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<div class="section" id="module-decimal">
<span id="decimal-decimal-fixed-point-and-floating-point-arithmetic"></span><h1>9.4. <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><code class="xref py py-mod docutils literal"><span class="pre">decimal</span></code></a> — Decimal fixed point and floating point arithmetic<a class="headerlink" href="#module-decimal" title="Permalink to this headline">¶</a></h1>
<p><strong>Source code:</strong> <a class="reference external" href="https://hg.python.org/cpython/file/3.5/Lib/decimal.py">Lib/decimal.py</a></p>
<hr class="docutils" />
<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"><span class="pre">decimal</span></code></a> module provides support for fast correctly-rounded
decimal floating point arithmetic. It offers several advantages over the
<a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal"><span class="pre">float</span></code></a> datatype:</p>
<ul>
<li><p class="first">Decimal “is based on a floating-point model which was designed with people
in mind, and necessarily has a paramount guiding principle – computers must
provide an arithmetic that works in the same way as the arithmetic that
people learn at school.” – excerpt from the decimal arithmetic specification.</p>
</li>
<li><p class="first">Decimal numbers can be represented exactly. In contrast, numbers like
<code class="xref py py-const docutils literal"><span class="pre">1.1</span></code> and <code class="xref py py-const docutils literal"><span class="pre">2.2</span></code> do not have exact representations in binary
floating point. End users typically would not expect <code class="docutils literal"><span class="pre">1.1</span> <span class="pre">+</span> <span class="pre">2.2</span></code> to display
as <code class="xref py py-const docutils literal"><span class="pre">3.3000000000000003</span></code> as it does with binary floating point.</p>
</li>
<li><p class="first">The exactness carries over into arithmetic. In decimal floating point, <code class="docutils literal"><span class="pre">0.1</span>
<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
is <code class="xref py py-const docutils literal"><span class="pre">5.5511151231257827e-017</span></code>. While near to zero, the differences
prevent reliable equality testing and differences can accumulate. For this
reason, decimal is preferred in accounting applications which have strict
equality invariants.</p>
</li>
<li><p class="first">The decimal module incorporates a notion of significant places so that <code class="docutils literal"><span class="pre">1.30</span>
<span class="pre">+</span> <span class="pre">1.20</span></code> is <code class="xref py py-const docutils literal"><span class="pre">2.50</span></code>. The trailing zero is kept to indicate significance.
This is the customary presentation for monetary applications. For
multiplication, the “schoolbook” approach uses all the figures in the
multiplicands. For instance, <code class="docutils literal"><span class="pre">1.3</span> <span class="pre">*</span> <span class="pre">1.2</span></code> gives <code class="xref py py-const docutils literal"><span class="pre">1.56</span></code> while <code class="docutils literal"><span class="pre">1.30</span> <span class="pre">*</span>
<span class="pre">1.20</span></code> gives <code class="xref py py-const docutils literal"><span class="pre">1.5600</span></code>.</p>
</li>
<li><p class="first">Unlike hardware based binary floating point, the decimal module has a user
alterable precision (defaulting to 28 places) which can be as large as needed for
a given problem:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="k">import</span> <span class="o">*</span>
<span class="gp">>>> </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>
<span class="gp">>>> </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>
<span class="go">Decimal('0.142857')</span>
<span class="gp">>>> </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>
<span class="gp">>>> </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>
<span class="go">Decimal('0.1428571428571428571428571429')</span>
</pre></div>
</div>
</li>
<li><p class="first">Both binary and decimal floating point are implemented in terms of published
standards. While the built-in float type exposes only a modest portion of its
capabilities, the decimal module exposes all required parts of the standard.
When needed, the programmer has full control over rounding and signal handling.
This includes an option to enforce exact arithmetic by using exceptions
to block any inexact operations.</p>
</li>
<li><p class="first">The decimal module was designed to support “without prejudice, both exact
unrounded decimal arithmetic (sometimes called fixed-point arithmetic)
and rounded floating-point arithmetic.” – excerpt from the decimal
arithmetic specification.</p>
</li>
</ul>
<p>The module design is centered around three concepts: the decimal number, the
context for arithmetic, and signals.</p>
<p>A decimal number is immutable. It has a sign, coefficient digits, and an
exponent. To preserve significance, the coefficient digits do not truncate
trailing zeros. Decimals also include special values such as
<code class="xref py py-const docutils literal"><span class="pre">Infinity</span></code>, <code class="xref py py-const docutils literal"><span class="pre">-Infinity</span></code>, and <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>. The standard also
differentiates <code class="xref py py-const docutils literal"><span class="pre">-0</span></code> from <code class="xref py py-const docutils literal"><span class="pre">+0</span></code>.</p>
<p>The context for arithmetic is an environment specifying precision, rounding
rules, limits on exponents, flags indicating the results of operations, and trap
enablers which determine whether signals are treated as exceptions. Rounding
options include <a class="reference internal" href="#decimal.ROUND_CEILING" title="decimal.ROUND_CEILING"><code class="xref py py-const docutils literal"><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"><span class="pre">ROUND_DOWN</span></code></a>,
<a class="reference internal" href="#decimal.ROUND_FLOOR" title="decimal.ROUND_FLOOR"><code class="xref py py-const docutils literal"><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"><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"><span class="pre">ROUND_HALF_EVEN</span></code></a>,
<a class="reference internal" href="#decimal.ROUND_HALF_UP" title="decimal.ROUND_HALF_UP"><code class="xref py py-const docutils literal"><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"><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"><span class="pre">ROUND_05UP</span></code></a>.</p>
<p>Signals are groups of exceptional conditions arising during the course of
computation. Depending on the needs of the application, signals may be ignored,
considered as informational, or treated as exceptions. The signals in the
decimal module are: <a class="reference internal" href="#decimal.Clamped" title="decimal.Clamped"><code class="xref py py-const docutils literal"><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"><span class="pre">InvalidOperation</span></code></a>,
<a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal"><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"><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"><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"><span class="pre">Subnormal</span></code></a>,
<a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-const docutils literal"><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"><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"><span class="pre">FloatOperation</span></code></a>.</p>
<p>For each signal there is a flag and a trap enabler. When a signal is
encountered, its flag is set to one, then, if the trap enabler is
set to one, an exception is raised. Flags are sticky, so the user needs to
reset them before monitoring a calculation.</p>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<ul class="last simple">
<li>IBM’s General Decimal Arithmetic Specification, <a class="reference external" href="http://speleotrove.com/decimal/decarith.html">The General Decimal Arithmetic
Specification</a>.</li>
</ul>
</div>
<div class="section" id="quick-start-tutorial">
<span id="decimal-tutorial"></span><h2>9.4.1. Quick-start Tutorial<a class="headerlink" href="#quick-start-tutorial" title="Permalink to this headline">¶</a></h2>
<p>The usual start to using decimals is importing the module, viewing the current
context with <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal"><span class="pre">getcontext()</span></code></a> and, if necessary, setting new values for
precision, rounding, or enabled traps:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">decimal</span> <span class="k">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">getcontext</span><span class="p">()</span>
<span class="go">Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,</span>
<span class="go"> capitals=1, clamp=0, flags=[], traps=[Overflow, DivisionByZero,</span>
<span class="go"> InvalidOperation])</span>
<span class="gp">>>> </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>
</pre></div>
</div>
<p>Decimal instances can be constructed from integers, strings, floats, or tuples.
Construction from an integer or a float performs an exact conversion of the
value of that integer or float. Decimal numbers include special values such as
<code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> which stands for “Not a number”, positive and negative
<code class="xref py py-const docutils literal"><span class="pre">Infinity</span></code>, and <code class="xref py py-const docutils literal"><span class="pre">-0</span></code>:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="go">Decimal('10')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.14'</span><span class="p">)</span>
<span class="go">Decimal('3.14')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="mf">3.14</span><span class="p">)</span>
<span class="go">Decimal('3.140000000000000124344978758017532527446746826171875')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('3.14')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('1.4142135623730951')</span>
<span class="gp">>>> </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">'0.5'</span><span class="p">)</span>
<span class="go">Decimal('1.414213562373095048801688724')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'NaN'</span><span class="p">)</span>
<span class="go">Decimal('NaN')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'-Infinity'</span><span class="p">)</span>
<span class="go">Decimal('-Infinity')</span>
</pre></div>
</div>
<p>If the <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal"><span class="pre">FloatOperation</span></code></a> signal is trapped, accidental mixing of
decimals and floats in constructors or ordering comparisons raises
an exception:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">c</span> <span class="o">=</span> <span class="n">getcontext</span><span class="p">()</span>
<span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="mf">3.14</span><span class="p">)</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<stdin>"</span>, line <span class="m">1</span>, in <span class="n"><module></span>
<span class="gr">decimal.FloatOperation</span>: <span class="n">[<class 'decimal.FloatOperation'>]</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.5'</span><span class="p">)</span> <span class="o"><</span> <span class="mf">3.7</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<stdin>"</span>, line <span class="m">1</span>, in <span class="n"><module></span>
<span class="gr">decimal.FloatOperation</span>: <span class="n">[<class 'decimal.FloatOperation'>]</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.5'</span><span class="p">)</span> <span class="o">==</span> <span class="mf">3.5</span>
<span class="go">True</span>
</pre></div>
</div>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.3.</span></p>
</div>
<p>The significance of a new Decimal is determined solely by the number of digits
input. Context precision and rounding only come into play during arithmetic
operations.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.0'</span><span class="p">)</span>
<span class="go">Decimal('3.0')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.1415926535'</span><span class="p">)</span>
<span class="go">Decimal('3.1415926535')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.1415926535'</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'2.7182818285'</span><span class="p">)</span>
<span class="go">Decimal('5.85987')</span>
<span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.1415926535'</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'2.7182818285'</span><span class="p">)</span>
<span class="go">Decimal('5.85988')</span>
</pre></div>
</div>
<p>If the internal limits of the C version are exceeded, constructing
a decimal raises <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-class docutils literal"><span class="pre">InvalidOperation</span></code></a>:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s2">"1e9999999999999999999"</span><span class="p">)</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<stdin>"</span>, line <span class="m">1</span>, in <span class="n"><module></span>
<span class="gr">decimal.InvalidOperation</span>: <span class="n">[<class 'decimal.InvalidOperation'>]</span>
</pre></div>
</div>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 3.3.</span></p>
</div>
<p>Decimals interact well with much of the rest of Python. Here is a small decimal
floating point flying circus:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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">'1.34 1.87 3.45 2.35 1.00 0.03 9.25'</span><span class="o">.</span><span class="n">split</span><span class="p">()))</span>
<span class="gp">>>> </span><span class="nb">max</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="go">Decimal('9.25')</span>
<span class="gp">>>> </span><span class="nb">min</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="go">Decimal('0.03')</span>
<span class="gp">>>> </span><span class="nb">sorted</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="go">[Decimal('0.03'), Decimal('1.00'), Decimal('1.34'), Decimal('1.87'),</span>
<span class="go"> Decimal('2.35'), Decimal('3.45'), Decimal('9.25')]</span>
<span class="gp">>>> </span><span class="nb">sum</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="go">Decimal('19.29')</span>
<span class="gp">>>> </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>
<span class="gp">>>> </span><span class="nb">str</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">'1.34'</span>
<span class="gp">>>> </span><span class="nb">float</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">1.34</span>
<span class="gp">>>> </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>
<span class="go">Decimal('1.3')</span>
<span class="gp">>>> </span><span class="nb">int</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">1</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">*</span> <span class="mi">5</span>
<span class="go">Decimal('6.70')</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">*</span> <span class="n">b</span>
<span class="go">Decimal('2.5058')</span>
<span class="gp">>>> </span><span class="n">c</span> <span class="o">%</span> <span class="n">a</span>
<span class="go">Decimal('0.77')</span>
</pre></div>
</div>
<p>And some mathematical functions are also available to Decimal:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </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>
<span class="go">Decimal('1.414213562373095048801688724')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('2.718281828459045235360287471')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'10'</span><span class="p">)</span><span class="o">.</span><span class="n">ln</span><span class="p">()</span>
<span class="go">Decimal('2.302585092994045684017991455')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'10'</span><span class="p">)</span><span class="o">.</span><span class="n">log10</span><span class="p">()</span>
<span class="go">Decimal('1')</span>
</pre></div>
</div>
<p>The <code class="xref py py-meth docutils literal"><span class="pre">quantize()</span></code> method rounds a number to a fixed exponent. This method is
useful for monetary applications that often round results to a fixed number of
places:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'7.325'</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">'.01'</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="go">Decimal('7.32')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'7.325'</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">'1.'</span><span class="p">),</span> <span class="n">rounding</span><span class="o">=</span><span class="n">ROUND_UP</span><span class="p">)</span>
<span class="go">Decimal('8')</span>
</pre></div>
</div>
<p>As shown above, the <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal"><span class="pre">getcontext()</span></code></a> function accesses the current context and
allows the settings to be changed. This approach meets the needs of most
applications.</p>
<p>For more advanced work, it may be useful to create alternate contexts using the
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"><span class="pre">setcontext()</span></code></a>
function.</p>
<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"><span class="pre">decimal</span></code></a> module provides two ready to
use standard contexts, <a class="reference internal" href="#decimal.BasicContext" title="decimal.BasicContext"><code class="xref py py-const docutils literal"><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"><span class="pre">ExtendedContext</span></code></a>. The
