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#### 12.2.64 logcount [Function]

`logcount` integer ⇒ number-of-on-bits

#### Arguments and Values::

integer—an integer.

number-of-on-bits—a non-negative integer.

#### Description::

Computes and returns the number of bits in the two’s-complement binary representation of integer that are ‘on’ or ‘set’. If integer is negative, the `0` bits are counted; otherwise, the `1` bits are counted.

#### Examples::

     (logcount 0) ⇒  0
     (logcount -1) ⇒  0
     (logcount 7) ⇒  3
     (logcount  13) ⇒  3 ;Two's-complement binary: ...0001101
     (logcount -13) ⇒  2 ;Two's-complement binary: ...1110011
     (logcount  30) ⇒  4 ;Two's-complement binary: ...0011110
     (logcount -30) ⇒  4 ;Two's-complement binary: ...1100010
     (logcount (expt 2 100)) ⇒  1
     (logcount (- (expt 2 100))) ⇒  100
     (logcount (- (1+ (expt 2 100)))) ⇒  1

#### Exceptional Situations::

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

#### Notes::

Even if the implementation does not represent integers internally in two’s complement binary, logcount behaves as if it did.

The following identity always holds:

        (logcount x)
     ≡ (logcount (- (+ x 1)))
     ≡ (logcount (lognot x))