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<h1 class="page-title">PEP 238 – Changing the Division Operator</h1>
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<dl class="rfc2822 field-list simple">
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<dt class="field-odd">Author<span class="colon">:</span></dt>
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<dd class="field-odd">Moshe Zadka <moshez at zadka.site.co.il>,
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Guido van Rossum <guido at python.org></dd>
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<dt class="field-even">Status<span class="colon">:</span></dt>
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<dd class="field-even"><abbr title="Accepted and implementation complete, or no longer active">Final</abbr></dd>
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<dt class="field-odd">Type<span class="colon">:</span></dt>
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<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>
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<dt class="field-even">Created<span class="colon">:</span></dt>
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<dd class="field-even">11-Mar-2001</dd>
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<dt class="field-odd">Python-Version<span class="colon">:</span></dt>
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<dd class="field-odd">2.2</dd>
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<dt class="field-even">Post-History<span class="colon">:</span></dt>
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<dd class="field-even">16-Mar-2001, 26-Jul-2001, 27-Jul-2001</dd>
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</dl>
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<section id="contents">
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<details><summary>Table of Contents</summary><ul class="simple">
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<li><a class="reference internal" href="#abstract">Abstract</a></li>
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<li><a class="reference internal" href="#motivation">Motivation</a></li>
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<li><a class="reference internal" href="#variations">Variations</a></li>
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<li><a class="reference internal" href="#alternatives">Alternatives</a></li>
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<li><a class="reference internal" href="#api-changes">API Changes</a></li>
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<li><a class="reference internal" href="#command-line-option">Command Line Option</a></li>
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<li><a class="reference internal" href="#semantics-of-floor-division">Semantics of Floor Division</a></li>
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<li><a class="reference internal" href="#semantics-of-true-division">Semantics of True Division</a></li>
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<li><a class="reference internal" href="#the-future-division-statement">The Future Division Statement</a></li>
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<li><a class="reference internal" href="#open-issues">Open Issues</a></li>
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<li><a class="reference internal" href="#resolved-issues">Resolved Issues</a></li>
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<li><a class="reference internal" href="#faq">FAQ</a><ul>
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<li><a class="reference internal" href="#when-will-python-3-0-be-released">When will Python 3.0 be released?</a></li>
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<li><a class="reference internal" href="#why-isn-t-true-division-called-float-division">Why isn’t true division called float division?</a></li>
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<li><a class="reference internal" href="#why-is-there-a-need-for-truediv-and-itruediv">Why is there a need for <code class="docutils literal notranslate"><span class="pre">__truediv__</span></code> and <code class="docutils literal notranslate"><span class="pre">__itruediv__</span></code>?</a></li>
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<li><a class="reference internal" href="#how-do-i-write-code-that-works-under-the-classic-rules-as-well-as-under-the-new-rules-without-using-or-a-future-division-statement">How do I write code that works under the classic rules as well as under the new rules without using <code class="docutils literal notranslate"><span class="pre">//</span></code> or a future division statement?</a></li>
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<li><a class="reference internal" href="#how-do-i-specify-the-division-semantics-for-input-compile-execfile-eval-and-exec">How do I specify the division semantics for <code class="docutils literal notranslate"><span class="pre">input()</span></code>, <code class="docutils literal notranslate"><span class="pre">compile()</span></code>, <code class="docutils literal notranslate"><span class="pre">execfile()</span></code>, <code class="docutils literal notranslate"><span class="pre">eval()</span></code> and <code class="docutils literal notranslate"><span class="pre">exec</span></code>?</a></li>
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<li><a class="reference internal" href="#what-about-code-compiled-by-the-codeop-module">What about code compiled by the codeop module?</a></li>
|
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<li><a class="reference internal" href="#will-there-be-conversion-tools-or-aids">Will there be conversion tools or aids?</a></li>
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<li><a class="reference internal" href="#why-is-my-question-not-answered-here">Why is my question not answered here?</a></li>
|
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</ul>
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</li>
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<li><a class="reference internal" href="#implementation">Implementation</a></li>
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<li><a class="reference internal" href="#copyright">Copyright</a></li>
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</ul>
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</details></section>
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<section id="abstract">
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<h2><a class="toc-backref" href="#abstract" role="doc-backlink">Abstract</a></h2>
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<p>The current division (<code class="docutils literal notranslate"><span class="pre">/</span></code>) operator has an ambiguous meaning for numerical
|
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arguments: it returns the floor of the mathematical result of division if the
|
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arguments are ints or longs, but it returns a reasonable approximation of the
|
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division result if the arguments are floats or complex. This makes
|
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expressions expecting float or complex results error-prone when integers are
|
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not expected but possible as inputs.</p>
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<p>We propose to fix this by introducing different operators for different
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operations: <code class="docutils literal notranslate"><span class="pre">x/y</span></code> to return a reasonable approximation of the mathematical
|
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result of the division (“true division”), <code class="docutils literal notranslate"><span class="pre">x//y</span></code> to return the floor
|
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(“floor division”). We call the current, mixed meaning of x/y
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“classic division”.</p>
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<p>Because of severe backwards compatibility issues, not to mention a major
|
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flamewar on c.l.py, we propose the following transitional measures (starting
|
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with Python 2.2):</p>
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<ul class="simple">
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<li>Classic division will remain the default in the Python 2.x series; true
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division will be standard in Python 3.0.</li>
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<li>The <code class="docutils literal notranslate"><span class="pre">//</span></code> operator will be available to request floor division
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unambiguously.</li>
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<li>The future division statement, spelled <code class="docutils literal notranslate"><span class="pre">from</span> <span class="pre">__future__</span> <span class="pre">import</span> <span class="pre">division</span></code>,
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will change the <code class="docutils literal notranslate"><span class="pre">/</span></code> operator to mean true division throughout the module.</li>
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<li>A command line option will enable run-time warnings for classic division
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|||
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applied to int or long arguments; another command line option will make true
|
|||
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division the default.</li>
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<li>The standard library will use the future division statement and the <code class="docutils literal notranslate"><span class="pre">//</span></code>
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operator when appropriate, so as to completely avoid classic division.</li>
|
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</ul>
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|||
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</section>
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<section id="motivation">
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<h2><a class="toc-backref" href="#motivation" role="doc-backlink">Motivation</a></h2>
|
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<p>The classic division operator makes it hard to write numerical expressions
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that are supposed to give correct results from arbitrary numerical inputs.