former is especially useful for debugging because many of the traps are
enabled:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">setcontext</span><span class="p">(</span><span class="n">myothercontext</span><span class="p">)</span>
<span class="gp">>>> </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>
<span class="go">Decimal('0.142857142857142857142857142857142857142857142857142857142857')</span>
<span class="gp">>>> </span><span class="n">ExtendedContext</span>
<span class="go">Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,</span>
<span class="go"> capitals=1, clamp=0, flags=[], traps=[])</span>
<span class="gp">>>> </span><span class="n">setcontext</span><span class="p">(</span><span class="n">ExtendedContext</span><span class="p">)</span>
<span class="gp">>>> </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>
<span class="go">Decimal('0.142857143')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('Infinity')</span>
<span class="gp">>>> </span><span class="n">setcontext</span><span class="p">(</span><span class="n">BasicContext</span><span class="p">)</span>
<span class="gp">>>> </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>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<pyshell#143>"</span>, line <span class="m">1</span>, in <span class="n">-toplevel-</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>
<span class="gr">DivisionByZero</span>: <span class="n">x / 0</span>
</pre></div>
</div>
<p>Contexts also have signal flags for monitoring exceptional conditions
encountered during computations. The flags remain set until explicitly cleared,
so it is best to clear the flags before each set of monitored computations by
using the <code class="xref py py-meth docutils literal"><span class="pre">clear_flags()</span></code> method.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">setcontext</span><span class="p">(</span><span class="n">ExtendedContext</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">getcontext</span><span class="p">()</span><span class="o">.</span><span class="n">clear_flags</span><span class="p">()</span>
<span class="gp">>>> </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>
<span class="go">Decimal('3.14159292')</span>
<span class="gp">>>> </span><span class="n">getcontext</span><span class="p">()</span>
<span class="go">Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,</span>
<span class="go"> capitals=1, clamp=0, flags=[Inexact, Rounded], traps=[])</span>
</pre></div>
</div>
<p>The <em>flags</em> entry shows that the rational approximation to <code class="xref py py-const docutils literal"><span class="pre">Pi</span></code> was
rounded (digits beyond the context precision were thrown away) and that the
result is inexact (some of the discarded digits were non-zero).</p>
<p>Individual traps are set using the dictionary in the <code class="xref py py-attr docutils literal"><span class="pre">traps</span></code> field of a
context:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">setcontext</span><span class="p">(</span><span class="n">ExtendedContext</span><span class="p">)</span>
<span class="gp">>>> </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>
<span class="go">Decimal('Infinity')</span>
<span class="gp">>>> </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>
<span class="gp">>>> </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>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<pyshell#112>"</span>, line <span class="m">1</span>, in <span class="n">-toplevel-</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>
<span class="gr">DivisionByZero</span>: <span class="n">x / 0</span>
</pre></div>
</div>
<p>Most programs adjust the current context only once, at the beginning of the
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"><span class="pre">Decimal</span></code></a> with
a single cast inside a loop. With context set and decimals created, the bulk of
the program manipulates the data no differently than with other Python numeric
types.</p>
</div>
<div class="section" id="decimal-objects">
<span id="decimal-decimal"></span><h2>9.4.2. Decimal objects<a class="headerlink" href="#decimal-objects" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="decimal.Decimal">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Decimal</code><span class="sig-paren">(</span><em>value="0"</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal" title="Permalink to this definition">¶</a></dt>
<dd><p>Construct a new <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> object based from <em>value</em>.</p>
<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"><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"><span class="pre">Decimal</span></code></a>
object. If no <em>value</em> is given, returns <code class="docutils literal"><span class="pre">Decimal('0')</span></code>. If <em>value</em> is a
string, it should conform to the decimal numeric string syntax after leading
and trailing whitespace characters are removed:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="n">sign</span> <span class="p">::</span><span class="o">=</span> <span class="s1">'+'</span> <span class="o">|</span> <span class="s1">'-'</span>
<span class="n">digit</span> <span class="p">::</span><span class="o">=</span> <span class="s1">'0'</span> <span class="o">|</span> <span class="s1">'1'</span> <span class="o">|</span> <span class="s1">'2'</span> <span class="o">|</span> <span class="s1">'3'</span> <span class="o">|</span> <span class="s1">'4'</span> <span class="o">|</span> <span class="s1">'5'</span> <span class="o">|</span> <span class="s1">'6'</span> <span class="o">|</span> <span class="s1">'7'</span> <span class="o">|</span> <span class="s1">'8'</span> <span class="o">|</span> <span class="s1">'9'</span>
<span class="n">indicator</span> <span class="p">::</span><span class="o">=</span> <span class="s1">'e'</span> <span class="o">|</span> <span class="s1">'E'</span>
<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>
<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">'.'</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">'.'</span><span class="p">]</span> <span class="n">digits</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">indicator</span> <span class="p">[</span><span class="n">sign</span><span class="p">]</span> <span class="n">digits</span>
<span class="n">infinity</span> <span class="p">::</span><span class="o">=</span> <span class="s1">'Infinity'</span> <span class="o">|</span> <span class="s1">'Inf'</span>
<span class="n">nan</span> <span class="p">::</span><span class="o">=</span> <span class="s1">'NaN'</span> <span class="p">[</span><span class="n">digits</span><span class="p">]</span> <span class="o">|</span> <span class="s1">'sNaN'</span> <span class="p">[</span><span class="n">digits</span><span class="p">]</span>
<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>
<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>
</pre></div>
</div>
<p>Other Unicode decimal digits are also permitted where <code class="docutils literal"><span class="pre">digit</span></code>
appears above. These include decimal digits from various other
alphabets (for example, Arabic-Indic and Devanāgarī digits) along
with the fullwidth digits <code class="docutils literal"><span class="pre">'\uff10'</span></code> through <code class="docutils literal"><span class="pre">'\uff19'</span></code>.</p>
<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"><span class="pre">tuple</span></code></a>, it should have three components, a sign
(<code class="xref py py-const docutils literal"><span class="pre">0</span></code> for positive or <code class="xref py py-const docutils literal"><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"><span class="pre">tuple</span></code></a> of
digits, and an integer exponent. For example, <code class="docutils literal"><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>
returns <code class="docutils literal"><span class="pre">Decimal('1.414')</span></code>.</p>
<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"><span class="pre">float</span></code></a>, the binary floating point value is losslessly
converted to its exact decimal equivalent. This conversion can often require
53 or more digits of precision. For example, <code class="docutils literal"><span class="pre">Decimal(float('1.1'))</span></code>
converts to
<code class="docutils literal"><span class="pre">Decimal('1.100000000000000088817841970012523233890533447265625')</span></code>.</p>
<p>The <em>context</em> precision does not affect how many digits are stored. That is
determined exclusively by the number of digits in <em>value</em>. For example,
<code class="docutils literal"><span class="pre">Decimal('3.00000')</span></code> records all five zeros even if the context precision is
only three.</p>
<p>The purpose of the <em>context</em> argument is determining what to do if <em>value</em> is a
malformed string. If the context traps <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal"><span class="pre">InvalidOperation</span></code></a>, an exception
is raised; otherwise, the constructor returns a new Decimal with the value of
<code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>.</p>
<p>Once constructed, <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> objects are immutable.</p>
<div class="versionchanged">
<p><span class="versionmodified">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"><span class="pre">float</span></code></a>
instance.</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 3.3: </span><a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal"><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"><span class="pre">FloatOperation</span></code></a>
trap is set. By default the trap is off.</p>
</div>
<p>Decimal floating point objects share many properties with the other built-in
numeric types such as <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal"><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"><span class="pre">int</span></code></a>. All of the usual math
operations and special methods apply. Likewise, decimal objects can be
copied, pickled, printed, used as dictionary keys, used as set elements,
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"><span class="pre">float</span></code></a> or
<a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal"><span class="pre">int</span></code></a>).</p>
<p>There are some small differences between arithmetic on Decimal objects and
arithmetic on integers and floats. When the remainder operator <code class="docutils literal"><span class="pre">%</span></code> is
applied to Decimal objects, the sign of the result is the sign of the
<em>dividend</em> rather than the sign of the divisor:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">1</span>
<span class="gp">>>> </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>
<span class="go">Decimal('-3')</span>
</pre></div>
</div>
<p>The integer division operator <code class="docutils literal"><span class="pre">//</span></code> behaves analogously, returning the
integer part of the true quotient (truncating towards zero) rather than its
floor, so as to preserve the usual identity <code class="docutils literal"><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>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="o">-</span><span class="mi">7</span> <span class="o">//</span> <span class="mi">4</span>
<span class="go">-2</span>
<span class="gp">>>> </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>
<span class="go">Decimal('-1')</span>
</pre></div>
</div>
<p>The <code class="docutils literal"><span class="pre">%</span></code> and <code class="docutils literal"><span class="pre">//</span></code> operators implement the <code class="docutils literal"><span class="pre">remainder</span></code> and
<code class="docutils literal"><span class="pre">divide-integer</span></code> operations (respectively) as described in the
specification.</p>
<p>Decimal objects cannot generally be combined with floats or
instances of <a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal"><span class="pre">fractions.Fraction</span></code></a> in arithmetic operations:
an attempt to add a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><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"><span class="pre">float</span></code></a>, for
example, will raise a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal"><span class="pre">TypeError</span></code></a>. However, it is possible to
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"><span class="pre">Decimal</span></code></a>
instance <code class="docutils literal"><span class="pre">x</span></code> with another number <code class="docutils literal"><span class="pre">y</span></code>. This avoids confusing results
when doing equality comparisons between numbers of different types.</p>
<div class="versionchanged">
<p><span class="versionmodified">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"><span class="pre">Decimal</span></code></a> instances and other
numeric types are now fully supported.</p>
</div>
<p>In addition to the standard numeric properties, decimal floating point
objects also have a number of specialized methods:</p>
<dl class="method">
<dt id="decimal.Decimal.adjusted">
<code class="descname">adjusted</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.adjusted" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the adjusted exponent after shifting out the coefficient’s
rightmost digits until only the lead digit remains:
<code class="docutils literal"><span class="pre">Decimal('321e+5').adjusted()</span></code> returns seven. Used for determining the
position of the most significant digit with respect to the decimal point.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.as_tuple">
<code class="descname">as_tuple</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.as_tuple" title="Permalink to this definition">¶</a></dt>
<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:
<code class="docutils literal"><span class="pre">DecimalTuple(sign,</span> <span class="pre">digits,</span> <span class="pre">exponent)</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.canonical">
<code class="descname">canonical</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.canonical" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the canonical encoding of the argument. Currently, the encoding of
a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instance is always canonical, so this operation returns
its argument unchanged.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.compare">
<code class="descname">compare</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">compare()</span></code></a> returns a
Decimal instance, and if either operand is a NaN then the result is a
NaN:</p>
<div class="highlight-python3"><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">==></span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'NaN'</span><span class="p">)</span>
<span class="n">a</span> <span class="o"><</span> <span class="n">b</span> <span class="o">==></span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'-1'</span><span class="p">)</span>
<span class="n">a</span> <span class="o">==</span> <span class="n">b</span> <span class="o">==></span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'0'</span><span class="p">)</span>
<span class="n">a</span> <span class="o">></span> <span class="n">b</span> <span class="o">==></span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.compare_signal">
<code class="descname">compare_signal</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare_signal" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">compare()</span></code></a> method, except that all
NaNs signal. That is, if neither operand is a signaling NaN then any
quiet NaN operand is treated as though it were a signaling NaN.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.compare_total">
<code class="descname">compare_total</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare_total" title="Permalink to this definition">¶</a></dt>
<dd><p>Compare two operands using their abstract representation rather than their
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"><span class="pre">compare()</span></code></a> method, but the result
gives a total ordering on <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instances. Two
<a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instances with the same numeric value but different
representations compare unequal in this ordering:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'12.0'</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">'12'</span><span class="p">))</span>
<span class="go">Decimal('-1')</span>
</pre></div>
</div>
<p>Quiet and signaling NaNs are also included in the total ordering. The
result of this function is <code class="docutils literal"><span class="pre">Decimal('0')</span></code> if both operands have the same
representation, <code class="docutils literal"><span class="pre">Decimal('-1')</span></code> if the first operand is lower in the
total order than the second, and <code class="docutils literal"><span class="pre">Decimal('1')</span></code> if the first operand is
higher in the total order than the second operand. See the specification
for details of the total order.</p>
<p>This operation is unaffected by context and is quiet: no flags are changed
and no rounding is performed. As an exception, the C version may raise
InvalidOperation if the second operand cannot be converted exactly.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.compare_total_mag">
<code class="descname">compare_total_mag</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.compare_total_mag" title="Permalink to this definition">¶</a></dt>
<dd><p>Compare two operands using their abstract representation rather than their
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"><span class="pre">compare_total()</span></code></a>, but ignoring the sign of each operand.
