6 7 -8 -7 -6 -5 -4 -3 -2 -1)

Allegro CL Implementation Details:
None.

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