249 lines
16 KiB
HTML
249 lines
16 KiB
HTML
|
||
<!DOCTYPE html>
|
||
<html lang="en">
|
||
<head>
|
||
<meta charset="utf-8">
|
||
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
||
<meta name="color-scheme" content="light dark">
|
||
<title>PEP 239 – Adding a Rational Type to Python | peps.python.org</title>
|
||
<link rel="shortcut icon" href="../_static/py.png">
|
||
<link rel="canonical" href="https://peps.python.org/pep-0239/">
|
||
<link rel="stylesheet" href="../_static/style.css" type="text/css">
|
||
<link rel="stylesheet" href="../_static/mq.css" type="text/css">
|
||
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" media="(prefers-color-scheme: light)" id="pyg-light">
|
||
<link rel="stylesheet" href="../_static/pygments_dark.css" type="text/css" media="(prefers-color-scheme: dark)" id="pyg-dark">
|
||
<link rel="alternate" type="application/rss+xml" title="Latest PEPs" href="https://peps.python.org/peps.rss">
|
||
<meta property="og:title" content='PEP 239 – Adding a Rational Type to Python | peps.python.org'>
|
||
<meta property="og:description" content="Python has no numeric type with the semantics of an unboundedly precise rational number. This proposal explains the semantics of such a type, and suggests builtin functions and literals to support such a type. This PEP suggests no literals for rationa...">
|
||
<meta property="og:type" content="website">
|
||
<meta property="og:url" content="https://peps.python.org/pep-0239/">
|
||
<meta property="og:site_name" content="Python Enhancement Proposals (PEPs)">
|
||
<meta property="og:image" content="https://peps.python.org/_static/og-image.png">
|
||
<meta property="og:image:alt" content="Python PEPs">
|
||
<meta property="og:image:width" content="200">
|
||
<meta property="og:image:height" content="200">
|
||
<meta name="description" content="Python has no numeric type with the semantics of an unboundedly precise rational number. This proposal explains the semantics of such a type, and suggests builtin functions and literals to support such a type. This PEP suggests no literals for rationa...">
|
||
<meta name="theme-color" content="#3776ab">
|
||
</head>
|
||
<body>
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" style="display: none;">
|
||
<symbol id="svg-sun-half" viewBox="0 0 24 24" pointer-events="all">
|
||
<title>Following system colour scheme</title>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="none"
|
||
stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
|
||
<circle cx="12" cy="12" r="9"></circle>
|
||
<path d="M12 3v18m0-12l4.65-4.65M12 14.3l7.37-7.37M12 19.6l8.85-8.85"></path>
|
||
</svg>
|
||
</symbol>
|
||
<symbol id="svg-moon" viewBox="0 0 24 24" pointer-events="all">
|
||
<title>Selected dark colour scheme</title>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="none"
|
||
stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
|
||
<path stroke="none" d="M0 0h24v24H0z" fill="none"></path>
|
||
<path d="M12 3c.132 0 .263 0 .393 0a7.5 7.5 0 0 0 7.92 12.446a9 9 0 1 1 -8.313 -12.454z"></path>
|
||
</svg>
|
||
</symbol>
|
||
<symbol id="svg-sun" viewBox="0 0 24 24" pointer-events="all">
|
||
<title>Selected light colour scheme</title>
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="none"
|
||
stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
|
||
<circle cx="12" cy="12" r="5"></circle>
|
||
<line x1="12" y1="1" x2="12" y2="3"></line>
|
||
<line x1="12" y1="21" x2="12" y2="23"></line>
|
||
<line x1="4.22" y1="4.22" x2="5.64" y2="5.64"></line>
|
||
<line x1="18.36" y1="18.36" x2="19.78" y2="19.78"></line>
|
||
<line x1="1" y1="12" x2="3" y2="12"></line>
|
||
<line x1="21" y1="12" x2="23" y2="12"></line>
|
||
<line x1="4.22" y1="19.78" x2="5.64" y2="18.36"></line>
|
||
<line x1="18.36" y1="5.64" x2="19.78" y2="4.22"></line>
|
||
</svg>
|
||
</symbol>
|
||
</svg>
|
||
<script>
|
||
|
||
document.documentElement.dataset.colour_scheme = localStorage.getItem("colour_scheme") || "auto"
|
||
</script>
|
||
<section id="pep-page-section">
|
||
<header>
|
||
<h1>Python Enhancement Proposals</h1>
|
||
<ul class="breadcrumbs">
|
||