<code class="docutils literal"><span class="pre">x.compare_total_mag(y)</span></code> is equivalent to
<code class="docutils literal"><span class="pre">x.copy_abs().compare_total(y.copy_abs())</span></code>.</p>
<p>This operation is unaffected by context and is quiet: no flags are changed
and no rounding is performed. As an exception, the C version may raise
InvalidOperation if the second operand cannot be converted exactly.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.conjugate">
<code class="descname">conjugate</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.conjugate" title="Permalink to this definition">¶</a></dt>
<dd><p>Just returns self, this method is only to comply with the Decimal
Specification.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.copy_abs">
<code class="descname">copy_abs</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.copy_abs" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the absolute value of the argument. This operation is unaffected
by the context and is quiet: no flags are changed and no rounding is
performed.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.copy_negate">
<code class="descname">copy_negate</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.copy_negate" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the negation of the argument. This operation is unaffected by the
context and is quiet: no flags are changed and no rounding is performed.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.copy_sign">
<code class="descname">copy_sign</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.copy_sign" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the first operand with the sign set to be the same as the
sign of the second operand. For example:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'2.3'</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">'-1.5'</span><span class="p">))</span>
<span class="go">Decimal('-2.3')</span>
</pre></div>
</div>
<p>This operation is unaffected by context and is quiet: no flags are changed
and no rounding is performed. As an exception, the C version may raise
InvalidOperation if the second operand cannot be converted exactly.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.exp">
<code class="descname">exp</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.exp" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the value of the (natural) exponential function <code class="docutils literal"><span class="pre">e**x</span></code> at the
given number. The result is 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"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">Decimal('2.718281828459045235360287471')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('2.561702493119680037517373933E+139')</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.from_float">
<code class="descname">from_float</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.from_float" title="Permalink to this definition">¶</a></dt>
<dd><p>Classmethod that converts a float to a decimal number, exactly.</p>
<p>Note <cite>Decimal.from_float(0.1)</cite> is not the same as <cite>Decimal(‘0.1’)</cite>.
Since 0.1 is not exactly representable in binary floating point, the
value is stored as the nearest representable value which is
<cite>0x1.999999999999ap-4</cite>. That equivalent value in decimal is
<cite>0.1000000000000000055511151231257827021181583404541015625</cite>.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">From Python 3.2 onwards, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instance
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"><span class="pre">float</span></code></a>.</p>
</div>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">Decimal('0.1000000000000000055511151231257827021181583404541015625')</span>
<span class="gp">>>> </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">'nan'</span><span class="p">))</span>
<span class="go">Decimal('NaN')</span>
<span class="gp">>>> </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">'inf'</span><span class="p">))</span>
<span class="go">Decimal('Infinity')</span>
<span class="gp">>>> </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">'-inf'</span><span class="p">))</span>
<span class="go">Decimal('-Infinity')</span>
</pre></div>
</div>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.1.</span></p>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.fma">
<code class="descname">fma</code><span class="sig-paren">(</span><em>other</em>, <em>third</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.fma" title="Permalink to this definition">¶</a></dt>
<dd><p>Fused multiply-add. Return self*other+third with no rounding of the
intermediate product self*other.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">Decimal('11')</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_canonical">
<code class="descname">is_canonical</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_canonical" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><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"><span class="pre">False</span></code></a>
otherwise. Currently, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instance is always canonical, so
this operation always returns <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_finite">
<code class="descname">is_finite</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_finite" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument is a finite number, and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> if the argument is an infinity or a NaN.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_infinite">
<code class="descname">is_infinite</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_infinite" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument is either positive or negative
infinity and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_nan">
<code class="descname">is_nan</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_nan" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument is a (quiet or signaling) NaN and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_normal">
<code class="descname">is_normal</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_normal" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument is a <em>normal</em> finite number. Return
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> if the argument is zero, subnormal, infinite or a NaN.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_qnan">
<code class="descname">is_qnan</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_qnan" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument is a quiet NaN, and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_signed">
<code class="descname">is_signed</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_signed" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument has a negative sign and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> otherwise. Note that zeros and NaNs can both carry signs.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_snan">
<code class="descname">is_snan</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_snan" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><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"><span class="pre">False</span></code></a>
otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_subnormal">
<code class="descname">is_subnormal</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_subnormal" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><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"><span class="pre">False</span></code></a>
otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.is_zero">
<code class="descname">is_zero</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.is_zero" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a> if the argument is a (positive or negative) zero and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal"><span class="pre">False</span></code></a> otherwise.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.ln">
<code class="descname">ln</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.ln" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the natural (base e) logarithm of the operand. The result is
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"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.log10">
<code class="descname">log10</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.log10" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the base ten logarithm of the operand. The result is 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"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.logb">
<code class="descname">logb</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logb" title="Permalink to this definition">¶</a></dt>
<dd><p>For a nonzero number, return the adjusted exponent of its operand as a
<a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instance. If the operand is a zero then
<code class="docutils literal"><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"><span class="pre">DivisionByZero</span></code></a> flag
is raised. If the operand is an infinity then <code class="docutils literal"><span class="pre">Decimal('Infinity')</span></code> is
returned.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.logical_and">
<code class="descname">logical_and</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_and" title="Permalink to this definition">¶</a></dt>
<dd><p><a class="reference internal" href="#decimal.Decimal.logical_and" title="decimal.Decimal.logical_and"><code class="xref py py-meth docutils literal"><span class="pre">logical_and()</span></code></a> is a logical operation which takes two <em>logical
operands</em> (see <a class="reference internal" href="#logical-operands-label"><span>Logical operands</span></a>). The result is the
digit-wise <code class="docutils literal"><span class="pre">and</span></code> of the two operands.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.logical_invert">
<code class="descname">logical_invert</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_invert" title="Permalink to this definition">¶</a></dt>
<dd><p><a class="reference internal" href="#decimal.Decimal.logical_invert" title="decimal.Decimal.logical_invert"><code class="xref py py-meth docutils literal"><span class="pre">logical_invert()</span></code></a> is a logical operation. The
result is the digit-wise inversion of the operand.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.logical_or">
<code class="descname">logical_or</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_or" title="Permalink to this definition">¶</a></dt>
<dd><p><a class="reference internal" href="#decimal.Decimal.logical_or" title="decimal.Decimal.logical_or"><code class="xref py py-meth docutils literal"><span class="pre">logical_or()</span></code></a> is a logical operation which takes two <em>logical
operands</em> (see <a class="reference internal" href="#logical-operands-label"><span>Logical operands</span></a>). The result is the
digit-wise <code class="docutils literal"><span class="pre">or</span></code> of the two operands.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.logical_xor">
<code class="descname">logical_xor</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.logical_xor" title="Permalink to this definition">¶</a></dt>
<dd><p><a class="reference internal" href="#decimal.Decimal.logical_xor" title="decimal.Decimal.logical_xor"><code class="xref py py-meth docutils literal"><span class="pre">logical_xor()</span></code></a> is a logical operation which takes two <em>logical
operands</em> (see <a class="reference internal" href="#logical-operands-label"><span>Logical operands</span></a>). The result is the
digit-wise exclusive or of the two operands.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.max">
<code class="descname">max</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.max" title="Permalink to this definition">¶</a></dt>
<dd><p>Like <code class="docutils literal"><span class="pre">max(self,</span> <span class="pre">other)</span></code> except that the context rounding rule is applied
before returning and that <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> values are either signaled or
ignored (depending on the context and whether they are signaling or
quiet).</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.max_mag">
<code class="descname">max_mag</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.max_mag" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">max()</span></code></a> method, but the comparison is done using the
absolute values of the operands.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.min">
<code class="descname">min</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.min" title="Permalink to this definition">¶</a></dt>
<dd><p>Like <code class="docutils literal"><span class="pre">min(self,</span> <span class="pre">other)</span></code> except that the context rounding rule is applied
before returning and that <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> values are either signaled or
ignored (depending on the context and whether they are signaling or
quiet).</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.min_mag">
<code class="descname">min_mag</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.min_mag" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">min()</span></code></a> method, but the comparison is done using the
absolute values of the operands.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.next_minus">
<code class="descname">next_minus</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.next_minus" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the largest number representable in the given context (or in the
current thread’s context if no context is given) that is smaller than the
given operand.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.next_plus">
<code class="descname">next_plus</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.next_plus" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the smallest number representable in the given context (or in the
current thread’s context if no context is given) that is larger than the
given operand.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.next_toward">
<code class="descname">next_toward</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.next_toward" title="Permalink to this definition">¶</a></dt>
<dd><p>If the two operands are unequal, return the number closest to the first
operand in the direction of the second operand. If both operands are
numerically equal, return a copy of the first operand with the sign set to
be the same as the sign of the second operand.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.normalize">
<code class="descname">normalize</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.normalize" title="Permalink to this definition">¶</a></dt>
<dd><p>Normalize the number by stripping the rightmost trailing zeros and
converting any result equal to <code class="xref py py-const docutils literal"><span class="pre">Decimal('0')</span></code> to
<code class="xref py py-const docutils literal"><span class="pre">Decimal('0e0')</span></code>. Used for producing canonical values for attributes
of an equivalence class. For example, <code class="docutils literal"><span class="pre">Decimal('32.100')</span></code> and
<code class="docutils literal"><span class="pre">Decimal('0.321000e+2')</span></code> both normalize to the equivalent value
<code class="docutils literal"><span class="pre">Decimal('32.1')</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.number_class">
<code class="descname">number_class</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.number_class" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a string describing the <em>class</em> of the operand. The returned value
is one of the following ten strings.</p>
<ul class="simple">
<li><code class="docutils literal"><span class="pre">"-Infinity"</span></code>, indicating that the operand is negative infinity.</li>
<li><code class="docutils literal"><span class="pre">"-Normal"</span></code>, indicating that the operand is a negative normal number.</li>
<li><code class="docutils literal"><span class="pre">"-Subnormal"</span></code>, indicating that the operand is negative and subnormal.</li>
<li><code class="docutils literal"><span class="pre">"-Zero"</span></code>, indicating that the operand is a negative zero.</li>
<li><code class="docutils literal"><span class="pre">"+Zero"</span></code>, indicating that the operand is a positive zero.</li>
<li><code class="docutils literal"><span class="pre">"+Subnormal"</span></code>, indicating that the operand is positive and subnormal.</li>
<li><code class="docutils literal"><span class="pre">"+Normal"</span></code>, indicating that the operand is a positive normal number.</li>
<li><code class="docutils literal"><span class="pre">"+Infinity"</span></code>, indicating that the operand is positive infinity.</li>
<li><code class="docutils literal"><span class="pre">"NaN"</span></code>, indicating that the operand is a quiet NaN (Not a Number).</li>
<li><code class="docutils literal"><span class="pre">"sNaN"</span></code>, indicating that the operand is a signaling NaN.</li>
</ul>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.quantize">
<code class="descname">quantize</code><span class="sig-paren">(</span><em>exp</em>, <em>rounding=None</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.quantize" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a value equal to the first operand after rounding and having the
exponent of the second operand.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'1.41421356'</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">'1.000'</span><span class="p">))</span>
<span class="go">Decimal('1.414')</span>
</pre></div>
</div>
<p>Unlike other operations, if the length of the coefficient after the
quantize operation would be greater than precision, then an
<a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal"><span class="pre">InvalidOperation</span></code></a> is signaled. This guarantees that, unless there
is an error condition, the quantized exponent is always equal to that of
the right-hand operand.</p>
<p>Also unlike other operations, quantize never signals Underflow, even if
the result is subnormal and inexact.</p>
<p>If the exponent of the second operand is larger than that of the first
then rounding may be necessary. In this case, the rounding mode is
determined by the <code class="docutils literal"><span class="pre">rounding</span></code> argument if given, else by the given
<code class="docutils literal"><span class="pre">context</span></code> argument; if neither argument is given the rounding mode of
the current thread’s context is used.</p>
<p>An error is returned whenever the resulting exponent is greater than
<code class="xref py py-attr docutils literal"><span class="pre">Emax</span></code> or less than <code class="xref py py-attr docutils literal"><span class="pre">Etiny</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.radix">
<code class="descname">radix</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.radix" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <code class="docutils literal"><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"><span class="pre">Decimal</span></code></a>
class does all its arithmetic. Included for compatibility with the
specification.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.remainder_near">
<code class="descname">remainder_near</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.remainder_near" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the remainder from dividing <em>self</em> by <em>other</em>. This differs from
<code class="docutils literal"><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
minimize its absolute value. More precisely, the return value is
<code class="docutils literal"><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"><span class="pre">n</span></code> is the integer nearest to the exact
value of <code class="docutils literal"><span class="pre">self</span> <span class="pre">/</span> <span class="pre">other</span></code>, and if two integers are equally near then the
even one is chosen.</p>
<p>If the result is zero then its sign will be the sign of <em>self</em>.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">Decimal('-2')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('5')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('-5')</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.rotate">
<code class="descname">rotate</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.rotate" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the result of rotating the digits of the first operand by an amount
specified by the second operand. The second operand must be an integer in
the range -precision through precision. The absolute value of the second
operand gives the number of places to rotate. If the second operand is
positive then rotation is to the left; otherwise rotation is to the right.