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For all other operators, one can write down a formula such as <code class="docutils literal notranslate"><span class="pre">x*y**2</span> <span class="pre">+</span> <span class="pre">z</span></code>,
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and the calculated result will be close to the mathematical result (within the
|
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limits of numerical accuracy, of course) for any numerical input type (int,
|
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long, float, or complex). But division poses a problem: if the expressions
|
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for both arguments happen to have an integral type, it implements floor
|
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division rather than true division.</p>
|
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<p>The problem is unique to dynamically typed languages: in a statically typed
|
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language like C, the inputs, typically function arguments, would be declared
|
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as double or float, and when a call passes an integer argument, it is
|
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|
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converted to double or float at the time of the call. Python doesn’t have
|
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argument type declarations, so integer arguments can easily find their way
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into an expression.</p>
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<p>The problem is particularly pernicious since ints are perfect substitutes for
|
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floats in all other circumstances: <code class="docutils literal notranslate"><span class="pre">math.sqrt(2)</span></code> returns the same value as
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">math.sqrt(2.0)</span></code>, <code class="docutils literal notranslate"><span class="pre">3.14*100</span></code> and <code class="docutils literal notranslate"><span class="pre">3.14*100.0</span></code> return the same value, and
|
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so on. Thus, the author of a numerical routine may only use floating point
|
|||
|
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numbers to test his code, and believe that it works correctly, and a user may
|
|||
|
|
accidentally pass in an integer input value and get incorrect results.</p>
|
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|
|
<p>Another way to look at this is that classic division makes it difficult to
|
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|
|
write polymorphic functions that work well with either float or int arguments;
|
|||
|
|
all other operators already do the right thing. No algorithm that works for
|
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|
|
both ints and floats has a need for truncating division in one case and true
|
|||
|
|
division in the other.</p>
|
|||
|
|
<p>The correct work-around is subtle: casting an argument to float() is wrong if
|
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|
|
it could be a complex number; adding 0.0 to an argument doesn’t preserve the
|
|||
|
|
sign of the argument if it was minus zero. The only solution without either
|
|||
|
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downside is multiplying an argument (typically the first) by 1.0. This leaves
|
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|
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the value and sign unchanged for float and complex, and turns int and long
|
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|
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into a float with the corresponding value.</p>
|
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|
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<p>It is the opinion of the authors that this is a real design bug in Python, and
|
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|
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that it should be fixed sooner rather than later. Assuming Python usage will
|
|||
|
|
continue to grow, the cost of leaving this bug in the language will eventually
|
|||
|
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outweigh the cost of fixing old code – there is an upper bound to the amount
|
|||
|
|
of code to be fixed, but the amount of code that might be affected by the bug
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|||
|
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in the future is unbounded.</p>
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|
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<p>Another reason for this change is the desire to ultimately unify Python’s
|
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|
|
numeric model. This is the subject of <a class="pep reference internal" href="../pep-0228/" title="PEP 228 – Reworking Python’s Numeric Model">PEP 228</a> (which is currently
|
|||
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incomplete). A unified numeric model removes most of the user’s need to be
|
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|
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aware of different numerical types. This is good for beginners, but also
|
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takes away concerns about different numeric behavior for advanced programmers.
|
|||
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(Of course, it won’t remove concerns about numerical stability and accuracy.)</p>
|
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<p>In a unified numeric model, the different types (int, long, float, complex,
|
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|
and possibly others, such as a new rational type) serve mostly as storage
|
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|
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optimizations, and to some extent to indicate orthogonal properties such as
|
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inexactness or complexity. In a unified model, the integer 1 should be
|
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indistinguishable from the floating point number 1.0 (except for its
|
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|
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inexactness), and both should behave the same in all numeric contexts.
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Clearly, in a unified numeric model, if <code class="docutils literal notranslate"><span class="pre">a==b</span></code> and <code class="docutils literal notranslate"><span class="pre">c==d</span></code>, <code class="docutils literal notranslate"><span class="pre">a/c</span></code> should
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|
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equal <code class="docutils literal notranslate"><span class="pre">b/d</span></code> (taking some liberties due to rounding for inexact numbers), and
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|
|
since everybody agrees that <code class="docutils literal notranslate"><span class="pre">1.0/2.0</span></code> equals 0.5, <code class="docutils literal notranslate"><span class="pre">1/2</span></code> should also equal
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0.5. Likewise, since <code class="docutils literal notranslate"><span class="pre">1//2</span></code> equals zero, <code class="docutils literal notranslate"><span class="pre">1.0//2.0</span></code> should also equal
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zero.</p>
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</section>
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<section id="variations">
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<h2><a class="toc-backref" href="#variations" role="doc-backlink">Variations</a></h2>
|
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|
|
<p>Aesthetically, <code class="docutils literal notranslate"><span class="pre">x//y</span></code> doesn’t please everyone, and hence several variations
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|
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have been proposed. They are addressed here:</p>
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|
|
<ul class="simple">
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|
|
<li><code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">div</span> <span class="pre">y</span></code>. This would introduce a new keyword. Since <code class="docutils literal notranslate"><span class="pre">div</span></code> is a
|
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|
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popular identifier, this would break a fair amount of existing code, unless
|
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|
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the new keyword was only recognized under a future division statement.