<li><a href="https://www.python.org/" title="The Python Programming Language">Python</a> » </li>
|
||
<li><a href="../pep-0000/">PEP Index</a> » </li>
|
||
<li>PEP 239</li>
|
||
</ul>
|
||
<button id="colour-scheme-cycler" onClick="setColourScheme(nextColourScheme())">
|
||
<svg aria-hidden="true" class="colour-scheme-icon-when-auto"><use href="#svg-sun-half"></use></svg>
|
||
<svg aria-hidden="true" class="colour-scheme-icon-when-dark"><use href="#svg-moon"></use></svg>
|
||
<svg aria-hidden="true" class="colour-scheme-icon-when-light"><use href="#svg-sun"></use></svg>
|
||
<span class="visually-hidden">Toggle light / dark / auto colour theme</span>
|
||
</button>
|
||
</header>
|
||
<article>
|
||
<section id="pep-content">
|
||
<h1 class="page-title">PEP 239 – Adding a Rational Type to Python</h1>
|
||
<dl class="rfc2822 field-list simple">
|
||
<dt class="field-odd">Author<span class="colon">:</span></dt>
|
||
<dd class="field-odd">Christopher A. Craig <python-pep at ccraig.org>, Moshe Zadka <moshez at zadka.site.co.il></dd>
|
||
<dt class="field-even">Status<span class="colon">:</span></dt>
|
||
<dd class="field-even"><abbr title="Formally declined and will not be accepted">Rejected</abbr></dd>
|
||
<dt class="field-odd">Type<span class="colon">:</span></dt>
|
||
<dd class="field-odd"><abbr title="Normative PEP with a new feature for Python, implementation change for CPython or interoperability standard for the ecosystem">Standards Track</abbr></dd>
|
||
<dt class="field-even">Created<span class="colon">:</span></dt>
|
||
<dd class="field-even">11-Mar-2001</dd>
|
||
<dt class="field-odd">Python-Version<span class="colon">:</span></dt>
|
||
<dd class="field-odd">2.2</dd>
|
||
<dt class="field-even">Post-History<span class="colon">:</span></dt>
|
||
<dd class="field-even">16-Mar-2001</dd>
|
||
</dl>
|
||
<hr class="docutils" />
|
||
<section id="contents">
|
||
<details><summary>Table of Contents</summary><ul class="simple">
|
||
<li><a class="reference internal" href="#abstract">Abstract</a></li>
|
||
<li><a class="reference internal" href="#rationale">Rationale</a></li>
|
||
<li><a class="reference internal" href="#rationaltype">RationalType</a></li>
|
||
<li><a class="reference internal" href="#the-rational-builtin">The rational() Builtin</a></li>
|
||
<li><a class="reference internal" href="#open-issues">Open Issues</a></li>
|
||
<li><a class="reference internal" href="#references">References</a></li>
|
||
<li><a class="reference internal" href="#copyright">Copyright</a></li>
|
||
</ul>
|
||
</details></section>
|
||
<div class="pep-banner sticky-banner deprecated rejected admonition warning">
|
||
<p class="admonition-title">Warning</p>
|
||
<p>This PEP has been rejected.</p>
|
||
<p class="close-button">×</p>
|
||
<p>The needs outlined in the rationale section
|
||
have been addressed to some extent by the acceptance of <a class="pep reference internal" href="../pep-0327/" title="PEP 327 – Decimal Data Type">PEP 327</a>
|
||
for decimal arithmetic. Guido also noted, “Rational arithmetic
|
||
was the default ‘exact’ arithmetic in ABC and it did not work out as
|
||
expected”. See the python-dev discussion on 17 June 2005 <a class="footnote-reference brackets" href="#id2" id="id1">[1]</a>.</p>
|
||
<p><em>Postscript:</em> With the acceptance of <a class="pep reference internal" href="../pep-3141/" title="PEP 3141 – A Type Hierarchy for Numbers">PEP 3141</a>, “A Type Hierarchy
|
||
for Numbers”, a ‘Rational’ numeric abstract base class was added
|
||
with a concrete implementation in the ‘fractions’ module.</p>
|
||
<p></p>
|
||
</div>
|
||
<section id="abstract">
|
||
<h2><a class="toc-backref" href="#abstract" role="doc-backlink">Abstract</a></h2>
|
||
<p>Python has no numeric type with the semantics of an unboundedly
|
||
precise rational number. This proposal explains the semantics of
|
||
such a type, and suggests builtin functions and literals to
|
||
support such a type. This PEP suggests no literals for rational
|
||
numbers; that is left for <a class="pep reference internal" href="../pep-0240/" title="PEP 240 – Adding a Rational Literal to Python">another PEP</a>.</p>
