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  99. <li><a class="reference internal" href="#quick-start-tutorial">Quick-start Tutorial</a></li>

  100. <li><a class="reference internal" href="#decimal-objects">Decimal objects</a><ul>

  101. <li><a class="reference internal" href="#logical-operands">Logical operands</a></li>

  102. </ul>

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  106. <li><a class="reference internal" href="#rounding-modes">Rounding modes</a></li>

  107. <li><a class="reference internal" href="#signals">Signals</a></li>

  108. <li><a class="reference internal" href="#floating-point-notes">Floating Point Notes</a><ul>

  109. <li><a class="reference internal" href="#mitigating-round-off-error-with-increased-precision">Mitigating round-off error with increased precision</a></li>

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  208.   <section id="module-decimal">

  209. <span id="decimal-decimal-fixed-point-and-floating-point-arithmetic"></span><h1><a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code></a> — Decimal fixed point and floating point arithmetic<a class="headerlink" href="#module-decimal" title="Link to this heading">¶</a></h1>

  210. <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.12/Lib/decimal.py">Lib/decimal.py</a></p>

  211. <hr class="docutils" />

  212. <p>The <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code></a> module provides support for fast correctly rounded

  213. decimal floating point arithmetic. It offers several advantages over the

  214. <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> datatype:</p>

  215. <ul>

  216. <li><p>Decimal “is based on a floating-point model which was designed with people

  217. in mind, and necessarily has a paramount guiding principle – computers must

  218. provide an arithmetic that works in the same way as the arithmetic that

  219. people learn at school.” – excerpt from the decimal arithmetic specification.</p></li>

  220. <li><p>Decimal numbers can be represented exactly.  In contrast, numbers like

  221. <code class="docutils literal notranslate"><span class="pre">1.1</span></code> and <code class="docutils literal notranslate"><span class="pre">2.2</span></code> do not have exact representations in binary

  222. floating point. End users typically would not expect <code class="docutils literal notranslate"><span class="pre">1.1</span> <span class="pre">+</span> <span class="pre">2.2</span></code> to display

  223. as <code class="docutils literal notranslate"><span class="pre">3.3000000000000003</span></code> as it does with binary floating point.</p></li>

  224. <li><p>The exactness carries over into arithmetic.  In decimal floating point, <code class="docutils literal notranslate"><span class="pre">0.1</span>

  225. <span class="pre">+</span> <span class="pre">0.1</span> <span class="pre">+</span> <span class="pre">0.1</span> <span class="pre">-</span> <span class="pre">0.3</span></code> is exactly equal to zero.  In binary floating point, the result

  226. is <code class="docutils literal notranslate"><span class="pre">5.5511151231257827e-017</span></code>.  While near to zero, the differences

  227. prevent reliable equality testing and differences can accumulate. For this

  228. reason, decimal is preferred in accounting applications which have strict

  229. equality invariants.</p></li>

  230. <li><p>The decimal module incorporates a notion of significant places so that <code class="docutils literal notranslate"><span class="pre">1.30</span>

  231. <span class="pre">+</span> <span class="pre">1.20</span></code> is <code class="docutils literal notranslate"><span class="pre">2.50</span></code>.  The trailing zero is kept to indicate significance.

  232. This is the customary presentation for monetary applications. For

  233. multiplication, the “schoolbook” approach uses all the figures in the

  234. multiplicands.  For instance, <code class="docutils literal notranslate"><span class="pre">1.3</span> <span class="pre">*</span> <span class="pre">1.2</span></code> gives <code class="docutils literal notranslate"><span class="pre">1.56</span></code> while <code class="docutils literal notranslate"><span class="pre">1.30</span> <span class="pre">*</span>

  235. <span class="pre">1.20</span></code> gives <code class="docutils literal notranslate"><span class="pre">1.5600</span></code>.</p></li>

  236. <li><p>Unlike hardware based binary floating point, the decimal module has a user

  237. alterable precision (defaulting to 28 places) which can be as large as needed for

  238. a given problem:</p>

  239. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="kn">import</span> <span class="o">*</span>

  240. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">6</span>

  241. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>

  242. <span class="go">Decimal(&#39;0.142857&#39;)</span>

  243. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">28</span>

  244. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>

  245. <span class="go">Decimal(&#39;0.1428571428571428571428571429&#39;)</span>

  246. </pre></div>

  247. </div>

  248. </li>

  249. <li><p>Both binary and decimal floating point are implemented in terms of published

  250. standards.  While the built-in float type exposes only a modest portion of its

  251. capabilities, the decimal module exposes all required parts of the standard.

  252. When needed, the programmer has full control over rounding and signal handling.

  253. This includes an option to enforce exact arithmetic by using exceptions

  254. to block any inexact operations.</p></li>

  255. <li><p>The decimal module was designed to support “without prejudice, both exact

  256. unrounded decimal arithmetic (sometimes called fixed-point arithmetic)

  257. and rounded floating-point arithmetic.”  – excerpt from the decimal

  258. arithmetic specification.</p></li>

  259. </ul>

  260. <p>The module design is centered around three concepts:  the decimal number, the

  261. context for arithmetic, and signals.</p>

  262. <p>A decimal number is immutable.  It has a sign, coefficient digits, and an

  263. exponent.  To preserve significance, the coefficient digits do not truncate

  264. trailing zeros.  Decimals also include special values such as

  265. <code class="docutils literal notranslate"><span class="pre">Infinity</span></code>, <code class="docutils literal notranslate"><span class="pre">-Infinity</span></code>, and <code class="docutils literal notranslate"><span class="pre">NaN</span></code>.  The standard also

  266. differentiates <code class="docutils literal notranslate"><span class="pre">-0</span></code> from <code class="docutils literal notranslate"><span class="pre">+0</span></code>.</p>

  267. <p>The context for arithmetic is an environment specifying precision, rounding

  268. rules, limits on exponents, flags indicating the results of operations, and trap

  269. enablers which determine whether signals are treated as exceptions.  Rounding

  270. options include <a class="reference internal" href="#decimal.ROUND_CEILING" title="decimal.ROUND_CEILING"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_CEILING</span></code></a>, <a class="reference internal" href="#decimal.ROUND_DOWN" title="decimal.ROUND_DOWN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_DOWN</span></code></a>,

  271. <a class="reference internal" href="#decimal.ROUND_FLOOR" title="decimal.ROUND_FLOOR"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_FLOOR</span></code></a>, <a class="reference internal" href="#decimal.ROUND_HALF_DOWN" title="decimal.ROUND_HALF_DOWN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_DOWN</span></code></a>, <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a>,

  272. <a class="reference internal" href="#decimal.ROUND_HALF_UP" title="decimal.ROUND_HALF_UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_UP</span></code></a>, <a class="reference internal" href="#decimal.ROUND_UP" title="decimal.ROUND_UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_UP</span></code></a>, and <a class="reference internal" href="#decimal.ROUND_05UP" title="decimal.ROUND_05UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_05UP</span></code></a>.</p>

  273. <p>Signals are groups of exceptional conditions arising during the course of

  274. computation.  Depending on the needs of the application, signals may be ignored,

  275. considered as informational, or treated as exceptions. The signals in the

  276. decimal module are: <a class="reference internal" href="#decimal.Clamped" title="decimal.Clamped"><code class="xref py py-const docutils literal notranslate"><span class="pre">Clamped</span></code></a>, <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a>,

  277. <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a>, <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate"><span class="pre">Inexact</span></code></a>, <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal notranslate"><span class="pre">Rounded</span></code></a>, <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-const docutils literal notranslate"><span class="pre">Subnormal</span></code></a>,

  278. <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-const docutils literal notranslate"><span class="pre">Overflow</span></code></a>, <a class="reference internal" href="#decimal.Underflow" title="decimal.Underflow"><code class="xref py py-const docutils literal notranslate"><span class="pre">Underflow</span></code></a> and <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-const docutils literal notranslate"><span class="pre">FloatOperation</span></code></a>.</p>

  279. <p>For each signal there is a flag and a trap enabler.  When a signal is

  280. encountered, its flag is set to one, then, if the trap enabler is

  281. set to one, an exception is raised.  Flags are sticky, so the user needs to

  282. reset them before monitoring a calculation.</p>

  283. <div class="admonition seealso">

  284. <p class="admonition-title">See also</p>

  285. <ul class="simple">

  286. <li><p>IBM’s General Decimal Arithmetic Specification, <a class="reference external" href="https://speleotrove.com/decimal/decarith.html">The General Decimal Arithmetic

  287. Specification</a>.</p></li>

  288. </ul>

  289. </div>

  290. <section id="quick-start-tutorial">

  291. <span id="decimal-tutorial"></span><h2>Quick-start Tutorial<a class="headerlink" href="#quick-start-tutorial" title="Link to this heading">¶</a></h2>

  292. <p>The usual start to using decimals is importing the module, viewing the current

  293. context with <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a> and, if necessary, setting new values for

  294. precision, rounding, or enabled traps:</p>

  295. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="kn">import</span> <span class="o">*</span>

  296. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span>

  297. <span class="go">Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,</span>

  298. <span class="go">        capitals=1, clamp=0, flags=[], traps=[Overflow, DivisionByZero,</span>

  299. <span class="go">        InvalidOperation])</span>

  300. 

  301. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">7</span>       <span class="c1"># Set a new precision</span>

  302. </pre></div>

  303. </div>

  304. <p>Decimal instances can be constructed from integers, strings, floats, or tuples.

  305. Construction from an integer or a float performs an exact conversion of the

  306. value of that integer or float.  Decimal numbers include special values such as

  307. <code class="docutils literal notranslate"><span class="pre">NaN</span></code> which stands for “Not a number”, positive and negative

  308. <code class="docutils literal notranslate"><span class="pre">Infinity</span></code>, and <code class="docutils literal notranslate"><span class="pre">-0</span></code>:</p>

  309. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">28</span>

  310. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>

  311. <span class="go">Decimal(&#39;10&#39;)</span>

  312. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.14&#39;</span><span class="p">)</span>

  313. <span class="go">Decimal(&#39;3.14&#39;)</span>

  314. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mf">3.14</span><span class="p">)</span>

  315. <span class="go">Decimal(&#39;3.140000000000000124344978758017532527446746826171875&#39;)</span>

  316. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="o">-</span><span class="mi">2</span><span class="p">))</span>

  317. <span class="go">Decimal(&#39;3.14&#39;)</span>

  318. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="mf">2.0</span> <span class="o">**</span> <span class="mf">0.5</span><span class="p">))</span>

  319. <span class="go">Decimal(&#39;1.4142135623730951&#39;)</span>

  320. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">**</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;0.5&#39;</span><span class="p">)</span>

  321. <span class="go">Decimal(&#39;1.414213562373095048801688724&#39;)</span>

  322. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;NaN&#39;</span><span class="p">)</span>

  323. <span class="go">Decimal(&#39;NaN&#39;)</span>

  324. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;-Infinity&#39;</span><span class="p">)</span>

  325. <span class="go">Decimal(&#39;-Infinity&#39;)</span>

  326. </pre></div>

  327. </div>

  328. <p>If the <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">FloatOperation</span></code></a> signal is trapped, accidental mixing of

  329. decimals and floats in constructors or ordering comparisons raises

  330. an exception:</p>

  331. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">c</span> <span class="o">=</span> <span class="n">getcontext</span><span class="p">()</span>

  332. <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span><span class="o">.</span><span class="n">traps</span><span class="p">[</span><span class="n">FloatOperation</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>

  333. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mf">3.14</span><span class="p">)</span>

  334. <span class="gt">Traceback (most recent call last):</span>

  335.   File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  336. <span class="gr">decimal.FloatOperation</span>: <span class="n">[&lt;class &#39;decimal.FloatOperation&#39;&gt;]</span>

  337. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.5&#39;</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">3.7</span>

  338. <span class="gt">Traceback (most recent call last):</span>

  339.   File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  340. <span class="gr">decimal.FloatOperation</span>: <span class="n">[&lt;class &#39;decimal.FloatOperation&#39;&gt;]</span>

  341. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.5&#39;</span><span class="p">)</span> <span class="o">==</span> <span class="mf">3.5</span>

  342. <span class="go">True</span>

  343. </pre></div>

  344. </div>

  345. <div class="versionadded">

  346. <p><span class="versionmodified added">New in version 3.3.</span></p>

  347. </div>

  348. <p>The significance of a new Decimal is determined solely by the number of digits

  349. input.  Context precision and rounding only come into play during arithmetic

  350. operations.</p>

  351. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">6</span>

  352. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.0&#39;</span><span class="p">)</span>

  353. <span class="go">Decimal(&#39;3.0&#39;)</span>

  354. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.1415926535&#39;</span><span class="p">)</span>

  355. <span class="go">Decimal(&#39;3.1415926535&#39;)</span>

  356. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.1415926535&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;2.7182818285&#39;</span><span class="p">)</span>

  357. <span class="go">Decimal(&#39;5.85987&#39;)</span>

  358. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">rounding</span> <span class="o">=</span> <span class="n">ROUND_UP</span>

  359. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.1415926535&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;2.7182818285&#39;</span><span class="p">)</span>

  360. <span class="go">Decimal(&#39;5.85988&#39;)</span>

  361. </pre></div>

  362. </div>

  363. <p>If the internal limits of the C version are exceeded, constructing

  364. a decimal raises <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-class docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a>:</p>

  365. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s2">&quot;1e9999999999999999999&quot;</span><span class="p">)</span>

  366. <span class="gt">Traceback (most recent call last):</span>

  367.   File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  368. <span class="gr">decimal.InvalidOperation</span>: <span class="n">[&lt;class &#39;decimal.InvalidOperation&#39;&gt;]</span>

  369. </pre></div>

  370. </div>

  371. <div class="versionchanged">

  372. <p><span class="versionmodified changed">Changed in version 3.3.</span></p>

  373. </div>

  374. <p>Decimals interact well with much of the rest of Python.  Here is a small decimal

  375. floating point flying circus:</p>

  376. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">data</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">Decimal</span><span class="p">,</span> <span class="s1">&#39;1.34 1.87 3.45 2.35 1.00 0.03 9.25&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()))</span>

  377. <span class="gp">&gt;&gt;&gt; </span><span class="nb">max</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>

  378. <span class="go">Decimal(&#39;9.25&#39;)</span>

  379. <span class="gp">&gt;&gt;&gt; </span><span class="nb">min</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>

  380. <span class="go">Decimal(&#39;0.03&#39;)</span>

  381. <span class="gp">&gt;&gt;&gt; </span><span class="nb">sorted</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>

  382. <span class="go">[Decimal(&#39;0.03&#39;), Decimal(&#39;1.00&#39;), Decimal(&#39;1.34&#39;), Decimal(&#39;1.87&#39;),</span>

  383. <span class="go"> Decimal(&#39;2.35&#39;), Decimal(&#39;3.45&#39;), Decimal(&#39;9.25&#39;)]</span>

  384. <span class="gp">&gt;&gt;&gt; </span><span class="nb">sum</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>

  385. <span class="go">Decimal(&#39;19.29&#39;)</span>

  386. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="n">c</span> <span class="o">=</span> <span class="n">data</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span>

  387. <span class="gp">&gt;&gt;&gt; </span><span class="nb">str</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>

  388. <span class="go">&#39;1.34&#39;</span>

  389. <span class="gp">&gt;&gt;&gt; </span><span class="nb">float</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>

  390. <span class="go">1.34</span>

  391. <span class="gp">&gt;&gt;&gt; </span><span class="nb">round</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>

  392. <span class="go">Decimal(&#39;1.3&#39;)</span>

  393. <span class="gp">&gt;&gt;&gt; </span><span class="nb">int</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>

  394. <span class="go">1</span>

  395. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">*</span> <span class="mi">5</span>

  396. <span class="go">Decimal(&#39;6.70&#39;)</span>

  397. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">*</span> <span class="n">b</span>

  398. <span class="go">Decimal(&#39;2.5058&#39;)</span>

  399. <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span> <span class="o">%</span> <span class="n">a</span>

  400. <span class="go">Decimal(&#39;0.77&#39;)</span>

  401. </pre></div>

  402. </div>

  403. <p>And some mathematical functions are also available to Decimal:</p>

  404. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">28</span>

  405. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">sqrt</span><span class="p">()</span>

  406. <span class="go">Decimal(&#39;1.414213562373095048801688724&#39;)</span>

  407. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">exp</span><span class="p">()</span>

  408. <span class="go">Decimal(&#39;2.718281828459045235360287471&#39;)</span>

  409. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;10&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">ln</span><span class="p">()</span>

  410. <span class="go">Decimal(&#39;2.302585092994045684017991455&#39;)</span>

  411. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;10&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">log10</span><span class="p">()</span>

  412. <span class="go">Decimal(&#39;1&#39;)</span>

  413. </pre></div>

  414. </div>

  415. <p>The <a class="reference internal" href="#decimal.Decimal.quantize" title="decimal.Decimal.quantize"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quantize()</span></code></a> method rounds a number to a fixed exponent.  This method is

  416. useful for monetary applications that often round results to a fixed number of

  417. places:</p>

  418. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;7.325&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;.01&#39;</span><span class="p">),</span> <span class="n">rounding</span><span class="o">=</span><span class="n">ROUND_DOWN</span><span class="p">)</span>

  419. <span class="go">Decimal(&#39;7.32&#39;)</span>

  420. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;7.325&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1.&#39;</span><span class="p">),</span> <span class="n">rounding</span><span class="o">=</span><span class="n">ROUND_UP</span><span class="p">)</span>

  421. <span class="go">Decimal(&#39;8&#39;)</span>

  422. </pre></div>

  423. </div>

  424. <p>As shown above, the <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a> function accesses the current context and

  425. allows the settings to be changed.  This approach meets the needs of most

  426. applications.</p>

  427. <p>For more advanced work, it may be useful to create alternate contexts using the

  428. Context() constructor.  To make an alternate active, use the <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">setcontext()</span></code></a>

  429. function.</p>

  430. <p>In accordance with the standard, the <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code></a> module provides two ready to

  431. use standard contexts, <a class="reference internal" href="#decimal.BasicContext" title="decimal.BasicContext"><code class="xref py py-const docutils literal notranslate"><span class="pre">BasicContext</span></code></a> and <a class="reference internal" href="#decimal.ExtendedContext" title="decimal.ExtendedContext"><code class="xref py py-const docutils literal notranslate"><span class="pre">ExtendedContext</span></code></a>. The

  432. former is especially useful for debugging because many of the traps are

  433. enabled:</p>

  434. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">myothercontext</span> <span class="o">=</span> <span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="mi">60</span><span class="p">,</span> <span class="n">rounding</span><span class="o">=</span><span class="n">ROUND_HALF_DOWN</span><span class="p">)</span>

  435. <span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">myothercontext</span><span class="p">)</span>

  436. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>

  437. <span class="go">Decimal(&#39;0.142857142857142857142857142857142857142857142857142857142857&#39;)</span>

  438. 

  439. <span class="gp">&gt;&gt;&gt; </span><span class="n">ExtendedContext</span>

  440. <span class="go">Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,</span>

  441. <span class="go">        capitals=1, clamp=0, flags=[], traps=[])</span>

  442. <span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">ExtendedContext</span><span class="p">)</span>

  443. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>

  444. <span class="go">Decimal(&#39;0.142857143&#39;)</span>

  445. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

  446. <span class="go">Decimal(&#39;Infinity&#39;)</span>

  447. 

