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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 notranslate"><span class="pre">decimal</span></code></a> — Decimal fixed point and floating point arithmetic<a class="headerlink" href="#module-decimal" title="本標題的永久連結">¶</a></h1>
<p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.7/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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">1.1</span></code> and <code class="xref py py-const docutils literal notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">1.56</span></code> while <code class="docutils literal notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">Infinity</span></code>, <code class="xref py py-const docutils literal notranslate"><span class="pre">-Infinity</span></code>, and <code class="xref py py-const docutils literal notranslate"><span class="pre">NaN</span></code>. The standard also
differentiates <code class="xref py py-const docutils literal notranslate"><span class="pre">-0</span></code> from <code class="xref py py-const docutils literal notranslate"><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 notranslate"><span class="pre">ROUND_CEILING</span></code></a>, <a class="reference internal" href="#decimal.ROUND_DOWN" title="decimal.ROUND_DOWN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_DOWN</span></code></a>,
<a class="reference internal" href="#decimal.ROUND_FLOOR" title="decimal.ROUND_FLOOR"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_FLOOR</span></code></a>, <a class="reference internal" href="#decimal.ROUND_HALF_DOWN" title="decimal.ROUND_HALF_DOWN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_DOWN</span></code></a>, <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a>,
<a class="reference internal" href="#decimal.ROUND_HALF_UP" title="decimal.ROUND_HALF_UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_HALF_UP</span></code></a>, <a class="reference internal" href="#decimal.ROUND_UP" title="decimal.ROUND_UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_UP</span></code></a>, and <a class="reference internal" href="#decimal.ROUND_05UP" title="decimal.ROUND_05UP"><code class="xref py py-const docutils literal notranslate"><span class="pre">ROUND_05UP</span></code></a>.</p>
<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 notranslate"><span class="pre">Clamped</span></code></a>, <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal notranslate"><span class="pre">InvalidOperation</span></code></a>,
<a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a>, <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate"><span class="pre">Inexact</span></code></a>, <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal notranslate"><span class="pre">Rounded</span></code></a>, <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-const docutils literal notranslate"><span class="pre">Subnormal</span></code></a>,
<a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-const docutils literal notranslate"><span class="pre">Overflow</span></code></a>, <a class="reference internal" href="#decimal.Underflow" title="decimal.Underflow"><code class="xref py py-const docutils literal notranslate"><span class="pre">Underflow</span></code></a> and <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-const docutils literal notranslate"><span class="pre">FloatOperation</span></code></a>.</p>
<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">也參考</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="本標題的永久連結">¶</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 notranslate"><span class="pre">getcontext()</span></code></a> and, if necessary, setting new values for
precision, rounding, or enabled traps:</p>
<div class="highlight-python3 notranslate"><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 notranslate"><span class="pre">NaN</span></code> which stands for 「Not a number」, positive and negative
<code class="xref py py-const docutils literal notranslate"><span class="pre">Infinity</span></code>, and <code class="xref py py-const docutils literal notranslate"><span class="pre">-0</span></code>:</p>
<div class="highlight-python3 notranslate"><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 notranslate"><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 notranslate"><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">3.3 版新加入.</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-pycon notranslate"><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 notranslate"><span class="pre">InvalidOperation</span></code></a>:</p>
<div class="highlight-python3 notranslate"><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">3.3 版更變.</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-pycon notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">BasicContext</span></code></a> and <a class="reference internal" href="#decimal.ExtendedContext" title="decimal.ExtendedContext"><code class="xref py py-const docutils literal notranslate"><span class="pre">ExtendedContext</span></code></a>. The
former is especially useful for debugging because many of the traps are
enabled:</p>
<div class="highlight-pycon notranslate"><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 notranslate"><span class="pre">clear_flags()</span></code> method.</p>
<div class="highlight-python3 notranslate"><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 notranslate"><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 notranslate"><span class="pre">traps</span></code> field of a
context:</p>
<div class="highlight-pycon notranslate"><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 notranslate"><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="本標題的永久連結">¶</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="本定義的永久連結">¶</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 notranslate"><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 notranslate"><span class="pre">float</span></code></a>, or another <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>
