## LIBRARY

```(import (rnrs))                     ;R6RS
(import (rnrs arithmetic fixnums))  ;R6RS
```

## SYNOPSIS

```(fixnum-width)
(least-fixnum)
(greatest-fixnum)
```

## DESCRIPTION

The fixnum range is defined as the closed interval [−2^(w−1), 2^(w−1)−1] such that w is an implementation-defined integer w ≥ 24. The fixnum-width procedure returns the implementation's w. The least-fixnum procedure returns −2^(w−1). The greatest-fixnum procedure returns 2^(w−1)−1.

The fixnum range is important to consider when using the fixnum procedures because these procedures require that their arguments and results are fixnums. They raise an exception when a result cannot be represented as a fixnum.

## IMPLEMENTATION NOTES

The fixnum width depends very much on implementation details and the machine. Here are some known fixnum widths.
Chez Scheme
The fixnum width is 61 or 30. If the machine's register width is m then the fixnum width is m - log2(m/8).
GNU Guile
The fixnum width is 62 or 30. This is the machine's register width minus two.
IronScheme
The fixnum width is 32.
Loko Scheme
The fixnum width is 61.

## RETURN VALUES

These procedures each return a single value; a fixnum as per the description above.

## EXAMPLES

```; The results are different for different implementations.
(fixnum-width)     =>  61
(least-fixnum)     => -1152921504606846976
(greatest-fixnum)  =>  1152921504606846975
```

## APPLICATION USAGE

This procedure is sometimes used in libraries that provide optimized variants of code for implementations where the fixnum width is large enough. If the fixnum width is 32 (or greater) then fixnums can represent all signed 32-bit integers.

## COMPATIBILITY

This procedure is only present in R6RS. An alternative to (fixnum-width) is (+ 1 (bitwise-length (greatest-fixnum))). But normally there is no need to use fixnum procedures if they are not available; generic arithmetic can be used instead and will give the same results.

## ERRORS

This procedure can raise exceptions with the following condition types:
&assertion (R6RS)
The wrong number of arguments was passed.

bitwise-length(3scm)

R6RS

## HISTORY

These procedures are new to the fixnum library in R6RS. Implementations have always had some kind of fixnum type but was normally not seen by the user.

## AUTHORS

This page is part of the scheme-manpages project. It includes materials from the RnRS documents. More information can be found at `https://github.com/schemedoc/manpages/`.

Markup created by unroff 1.0sc,    March 04, 2023.