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|
|
Since it is expected that the majority of code that needs to be converted is
|
|||
|
|
dividing integers, this would greatly increase the need for the future
|
|||
|
|
division statement. Even with a future statement, the general sentiment
|
|||
|
|
against adding new keywords unless absolutely necessary argues against this.</li>
|
|||
|
|
<li><code class="docutils literal notranslate"><span class="pre">div(x,</span> <span class="pre">y)</span></code>. This makes the conversion of old code much harder.
|
|||
|
|
Replacing <code class="docutils literal notranslate"><span class="pre">x/y</span></code> with <code class="docutils literal notranslate"><span class="pre">x//y</span></code> or <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">div</span> <span class="pre">y</span></code> can be done with a simple
|
|||
|
|
query replace; in most cases the programmer can easily verify that a
|
|||
|
|
particular module only works with integers so all occurrences of <code class="docutils literal notranslate"><span class="pre">x/y</span></code> can
|
|||
|
|
be replaced. (The query replace is still needed to weed out slashes
|
|||
|
|
occurring in comments or string literals.) Replacing <code class="docutils literal notranslate"><span class="pre">x/y</span></code> with
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">div(x,</span> <span class="pre">y)</span></code> would require a much more intelligent tool, since the extent
|
|||
|
|
of the expressions to the left and right of the <code class="docutils literal notranslate"><span class="pre">/</span></code> must be analyzed
|
|||
|
|
before the placement of the <code class="docutils literal notranslate"><span class="pre">div(</span></code> and <code class="docutils literal notranslate"><span class="pre">)</span></code> part can be decided.</li>
|
|||
|
|
<li><code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">\</span> <span class="pre">y</span></code>. The backslash is already a token, meaning line continuation, and
|
|||
|
|
in general it suggests an <em>escape</em> to Unix eyes. In addition (this due to
|
|||
|
|
Terry Reedy) this would make things like <code class="docutils literal notranslate"><span class="pre">eval("x\y")</span></code> harder to get
|
|||
|
|
right.</li>
|
|||
|
|
</ul>
|
|||
|
|
</section>
|
|||
|
|
<section id="alternatives">
|
|||
|
|
<h2><a class="toc-backref" href="#alternatives" role="doc-backlink">Alternatives</a></h2>
|
|||
|
|
<p>In order to reduce the amount of old code that needs to be converted, several
|
|||
|
|
alternative proposals have been put forth. Here is a brief discussion of each
|
|||
|
|
proposal (or category of proposals). If you know of an alternative that was
|
|||
|
|
discussed on c.l.py that isn’t mentioned here, please mail the second author.</p>
|
|||
|
|
<ul class="simple">
|
|||
|
|
<li>Let <code class="docutils literal notranslate"><span class="pre">/</span></code> keep its classic semantics; introduce <code class="docutils literal notranslate"><span class="pre">//</span></code> for true division.
|
|||
|
|
This still leaves a broken operator in the language, and invites to use the
|
|||
|
|
broken behavior. It also shuts off the road to a unified numeric model a la
|
|||
|
|
<a class="pep reference internal" href="../pep-0228/" title="PEP 228 – Reworking Python’s Numeric Model">PEP 228</a>.</li>
|
|||
|
|
<li>Let int division return a special “portmanteau” type that behaves as an
|
|||
|
|
integer in integer context, but like a float in a float context. The
|
|||
|
|
problem with this is that after a few operations, the int and the float
|
|||
|
|
value could be miles apart, it’s unclear which value should be used in
|
|||
|
|
comparisons, and of course many contexts (like conversion to string) don’t
|
|||
|
|
have a clear integer or float preference.</li>
|
|||
|
|
<li>Use a directive to use specific division semantics in a module, rather than
|
|||
|
|
a future statement. This retains classic division as a permanent wart in
|
|||
|
|
the language, requiring future generations of Python programmers to be
|
|||
|
|
aware of the problem and the remedies.</li>
|
|||
|
|
<li>Use <code class="docutils literal notranslate"><span class="pre">from</span> <span class="pre">__past__</span> <span class="pre">import</span> <span class="pre">division</span></code> to use classic division semantics in a
|
|||
|
|
module. This also retains the classic division as a permanent wart, or at
|
|||
|
|
least for a long time (eventually the past division statement could raise an
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">ImportError</span></code>).</li>
|
|||
|
|
<li>Use a directive (or some other way) to specify the Python version for which
|
|||
|
|
a specific piece of code was developed. This requires future Python
|
|||
|
|
interpreters to be able to emulate <em>exactly</em> several previous versions of
|
|||
|
|
Python, and moreover to do so for multiple versions within the same
|
|||
|
|
interpreter. This is way too much work. A much simpler solution is to keep
|
|||
|
|
multiple interpreters installed. Another argument against this is that the
|
|||
|
|
version directive is almost always overspecified: most code written for
|
|||
|
|
Python X.Y, works for Python X.(Y-1) and X.(Y+1) as well, so specifying X.Y
|
|||
|
|
as a version is more constraining than it needs to be. At the same time,
|
|||
|
|
there’s no way to know at which future or past version the code will break.</li>
|
|||
|
|
</ul>
|
|||
|
|
</section>
|
|||
|
|
<section id="api-changes">
|
|||
|
|
<h2><a class="toc-backref" href="#api-changes" role="doc-backlink">API Changes</a></h2>
|
|||
|
|
<p>During the transitional phase, we have to support <em>three</em> division operators
|
|||
|
|
within the same program: classic division (for <code class="docutils literal notranslate"><span class="pre">/</span></code> in modules without a
|
|||
|
|
future division statement), true division (for <code class="docutils literal notranslate"><span class="pre">/</span></code> in modules with a future
|
|||
|
|
division statement), and floor division (for <code class="docutils literal notranslate"><span class="pre">//</span></code>). Each operator comes in
|
|||
|
|
two flavors: regular, and as an augmented assignment operator (<code class="docutils literal notranslate"><span class="pre">/=</span></code> or
