logcount (Function)

Syntax:

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))