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))