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">//=</span></code>).</p>
|
|||
|
|
<p>The names associated with these variations are:</p>
|
|||
|
|
<ul>
|
|||
|
|
<li>Overloaded operator methods:<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">__div__</span><span class="p">(),</span> <span class="fm">__floordiv__</span><span class="p">(),</span> <span class="fm">__truediv__</span><span class="p">();</span>
|
|||
|
|
<span class="n">__idiv__</span><span class="p">(),</span> <span class="fm">__ifloordiv__</span><span class="p">(),</span> <span class="fm">__itruediv__</span><span class="p">()</span><span class="o">.</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
<li>Abstract API C functions:<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">PyNumber_Divide</span><span class="p">(),</span> <span class="n">PyNumber_FloorDivide</span><span class="p">(),</span>
|
|||
|
|
<span class="n">PyNumber_TrueDivide</span><span class="p">();</span>
|
|||
|
|
|
|||
|
|
<span class="n">PyNumber_InPlaceDivide</span><span class="p">(),</span> <span class="n">PyNumber_InPlaceFloorDivide</span><span class="p">(),</span>
|
|||
|
|
<span class="n">PyNumber_InPlaceTrueDivide</span><span class="p">()</span><span class="o">.</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
<li>Byte code opcodes:<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">BINARY_DIVIDE</span><span class="p">,</span> <span class="n">BINARY_FLOOR_DIVIDE</span><span class="p">,</span> <span class="n">BINARY_TRUE_DIVIDE</span><span class="p">;</span>
|
|||
|
|
<span class="n">INPLACE_DIVIDE</span><span class="p">,</span> <span class="n">INPLACE_FLOOR_DIVIDE</span><span class="p">,</span> <span class="n">INPLACE_TRUE_DIVIDE</span><span class="o">.</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
<li>PyNumberMethod slots:<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">nb_divide</span><span class="p">,</span> <span class="n">nb_floor_divide</span><span class="p">,</span> <span class="n">nb_true_divide</span><span class="p">,</span>
|
|||
|
|
<span class="n">nb_inplace_divide</span><span class="p">,</span> <span class="n">nb_inplace_floor_divide</span><span class="p">,</span>
|
|||
|
|
<span class="n">nb_inplace_true_divide</span><span class="o">.</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
</li>
|
|||
|
|
</ul>
|
|||
|
|
<p>The added <code class="docutils literal notranslate"><span class="pre">PyNumberMethod</span></code> slots require an additional flag in <code class="docutils literal notranslate"><span class="pre">tp_flags</span></code>;
|
|||
|
|
this flag will be named <code class="docutils literal notranslate"><span class="pre">Py_TPFLAGS_HAVE_NEWDIVIDE</span></code> and will be included in
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">Py_TPFLAGS_DEFAULT</span></code>.</p>
|
|||
|
|
<p>The true and floor division APIs will look for the corresponding slots and
|
|||
|
|
call that; when that slot is <code class="docutils literal notranslate"><span class="pre">NULL</span></code>, they will raise an exception. There is
|
|||
|
|
no fallback to the classic divide slot.</p>
|
|||
|
|
<p>In Python 3.0, the classic division semantics will be removed; the classic
|
|||
|
|
division APIs will become synonymous with true division.</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="command-line-option">
|
|||
|
|
<h2><a class="toc-backref" href="#command-line-option" role="doc-backlink">Command Line Option</a></h2>
|
|||
|
|
<p>The <code class="docutils literal notranslate"><span class="pre">-Q</span></code> command line option takes a string argument that can take four
|
|||
|
|
values: <code class="docutils literal notranslate"><span class="pre">old</span></code>, <code class="docutils literal notranslate"><span class="pre">warn</span></code>, <code class="docutils literal notranslate"><span class="pre">warnall</span></code>, or <code class="docutils literal notranslate"><span class="pre">new</span></code>. The default is <code class="docutils literal notranslate"><span class="pre">old</span></code>
|
|||
|
|
in Python 2.2 but will change to <code class="docutils literal notranslate"><span class="pre">warn</span></code> in later 2.x versions. The <code class="docutils literal notranslate"><span class="pre">old</span></code>
|
|||
|
|
value means the classic division operator acts as described. The <code class="docutils literal notranslate"><span class="pre">warn</span></code>
|
|||
|
|
value means the classic division operator issues a warning (a
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">DeprecationWarning</span></code> using the standard warning framework) when applied
|
|||
|
|
to ints or longs. The <code class="docutils literal notranslate"><span class="pre">warnall</span></code> value also issues warnings for classic
|
|||
|
|
division when applied to floats or complex; this is for use by the
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">fixdiv.py</span></code> conversion script mentioned below. The <code class="docutils literal notranslate"><span class="pre">new</span></code> value changes
|
|||
|
|
the default globally so that the <code class="docutils literal notranslate"><span class="pre">/</span></code> operator is always interpreted as
|
|||
|
|
true division. The <code class="docutils literal notranslate"><span class="pre">new</span></code> option is only intended for use in certain
|
|||
|
|
educational environments, where true division is required, but asking the
|
|||
|
|
students to include the future division statement in all their code would be a
|
|||
|
|
problem.</p>
|
|||
|
|
<p>This option will not be supported in Python 3.0; Python 3.0 will always
|
|||
|
|
interpret <code class="docutils literal notranslate"><span class="pre">/</span></code> as true division.</p>
|
|||
|
|
<p>(This option was originally proposed as <code class="docutils literal notranslate"><span class="pre">-D</span></code>, but that turned out to be an
|
|||
|
|
existing option for Jython, hence the Q – mnemonic for Quotient. Other names
|
|||
|
|
have been proposed, like <code class="docutils literal notranslate"><span class="pre">-Qclassic</span></code>, <code class="docutils literal notranslate"><span class="pre">-Qclassic-warn</span></code>, <code class="docutils literal notranslate"><span class="pre">-Qtrue</span></code>, or
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">-Qold_division</span></code> etc.; these seem more verbose to me without much advantage.