The coefficient of the first operand is padded on the left with zeros to
length precision if necessary. The sign and exponent of the first operand
are unchanged.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.same_quantum">
<code class="descname">same_quantum</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.same_quantum" title="Permalink to this definition">¶</a></dt>
<dd><p>Test whether self and other have the same exponent or whether both are
<code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>.</p>
<p>This operation is unaffected by context and is quiet: no flags are changed
and no rounding is performed. As an exception, the C version may raise
InvalidOperation if the second operand cannot be converted exactly.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.scaleb">
<code class="descname">scaleb</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.scaleb" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the first operand with exponent adjusted by the second.
Equivalently, return the first operand multiplied by <code class="docutils literal"><span class="pre">10**other</span></code>. The
second operand must be an integer.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.shift">
<code class="descname">shift</code><span class="sig-paren">(</span><em>other</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.shift" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the result of shifting the digits of the first operand by an amount
specified by the second operand. The second operand must be an integer in
the range -precision through precision. The absolute value of the second
operand gives the number of places to shift. If the second operand is
positive then the shift is to the left; otherwise the shift is to the
right. Digits shifted into the coefficient are zeros. The sign and
exponent of the first operand are unchanged.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.sqrt">
<code class="descname">sqrt</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.sqrt" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the square root of the argument to full precision.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.to_eng_string">
<code class="descname">to_eng_string</code><span class="sig-paren">(</span><em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_eng_string" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert to a string, using engineering notation if an exponent is needed.</p>
<p>Engineering notation has an exponent which is a multiple of 3. This
can leave up to 3 digits to the left of the decimal place and may
require the addition of either one or two trailing zeros.</p>
<p>For example, this converts <code class="docutils literal"><span class="pre">Decimal('123E+1')</span></code> to <code class="docutils literal"><span class="pre">Decimal('1.23E+3')</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.to_integral">
<code class="descname">to_integral</code><span class="sig-paren">(</span><em>rounding=None</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_integral" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">to_integral_value()</span></code></a> method. The <code class="docutils literal"><span class="pre">to_integral</span></code>
name has been kept for compatibility with older versions.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.to_integral_exact">
<code class="descname">to_integral_exact</code><span class="sig-paren">(</span><em>rounding=None</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_integral_exact" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">Inexact</span></code></a> or
<a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal"><span class="pre">Rounded</span></code></a> as appropriate if rounding occurs. The rounding mode is
determined by the <code class="docutils literal"><span class="pre">rounding</span></code> parameter if given, else by the given
<code class="docutils literal"><span class="pre">context</span></code>. If neither parameter is given then the rounding mode of the
current context is used.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Decimal.to_integral_value">
<code class="descname">to_integral_value</code><span class="sig-paren">(</span><em>rounding=None</em>, <em>context=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.to_integral_value" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">Inexact</span></code></a> or
<a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal"><span class="pre">Rounded</span></code></a>. If given, applies <em>rounding</em>; otherwise, uses the
rounding method in either the supplied <em>context</em> or the current context.</p>
</dd></dl>
</dd></dl>
<div class="section" id="logical-operands">
<span id="logical-operands-label"></span><h3>9.4.2.1. Logical operands<a class="headerlink" href="#logical-operands" title="Permalink to this headline">¶</a></h3>
<p>The <code class="xref py py-meth docutils literal"><span class="pre">logical_and()</span></code>, <code class="xref py py-meth docutils literal"><span class="pre">logical_invert()</span></code>, <code class="xref py py-meth docutils literal"><span class="pre">logical_or()</span></code>,
and <code class="xref py py-meth docutils literal"><span class="pre">logical_xor()</span></code> methods expect their arguments to be <em>logical
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"><span class="pre">Decimal</span></code></a> instance whose
exponent and sign are both zero, and whose digits are all either
<code class="xref py py-const docutils literal"><span class="pre">0</span></code> or <code class="xref py py-const docutils literal"><span class="pre">1</span></code>.</p>
</div>
</div>
<div class="section" id="context-objects">
<span id="decimal-context"></span><h2>9.4.3. Context objects<a class="headerlink" href="#context-objects" title="Permalink to this headline">¶</a></h2>
<p>Contexts are environments for arithmetic operations. They govern precision, set
rules for rounding, determine which signals are treated as exceptions, and limit
the range for exponents.</p>
<p>Each thread has its own current context which is accessed or changed using the
<a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal"><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"><span class="pre">setcontext()</span></code></a> functions:</p>
<dl class="function">
<dt id="decimal.getcontext">
<code class="descclassname">decimal.</code><code class="descname">getcontext</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.getcontext" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the current context for the active thread.</p>
</dd></dl>
<dl class="function">
<dt id="decimal.setcontext">
<code class="descclassname">decimal.</code><code class="descname">setcontext</code><span class="sig-paren">(</span><em>c</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.setcontext" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the current context for the active thread to <em>c</em>.</p>
</dd></dl>
<p>You can also use the <a class="reference internal" href="../reference/compound_stmts.html#with"><code class="xref std std-keyword docutils literal"><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"><span class="pre">localcontext()</span></code></a>
function to temporarily change the active context.</p>
<dl class="function">
<dt id="decimal.localcontext">
<code class="descclassname">decimal.</code><code class="descname">localcontext</code><span class="sig-paren">(</span><em>ctx=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.localcontext" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a context manager that will set the current context for the active thread
to a copy of <em>ctx</em> on entry to the with-statement and restore the previous context
when exiting the with-statement. If no context is specified, a copy of the
current context is used.</p>
<p>For example, the following code sets the current decimal precision to 42 places,
performs a calculation, and then automatically restores the previous context:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">decimal</span> <span class="k">import</span> <span class="n">localcontext</span>
<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>
<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>
<span class="n">s</span> <span class="o">=</span> <span class="n">calculate_something</span><span class="p">()</span>
<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>
</pre></div>
</div>
</dd></dl>
<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"><span class="pre">Context</span></code></a> constructor
described below. In addition, the module provides three pre-made contexts:</p>
<dl class="class">
<dt id="decimal.BasicContext">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">BasicContext</code><a class="headerlink" href="#decimal.BasicContext" title="Permalink to this definition">¶</a></dt>
<dd><p>This is a standard context defined by the General Decimal Arithmetic
Specification. Precision is set to nine. Rounding is set to
<a class="reference internal" href="#decimal.ROUND_HALF_UP" title="decimal.ROUND_HALF_UP"><code class="xref py py-const docutils literal"><span class="pre">ROUND_HALF_UP</span></code></a>. All flags are cleared. All traps are enabled (treated
as exceptions) except <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal"><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"><span class="pre">Rounded</span></code></a>, and
<a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-const docutils literal"><span class="pre">Subnormal</span></code></a>.</p>
<p>Because many of the traps are enabled, this context is useful for debugging.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.ExtendedContext">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">ExtendedContext</code><a class="headerlink" href="#decimal.ExtendedContext" title="Permalink to this definition">¶</a></dt>
<dd><p>This is a standard context defined by the General Decimal Arithmetic
Specification. Precision is set to nine. Rounding is set to
<a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal"><span class="pre">ROUND_HALF_EVEN</span></code></a>. All flags are cleared. No traps are enabled (so that
exceptions are not raised during computations).</p>
<p>Because the traps are disabled, this context is useful for applications that
prefer to have result value of <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> or <code class="xref py py-const docutils literal"><span class="pre">Infinity</span></code> instead of
raising exceptions. This allows an application to complete a run in the
presence of conditions that would otherwise halt the program.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.DefaultContext">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">DefaultContext</code><a class="headerlink" href="#decimal.DefaultContext" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">Context</span></code></a> constructor as a prototype for new
contexts. Changing a field (such a precision) has the effect of changing the
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"><span class="pre">Context</span></code></a> constructor.</p>
<p>This context is most useful in multi-threaded environments. Changing one of the
fields before threads are started has the effect of setting system-wide
defaults. Changing the fields after threads have started is not recommended as
it would require thread synchronization to prevent race conditions.</p>
<p>In single threaded environments, it is preferable to not use this context at
all. Instead, simply create contexts explicitly as described below.</p>
<p>The default values are <code class="xref py py-attr docutils literal"><span class="pre">prec</span></code>=<code class="xref py py-const docutils literal"><span class="pre">28</span></code>,
<code class="xref py py-attr docutils literal"><span class="pre">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"><span class="pre">ROUND_HALF_EVEN</span></code></a>,
and enabled traps for <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-class docutils literal"><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"><span class="pre">InvalidOperation</span></code></a>, and
<a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-class docutils literal"><span class="pre">DivisionByZero</span></code></a>.</p>
</dd></dl>
<p>In addition to the three supplied contexts, new contexts can be created with the
<a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal"><span class="pre">Context</span></code></a> constructor.</p>
<dl class="class">
<dt id="decimal.Context">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Context</code><span class="sig-paren">(</span><em>prec=None</em>, <em>rounding=None</em>, <em>Emin=None</em>, <em>Emax=None</em>, <em>capitals=None</em>, <em>clamp=None</em>, <em>flags=None</em>, <em>traps=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">None</span></code></a>, the
default values are copied from the <a class="reference internal" href="#decimal.DefaultContext" title="decimal.DefaultContext"><code class="xref py py-const docutils literal"><span class="pre">DefaultContext</span></code></a>. If the <em>flags</em>
field is not specified or is <a class="reference internal" href="constants.html#None" title="None"><code class="xref py py-const docutils literal"><span class="pre">None</span></code></a>, all flags are cleared.</p>
<p><em>prec</em> is an integer in the range [<code class="xref py py-const docutils literal"><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"><span class="pre">MAX_PREC</span></code></a>] that sets
the precision for arithmetic operations in the context.</p>
<p>The <em>rounding</em> option is one of the constants listed in the section
<a class="reference internal" href="#rounding-modes">Rounding Modes</a>.</p>
<p>The <em>traps</em> and <em>flags</em> fields list any signals to be set. Generally, new
contexts should only set traps and leave the flags clear.</p>
<p>The <em>Emin</em> and <em>Emax</em> fields are integers specifying the outer limits allowable
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"><span class="pre">MIN_EMIN</span></code></a>, <code class="xref py py-const docutils literal"><span class="pre">0</span></code>],
<em>Emax</em> in the range [<code class="xref py py-const docutils literal"><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"><span class="pre">MAX_EMAX</span></code></a>].</p>
<p>The <em>capitals</em> field is either <code class="xref py py-const docutils literal"><span class="pre">0</span></code> or <code class="xref py py-const docutils literal"><span class="pre">1</span></code> (the default). If set to
<code class="xref py py-const docutils literal"><span class="pre">1</span></code>, exponents are printed with a capital <code class="xref py py-const docutils literal"><span class="pre">E</span></code>; otherwise, a
lowercase <code class="xref py py-const docutils literal"><span class="pre">e</span></code> is used: <code class="xref py py-const docutils literal"><span class="pre">Decimal('6.02e+23')</span></code>.</p>
<p>The <em>clamp</em> field is either <code class="xref py py-const docutils literal"><span class="pre">0</span></code> (the default) or <code class="xref py py-const docutils literal"><span class="pre">1</span></code>.
