logcount integer → number-of-on-bits

integer — an integer.

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

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.

(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

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

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))