|
|||
|
|
After all the term classic division is not used in the language at all (only
|
|||
|
|
in the PEP), and the term true division is rarely used in the language – only
|
|||
|
|
in <code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>.)</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="semantics-of-floor-division">
|
|||
|
|
<h2><a class="toc-backref" href="#semantics-of-floor-division" role="doc-backlink">Semantics of Floor Division</a></h2>
|
|||
|
|
<p>Floor division will be implemented in all the Python numeric types, and will
|
|||
|
|
have the semantics of:</p>
|
|||
|
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">//</span> <span class="n">b</span> <span class="o">==</span> <span class="n">floor</span><span class="p">(</span><span class="n">a</span><span class="o">/</span><span class="n">b</span><span class="p">)</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
<p>except that the result type will be the common type into which <em>a</em> and <em>b</em> are
|
|||
|
|
coerced before the operation.</p>
|
|||
|
|
<p>Specifically, if <em>a</em> and <em>b</em> are of the same type, <code class="docutils literal notranslate"><span class="pre">a//b</span></code> will be of that
|
|||
|
|
type too. If the inputs are of different types, they are first coerced to a
|
|||
|
|
common type using the same rules used for all other arithmetic operators.</p>
|
|||
|
|
<p>In particular, if <em>a</em> and <em>b</em> are both ints or longs, the result has the same
|
|||
|
|
type and value as for classic division on these types (including the case of
|
|||
|
|
mixed input types; <code class="docutils literal notranslate"><span class="pre">int//long</span></code> and <code class="docutils literal notranslate"><span class="pre">long//int</span></code> will both return a long).</p>
|
|||
|
|
<p>For floating point inputs, the result is a float. For example:</p>
|
|||
|
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">3.5</span><span class="o">//</span><span class="mf">2.0</span> <span class="o">==</span> <span class="mf">1.0</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
<p>For complex numbers, <code class="docutils literal notranslate"><span class="pre">//</span></code> raises an exception, since <code class="docutils literal notranslate"><span class="pre">floor()</span></code> of a
|
|||
|
|
complex number is not allowed.</p>
|
|||
|
|
<p>For user-defined classes and extension types, all semantics are up to the
|
|||
|
|
implementation of the class or type.</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="semantics-of-true-division">
|
|||
|
|
<h2><a class="toc-backref" href="#semantics-of-true-division" role="doc-backlink">Semantics of True Division</a></h2>
|
|||
|
|
<p>True division for ints and longs will convert the arguments to float and then
|
|||
|
|
apply a float division. That is, even <code class="docutils literal notranslate"><span class="pre">2/1</span></code> will return a <code class="docutils literal notranslate"><span class="pre">float</span> <span class="pre">(2.0)</span></code>,
|
|||
|
|
not an int. For floats and complex, it will be the same as classic division.</p>
|
|||
|
|
<p>The 2.2 implementation of true division acts as if the float type had
|
|||
|
|
unbounded range, so that overflow doesn’t occur unless the magnitude of the
|
|||
|
|
mathematical <em>result</em> is too large to represent as a float. For example,
|
|||
|
|
after <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">=</span> <span class="pre">1L</span> <span class="pre"><<</span> <span class="pre">40000</span></code>, <code class="docutils literal notranslate"><span class="pre">float(x)</span></code> raises <code class="docutils literal notranslate"><span class="pre">OverflowError</span></code> (note that
|
|||
|
|
this is also new in 2.2: previously the outcome was platform-dependent, most
|
|||
|
|
commonly a float infinity). But <code class="docutils literal notranslate"><span class="pre">x/x</span></code> returns 1.0 without exception,
|
|||
|
|
while <code class="docutils literal notranslate"><span class="pre">x/1</span></code> raises <code class="docutils literal notranslate"><span class="pre">OverflowError</span></code>.</p>
|
|||
|
|
<p>Note that for int and long arguments, true division may lose information; this
|
|||
|
|
is in the nature of true division (as long as rationals are not in the
|
|||
|
|
language). Algorithms that consciously use longs should consider using
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">//</span></code>, as true division of longs retains no more than 53 bits of precision
|
|||
|
|
(on most platforms).</p>
|
|||
|
|
<p>If and when a rational type is added to Python (see <a class="pep reference internal" href="../pep-0239/" title="PEP 239 – Adding a Rational Type to Python">PEP 239</a>), true
|
|||
|
|
division for ints and longs should probably return a rational. This avoids
|
|||
|
|
the problem with true division of ints and longs losing information. But
|
|||
|
|
until then, for consistency, float is the only choice for true division.</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="the-future-division-statement">
|
|||
|
|
<h2><a class="toc-backref" href="#the-future-division-statement" role="doc-backlink">The Future Division Statement</a></h2>
|
|||
|
|
<p>If <code class="docutils literal notranslate"><span class="pre">from</span> <span class="pre">__future__</span> <span class="pre">import</span> <span class="pre">division</span></code> is present in a module, or if
