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### integer-length (Function)

##### Syntax:
— 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)`.