12.2.57 integer-length [Function]

integer-length integer => number-of-bits

Arguments and Values::

integer—an integer.

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

Description::

Returns the number of bits needed to represent integer in binary two's-complement format.

Examples::

      (integer-length 0) =>  0
      (integer-length 1) =>  1
      (integer-length 3) =>  2
      (integer-length 4) =>  3
      (integer-length 7) =>  3
      (integer-length -1) =>  0
      (integer-length -4) =>  2
      (integer-length -7) =>  3
      (integer-length -8) =>  3
      (integer-length (expt 2 9)) =>  10
      (integer-length (1- (expt 2 9))) =>  9
      (integer-length (- (expt 2 9))) =>  9
      (integer-length (- (1+ (expt 2 9)))) =>  10

Exceptional Situations::

Should signal an error of type type-error if integer is not an integer.

Notes::

This function could have been defined by:

     (defun integer-length (integer)
       (ceiling (log (if (minusp integer)
                         (- integer)
                         (1+ integer))
                     2)))

If integer is non-negative, then its value can be represented in unsigned binary form in a field whose width in bits is no smaller than (integer-length integer). Regardless of the sign of integer, its value can be represented in signed binary two's-complement form in a field whose width in bits is no smaller than (+ (integer-length integer) 1).