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">-Qnew</span></code> is used, the <code class="docutils literal notranslate"><span class="pre">/</span></code> and <code class="docutils literal notranslate"><span class="pre">/=</span></code> operators are translated to true
|
|||
|
|
division opcodes; otherwise they are translated to classic division (until
|
|||
|
|
Python 3.0 comes along, where they are always translated to true division).</p>
|
|||
|
|
<p>The future division statement has no effect on the recognition or translation
|
|||
|
|
of <code class="docutils literal notranslate"><span class="pre">//</span></code> and <code class="docutils literal notranslate"><span class="pre">//=</span></code>.</p>
|
|||
|
|
<p>See <a class="pep reference internal" href="../pep-0236/" title="PEP 236 – Back to the __future__">PEP 236</a> for the general rules for future statements.</p>
|
|||
|
|
<p>(It has been proposed to use a longer phrase, like <em>true_division</em> or
|
|||
|
|
<em>modern_division</em>. These don’t seem to add much information.)</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="open-issues">
|
|||
|
|
<h2><a class="toc-backref" href="#open-issues" role="doc-backlink">Open Issues</a></h2>
|
|||
|
|
<p>We expect that these issues will be resolved over time, as more feedback is
|
|||
|
|
received or we gather more experience with the initial implementation.</p>
|
|||
|
|
<ul class="simple">
|
|||
|
|
<li>It has been proposed to call <code class="docutils literal notranslate"><span class="pre">//</span></code> the quotient operator, and the <code class="docutils literal notranslate"><span class="pre">/</span></code>
|
|||
|
|
operator the ratio operator. I’m not sure about this – for some people
|
|||
|
|
quotient is just a synonym for division, and ratio suggests rational
|
|||
|
|
numbers, which is wrong. I prefer the terminology to be slightly awkward
|
|||
|
|
if that avoids unambiguity. Also, for some folks <em>quotient</em> suggests
|
|||
|
|
truncation towards zero, not towards infinity as <em>floor division</em>
|
|||
|
|
says explicitly.</li>
|
|||
|
|
<li>It has been argued that a command line option to change the default is
|
|||
|
|
evil. It can certainly be dangerous in the wrong hands: for example, it
|
|||
|
|
would be impossible to combine a 3rd party library package that requires
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">-Qnew</span></code> with another one that requires <code class="docutils literal notranslate"><span class="pre">-Qold</span></code>. But I believe that the
|
|||
|
|
VPython folks need a way to enable true division by default, and other
|
|||
|
|
educators might need the same. These usually have enough control over the
|
|||
|
|
library packages available in their environment.</li>
|
|||
|
|
<li>For classes to have to support all three of <code class="docutils literal notranslate"><span class="pre">__div__()</span></code>,
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">__floordiv__()</span></code> and <code class="docutils literal notranslate"><span class="pre">__truediv__()</span></code> seems painful; and what to do in
|
|||
|
|
3.0? Maybe we only need <code class="docutils literal notranslate"><span class="pre">__div__()</span></code> and <code class="docutils literal notranslate"><span class="pre">__floordiv__()</span></code>, or maybe at
|
|||
|
|
least true division should try <code class="docutils literal notranslate"><span class="pre">__truediv__()</span></code> first and <code class="docutils literal notranslate"><span class="pre">__div__()</span></code>
|
|||
|
|
second.</li>
|
|||
|
|
</ul>
|
|||
|
|
</section>
|
|||
|
|
<section id="resolved-issues">
|
|||
|
|
<h2><a class="toc-backref" href="#resolved-issues" role="doc-backlink">Resolved Issues</a></h2>
|
|||
|
|
<ul>
|
|||
|
|
<li>Issue: For very large long integers, the definition of true division as
|
|||
|
|
returning a float causes problems, since the range of Python longs is much
|
|||
|
|
larger than that of Python floats. This problem will disappear if and when
|
|||
|
|
rational numbers are supported.<p>Resolution: For long true division, Python uses an internal float type with
|
|||
|
|
native double precision but unbounded range, so that OverflowError doesn’t
|
|||
|
|
occur unless the quotient is too large to represent as a native double.</p>
|
|||
|
|
</li>
|
|||
|
|
<li>Issue: In the interim, maybe the long-to-float conversion could be made to
|
|||
|
|
raise <code class="docutils literal notranslate"><span class="pre">OverflowError</span></code> if the long is out of range.<p>Resolution: This has been implemented, but, as above, the magnitude of the
|
|||
|
|
inputs to long true division doesn’t matter; only the magnitude of the
|
|||
|
|
quotient matters.</p>
|
|||
|
|
</li>
|
|||
|
|
<li>Issue: Tim Peters will make sure that whenever an in-range float is
|
|||
|
|
returned, decent precision is guaranteed.<p>Resolution: Provided the quotient of long true division is representable as
|
|||
|
|
a float, it suffers no more than 3 rounding errors: one each for converting
|
|||
|
|
the inputs to an internal float type with native double precision but
|
|||
|
|
unbounded range, and one more for the division. However, note that if the
|
|||
|
|
magnitude of the quotient is too <em>small</em> to represent as a native double,
|
|||
|
|
0.0 is returned without exception (“silent underflow”).</p>
|
|||
|
|
</li>
|
|||
|
|
</ul>
|
|||
|
|
</section>
|
|||
|
|
<section id="faq">
|
|||
|
|
<h2><a class="toc-backref" href="#faq" role="doc-backlink">FAQ</a></h2>
|
|||
|
|
<section id="when-will-python-3-0-be-released">
|
|||
|
|
<h3><a class="toc-backref" href="#when-will-python-3-0-be-released" role="doc-backlink">When will Python 3.0 be released?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>We don’t plan that long ahead, so we can’t say for sure. We want to allow
