# Function BOOLE

### Syntax

• boole op integer-1 integer-2result-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 following table.

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

```

The below 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

▷
#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

▷
#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

</blockquote>

====Affected By====
None.

====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.

Function 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)

```