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<div class="section" id="module-math">
<h1>10.2. <tt class="xref docutils literal"><span class="pre">math</span></tt> — Mathematical functions<a class="headerlink" href="#module-math" title="Permalink to this headline">¶</a></h1>
<p>This module is always available. It provides access to the mathematical
functions defined by the C standard.</p>
<p>These functions cannot be used with complex numbers; use the functions of the
same name from the <a title="Mathematical functions for complex numbers." class="reference external" href="cmath.html#module-cmath"><tt class="xref docutils literal"><span class="pre">cmath</span></tt></a> module if you require support for complex
numbers. The distinction between functions which support complex numbers and
those which don’t is made since most users do not want to learn quite as much
mathematics as required to understand complex numbers. Receiving an exception
instead of a complex result allows earlier detection of the unexpected complex
number used as a parameter, so that the programmer can determine how and why it
was generated in the first place.</p>
<p>The following functions are provided by this module. Except when explicitly
noted otherwise, all return values are floats.</p>
<div class="section" id="number-theoretic-and-representation-functions">
<h2>10.2.1. Number-theoretic and representation functions<a class="headerlink" href="#number-theoretic-and-representation-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="math.ceil">
<tt class="descclassname">math.</tt><tt class="descname">ceil</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.ceil" title="Permalink to this definition">¶</a></dt>
<dd>Return the ceiling of <em>x</em> as a float, the smallest integer value greater than or
equal to <em>x</em>.</dd></dl>
<dl class="function">
<dt id="math.copysign">
<tt class="descclassname">math.</tt><tt class="descname">copysign</tt><big>(</big><em>x</em>, <em>y</em><big>)</big><a class="headerlink" href="#math.copysign" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>x</em> with the sign of <em>y</em>. <tt class="docutils literal"><span class="pre">copysign</span></tt> copies the sign bit of an IEEE
754 float, <tt class="docutils literal"><span class="pre">copysign(1,</span> <span class="pre">-0.0)</span></tt> returns <em>-1.0</em>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.fabs">
<tt class="descclassname">math.</tt><tt class="descname">fabs</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.fabs" title="Permalink to this definition">¶</a></dt>
<dd>Return the absolute value of <em>x</em>.</dd></dl>
<dl class="function">
<dt id="math.factorial">
<tt class="descclassname">math.</tt><tt class="descname">factorial</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.factorial" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>x</em> factorial. Raises <a title="exceptions.ValueError" class="reference external" href="exceptions.html#exceptions.ValueError"><tt class="xref docutils literal"><span class="pre">ValueError</span></tt></a> if <em>x</em> is not integral or
is negative.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.floor">
<tt class="descclassname">math.</tt><tt class="descname">floor</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.floor" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the floor of <em>x</em> as a float, the largest integer value less than or equal
to <em>x</em>.</p>
<p class="versionchanged">
<span class="versionmodified">Changed in version 2.6: </span>Added <tt class="xref docutils literal"><span class="pre">__floor__()</span></tt> delegation.</p>
</dd></dl>
<dl class="function">
<dt id="math.fmod">
<tt class="descclassname">math.</tt><tt class="descname">fmod</tt><big>(</big><em>x</em>, <em>y</em><big>)</big><a class="headerlink" href="#math.fmod" title="Permalink to this definition">¶</a></dt>
<dd>Return <tt class="docutils literal"><span class="pre">fmod(x,</span> <span class="pre">y)</span></tt>, as defined by the platform C library. Note that the
Python expression <tt class="docutils literal"><span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></tt> may not return the same result. The intent of the C
standard is that <tt class="docutils literal"><span class="pre">fmod(x,</span> <span class="pre">y)</span></tt> be exactly (mathematically; to infinite
precision) equal to <tt class="docutils literal"><span class="pre">x</span> <span class="pre">-</span> <span class="pre">n*y</span></tt> for some integer <em>n</em> such that the result has