|
||
</section>
|
||
<section id="rationale">
|
||
<h2><a class="toc-backref" href="#rationale" role="doc-backlink">Rationale</a></h2>
|
||
<p>While sometimes slower and more memory intensive (in general,
|
||
unboundedly so) rational arithmetic captures more closely the
|
||
mathematical ideal of numbers, and tends to have behavior which is
|
||
less surprising to newbies. Though many Python implementations of
|
||
rational numbers have been written, none of these exist in the
|
||
core, or are documented in any way. This has made them much less
|
||
accessible to people who are less Python-savvy.</p>
|
||
</section>
|
||
<section id="rationaltype">
|
||
<h2><a class="toc-backref" href="#rationaltype" role="doc-backlink">RationalType</a></h2>
|
||
<p>There will be a new numeric type added called <code class="docutils literal notranslate"><span class="pre">RationalType</span></code>. Its
|
||
unary operators will do the obvious thing. Binary operators will
|
||
coerce integers and long integers to rationals, and rationals to
|
||
floats and complexes.</p>
|
||
<p>The following attributes will be supported: <code class="docutils literal notranslate"><span class="pre">.numerator</span></code> and
|
||
<code class="docutils literal notranslate"><span class="pre">.denominator</span></code>. The language definition will promise that:</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">r</span><span class="o">.</span><span class="n">denominator</span> <span class="o">*</span> <span class="n">r</span> <span class="o">==</span> <span class="n">r</span><span class="o">.</span><span class="n">numerator</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>that the GCD of the numerator and the denominator is 1 and that
|
||
the denominator is positive.</p>
|
||
<p>The method <code class="docutils literal notranslate"><span class="pre">r.trim(max_denominator)</span></code> will return the closest
|
||
rational <code class="docutils literal notranslate"><span class="pre">s</span></code> to <code class="docutils literal notranslate"><span class="pre">r</span></code> such that <code class="docutils literal notranslate"><span class="pre">abs(s.denominator)</span> <span class="pre"><=</span> <span class="pre">max_denominator</span></code>.</p>
|
||
</section>
|
||
<section id="the-rational-builtin">
|
||
<h2><a class="toc-backref" href="#the-rational-builtin" role="doc-backlink">The rational() Builtin</a></h2>
|
||
<p>This function will have the signature <code class="docutils literal notranslate"><span class="pre">rational(n,</span> <span class="pre">d=1)</span></code>. <code class="docutils literal notranslate"><span class="pre">n</span></code> and <code class="docutils literal notranslate"><span class="pre">d</span></code>
|
||
must both be integers, long integers or rationals. A guarantee is
|
||
made that:</p>
|
||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">rational</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span> <span class="o">*</span> <span class="n">d</span> <span class="o">==</span> <span class="n">n</span>
|
||
</pre></div>
|
||
</div>
|
||
</section>
|
||
<section id="open-issues">
|
||
<h2><a class="toc-backref" href="#open-issues" role="doc-backlink">Open Issues</a></h2>
|
||
<ul>
|
||
<li>Maybe the type should be called rat instead of rational.
|
||
Somebody proposed that we have “abstract” pure mathematical
|
||
types named complex, real, rational, integer, and “concrete”
|
||
representation types with names like float, rat, long, int.</li>
|
||
<li>Should a rational number with an integer value be allowed as a
|
||
sequence index? For example, should <code class="docutils literal notranslate"><span class="pre">s[5/3</span> <span class="pre">-</span> <span class="pre">2/3]</span></code> be equivalent
|
||
to <code class="docutils literal notranslate"><span class="pre">s[1]</span></code>?</li>
|
||
<li>Should <code class="docutils literal notranslate"><span class="pre">shift</span></code> and <code class="docutils literal notranslate"><span class="pre">mask</span></code> operators be allowed for rational numbers?