If set to <code class="xref py py-const docutils literal"><span class="pre">1</span></code>, the exponent <code class="docutils literal"><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"><span class="pre">Decimal</span></code></a>
instance representable in this context is strictly limited to the
range <code class="docutils literal"><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"><=</span> <span class="pre">e</span> <span class="pre"><=</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
<code class="xref py py-const docutils literal"><span class="pre">0</span></code> then a weaker condition holds: the adjusted exponent of
the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> instance is at most <code class="docutils literal"><span class="pre">Emax</span></code>. When <em>clamp</em> is
<code class="xref py py-const docutils literal"><span class="pre">1</span></code>, a large normal number will, where possible, have its
exponent reduced and a corresponding number of zeros added to its
coefficient, in order to fit the exponent constraints; this
preserves the value of the number but loses information about
significant trailing zeros. For example:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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">'1.23e999'</span><span class="p">)</span>
<span class="go">Decimal('1.23000E+999')</span>
</pre></div>
</div>
<p>A <em>clamp</em> value of <code class="xref py py-const docutils literal"><span class="pre">1</span></code> allows compatibility with the
fixed-width decimal interchange formats specified in IEEE 754.</p>
<p>The <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal"><span class="pre">Context</span></code></a> class defines several general purpose methods as well as
a large number of methods for doing arithmetic directly in a given context.
In addition, for each of the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> methods described above (with
the exception of the <code class="xref py py-meth docutils literal"><span class="pre">adjusted()</span></code> and <code class="xref py py-meth docutils literal"><span class="pre">as_tuple()</span></code> methods) there is
a corresponding <a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-class docutils literal"><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"><span class="pre">Context</span></code></a>
instance <code class="docutils literal"><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"><span class="pre">Decimal</span></code></a> instance <code class="docutils literal"><span class="pre">x</span></code>, <code class="docutils literal"><span class="pre">C.exp(x)</span></code> is
equivalent to <code class="docutils literal"><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"><span class="pre">Context</span></code></a> method accepts a
Python integer (an instance of <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal"><span class="pre">int</span></code></a>) anywhere that a
Decimal instance is accepted.</p>
<dl class="method">
<dt id="decimal.Context.clear_flags">
<code class="descname">clear_flags</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.clear_flags" title="Permalink to this definition">¶</a></dt>
<dd><p>Resets all of the flags to <code class="xref py py-const docutils literal"><span class="pre">0</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.clear_traps">
<code class="descname">clear_traps</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.clear_traps" title="Permalink to this definition">¶</a></dt>
<dd><p>Resets all of the traps to <code class="xref py py-const docutils literal"><span class="pre">0</span></code>.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.3.</span></p>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.copy">
<code class="descname">copy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a duplicate of the context.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.copy_decimal">
<code class="descname">copy_decimal</code><span class="sig-paren">(</span><em>num</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_decimal" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a copy of the Decimal instance num.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.create_decimal">
<code class="descname">create_decimal</code><span class="sig-paren">(</span><em>num</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.create_decimal" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a new Decimal instance from <em>num</em> but using <em>self</em> as
context. Unlike the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> constructor, the context precision,
rounding method, flags, and traps are applied to the conversion.</p>
<p>This is useful because constants are often given to a greater precision
than is needed by the application. Another benefit is that rounding
immediately eliminates unintended effects from digits beyond the current
precision. In the following example, using unrounded inputs means that
adding zero to a sum can change the result:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.4445'</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'1.0023'</span><span class="p">)</span>
<span class="go">Decimal('4.45')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.4445'</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">'1.0023'</span><span class="p">)</span>
<span class="go">Decimal('4.44')</span>
</pre></div>
</div>
<p>This method implements the to-number operation of the IBM specification.
If the argument is a string, no leading or trailing whitespace is
permitted.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.create_decimal_from_float">
<code class="descname">create_decimal_from_float</code><span class="sig-paren">(</span><em>f</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.create_decimal_from_float" title="Permalink to this definition">¶</a></dt>
<dd><p>Creates a new Decimal instance from a float <em>f</em> but rounding using <em>self</em>
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"><span class="pre">Decimal.from_float()</span></code></a> class method,
the context precision, rounding method, flags, and traps are applied to
the conversion.</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </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>
<span class="go">Decimal('3.1415')</span>
<span class="gp">>>> </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>
<span class="gp">>>> </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>
<span class="gt">Traceback (most recent call last):</span>
<span class="o">...</span>
<span class="gr">decimal.Inexact</span>: <span class="n">None</span>
</pre></div>
</div>
<div class="versionadded">
<p><span class="versionmodified">New in version 3.1.</span></p>
</div>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.Etiny">
<code class="descname">Etiny</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.Etiny" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a value equal to <code class="docutils literal"><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
value for subnormal results. When underflow occurs, the exponent is set
to <a class="reference internal" href="#decimal.Context.Etiny" title="decimal.Context.Etiny"><code class="xref py py-const docutils literal"><span class="pre">Etiny</span></code></a>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.Etop">
<code class="descname">Etop</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.Etop" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a value equal to <code class="docutils literal"><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>
</dd></dl>
<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"><span class="pre">Decimal</span></code></a>
instances and then apply arithmetic operations which take place within the
current context for the active thread. An alternative approach is to use
context methods for calculating within a specific context. The methods are
similar to those for the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> class and are only briefly
recounted here.</p>
<dl class="method">
<dt id="decimal.Context.abs">
<code class="descname">abs</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.abs" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the absolute value of <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.add">
<code class="descname">add</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.add" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the sum of <em>x</em> and <em>y</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.canonical">
<code class="descname">canonical</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.canonical" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the same Decimal object <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.compare">
<code class="descname">compare</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares <em>x</em> and <em>y</em> numerically.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.compare_signal">
<code class="descname">compare_signal</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare_signal" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares the values of the two operands numerically.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.compare_total">
<code class="descname">compare_total</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare_total" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares two operands using their abstract representation.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.compare_total_mag">
<code class="descname">compare_total_mag</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.compare_total_mag" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares two operands using their abstract representation, ignoring sign.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.copy_abs">
<code class="descname">copy_abs</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_abs" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a copy of <em>x</em> with the sign set to 0.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.copy_negate">
<code class="descname">copy_negate</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_negate" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a copy of <em>x</em> with the sign inverted.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.copy_sign">
<code class="descname">copy_sign</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.copy_sign" title="Permalink to this definition">¶</a></dt>
<dd><p>Copies the sign from <em>y</em> to <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.divide">
<code class="descname">divide</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.divide" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>x</em> divided by <em>y</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.divide_int">
<code class="descname">divide_int</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.divide_int" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>x</em> divided by <em>y</em>, truncated to an integer.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.divmod">
<code class="descname">divmod</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.divmod" title="Permalink to this definition">¶</a></dt>
<dd><p>Divides two numbers and returns the integer part of the result.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.exp">
<code class="descname">exp</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.exp" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <cite>e ** x</cite>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.fma">
<code class="descname">fma</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>z</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.fma" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <em>x</em> multiplied by <em>y</em>, plus <em>z</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_canonical">
<code class="descname">is_canonical</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_canonical" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is canonical; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_finite">
<code class="descname">is_finite</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_finite" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is finite; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_infinite">
<code class="descname">is_infinite</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_infinite" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is infinite; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_nan">
<code class="descname">is_nan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_nan" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is a qNaN or sNaN; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_normal">
<code class="descname">is_normal</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_normal" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is a normal number; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_qnan">
<code class="descname">is_qnan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_qnan" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is a quiet NaN; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_signed">
<code class="descname">is_signed</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_signed" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is negative; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_snan">
<code class="descname">is_snan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_snan" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is a signaling NaN; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_subnormal">
<code class="descname">is_subnormal</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_subnormal" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is subnormal; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.is_zero">
<code class="descname">is_zero</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.is_zero" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if <em>x</em> is a zero; otherwise returns <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.ln">
<code class="descname">ln</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.ln" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the natural (base e) logarithm of <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.log10">
<code class="descname">log10</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.log10" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the base 10 logarithm of <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.logb">
<code class="descname">logb</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logb" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the exponent of the magnitude of the operand’s MSD.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.logical_and">
<code class="descname">logical_and</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_and" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the logical operation <em>and</em> between each operand’s digits.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.logical_invert">
<code class="descname">logical_invert</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_invert" title="Permalink to this definition">¶</a></dt>
<dd><p>Invert all the digits in <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.logical_or">
<code class="descname">logical_or</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_or" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the logical operation <em>or</em> between each operand’s digits.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.logical_xor">
<code class="descname">logical_xor</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.logical_xor" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the logical operation <em>xor</em> between each operand’s digits.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.max">
<code class="descname">max</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.max" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares two values numerically and returns the maximum.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.max_mag">
<code class="descname">max_mag</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.max_mag" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares the values numerically with their sign ignored.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.min">
<code class="descname">min</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.min" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares two values numerically and returns the minimum.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.min_mag">
<code class="descname">min_mag</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.min_mag" title="Permalink to this definition">¶</a></dt>
<dd><p>Compares the values numerically with their sign ignored.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.minus">
<code class="descname">minus</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.minus" title="Permalink to this definition">¶</a></dt>
<dd><p>Minus corresponds to the unary prefix minus operator in Python.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.multiply">
<code class="descname">multiply</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.multiply" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the product of <em>x</em> and <em>y</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.next_minus">
<code class="descname">next_minus</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.next_minus" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the largest representable number smaller than <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.next_plus">
<code class="descname">next_plus</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.next_plus" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the smallest representable number larger than <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.next_toward">
<code class="descname">next_toward</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.next_toward" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the number closest to <em>x</em>, in direction towards <em>y</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.normalize">
<code class="descname">normalize</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.normalize" title="Permalink to this definition">¶</a></dt>
<dd><p>Reduces <em>x</em> to its simplest form.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.number_class">
<code class="descname">number_class</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.number_class" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns an indication of the class of <em>x</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.plus">
<code class="descname">plus</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.plus" title="Permalink to this definition">¶</a></dt>
<dd><p>Plus corresponds to the unary prefix plus operator in Python. This
operation applies the context precision and rounding, so it is <em>not</em> an
identity operation.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.power">
<code class="descname">power</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>modulo=None</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.power" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <code class="docutils literal"><span class="pre">x</span></code> to the power of <code class="docutils literal"><span class="pre">y</span></code>, reduced modulo <code class="docutils literal"><span class="pre">modulo</span></code> if given.</p>
<p>With two arguments, compute <code class="docutils literal"><span class="pre">x**y</span></code>. If <code class="docutils literal"><span class="pre">x</span></code> is negative then <code class="docutils literal"><span class="pre">y</span></code>
must be integral. The result will be inexact unless <code class="docutils literal"><span class="pre">y</span></code> is integral and
the result is finite and can be expressed exactly in ‘precision’ digits.