object. If no <em>value</em> is given, returns <code class="docutils literal notranslate"><span class="pre">Decimal('0')</span></code>. If <em>value</em> is a
string, it should conform to the decimal numeric string syntax after leading
and trailing whitespace characters, as well as underscores throughout, are removed:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">sign</span> <span class="p">::</span><span class="o">=</span> <span class="s1">'+'</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 notranslate"><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 notranslate"><span class="pre">'\uff10'</span></code> through <code class="docutils literal notranslate"><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 notranslate"><span class="pre">tuple</span></code></a>, it should have three components, a sign
(<code class="xref py py-const docutils literal notranslate"><span class="pre">0</span></code> for positive or <code class="xref py py-const docutils literal notranslate"><span class="pre">1</span></code> for negative), a <a class="reference internal" href="stdtypes.html#tuple" title="tuple"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a> of
digits, and an integer exponent. For example, <code class="docutils literal notranslate"><span class="pre">Decimal((0,</span> <span class="pre">(1,</span> <span class="pre">4,</span> <span class="pre">1,</span> <span class="pre">4),</span> <span class="pre">-3))</span></code>
returns <code class="docutils literal notranslate"><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 notranslate"><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 notranslate"><span class="pre">Decimal(float('1.1'))</span></code>
converts to
<code class="docutils literal notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">Decimal</span></code></a> objects are immutable.</p>
<div class="versionchanged">
<p><span class="versionmodified">3.2 版更變: </span>The argument to the constructor is now permitted to be a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>
instance.</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">3.3 版更變: </span><a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> arguments raise an exception if the <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate"><span class="pre">FloatOperation</span></code></a>
trap is set. By default the trap is off.</p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">3.6 版更變: </span>Underscores are allowed for grouping, as with integral and floating-point
literals in code.</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 notranslate"><span class="pre">float</span></code></a> and <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>. All of the usual math
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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">(x</span> <span class="pre">//</span> <span class="pre">y)</span> <span class="pre">*</span> <span class="pre">y</span> <span class="pre">+</span> <span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></code>:</p>
<div class="highlight-python3 notranslate"><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 notranslate"><span class="pre">%</span></code> and <code class="docutils literal notranslate"><span class="pre">//</span></code> operators implement the <code class="docutils literal notranslate"><span class="pre">remainder</span></code> and
<code class="docutils literal notranslate"><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 notranslate"><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 notranslate"><span class="pre">Decimal</span></code></a> to a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, for
example, will raise a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a>. However, it is possible to
use Python’s comparison operators to compare a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>
instance <code class="docutils literal notranslate"><span class="pre">x</span></code> with another number <code class="docutils literal notranslate"><span class="pre">y</span></code>. This avoids confusing results
when doing equality comparisons between numbers of different types.</p>
<div class="versionchanged">
<p><span class="versionmodified">3.2 版更變: </span>Mixed-type comparisons between <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instances and other
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="本定義的永久連結">¶</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 notranslate"><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_integer_ratio">
<code class="descname">as_integer_ratio</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#decimal.Decimal.as_integer_ratio" title="本定義的永久連結">¶</a></dt>
<dd><p>Return a pair <code class="docutils literal notranslate"><span class="pre">(n,</span> <span class="pre">d)</span></code> of integers that represent the given
<a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance as a fraction, in lowest terms and
with a positive denominator:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></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="o">.</span><span class="n">as_integer_ratio</span><span class="p">()</span>
<span class="go">(-157, 50)</span>
</pre></div>
</div>
<p>The conversion is exact. Raise OverflowError on infinities and ValueError
on NaNs.</p>
</dd></dl>
<div class="versionadded">
<p><span class="versionmodified">3.6 版新加入.</span></p>
</div>
<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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="ow">or</span> <span class="n">b</span> <span class="ow">is</span> <span class="n">a</span> <span class="n">NaN</span> <span class="o">==></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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">Decimal('0')</span></code> if both operands have the same
representation, <code class="docutils literal notranslate"><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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><span class="pre">compare_total()</span></code></a>, but ignoring the sign of each operand.