|
||
For rational numbers with integer values?</li>
|
||
<li>Marcin ‘Qrczak’ Kowalczyk summarized the arguments for and
|
||
against unifying ints with rationals nicely on c.l.py<p>Arguments for unifying ints with rationals:</p>
|
||
<ul class="simple">
|
||
<li>Since <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">==</span> <span class="pre">2/1</span></code> and maybe <code class="docutils literal notranslate"><span class="pre">str(2/1)</span> <span class="pre">==</span> <span class="pre">'2'</span></code>, it reduces surprises
|
||
where objects seem equal but behave differently.</li>
|
||
<li><code class="docutils literal notranslate"><span class="pre">/</span></code> can be freely used for integer division when I <em>know</em> that
|
||
there is no remainder (if I am wrong and there is a remainder,
|
||
there will probably be some exception later).</li>
|
||
</ul>
|
||
<p>Arguments against:</p>
|
||
<ul class="simple">
|
||
<li>When I use the result of <code class="docutils literal notranslate"><span class="pre">/</span></code> as a sequence index, it’s usually
|
||
an error which should not be hidden by making the program
|
||
working for some data, since it will break for other data.</li>
|
||
<li>(this assumes that after unification int and rational would be
|
||
different types:) Types should rarely depend on values. It’s
|
||
easier to reason when the type of a variable is known: I know
|
||
how I can use it. I can determine that something is an int and
|
||
expect that other objects used in this place will be ints too.</li>
|
||
<li>(this assumes the same type for them:) Int is a good type in
|
||
itself, not to be mixed with rationals. The fact that
|
||
something is an integer should be expressible as a statement
|
||
about its type. Many operations require ints and don’t accept
|
||
rationals. It’s natural to think about them as about different
|
||
types.</li>
|
||
</ul>
|
||
</li>
|
||
</ul>
|
||
</section>
|
||
<section id="references">
|
||
<h2><a class="toc-backref" href="#references" role="doc-backlink">References</a></h2>
|
||
<aside class="footnote-list brackets">
|
||
<aside class="footnote brackets" id="id2" role="doc-footnote">
|
||
<dt class="label" id="id2">[<a href="#id1">1</a>]</dt>
|
||
<dd>Raymond Hettinger, Propose rejection of PEPs 239 and 240 – a builtin
|
||
rational type and rational literals
|
||
<a class="reference external" href="https://mail.python.org/pipermail/python-dev/2005-June/054281.html">https://mail.python.org/pipermail/python-dev/2005-June/054281.html</a></aside>
|
||
</aside>
|
||
</section>
|
||
<section id="copyright">
|
||
<h2><a class="toc-backref" href="#copyright" role="doc-backlink">Copyright</a></h2>
|
||
<p>This document has been placed in the public domain.</p>
|
||
</section>
|
||
</section>
|
||
<hr class="docutils" />
|
||
<p>Source: <a class="reference external" href="https://github.com/python/peps/blob/main/peps/pep-0239.rst">https://github.com/python/peps/blob/main/peps/pep-0239.rst</a></p>
|
||
<p>Last modified: <a class="reference external" href="https://github.com/python/peps/commits/main/peps/pep-0239.rst">2024-04-14 20:08:31 GMT</a></p>
|
||
|
||
</article>
|
||
<nav id="pep-sidebar">
|
||
<h2>Contents</h2>
|
||
<ul>
|
||
<li><a class="reference internal" href="#abstract">Abstract</a></li>
|
||
<li><a class="reference internal" href="#rationale">Rationale</a></li>
|
||
<li><a class="reference internal" href="#rationaltype">RationalType</a></li>
|
||
<li><a class="reference internal" href="#the-rational-builtin">The rational() Builtin</a></li>
|
||
<li><a class="reference internal" href="#open-issues">Open Issues</a></li>
|
||
<li><a class="reference internal" href="#references">References</a></li>
|
||
<li><a class="reference internal" href="#copyright">Copyright</a></li>
|
||
</ul>
|
||
|
||
<br>
|
||
<a id="source" href="https://github.com/python/peps/blob/main/peps/pep-0239.rst">Page Source (GitHub)</a>
|
||
</nav>
|
||
</section>
|
||
<script src="../_static/colour_scheme.js"></script>
|
||
<script src="../_static/wrap_tables.js"></script>
|
||
<script src="../_static/sticky_banner.js"></script>
|
||
</body>
|
||
</html> |