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))

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