  448. <span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">BasicContext</span><span class="p">)</span>

  449. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

  450. <span class="gt">Traceback (most recent call last):</span>

  451.   File <span class="nb">&quot;&lt;pyshell#143&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">-toplevel-</span>

  452. <span class="w">    </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

  453. <span class="gr">DivisionByZero</span>: <span class="n">x / 0</span>

  454. </pre></div>

  455. </div>

  456. <p>Contexts also have signal flags for monitoring exceptional conditions

  457. encountered during computations.  The flags remain set until explicitly cleared,

  458. so it is best to clear the flags before each set of monitored computations by

  459. using the <a class="reference internal" href="#decimal.Context.clear_flags" title="decimal.Context.clear_flags"><code class="xref py py-meth docutils literal notranslate"><span class="pre">clear_flags()</span></code></a> method.</p>

  460. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">ExtendedContext</span><span class="p">)</span>

  461. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">clear_flags</span><span class="p">()</span>

  462. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">355</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">113</span><span class="p">)</span>

  463. <span class="go">Decimal(&#39;3.14159292&#39;)</span>

  464. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span>

  465. <span class="go">Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,</span>

  466. <span class="go">        capitals=1, clamp=0, flags=[Inexact, Rounded], traps=[])</span>

  467. </pre></div>

  468. </div>

  469. <p>The <em>flags</em> entry shows that the rational approximation to pi was

  470. rounded (digits beyond the context precision were thrown away) and that the

  471. result is inexact (some of the discarded digits were non-zero).</p>

  472. <p>Individual traps are set using the dictionary in the <code class="xref py py-attr docutils literal notranslate"><span class="pre">traps</span></code>

  473. attribute of a context:</p>

  474. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">ExtendedContext</span><span class="p">)</span>

  475. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

  476. <span class="go">Decimal(&#39;Infinity&#39;)</span>

  477. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">traps</span><span class="p">[</span><span class="n">DivisionByZero</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>

  478. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

  479. <span class="gt">Traceback (most recent call last):</span>

  480.   File <span class="nb">&quot;&lt;pyshell#112&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">-toplevel-</span>

  481. <span class="w">    </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

  482. <span class="gr">DivisionByZero</span>: <span class="n">x / 0</span>

  483. </pre></div>

  484. </div>

  485. <p>Most programs adjust the current context only once, at the beginning of the

  486. program.  And, in many applications, data is converted to <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> with

  487. a single cast inside a loop.  With context set and decimals created, the bulk of

  488. the program manipulates the data no differently than with other Python numeric

  489. types.</p>

  490. </section>

  491. <section id="decimal-objects">

  492. <span id="decimal-decimal"></span><h2>Decimal objects<a class="headerlink" href="#decimal-objects" title="Link to this heading">¶</a></h2>

  493. <dl class="py class">

  494. <dt class="sig sig-object py" id="decimal.Decimal">

  495. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Decimal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'0'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal" title="Link to this definition">¶</a></dt>

  496. <dd><p>Construct a new <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> object based from <em>value</em>.</p>

  497. <p><em>value</em> can be an integer, string, tuple, <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, or another <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>

  498. object. If no <em>value</em> is given, returns <code class="docutils literal notranslate"><span class="pre">Decimal('0')</span></code>.  If <em>value</em> is a

  499. string, it should conform to the decimal numeric string syntax after leading

  500. and trailing whitespace characters, as well as underscores throughout, are removed:</p>

  501. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">sign</span>           <span class="p">:</span><span class="o">:=</span>  <span class="s1">&#39;+&#39;</span> <span class="o">|</span> <span class="s1">&#39;-&#39;</span>

  502. <span class="n">digit</span>          <span class="p">:</span><span class="o">:=</span>  <span class="s1">&#39;0&#39;</span> <span class="o">|</span> <span class="s1">&#39;1&#39;</span> <span class="o">|</span> <span class="s1">&#39;2&#39;</span> <span class="o">|</span> <span class="s1">&#39;3&#39;</span> <span class="o">|</span> <span class="s1">&#39;4&#39;</span> <span class="o">|</span> <span class="s1">&#39;5&#39;</span> <span class="o">|</span> <span class="s1">&#39;6&#39;</span> <span class="o">|</span> <span class="s1">&#39;7&#39;</span> <span class="o">|</span> <span class="s1">&#39;8&#39;</span> <span class="o">|</span> <span class="s1">&#39;9&#39;</span>

  503. <span class="n">indicator</span>      <span class="p">:</span><span class="o">:=</span>  <span class="s1">&#39;e&#39;</span> <span class="o">|</span> <span class="s1">&#39;E&#39;</span>

  504. <span class="n">digits</span>         <span class="p">:</span><span class="o">:=</span>  <span class="n">digit</span> <span class="p">[</span><span class="n">digit</span><span class="p">]</span><span class="o">...</span>

  505. <span class="n">decimal</span><span class="o">-</span><span class="n">part</span>   <span class="p">:</span><span class="o">:=</span>  <span class="n">digits</span> <span class="s1">&#39;.&#39;</span> <span class="p">[</span><span class="n">digits</span><span class="p">]</span> <span class="o">|</span> <span class="p">[</span><span class="s1">&#39;.&#39;</span><span class="p">]</span> <span class="n">digits</span>

  506. <span class="n">exponent</span><span class="o">-</span><span class="n">part</span>  <span class="p">:</span><span class="o">:=</span>  <span class="n">indicator</span> <span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="n">digits</span>

  507. <span class="n">infinity</span>       <span class="p">:</span><span class="o">:=</span>  <span class="s1">&#39;Infinity&#39;</span> <span class="o">|</span> <span class="s1">&#39;Inf&#39;</span>

  508. <span class="n">nan</span>            <span class="p">:</span><span class="o">:=</span>  <span class="s1">&#39;NaN&#39;</span> <span class="p">[</span><span class="n">digits</span><span class="p">]</span> <span class="o">|</span> <span class="s1">&#39;sNaN&#39;</span> <span class="p">[</span><span class="n">digits</span><span class="p">]</span>

  509. <span class="n">numeric</span><span class="o">-</span><span class="n">value</span>  <span class="p">:</span><span class="o">:=</span>  <span class="n">decimal</span><span class="o">-</span><span class="n">part</span> <span class="p">[</span><span class="n">exponent</span><span class="o">-</span><span class="n">part</span><span class="p">]</span> <span class="o">|</span> <span class="n">infinity</span>

  510. <span class="n">numeric</span><span class="o">-</span><span class="n">string</span> <span class="p">:</span><span class="o">:=</span>  <span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="n">numeric</span><span class="o">-</span><span class="n">value</span> <span class="o">|</span> <span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="n">nan</span>

  511. </pre></div>

  512. </div>

  513. <p>Other Unicode decimal digits are also permitted where <code class="docutils literal notranslate"><span class="pre">digit</span></code>

  514. appears above.  These include decimal digits from various other

  515. alphabets (for example, Arabic-Indic and Devanāgarī digits) along

  516. with the fullwidth digits <code class="docutils literal notranslate"><span class="pre">'\uff10'</span></code> through <code class="docutils literal notranslate"><span class="pre">'\uff19'</span></code>.</p>

  517. <p>If <em>value</em> is a <a class="reference internal" href="stdtypes.html#tuple" title="tuple"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>, it should have three components, a sign

  518. (<code class="docutils literal notranslate"><span class="pre">0</span></code> for positive or <code class="docutils literal notranslate"><span class="pre">1</span></code> for negative), a <a class="reference internal" href="stdtypes.html#tuple" title="tuple"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a> of

  519. digits, and an integer exponent. For example, <code class="docutils literal notranslate"><span class="pre">Decimal((0,</span> <span class="pre">(1,</span> <span class="pre">4,</span> <span class="pre">1,</span> <span class="pre">4),</span> <span class="pre">-3))</span></code>

  520. returns <code class="docutils literal notranslate"><span class="pre">Decimal('1.414')</span></code>.</p>

  521. <p>If <em>value</em> is a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, the binary floating point value is losslessly

  522. converted to its exact decimal equivalent.  This conversion can often require

  523. 53 or more digits of precision.  For example, <code class="docutils literal notranslate"><span class="pre">Decimal(float('1.1'))</span></code>

  524. converts to

  525. <code class="docutils literal notranslate"><span class="pre">Decimal('1.100000000000000088817841970012523233890533447265625')</span></code>.</p>

  526. <p>The <em>context</em> precision does not affect how many digits are stored. That is

  527. determined exclusively by the number of digits in <em>value</em>. For example,

  528. <code class="docutils literal notranslate"><span class="pre">Decimal('3.00000')</span></code> records all five zeros even if the context precision is

  529. only three.</p>

  530. <p>The purpose of the <em>context</em> argument is determining what to do if <em>value</em> is a

  531. malformed string.  If the context traps <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a>, an exception

  532. is raised; otherwise, the constructor returns a new Decimal with the value of

  533. <code class="docutils literal notranslate"><span class="pre">NaN</span></code>.</p>

  534. <p>Once constructed, <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> objects are immutable.</p>

  535. <div class="versionchanged">

  536. <p><span class="versionmodified changed">Changed in version 3.2: </span>The argument to the constructor is now permitted to be a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>

  537. instance.</p>

  538. </div>

  539. <div class="versionchanged">

  540. <p><span class="versionmodified changed">Changed in version 3.3: </span><a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> arguments raise an exception if the <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">FloatOperation</span></code></a>

  541. trap is set. By default the trap is off.</p>

  542. </div>

  543. <div class="versionchanged">

  544. <p><span class="versionmodified changed">Changed in version 3.6: </span>Underscores are allowed for grouping, as with integral and floating-point

  545. literals in code.</p>

  546. </div>

  547. <p>Decimal floating point objects share many properties with the other built-in

  548. numeric types such as <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> and <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>.  All of the usual math

  549. operations and special methods apply.  Likewise, decimal objects can be

  550. copied, pickled, printed, used as dictionary keys, used as set elements,

  551. compared, sorted, and coerced to another type (such as <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> or

  552. <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>).</p>

  553. <p>There are some small differences between arithmetic on Decimal objects and

  554. arithmetic on integers and floats.  When the remainder operator <code class="docutils literal notranslate"><span class="pre">%</span></code> is

  555. applied to Decimal objects, the sign of the result is the sign of the

  556. <em>dividend</em> rather than the sign of the divisor:</p>

  557. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">)</span> <span class="o">%</span> <span class="mi">4</span>

  558. <span class="go">1</span>

  559. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">)</span> <span class="o">%</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>

  560. <span class="go">Decimal(&#39;-3&#39;)</span>

  561. </pre></div>

  562. </div>

  563. <p>The integer division operator <code class="docutils literal notranslate"><span class="pre">//</span></code> behaves analogously, returning the

  564. integer part of the true quotient (truncating towards zero) rather than its

  565. floor, so as to preserve the usual identity <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">(x</span> <span class="pre">//</span> <span class="pre">y)</span> <span class="pre">*</span> <span class="pre">y</span> <span class="pre">+</span> <span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></code>:</p>

  566. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="o">-</span><span class="mi">7</span> <span class="o">//</span> <span class="mi">4</span>

  567. <span class="go">-2</span>

  568. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="o">-</span><span class="mi">7</span><span class="p">)</span> <span class="o">//</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>

  569. <span class="go">Decimal(&#39;-1&#39;)</span>

  570. </pre></div>

  571. </div>

  572. <p>The <code class="docutils literal notranslate"><span class="pre">%</span></code> and <code class="docutils literal notranslate"><span class="pre">//</span></code> operators implement the <code class="docutils literal notranslate"><span class="pre">remainder</span></code> and

  573. <code class="docutils literal notranslate"><span class="pre">divide-integer</span></code> operations (respectively) as described in the

  574. specification.</p>

  575. <p>Decimal objects cannot generally be combined with floats or

  576. instances of <a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate"><span class="pre">fractions.Fraction</span></code></a> in arithmetic operations:

  577. an attempt to add a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> to a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, for

  578. example, will raise a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a>.  However, it is possible to

  579. use Python’s comparison operators to compare a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>

  580. instance <code class="docutils literal notranslate"><span class="pre">x</span></code> with another number <code class="docutils literal notranslate"><span class="pre">y</span></code>.  This avoids confusing results

  581. when doing equality comparisons between numbers of different types.</p>

  582. <div class="versionchanged">

  583. <p><span class="versionmodified changed">Changed in version 3.2: </span>Mixed-type comparisons between <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instances and other

  584. numeric types are now fully supported.</p>

  585. </div>

  586. <p>In addition to the standard numeric properties, decimal floating point

  587. objects also have a number of specialized methods:</p>

  588. <dl class="py method">

  589. <dt class="sig sig-object py" id="decimal.Decimal.adjusted">

  590. <span class="sig-name descname"><span class="pre">adjusted</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.adjusted" title="Link to this definition">¶</a></dt>

  591. <dd><p>Return the adjusted exponent after shifting out the coefficient’s

  592. rightmost digits until only the lead digit remains:

  593. <code class="docutils literal notranslate"><span class="pre">Decimal('321e+5').adjusted()</span></code> returns seven.  Used for determining the

  594. position of the most significant digit with respect to the decimal point.</p>

  595. </dd></dl>

  596. 

  597. <dl class="py method">

  598. <dt class="sig sig-object py" id="decimal.Decimal.as_integer_ratio">

  599. <span class="sig-name descname"><span class="pre">as_integer_ratio</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.as_integer_ratio" title="Link to this definition">¶</a></dt>

  600. <dd><p>Return a pair <code class="docutils literal notranslate"><span class="pre">(n,</span> <span class="pre">d)</span></code> of integers that represent the given

  601. <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance as a fraction, in lowest terms and

  602. with a positive denominator:</p>

  603. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;-3.14&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">as_integer_ratio</span><span class="p">()</span>

  604. <span class="go">(-157, 50)</span>

  605. </pre></div>

  606. </div>

  607. <p>The conversion is exact.  Raise OverflowError on infinities and ValueError

  608. on NaNs.</p>

  609. </dd></dl>

  610. 

  611. <div class="versionadded">

  612. <p><span class="versionmodified added">New in version 3.6.</span></p>

  613. </div>

  614. <dl class="py method">

  615. <dt class="sig sig-object py" id="decimal.Decimal.as_tuple">

  616. <span class="sig-name descname"><span class="pre">as_tuple</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.as_tuple" title="Link to this definition">¶</a></dt>

  617. <dd><p>Return a <a class="reference internal" href="../glossary.html#term-named-tuple"><span class="xref std std-term">named tuple</span></a> representation of the number:

  618. <code class="docutils literal notranslate"><span class="pre">DecimalTuple(sign,</span> <span class="pre">digits,</span> <span class="pre">exponent)</span></code>.</p>

  619. </dd></dl>

  620. 

  621. <dl class="py method">

  622. <dt class="sig sig-object py" id="decimal.Decimal.canonical">

  623. <span class="sig-name descname"><span class="pre">canonical</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.canonical" title="Link to this definition">¶</a></dt>

  624. <dd><p>Return the canonical encoding of the argument.  Currently, the encoding of

  625. a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance is always canonical, so this operation returns

  626. its argument unchanged.</p>

  627. </dd></dl>

  628. 

  629. <dl class="py method">

  630. <dt class="sig sig-object py" id="decimal.Decimal.compare">

  631. <span class="sig-name descname"><span class="pre">compare</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare" title="Link to this definition">¶</a></dt>

  632. <dd><p>Compare the values of two Decimal instances.  <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><code class="xref py py-meth docutils literal notranslate"><span class="pre">compare()</span></code></a> returns a

  633. Decimal instance, and if either operand is a NaN then the result is a

  634. NaN:</p>

  635. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="ow">or</span> <span class="n">b</span> <span class="ow">is</span> <span class="n">a</span> <span class="n">NaN</span>  <span class="o">==&gt;</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;NaN&#39;</span><span class="p">)</span>

  636. <span class="n">a</span> <span class="o">&lt;</span> <span class="n">b</span>            <span class="o">==&gt;</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;-1&#39;</span><span class="p">)</span>

  637. <span class="n">a</span> <span class="o">==</span> <span class="n">b</span>           <span class="o">==&gt;</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">)</span>

  638. <span class="n">a</span> <span class="o">&gt;</span> <span class="n">b</span>            <span class="o">==&gt;</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1&#39;</span><span class="p">)</span>

  639. </pre></div>

  640. </div>

  641. </dd></dl>

  642. 

  643. <dl class="py method">

  644. <dt class="sig sig-object py" id="decimal.Decimal.compare_signal">

  645. <span class="sig-name descname"><span class="pre">compare_signal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare_signal" title="Link to this definition">¶</a></dt>

  646. <dd><p>This operation is identical to the <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><code class="xref py py-meth docutils literal notranslate"><span class="pre">compare()</span></code></a> method, except that all

  647. NaNs signal.  That is, if neither operand is a signaling NaN then any

  648. quiet NaN operand is treated as though it were a signaling NaN.</p>

  649. </dd></dl>

  650. 

  651. <dl class="py method">

  652. <dt class="sig sig-object py" id="decimal.Decimal.compare_total">

  653. <span class="sig-name descname"><span class="pre">compare_total</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare_total" title="Link to this definition">¶</a></dt>

  654. <dd><p>Compare two operands using their abstract representation rather than their

  655. numerical value.  Similar to the <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><code class="xref py py-meth docutils literal notranslate"><span class="pre">compare()</span></code></a> method, but the result

  656. gives a total ordering on <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instances.  Two

  657. <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instances with the same numeric value but different

  658. representations compare unequal in this ordering:</p>

  659. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;12.0&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">compare_total</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;12&#39;</span><span class="p">))</span>

  660. <span class="go">Decimal(&#39;-1&#39;)</span>

  661. </pre></div>

  662. </div>

  663. <p>Quiet and signaling NaNs are also included in the total ordering.  The

  664. result of this function is <code class="docutils literal notranslate"><span class="pre">Decimal('0')</span></code> if both operands have the same

  665. representation, <code class="docutils literal notranslate"><span class="pre">Decimal('-1')</span></code> if the first operand is lower in the

  666. total order than the second, and <code class="docutils literal notranslate"><span class="pre">Decimal('1')</span></code> if the first operand is

  667. higher in the total order than the second operand.  See the specification

  668. for details of the total order.</p>

  669. <p>This operation is unaffected by context and is quiet: no flags are changed

  670. and no rounding is performed.  As an exception, the C version may raise

  671. InvalidOperation if the second operand cannot be converted exactly.</p>

  672. </dd></dl>

  673. 

  674. <dl class="py method">

  675. <dt class="sig sig-object py" id="decimal.Decimal.compare_total_mag">

  676. <span class="sig-name descname"><span class="pre">compare_total_mag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare_total_mag" title="Link to this definition">¶</a></dt>

  677. <dd><p>Compare two operands using their abstract representation rather than their

  678. value as in <a class="reference internal" href="#decimal.Decimal.compare_total" title="decimal.Decimal.compare_total"><code class="xref py py-meth docutils literal notranslate"><span class="pre">compare_total()</span></code></a>, but ignoring the sign of each operand.

  679. <code class="docutils literal notranslate"><span class="pre">x.compare_total_mag(y)</span></code> is equivalent to

  680. <code class="docutils literal notranslate"><span class="pre">x.copy_abs().compare_total(y.copy_abs())</span></code>.</p>

  681. <p>This operation is unaffected by context and is quiet: no flags are changed

  682. and no rounding is performed.  As an exception, the C version may raise

  683. InvalidOperation if the second operand cannot be converted exactly.</p>

  684. </dd></dl>

  685. 

  686. <dl class="py method">

  687. <dt class="sig sig-object py" id="decimal.Decimal.conjugate">

  688. <span class="sig-name descname"><span class="pre">conjugate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.conjugate" title="Link to this definition">¶</a></dt>

  689. <dd><p>Just returns self, this method is only to comply with the Decimal

  690. Specification.</p>

  691. </dd></dl>

  692. 

  693. <dl class="py method">

  694. <dt class="sig sig-object py" id="decimal.Decimal.copy_abs">

  695. <span class="sig-name descname"><span class="pre">copy_abs</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.copy_abs" title="Link to this definition">¶</a></dt>

  696. <dd><p>Return the absolute value of the argument.  This operation is unaffected

  697. by the context and is quiet: no flags are changed and no rounding is

  698. performed.</p>

  699. </dd></dl>

  700. 

  701. <dl class="py method">

  702. <dt class="sig sig-object py" id="decimal.Decimal.copy_negate">

  703. <span class="sig-name descname"><span class="pre">copy_negate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.copy_negate" title="Link to this definition">¶</a></dt>

  704. <dd><p>Return the negation of the argument.  This operation is unaffected by the

  705. context and is quiet: no flags are changed and no rounding is performed.</p>

  706. </dd></dl>

  707. 

  708. <dl class="py method">

  709. <dt class="sig sig-object py" id="decimal.Decimal.copy_sign">

  710. <span class="sig-name descname"><span class="pre">copy_sign</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.copy_sign" title="Link to this definition">¶</a></dt>

  711. <dd><p>Return a copy of the first operand with the sign set to be the same as the

  712. sign of the second operand.  For example:</p>

  713. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;2.3&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">copy_sign</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;-1.5&#39;</span><span class="p">))</span>

  714. <span class="go">Decimal(&#39;-2.3&#39;)</span>

  715. </pre></div>

  716. </div>

  717. <p>This operation is unaffected by context and is quiet: no flags are changed

  718. and no rounding is performed.  As an exception, the C version may raise

  719. InvalidOperation if the second operand cannot be converted exactly.</p>

  720. </dd></dl>

  721. 

  722. <dl class="py method">

  723. <dt class="sig sig-object py" id="decimal.Decimal.exp">

  724. <span class="sig-name descname"><span class="pre">exp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.exp" title="Link to this definition">¶</a></dt>

  725. <dd><p>Return the value of the (natural) exponential function <code class="docutils literal notranslate"><span class="pre">e**x</span></code> at the

  726. given number.  The result is correctly rounded using the

  727. <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>

  728. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">exp</span><span class="p">()</span>

  729. <span class="go">Decimal(&#39;2.718281828459045235360287471&#39;)</span>

  730. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">321</span><span class="p">)</span><span class="o">.</span><span class="n">exp</span><span class="p">()</span>

  731. <span class="go">Decimal(&#39;2.561702493119680037517373933E+139&#39;)</span>

  732. </pre></div>

  733. </div>

  734. </dd></dl>

  735. 

  736. <dl class="py method">

  737. <dt class="sig sig-object py" id="decimal.Decimal.from_float">

  738. <em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_float</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.from_float" title="Link to this definition">¶</a></dt>

  739. <dd><p>Alternative constructor that only accepts instances of <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> or

  740. <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>.</p>

  741. <p>Note <code class="docutils literal notranslate"><span class="pre">Decimal.from_float(0.1)</span></code> is not the same as <code class="docutils literal notranslate"><span class="pre">Decimal('0.1')</span></code>.

  742. Since 0.1 is not exactly representable in binary floating point, the

  743. value is stored as the nearest representable value which is

  744. <code class="docutils literal notranslate"><span class="pre">0x1.999999999999ap-4</span></code>.  That equivalent value in decimal is

  745. <code class="docutils literal notranslate"><span class="pre">0.1000000000000000055511151231257827021181583404541015625</span></code>.</p>

  746. <div class="admonition note">

  747. <p class="admonition-title">Note</p>

  748. <p>From Python 3.2 onwards, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance

  749. can also be constructed directly from a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>.</p>

  750. </div>

  751. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="o">.</span><span class="n">from_float</span><span class="p">(</span><span class="mf">0.1</span><span class="p">)</span>

  752. <span class="go">Decimal(&#39;0.1000000000000000055511151231257827021181583404541015625&#39;)</span>

  753. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="o">.</span><span class="n">from_float</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="s1">&#39;nan&#39;</span><span class="p">))</span>

  754. <span class="go">Decimal(&#39;NaN&#39;)</span>

  755. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="o">.</span><span class="n">from_float</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="s1">&#39;inf&#39;</span><span class="p">))</span>

  756. <span class="go">Decimal(&#39;Infinity&#39;)</span>

  757. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="o">.</span><span class="n">from_float</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="s1">&#39;-inf&#39;</span><span class="p">))</span>

  758. <span class="go">Decimal(&#39;-Infinity&#39;)</span>

  759. </pre></div>

  760. </div>

  761. <div class="versionadded">

  762. <p><span class="versionmodified added">New in version 3.1.</span></p>

  763. </div>

  764. </dd></dl>

  765. 

  766. <dl class="py method">

  767. <dt class="sig sig-object py" id="decimal.Decimal.fma">

  768. <span class="sig-name descname"><span class="pre">fma</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">third</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.fma" title="Link to this definition">¶</a></dt>

  769. <dd><p>Fused multiply-add.  Return self*other+third with no rounding of the

  770. intermediate product self*other.</p>

  771. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">fma</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>

  772. <span class="go">Decimal(&#39;11&#39;)</span>

  773. </pre></div>

  774. </div>

  775. </dd></dl>

  776. 