the same sign as <em>x</em> and magnitude less than <tt class="docutils literal"><span class="pre">abs(y)</span></tt>. Python’s <tt class="docutils literal"><span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></tt>
returns a result with the sign of <em>y</em> instead, and may not be exactly computable
for float arguments. For example, <tt class="docutils literal"><span class="pre">fmod(-1e-100,</span> <span class="pre">1e100)</span></tt> is <tt class="docutils literal"><span class="pre">-1e-100</span></tt>, but
the result of Python’s <tt class="docutils literal"><span class="pre">-1e-100</span> <span class="pre">%</span> <span class="pre">1e100</span></tt> is <tt class="docutils literal"><span class="pre">1e100-1e-100</span></tt>, which cannot be
represented exactly as a float, and rounds to the surprising <tt class="docutils literal"><span class="pre">1e100</span></tt>. For
this reason, function <a title="math.fmod" class="reference internal" href="#math.fmod"><tt class="xref docutils literal"><span class="pre">fmod()</span></tt></a> is generally preferred when working with
floats, while Python’s <tt class="docutils literal"><span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></tt> is preferred when working with integers.</dd></dl>
<dl class="function">
<dt id="math.frexp">
<tt class="descclassname">math.</tt><tt class="descname">frexp</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.frexp" title="Permalink to this definition">¶</a></dt>
<dd>Return the mantissa and exponent of <em>x</em> as the pair <tt class="docutils literal"><span class="pre">(m,</span> <span class="pre">e)</span></tt>. <em>m</em> is a float
and <em>e</em> is an integer such that <tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">m</span> <span class="pre">*</span> <span class="pre">2**e</span></tt> exactly. If <em>x</em> is zero,
returns <tt class="docutils literal"><span class="pre">(0.0,</span> <span class="pre">0)</span></tt>, otherwise <tt class="docutils literal"><span class="pre">0.5</span> <span class="pre"><=</span> <span class="pre">abs(m)</span> <span class="pre"><</span> <span class="pre">1</span></tt>. This is used to “pick
apart” the internal representation of a float in a portable way.</dd></dl>
<dl class="function">
<dt id="math.fsum">
<tt class="descclassname">math.</tt><tt class="descname">fsum</tt><big>(</big><em>iterable</em><big>)</big><a class="headerlink" href="#math.fsum" title="Permalink to this definition">¶</a></dt>
<dd><p>Return an accurate floating point sum of values in the iterable. Avoids
loss of precision by tracking multiple intermediate partial sums:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">sum</span><span class="p">([</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">])</span>
<span class="go">0.99999999999999989</span>
<span class="gp">>>> </span><span class="n">fsum</span><span class="p">([</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">])</span>
<span class="go">1.0</span>
</pre></div>
</div>
<p>The algorithm’s accuracy depends on IEEE-754 arithmetic guarantees and the
typical case where the rounding mode is half-even. On some non-Windows
builds, the underlying C library uses extended precision addition and may
occasionally double-round an intermediate sum causing it to be off in its
least significant bit.</p>
<p>For further discussion and two alternative approaches, see the <a class="reference external" href="http://code.activestate.com/recipes/393090/">ASPN cookbook
recipes for accurate floating point summation</a>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.isinf">
<tt class="descclassname">math.</tt><tt class="descname">isinf</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.isinf" title="Permalink to this definition">¶</a></dt>
<dd><p>Checks if the float <em>x</em> is positive or negative infinite.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.isnan">
<tt class="descclassname">math.</tt><tt class="descname">isnan</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.isnan" title="Permalink to this definition">¶</a></dt>
<dd><p>Checks if the float <em>x</em> is a NaN (not a number). NaNs are part of the
IEEE 754 standards. Operation like but not limited to <tt class="docutils literal"><span class="pre">inf</span> <span class="pre">*</span> <span class="pre">0</span></tt>,
<tt class="docutils literal"><span class="pre">inf</span> <span class="pre">/</span> <span class="pre">inf</span></tt> or any operation involving a NaN, e.g. <tt class="docutils literal"><span class="pre">nan</span> <span class="pre">*</span> <span class="pre">1</span></tt>, return