The rounding mode of the context is used. Results are always correctly-rounded
in the Python version.</p>
<div class="versionchanged">
<p><span class="versionmodified">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"><span class="pre">power()</span></code></a> in terms of the correctly-rounded
<a class="reference internal" href="#decimal.Context.exp" title="decimal.Context.exp"><code class="xref py py-meth docutils literal"><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"><span class="pre">ln()</span></code></a> functions. The result is well-defined but
only “almost always correctly-rounded”.</p>
</div>
<p>With three arguments, compute <code class="docutils literal"><span class="pre">(x**y)</span> <span class="pre">%</span> <span class="pre">modulo</span></code>. For the three argument
form, the following restrictions on the arguments hold:</p>
<blockquote>
<div><ul class="simple">
<li>all three arguments must be integral</li>
<li><code class="docutils literal"><span class="pre">y</span></code> must be nonnegative</li>
<li>at least one of <code class="docutils literal"><span class="pre">x</span></code> or <code class="docutils literal"><span class="pre">y</span></code> must be nonzero</li>
<li><code class="docutils literal"><span class="pre">modulo</span></code> must be nonzero and have at most ‘precision’ digits</li>
</ul>
</div></blockquote>
<p>The value resulting from <code class="docutils literal"><span class="pre">Context.power(x,</span> <span class="pre">y,</span> <span class="pre">modulo)</span></code> is
equal to the value that would be obtained by computing <code class="docutils literal"><span class="pre">(x**y)</span>
<span class="pre">%</span> <span class="pre">modulo</span></code> with unbounded precision, but is computed more
efficiently. The exponent of the result is zero, regardless of
the exponents of <code class="docutils literal"><span class="pre">x</span></code>, <code class="docutils literal"><span class="pre">y</span></code> and <code class="docutils literal"><span class="pre">modulo</span></code>. The result is
always exact.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.quantize">
<code class="descname">quantize</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.quantize" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a value equal to <em>x</em> (rounded), having the exponent of <em>y</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.radix">
<code class="descname">radix</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.radix" title="Permalink to this definition">¶</a></dt>
<dd><p>Just returns 10, as this is Decimal, :)</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.remainder">
<code class="descname">remainder</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.remainder" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the remainder from integer division.</p>
<p>The sign of the result, if non-zero, is the same as that of the original
dividend.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.remainder_near">
<code class="descname">remainder_near</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.remainder_near" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><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
of <code class="docutils literal"><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>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.rotate">
<code class="descname">rotate</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.rotate" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a rotated copy of <em>x</em>, <em>y</em> times.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.same_quantum">
<code class="descname">same_quantum</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.same_quantum" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">True</span></code> if the two operands have the same exponent.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.scaleb">
<code class="descname">scaleb</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.scaleb" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the first operand after adding the second value its exp.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.shift">
<code class="descname">shift</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.shift" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a shifted copy of <em>x</em>, <em>y</em> times.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.sqrt">
<code class="descname">sqrt</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.sqrt" title="Permalink to this definition">¶</a></dt>
<dd><p>Square root of a non-negative number to context precision.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.subtract">
<code class="descname">subtract</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.subtract" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the difference between <em>x</em> and <em>y</em>.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.to_eng_string">
<code class="descname">to_eng_string</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.to_eng_string" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert to a string, using engineering notation if an exponent is needed.</p>
<p>Engineering notation has an exponent which is a multiple of 3. This
can leave up to 3 digits to the left of the decimal place and may
require the addition of either one or two trailing zeros.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.to_integral_exact">
<code class="descname">to_integral_exact</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.to_integral_exact" title="Permalink to this definition">¶</a></dt>
<dd><p>Rounds to an integer.</p>
</dd></dl>
<dl class="method">
<dt id="decimal.Context.to_sci_string">
<code class="descname">to_sci_string</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Context.to_sci_string" title="Permalink to this definition">¶</a></dt>
<dd><p>Converts a number to a string using scientific notation.</p>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="constants">
<span id="decimal-rounding-modes"></span><h2>9.4.4. Constants<a class="headerlink" href="#constants" title="Permalink to this headline">¶</a></h2>
<p>The constants in this section are only relevant for the C module. They
are also included in the pure Python version for compatibility.</p>
<table border="1" class="docutils">
<colgroup>
<col width="29%" />
<col width="29%" />
<col width="42%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head"> </th>
<th class="head">32-bit</th>
<th class="head">64-bit</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><dl class="first last data">
<dt id="decimal.MAX_PREC">
<code class="descclassname">decimal.</code><code class="descname">MAX_PREC</code><a class="headerlink" href="#decimal.MAX_PREC" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</td>
<td><code class="xref py py-const docutils literal"><span class="pre">425000000</span></code></td>
<td><code class="xref py py-const docutils literal"><span class="pre">999999999999999999</span></code></td>
</tr>
<tr class="row-odd"><td><dl class="first last data">
<dt id="decimal.MAX_EMAX">
<code class="descclassname">decimal.</code><code class="descname">MAX_EMAX</code><a class="headerlink" href="#decimal.MAX_EMAX" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</td>
<td><code class="xref py py-const docutils literal"><span class="pre">425000000</span></code></td>
<td><code class="xref py py-const docutils literal"><span class="pre">999999999999999999</span></code></td>
</tr>
<tr class="row-even"><td><dl class="first last data">
<dt id="decimal.MIN_EMIN">
<code class="descclassname">decimal.</code><code class="descname">MIN_EMIN</code><a class="headerlink" href="#decimal.MIN_EMIN" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</td>
<td><code class="xref py py-const docutils literal"><span class="pre">-425000000</span></code></td>
<td><code class="xref py py-const docutils literal"><span class="pre">-999999999999999999</span></code></td>
</tr>
<tr class="row-odd"><td><dl class="first last data">
<dt id="decimal.MIN_ETINY">
<code class="descclassname">decimal.</code><code class="descname">MIN_ETINY</code><a class="headerlink" href="#decimal.MIN_ETINY" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</td>
<td><code class="xref py py-const docutils literal"><span class="pre">-849999999</span></code></td>
<td><code class="xref py py-const docutils literal"><span class="pre">-1999999999999999997</span></code></td>
</tr>
</tbody>
</table>
<dl class="data">
<dt id="decimal.HAVE_THREADS">
<code class="descclassname">decimal.</code><code class="descname">HAVE_THREADS</code><a class="headerlink" href="#decimal.HAVE_THREADS" title="Permalink to this definition">¶</a></dt>
<dd><p>The default value is <code class="docutils literal"><span class="pre">True</span></code>. If Python is compiled without threads, the
C version automatically disables the expensive thread local context
machinery. In this case, the value is <code class="docutils literal"><span class="pre">False</span></code>.</p>
</dd></dl>
</div>
<div class="section" id="rounding-modes">
<h2>9.4.5. Rounding modes<a class="headerlink" href="#rounding-modes" title="Permalink to this headline">¶</a></h2>
<dl class="data">
<dt id="decimal.ROUND_CEILING">
<code class="descclassname">decimal.</code><code class="descname">ROUND_CEILING</code><a class="headerlink" href="#decimal.ROUND_CEILING" title="Permalink to this definition">¶</a></dt>
<dd><p>Round towards <code class="xref py py-const docutils literal"><span class="pre">Infinity</span></code>.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_DOWN">
<code class="descclassname">decimal.</code><code class="descname">ROUND_DOWN</code><a class="headerlink" href="#decimal.ROUND_DOWN" title="Permalink to this definition">¶</a></dt>
<dd><p>Round towards zero.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_FLOOR">
<code class="descclassname">decimal.</code><code class="descname">ROUND_FLOOR</code><a class="headerlink" href="#decimal.ROUND_FLOOR" title="Permalink to this definition">¶</a></dt>
<dd><p>Round towards <code class="xref py py-const docutils literal"><span class="pre">-Infinity</span></code>.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_HALF_DOWN">
<code class="descclassname">decimal.</code><code class="descname">ROUND_HALF_DOWN</code><a class="headerlink" href="#decimal.ROUND_HALF_DOWN" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest with ties going towards zero.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_HALF_EVEN">
<code class="descclassname">decimal.</code><code class="descname">ROUND_HALF_EVEN</code><a class="headerlink" href="#decimal.ROUND_HALF_EVEN" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest with ties going to nearest even integer.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_HALF_UP">
<code class="descclassname">decimal.</code><code class="descname">ROUND_HALF_UP</code><a class="headerlink" href="#decimal.ROUND_HALF_UP" title="Permalink to this definition">¶</a></dt>
<dd><p>Round to nearest with ties going away from zero.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_UP">
<code class="descclassname">decimal.</code><code class="descname">ROUND_UP</code><a class="headerlink" href="#decimal.ROUND_UP" title="Permalink to this definition">¶</a></dt>
<dd><p>Round away from zero.</p>
</dd></dl>
<dl class="data">
<dt id="decimal.ROUND_05UP">
<code class="descclassname">decimal.</code><code class="descname">ROUND_05UP</code><a class="headerlink" href="#decimal.ROUND_05UP" title="Permalink to this definition">¶</a></dt>
<dd><p>Round away from zero if last digit after rounding towards zero would have
been 0 or 5; otherwise round towards zero.</p>
</dd></dl>
</div>
<div class="section" id="signals">
<span id="decimal-signals"></span><h2>9.4.6. Signals<a class="headerlink" href="#signals" title="Permalink to this headline">¶</a></h2>
<p>Signals represent conditions that arise during computation. Each corresponds to
one context flag and one context trap enabler.</p>
<p>The context flag is set whenever the condition is encountered. After the
computation, flags may be checked for informational purposes (for instance, to
determine whether a computation was exact). After checking the flags, be sure to
clear all flags before starting the next computation.</p>
<p>If the context’s trap enabler is set for the signal, then the condition causes a
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"><span class="pre">DivisionByZero</span></code></a> trap
is set, then a <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-exc docutils literal"><span class="pre">DivisionByZero</span></code></a> exception is raised upon encountering the
condition.</p>
<dl class="class">
<dt id="decimal.Clamped">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Clamped</code><a class="headerlink" href="#decimal.Clamped" title="Permalink to this definition">¶</a></dt>
<dd><p>Altered an exponent to fit representation constraints.</p>
<p>Typically, clamping occurs when an exponent falls outside the context’s
<code class="xref py py-attr docutils literal"><span class="pre">Emin</span></code> and <code class="xref py py-attr docutils literal"><span class="pre">Emax</span></code> limits. If possible, the exponent is reduced to
fit by adding zeros to the coefficient.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.DecimalException">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">DecimalException</code><a class="headerlink" href="#decimal.DecimalException" title="Permalink to this definition">¶</a></dt>
<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"><span class="pre">ArithmeticError</span></code></a>.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.DivisionByZero">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">DivisionByZero</code><a class="headerlink" href="#decimal.DivisionByZero" title="Permalink to this definition">¶</a></dt>
<dd><p>Signals the division of a non-infinite number by zero.</p>
<p>Can occur with division, modulo division, or when raising a number to a negative
power. If this signal is not trapped, returns <code class="xref py py-const docutils literal"><span class="pre">Infinity</span></code> or
<code class="xref py py-const docutils literal"><span class="pre">-Infinity</span></code> with the sign determined by the inputs to the calculation.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.Inexact">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Inexact</code><a class="headerlink" href="#decimal.Inexact" title="Permalink to this definition">¶</a></dt>
<dd><p>Indicates that rounding occurred and the result is not exact.</p>
<p>Signals when non-zero digits were discarded during rounding. The rounded result
is returned. The signal flag or trap is used to detect when results are
inexact.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.InvalidOperation">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">InvalidOperation</code><a class="headerlink" href="#decimal.InvalidOperation" title="Permalink to this definition">¶</a></dt>
<dd><p>An invalid operation was performed.</p>
<p>Indicates that an operation was requested that does not make sense. If not
trapped, returns <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>. Possible causes include:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="n">Infinity</span> <span class="o">-</span> <span class="n">Infinity</span>
<span class="mi">0</span> <span class="o">*</span> <span class="n">Infinity</span>
<span class="n">Infinity</span> <span class="o">/</span> <span class="n">Infinity</span>
<span class="n">x</span> <span class="o">%</span> <span class="mi">0</span>
<span class="n">Infinity</span> <span class="o">%</span> <span class="n">x</span>
<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">></span> <span class="mi">0</span>
<span class="mi">0</span> <span class="o">**</span> <span class="mi">0</span>
<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>
<span class="n">x</span> <span class="o">**</span> <span class="n">Infinity</span>
</pre></div>
</div>
</dd></dl>
<dl class="class">
<dt id="decimal.Overflow">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Overflow</code><a class="headerlink" href="#decimal.Overflow" title="Permalink to this definition">¶</a></dt>
<dd><p>Numerical overflow.</p>
<p>Indicates the exponent is larger than <code class="xref py py-attr docutils literal"><span class="pre">Emax</span></code> after rounding has
occurred. If not trapped, the result depends on the rounding mode, either
pulling inward to the largest representable finite number or rounding outward
to <code class="xref py py-const docutils literal"><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"><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"><span class="pre">Rounded</span></code></a>
are also signaled.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.Rounded">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Rounded</code><a class="headerlink" href="#decimal.Rounded" title="Permalink to this definition">¶</a></dt>
<dd><p>Rounding occurred though possibly no information was lost.</p>
<p>Signaled whenever rounding discards digits; even if those digits are zero
(such as rounding <code class="xref py py-const docutils literal"><span class="pre">5.00</span></code> to <code class="xref py py-const docutils literal"><span class="pre">5.0</span></code>). If not trapped, returns
the result unchanged. This signal is used to detect loss of significant
digits.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.Subnormal">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Subnormal</code><a class="headerlink" href="#decimal.Subnormal" title="Permalink to this definition">¶</a></dt>
<dd><p>Exponent was lower than <code class="xref py py-attr docutils literal"><span class="pre">Emin</span></code> prior to rounding.</p>
<p>Occurs when an operation result is subnormal (the exponent is too small). If
not trapped, returns the result unchanged.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.Underflow">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">Underflow</code><a class="headerlink" href="#decimal.Underflow" title="Permalink to this definition">¶</a></dt>
<dd><p>Numerical underflow with result rounded to zero.</p>
<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"><span class="pre">Inexact</span></code></a>
and <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-class docutils literal"><span class="pre">Subnormal</span></code></a> are also signaled.</p>
</dd></dl>
<dl class="class">
<dt id="decimal.FloatOperation">
<em class="property">class </em><code class="descclassname">decimal.</code><code class="descname">FloatOperation</code><a class="headerlink" href="#decimal.FloatOperation" title="Permalink to this definition">¶</a></dt>
<dd><p>Enable stricter semantics for mixing floats and Decimals.</p>
<p>If the signal is not trapped (default), mixing floats and Decimals is
permitted in the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> constructor,
<a class="reference internal" href="#decimal.Context.create_decimal" title="decimal.Context.create_decimal"><code class="xref py py-meth docutils literal"><span class="pre">create_decimal()</span></code></a> and all comparison operators.