  777. <dl class="py method">

  778. <dt class="sig sig-object py" id="decimal.Decimal.is_canonical">

  779. <span class="sig-name descname"><span class="pre">is_canonical</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_canonical" title="Link to this definition">¶</a></dt>

  780. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is canonical and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a>

  781. otherwise.  Currently, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance is always canonical, so

  782. this operation always returns <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a>.</p>

  783. </dd></dl>

  784. 

  785. <dl class="py method">

  786. <dt class="sig sig-object py" id="decimal.Decimal.is_finite">

  787. <span class="sig-name descname"><span class="pre">is_finite</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_finite" title="Link to this definition">¶</a></dt>

  788. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a finite number, and

  789. <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> if the argument is an infinity or a NaN.</p>

  790. </dd></dl>

  791. 

  792. <dl class="py method">

  793. <dt class="sig sig-object py" id="decimal.Decimal.is_infinite">

  794. <span class="sig-name descname"><span class="pre">is_infinite</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_infinite" title="Link to this definition">¶</a></dt>

  795. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is either positive or negative

  796. infinity and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>

  797. </dd></dl>

  798. 

  799. <dl class="py method">

  800. <dt class="sig sig-object py" id="decimal.Decimal.is_nan">

  801. <span class="sig-name descname"><span class="pre">is_nan</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_nan" title="Link to this definition">¶</a></dt>

  802. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a (quiet or signaling) NaN and

  803. <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>

  804. </dd></dl>

  805. 

  806. <dl class="py method">

  807. <dt class="sig sig-object py" id="decimal.Decimal.is_normal">

  808. <span class="sig-name descname"><span class="pre">is_normal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_normal" title="Link to this definition">¶</a></dt>

  809. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a <em>normal</em> finite number.  Return

  810. <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> if the argument is zero, subnormal, infinite or a NaN.</p>

  811. </dd></dl>

  812. 

  813. <dl class="py method">

  814. <dt class="sig sig-object py" id="decimal.Decimal.is_qnan">

  815. <span class="sig-name descname"><span class="pre">is_qnan</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_qnan" title="Link to this definition">¶</a></dt>

  816. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a quiet NaN, and

  817. <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>

  818. </dd></dl>

  819. 

  820. <dl class="py method">

  821. <dt class="sig sig-object py" id="decimal.Decimal.is_signed">

  822. <span class="sig-name descname"><span class="pre">is_signed</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_signed" title="Link to this definition">¶</a></dt>

  823. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument has a negative sign and

  824. <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.  Note that zeros and NaNs can both carry signs.</p>

  825. </dd></dl>

  826. 

  827. <dl class="py method">

  828. <dt class="sig sig-object py" id="decimal.Decimal.is_snan">

  829. <span class="sig-name descname"><span class="pre">is_snan</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_snan" title="Link to this definition">¶</a></dt>

  830. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a signaling NaN and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a>

  831. otherwise.</p>

  832. </dd></dl>

  833. 

  834. <dl class="py method">

  835. <dt class="sig sig-object py" id="decimal.Decimal.is_subnormal">

  836. <span class="sig-name descname"><span class="pre">is_subnormal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_subnormal" title="Link to this definition">¶</a></dt>

  837. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is subnormal, and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a>

  838. otherwise.</p>

  839. </dd></dl>

  840. 

  841. <dl class="py method">

  842. <dt class="sig sig-object py" id="decimal.Decimal.is_zero">

  843. <span class="sig-name descname"><span class="pre">is_zero</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_zero" title="Link to this definition">¶</a></dt>

  844. <dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a (positive or negative) zero and

  845. <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>

  846. </dd></dl>

  847. 

  848. <dl class="py method">

  849. <dt class="sig sig-object py" id="decimal.Decimal.ln">

  850. <span class="sig-name descname"><span class="pre">ln</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.ln" title="Link to this definition">¶</a></dt>

  851. <dd><p>Return the natural (base e) logarithm of the operand.  The result is

  852. correctly rounded using the <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>

  853. </dd></dl>

  854. 

  855. <dl class="py method">

  856. <dt class="sig sig-object py" id="decimal.Decimal.log10">

  857. <span class="sig-name descname"><span class="pre">log10</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.log10" title="Link to this definition">¶</a></dt>

  858. <dd><p>Return the base ten logarithm of the operand.  The result is correctly

  859. rounded using the <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>

  860. </dd></dl>

  861. 

  862. <dl class="py method">

  863. <dt class="sig sig-object py" id="decimal.Decimal.logb">

  864. <span class="sig-name descname"><span class="pre">logb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logb" title="Link to this definition">¶</a></dt>

  865. <dd><p>For a nonzero number, return the adjusted exponent of its operand as a

  866. <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance.  If the operand is a zero then

  867. <code class="docutils literal notranslate"><span class="pre">Decimal('-Infinity')</span></code> is returned and the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a> flag

  868. is raised.  If the operand is an infinity then <code class="docutils literal notranslate"><span class="pre">Decimal('Infinity')</span></code> is

  869. returned.</p>

  870. </dd></dl>

  871. 

  872. <dl class="py method">

  873. <dt class="sig sig-object py" id="decimal.Decimal.logical_and">

  874. <span class="sig-name descname"><span class="pre">logical_and</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_and" title="Link to this definition">¶</a></dt>

  875. <dd><p><a class="reference internal" href="#decimal.Decimal.logical_and" title="decimal.Decimal.logical_and"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_and()</span></code></a> is a logical operation which takes two <em>logical

  876. operands</em> (see <a class="reference internal" href="#logical-operands-label"><span class="std std-ref">Logical operands</span></a>).  The result is the

  877. digit-wise <code class="docutils literal notranslate"><span class="pre">and</span></code> of the two operands.</p>

  878. </dd></dl>

  879. 

  880. <dl class="py method">

  881. <dt class="sig sig-object py" id="decimal.Decimal.logical_invert">

  882. <span class="sig-name descname"><span class="pre">logical_invert</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_invert" title="Link to this definition">¶</a></dt>

  883. <dd><p><a class="reference internal" href="#decimal.Decimal.logical_invert" title="decimal.Decimal.logical_invert"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_invert()</span></code></a> is a logical operation.  The

  884. result is the digit-wise inversion of the operand.</p>

  885. </dd></dl>

  886. 

  887. <dl class="py method">

  888. <dt class="sig sig-object py" id="decimal.Decimal.logical_or">

  889. <span class="sig-name descname"><span class="pre">logical_or</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_or" title="Link to this definition">¶</a></dt>

  890. <dd><p><a class="reference internal" href="#decimal.Decimal.logical_or" title="decimal.Decimal.logical_or"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_or()</span></code></a> is a logical operation which takes two <em>logical

  891. operands</em> (see <a class="reference internal" href="#logical-operands-label"><span class="std std-ref">Logical operands</span></a>).  The result is the

  892. digit-wise <code class="docutils literal notranslate"><span class="pre">or</span></code> of the two operands.</p>

  893. </dd></dl>

  894. 

  895. <dl class="py method">

  896. <dt class="sig sig-object py" id="decimal.Decimal.logical_xor">

  897. <span class="sig-name descname"><span class="pre">logical_xor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_xor" title="Link to this definition">¶</a></dt>

  898. <dd><p><a class="reference internal" href="#decimal.Decimal.logical_xor" title="decimal.Decimal.logical_xor"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_xor()</span></code></a> is a logical operation which takes two <em>logical

  899. operands</em> (see <a class="reference internal" href="#logical-operands-label"><span class="std std-ref">Logical operands</span></a>).  The result is the

  900. digit-wise exclusive or of the two operands.</p>

  901. </dd></dl>

  902. 

  903. <dl class="py method">

  904. <dt class="sig sig-object py" id="decimal.Decimal.max">

  905. <span class="sig-name descname"><span class="pre">max</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.max" title="Link to this definition">¶</a></dt>

  906. <dd><p>Like <code class="docutils literal notranslate"><span class="pre">max(self,</span> <span class="pre">other)</span></code> except that the context rounding rule is applied

  907. before returning and that <code class="docutils literal notranslate"><span class="pre">NaN</span></code> values are either signaled or

  908. ignored (depending on the context and whether they are signaling or

  909. quiet).</p>

  910. </dd></dl>

  911. 

  912. <dl class="py method">

  913. <dt class="sig sig-object py" id="decimal.Decimal.max_mag">

  914. <span class="sig-name descname"><span class="pre">max_mag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.max_mag" title="Link to this definition">¶</a></dt>

  915. <dd><p>Similar to the <a class="reference internal" href="#decimal.Decimal.max" title="decimal.Decimal.max"><code class="xref py py-meth docutils literal notranslate"><span class="pre">max()</span></code></a> method, but the comparison is done using the

  916. absolute values of the operands.</p>

  917. </dd></dl>

  918. 

  919. <dl class="py method">

  920. <dt class="sig sig-object py" id="decimal.Decimal.min">

  921. <span class="sig-name descname"><span class="pre">min</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.min" title="Link to this definition">¶</a></dt>

  922. <dd><p>Like <code class="docutils literal notranslate"><span class="pre">min(self,</span> <span class="pre">other)</span></code> except that the context rounding rule is applied

  923. before returning and that <code class="docutils literal notranslate"><span class="pre">NaN</span></code> values are either signaled or

  924. ignored (depending on the context and whether they are signaling or

  925. quiet).</p>

  926. </dd></dl>

  927. 

  928. <dl class="py method">

  929. <dt class="sig sig-object py" id="decimal.Decimal.min_mag">

  930. <span class="sig-name descname"><span class="pre">min_mag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.min_mag" title="Link to this definition">¶</a></dt>

  931. <dd><p>Similar to the <a class="reference internal" href="#decimal.Decimal.min" title="decimal.Decimal.min"><code class="xref py py-meth docutils literal notranslate"><span class="pre">min()</span></code></a> method, but the comparison is done using the

  932. absolute values of the operands.</p>

  933. </dd></dl>

  934. 

  935. <dl class="py method">

  936. <dt class="sig sig-object py" id="decimal.Decimal.next_minus">

  937. <span class="sig-name descname"><span class="pre">next_minus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.next_minus" title="Link to this definition">¶</a></dt>

  938. <dd><p>Return the largest number representable in the given context (or in the

  939. current thread’s context if no context is given) that is smaller than the

  940. given operand.</p>

  941. </dd></dl>

  942. 

  943. <dl class="py method">

  944. <dt class="sig sig-object py" id="decimal.Decimal.next_plus">

  945. <span class="sig-name descname"><span class="pre">next_plus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.next_plus" title="Link to this definition">¶</a></dt>

  946. <dd><p>Return the smallest number representable in the given context (or in the

  947. current thread’s context if no context is given) that is larger than the

  948. given operand.</p>

  949. </dd></dl>

  950. 

  951. <dl class="py method">

  952. <dt class="sig sig-object py" id="decimal.Decimal.next_toward">

  953. <span class="sig-name descname"><span class="pre">next_toward</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.next_toward" title="Link to this definition">¶</a></dt>

  954. <dd><p>If the two operands are unequal, return the number closest to the first

  955. operand in the direction of the second operand.  If both operands are

  956. numerically equal, return a copy of the first operand with the sign set to

  957. be the same as the sign of the second operand.</p>

  958. </dd></dl>

  959. 

  960. <dl class="py method">

  961. <dt class="sig sig-object py" id="decimal.Decimal.normalize">

  962. <span class="sig-name descname"><span class="pre">normalize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.normalize" title="Link to this definition">¶</a></dt>

  963. <dd><p>Used for producing canonical values of an equivalence

  964. class within either the current context or the specified context.</p>

  965. <p>This has the same semantics as the unary plus operation, except that if

  966. the final result is finite it is reduced to its simplest form, with all

  967. trailing zeros removed and its sign preserved. That is, while the

  968. coefficient is non-zero and a multiple of ten the coefficient is divided

  969. by ten and the exponent is incremented by 1. Otherwise (the coefficient is

  970. zero) the exponent is set to 0. In all cases the sign is unchanged.</p>

  971. <p>For example, <code class="docutils literal notranslate"><span class="pre">Decimal('32.100')</span></code> and <code class="docutils literal notranslate"><span class="pre">Decimal('0.321000e+2')</span></code> both

  972. normalize to the equivalent value <code class="docutils literal notranslate"><span class="pre">Decimal('32.1')</span></code>.</p>

  973. <p>Note that rounding is applied <em>before</em> reducing to simplest form.</p>

  974. <p>In the latest versions of the specification, this operation is also known

  975. as <code class="docutils literal notranslate"><span class="pre">reduce</span></code>.</p>

  976. </dd></dl>

  977. 

  978. <dl class="py method">

  979. <dt class="sig sig-object py" id="decimal.Decimal.number_class">

  980. <span class="sig-name descname"><span class="pre">number_class</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.number_class" title="Link to this definition">¶</a></dt>

  981. <dd><p>Return a string describing the <em>class</em> of the operand.  The returned value

  982. is one of the following ten strings.</p>

  983. <ul class="simple">

  984. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;-Infinity&quot;</span></code>, indicating that the operand is negative infinity.</p></li>

  985. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;-Normal&quot;</span></code>, indicating that the operand is a negative normal number.</p></li>

  986. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;-Subnormal&quot;</span></code>, indicating that the operand is negative and subnormal.</p></li>

  987. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;-Zero&quot;</span></code>, indicating that the operand is a negative zero.</p></li>

  988. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;+Zero&quot;</span></code>, indicating that the operand is a positive zero.</p></li>

  989. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;+Subnormal&quot;</span></code>, indicating that the operand is positive and subnormal.</p></li>

  990. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;+Normal&quot;</span></code>, indicating that the operand is a positive normal number.</p></li>

  991. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;+Infinity&quot;</span></code>, indicating that the operand is positive infinity.</p></li>

  992. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;NaN&quot;</span></code>, indicating that the operand is a quiet NaN (Not a Number).</p></li>

  993. <li><p><code class="docutils literal notranslate"><span class="pre">&quot;sNaN&quot;</span></code>, indicating that the operand is a signaling NaN.</p></li>

  994. </ul>

  995. </dd></dl>

  996. 

  997. <dl class="py method">

  998. <dt class="sig sig-object py" id="decimal.Decimal.quantize">

  999. <span class="sig-name descname"><span class="pre">quantize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">exp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rounding</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.quantize" title="Link to this definition">¶</a></dt>

  1000. <dd><p>Return a value equal to the first operand after rounding and having the

  1001. exponent of the second operand.</p>

  1002. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1.41421356&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1.000&#39;</span><span class="p">))</span>

  1003. <span class="go">Decimal(&#39;1.414&#39;)</span>

  1004. </pre></div>

  1005. </div>

  1006. <p>Unlike other operations, if the length of the coefficient after the

  1007. quantize operation would be greater than precision, then an

  1008. <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a> is signaled. This guarantees that, unless there

  1009. is an error condition, the quantized exponent is always equal to that of

  1010. the right-hand operand.</p>

  1011. <p>Also unlike other operations, quantize never signals Underflow, even if

  1012. the result is subnormal and inexact.</p>

  1013. <p>If the exponent of the second operand is larger than that of the first

  1014. then rounding may be necessary.  In this case, the rounding mode is

  1015. determined by the <code class="docutils literal notranslate"><span class="pre">rounding</span></code> argument if given, else by the given

  1016. <code class="docutils literal notranslate"><span class="pre">context</span></code> argument; if neither argument is given the rounding mode of

  1017. the current thread’s context is used.</p>

  1018. <p>An error is returned whenever the resulting exponent is greater than

  1019. <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emax</span></code> or less than <a class="reference internal" href="#decimal.Context.Etiny" title="decimal.Context.Etiny"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Etiny()</span></code></a>.</p>

  1020. </dd></dl>

  1021. 

  1022. <dl class="py method">

  1023. <dt class="sig sig-object py" id="decimal.Decimal.radix">

  1024. <span class="sig-name descname"><span class="pre">radix</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.radix" title="Link to this definition">¶</a></dt>

  1025. <dd><p>Return <code class="docutils literal notranslate"><span class="pre">Decimal(10)</span></code>, the radix (base) in which the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>

  1026. class does all its arithmetic.  Included for compatibility with the

  1027. specification.</p>

  1028. </dd></dl>

  1029. 

  1030. <dl class="py method">

  1031. <dt class="sig sig-object py" id="decimal.Decimal.remainder_near">

  1032. <span class="sig-name descname"><span class="pre">remainder_near</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.remainder_near" title="Link to this definition">¶</a></dt>

  1033. <dd><p>Return the remainder from dividing <em>self</em> by <em>other</em>.  This differs from

  1034. <code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">%</span> <span class="pre">other</span></code> in that the sign of the remainder is chosen so as to

  1035. minimize its absolute value.  More precisely, the return value is

  1036. <code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">-</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">other</span></code> where <code class="docutils literal notranslate"><span class="pre">n</span></code> is the integer nearest to the exact

  1037. value of <code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">/</span> <span class="pre">other</span></code>, and if two integers are equally near then the

  1038. even one is chosen.</p>

  1039. <p>If the result is zero then its sign will be the sign of <em>self</em>.</p>

  1040. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">18</span><span class="p">)</span><span class="o">.</span><span class="n">remainder_near</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>

  1041. <span class="go">Decimal(&#39;-2&#39;)</span>

  1042. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">25</span><span class="p">)</span><span class="o">.</span><span class="n">remainder_near</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>

  1043. <span class="go">Decimal(&#39;5&#39;)</span>

  1044. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">35</span><span class="p">)</span><span class="o">.</span><span class="n">remainder_near</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">))</span>

  1045. <span class="go">Decimal(&#39;-5&#39;)</span>

  1046. </pre></div>

  1047. </div>

  1048. </dd></dl>

  1049. 

  1050. <dl class="py method">

  1051. <dt class="sig sig-object py" id="decimal.Decimal.rotate">

  1052. <span class="sig-name descname"><span class="pre">rotate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.rotate" title="Link to this definition">¶</a></dt>

  1053. <dd><p>Return the result of rotating the digits of the first operand by an amount

  1054. specified by the second operand.  The second operand must be an integer in

  1055. the range -precision through precision.  The absolute value of the second

  1056. operand gives the number of places to rotate.  If the second operand is

  1057. positive then rotation is to the left; otherwise rotation is to the right.

  1058. The coefficient of the first operand is padded on the left with zeros to

  1059. length precision if necessary.  The sign and exponent of the first operand

  1060. are unchanged.</p>

  1061. </dd></dl>

  1062. 

  1063. <dl class="py method">

  1064. <dt class="sig sig-object py" id="decimal.Decimal.same_quantum">

  1065. <span class="sig-name descname"><span class="pre">same_quantum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.same_quantum" title="Link to this definition">¶</a></dt>

  1066. <dd><p>Test whether self and other have the same exponent or whether both are

  1067. <code class="docutils literal notranslate"><span class="pre">NaN</span></code>.</p>

  1068. <p>This operation is unaffected by context and is quiet: no flags are changed

  1069. and no rounding is performed.  As an exception, the C version may raise

  1070. InvalidOperation if the second operand cannot be converted exactly.</p>

  1071. </dd></dl>

  1072. 

  1073. <dl class="py method">

  1074. <dt class="sig sig-object py" id="decimal.Decimal.scaleb">

  1075. <span class="sig-name descname"><span class="pre">scaleb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.scaleb" title="Link to this definition">¶</a></dt>

  1076. <dd><p>Return the first operand with exponent adjusted by the second.

  1077. Equivalently, return the first operand multiplied by <code class="docutils literal notranslate"><span class="pre">10**other</span></code>.  The

  1078. second operand must be an integer.</p>

  1079. </dd></dl>

  1080. 

  1081. <dl class="py method">

  1082. <dt class="sig sig-object py" id="decimal.Decimal.shift">

  1083. <span class="sig-name descname"><span class="pre">shift</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.shift" title="Link to this definition">¶</a></dt>

  1084. <dd><p>Return the result of shifting the digits of the first operand by an amount

  1085. specified by the second operand.  The second operand must be an integer in

  1086. the range -precision through precision.  The absolute value of the second

  1087. operand gives the number of places to shift.  If the second operand is

  1088. positive then the shift is to the left; otherwise the shift is to the

  1089. right.  Digits shifted into the coefficient are zeros.  The sign and

  1090. exponent of the first operand are unchanged.</p>

  1091. </dd></dl>

  1092. 

  1093. <dl class="py method">

  1094. <dt class="sig sig-object py" id="decimal.Decimal.sqrt">

  1095. <span class="sig-name descname"><span class="pre">sqrt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.sqrt" title="Link to this definition">¶</a></dt>

  1096. <dd><p>Return the square root of the argument to full precision.</p>

  1097. </dd></dl>

  1098. 

  1099. <dl class="py method">

  1100. <dt class="sig sig-object py" id="decimal.Decimal.to_eng_string">

  1101. <span class="sig-name descname"><span class="pre">to_eng_string</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_eng_string" title="Link to this definition">¶</a></dt>

  1102. <dd><p>Convert to a string, using engineering notation if an exponent is needed.</p>

  1103. <p>Engineering notation has an exponent which is a multiple of 3.  This

  1104. can leave up to 3 digits to the left of the decimal place and may

  1105. require the addition of either one or two trailing zeros.</p>

  1106. <p>For example, this converts <code class="docutils literal notranslate"><span class="pre">Decimal('123E+1')</span></code> to <code class="docutils literal notranslate"><span class="pre">Decimal('1.23E+3')</span></code>.</p>

  1107. </dd></dl>

  1108. 

  1109. <dl class="py method">

  1110. <dt class="sig sig-object py" id="decimal.Decimal.to_integral">

  1111. <span class="sig-name descname"><span class="pre">to_integral</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rounding</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_integral" title="Link to this definition">¶</a></dt>

  1112. <dd><p>Identical to the <a class="reference internal" href="#decimal.Decimal.to_integral_value" title="decimal.Decimal.to_integral_value"><code class="xref py py-meth docutils literal notranslate"><span class="pre">to_integral_value()</span></code></a> method.  The <code class="docutils literal notranslate"><span class="pre">to_integral</span></code>

  1113. name has been kept for compatibility with older versions.</p>

  1114. </dd></dl>

  1115. 