|
|||
|
|
at least two years for the transition. If Python 3.0 comes out sooner,
|
|||
|
|
we’ll keep the 2.x line alive for backwards compatibility until at least
|
|||
|
|
two years from the release of Python 2.2. In practice, you will be able
|
|||
|
|
to continue to use the Python 2.x line for several years after Python 3.0
|
|||
|
|
is released, so you can take your time with the transition. Sites are
|
|||
|
|
expected to have both Python 2.x and Python 3.x installed simultaneously.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="why-isn-t-true-division-called-float-division">
|
|||
|
|
<h3><a class="toc-backref" href="#why-isn-t-true-division-called-float-division" role="doc-backlink">Why isn’t true division called float division?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>Because I want to keep the door open to <em>possibly</em> introducing rationals
|
|||
|
|
and making 1/2 return a rational rather than a float. See <a class="pep reference internal" href="../pep-0239/" title="PEP 239 – Adding a Rational Type to Python">PEP 239</a>.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="why-is-there-a-need-for-truediv-and-itruediv">
|
|||
|
|
<h3><a class="toc-backref" href="#why-is-there-a-need-for-truediv-and-itruediv" role="doc-backlink">Why is there a need for <code class="docutils literal notranslate"><span class="pre">__truediv__</span></code> and <code class="docutils literal notranslate"><span class="pre">__itruediv__</span></code>?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>We don’t want to make user-defined classes second-class citizens.
|
|||
|
|
Certainly not with the type/class unification going on.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="how-do-i-write-code-that-works-under-the-classic-rules-as-well-as-under-the-new-rules-without-using-or-a-future-division-statement">
|
|||
|
|
<h3><a class="toc-backref" href="#how-do-i-write-code-that-works-under-the-classic-rules-as-well-as-under-the-new-rules-without-using-or-a-future-division-statement" role="doc-backlink">How do I write code that works under the classic rules as well as under the new rules without using <code class="docutils literal notranslate"><span class="pre">//</span></code> or a future division statement?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>Use <code class="docutils literal notranslate"><span class="pre">x*1.0/y</span></code> for true division, <code class="docutils literal notranslate"><span class="pre">divmod(x,</span> <span class="pre">y)</span></code> (<a class="pep reference internal" href="../pep-0228/" title="PEP 228 – Reworking Python’s Numeric Model">PEP 228</a>) for int
|
|||
|
|
division. Especially the latter is best hidden inside a function. You
|
|||
|
|
may also write <code class="docutils literal notranslate"><span class="pre">float(x)/y</span></code> for true division if you are sure that you
|
|||
|
|
don’t expect complex numbers. If you know your integers are never
|
|||
|
|
negative, you can use <code class="docutils literal notranslate"><span class="pre">int(x/y)</span></code> – while the documentation of <code class="docutils literal notranslate"><span class="pre">int()</span></code>
|
|||
|
|
says that <code class="docutils literal notranslate"><span class="pre">int()</span></code> can round or truncate depending on the C
|
|||
|
|
implementation, we know of no C implementation that doesn’t truncate, and
|
|||
|
|
we’re going to change the spec for <code class="docutils literal notranslate"><span class="pre">int()</span></code> to promise truncation. Note
|
|||
|
|
that classic division (and floor division) round towards negative
|
|||
|
|
infinity, while <code class="docutils literal notranslate"><span class="pre">int()</span></code> rounds towards zero, giving different answers
|
|||
|
|
for negative numbers.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="how-do-i-specify-the-division-semantics-for-input-compile-execfile-eval-and-exec">
|
|||
|
|
<h3><a class="toc-backref" href="#how-do-i-specify-the-division-semantics-for-input-compile-execfile-eval-and-exec" role="doc-backlink">How do I specify the division semantics for <code class="docutils literal notranslate"><span class="pre">input()</span></code>, <code class="docutils literal notranslate"><span class="pre">compile()</span></code>, <code class="docutils literal notranslate"><span class="pre">execfile()</span></code>, <code class="docutils literal notranslate"><span class="pre">eval()</span></code> and <code class="docutils literal notranslate"><span class="pre">exec</span></code>?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>They inherit the choice from the invoking module. <a class="pep reference internal" href="../pep-0236/" title="PEP 236 – Back to the __future__">PEP 236</a> now lists
|
|||
|
|
this as a resolved problem, referring to <a class="pep reference internal" href="../pep-0264/" title="PEP 264 – Future statements in simulated shells">PEP 264</a>.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="what-about-code-compiled-by-the-codeop-module">
|
|||
|
|
<h3><a class="toc-backref" href="#what-about-code-compiled-by-the-codeop-module" role="doc-backlink">What about code compiled by the codeop module?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>This is dealt with properly; see <a class="pep reference internal" href="../pep-0264/" title="PEP 264 – Future statements in simulated shells">PEP 264</a>.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="will-there-be-conversion-tools-or-aids">
|
|||
|
|
