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A *fixnum* is an exact integer that is small enough to fit in a
machine word. In MIT/GNU Scheme, fixnums are typically 24 or 26 bits,
depending on the machine; it is reasonable to assume that fixnums are at
least 24 bits. Fixnums are signed; they are encoded using 2’s
complement.

All exact integers that are small enough to be encoded as fixnums are
always encoded as fixnums — in other words, any exact integer that is
not a fixnum is too big to be encoded as such. For this reason, small
constants such as `0`

or `1`

are guaranteed to be fixnums.

- procedure:
**fix:fixnum?***object*¶ -
Returns

`#t`

if`object`is a fixnum; otherwise returns`#f`

.

Here is an expression that determines the largest fixnum:

(let loop ((n 1)) (if (fix:fixnum? n) (loop (* n 2)) (- n 1)))

A similar expression determines the smallest fixnum.

- procedure:
**fix:=***fixnum fixnum*¶ - procedure:
**fix:<***fixnum fixnum*¶ - procedure:
**fix:>***fixnum fixnum*¶ - procedure:
**fix:<=***fixnum fixnum*¶ - procedure:
**fix:>=***fixnum fixnum*¶ -
These are the standard order and equality predicates on fixnums. When compiled, they do not check the types of their arguments.

- procedure:
**fix:zero?***fixnum*¶ - procedure:
**fix:positive?***fixnum*¶ - procedure:
**fix:negative?***fixnum*¶ These procedures compare their argument to zero. When compiled, they do not check the type of their argument. The code produced by the following expressions is identical:

(fix:zero?

`fixnum`) (fix:=`fixnum`0)Similarly,

`fix:positive?`

and`fix:negative?`

produce code identical to equivalent expressions using`fix:>`

and`fix:<`

.

- procedure:
**fix:+***fixnum fixnum*¶ - procedure:
**fix:-***fixnum fixnum*¶ - procedure:
**fix:****fixnum fixnum*¶ - procedure:
**fix:quotient***fixnum fixnum*¶ - procedure:
**fix:remainder***fixnum fixnum*¶ - procedure:
**fix:gcd***fixnum fixnum*¶ - procedure:
**fix:1+***fixnum*¶ - procedure:
**fix:-1+***fixnum*¶ These procedures are the standard arithmetic operations on fixnums. When compiled, they do not check the types of their arguments. Furthermore, they do not check to see if the result can be encoded as a fixnum. If the result is too large to be encoded as a fixnum, a malformed object is returned, with potentially disastrous effect on the garbage collector.

- procedure:
**fix:divide***fixnum fixnum*¶ -
This procedure is like

`integer-divide`

, except that its arguments and its results must be fixnums. It should be used in conjunction with`integer-divide-quotient`

and`integer-divide-remainder`

.

The following are *bitwise-logical* operations on fixnums.

- procedure:
**fix:not***fixnum*¶ This returns the bitwise-logical inverse of its argument. When compiled, it does not check the type of its argument.

(fix:not 0) ⇒ -1 (fix:not -1) ⇒ 0 (fix:not 1) ⇒ -2 (fix:not -34) ⇒ 33

- procedure:
**fix:and***fixnum fixnum*¶ This returns the bitwise-logical “and” of its arguments. When compiled, it does not check the types of its arguments.

(fix:and #x43 #x0f) ⇒ 3 (fix:and #x43 #xf0) ⇒ #x40

- procedure:
**fix:andc***fixnum fixnum*¶ Returns the bitwise-logical “and” of the first argument with the bitwise-logical inverse of the second argument. When compiled, it does not check the types of its arguments.

(fix:andc #x43 #x0f) ⇒ #x40 (fix:andc #x43 #xf0) ⇒ 3

- procedure:
**fix:or***fixnum fixnum*¶ This returns the bitwise-logical “inclusive or” of its arguments. When compiled, it does not check the types of its arguments.

(fix:or #x40 3) ⇒ #x43 (fix:or #x41 3) ⇒ #x43

- procedure:
**fix:xor***fixnum fixnum*¶ This returns the bitwise-logical “exclusive or” of its arguments. When compiled, it does not check the types of its arguments.

(fix:xor #x40 3) ⇒ #x43 (fix:xor #x41 3) ⇒ #x42

- procedure:
**fix:lsh***fixnum1 fixnum2*¶ This procedure returns the result of shifting

`fixnum1`by`fixnum2`bits. If`fixnum2`is positive,`fixnum1`is shifted left; if negative, it is shifted right*arithmetically*in signed two’s-complement. When compiled, it does not check the types of its arguments, nor the validity of its result.(fix:lsh 1 10) ⇒ #x400 (fix:lsh #x432 -10) ⇒ 1 (fix:lsh -1 3) ⇒ -8 (fix:lsh -128 -4) ⇒ -8

**Warning:**In the past, the semantics of`fix:lsh`

when both arguments were negative has been inconsistent.