  1116. <dl class="py method">

  1117. <dt class="sig sig-object py" id="decimal.Decimal.to_integral_exact">

  1118. <span class="sig-name descname"><span class="pre">to_integral_exact</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rounding</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_integral_exact" title="Link to this definition">¶</a></dt>

  1119. <dd><p>Round to the nearest integer, signaling <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate"><span class="pre">Inexact</span></code></a> or

  1120. <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal notranslate"><span class="pre">Rounded</span></code></a> as appropriate if rounding occurs.  The rounding mode is

  1121. determined by the <code class="docutils literal notranslate"><span class="pre">rounding</span></code> parameter if given, else by the given

  1122. <code class="docutils literal notranslate"><span class="pre">context</span></code>.  If neither parameter is given then the rounding mode of the

  1123. current context is used.</p>

  1124. </dd></dl>

  1125. 

  1126. <dl class="py method">

  1127. <dt class="sig sig-object py" id="decimal.Decimal.to_integral_value">

  1128. <span class="sig-name descname"><span class="pre">to_integral_value</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rounding</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">context</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_integral_value" title="Link to this definition">¶</a></dt>

  1129. <dd><p>Round to the nearest integer without signaling <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate"><span class="pre">Inexact</span></code></a> or

  1130. <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal notranslate"><span class="pre">Rounded</span></code></a>.  If given, applies <em>rounding</em>; otherwise, uses the

  1131. rounding method in either the supplied <em>context</em> or the current context.</p>

  1132. </dd></dl>

  1133. 

  1134. </dd></dl>

  1135. 

  1136. <section id="logical-operands">

  1137. <span id="logical-operands-label"></span><h3>Logical operands<a class="headerlink" href="#logical-operands" title="Link to this heading">¶</a></h3>

  1138. <p>The <a class="reference internal" href="#decimal.Decimal.logical_and" title="decimal.Decimal.logical_and"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_and()</span></code></a>, <a class="reference internal" href="#decimal.Decimal.logical_invert" title="decimal.Decimal.logical_invert"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_invert()</span></code></a>, <a class="reference internal" href="#decimal.Decimal.logical_or" title="decimal.Decimal.logical_or"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_or()</span></code></a>,

  1139. and <a class="reference internal" href="#decimal.Decimal.logical_xor" title="decimal.Decimal.logical_xor"><code class="xref py py-meth docutils literal notranslate"><span class="pre">logical_xor()</span></code></a> methods expect their arguments to be <em>logical

  1140. operands</em>.  A <em>logical operand</em> is a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance whose

  1141. exponent and sign are both zero, and whose digits are all either

  1142. <code class="docutils literal notranslate"><span class="pre">0</span></code> or <code class="docutils literal notranslate"><span class="pre">1</span></code>.</p>

  1143. </section>

  1144. </section>

  1145. <section id="context-objects">

  1146. <span id="decimal-context"></span><h2>Context objects<a class="headerlink" href="#context-objects" title="Link to this heading">¶</a></h2>

  1147. <p>Contexts are environments for arithmetic operations.  They govern precision, set

  1148. rules for rounding, determine which signals are treated as exceptions, and limit

  1149. the range for exponents.</p>

  1150. <p>Each thread has its own current context which is accessed or changed using the

  1151. <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a> and <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">setcontext()</span></code></a> functions:</p>

  1152. <dl class="py function">

  1153. <dt class="sig sig-object py" id="decimal.getcontext">

  1154. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">getcontext</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.getcontext" title="Link to this definition">¶</a></dt>

  1155. <dd><p>Return the current context for the active thread.</p>

  1156. </dd></dl>

  1157. 

  1158. <dl class="py function">

  1159. <dt class="sig sig-object py" id="decimal.setcontext">

  1160. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">setcontext</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">c</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.setcontext" title="Link to this definition">¶</a></dt>

  1161. <dd><p>Set the current context for the active thread to <em>c</em>.</p>

  1162. </dd></dl>

  1163. 

  1164. <p>You can also use the <a class="reference internal" href="../reference/compound_stmts.html#with"><code class="xref std std-keyword docutils literal notranslate"><span class="pre">with</span></code></a> statement and the <a class="reference internal" href="#decimal.localcontext" title="decimal.localcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">localcontext()</span></code></a>

  1165. function to temporarily change the active context.</p>

  1166. <dl class="py function">

  1167. <dt class="sig sig-object py" id="decimal.localcontext">

  1168. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">localcontext</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ctx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.localcontext" title="Link to this definition">¶</a></dt>

  1169. <dd><p>Return a context manager that will set the current context for the active thread

  1170. to a copy of <em>ctx</em> on entry to the with-statement and restore the previous context

  1171. when exiting the with-statement. If no context is specified, a copy of the

  1172. current context is used.  The <em>kwargs</em> argument is used to set the attributes

  1173. of the new context.</p>

  1174. <p>For example, the following code sets the current decimal precision to 42 places,

  1175. performs a calculation, and then automatically restores the previous context:</p>

  1176. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">decimal</span> <span class="kn">import</span> <span class="n">localcontext</span>

  1177. 

  1178. <span class="k">with</span> <span class="n">localcontext</span><span class="p">()</span> <span class="k">as</span> <span class="n">ctx</span><span class="p">:</span>

  1179.     <span class="n">ctx</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">42</span>   <span class="c1"># Perform a high precision calculation</span>

  1180.     <span class="n">s</span> <span class="o">=</span> <span class="n">calculate_something</span><span class="p">()</span>

  1181. <span class="n">s</span> <span class="o">=</span> <span class="o">+</span><span class="n">s</span>  <span class="c1"># Round the final result back to the default precision</span>

  1182. </pre></div>

  1183. </div>

  1184. <p>Using keyword arguments, the code would be the following:</p>

  1185. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">decimal</span> <span class="kn">import</span> <span class="n">localcontext</span>

  1186. 

  1187. <span class="k">with</span> <span class="n">localcontext</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span> <span class="k">as</span> <span class="n">ctx</span><span class="p">:</span>

  1188.     <span class="n">s</span> <span class="o">=</span> <span class="n">calculate_something</span><span class="p">()</span>

  1189. <span class="n">s</span> <span class="o">=</span> <span class="o">+</span><span class="n">s</span>

  1190. </pre></div>

  1191. </div>

  1192. <p>Raises <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a> if <em>kwargs</em> supplies an attribute that <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> doesn’t

  1193. support.  Raises either <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a> or <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ValueError</span></code></a> if <em>kwargs</em> supplies an

  1194. invalid value for an attribute.</p>

  1195. <div class="versionchanged">

  1196. <p><span class="versionmodified changed">Changed in version 3.11: </span><a class="reference internal" href="#decimal.localcontext" title="decimal.localcontext"><code class="xref py py-meth docutils literal notranslate"><span class="pre">localcontext()</span></code></a> now supports setting context attributes through the use of keyword arguments.</p>

  1197. </div>

  1198. </dd></dl>

  1199. 

  1200. <p>New contexts can also be created using the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> constructor

  1201. described below. In addition, the module provides three pre-made contexts:</p>

  1202. <dl class="py class">

  1203. <dt class="sig sig-object py" id="decimal.BasicContext">

  1204. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">BasicContext</span></span><a class="headerlink" href="#decimal.BasicContext" title="Link to this definition">¶</a></dt>

  1205. <dd><p>This is a standard context defined by the General Decimal Arithmetic

  1206. Specification.  Precision is set to nine.  Rounding is set to

  1207. <a class="reference internal" href="#decimal.ROUND_HALF_UP" title="decimal.ROUND_HALF_UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_UP</span></code></a>.  All flags are cleared.  All traps are enabled (treated

  1208. as exceptions) except <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate"><span class="pre">Inexact</span></code></a>, <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal notranslate"><span class="pre">Rounded</span></code></a>, and

  1209. <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-const docutils literal notranslate"><span class="pre">Subnormal</span></code></a>.</p>

  1210. <p>Because many of the traps are enabled, this context is useful for debugging.</p>

  1211. </dd></dl>

  1212. 

  1213. <dl class="py class">

  1214. <dt class="sig sig-object py" id="decimal.ExtendedContext">

  1215. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ExtendedContext</span></span><a class="headerlink" href="#decimal.ExtendedContext" title="Link to this definition">¶</a></dt>

  1216. <dd><p>This is a standard context defined by the General Decimal Arithmetic

  1217. Specification.  Precision is set to nine.  Rounding is set to

  1218. <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a>.  All flags are cleared.  No traps are enabled (so that

  1219. exceptions are not raised during computations).</p>

  1220. <p>Because the traps are disabled, this context is useful for applications that

  1221. prefer to have result value of <code class="docutils literal notranslate"><span class="pre">NaN</span></code> or <code class="docutils literal notranslate"><span class="pre">Infinity</span></code> instead of

  1222. raising exceptions.  This allows an application to complete a run in the

  1223. presence of conditions that would otherwise halt the program.</p>

  1224. </dd></dl>

  1225. 

  1226. <dl class="py class">

  1227. <dt class="sig sig-object py" id="decimal.DefaultContext">

  1228. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">DefaultContext</span></span><a class="headerlink" href="#decimal.DefaultContext" title="Link to this definition">¶</a></dt>

  1229. <dd><p>This context is used by the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> constructor as a prototype for new

  1230. contexts.  Changing a field (such a precision) has the effect of changing the

  1231. default for new contexts created by the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> constructor.</p>

  1232. <p>This context is most useful in multi-threaded environments.  Changing one of the

  1233. fields before threads are started has the effect of setting system-wide

  1234. defaults.  Changing the fields after threads have started is not recommended as

  1235. it would require thread synchronization to prevent race conditions.</p>

  1236. <p>In single threaded environments, it is preferable to not use this context at

  1237. all.  Instead, simply create contexts explicitly as described below.</p>

  1238. <p>The default values are <code class="xref py py-attr docutils literal notranslate"><span class="pre">Context.prec</span></code>=<code class="docutils literal notranslate"><span class="pre">28</span></code>,

  1239. <code class="xref py py-attr docutils literal notranslate"><span class="pre">Context.rounding</span></code>=<a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a>,

  1240. and enabled traps for <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-class docutils literal notranslate"><span class="pre">Overflow</span></code></a>, <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-class docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a>, and

  1241. <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-class docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a>.</p>

  1242. </dd></dl>

  1243. 

  1244. <p>In addition to the three supplied contexts, new contexts can be created with the

  1245. <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> constructor.</p>

  1246. <dl class="py class">

  1247. <dt class="sig sig-object py" id="decimal.Context">

  1248. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Context</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prec</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rounding</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Emin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Emax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">capitals</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">clamp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">flags</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">traps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context" title="Link to this definition">¶</a></dt>

  1249. <dd><p>Creates a new context.  If a field is not specified or is <a class="reference internal" href="constants.html#None" title="None"><code class="xref py py-const docutils literal notranslate"><span class="pre">None</span></code></a>, the

  1250. default values are copied from the <a class="reference internal" href="#decimal.DefaultContext" title="decimal.DefaultContext"><code class="xref py py-const docutils literal notranslate"><span class="pre">DefaultContext</span></code></a>.  If the <em>flags</em>

  1251. field is not specified or is <a class="reference internal" href="constants.html#None" title="None"><code class="xref py py-const docutils literal notranslate"><span class="pre">None</span></code></a>, all flags are cleared.</p>

  1252. <p><em>prec</em> is an integer in the range [<code class="docutils literal notranslate"><span class="pre">1</span></code>, <a class="reference internal" href="#decimal.MAX_PREC" title="decimal.MAX_PREC"><code class="xref py py-const docutils literal notranslate"><span class="pre">MAX_PREC</span></code></a>] that sets

  1253. the precision for arithmetic operations in the context.</p>

  1254. <p>The <em>rounding</em> option is one of the constants listed in the section

  1255. <a class="reference internal" href="#rounding-modes">Rounding Modes</a>.</p>

  1256. <p>The <em>traps</em> and <em>flags</em> fields list any signals to be set. Generally, new

  1257. contexts should only set traps and leave the flags clear.</p>

  1258. <p>The <em>Emin</em> and <em>Emax</em> fields are integers specifying the outer limits allowable

  1259. for exponents. <em>Emin</em> must be in the range [<a class="reference internal" href="#decimal.MIN_EMIN" title="decimal.MIN_EMIN"><code class="xref py py-const docutils literal notranslate"><span class="pre">MIN_EMIN</span></code></a>, <code class="docutils literal notranslate"><span class="pre">0</span></code>],

  1260. <em>Emax</em> in the range [<code class="docutils literal notranslate"><span class="pre">0</span></code>, <a class="reference internal" href="#decimal.MAX_EMAX" title="decimal.MAX_EMAX"><code class="xref py py-const docutils literal notranslate"><span class="pre">MAX_EMAX</span></code></a>].</p>

  1261. <p>The <em>capitals</em> field is either <code class="docutils literal notranslate"><span class="pre">0</span></code> or <code class="docutils literal notranslate"><span class="pre">1</span></code> (the default). If set to

  1262. <code class="docutils literal notranslate"><span class="pre">1</span></code>, exponents are printed with a capital <code class="docutils literal notranslate"><span class="pre">E</span></code>; otherwise, a

  1263. lowercase <code class="docutils literal notranslate"><span class="pre">e</span></code> is used: <code class="docutils literal notranslate"><span class="pre">Decimal('6.02e+23')</span></code>.</p>

  1264. <p>The <em>clamp</em> field is either <code class="docutils literal notranslate"><span class="pre">0</span></code> (the default) or <code class="docutils literal notranslate"><span class="pre">1</span></code>.

  1265. If set to <code class="docutils literal notranslate"><span class="pre">1</span></code>, the exponent <code class="docutils literal notranslate"><span class="pre">e</span></code> of a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>

  1266. instance representable in this context is strictly limited to the

  1267. range <code class="docutils literal notranslate"><span class="pre">Emin</span> <span class="pre">-</span> <span class="pre">prec</span> <span class="pre">+</span> <span class="pre">1</span> <span class="pre">&lt;=</span> <span class="pre">e</span> <span class="pre">&lt;=</span> <span class="pre">Emax</span> <span class="pre">-</span> <span class="pre">prec</span> <span class="pre">+</span> <span class="pre">1</span></code>.  If <em>clamp</em> is

  1268. <code class="docutils literal notranslate"><span class="pre">0</span></code> then a weaker condition holds: the adjusted exponent of

  1269. the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance is at most <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emax</span></code>.  When <em>clamp</em> is

  1270. <code class="docutils literal notranslate"><span class="pre">1</span></code>, a large normal number will, where possible, have its

  1271. exponent reduced and a corresponding number of zeros added to its

  1272. coefficient, in order to fit the exponent constraints; this

  1273. preserves the value of the number but loses information about

  1274. significant trailing zeros.  For example:</p>

  1275. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">Emax</span><span class="o">=</span><span class="mi">999</span><span class="p">,</span> <span class="n">clamp</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">create_decimal</span><span class="p">(</span><span class="s1">&#39;1.23e999&#39;</span><span class="p">)</span>

  1276. <span class="go">Decimal(&#39;1.23000E+999&#39;)</span>

  1277. </pre></div>

  1278. </div>

  1279. <p>A <em>clamp</em> value of <code class="docutils literal notranslate"><span class="pre">1</span></code> allows compatibility with the

  1280. fixed-width decimal interchange formats specified in IEEE 754.</p>

  1281. <p>The <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> class defines several general purpose methods as well as

  1282. a large number of methods for doing arithmetic directly in a given context.

  1283. In addition, for each of the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> methods described above (with

  1284. the exception of the <a class="reference internal" href="#decimal.Decimal.adjusted" title="decimal.Decimal.adjusted"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjusted()</span></code></a> and <a class="reference internal" href="#decimal.Decimal.as_tuple" title="decimal.Decimal.as_tuple"><code class="xref py py-meth docutils literal notranslate"><span class="pre">as_tuple()</span></code></a> methods) there is

  1285. a corresponding <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> method.  For example, for a <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a>

  1286. instance <code class="docutils literal notranslate"><span class="pre">C</span></code> and <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance <code class="docutils literal notranslate"><span class="pre">x</span></code>, <code class="docutils literal notranslate"><span class="pre">C.exp(x)</span></code> is

  1287. equivalent to <code class="docutils literal notranslate"><span class="pre">x.exp(context=C)</span></code>.  Each <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> method accepts a

  1288. Python integer (an instance of <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>) anywhere that a

  1289. Decimal instance is accepted.</p>

  1290. <dl class="py method">

  1291. <dt class="sig sig-object py" id="decimal.Context.clear_flags">

  1292. <span class="sig-name descname"><span class="pre">clear_flags</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.clear_flags" title="Link to this definition">¶</a></dt>

  1293. <dd><p>Resets all of the flags to <code class="docutils literal notranslate"><span class="pre">0</span></code>.</p>

  1294. </dd></dl>

  1295. 

  1296. <dl class="py method">

  1297. <dt class="sig sig-object py" id="decimal.Context.clear_traps">

  1298. <span class="sig-name descname"><span class="pre">clear_traps</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.clear_traps" title="Link to this definition">¶</a></dt>

  1299. <dd><p>Resets all of the traps to <code class="docutils literal notranslate"><span class="pre">0</span></code>.</p>

  1300. <div class="versionadded">

  1301. <p><span class="versionmodified added">New in version 3.3.</span></p>

  1302. </div>

  1303. </dd></dl>

  1304. 

  1305. <dl class="py method">

  1306. <dt class="sig sig-object py" id="decimal.Context.copy">

  1307. <span class="sig-name descname"><span class="pre">copy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy" title="Link to this definition">¶</a></dt>

  1308. <dd><p>Return a duplicate of the context.</p>

  1309. </dd></dl>

  1310. 

  1311. <dl class="py method">

  1312. <dt class="sig sig-object py" id="decimal.Context.copy_decimal">

  1313. <span class="sig-name descname"><span class="pre">copy_decimal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">num</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_decimal" title="Link to this definition">¶</a></dt>

  1314. <dd><p>Return a copy of the Decimal instance num.</p>

  1315. </dd></dl>

  1316. 

  1317. <dl class="py method">

  1318. <dt class="sig sig-object py" id="decimal.Context.create_decimal">

  1319. <span class="sig-name descname"><span class="pre">create_decimal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">num</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.create_decimal" title="Link to this definition">¶</a></dt>

  1320. <dd><p>Creates a new Decimal instance from <em>num</em> but using <em>self</em> as

  1321. context. Unlike the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> constructor, the context precision,

  1322. rounding method, flags, and traps are applied to the conversion.</p>

  1323. <p>This is useful because constants are often given to a greater precision

  1324. than is needed by the application.  Another benefit is that rounding

  1325. immediately eliminates unintended effects from digits beyond the current

  1326. precision. In the following example, using unrounded inputs means that

  1327. adding zero to a sum can change the result:</p>

  1328. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">3</span>

  1329. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.4445&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1.0023&#39;</span><span class="p">)</span>

  1330. <span class="go">Decimal(&#39;4.45&#39;)</span>

  1331. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.4445&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1.0023&#39;</span><span class="p">)</span>

  1332. <span class="go">Decimal(&#39;4.44&#39;)</span>

  1333. </pre></div>

  1334. </div>

  1335. <p>This method implements the to-number operation of the IBM specification.

  1336. If the argument is a string, no leading or trailing whitespace or

  1337. underscores are permitted.</p>

  1338. </dd></dl>

  1339. 

  1340. <dl class="py method">

  1341. <dt class="sig sig-object py" id="decimal.Context.create_decimal_from_float">

  1342. <span class="sig-name descname"><span class="pre">create_decimal_from_float</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.create_decimal_from_float" title="Link to this definition">¶</a></dt>

  1343. <dd><p>Creates a new Decimal instance from a float <em>f</em> but rounding using <em>self</em>

  1344. as the context.  Unlike the <a class="reference internal" href="#decimal.Decimal.from_float" title="decimal.Decimal.from_float"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Decimal.from_float()</span></code></a> class method,

  1345. the context precision, rounding method, flags, and traps are applied to

  1346. the conversion.</p>

  1347. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">context</span> <span class="o">=</span> <span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">rounding</span><span class="o">=</span><span class="n">ROUND_DOWN</span><span class="p">)</span>

  1348. <span class="gp">&gt;&gt;&gt; </span><span class="n">context</span><span class="o">.</span><span class="n">create_decimal_from_float</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>

  1349. <span class="go">Decimal(&#39;3.1415&#39;)</span>

  1350. <span class="gp">&gt;&gt;&gt; </span><span class="n">context</span> <span class="o">=</span> <span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">traps</span><span class="o">=</span><span class="p">[</span><span class="n">Inexact</span><span class="p">])</span>

  1351. <span class="gp">&gt;&gt;&gt; </span><span class="n">context</span><span class="o">.</span><span class="n">create_decimal_from_float</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>

  1352. <span class="gt">Traceback (most recent call last):</span>

  1353. <span class="w">    </span><span class="o">...</span>

  1354. <span class="gr">decimal.Inexact</span>: <span class="n">None</span>

  1355. </pre></div>

  1356. </div>

  1357. <div class="versionadded">

  1358. <p><span class="versionmodified added">New in version 3.1.</span></p>

  1359. </div>

  1360. </dd></dl>

  1361. 

  1362. <dl class="py method">

  1363. <dt class="sig sig-object py" id="decimal.Context.Etiny">

  1364. <span class="sig-name descname"><span class="pre">Etiny</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.Etiny" title="Link to this definition">¶</a></dt>

  1365. <dd><p>Returns a value equal to <code class="docutils literal notranslate"><span class="pre">Emin</span> <span class="pre">-</span> <span class="pre">prec</span> <span class="pre">+</span> <span class="pre">1</span></code> which is the minimum exponent

  1366. value for subnormal results.  When underflow occurs, the exponent is set

  1367. to <a class="reference internal" href="#decimal.Context.Etiny" title="decimal.Context.Etiny"><code class="xref py py-const docutils literal notranslate"><span class="pre">Etiny</span></code></a>.</p>

  1368. </dd></dl>

  1369. 

  1370. <dl class="py method">

  1371. <dt class="sig sig-object py" id="decimal.Context.Etop">

  1372. <span class="sig-name descname"><span class="pre">Etop</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.Etop" title="Link to this definition">¶</a></dt>

  1373. <dd><p>Returns a value equal to <code class="docutils literal notranslate"><span class="pre">Emax</span> <span class="pre">-</span> <span class="pre">prec</span> <span class="pre">+</span> <span class="pre">1</span></code>.</p>

  1374. </dd></dl>

  1375. 