<code class="docutils literal notranslate"><span class="pre">x.compare_total_mag(y)</span></code> is equivalent to
<code class="docutils literal notranslate"><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="本定義的永久連結">¶</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="本定義的永久連結">¶</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="本定義的永久連結">¶</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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</a></dt>
<dd><p>Return the value of the (natural) exponential function <code class="docutils literal notranslate"><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 notranslate"><span class="pre">ROUND_HALF_EVEN</span></code></a> rounding mode.</p>
<div class="highlight-python3 notranslate"><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="本定義的永久連結">¶</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">備註</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 notranslate"><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 notranslate"><span class="pre">float</span></code></a>.</p>
</div>
<div class="highlight-pycon notranslate"><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">3.1 版新加入.</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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is canonical and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a>
otherwise. Currently, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a> instance is always canonical, so
this operation always returns <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a>.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a finite number, and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> if the argument is an infinity or a NaN.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is either positive or negative
infinity and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a (quiet or signaling) NaN and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a <em>normal</em> finite number. Return
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> if the argument is zero, subnormal, infinite or a NaN.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a quiet NaN, and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument has a negative sign and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise. Note that zeros and NaNs can both carry signs.</p>
</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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a signaling NaN and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a>
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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is subnormal, and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a>
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="本定義的永久連結">¶</a></dt>
<dd><p>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate"><span class="pre">True</span></code></a> if the argument is a (positive or negative) zero and
<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate"><span class="pre">False</span></code></a> otherwise.</p>
</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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><span class="pre">Decimal</span></code></a> instance. If the operand is a zero then
<code class="docutils literal notranslate"><span class="pre">Decimal('-Infinity')</span></code> is returned and the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal notranslate"><span class="pre">DivisionByZero</span></code></a> flag
is raised. If the operand is an infinity then <code class="docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 class="std std-ref">Logical operands</span></a>). The result is the
digit-wise <code class="docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 class="std std-ref">Logical operands</span></a>). The result is the
digit-wise <code class="docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 class="std std-ref">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="本定義的永久連結">¶</a></dt>
<dd><p>Like <code class="docutils literal notranslate"><span class="pre">max(self,</span> <span class="pre">other)</span></code> except that the context rounding rule is applied
before returning and that <code class="xref py py-const docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</a></dt>
<dd><p>Like <code class="docutils literal notranslate"><span class="pre">min(self,</span> <span class="pre">other)</span></code> except that the context rounding rule is applied
before returning and that <code class="xref py py-const docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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="本定義的永久連結">¶</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="本定義的永久連結">¶</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="本定義的永久連結">¶</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 notranslate"><span class="pre">Decimal('0')</span></code> to
<code class="xref py py-const docutils literal notranslate"><span class="pre">Decimal('0e0')</span></code>. Used for producing canonical values for attributes
of an equivalence class. For example, <code class="docutils literal notranslate"><span class="pre">Decimal('32.100')</span></code> and
<code class="docutils literal notranslate"><span class="pre">Decimal('0.321000e+2')</span></code> both normalize to the equivalent value
<code class="docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><span class="pre">"-Infinity"</span></code>, indicating that the operand is negative infinity.</li>
<li><code class="docutils literal notranslate"><span class="pre">"-Normal"</span></code>, indicating that the operand is a negative normal number.</li>
<li><code class="docutils literal notranslate"><span class="pre">"-Subnormal"</span></code>, indicating that the operand is negative and subnormal.</li>
<li><code class="docutils literal notranslate"><span class="pre">"-Zero"</span></code>, indicating that the operand is a negative zero.</li>
<li><code class="docutils literal notranslate"><span class="pre">"+Zero"</span></code>, indicating that the operand is a positive zero.</li>
<li><code class="docutils literal notranslate"><span class="pre">"+Subnormal"</span></code>, indicating that the operand is positive and subnormal.</li>
<li><code class="docutils literal notranslate"><span class="pre">"+Normal"</span></code>, indicating that the operand is a positive normal number.</li>
<li><code class="docutils literal notranslate"><span class="pre">"+Infinity"</span></code>, indicating that the operand is positive infinity.</li>
<li><code class="docutils literal notranslate"><span class="pre">"NaN"</span></code>, indicating that the operand is a quiet NaN (Not a Number).</li>
<li><code class="docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">rounding</span></code> argument if given, else by the given
<code class="docutils literal notranslate"><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 notranslate"><span class="pre">Emax</span></code> or less than <code class="xref py py-attr docutils literal notranslate"><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="本定義的永久連結">¶</a></dt>
<dd><p>Return <code class="docutils literal notranslate"><span class="pre">Decimal(10)</span></code>, the radix (base) in which the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate"><span class="pre">Decimal</span></code></a>
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="本定義的永久連結">¶</a></dt>
<dd><p>Return the remainder from dividing <em>self</em> by <em>other</em>. This differs from
<code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">%</span> <span class="pre">other</span></code> in that the sign of the remainder is chosen so as to
minimize its absolute value. More precisely, the return value is
<code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">-</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">other</span></code> where <code class="docutils literal notranslate"><span class="pre">n</span></code> is the integer nearest to the exact
value of <code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">/</span> <span class="pre">other</span></code>, and if two integers are equally near then the
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 notranslate"><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="本定義的永久連結">¶</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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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 notranslate"><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="本定義的永久連結">¶</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="本定義的永久連結">¶</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="本定義的永久連結">¶</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 notranslate"><span class="pre">Decimal('123E+1')</span></code> to <code class="docutils literal notranslate"><span class="pre">Decimal('1.23E+3')</span></code>.</p>
</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="本定義的永久連結">¶</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 notranslate"><span class="pre">to_integral_value()</span></code></a> method. The <code class="docutils literal notranslate"><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="本定義的永久連結">¶</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 notranslate"><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 notranslate"><span class="pre">Rounded</span></code></a> as appropriate if rounding occurs. The rounding mode is
determined by the <code class="docutils literal notranslate"><span class="pre">rounding</span></code> parameter if given, else by the given
<code class="docutils literal notranslate"><span class="pre">context</span></code>. If neither parameter is given then the rounding mode of the
current context is used.</p>
</dd></dl>