Both conversion and comparisons are exact. Any occurrence of a mixed
operation is silently recorded by setting <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal"><span class="pre">FloatOperation</span></code></a> in the
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"><span class="pre">from_float()</span></code></a>
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"><span class="pre">create_decimal_from_float()</span></code></a> do not set the flag.</p>
<p>Otherwise (the signal is trapped), only equality comparisons and explicit
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"><span class="pre">FloatOperation</span></code></a>.</p>
</dd></dl>
<p>The following table summarizes the hierarchy of signals:</p>
<div class="highlight-python3"><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>
<span class="n">DecimalException</span>
<span class="n">Clamped</span>
<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>
<span class="n">Inexact</span>
<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>
<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>
<span class="n">InvalidOperation</span>
<span class="n">Rounded</span>
<span class="n">Subnormal</span>
<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>
</pre></div>
</div>
</div>
<div class="section" id="floating-point-notes">
<span id="decimal-notes"></span><h2>9.4.7. Floating Point Notes<a class="headerlink" href="#floating-point-notes" title="Permalink to this headline">¶</a></h2>
<div class="section" id="mitigating-round-off-error-with-increased-precision">
<h3>9.4.7.1. Mitigating round-off error with increased precision<a class="headerlink" href="#mitigating-round-off-error-with-increased-precision" title="Permalink to this headline">¶</a></h3>
<p>The use of decimal floating point eliminates decimal representation error
(making it possible to represent <code class="xref py py-const docutils literal"><span class="pre">0.1</span></code> exactly); however, some operations
can still incur round-off error when non-zero digits exceed the fixed precision.</p>
<p>The effects of round-off error can be amplified by the addition or subtraction
of nearly offsetting quantities resulting in loss of significance. Knuth
provides two instructive examples where rounded floating point arithmetic with
insufficient precision causes the breakdown of the associative and distributive
properties of addition:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="c1"># Examples from Seminumerical Algorithms, Section 4.2.2.</span>
<span class="o">>>></span> <span class="kn">from</span> <span class="nn">decimal</span> <span class="k">import</span> <span class="n">Decimal</span><span class="p">,</span> <span class="n">getcontext</span>
<span class="o">>>></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>
<span class="o">>>></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">'7.51111111'</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">v</span><span class="p">)</span> <span class="o">+</span> <span class="n">w</span>
<span class="n">Decimal</span><span class="p">(</span><span class="s1">'9.5111111'</span><span class="p">)</span>
<span class="o">>>></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>
<span class="n">Decimal</span><span class="p">(</span><span class="s1">'10'</span><span class="p">)</span>
<span class="o">>>></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">'6.0000003'</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">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>
<span class="n">Decimal</span><span class="p">(</span><span class="s1">'0.01'</span><span class="p">)</span>
<span class="o">>>></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>
<span class="n">Decimal</span><span class="p">(</span><span class="s1">'0.0060000'</span><span class="p">)</span>
</pre></div>
</div>
<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"><span class="pre">decimal</span></code></a> module makes it possible to restore the identities by
expanding the precision sufficiently to avoid loss of significance:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </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">'7.51111111'</span><span class="p">)</span>
<span class="gp">>>> </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>
<span class="go">Decimal('9.51111111')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('9.51111111')</span>
<span class="go">>>></span>
<span class="gp">>>> </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">'6.0000003'</span><span class="p">)</span>
<span class="gp">>>> </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>
<span class="go">Decimal('0.0060000')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('0.0060000')</span>
</pre></div>
</div>
</div>
<div class="section" id="special-values">
<h3>9.4.7.2. Special values<a class="headerlink" href="#special-values" title="Permalink to this headline">¶</a></h3>
<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"><span class="pre">decimal</span></code></a> module provides special values
including <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>, <code class="xref py py-const docutils literal"><span class="pre">sNaN</span></code>, <code class="xref py py-const docutils literal"><span class="pre">-Infinity</span></code>, <code class="xref py py-const docutils literal"><span class="pre">Infinity</span></code>,
and two zeros, <code class="xref py py-const docutils literal"><span class="pre">+0</span></code> and <code class="xref py py-const docutils literal"><span class="pre">-0</span></code>.</p>
<p>Infinities can be constructed directly with: <code class="docutils literal"><span class="pre">Decimal('Infinity')</span></code>. Also,
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"><span class="pre">DivisionByZero</span></code></a> signal is
not trapped. Likewise, when the <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-exc docutils literal"><span class="pre">Overflow</span></code></a> signal is not trapped, infinity
can result from rounding beyond the limits of the largest representable number.</p>
<p>The infinities are signed (affine) and can be used in arithmetic operations
where they get treated as very large, indeterminate numbers. For instance,
adding a constant to infinity gives another infinite result.</p>
<p>Some operations are indeterminate and return <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>, or if the
<a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-exc docutils literal"><span class="pre">InvalidOperation</span></code></a> signal is trapped, raise an exception. For example,
<code class="docutils literal"><span class="pre">0/0</span></code> returns <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> which means “not a number”. This variety of
<code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> is quiet and, once created, will flow through other computations
always resulting in another <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code>. This behavior can be useful for a
series of computations that occasionally have missing inputs — it allows the
calculation to proceed while flagging specific results as invalid.</p>
<p>A variant is <code class="xref py py-const docutils literal"><span class="pre">sNaN</span></code> which signals rather than remaining quiet after every
operation. This is a useful return value when an invalid result needs to
interrupt a calculation for special handling.</p>
<p>The behavior of Python’s comparison operators can be a little surprising where a
<code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> is involved. A test for equality where one of the operands is a
quiet or signaling <code class="xref py py-const docutils literal"><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"><span class="pre">False</span></code></a> (even when doing
<code class="docutils literal"><span class="pre">Decimal('NaN')==Decimal('NaN')</span></code>), while a test for inequality always returns
<a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal"><span class="pre">True</span></code></a>. An attempt to compare two Decimals using any of the <code class="docutils literal"><span class="pre"><</span></code>,
<code class="docutils literal"><span class="pre"><=</span></code>, <code class="docutils literal"><span class="pre">></span></code> or <code class="docutils literal"><span class="pre">>=</span></code> operators will raise the <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-exc docutils literal"><span class="pre">InvalidOperation</span></code></a> signal
if either operand is a <code class="xref py py-const docutils literal"><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"><span class="pre">False</span></code></a> if this signal is
not trapped. Note that the General Decimal Arithmetic specification does not
specify the behavior of direct comparisons; these rules for comparisons
involving a <code class="xref py py-const docutils literal"><span class="pre">NaN</span></code> were taken from the IEEE 854 standard (see Table 3 in
section 5.7). To ensure strict standards-compliance, use the <code class="xref py py-meth docutils literal"><span class="pre">compare()</span></code>
and <code class="xref py py-meth docutils literal"><span class="pre">compare-signal()</span></code> methods instead.</p>
<p>The signed zeros can result from calculations that underflow. They keep the sign
that would have resulted if the calculation had been carried out to greater
precision. Since their magnitude is zero, both positive and negative zeros are
treated as equal and their sign is informational.</p>
<p>In addition to the two signed zeros which are distinct yet equal, there are
various representations of zero with differing precisions yet equivalent in
value. This takes a bit of getting used to. For an eye accustomed to
normalized floating point representations, it is not immediately obvious that
the following calculation returns a value equal to zero:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="mi">1</span> <span class="o">/</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'Infinity'</span><span class="p">)</span>
<span class="go">Decimal('0E-1000026')</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="working-with-threads">
<span id="decimal-threads"></span><h2>9.4.8. Working with threads<a class="headerlink" href="#working-with-threads" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal"><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"><span class="pre">Context</span></code></a> object for
each thread. Having separate thread contexts means that threads may make
changes (such as <code class="docutils literal"><span class="pre">getcontext().prec=10</span></code>) without interfering with other threads.</p>
<p>Likewise, the <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal"><span class="pre">setcontext()</span></code></a> function automatically assigns its target to
the current thread.</p>
<p>If <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal"><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"><span class="pre">getcontext()</span></code></a>, then
<a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal"><span class="pre">getcontext()</span></code></a> will automatically create a new context for use in the
current thread.</p>
<p>The new context is copied from a prototype context called <em>DefaultContext</em>. To
control the defaults so that each thread will use the same values throughout the
application, directly modify the <em>DefaultContext</em> object. This should be done
<em>before</em> any threads are started so that there won’t be a race condition between
threads calling <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal"><span class="pre">getcontext()</span></code></a>. For example:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="c1"># Set applicationwide defaults for all threads about to be launched</span>
<span class="n">DefaultContext</span><span class="o">.</span><span class="n">prec</span> <span class="o">=</span> <span class="mi">12</span>
<span class="n">DefaultContext</span><span class="o">.</span><span class="n">rounding</span> <span class="o">=</span> <span class="n">ROUND_DOWN</span>
<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>
<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>
<span class="n">setcontext</span><span class="p">(</span><span class="n">DefaultContext</span><span class="p">)</span>
<span class="c1"># Afterwards, the threads can be started</span>
<span class="n">t1</span><span class="o">.</span><span class="n">start</span><span class="p">()</span>
<span class="n">t2</span><span class="o">.</span><span class="n">start</span><span class="p">()</span>
<span class="n">t3</span><span class="o">.</span><span class="n">start</span><span class="p">()</span>
<span class="o">.</span> <span class="o">.</span> <span class="o">.</span>
</pre></div>
</div>
</div>
<div class="section" id="recipes">
<span id="decimal-recipes"></span><h2>9.4.9. Recipes<a class="headerlink" href="#recipes" title="Permalink to this headline">¶</a></h2>
<p>Here are a few recipes that serve as utility functions and that demonstrate ways
to work with the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal"><span class="pre">Decimal</span></code></a> class:</p>
<div class="highlight-python3"><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">''</span><span class="p">,</span> <span class="n">sep</span><span class="o">=</span><span class="s1">','</span><span class="p">,</span> <span class="n">dp</span><span class="o">=</span><span class="s1">'.'</span><span class="p">,</span>
<span class="n">pos</span><span class="o">=</span><span class="s1">''</span><span class="p">,</span> <span class="n">neg</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">trailneg</span><span class="o">=</span><span class="s1">''</span><span class="p">):</span>
<span class="sd">"""Convert Decimal to a money formatted string.</span>
<span class="sd"> places: required number of places after the decimal point</span>
<span class="sd"> curr: optional currency symbol before the sign (may be blank)</span>
<span class="sd"> sep: optional grouping separator (comma, period, space, or blank)</span>
<span class="sd"> dp: decimal point indicator (comma or period)</span>
<span class="sd"> only specify as blank when places is zero</span>
<span class="sd"> pos: optional sign for positive numbers: '+', space or blank</span>
<span class="sd"> neg: optional sign for negative numbers: '-', '(', space or blank</span>
<span class="sd"> trailneg:optional trailing minus indicator: '-', ')', space or blank</span>
<span class="sd"> >>> d = Decimal('-1234567.8901')</span>
<span class="sd"> >>> moneyfmt(d, curr='$')</span>
<span class="sd"> '-$1,234,567.89'</span>
<span class="sd"> >>> moneyfmt(d, places=0, sep='.', dp='', neg='', trailneg='-')</span>
<span class="sd"> '1.234.568-'</span>
<span class="sd"> >>> moneyfmt(d, curr='$', neg='(', trailneg=')')</span>
<span class="sd"> '($1,234,567.89)'</span>
<span class="sd"> >>> moneyfmt(Decimal(123456789), sep=' ')</span>
<span class="sd"> '123 456 789.00'</span>
<span class="sd"> >>> moneyfmt(Decimal('-0.02'), neg='<', trailneg='>')</span>
<span class="sd"> '<0.02>'</span>
<span class="sd"> """</span>
<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 --> '0.01'</span>
<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>
<span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
<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>
<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>
<span class="k">if</span> <span class="n">sign</span><span class="p">:</span>
<span class="n">build</span><span class="p">(</span><span class="n">trailneg</span><span class="p">)</span>
<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>
<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">'0'</span><span class="p">)</span>
<span class="k">if</span> <span class="n">places</span><span class="p">:</span>
<span class="n">build</span><span class="p">(</span><span class="n">dp</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">digits</span><span class="p">:</span>
<span class="n">build</span><span class="p">(</span><span class="s1">'0'</span><span class="p">)</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">digits</span><span class="p">:</span>
<span class="n">build</span><span class="p">(</span><span class="nb">next</span><span class="p">())</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<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>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">build</span><span class="p">(</span><span class="n">sep</span><span class="p">)</span>
<span class="n">build</span><span class="p">(</span><span class="n">curr</span><span class="p">)</span>