  1376. <p>The usual approach to working with decimals is to create <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>

  1377. instances and then apply arithmetic operations which take place within the

  1378. current context for the active thread.  An alternative approach is to use

  1379. context methods for calculating within a specific context.  The methods are

  1380. similar to those for the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> class and are only briefly

  1381. recounted here.</p>

  1382. <dl class="py method">

  1383. <dt class="sig sig-object py" id="decimal.Context.abs">

  1384. <span class="sig-name descname"><span class="pre">abs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.abs" title="Link to this definition">¶</a></dt>

  1385. <dd><p>Returns the absolute value of <em>x</em>.</p>

  1386. </dd></dl>

  1387. 

  1388. <dl class="py method">

  1389. <dt class="sig sig-object py" id="decimal.Context.add">

  1390. <span class="sig-name descname"><span class="pre">add</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.add" title="Link to this definition">¶</a></dt>

  1391. <dd><p>Return the sum of <em>x</em> and <em>y</em>.</p>

  1392. </dd></dl>

  1393. 

  1394. <dl class="py method">

  1395. <dt class="sig sig-object py" id="decimal.Context.canonical">

  1396. <span class="sig-name descname"><span class="pre">canonical</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.canonical" title="Link to this definition">¶</a></dt>

  1397. <dd><p>Returns the same Decimal object <em>x</em>.</p>

  1398. </dd></dl>

  1399. 

  1400. <dl class="py method">

  1401. <dt class="sig sig-object py" id="decimal.Context.compare">

  1402. <span class="sig-name descname"><span class="pre">compare</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare" title="Link to this definition">¶</a></dt>

  1403. <dd><p>Compares <em>x</em> and <em>y</em> numerically.</p>

  1404. </dd></dl>

  1405. 

  1406. <dl class="py method">

  1407. <dt class="sig sig-object py" id="decimal.Context.compare_signal">

  1408. <span class="sig-name descname"><span class="pre">compare_signal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare_signal" title="Link to this definition">¶</a></dt>

  1409. <dd><p>Compares the values of the two operands numerically.</p>

  1410. </dd></dl>

  1411. 

  1412. <dl class="py method">

  1413. <dt class="sig sig-object py" id="decimal.Context.compare_total">

  1414. <span class="sig-name descname"><span class="pre">compare_total</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare_total" title="Link to this definition">¶</a></dt>

  1415. <dd><p>Compares two operands using their abstract representation.</p>

  1416. </dd></dl>

  1417. 

  1418. <dl class="py method">

  1419. <dt class="sig sig-object py" id="decimal.Context.compare_total_mag">

  1420. <span class="sig-name descname"><span class="pre">compare_total_mag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare_total_mag" title="Link to this definition">¶</a></dt>

  1421. <dd><p>Compares two operands using their abstract representation, ignoring sign.</p>

  1422. </dd></dl>

  1423. 

  1424. <dl class="py method">

  1425. <dt class="sig sig-object py" id="decimal.Context.copy_abs">

  1426. <span class="sig-name descname"><span class="pre">copy_abs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_abs" title="Link to this definition">¶</a></dt>

  1427. <dd><p>Returns a copy of <em>x</em> with the sign set to 0.</p>

  1428. </dd></dl>

  1429. 

  1430. <dl class="py method">

  1431. <dt class="sig sig-object py" id="decimal.Context.copy_negate">

  1432. <span class="sig-name descname"><span class="pre">copy_negate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_negate" title="Link to this definition">¶</a></dt>

  1433. <dd><p>Returns a copy of <em>x</em> with the sign inverted.</p>

  1434. </dd></dl>

  1435. 

  1436. <dl class="py method">

  1437. <dt class="sig sig-object py" id="decimal.Context.copy_sign">

  1438. <span class="sig-name descname"><span class="pre">copy_sign</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_sign" title="Link to this definition">¶</a></dt>

  1439. <dd><p>Copies the sign from <em>y</em> to <em>x</em>.</p>

  1440. </dd></dl>

  1441. 

  1442. <dl class="py method">

  1443. <dt class="sig sig-object py" id="decimal.Context.divide">

  1444. <span class="sig-name descname"><span class="pre">divide</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.divide" title="Link to this definition">¶</a></dt>

  1445. <dd><p>Return <em>x</em> divided by <em>y</em>.</p>

  1446. </dd></dl>

  1447. 

  1448. <dl class="py method">

  1449. <dt class="sig sig-object py" id="decimal.Context.divide_int">

  1450. <span class="sig-name descname"><span class="pre">divide_int</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.divide_int" title="Link to this definition">¶</a></dt>

  1451. <dd><p>Return <em>x</em> divided by <em>y</em>, truncated to an integer.</p>

  1452. </dd></dl>

  1453. 

  1454. <dl class="py method">

  1455. <dt class="sig sig-object py" id="decimal.Context.divmod">

  1456. <span class="sig-name descname"><span class="pre">divmod</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.divmod" title="Link to this definition">¶</a></dt>

  1457. <dd><p>Divides two numbers and returns the integer part of the result.</p>

  1458. </dd></dl>

  1459. 

  1460. <dl class="py method">

  1461. <dt class="sig sig-object py" id="decimal.Context.exp">

  1462. <span class="sig-name descname"><span class="pre">exp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.exp" title="Link to this definition">¶</a></dt>

  1463. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">e</span> <span class="pre">**</span> <span class="pre">x</span></code>.</p>

  1464. </dd></dl>

  1465. 

  1466. <dl class="py method">

  1467. <dt class="sig sig-object py" id="decimal.Context.fma">

  1468. <span class="sig-name descname"><span class="pre">fma</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.fma" title="Link to this definition">¶</a></dt>

  1469. <dd><p>Returns <em>x</em> multiplied by <em>y</em>, plus <em>z</em>.</p>

  1470. </dd></dl>

  1471. 

  1472. <dl class="py method">

  1473. <dt class="sig sig-object py" id="decimal.Context.is_canonical">

  1474. <span class="sig-name descname"><span class="pre">is_canonical</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_canonical" title="Link to this definition">¶</a></dt>

  1475. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is canonical; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1476. </dd></dl>

  1477. 

  1478. <dl class="py method">

  1479. <dt class="sig sig-object py" id="decimal.Context.is_finite">

  1480. <span class="sig-name descname"><span class="pre">is_finite</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_finite" title="Link to this definition">¶</a></dt>

  1481. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is finite; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1482. </dd></dl>

  1483. 

  1484. <dl class="py method">

  1485. <dt class="sig sig-object py" id="decimal.Context.is_infinite">

  1486. <span class="sig-name descname"><span class="pre">is_infinite</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_infinite" title="Link to this definition">¶</a></dt>

  1487. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is infinite; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1488. </dd></dl>

  1489. 

  1490. <dl class="py method">

  1491. <dt class="sig sig-object py" id="decimal.Context.is_nan">

  1492. <span class="sig-name descname"><span class="pre">is_nan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_nan" title="Link to this definition">¶</a></dt>

  1493. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is a qNaN or sNaN; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1494. </dd></dl>

  1495. 

  1496. <dl class="py method">

  1497. <dt class="sig sig-object py" id="decimal.Context.is_normal">

  1498. <span class="sig-name descname"><span class="pre">is_normal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_normal" title="Link to this definition">¶</a></dt>

  1499. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is a normal number; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1500. </dd></dl>

  1501. 

  1502. <dl class="py method">

  1503. <dt class="sig sig-object py" id="decimal.Context.is_qnan">

  1504. <span class="sig-name descname"><span class="pre">is_qnan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_qnan" title="Link to this definition">¶</a></dt>

  1505. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is a quiet NaN; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1506. </dd></dl>

  1507. 

  1508. <dl class="py method">

  1509. <dt class="sig sig-object py" id="decimal.Context.is_signed">

  1510. <span class="sig-name descname"><span class="pre">is_signed</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_signed" title="Link to this definition">¶</a></dt>

  1511. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is negative; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1512. </dd></dl>

  1513. 

  1514. <dl class="py method">

  1515. <dt class="sig sig-object py" id="decimal.Context.is_snan">

  1516. <span class="sig-name descname"><span class="pre">is_snan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_snan" title="Link to this definition">¶</a></dt>

  1517. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is a signaling NaN; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1518. </dd></dl>

  1519. 

  1520. <dl class="py method">

  1521. <dt class="sig sig-object py" id="decimal.Context.is_subnormal">

  1522. <span class="sig-name descname"><span class="pre">is_subnormal</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_subnormal" title="Link to this definition">¶</a></dt>

  1523. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is subnormal; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1524. </dd></dl>

  1525. 

  1526. <dl class="py method">

  1527. <dt class="sig sig-object py" id="decimal.Context.is_zero">

  1528. <span class="sig-name descname"><span class="pre">is_zero</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_zero" title="Link to this definition">¶</a></dt>

  1529. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if <em>x</em> is a zero; otherwise returns <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>

  1530. </dd></dl>

  1531. 

  1532. <dl class="py method">

  1533. <dt class="sig sig-object py" id="decimal.Context.ln">

  1534. <span class="sig-name descname"><span class="pre">ln</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.ln" title="Link to this definition">¶</a></dt>

  1535. <dd><p>Returns the natural (base e) logarithm of <em>x</em>.</p>

  1536. </dd></dl>

  1537. 

  1538. <dl class="py method">

  1539. <dt class="sig sig-object py" id="decimal.Context.log10">

  1540. <span class="sig-name descname"><span class="pre">log10</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.log10" title="Link to this definition">¶</a></dt>

  1541. <dd><p>Returns the base 10 logarithm of <em>x</em>.</p>

  1542. </dd></dl>

  1543. 

  1544. <dl class="py method">

  1545. <dt class="sig sig-object py" id="decimal.Context.logb">

  1546. <span class="sig-name descname"><span class="pre">logb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logb" title="Link to this definition">¶</a></dt>

  1547. <dd><p>Returns the exponent of the magnitude of the operand’s MSD.</p>

  1548. </dd></dl>

  1549. 

  1550. <dl class="py method">

  1551. <dt class="sig sig-object py" id="decimal.Context.logical_and">

  1552. <span class="sig-name descname"><span class="pre">logical_and</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_and" title="Link to this definition">¶</a></dt>

  1553. <dd><p>Applies the logical operation <em>and</em> between each operand’s digits.</p>

  1554. </dd></dl>

  1555. 

  1556. <dl class="py method">

  1557. <dt class="sig sig-object py" id="decimal.Context.logical_invert">

  1558. <span class="sig-name descname"><span class="pre">logical_invert</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_invert" title="Link to this definition">¶</a></dt>

  1559. <dd><p>Invert all the digits in <em>x</em>.</p>

  1560. </dd></dl>

  1561. 

  1562. <dl class="py method">

  1563. <dt class="sig sig-object py" id="decimal.Context.logical_or">

  1564. <span class="sig-name descname"><span class="pre">logical_or</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_or" title="Link to this definition">¶</a></dt>

  1565. <dd><p>Applies the logical operation <em>or</em> between each operand’s digits.</p>

  1566. </dd></dl>

  1567. 

  1568. <dl class="py method">

  1569. <dt class="sig sig-object py" id="decimal.Context.logical_xor">

  1570. <span class="sig-name descname"><span class="pre">logical_xor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_xor" title="Link to this definition">¶</a></dt>

  1571. <dd><p>Applies the logical operation <em>xor</em> between each operand’s digits.</p>

  1572. </dd></dl>

  1573. 

  1574. <dl class="py method">

  1575. <dt class="sig sig-object py" id="decimal.Context.max">

  1576. <span class="sig-name descname"><span class="pre">max</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.max" title="Link to this definition">¶</a></dt>

  1577. <dd><p>Compares two values numerically and returns the maximum.</p>

  1578. </dd></dl>

  1579. 

  1580. <dl class="py method">

  1581. <dt class="sig sig-object py" id="decimal.Context.max_mag">

  1582. <span class="sig-name descname"><span class="pre">max_mag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.max_mag" title="Link to this definition">¶</a></dt>

  1583. <dd><p>Compares the values numerically with their sign ignored.</p>

  1584. </dd></dl>

  1585. 

  1586. <dl class="py method">

  1587. <dt class="sig sig-object py" id="decimal.Context.min">

  1588. <span class="sig-name descname"><span class="pre">min</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.min" title="Link to this definition">¶</a></dt>

  1589. <dd><p>Compares two values numerically and returns the minimum.</p>

  1590. </dd></dl>

  1591. 

  1592. <dl class="py method">

  1593. <dt class="sig sig-object py" id="decimal.Context.min_mag">

  1594. <span class="sig-name descname"><span class="pre">min_mag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.min_mag" title="Link to this definition">¶</a></dt>

  1595. <dd><p>Compares the values numerically with their sign ignored.</p>

  1596. </dd></dl>

  1597. 

  1598. <dl class="py method">

  1599. <dt class="sig sig-object py" id="decimal.Context.minus">

  1600. <span class="sig-name descname"><span class="pre">minus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.minus" title="Link to this definition">¶</a></dt>

  1601. <dd><p>Minus corresponds to the unary prefix minus operator in Python.</p>

  1602. </dd></dl>

  1603. 

  1604. <dl class="py method">

  1605. <dt class="sig sig-object py" id="decimal.Context.multiply">

  1606. <span class="sig-name descname"><span class="pre">multiply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.multiply" title="Link to this definition">¶</a></dt>

  1607. <dd><p>Return the product of <em>x</em> and <em>y</em>.</p>

  1608. </dd></dl>

  1609. 

  1610. <dl class="py method">

  1611. <dt class="sig sig-object py" id="decimal.Context.next_minus">

  1612. <span class="sig-name descname"><span class="pre">next_minus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.next_minus" title="Link to this definition">¶</a></dt>

  1613. <dd><p>Returns the largest representable number smaller than <em>x</em>.</p>

  1614. </dd></dl>

  1615. 

  1616. <dl class="py method">

  1617. <dt class="sig sig-object py" id="decimal.Context.next_plus">

  1618. <span class="sig-name descname"><span class="pre">next_plus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.next_plus" title="Link to this definition">¶</a></dt>

  1619. <dd><p>Returns the smallest representable number larger than <em>x</em>.</p>

  1620. </dd></dl>

  1621. 

  1622. <dl class="py method">

  1623. <dt class="sig sig-object py" id="decimal.Context.next_toward">

  1624. <span class="sig-name descname"><span class="pre">next_toward</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.next_toward" title="Link to this definition">¶</a></dt>

  1625. <dd><p>Returns the number closest to <em>x</em>, in direction towards <em>y</em>.</p>

  1626. </dd></dl>

  1627. 

  1628. <dl class="py method">

  1629. <dt class="sig sig-object py" id="decimal.Context.normalize">

  1630. <span class="sig-name descname"><span class="pre">normalize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.normalize" title="Link to this definition">¶</a></dt>

  1631. <dd><p>Reduces <em>x</em> to its simplest form.</p>

  1632. </dd></dl>

  1633. 

  1634. <dl class="py method">

  1635. <dt class="sig sig-object py" id="decimal.Context.number_class">

  1636. <span class="sig-name descname"><span class="pre">number_class</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.number_class" title="Link to this definition">¶</a></dt>

  1637. <dd><p>Returns an indication of the class of <em>x</em>.</p>

  1638. </dd></dl>

  1639. 

  1640. <dl class="py method">

  1641. <dt class="sig sig-object py" id="decimal.Context.plus">

  1642. <span class="sig-name descname"><span class="pre">plus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.plus" title="Link to this definition">¶</a></dt>

  1643. <dd><p>Plus corresponds to the unary prefix plus operator in Python.  This

  1644. operation applies the context precision and rounding, so it is <em>not</em> an

  1645. identity operation.</p>

  1646. </dd></dl>

  1647. 

  1648. <dl class="py method">

  1649. <dt class="sig sig-object py" id="decimal.Context.power">

  1650. <span class="sig-name descname"><span class="pre">power</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">modulo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.power" title="Link to this definition">¶</a></dt>

  1651. <dd><p>Return <code class="docutils literal notranslate"><span class="pre">x</span></code> to the power of <code class="docutils literal notranslate"><span class="pre">y</span></code>, reduced modulo <code class="docutils literal notranslate"><span class="pre">modulo</span></code> if given.</p>

  1652. <p>With two arguments, compute <code class="docutils literal notranslate"><span class="pre">x**y</span></code>.  If <code class="docutils literal notranslate"><span class="pre">x</span></code> is negative then <code class="docutils literal notranslate"><span class="pre">y</span></code>

  1653. must be integral.  The result will be inexact unless <code class="docutils literal notranslate"><span class="pre">y</span></code> is integral and

  1654. the result is finite and can be expressed exactly in ‘precision’ digits.

  1655. The rounding mode of the context is used. Results are always correctly rounded

  1656. in the Python version.</p>

  1657. <p><code class="docutils literal notranslate"><span class="pre">Decimal(0)</span> <span class="pre">**</span> <span class="pre">Decimal(0)</span></code> results in <code class="docutils literal notranslate"><span class="pre">InvalidOperation</span></code>, and if <code class="docutils literal notranslate"><span class="pre">InvalidOperation</span></code>

  1658. is not trapped, then results in <code class="docutils literal notranslate"><span class="pre">Decimal('NaN')</span></code>.</p>

  1659. <div class="versionchanged">

  1660. <p><span class="versionmodified changed">Changed in version 3.3: </span>The C module computes <a class="reference internal" href="#decimal.Context.power" title="decimal.Context.power"><code class="xref py py-meth docutils literal notranslate"><span class="pre">power()</span></code></a> in terms of the correctly rounded

  1661. <a class="reference internal" href="#decimal.Context.exp" title="decimal.Context.exp"><code class="xref py py-meth docutils literal notranslate"><span class="pre">exp()</span></code></a> and <a class="reference internal" href="#decimal.Context.ln" title="decimal.Context.ln"><code class="xref py py-meth docutils literal notranslate"><span class="pre">ln()</span></code></a> functions. The result is well-defined but

  1662. only “almost always correctly rounded”.</p>

  1663. </div>

  1664. <p>With three arguments, compute <code class="docutils literal notranslate"><span class="pre">(x**y)</span> <span class="pre">%</span> <span class="pre">modulo</span></code>.  For the three argument

  1665. form, the following restrictions on the arguments hold:</p>

  1666. <ul class="simple">

  1667. <li><p>all three arguments must be integral</p></li>

  1668. <li><p><code class="docutils literal notranslate"><span class="pre">y</span></code> must be nonnegative</p></li>

  1669. <li><p>at least one of <code class="docutils literal notranslate"><span class="pre">x</span></code> or <code class="docutils literal notranslate"><span class="pre">y</span></code> must be nonzero</p></li>

  1670. <li><p><code class="docutils literal notranslate"><span class="pre">modulo</span></code> must be nonzero and have at most ‘precision’ digits</p></li>

  1671. </ul>

  1672. <p>The value resulting from <code class="docutils literal notranslate"><span class="pre">Context.power(x,</span> <span class="pre">y,</span> <span class="pre">modulo)</span></code> is

  1673. equal to the value that would be obtained by computing <code class="docutils literal notranslate"><span class="pre">(x**y)</span>

  1674. <span class="pre">%</span> <span class="pre">modulo</span></code> with unbounded precision, but is computed more

  1675. efficiently.  The exponent of the result is zero, regardless of

  1676. the exponents of <code class="docutils literal notranslate"><span class="pre">x</span></code>, <code class="docutils literal notranslate"><span class="pre">y</span></code> and <code class="docutils literal notranslate"><span class="pre">modulo</span></code>.  The result is

  1677. always exact.</p>

  1678. </dd></dl>

  1679. 

  1680. <dl class="py method">

  1681. <dt class="sig sig-object py" id="decimal.Context.quantize">

  1682. <span class="sig-name descname"><span class="pre">quantize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.quantize" title="Link to this definition">¶</a></dt>

  1683. <dd><p>Returns a value equal to <em>x</em> (rounded), having the exponent of <em>y</em>.</p>

  1684. </dd></dl>

  1685. 

  1686. <dl class="py method">

  1687. <dt class="sig sig-object py" id="decimal.Context.radix">

  1688. <span class="sig-name descname"><span class="pre">radix</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.radix" title="Link to this definition">¶</a></dt>

  1689. <dd><p>Just returns 10, as this is Decimal, :)</p>

  1690. </dd></dl>

  1691. 

  1692. <dl class="py method">

  1693. <dt class="sig sig-object py" id="decimal.Context.remainder">

  1694. <span class="sig-name descname"><span class="pre">remainder</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.remainder" title="Link to this definition">¶</a></dt>

  1695. <dd><p>Returns the remainder from integer division.</p>

  1696. <p>The sign of the result, if non-zero, is the same as that of the original

  1697. dividend.</p>

  1698. </dd></dl>

  1699. 

  1700. <dl class="py method">

  1701. <dt class="sig sig-object py" id="decimal.Context.remainder_near">

  1702. <span class="sig-name descname"><span class="pre">remainder_near</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.remainder_near" title="Link to this definition">¶</a></dt>

  1703. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">y</span> <span class="pre">*</span> <span class="pre">n</span></code>, where <em>n</em> is the integer nearest the exact value

  1704. of <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">/</span> <span class="pre">y</span></code> (if the result is 0 then its sign will be the sign of <em>x</em>).</p>

  1705. </dd></dl>

  1706. 

  1707. <dl class="py method">

  1708. <dt class="sig sig-object py" id="decimal.Context.rotate">

  1709. <span class="sig-name descname"><span class="pre">rotate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.rotate" title="Link to this definition">¶</a></dt>

  1710. <dd><p>Returns a rotated copy of <em>x</em>, <em>y</em> times.</p>

  1711. </dd></dl>

  1712. 

  1713. <dl class="py method">

  1714. <dt class="sig sig-object py" id="decimal.Context.same_quantum">

  1715. <span class="sig-name descname"><span class="pre">same_quantum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.same_quantum" title="Link to this definition">¶</a></dt>

  1716. <dd><p>Returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if the two operands have the same exponent.</p>

  1717. </dd></dl>

  1718. 

  1719. <dl class="py method">

  1720. <dt class="sig sig-object py" id="decimal.Context.scaleb">

  1721. <span class="sig-name descname"><span class="pre">scaleb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.scaleb" title="Link to this definition">¶</a></dt>

  1722. <dd><p>Returns the first operand after adding the second value its exp.</p>

  1723. </dd></dl>

  1724. 

