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NAME
====

Math::FractionalPart provides several routines to operate with the fractional parts of a number. All routines also operate on complex numbers.

SYNOPSIS
========

```raku
use Math::FractionalPart :afrac;
say (afrac -3.2); # Output <<0.2>>
say (frac -3.2);  # Output <<-0.2>>
```

DESCRIPTION
===========

There are three different algebraic functions that operate on numbers and return their fractional parts. They all return the same result when operating on non-negative numbers, but all three return different results when operating on negative numbers. See the [References](#References) for more details. Note that Ref. 2 shows *frac* operating in the *complex plane* as `frac(x + i y) = frac(x) + i frac(y)`.

The following table shows the routines that have been implemented in this module.

<table class="pod-table">
<thead><tr>
<th>Name</th> <th>Raku formula</th> <th>Example</th> <th>Notes</th>
</tr></thead>
<tbody>
<tr> <td>frac</td> <td>x - floor(x)</td> <td>frac(-1.3): 0.7</td> <td>1</td> </tr> <tr> <td>afrac</td> <td>abs(x) - floor(abs(x))</td> <td>afrac(-1.3): 0.3</td> <td>2</td> </tr> <tr> <td>ofrac</td> <td>x - floor(abs(x)) * sign(x)</td> <td>ofrac(-1.3): -0.3</td> <td>3</td> </tr>
</tbody>
</table>

Notes
=====

1. See Ref. 1, *frac* version 1 (per Graham, Knuth, et alii, 1992).

2. See Ref. 1, *frac* version 2 (per Dainith, 2004); Ref. 3, p. 7. Consider mnemonic 'a' for 'absolute value' or 'astronomical'.

3. See Ref. 1, *frac* version 3 (an *odd function*); Ref. 2: Wolfram's *FractionPart* function. Consider mnemonic 'o' for 'odd function'.

References
==========

1. Wikipedia article on [Fractional Part](https://en.m.wikipedia.org/wiki/Fractional_part).

2. Wolfram article on [Fractional Part](https://mathworld.wolfram.com/FractionalPart.html).

3. *Celestial Calculations: A Gentle Introduction to Computational Astronomy*, J. L. Lawrence, 2018, MIT Press.

AUTHOR
======

Tom Browder <tbrowder@cpan.org>

COPYRIGHT AND LICENSE
=====================

© 2021 Tom Browder

This library is free software; you can redistribute it or modify it under the Artistic License 2.0.