<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>
<span class="k">return</span> <span class="s1">''</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>
<span class="k">def</span> <span class="nf">pi</span><span class="p">():</span>
<span class="sd">"""Compute Pi to the current precision.</span>
<span class="sd"> >>> print(pi())</span>
<span class="sd"> 3.141592653589793238462643383</span>
<span class="sd"> """</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">2</span> <span class="c1"># extra digits for intermediate steps</span>
<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 "three=3.0" for regular floats</span>
<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>
<span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>
<span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>
<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>
<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>
<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>
<span class="n">s</span> <span class="o">+=</span> <span class="n">t</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">2</span>
<span class="k">return</span> <span class="o">+</span><span class="n">s</span> <span class="c1"># unary plus applies the new precision</span>
<span class="k">def</span> <span class="nf">exp</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="sd">"""Return e raised to the power of x. Result type matches input type.</span>
<span class="sd"> >>> print(exp(Decimal(1)))</span>
<span class="sd"> 2.718281828459045235360287471</span>
<span class="sd"> >>> print(exp(Decimal(2)))</span>
<span class="sd"> 7.389056098930650227230427461</span>
<span class="sd"> >>> print(exp(2.0))</span>
<span class="sd"> 7.38905609893</span>
<span class="sd"> >>> print(exp(2+0j))</span>
<span class="sd"> (7.38905609893+0j)</span>
<span class="sd"> """</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">2</span>
<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>
<span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>
<span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">fact</span> <span class="o">*=</span> <span class="n">i</span>
<span class="n">num</span> <span class="o">*=</span> <span class="n">x</span>
<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="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="k">return</span> <span class="o">+</span><span class="n">s</span>
<span class="k">def</span> <span class="nf">cos</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="sd">"""Return the cosine of x as measured in radians.</span>
<span class="sd"> The Taylor series approximation works best for a small value of x.</span>
<span class="sd"> For larger values, first compute x = x % (2 * pi).</span>
<span class="sd"> >>> print(cos(Decimal('0.5')))</span>
<span class="sd"> 0.8775825618903727161162815826</span>
<span class="sd"> >>> print(cos(0.5))</span>
<span class="sd"> 0.87758256189</span>
<span class="sd"> >>> print(cos(0.5+0j))</span>
<span class="sd"> (0.87758256189+0j)</span>
<span class="sd"> """</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">2</span>
<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>
<span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>
<span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">2</span>
<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>
<span class="n">num</span> <span class="o">*=</span> <span class="n">x</span> <span class="o">*</span> <span class="n">x</span>
<span class="n">sign</span> <span class="o">*=</span> <span class="o">-</span><span class="mi">1</span>
<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>
<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="k">return</span> <span class="o">+</span><span class="n">s</span>
<span class="k">def</span> <span class="nf">sin</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="sd">"""Return the sine of x as measured in radians.</span>
<span class="sd"> The Taylor series approximation works best for a small value of x.</span>
<span class="sd"> For larger values, first compute x = x % (2 * pi).</span>
<span class="sd"> >>> print(sin(Decimal('0.5')))</span>
<span class="sd"> 0.4794255386042030002732879352</span>
<span class="sd"> >>> print(sin(0.5))</span>
<span class="sd"> 0.479425538604</span>
<span class="sd"> >>> print(sin(0.5+0j))</span>
<span class="sd"> (0.479425538604+0j)</span>
<span class="sd"> """</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">2</span>
<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>
<span class="k">while</span> <span class="n">s</span> <span class="o">!=</span> <span class="n">lasts</span><span class="p">:</span>
<span class="n">lasts</span> <span class="o">=</span> <span class="n">s</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">2</span>
<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>
<span class="n">num</span> <span class="o">*=</span> <span class="n">x</span> <span class="o">*</span> <span class="n">x</span>
<span class="n">sign</span> <span class="o">*=</span> <span class="o">-</span><span class="mi">1</span>
<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>
<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="k">return</span> <span class="o">+</span><span class="n">s</span>
</pre></div>
</div>
</div>
<div class="section" id="decimal-faq">
<span id="id1"></span><h2>9.4.10. Decimal FAQ<a class="headerlink" href="#decimal-faq" title="Permalink to this headline">¶</a></h2>
<p>Q. It is cumbersome to type <code class="docutils literal"><span class="pre">decimal.Decimal('1234.5')</span></code>. Is there a way to
minimize typing when using the interactive interpreter?</p>
<p>A. Some users abbreviate the constructor to just a single letter:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">D</span> <span class="o">=</span> <span class="n">decimal</span><span class="o">.</span><span class="n">Decimal</span>
<span class="gp">>>> </span><span class="n">D</span><span class="p">(</span><span class="s1">'1.23'</span><span class="p">)</span> <span class="o">+</span> <span class="n">D</span><span class="p">(</span><span class="s1">'3.45'</span><span class="p">)</span>
<span class="go">Decimal('4.68')</span>
</pre></div>
</div>
<p>Q. In a fixed-point application with two decimal places, some inputs have many
places and need to be rounded. Others are not supposed to have excess digits
and need to be validated. What methods should be used?</p>
<p>A. The <code class="xref py py-meth docutils literal"><span class="pre">quantize()</span></code> method rounds to a fixed number of decimal places. If
the <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal"><span class="pre">Inexact</span></code></a> trap is set, it is also useful for validation:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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('0.01')</span>
</pre></div>
</div>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># Round to two places</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.214'</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="go">Decimal('3.21')</span>
</pre></div>
</div>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># Validate that a number does not exceed two places</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.21'</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>
<span class="go">Decimal('3.21')</span>
</pre></div>
</div>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.214'</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>
<span class="gt">Traceback (most recent call last):</span>
<span class="c">...</span>
<span class="gr">Inexact</span>: <span class="n">None</span>
</pre></div>
</div>
<p>Q. Once I have valid two place inputs, how do I maintain that invariant
throughout an application?</p>
<p>A. Some operations like addition, subtraction, and multiplication by an integer
will automatically preserve fixed point. Others operations, like division and
non-integer multiplication, will change the number of decimal places and need to
be followed-up with a <code class="xref py py-meth docutils literal"><span class="pre">quantize()</span></code> step:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'102.72'</span><span class="p">)</span> <span class="c1"># Initial fixed-point values</span>
<span class="gp">>>> </span><span class="n">b</span> <span class="o">=</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.17'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span> <span class="c1"># Addition preserves fixed-point</span>
<span class="go">Decimal('105.89')</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span>
<span class="go">Decimal('99.55')</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">*</span> <span class="mi">42</span> <span class="c1"># So does integer multiplication</span>
<span class="go">Decimal('4314.24')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('325.62')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('0.03')</span>
</pre></div>
</div>
<p>In developing fixed-point applications, it is convenient to define functions
to handle the <code class="xref py py-meth docutils literal"><span class="pre">quantize()</span></code> step:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<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>
<span class="gp">>>> </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>
<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>
</pre></div>
</div>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">Decimal('325.62')</span>
<span class="gp">>>> </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>
<span class="go">Decimal('0.03')</span>
</pre></div>
</div>
<p>Q. There are many ways to express the same value. The numbers <code class="xref py py-const docutils literal"><span class="pre">200</span></code>,
<code class="xref py py-const docutils literal"><span class="pre">200.000</span></code>, <code class="xref py py-const docutils literal"><span class="pre">2E2</span></code>, and <code class="xref py py-const docutils literal"><span class="pre">02E+4</span></code> all have the same value at
various precisions. Is there a way to transform them to a single recognizable
canonical value?</p>
<p>A. The <code class="xref py py-meth docutils literal"><span class="pre">normalize()</span></code> method maps all equivalent values to a single
representative:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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">'200 200.000 2E2 .02E+4'</span><span class="o">.</span><span class="n">split</span><span class="p">())</span>
<span class="gp">>>> </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>
<span class="go">[Decimal('2E+2'), Decimal('2E+2'), Decimal('2E+2'), Decimal('2E+2')]</span>
</pre></div>
</div>
<p>Q. Some decimal values always print with exponential notation. Is there a way
to get a non-exponential representation?</p>
<p>A. For some values, exponential notation is the only way to express the number
of significant places in the coefficient. For example, expressing
<code class="xref py py-const docutils literal"><span class="pre">5.0E+3</span></code> as <code class="xref py py-const docutils literal"><span class="pre">5000</span></code> keeps the value constant but cannot show the
original’s two-place significance.</p>
<p>If an application does not care about tracking significance, it is easy to
remove the exponent and trailing zeroes, losing significance, but keeping the
value unchanged:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<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>
</pre></div>
</div>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">remove_exponent</span><span class="p">(</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'5E+3'</span><span class="p">))</span>
<span class="go">Decimal('5000')</span>
</pre></div>
</div>
<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"><span class="pre">Decimal</span></code></a>?</p>
<p>A. Yes, any binary floating point number can be exactly expressed as a
Decimal though an exact conversion may take more precision than intuition would
suggest:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="go">Decimal('3.141592653589793115997963468544185161590576171875')</span>
</pre></div>
</div>
<p>Q. Within a complex calculation, how can I make sure that I haven’t gotten a
spurious result because of insufficient precision or rounding anomalies.</p>
<p>A. The decimal module makes it easy to test results. A best practice is to
re-run calculations using greater precision and with various rounding modes.
Widely differing results indicate insufficient precision, rounding mode issues,
ill-conditioned inputs, or a numerically unstable algorithm.</p>
<p>Q. I noticed that context precision is applied to the results of operations but
not to the inputs. Is there anything to watch out for when mixing values of
different precisions?</p>
<p>A. Yes. The principle is that all values are considered to be exact and so is
the arithmetic on those values. Only the results are rounded. The advantage
for inputs is that “what you type is what you get”. A disadvantage is that the
results can look odd if you forget that the inputs haven’t been rounded:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.104'</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'2.104'</span><span class="p">)</span>
<span class="go">Decimal('5.21')</span>
<span class="gp">>>> </span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'3.104'</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'0.000'</span><span class="p">)</span> <span class="o">+</span> <span class="n">Decimal</span><span class="p">(</span><span class="s1">'2.104'</span><span class="p">)</span>
<span class="go">Decimal('5.20')</span>
</pre></div>
</div>
<p>The solution is either to increase precision or to force rounding of inputs
using the unary plus operation:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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>
<span class="gp">>>> </span><span class="o">+</span><span class="n">Decimal</span><span class="p">(</span><span class="s1">'1.23456789'</span><span class="p">)</span> <span class="c1"># unary plus triggers rounding</span>
<span class="go">Decimal('1.23')</span>
</pre></div>
</div>
<p>Alternatively, inputs can be rounded upon creation using the
<a class="reference internal" href="#decimal.Context.create_decimal" title="decimal.Context.create_decimal"><code class="xref py py-meth docutils literal"><span class="pre">Context.create_decimal()</span></code></a> method:</p>
<div class="highlight-python3"><div class="highlight"><pre><span></span><span class="gp">>>> </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">'1.2345678'</span><span class="p">)</span>
<span class="go">Decimal('1.2345')</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
</div>
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<div class="sphinxsidebarwrapper">
<h3><a href="../contents.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">9.4. <code class="docutils literal"><span class="pre">decimal</span></code> — Decimal fixed point and floating point arithmetic</a><ul>
<li><a class="reference internal" href="#quick-start-tutorial">9.4.1. Quick-start Tutorial</a></li>
<li><a class="reference internal" href="#decimal-objects">9.4.2. Decimal objects</a><ul>
<li><a class="reference internal" href="#logical-operands">9.4.2.1. Logical operands</a></li>
</ul>
</li>
<li><a class="reference internal" href="#context-objects">9.4.3. Context objects</a></li>
<li><a class="reference internal" href="#constants">9.4.4. Constants</a></li>
<li><a class="reference internal" href="#rounding-modes">9.4.5. Rounding modes</a></li>
<li><a class="reference internal" href="#signals">9.4.6. Signals</a></li>
<li><a class="reference internal" href="#floating-point-notes">9.4.7. Floating Point Notes</a><ul>
<li><a class="reference internal" href="#mitigating-round-off-error-with-increased-precision">9.4.7.1. Mitigating round-off error with increased precision</a></li>
<li><a class="reference internal" href="#special-values">9.4.7.2. Special values</a></li>
</ul>
</li>
<li><a class="reference internal" href="#working-with-threads">9.4.8. Working with threads</a></li>
<li><a class="reference internal" href="#recipes">9.4.9. Recipes</a></li>
<li><a class="reference internal" href="#decimal-faq">9.4.10. Decimal FAQ</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="cmath.html"
title="previous chapter">9.3. <code class="docutils literal"><span class="pre">cmath</span></code> — Mathematical functions for complex numbers</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="fractions.html"
title="next chapter">9.5. <code class="docutils literal"><span class="pre">fractions</span></code> — Rational numbers</a></p>
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