  1725. <dl class="py method">

  1726. <dt class="sig sig-object py" id="decimal.Context.shift">

  1727. <span class="sig-name descname"><span class="pre">shift</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.shift" title="Link to this definition">¶</a></dt>

  1728. <dd><p>Returns a shifted copy of <em>x</em>, <em>y</em> times.</p>

  1729. </dd></dl>

  1730. 

  1731. <dl class="py method">

  1732. <dt class="sig sig-object py" id="decimal.Context.sqrt">

  1733. <span class="sig-name descname"><span class="pre">sqrt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.sqrt" title="Link to this definition">¶</a></dt>

  1734. <dd><p>Square root of a non-negative number to context precision.</p>

  1735. </dd></dl>

  1736. 

  1737. <dl class="py method">

  1738. <dt class="sig sig-object py" id="decimal.Context.subtract">

  1739. <span class="sig-name descname"><span class="pre">subtract</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.subtract" title="Link to this definition">¶</a></dt>

  1740. <dd><p>Return the difference between <em>x</em> and <em>y</em>.</p>

  1741. </dd></dl>

  1742. 

  1743. <dl class="py method">

  1744. <dt class="sig sig-object py" id="decimal.Context.to_eng_string">

  1745. <span class="sig-name descname"><span class="pre">to_eng_string</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.to_eng_string" title="Link to this definition">¶</a></dt>

  1746. <dd><p>Convert to a string, using engineering notation if an exponent is needed.</p>

  1747. <p>Engineering notation has an exponent which is a multiple of 3.  This

  1748. can leave up to 3 digits to the left of the decimal place and may

  1749. require the addition of either one or two trailing zeros.</p>

  1750. </dd></dl>

  1751. 

  1752. <dl class="py method">

  1753. <dt class="sig sig-object py" id="decimal.Context.to_integral_exact">

  1754. <span class="sig-name descname"><span class="pre">to_integral_exact</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.to_integral_exact" title="Link to this definition">¶</a></dt>

  1755. <dd><p>Rounds to an integer.</p>

  1756. </dd></dl>

  1757. 

  1758. <dl class="py method">

  1759. <dt class="sig sig-object py" id="decimal.Context.to_sci_string">

  1760. <span class="sig-name descname"><span class="pre">to_sci_string</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.to_sci_string" title="Link to this definition">¶</a></dt>

  1761. <dd><p>Converts a number to a string using scientific notation.</p>

  1762. </dd></dl>

  1763. 

  1764. </dd></dl>

  1765. 

  1766. </section>

  1767. <section id="constants">

  1768. <span id="decimal-rounding-modes"></span><h2>Constants<a class="headerlink" href="#constants" title="Link to this heading">¶</a></h2>

  1769. <p>The constants in this section are only relevant for the C module. They

  1770. are also included in the pure Python version for compatibility.</p>

  1771. <table class="docutils align-default">

  1772. <thead>

  1773. <tr class="row-odd"><th class="head"></th>

  1774. <th class="head"><p>32-bit</p></th>

  1775. <th class="head"><p>64-bit</p></th>

  1776. </tr>

  1777. </thead>

  1778. <tbody>

  1779. <tr class="row-even"><td><dl class="py data">

  1780. <dt class="sig sig-object py" id="decimal.MAX_PREC">

  1781. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">MAX_PREC</span></span><a class="headerlink" href="#decimal.MAX_PREC" title="Link to this definition">¶</a></dt>

  1782. <dd></dd></dl>

  1783. 

  1784. </td>

  1785. <td><p><code class="docutils literal notranslate"><span class="pre">425000000</span></code></p></td>

  1786. <td><p><code class="docutils literal notranslate"><span class="pre">999999999999999999</span></code></p></td>

  1787. </tr>

  1788. <tr class="row-odd"><td><dl class="py data">

  1789. <dt class="sig sig-object py" id="decimal.MAX_EMAX">

  1790. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">MAX_EMAX</span></span><a class="headerlink" href="#decimal.MAX_EMAX" title="Link to this definition">¶</a></dt>

  1791. <dd></dd></dl>

  1792. 

  1793. </td>

  1794. <td><p><code class="docutils literal notranslate"><span class="pre">425000000</span></code></p></td>

  1795. <td><p><code class="docutils literal notranslate"><span class="pre">999999999999999999</span></code></p></td>

  1796. </tr>

  1797. <tr class="row-even"><td><dl class="py data">

  1798. <dt class="sig sig-object py" id="decimal.MIN_EMIN">

  1799. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">MIN_EMIN</span></span><a class="headerlink" href="#decimal.MIN_EMIN" title="Link to this definition">¶</a></dt>

  1800. <dd></dd></dl>

  1801. 

  1802. </td>

  1803. <td><p><code class="docutils literal notranslate"><span class="pre">-425000000</span></code></p></td>

  1804. <td><p><code class="docutils literal notranslate"><span class="pre">-999999999999999999</span></code></p></td>

  1805. </tr>

  1806. <tr class="row-odd"><td><dl class="py data">

  1807. <dt class="sig sig-object py" id="decimal.MIN_ETINY">

  1808. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">MIN_ETINY</span></span><a class="headerlink" href="#decimal.MIN_ETINY" title="Link to this definition">¶</a></dt>

  1809. <dd></dd></dl>

  1810. 

  1811. </td>

  1812. <td><p><code class="docutils literal notranslate"><span class="pre">-849999999</span></code></p></td>

  1813. <td><p><code class="docutils literal notranslate"><span class="pre">-1999999999999999997</span></code></p></td>

  1814. </tr>

  1815. </tbody>

  1816. </table>

  1817. <dl class="py data">

  1818. <dt class="sig sig-object py" id="decimal.HAVE_THREADS">

  1819. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">HAVE_THREADS</span></span><a class="headerlink" href="#decimal.HAVE_THREADS" title="Link to this definition">¶</a></dt>

  1820. <dd><p>The value is <code class="docutils literal notranslate"><span class="pre">True</span></code>.  Deprecated, because Python now always has threads.</p>

  1821. </dd></dl>

  1822. 

  1823. <div class="deprecated">

  1824. <p><span class="versionmodified deprecated">Deprecated since version 3.9.</span></p>

  1825. </div>

  1826. <dl class="py data">

  1827. <dt class="sig sig-object py" id="decimal.HAVE_CONTEXTVAR">

  1828. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">HAVE_CONTEXTVAR</span></span><a class="headerlink" href="#decimal.HAVE_CONTEXTVAR" title="Link to this definition">¶</a></dt>

  1829. <dd><p>The default value is <code class="docutils literal notranslate"><span class="pre">True</span></code>. If Python is <a class="reference internal" href="../using/configure.html#cmdoption-without-decimal-contextvar"><code class="xref std std-option docutils literal notranslate"><span class="pre">configured</span> <span class="pre">using</span>

  1830. <span class="pre">the</span> <span class="pre">--without-decimal-contextvar</span> <span class="pre">option</span></code></a>,

  1831. the C version uses a thread-local rather than a coroutine-local context and the value

  1832. is <code class="docutils literal notranslate"><span class="pre">False</span></code>.  This is slightly faster in some nested context scenarios.</p>

  1833. </dd></dl>

  1834. 

  1835. <div class="versionadded">

  1836. <p><span class="versionmodified added">New in version 3.8.3.</span></p>

  1837. </div>

  1838. </section>

  1839. <section id="rounding-modes">

  1840. <h2>Rounding modes<a class="headerlink" href="#rounding-modes" title="Link to this heading">¶</a></h2>

  1841. <dl class="py data">

  1842. <dt class="sig sig-object py" id="decimal.ROUND_CEILING">

  1843. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_CEILING</span></span><a class="headerlink" href="#decimal.ROUND_CEILING" title="Link to this definition">¶</a></dt>

  1844. <dd><p>Round towards <code class="docutils literal notranslate"><span class="pre">Infinity</span></code>.</p>

  1845. </dd></dl>

  1846. 

  1847. <dl class="py data">

  1848. <dt class="sig sig-object py" id="decimal.ROUND_DOWN">

  1849. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_DOWN</span></span><a class="headerlink" href="#decimal.ROUND_DOWN" title="Link to this definition">¶</a></dt>

  1850. <dd><p>Round towards zero.</p>

  1851. </dd></dl>

  1852. 

  1853. <dl class="py data">

  1854. <dt class="sig sig-object py" id="decimal.ROUND_FLOOR">

  1855. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_FLOOR</span></span><a class="headerlink" href="#decimal.ROUND_FLOOR" title="Link to this definition">¶</a></dt>

  1856. <dd><p>Round towards <code class="docutils literal notranslate"><span class="pre">-Infinity</span></code>.</p>

  1857. </dd></dl>

  1858. 

  1859. <dl class="py data">

  1860. <dt class="sig sig-object py" id="decimal.ROUND_HALF_DOWN">

  1861. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_HALF_DOWN</span></span><a class="headerlink" href="#decimal.ROUND_HALF_DOWN" title="Link to this definition">¶</a></dt>

  1862. <dd><p>Round to nearest with ties going towards zero.</p>

  1863. </dd></dl>

  1864. 

  1865. <dl class="py data">

  1866. <dt class="sig sig-object py" id="decimal.ROUND_HALF_EVEN">

  1867. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_HALF_EVEN</span></span><a class="headerlink" href="#decimal.ROUND_HALF_EVEN" title="Link to this definition">¶</a></dt>

  1868. <dd><p>Round to nearest with ties going to nearest even integer.</p>

  1869. </dd></dl>

  1870. 

  1871. <dl class="py data">

  1872. <dt class="sig sig-object py" id="decimal.ROUND_HALF_UP">

  1873. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_HALF_UP</span></span><a class="headerlink" href="#decimal.ROUND_HALF_UP" title="Link to this definition">¶</a></dt>

  1874. <dd><p>Round to nearest with ties going away from zero.</p>

  1875. </dd></dl>

  1876. 

  1877. <dl class="py data">

  1878. <dt class="sig sig-object py" id="decimal.ROUND_UP">

  1879. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_UP</span></span><a class="headerlink" href="#decimal.ROUND_UP" title="Link to this definition">¶</a></dt>

  1880. <dd><p>Round away from zero.</p>

  1881. </dd></dl>

  1882. 

  1883. <dl class="py data">

  1884. <dt class="sig sig-object py" id="decimal.ROUND_05UP">

  1885. <span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">ROUND_05UP</span></span><a class="headerlink" href="#decimal.ROUND_05UP" title="Link to this definition">¶</a></dt>

  1886. <dd><p>Round away from zero if last digit after rounding towards zero would have

  1887. been 0 or 5; otherwise round towards zero.</p>

  1888. </dd></dl>

  1889. 

  1890. </section>

  1891. <section id="signals">

  1892. <span id="decimal-signals"></span><h2>Signals<a class="headerlink" href="#signals" title="Link to this heading">¶</a></h2>

  1893. <p>Signals represent conditions that arise during computation. Each corresponds to

  1894. one context flag and one context trap enabler.</p>

  1895. <p>The context flag is set whenever the condition is encountered. After the

  1896. computation, flags may be checked for informational purposes (for instance, to

  1897. determine whether a computation was exact). After checking the flags, be sure to

  1898. clear all flags before starting the next computation.</p>

  1899. <p>If the context’s trap enabler is set for the signal, then the condition causes a

  1900. Python exception to be raised.  For example, if the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-class docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a> trap

  1901. is set, then a <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-exc docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a> exception is raised upon encountering the

  1902. condition.</p>

  1903. <dl class="py class">

  1904. <dt class="sig sig-object py" id="decimal.Clamped">

  1905. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Clamped</span></span><a class="headerlink" href="#decimal.Clamped" title="Link to this definition">¶</a></dt>

  1906. <dd><p>Altered an exponent to fit representation constraints.</p>

  1907. <p>Typically, clamping occurs when an exponent falls outside the context’s

  1908. <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emin</span></code> and <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emax</span></code> limits.  If possible, the exponent is reduced to

  1909. fit by adding zeros to the coefficient.</p>

  1910. </dd></dl>

  1911. 

  1912. <dl class="py class">

  1913. <dt class="sig sig-object py" id="decimal.DecimalException">

  1914. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">DecimalException</span></span><a class="headerlink" href="#decimal.DecimalException" title="Link to this definition">¶</a></dt>

  1915. <dd><p>Base class for other signals and a subclass of <a class="reference internal" href="exceptions.html#ArithmeticError" title="ArithmeticError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ArithmeticError</span></code></a>.</p>

  1916. </dd></dl>

  1917. 

  1918. <dl class="py class">

  1919. <dt class="sig sig-object py" id="decimal.DivisionByZero">

  1920. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">DivisionByZero</span></span><a class="headerlink" href="#decimal.DivisionByZero" title="Link to this definition">¶</a></dt>

  1921. <dd><p>Signals the division of a non-infinite number by zero.</p>

  1922. <p>Can occur with division, modulo division, or when raising a number to a negative

  1923. power.  If this signal is not trapped, returns <code class="docutils literal notranslate"><span class="pre">Infinity</span></code> or

  1924. <code class="docutils literal notranslate"><span class="pre">-Infinity</span></code> with the sign determined by the inputs to the calculation.</p>

  1925. </dd></dl>

  1926. 

  1927. <dl class="py class">

  1928. <dt class="sig sig-object py" id="decimal.Inexact">

  1929. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Inexact</span></span><a class="headerlink" href="#decimal.Inexact" title="Link to this definition">¶</a></dt>

  1930. <dd><p>Indicates that rounding occurred and the result is not exact.</p>

  1931. <p>Signals when non-zero digits were discarded during rounding. The rounded result

  1932. is returned.  The signal flag or trap is used to detect when results are

  1933. inexact.</p>

  1934. </dd></dl>

  1935. 

  1936. <dl class="py class">

  1937. <dt class="sig sig-object py" id="decimal.InvalidOperation">

  1938. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">InvalidOperation</span></span><a class="headerlink" href="#decimal.InvalidOperation" title="Link to this definition">¶</a></dt>

  1939. <dd><p>An invalid operation was performed.</p>

  1940. <p>Indicates that an operation was requested that does not make sense. If not

  1941. trapped, returns <code class="docutils literal notranslate"><span class="pre">NaN</span></code>.  Possible causes include:</p>

  1942. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">Infinity</span> <span class="o">-</span> <span class="n">Infinity</span>

  1943. <span class="mi">0</span> <span class="o">*</span> <span class="n">Infinity</span>

  1944. <span class="n">Infinity</span> <span class="o">/</span> <span class="n">Infinity</span>

  1945. <span class="n">x</span> <span class="o">%</span> <span class="mi">0</span>

  1946. <span class="n">Infinity</span> <span class="o">%</span> <span class="n">x</span>

  1947. <span class="n">sqrt</span><span class="p">(</span><span class="o">-</span><span class="n">x</span><span class="p">)</span> <span class="ow">and</span> <span class="n">x</span> <span class="o">&gt;</span> <span class="mi">0</span>

  1948. <span class="mi">0</span> <span class="o">**</span> <span class="mi">0</span>

  1949. <span class="n">x</span> <span class="o">**</span> <span class="p">(</span><span class="n">non</span><span class="o">-</span><span class="n">integer</span><span class="p">)</span>

  1950. <span class="n">x</span> <span class="o">**</span> <span class="n">Infinity</span>

  1951. </pre></div>

  1952. </div>

  1953. </dd></dl>

  1954. 

  1955. <dl class="py class">

  1956. <dt class="sig sig-object py" id="decimal.Overflow">

  1957. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Overflow</span></span><a class="headerlink" href="#decimal.Overflow" title="Link to this definition">¶</a></dt>

  1958. <dd><p>Numerical overflow.</p>

  1959. <p>Indicates the exponent is larger than <code class="xref py py-attr docutils literal notranslate"><span class="pre">Context.Emax</span></code> after rounding has

  1960. occurred.  If not trapped, the result depends on the rounding mode, either

  1961. pulling inward to the largest representable finite number or rounding outward

  1962. to <code class="docutils literal notranslate"><span class="pre">Infinity</span></code>.  In either case, <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-class docutils literal notranslate"><span class="pre">Inexact</span></code></a> and <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-class docutils literal notranslate"><span class="pre">Rounded</span></code></a>

  1963. are also signaled.</p>

  1964. </dd></dl>

  1965. 

  1966. <dl class="py class">

  1967. <dt class="sig sig-object py" id="decimal.Rounded">

  1968. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Rounded</span></span><a class="headerlink" href="#decimal.Rounded" title="Link to this definition">¶</a></dt>

  1969. <dd><p>Rounding occurred though possibly no information was lost.</p>

  1970. <p>Signaled whenever rounding discards digits; even if those digits are zero

  1971. (such as rounding <code class="docutils literal notranslate"><span class="pre">5.00</span></code> to <code class="docutils literal notranslate"><span class="pre">5.0</span></code>).  If not trapped, returns

  1972. the result unchanged.  This signal is used to detect loss of significant

  1973. digits.</p>

  1974. </dd></dl>

  1975. 

  1976. <dl class="py class">

  1977. <dt class="sig sig-object py" id="decimal.Subnormal">

  1978. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Subnormal</span></span><a class="headerlink" href="#decimal.Subnormal" title="Link to this definition">¶</a></dt>

  1979. <dd><p>Exponent was lower than <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emin</span></code> prior to rounding.</p>

  1980. <p>Occurs when an operation result is subnormal (the exponent is too small). If

  1981. not trapped, returns the result unchanged.</p>

  1982. </dd></dl>

  1983. 

  1984. <dl class="py class">

  1985. <dt class="sig sig-object py" id="decimal.Underflow">

  1986. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">Underflow</span></span><a class="headerlink" href="#decimal.Underflow" title="Link to this definition">¶</a></dt>

  1987. <dd><p>Numerical underflow with result rounded to zero.</p>

  1988. <p>Occurs when a subnormal result is pushed to zero by rounding. <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-class docutils literal notranslate"><span class="pre">Inexact</span></code></a>

  1989. and <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Subnormal</span></code></a> are also signaled.</p>

  1990. </dd></dl>

  1991. 

  1992. <dl class="py class">

  1993. <dt class="sig sig-object py" id="decimal.FloatOperation">

  1994. <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">decimal.</span></span><span class="sig-name descname"><span class="pre">FloatOperation</span></span><a class="headerlink" href="#decimal.FloatOperation" title="Link to this definition">¶</a></dt>

  1995. <dd><p>Enable stricter semantics for mixing floats and Decimals.</p>

  1996. <p>If the signal is not trapped (default), mixing floats and Decimals is

  1997. permitted in the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> constructor,

  1998. <a class="reference internal" href="#decimal.Context.create_decimal" title="decimal.Context.create_decimal"><code class="xref py py-meth docutils literal notranslate"><span class="pre">create_decimal()</span></code></a> and all comparison operators.

  1999. Both conversion and comparisons are exact. Any occurrence of a mixed

  2000. operation is silently recorded by setting <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">FloatOperation</span></code></a> in the

  2001. context flags. Explicit conversions with <a class="reference internal" href="#decimal.Decimal.from_float" title="decimal.Decimal.from_float"><code class="xref py py-meth docutils literal notranslate"><span class="pre">from_float()</span></code></a>

  2002. or <a class="reference internal" href="#decimal.Context.create_decimal_from_float" title="decimal.Context.create_decimal_from_float"><code class="xref py py-meth docutils literal notranslate"><span class="pre">create_decimal_from_float()</span></code></a> do not set the flag.</p>

  2003. <p>Otherwise (the signal is trapped), only equality comparisons and explicit

  2004. conversions are silent. All other mixed operations raise <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">FloatOperation</span></code></a>.</p>

  2005. </dd></dl>

  2006. 

  2007. <p>The following table summarizes the hierarchy of signals:</p>

  2008. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">exceptions</span><span class="o">.</span><span class="n">ArithmeticError</span><span class="p">(</span><span class="n">exceptions</span><span class="o">.</span><span class="n">Exception</span><span class="p">)</span>

  2009.     <span class="n">DecimalException</span>

  2010.         <span class="n">Clamped</span>

  2011.         <span class="n">DivisionByZero</span><span class="p">(</span><span class="n">DecimalException</span><span class="p">,</span> <span class="n">exceptions</span><span class="o">.</span><span class="n">ZeroDivisionError</span><span class="p">)</span>

  2012.         <span class="n">Inexact</span>

  2013.             <span class="n">Overflow</span><span class="p">(</span><span class="n">Inexact</span><span class="p">,</span> <span class="n">Rounded</span><span class="p">)</span>

  2014.             <span class="n">Underflow</span><span class="p">(</span><span class="n">Inexact</span><span class="p">,</span> <span class="n">Rounded</span><span class="p">,</span> <span class="n">Subnormal</span><span class="p">)</span>

  2015.         <span class="n">InvalidOperation</span>

  2016.         <span class="n">Rounded</span>

  2017.         <span class="n">Subnormal</span>

  2018.         <span class="n">FloatOperation</span><span class="p">(</span><span class="n">DecimalException</span><span class="p">,</span> <span class="n">exceptions</span><span class="o">.</span><span class="n">TypeError</span><span class="p">)</span>

  2019. </pre></div>

  2020. </div>

  2021. </section>

  2022. <section id="floating-point-notes">

  2023. <span id="decimal-notes"></span><h2>Floating Point Notes<a class="headerlink" href="#floating-point-notes" title="Link to this heading">¶</a></h2>

  2024. <section id="mitigating-round-off-error-with-increased-precision">

  2025. <h3>Mitigating round-off error with increased precision<a class="headerlink" href="#mitigating-round-off-error-with-increased-precision" title="Link to this heading">¶</a></h3>

  2026. <p>The use of decimal floating point eliminates decimal representation error

  2027. (making it possible to represent <code class="docutils literal notranslate"><span class="pre">0.1</span></code> exactly); however, some operations

  2028. can still incur round-off error when non-zero digits exceed the fixed precision.</p>

  2029. <p>The effects of round-off error can be amplified by the addition or subtraction

  2030. of nearly offsetting quantities resulting in loss of significance.  Knuth

  2031. provides two instructive examples where rounded floating point arithmetic with

  2032. insufficient precision causes the breakdown of the associative and distributive

  2033. properties of addition:</p>

  2034. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="go"># Examples from Seminumerical Algorithms, Section 4.2.2.</span>

  2035. <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="kn">import</span> <span class="n">Decimal</span><span class="p">,</span> <span class="n">getcontext</span>

  2036. <span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">8</span>

  2037. 

