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Function INTEGER-LENGTH

Syntax:

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

Side Effects: None.

Affected By: None.

Exceptional Situations:

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

See Also: None.

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)`.

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