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#### 7.6.2.19 rnrs arithmetic fixnums

The `(rnrs arithmetic fixnums (6))`

library provides procedures for
performing arithmetic operations on an implementation-dependent range of
exact integer values, which R6RS refers to as *fixnums*. In Guile,
the size of a fixnum is determined by the size of the `SCM`

type; a
single SCM struct is guaranteed to be able to hold an entire fixnum,
making fixnum computations particularly
efficient—(see section The SCM Type). On 32-bit systems, the most
negative and most positive fixnum values are, respectively, -536870912
and 536870911.

Unless otherwise specified, all of the procedures below take fixnums as
arguments, and will raise an `&assertion`

condition if passed a
non-fixnum argument or an `&implementation-restriction`

condition
if their result is not itself a fixnum.

- Scheme Procedure:
**fixnum-width** - Scheme Procedure:
**least-fixnum** - Scheme Procedure:
**greatest-fixnum** These procedures return, respectively, the maximum number of bits necessary to represent a fixnum value in Guile, the minimum fixnum value, and the maximum fixnum value.

- Scheme Procedure:
**fx=?***fx1 fx2 fx3 ...* - Scheme Procedure:
**fx>?***fx1 fx2 fx3 ...* - Scheme Procedure:
**fx<?***fx1 fx2 fx3 ...* - Scheme Procedure:
**fx>=?***fx1 fx2 fx3 ...* - Scheme Procedure:
**fx<=?***fx1 fx2 fx3 ...* These procedures return

`#t`

if their fixnum arguments are (respectively): equal, monotonically increasing, monotonically decreasing, monotonically nondecreasing, or monotonically nonincreasing;`#f`

otherwise.

- Scheme Procedure:
**fxzero?***fx* - Scheme Procedure:
**fxpositive?***fx* - Scheme Procedure:
**fxnegative?***fx* - Scheme Procedure:
**fxodd?***fx* - Scheme Procedure:
**fxeven?***fx* These numerical predicates return

`#t`

if`fx`is, respectively, zero, greater than zero, less than zero, odd, or even;`#f`

otherwise.

- Scheme Procedure:
**fxmax***fx1 fx2 ...* - Scheme Procedure:
**fxmin***fx1 fx2 ...* These procedures return the maximum or minimum of their arguments.

- Scheme Procedure:
**fx+***fx1 fx2* - Scheme Procedure:
**fx****fx1 fx2* These procedures return the sum or product of their arguments.

- Scheme Procedure:
**fx-***fx1 fx2* - Scheme Procedure:
**fx-***fx* Returns the difference of

`fx1`and`fx2`, or the negation of`fx`, if called with a single argument.An

`&assertion`

condition is raised if the result is not itself a fixnum.

- Scheme Procedure:
**fxdiv-and-mod***fx1 fx2* - Scheme Procedure:
**fxdiv***fx1 fx2* - Scheme Procedure:
**fxmod***fx1 fx2* - Scheme Procedure:
**fxdiv0-and-mod0***fx1 fx2* - Scheme Procedure:
**fxdiv0***fx1 fx2* - Scheme Procedure:
**fxmod0***fx1 fx2* These procedures implement number-theoretic division on fixnums; See (rnrs base), for a description of their semantics.

- Scheme Procedure:
**fx+/carry***fx1 fx2 fx3* Returns the two fixnum results of the following computation:

(let* ((s (+ fx1 fx2 fx3)) (s0 (mod0 s (expt 2 (fixnum-width)))) (s1 (div0 s (expt 2 (fixnum-width))))) (values s0 s1))

- Scheme Procedure:
**fx-/carry***fx1 fx2 fx3* Returns the two fixnum results of the following computation:

(let* ((d (- fx1 fx2 fx3)) (d0 (mod0 d (expt 2 (fixnum-width)))) (d1 (div0 d (expt 2 (fixnum-width))))) (values d0 d1))

- Scheme Procedure:
**fx*/carry***fx1 fx2 fx3* Returns the two fixnum results of the following computation: (let* ((s (+ (* fx1 fx2) fx3)) (s0 (mod0 s (expt 2 (fixnum-width)))) (s1 (div0 s (expt 2 (fixnum-width))))) (values s0 s1))

- Scheme Procedure:
**fxnot***fx* - Scheme Procedure:
**fxand***fx1 ...* - Scheme Procedure:
**fxior***fx1 ...* - Scheme Procedure:
**fxxor***fx1 ...* These procedures are identical to the

`lognot`

,`logand`

,`logior`

, and`logxor`

procedures provided by Guile’s core library. See section Bitwise Operations, for documentation.

- Scheme Procedure:
**fxif***fx1 fx2 fx3* Returns the bitwise “if” of its fixnum arguments. The bit at position

`i`

in the return value will be the`i`

th bit from`fx2`if the`i`

th bit of`fx1`is 1, the`i`

th bit from`fx3`.

- Scheme Procedure:
**fxbit-count***fx* Returns the number of 1 bits in the two’s complement representation of

`fx`.

- Scheme Procedure:
**fxfirst-bit-set***fx* Returns the index of the least significant 1 bit in the two’s complement representation of

`fx`.

- Scheme Procedure:
**fxbit-set?***fx1 fx2* Returns

`#t`

if the`fx2`th bit in the two’s complement representation of`fx1`is 1,`#f`

otherwise.

- Scheme Procedure:
**fxcopy-bit***fx1 fx2 fx3* Returns the result of setting the

`fx2`th bit of`fx1`to the`fx2`th bit of`fx3`.

- Scheme Procedure:
**fxbit-field***fx1 fx2 fx3* Returns the integer representation of the contiguous sequence of bits in

`fx1`that starts at position`fx2`(inclusive) and ends at position`fx3`(exclusive).

- Scheme Procedure:
**fxcopy-bit-field***fx1 fx2 fx3 fx4* Returns the result of replacing the bit field in

`fx1`with start and end positions`fx2`and`fx3`with the corresponding bit field from`fx4`.

- Scheme Procedure:
**fxarithmetic-shift***fx1 fx2* - Scheme Procedure:
**fxarithmetic-shift-left***fx1 fx2* - Scheme Procedure:
**fxarithmetic-shift-right***fx1 fx2* Returns the result of shifting the bits of

`fx1`right or left by the`fx2`positions.`fxarithmetic-shift`

is identical to`fxarithmetic-shift-left`

.

- Scheme Procedure:
**fxrotate-bit-field***fx1 fx2 fx3 fx4* Returns the result of cyclically permuting the bit field in

`fx1`with start and end positions`fx2`and`fx3`by`fx4`bits in the direction of more significant bits.

- Scheme Procedure:
**fxreverse-bit-field***fx1 fx2 fx3* Returns the result of reversing the order of the bits of

`fx1`between position`fx2`(inclusive) and position`fx3`(exclusive).

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