  2038. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">11111113</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="o">-</span><span class="mi">11111111</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;7.51111111&#39;</span><span class="p">)</span>

  2039. <span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="n">u</span> <span class="o">+</span> <span class="n">v</span><span class="p">)</span> <span class="o">+</span> <span class="n">w</span>

  2040. <span class="go">Decimal(&#39;9.5111111&#39;)</span>

  2041. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span> <span class="o">+</span> <span class="p">(</span><span class="n">v</span> <span class="o">+</span> <span class="n">w</span><span class="p">)</span>

  2042. <span class="go">Decimal(&#39;10&#39;)</span>

  2043. 

  2044. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">20000</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;6.0000003&#39;</span><span class="p">)</span>

  2045. <span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="n">u</span><span class="o">*</span><span class="n">v</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">u</span><span class="o">*</span><span class="n">w</span><span class="p">)</span>

  2046. <span class="go">Decimal(&#39;0.01&#39;)</span>

  2047. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span> <span class="o">*</span> <span class="p">(</span><span class="n">v</span><span class="o">+</span><span class="n">w</span><span class="p">)</span>

  2048. <span class="go">Decimal(&#39;0.0060000&#39;)</span>

  2049. </pre></div>

  2050. </div>

  2051. <p>The <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code></a> module makes it possible to restore the identities by

  2052. expanding the precision sufficiently to avoid loss of significance:</p>

  2053. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">20</span>

  2054. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">11111113</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="o">-</span><span class="mi">11111111</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;7.51111111&#39;</span><span class="p">)</span>

  2055. <span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="n">u</span> <span class="o">+</span> <span class="n">v</span><span class="p">)</span> <span class="o">+</span> <span class="n">w</span>

  2056. <span class="go">Decimal(&#39;9.51111111&#39;)</span>

  2057. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span> <span class="o">+</span> <span class="p">(</span><span class="n">v</span> <span class="o">+</span> <span class="n">w</span><span class="p">)</span>

  2058. <span class="go">Decimal(&#39;9.51111111&#39;)</span>

  2059. <span class="gp">&gt;&gt;&gt;</span>

  2060. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">20000</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">),</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;6.0000003&#39;</span><span class="p">)</span>

  2061. <span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="n">u</span><span class="o">*</span><span class="n">v</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">u</span><span class="o">*</span><span class="n">w</span><span class="p">)</span>

  2062. <span class="go">Decimal(&#39;0.0060000&#39;)</span>

  2063. <span class="gp">&gt;&gt;&gt; </span><span class="n">u</span> <span class="o">*</span> <span class="p">(</span><span class="n">v</span><span class="o">+</span><span class="n">w</span><span class="p">)</span>

  2064. <span class="go">Decimal(&#39;0.0060000&#39;)</span>

  2065. </pre></div>

  2066. </div>

  2067. </section>

  2068. <section id="special-values">

  2069. <h3>Special values<a class="headerlink" href="#special-values" title="Link to this heading">¶</a></h3>

  2070. <p>The number system for the <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic  Specification."><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code></a> module provides special values

  2071. including <code class="docutils literal notranslate"><span class="pre">NaN</span></code>, <code class="docutils literal notranslate"><span class="pre">sNaN</span></code>, <code class="docutils literal notranslate"><span class="pre">-Infinity</span></code>, <code class="docutils literal notranslate"><span class="pre">Infinity</span></code>,

  2072. and two zeros, <code class="docutils literal notranslate"><span class="pre">+0</span></code> and <code class="docutils literal notranslate"><span class="pre">-0</span></code>.</p>

  2073. <p>Infinities can be constructed directly with:  <code class="docutils literal notranslate"><span class="pre">Decimal('Infinity')</span></code>. Also,

  2074. they can arise from dividing by zero when the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-exc docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a> signal is

  2075. not trapped.  Likewise, when the <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-exc docutils literal notranslate"><span class="pre">Overflow</span></code></a> signal is not trapped, infinity

  2076. can result from rounding beyond the limits of the largest representable number.</p>

  2077. <p>The infinities are signed (affine) and can be used in arithmetic operations

  2078. where they get treated as very large, indeterminate numbers.  For instance,

  2079. adding a constant to infinity gives another infinite result.</p>

  2080. <p>Some operations are indeterminate and return <code class="docutils literal notranslate"><span class="pre">NaN</span></code>, or if the

  2081. <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a> signal is trapped, raise an exception.  For example,

  2082. <code class="docutils literal notranslate"><span class="pre">0/0</span></code> returns <code class="docutils literal notranslate"><span class="pre">NaN</span></code> which means “not a number”.  This variety of

  2083. <code class="docutils literal notranslate"><span class="pre">NaN</span></code> is quiet and, once created, will flow through other computations

  2084. always resulting in another <code class="docutils literal notranslate"><span class="pre">NaN</span></code>.  This behavior can be useful for a

  2085. series of computations that occasionally have missing inputs — it allows the

  2086. calculation to proceed while flagging specific results as invalid.</p>

  2087. <p>A variant is <code class="docutils literal notranslate"><span class="pre">sNaN</span></code> which signals rather than remaining quiet after every

  2088. operation.  This is a useful return value when an invalid result needs to

  2089. interrupt a calculation for special handling.</p>

  2090. <p>The behavior of Python’s comparison operators can be a little surprising where a

  2091. <code class="docutils literal notranslate"><span class="pre">NaN</span></code> is involved.  A test for equality where one of the operands is a

  2092. quiet or signaling <code class="docutils literal notranslate"><span class="pre">NaN</span></code> always returns <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> (even when doing

  2093. <code class="docutils literal notranslate"><span class="pre">Decimal('NaN')==Decimal('NaN')</span></code>), while a test for inequality always returns

  2094. <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a>.  An attempt to compare two Decimals using any of the <code class="docutils literal notranslate"><span class="pre">&lt;</span></code>,

  2095. <code class="docutils literal notranslate"><span class="pre">&lt;=</span></code>, <code class="docutils literal notranslate"><span class="pre">&gt;</span></code> or <code class="docutils literal notranslate"><span class="pre">&gt;=</span></code> operators will raise the <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a> signal

  2096. if either operand is a <code class="docutils literal notranslate"><span class="pre">NaN</span></code>, and return <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> if this signal is

  2097. not trapped.  Note that the General Decimal Arithmetic specification does not

  2098. specify the behavior of direct comparisons; these rules for comparisons

  2099. involving a <code class="docutils literal notranslate"><span class="pre">NaN</span></code> were taken from the IEEE 854 standard (see Table 3 in

  2100. section 5.7).  To ensure strict standards-compliance, use the <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><code class="xref py py-meth docutils literal notranslate"><span class="pre">compare()</span></code></a>

  2101. and <a class="reference internal" href="#decimal.Decimal.compare_signal" title="decimal.Decimal.compare_signal"><code class="xref py py-meth docutils literal notranslate"><span class="pre">compare_signal()</span></code></a> methods instead.</p>

  2102. <p>The signed zeros can result from calculations that underflow. They keep the sign

  2103. that would have resulted if the calculation had been carried out to greater

  2104. precision.  Since their magnitude is zero, both positive and negative zeros are

  2105. treated as equal and their sign is informational.</p>

  2106. <p>In addition to the two signed zeros which are distinct yet equal, there are

  2107. various representations of zero with differing precisions yet equivalent in

  2108. value.  This takes a bit of getting used to.  For an eye accustomed to

  2109. normalized floating point representations, it is not immediately obvious that

  2110. the following calculation returns a value equal to zero:</p>

  2111. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="mi">1</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;Infinity&#39;</span><span class="p">)</span>

  2112. <span class="go">Decimal(&#39;0E-1000026&#39;)</span>

  2113. </pre></div>

  2114. </div>

  2115. </section>

  2116. </section>

  2117. <section id="working-with-threads">

  2118. <span id="decimal-threads"></span><h2>Working with threads<a class="headerlink" href="#working-with-threads" title="Link to this heading">¶</a></h2>

  2119. <p>The <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a> function accesses a different <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal notranslate"><span class="pre">Context</span></code></a> object for

  2120. each thread.  Having separate thread contexts means that threads may make

  2121. changes (such as <code class="docutils literal notranslate"><span class="pre">getcontext().prec=10</span></code>) without interfering with other threads.</p>

  2122. <p>Likewise, the <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">setcontext()</span></code></a> function automatically assigns its target to

  2123. the current thread.</p>

  2124. <p>If <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">setcontext()</span></code></a> has not been called before <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a>, then

  2125. <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a> will automatically create a new context for use in the

  2126. current thread.</p>

  2127. <p>The new context is copied from a prototype context called <em>DefaultContext</em>. To

  2128. control the defaults so that each thread will use the same values throughout the

  2129. application, directly modify the <em>DefaultContext</em> object. This should be done

  2130. <em>before</em> any threads are started so that there won’t be a race condition between

  2131. threads calling <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate"><span class="pre">getcontext()</span></code></a>. For example:</p>

  2132. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Set applicationwide defaults for all threads about to be launched</span>

  2133. <span class="n">DefaultContext</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">12</span>

  2134. <span class="n">DefaultContext</span><span class="o">.</span><span class="n">rounding</span> <span class="o">=</span> <span class="n">ROUND_DOWN</span>

  2135. <span class="n">DefaultContext</span><span class="o">.</span><span class="n">traps</span> <span class="o">=</span> <span class="n">ExtendedContext</span><span class="o">.</span><span class="n">traps</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>

  2136. <span class="n">DefaultContext</span><span class="o">.</span><span class="n">traps</span><span class="p">[</span><span class="n">InvalidOperation</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>

  2137. <span class="n">setcontext</span><span class="p">(</span><span class="n">DefaultContext</span><span class="p">)</span>

  2138. 

  2139. <span class="c1"># Afterwards, the threads can be started</span>

  2140. <span class="n">t1</span><span class="o">.</span><span class="n">start</span><span class="p">()</span>

  2141. <span class="n">t2</span><span class="o">.</span><span class="n">start</span><span class="p">()</span>

  2142. <span class="n">t3</span><span class="o">.</span><span class="n">start</span><span class="p">()</span>

  2143.  <span class="o">.</span> <span class="o">.</span> <span class="o">.</span>

  2144. </pre></div>

  2145. </div>

  2146. </section>

  2147. <section id="recipes">

  2148. <span id="decimal-recipes"></span><h2>Recipes<a class="headerlink" href="#recipes" title="Link to this heading">¶</a></h2>

  2149. <p>Here are a few recipes that serve as utility functions and that demonstrate ways

  2150. to work with the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> class:</p>

  2151. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">moneyfmt</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">places</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">curr</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="n">sep</span><span class="o">=</span><span class="s1">&#39;,&#39;</span><span class="p">,</span> <span class="n">dp</span><span class="o">=</span><span class="s1">&#39;.&#39;</span><span class="p">,</span>

  2152.              <span class="n">pos</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="n">neg</span><span class="o">=</span><span class="s1">&#39;-&#39;</span><span class="p">,</span> <span class="n">trailneg</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">):</span>

  2153. <span class="w">    </span><span class="sd">&quot;&quot;&quot;Convert Decimal to a money formatted string.</span>

  2154. 

  2155. <span class="sd">    places:  required number of places after the decimal point</span>

  2156. <span class="sd">    curr:    optional currency symbol before the sign (may be blank)</span>

  2157. <span class="sd">    sep:     optional grouping separator (comma, period, space, or blank)</span>

  2158. <span class="sd">    dp:      decimal point indicator (comma or period)</span>

  2159. <span class="sd">             only specify as blank when places is zero</span>

  2160. <span class="sd">    pos:     optional sign for positive numbers: &#39;+&#39;, space or blank</span>

  2161. <span class="sd">    neg:     optional sign for negative numbers: &#39;-&#39;, &#39;(&#39;, space or blank</span>

  2162. <span class="sd">    trailneg:optional trailing minus indicator:  &#39;-&#39;, &#39;)&#39;, space or blank</span>

  2163. 

  2164. <span class="sd">    &gt;&gt;&gt; d = Decimal(&#39;-1234567.8901&#39;)</span>

  2165. <span class="sd">    &gt;&gt;&gt; moneyfmt(d, curr=&#39;$&#39;)</span>

  2166. <span class="sd">    &#39;-$1,234,567.89&#39;</span>

  2167. <span class="sd">    &gt;&gt;&gt; moneyfmt(d, places=0, sep=&#39;.&#39;, dp=&#39;&#39;, neg=&#39;&#39;, trailneg=&#39;-&#39;)</span>

  2168. <span class="sd">    &#39;1.234.568-&#39;</span>

  2169. <span class="sd">    &gt;&gt;&gt; moneyfmt(d, curr=&#39;$&#39;, neg=&#39;(&#39;, trailneg=&#39;)&#39;)</span>

  2170. <span class="sd">    &#39;($1,234,567.89)&#39;</span>

  2171. <span class="sd">    &gt;&gt;&gt; moneyfmt(Decimal(123456789), sep=&#39; &#39;)</span>

  2172. <span class="sd">    &#39;123 456 789.00&#39;</span>

  2173. <span class="sd">    &gt;&gt;&gt; moneyfmt(Decimal(&#39;-0.02&#39;), neg=&#39;&lt;&#39;, trailneg=&#39;&gt;&#39;)</span>

  2174. <span class="sd">    &#39;&lt;0.02&gt;&#39;</span>

  2175. 

  2176. <span class="sd">    &quot;&quot;&quot;</span>

  2177.     <span class="n">q</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="o">**</span> <span class="o">-</span><span class="n">places</span>      <span class="c1"># 2 places --&gt; &#39;0.01&#39;</span>

  2178.     <span class="n">sign</span><span class="p">,</span> <span class="n">digits</span><span class="p">,</span> <span class="n">exp</span> <span class="o">=</span> <span class="n">value</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">q</span><span class="p">)</span><span class="o">.</span><span class="n">as_tuple</span><span class="p">()</span>

  2179.     <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>

  2180.     <span class="n">digits</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">digits</span><span class="p">))</span>

  2181.     <span class="n">build</span><span class="p">,</span> <span class="nb">next</span> <span class="o">=</span> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">,</span> <span class="n">digits</span><span class="o">.</span><span class="n">pop</span>

  2182.     <span class="k">if</span> <span class="n">sign</span><span class="p">:</span>

  2183.         <span class="n">build</span><span class="p">(</span><span class="n">trailneg</span><span class="p">)</span>

  2184.     <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">places</span><span class="p">):</span>

  2185.         <span class="n">build</span><span class="p">(</span><span class="nb">next</span><span class="p">()</span> <span class="k">if</span> <span class="n">digits</span> <span class="k">else</span> <span class="s1">&#39;0&#39;</span><span class="p">)</span>

  2186.     <span class="k">if</span> <span class="n">places</span><span class="p">:</span>

  2187.         <span class="n">build</span><span class="p">(</span><span class="n">dp</span><span class="p">)</span>

  2188.     <span class="k">if</span> <span class="ow">not</span> <span class="n">digits</span><span class="p">:</span>

  2189.         <span class="n">build</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">)</span>

  2190.     <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>

  2191.     <span class="k">while</span> <span class="n">digits</span><span class="p">:</span>

  2192.         <span class="n">build</span><span class="p">(</span><span class="nb">next</span><span class="p">())</span>

  2193.         <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>

  2194.         <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">3</span> <span class="ow">and</span> <span class="n">digits</span><span class="p">:</span>

  2195.             <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>

  2196.             <span class="n">build</span><span class="p">(</span><span class="n">sep</span><span class="p">)</span>

  2197.     <span class="n">build</span><span class="p">(</span><span class="n">curr</span><span class="p">)</span>

  2198.     <span class="n">build</span><span class="p">(</span><span class="n">neg</span> <span class="k">if</span> <span class="n">sign</span> <span class="k">else</span> <span class="n">pos</span><span class="p">)</span>

  2199.     <span class="k">return</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">reversed</span><span class="p">(</span><span class="n">result</span><span class="p">))</span>

  2200. 

  2201. <span class="k">def</span> <span class="nf">pi</span><span class="p">():</span>

  2202. <span class="w">    </span><span class="sd">&quot;&quot;&quot;Compute Pi to the current precision.</span>

  2203. 

  2204. <span class="sd">    &gt;&gt;&gt; print(pi())</span>

  2205. <span class="sd">    3.141592653589793238462643383</span>

  2206. 

  2207. <span class="sd">    &quot;&quot;&quot;</span>

  2208.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">+=</span> <span class="mi">2</span>  <span class="c1"># extra digits for intermediate steps</span>

  2209.     <span class="n">three</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>      <span class="c1"># substitute &quot;three=3.0&quot; for regular floats</span>

  2210.     <span class="n">lasts</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">na</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">da</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">three</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">24</span>

  2211.     <span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>

  2212.         <span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>

  2213.         <span class="n">n</span><span class="p">,</span> <span class="n">na</span> <span class="o">=</span> <span class="n">n</span><span class="o">+</span><span class="n">na</span><span class="p">,</span> <span class="n">na</span><span class="o">+</span><span class="mi">8</span>

  2214.         <span class="n">d</span><span class="p">,</span> <span class="n">da</span> <span class="o">=</span> <span class="n">d</span><span class="o">+</span><span class="n">da</span><span class="p">,</span> <span class="n">da</span><span class="o">+</span><span class="mi">32</span>

  2215.         <span class="n">t</span> <span class="o">=</span> <span class="p">(</span><span class="n">t</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span> <span class="o">/</span> <span class="n">d</span>

  2216.         <span class="n">s</span> <span class="o">+=</span> <span class="n">t</span>

  2217.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">-=</span> <span class="mi">2</span>

  2218.     <span class="k">return</span> <span class="o">+</span><span class="n">s</span>               <span class="c1"># unary plus applies the new precision</span>

  2219. 

  2220. <span class="k">def</span> <span class="nf">exp</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>

  2221. <span class="w">    </span><span class="sd">&quot;&quot;&quot;Return e raised to the power of x.  Result type matches input type.</span>

  2222. 

  2223. <span class="sd">    &gt;&gt;&gt; print(exp(Decimal(1)))</span>

  2224. <span class="sd">    2.718281828459045235360287471</span>

  2225. <span class="sd">    &gt;&gt;&gt; print(exp(Decimal(2)))</span>

  2226. <span class="sd">    7.389056098930650227230427461</span>

  2227. <span class="sd">    &gt;&gt;&gt; print(exp(2.0))</span>

  2228. <span class="sd">    7.38905609893</span>

  2229. <span class="sd">    &gt;&gt;&gt; print(exp(2+0j))</span>

  2230. <span class="sd">    (7.38905609893+0j)</span>

  2231. 

  2232. <span class="sd">    &quot;&quot;&quot;</span>

  2233.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">+=</span> <span class="mi">2</span>

  2234.     <span class="n">i</span><span class="p">,</span> <span class="n">lasts</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">fact</span><span class="p">,</span> <span class="n">num</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span>

  2235.     <span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>

  2236.         <span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>

  2237.         <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>

  2238.         <span class="n">fact</span> <span class="o">*=</span> <span class="n">i</span>

  2239.         <span class="n">num</span> <span class="o">*=</span> <span class="n">x</span>

  2240.         <span class="n">s</span> <span class="o">+=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">fact</span>

  2241.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">-=</span> <span class="mi">2</span>

  2242.     <span class="k">return</span> <span class="o">+</span><span class="n">s</span>

  2243. 

  2244. <span class="k">def</span> <span class="nf">cos</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>

  2245. <span class="w">    </span><span class="sd">&quot;&quot;&quot;Return the cosine of x as measured in radians.</span>

  2246. 

  2247. <span class="sd">    The Taylor series approximation works best for a small value of x.</span>

  2248. <span class="sd">    For larger values, first compute x = x % (2 * pi).</span>

  2249. 

  2250. <span class="sd">    &gt;&gt;&gt; print(cos(Decimal(&#39;0.5&#39;)))</span>

  2251. <span class="sd">    0.8775825618903727161162815826</span>

  2252. <span class="sd">    &gt;&gt;&gt; print(cos(0.5))</span>

  2253. <span class="sd">    0.87758256189</span>

  2254. <span class="sd">    &gt;&gt;&gt; print(cos(0.5+0j))</span>

  2255. <span class="sd">    (0.87758256189+0j)</span>

  2256. 

  2257. <span class="sd">    &quot;&quot;&quot;</span>

  2258.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">+=</span> <span class="mi">2</span>

  2259.     <span class="n">i</span><span class="p">,</span> <span class="n">lasts</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">fact</span><span class="p">,</span> <span class="n">num</span><span class="p">,</span> <span class="n">sign</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span>

  2260.     <span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>

  2261.         <span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>

  2262.         <span class="n">i</span> <span class="o">+=</span> <span class="mi">2</span>

  2263.         <span class="n">fact</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>

  2264.         <span class="n">num</span> <span class="o">*=</span> <span class="n">x</span> <span class="o">*</span> <span class="n">x</span>

  2265.         <span class="n">sign</span> <span class="o">*=</span> <span class="o">-</span><span class="mi">1</span>

  2266.         <span class="n">s</span> <span class="o">+=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">fact</span> <span class="o">*</span> <span class="n">sign</span>

  2267.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">-=</span> <span class="mi">2</span>

  2268.     <span class="k">return</span> <span class="o">+</span><span class="n">s</span>

  2269. 

  2270. <span class="k">def</span> <span class="nf">sin</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>

  2271. <span class="w">    </span><span class="sd">&quot;&quot;&quot;Return the sine of x as measured in radians.</span>

  2272. 

  2273. <span class="sd">    The Taylor series approximation works best for a small value of x.</span>

  2274. <span class="sd">    For larger values, first compute x = x % (2 * pi).</span>

  2275. 

  2276. <span class="sd">    &gt;&gt;&gt; print(sin(Decimal(&#39;0.5&#39;)))</span>

  2277. <span class="sd">    0.4794255386042030002732879352</span>

  2278. <span class="sd">    &gt;&gt;&gt; print(sin(0.5))</span>

  2279. <span class="sd">    0.479425538604</span>

  2280. <span class="sd">    &gt;&gt;&gt; print(sin(0.5+0j))</span>

  2281. <span class="sd">    (0.479425538604+0j)</span>

  2282. 