<h3><a class="toc-backref" href="#will-there-be-conversion-tools-or-aids" role="doc-backlink">Will there be conversion tools or aids?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>Certainly. While these are outside the scope of the PEP, I should point
|
|||
|
|
out two simple tools that will be released with Python 2.2a3:
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">Tools/scripts/finddiv.py</span></code> finds division operators (slightly smarter
|
|||
|
|
than <code class="docutils literal notranslate"><span class="pre">grep</span> <span class="pre">/</span></code>) and <code class="docutils literal notranslate"><span class="pre">Tools/scripts/fixdiv.py</span></code> can produce patches based
|
|||
|
|
on run-time analysis.</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="why-is-my-question-not-answered-here">
|
|||
|
|
<h3><a class="toc-backref" href="#why-is-my-question-not-answered-here" role="doc-backlink">Why is my question not answered here?</a></h3>
|
|||
|
|
<blockquote>
|
|||
|
|
<div>Because we weren’t aware of it. If it’s been discussed on c.l.py and you
|
|||
|
|
believe the answer is of general interest, please notify the second
|
|||
|
|
author. (We don’t have the time or inclination to answer every question
|
|||
|
|
sent in private email, hence the requirement that it be discussed on
|
|||
|
|
c.l.py first.)</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
</section>
|
|||
|
|
<section id="implementation">
|
|||
|
|
<h2><a class="toc-backref" href="#implementation" role="doc-backlink">Implementation</a></h2>
|
|||
|
|
<p>Essentially everything mentioned here is implemented in CVS and will be
|
|||
|
|
released with Python 2.2a3; most of it was already released with Python 2.2a2.</p>
|
|||
|
|
</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-0238.rst">https://github.com/python/peps/blob/main/peps/pep-0238.rst</a></p>
|
|||
|
|
<p>Last modified: <a class="reference external" href="https://github.com/python/peps/commits/main/peps/pep-0238.rst">2023-09-09 17:39:29 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="#motivation">Motivation</a></li>
|
|||
|
|
<li><a class="reference internal" href="#variations">Variations</a></li>
|
|||
|
|
<li><a class="reference internal" href="#alternatives">Alternatives</a></li>
|
|||
|
|
<li><a class="reference internal" href="#api-changes">API Changes</a></li>
|
|||
|
|
<li><a class="reference internal" href="#command-line-option">Command Line Option</a></li>
|
|||
|
|
<li><a class="reference internal" href="#semantics-of-floor-division">Semantics of Floor Division</a></li>
|
|||
|
|
<li><a class="reference internal" href="#semantics-of-true-division">Semantics of True Division</a></li>
|
|||
|
|
<li><a class="reference internal" href="#the-future-division-statement">The Future Division Statement</a></li>
|
|||
|
|
<li><a class="reference internal" href="#open-issues">Open Issues</a></li>
|
|||
|
|
<li><a class="reference internal" href="#resolved-issues">Resolved Issues</a></li>
|
|||
|
|
<li><a class="reference internal" href="#faq">FAQ</a><ul>
|
|||
|
|
<li><a class="reference internal" href="#when-will-python-3-0-be-released">When will Python 3.0 be released?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#why-isn-t-true-division-called-float-division">Why isn’t true division called float division?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#why-is-there-a-need-for-truediv-and-itruediv">Why is there a need for <code class="docutils literal notranslate"><span class="pre">__truediv__</span></code> and <code class="docutils literal notranslate"><span class="pre">__itruediv__</span></code>?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#how-do-i-write-code-that-works-under-the-classic-rules-as-well-as-under-the-new-rules-without-using-or-a-future-division-statement">How do I write code that works under the classic rules as well as under the new rules without using <code class="docutils literal notranslate"><span class="pre">//</span></code> or a future division statement?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#how-do-i-specify-the-division-semantics-for-input-compile-execfile-eval-and-exec">How do I specify the division semantics for <code class="docutils literal notranslate"><span class="pre">input()</span></code>, <code class="docutils literal notranslate"><span class="pre">compile()</span></code>, <code class="docutils literal notranslate"><span class="pre">execfile()</span></code>, <code class="docutils literal notranslate"><span class="pre">eval()</span></code> and <code class="docutils literal notranslate"><span class="pre">exec</span></code>?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#what-about-code-compiled-by-the-codeop-module">What about code compiled by the codeop module?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#will-there-be-conversion-tools-or-aids">Will there be conversion tools or aids?</a></li>
|
|||
|
|
<li><a class="reference internal" href="#why-is-my-question-not-answered-here">Why is my question not answered here?</a></li>
|
|||
|
|
</ul>
|
|||
|
|
</li>
|
|||
|
|
<li><a class="reference internal" href="#implementation">Implementation</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-0238.rst">Page Source (GitHub)</a>
|
|||
|
|
</nav>
|
|||
|
|
</section>
|
|||
|
|
<script src="../_static/colour_scheme.js"></script>
|
|||
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|
<script src="../_static/wrap_tables.js"></script>
|
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|
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|
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</html>
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