  2283. <span class="sd">    &quot;&quot;&quot;</span>

  2284.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">+=</span> <span class="mi">2</span>

  2285.     <span class="n">i</span><span class="p">,</span> <span class="n">lasts</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">fact</span><span class="p">,</span> <span class="n">num</span><span class="p">,</span> <span class="n">sign</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="mi">1</span>

  2286.     <span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>

  2287.         <span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>

  2288.         <span class="n">i</span> <span class="o">+=</span> <span class="mi">2</span>

  2289.         <span class="n">fact</span> <span class="o">*=</span> <span class="n">i</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>

  2290.         <span class="n">num</span> <span class="o">*=</span> <span class="n">x</span> <span class="o">*</span> <span class="n">x</span>

  2291.         <span class="n">sign</span> <span class="o">*=</span> <span class="o">-</span><span class="mi">1</span>

  2292.         <span class="n">s</span> <span class="o">+=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">fact</span> <span class="o">*</span> <span class="n">sign</span>

  2293.     <span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">-=</span> <span class="mi">2</span>

  2294.     <span class="k">return</span> <span class="o">+</span><span class="n">s</span>

  2295. </pre></div>

  2296. </div>

  2297. </section>

  2298. <section id="decimal-faq">

  2299. <span id="id1"></span><h2>Decimal FAQ<a class="headerlink" href="#decimal-faq" title="Link to this heading">¶</a></h2>

  2300. <p>Q. It is cumbersome to type <code class="docutils literal notranslate"><span class="pre">decimal.Decimal('1234.5')</span></code>.  Is there a way to

  2301. minimize typing when using the interactive interpreter?</p>

  2302. <p>A. Some users abbreviate the constructor to just a single letter:</p>

  2303. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">D</span> <span class="o">=</span> <span class="n">decimal</span><span class="o">.</span><span class="n">Decimal</span>

  2304. <span class="gp">&gt;&gt;&gt; </span><span class="n">D</span><span class="p">(</span><span class="s1">&#39;1.23&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">D</span><span class="p">(</span><span class="s1">&#39;3.45&#39;</span><span class="p">)</span>

  2305. <span class="go">Decimal(&#39;4.68&#39;)</span>

  2306. </pre></div>

  2307. </div>

  2308. <p>Q. In a fixed-point application with two decimal places, some inputs have many

  2309. places and need to be rounded.  Others are not supposed to have excess digits

  2310. and need to be validated.  What methods should be used?</p>

  2311. <p>A. The <a class="reference internal" href="#decimal.Decimal.quantize" title="decimal.Decimal.quantize"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quantize()</span></code></a> method rounds to a fixed number of decimal places. If

  2312. the <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate"><span class="pre">Inexact</span></code></a> trap is set, it is also useful for validation:</p>

  2313. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">TWOPLACES</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="o">**</span> <span class="o">-</span><span class="mi">2</span>       <span class="c1"># same as Decimal(&#39;0.01&#39;)</span>

  2314. </pre></div>

  2315. </div>

  2316. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Round to two places</span>

  2317. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.214&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">TWOPLACES</span><span class="p">)</span>

  2318. <span class="go">Decimal(&#39;3.21&#39;)</span>

  2319. </pre></div>

  2320. </div>

  2321. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Validate that a number does not exceed two places</span>

  2322. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.21&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">TWOPLACES</span><span class="p">,</span> <span class="n">context</span><span class="o">=</span><span class="n">Context</span><span class="p">(</span><span class="n">traps</span><span class="o">=</span><span class="p">[</span><span class="n">Inexact</span><span class="p">]))</span>

  2323. <span class="go">Decimal(&#39;3.21&#39;)</span>

  2324. </pre></div>

  2325. </div>

  2326. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.214&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">TWOPLACES</span><span class="p">,</span> <span class="n">context</span><span class="o">=</span><span class="n">Context</span><span class="p">(</span><span class="n">traps</span><span class="o">=</span><span class="p">[</span><span class="n">Inexact</span><span class="p">]))</span>

  2327. <span class="gt">Traceback (most recent call last):</span>

  2328. <span class="w">   </span><span class="c">...</span>

  2329. <span class="gr">Inexact</span>: <span class="n">None</span>

  2330. </pre></div>

  2331. </div>

  2332. <p>Q. Once I have valid two place inputs, how do I maintain that invariant

  2333. throughout an application?</p>

  2334. <p>A. Some operations like addition, subtraction, and multiplication by an integer

  2335. will automatically preserve fixed point.  Others operations, like division and

  2336. non-integer multiplication, will change the number of decimal places and need to

  2337. be followed-up with a <a class="reference internal" href="#decimal.Decimal.quantize" title="decimal.Decimal.quantize"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quantize()</span></code></a> step:</p>

  2338. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;102.72&#39;</span><span class="p">)</span>           <span class="c1"># Initial fixed-point values</span>

  2339. <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.17&#39;</span><span class="p">)</span>

  2340. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span>                           <span class="c1"># Addition preserves fixed-point</span>

  2341. <span class="go">Decimal(&#39;105.89&#39;)</span>

  2342. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span>

  2343. <span class="go">Decimal(&#39;99.55&#39;)</span>

  2344. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">*</span> <span class="mi">42</span>                          <span class="c1"># So does integer multiplication</span>

  2345. <span class="go">Decimal(&#39;4314.24&#39;)</span>

  2346. <span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="n">a</span> <span class="o">*</span> <span class="n">b</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">TWOPLACES</span><span class="p">)</span>     <span class="c1"># Must quantize non-integer multiplication</span>

  2347. <span class="go">Decimal(&#39;325.62&#39;)</span>

  2348. <span class="gp">&gt;&gt;&gt; </span><span class="p">(</span><span class="n">b</span> <span class="o">/</span> <span class="n">a</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">TWOPLACES</span><span class="p">)</span>     <span class="c1"># And quantize division</span>

  2349. <span class="go">Decimal(&#39;0.03&#39;)</span>

  2350. </pre></div>

  2351. </div>

  2352. <p>In developing fixed-point applications, it is convenient to define functions

  2353. to handle the <a class="reference internal" href="#decimal.Decimal.quantize" title="decimal.Decimal.quantize"><code class="xref py py-meth docutils literal notranslate"><span class="pre">quantize()</span></code></a> step:</p>

  2354. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">mul</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">fp</span><span class="o">=</span><span class="n">TWOPLACES</span><span class="p">):</span>

  2355. <span class="gp">... </span>    <span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">*</span> <span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span>

  2356. <span class="gp">...</span>

  2357. <span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">div</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">fp</span><span class="o">=</span><span class="n">TWOPLACES</span><span class="p">):</span>

  2358. <span class="gp">... </span>    <span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">/</span> <span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span>

  2359. </pre></div>

  2360. </div>

  2361. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">mul</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>                       <span class="c1"># Automatically preserve fixed-point</span>

  2362. <span class="go">Decimal(&#39;325.62&#39;)</span>

  2363. <span class="gp">&gt;&gt;&gt; </span><span class="n">div</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>

  2364. <span class="go">Decimal(&#39;0.03&#39;)</span>

  2365. </pre></div>

  2366. </div>

  2367. <p>Q. There are many ways to express the same value.  The numbers <code class="docutils literal notranslate"><span class="pre">200</span></code>,

  2368. <code class="docutils literal notranslate"><span class="pre">200.000</span></code>, <code class="docutils literal notranslate"><span class="pre">2E2</span></code>, and <code class="docutils literal notranslate"><span class="pre">.02E+4</span></code> all have the same value at

  2369. various precisions. Is there a way to transform them to a single recognizable

  2370. canonical value?</p>

  2371. <p>A. The <a class="reference internal" href="#decimal.Decimal.normalize" title="decimal.Decimal.normalize"><code class="xref py py-meth docutils literal notranslate"><span class="pre">normalize()</span></code></a> method maps all equivalent values to a single

  2372. representative:</p>

  2373. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">values</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">Decimal</span><span class="p">,</span> <span class="s1">&#39;200 200.000 2E2 .02E+4&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">())</span>

  2374. <span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">v</span><span class="o">.</span><span class="n">normalize</span><span class="p">()</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">values</span><span class="p">]</span>

  2375. <span class="go">[Decimal(&#39;2E+2&#39;), Decimal(&#39;2E+2&#39;), Decimal(&#39;2E+2&#39;), Decimal(&#39;2E+2&#39;)]</span>

  2376. </pre></div>

  2377. </div>

  2378. <p>Q. When does rounding occur in a computation?</p>

  2379. <p>A. It occurs <em>after</em> the computation.  The philosophy of the decimal

  2380. specification is that numbers are considered exact and are created

  2381. independent of the current context.  They can even have greater

  2382. precision than current context.  Computations process with those

  2383. exact inputs and then rounding (or other context operations) is

  2384. applied to the <em>result</em> of the computation:</p>

  2385. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">5</span>

  2386. <span class="gp">&gt;&gt;&gt; </span><span class="n">pi</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.1415926535&#39;</span><span class="p">)</span>   <span class="c1"># More than 5 digits</span>

  2387. <span class="gp">&gt;&gt;&gt; </span><span class="n">pi</span>                             <span class="c1"># All digits are retained</span>

  2388. <span class="go">Decimal(&#39;3.1415926535&#39;)</span>

  2389. <span class="gp">&gt;&gt;&gt; </span><span class="n">pi</span> <span class="o">+</span> <span class="mi">0</span>                         <span class="c1"># Rounded after an addition</span>

  2390. <span class="go">Decimal(&#39;3.1416&#39;)</span>

  2391. <span class="gp">&gt;&gt;&gt; </span><span class="n">pi</span> <span class="o">-</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;0.00005&#39;</span><span class="p">)</span>        <span class="c1"># Subtract unrounded numbers, then round</span>

  2392. <span class="go">Decimal(&#39;3.1415&#39;)</span>

  2393. <span class="gp">&gt;&gt;&gt; </span><span class="n">pi</span> <span class="o">+</span> <span class="mi">0</span> <span class="o">-</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;0.00005&#39;</span><span class="p">)</span><span class="o">.</span>   <span class="c1"># Intermediate values are rounded</span>

  2394. <span class="go">Decimal(&#39;3.1416&#39;)</span>

  2395. </pre></div>

  2396. </div>

  2397. <p>Q. Some decimal values always print with exponential notation.  Is there a way

  2398. to get a non-exponential representation?</p>

  2399. <p>A. For some values, exponential notation is the only way to express the number

  2400. of significant places in the coefficient.  For example, expressing

  2401. <code class="docutils literal notranslate"><span class="pre">5.0E+3</span></code> as <code class="docutils literal notranslate"><span class="pre">5000</span></code> keeps the value constant but cannot show the

  2402. original’s two-place significance.</p>

  2403. <p>If an application does not care about tracking significance, it is easy to

  2404. remove the exponent and trailing zeroes, losing significance, but keeping the

  2405. value unchanged:</p>

  2406. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">remove_exponent</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>

  2407. <span class="gp">... </span>    <span class="k">return</span> <span class="n">d</span><span class="o">.</span><span class="n">quantize</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span> <span class="k">if</span> <span class="n">d</span> <span class="o">==</span> <span class="n">d</span><span class="o">.</span><span class="n">to_integral</span><span class="p">()</span> <span class="k">else</span> <span class="n">d</span><span class="o">.</span><span class="n">normalize</span><span class="p">()</span>

  2408. </pre></div>

  2409. </div>

  2410. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">remove_exponent</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;5E+3&#39;</span><span class="p">))</span>

  2411. <span class="go">Decimal(&#39;5000&#39;)</span>

  2412. </pre></div>

  2413. </div>

  2414. <p>Q. Is there a way to convert a regular float to a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>?</p>

  2415. <p>A. Yes, any binary floating point number can be exactly expressed as a

  2416. Decimal though an exact conversion may take more precision than intuition would

  2417. suggest:</p>

  2418. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>

  2419. <span class="go">Decimal(&#39;3.141592653589793115997963468544185161590576171875&#39;)</span>

  2420. </pre></div>

  2421. </div>

  2422. <p>Q. Within a complex calculation, how can I make sure that I haven’t gotten a

  2423. spurious result because of insufficient precision or rounding anomalies.</p>

  2424. <p>A. The decimal module makes it easy to test results.  A best practice is to

  2425. re-run calculations using greater precision and with various rounding modes.

  2426. Widely differing results indicate insufficient precision, rounding mode issues,

  2427. ill-conditioned inputs, or a numerically unstable algorithm.</p>

  2428. <p>Q. I noticed that context precision is applied to the results of operations but

  2429. not to the inputs.  Is there anything to watch out for when mixing values of

  2430. different precisions?</p>

  2431. <p>A. Yes.  The principle is that all values are considered to be exact and so is

  2432. the arithmetic on those values.  Only the results are rounded.  The advantage

  2433. for inputs is that “what you type is what you get”.  A disadvantage is that the

  2434. results can look odd if you forget that the inputs haven’t been rounded:</p>

  2435. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">3</span>

  2436. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.104&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;2.104&#39;</span><span class="p">)</span>

  2437. <span class="go">Decimal(&#39;5.21&#39;)</span>

  2438. <span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;3.104&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;0.000&#39;</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;2.104&#39;</span><span class="p">)</span>

  2439. <span class="go">Decimal(&#39;5.20&#39;)</span>

  2440. </pre></div>

  2441. </div>

  2442. <p>The solution is either to increase precision or to force rounding of inputs

  2443. using the unary plus operation:</p>

  2444. <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">3</span>

  2445. <span class="gp">&gt;&gt;&gt; </span><span class="o">+</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">&#39;1.23456789&#39;</span><span class="p">)</span>      <span class="c1"># unary plus triggers rounding</span>

  2446. <span class="go">Decimal(&#39;1.23&#39;)</span>

  2447. </pre></div>

  2448. </div>

  2449. <p>Alternatively, inputs can be rounded upon creation using the

  2450. <a class="reference internal" href="#decimal.Context.create_decimal" title="decimal.Context.create_decimal"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Context.create_decimal()</span></code></a> method:</p>

  2451. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">rounding</span><span class="o">=</span><span class="n">ROUND_DOWN</span><span class="p">)</span><span class="o">.</span><span class="n">create_decimal</span><span class="p">(</span><span class="s1">&#39;1.2345678&#39;</span><span class="p">)</span>

  2452. <span class="go">Decimal(&#39;1.2345&#39;)</span>

  2453. </pre></div>

  2454. </div>

  2455. <p>Q. Is the CPython implementation fast for large numbers?</p>

  2456. <p>A. Yes.  In the CPython and PyPy3 implementations, the C/CFFI versions of

  2457. the decimal module integrate the high speed <a class="reference external" href="https://www.bytereef.org/mpdecimal/doc/libmpdec/index.html">libmpdec</a> library for

  2458. arbitrary precision correctly rounded decimal floating point arithmetic <a class="footnote-reference brackets" href="#id4" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a>.

  2459. <code class="docutils literal notranslate"><span class="pre">libmpdec</span></code> uses <a class="reference external" href="https://en.wikipedia.org/wiki/Karatsuba_algorithm">Karatsuba multiplication</a>

  2460. for medium-sized numbers and the <a class="reference external" href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general)#Number-theoretic_transform">Number Theoretic Transform</a>

  2461. for very large numbers.</p>

  2462. <p>The context must be adapted for exact arbitrary precision arithmetic. <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emin</span></code>

  2463. and <code class="xref py py-attr docutils literal notranslate"><span class="pre">Emax</span></code> should always be set to the maximum values, <code class="xref py py-attr docutils literal notranslate"><span class="pre">clamp</span></code>

  2464. should always be 0 (the default).  Setting <code class="xref py py-attr docutils literal notranslate"><span class="pre">prec</span></code> requires some care.</p>

  2465. <p>The easiest approach for trying out bignum arithmetic is to use the maximum

  2466. value for <code class="xref py py-attr docutils literal notranslate"><span class="pre">prec</span></code> as well <a class="footnote-reference brackets" href="#id5" id="id3" role="doc-noteref"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></a>:</p>

  2467. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="n">MAX_PREC</span><span class="p">,</span> <span class="n">Emax</span><span class="o">=</span><span class="n">MAX_EMAX</span><span class="p">,</span> <span class="n">Emin</span><span class="o">=</span><span class="n">MIN_EMIN</span><span class="p">))</span>

  2468. <span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">**</span> <span class="mi">256</span>

  2469. <span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">/</span> <span class="mi">128</span>

  2470. <span class="go">Decimal(&#39;904625697166532776746648320380374280103671755200316906558262375061821325312&#39;)</span>

  2471. </pre></div>

  2472. </div>

  2473. <p>For inexact results, <a class="reference internal" href="#decimal.MAX_PREC" title="decimal.MAX_PREC"><code class="xref py py-attr docutils literal notranslate"><span class="pre">MAX_PREC</span></code></a> is far too large on 64-bit platforms and

  2474. the available memory will be insufficient:</p>

  2475. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span>

  2476. <span class="gt">Traceback (most recent call last):</span>

  2477.   File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  2478. <span class="gr">MemoryError</span>

  2479. </pre></div>

  2480. </div>

  2481. <p>On systems with overallocation (e.g. Linux), a more sophisticated approach is to

  2482. adjust <code class="xref py py-attr docutils literal notranslate"><span class="pre">prec</span></code> to the amount of available RAM.  Suppose that you have 8GB of

  2483. RAM and expect 10 simultaneous operands using a maximum of 500MB each:</p>

  2484. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">sys</span>

  2485. <span class="gp">&gt;&gt;&gt;</span>

  2486. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># Maximum number of digits for a single operand using 500MB in 8-byte words</span>

  2487. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># with 19 digits per word (4-byte and 9 digits for the 32-bit build):</span>

  2488. <span class="gp">&gt;&gt;&gt; </span><span class="n">maxdigits</span> <span class="o">=</span> <span class="mi">19</span> <span class="o">*</span> <span class="p">((</span><span class="mi">500</span> <span class="o">*</span> <span class="mi">1024</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">//</span> <span class="mi">8</span><span class="p">)</span>

  2489. <span class="gp">&gt;&gt;&gt;</span>

  2490. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># Check that this works:</span>

  2491. <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span> <span class="o">=</span> <span class="n">Context</span><span class="p">(</span><span class="n">prec</span><span class="o">=</span><span class="n">maxdigits</span><span class="p">,</span> <span class="n">Emax</span><span class="o">=</span><span class="n">MAX_EMAX</span><span class="p">,</span> <span class="n">Emin</span><span class="o">=</span><span class="n">MIN_EMIN</span><span class="p">)</span>

  2492. <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span><span class="o">.</span><span class="n">traps</span><span class="p">[</span><span class="n">Inexact</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>

  2493. <span class="gp">&gt;&gt;&gt; </span><span class="n">setcontext</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>

  2494. <span class="gp">&gt;&gt;&gt;</span>

  2495. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># Fill the available precision with nines:</span>

  2496. <span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">logical_invert</span><span class="p">()</span> <span class="o">*</span> <span class="mi">9</span>

  2497. <span class="gp">&gt;&gt;&gt; </span><span class="n">sys</span><span class="o">.</span><span class="n">getsizeof</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>

  2498. <span class="go">524288112</span>

  2499. <span class="gp">&gt;&gt;&gt; </span><span class="n">x</span> <span class="o">+</span> <span class="mi">2</span>

  2500. <span class="gt">Traceback (most recent call last):</span>

  2501.   File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  2502. <span class="gr">  decimal.Inexact</span>: <span class="n">[&lt;class &#39;decimal.Inexact&#39;&gt;]</span>

  2503. </pre></div>

  2504. </div>

  2505. <p>In general (and especially on systems without overallocation), it is recommended

  2506. to estimate even tighter bounds and set the <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Inexact</span></code></a> trap if all calculations

  2507. are expected to be exact.</p>

  2508. <aside class="footnote-list brackets">

  2509. <aside class="footnote brackets" id="id4" role="doc-footnote">

  2510. <span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">1</a><span class="fn-bracket">]</span></span>

  2511. <div class="versionadded">

  2512. <p><span class="versionmodified added">New in version 3.3.</span></p>

  2513. </div>

  2514. </aside>

  2515. <aside class="footnote brackets" id="id5" role="doc-footnote">

  2516. <span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">2</a><span class="fn-bracket">]</span></span>

  2517. <div class="versionchanged">

  2518. <p><span class="versionmodified changed">Changed in version 3.9: </span>This approach now works for all exact results except for non-integer powers.</p>

  2519. </div>

  2520. </aside>

  2521. </aside>

  2522. </section>

  2523. </section>

  2524. 

  2525. 

  2526.             <div class="clearer"></div>

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  2530.       <div class="sphinxsidebar" role="navigation" aria-label="main navigation">

  2531.         <div class="sphinxsidebarwrapper">

  2532.   <div>

  2533.     <h3><a href="../contents.html">Table of Contents</a></h3>

  2534.     <ul>

  2535. <li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">decimal</span></code> — Decimal fixed point and floating point arithmetic</a><ul>

  2536. <li><a class="reference internal" href="#quick-start-tutorial">Quick-start Tutorial</a></li>

  2537. <li><a class="reference internal" href="#decimal-objects">Decimal objects</a><ul>

  2538. <li><a class="reference internal" href="#logical-operands">Logical operands</a></li>

  2539. </ul>

  2540. </li>

  2541. <li><a class="reference internal" href="#context-objects">Context objects</a></li>

  2542. <li><a class="reference internal" href="#constants">Constants</a></li>

  2543. <li><a class="reference internal" href="#rounding-modes">Rounding modes</a></li>

  2544. <li><a class="reference internal" href="#signals">Signals</a></li>

  2545. <li><a class="reference internal" href="#floating-point-notes">Floating Point Notes</a><ul>

  2546. <li><a class="reference internal" href="#mitigating-round-off-error-with-increased-precision">Mitigating round-off error with increased precision</a></li>

  2547. <li><a class="reference internal" href="#special-values">Special values</a></li>

  2548. </ul>

  2549. </li>

  2550. <li><a class="reference internal" href="#working-with-threads">Working with threads</a></li>

  2551. <li><a class="reference internal" href="#recipes">Recipes</a></li>

  2552. <li><a class="reference internal" href="#decimal-faq">Decimal FAQ</a></li>

  2553. </ul>

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