a NaN.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.ldexp">
<tt class="descclassname">math.</tt><tt class="descname">ldexp</tt><big>(</big><em>x</em>, <em>i</em><big>)</big><a class="headerlink" href="#math.ldexp" title="Permalink to this definition">¶</a></dt>
<dd>Return <tt class="docutils literal"><span class="pre">x</span> <span class="pre">*</span> <span class="pre">(2**i)</span></tt>. This is essentially the inverse of function
<a title="math.frexp" class="reference internal" href="#math.frexp"><tt class="xref docutils literal"><span class="pre">frexp()</span></tt></a>.</dd></dl>
<dl class="function">
<dt id="math.modf">
<tt class="descclassname">math.</tt><tt class="descname">modf</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.modf" title="Permalink to this definition">¶</a></dt>
<dd>Return the fractional and integer parts of <em>x</em>. Both results carry the sign
of <em>x</em> and are floats.</dd></dl>
<dl class="function">
<dt id="math.trunc">
<tt class="descclassname">math.</tt><tt class="descname">trunc</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.trunc" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the <tt class="xref docutils literal"><span class="pre">Real</span></tt> value <em>x</em> truncated to an <tt class="xref docutils literal"><span class="pre">Integral</span></tt> (usually
a long integer). Delegates to <tt class="docutils literal"><span class="pre">x.__trunc__()</span></tt>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<p>Note that <a title="math.frexp" class="reference internal" href="#math.frexp"><tt class="xref docutils literal"><span class="pre">frexp()</span></tt></a> and <a title="math.modf" class="reference internal" href="#math.modf"><tt class="xref docutils literal"><span class="pre">modf()</span></tt></a> have a different call/return pattern
than their C equivalents: they take a single argument and return a pair of
values, rather than returning their second return value through an ‘output
parameter’ (there is no such thing in Python).</p>
<p>For the <a title="math.ceil" class="reference internal" href="#math.ceil"><tt class="xref docutils literal"><span class="pre">ceil()</span></tt></a>, <a title="math.floor" class="reference internal" href="#math.floor"><tt class="xref docutils literal"><span class="pre">floor()</span></tt></a>, and <a title="math.modf" class="reference internal" href="#math.modf"><tt class="xref docutils literal"><span class="pre">modf()</span></tt></a> functions, note that <em>all</em>
floating-point numbers of sufficiently large magnitude are exact integers.
Python floats typically carry no more than 53 bits of precision (the same as the
platform C double type), in which case any float <em>x</em> with <tt class="docutils literal"><span class="pre">abs(x)</span> <span class="pre">>=</span> <span class="pre">2**52</span></tt>
necessarily has no fractional bits.</p>
</div>
<div class="section" id="power-and-logarithmic-functions">
<h2>10.2.2. Power and logarithmic functions<a class="headerlink" href="#power-and-logarithmic-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="math.exp">
<tt class="descclassname">math.</tt><tt class="descname">exp</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.exp" title="Permalink to this definition">¶</a></dt>
<dd>Return <tt class="docutils literal"><span class="pre">e**x</span></tt>.</dd></dl>
<dl class="function">
<dt id="math.log">
<tt class="descclassname">math.</tt><tt class="descname">log</tt><big>(</big><em>x</em><span class="optional">[</span>, <em>base</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#math.log" title="Permalink to this definition">¶</a></dt>
<dd><p>With one argument, return the natural logarithm of <em>x</em> (to base <em>e</em>).</p>
<p>With two arguments, return the logarithm of <em>x</em> to the given <em>base</em>,
calculated as <tt class="docutils literal"><span class="pre">log(x)/log(base)</span></tt>.</p>
<p class="versionchanged">
<span class="versionmodified">Changed in version 2.3: </span><em>base</em> argument added.</p>
</dd></dl>
<dl class="function">
<dt id="math.log1p">
<tt class="descclassname">math.</tt><tt class="descname">log1p</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.log1p" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the natural logarithm of <em>1+x</em> (base <em>e</em>). The
result is calculated in a way which is accurate for <em>x</em> near zero.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.log10">
<tt class="descclassname">math.</tt><tt class="descname">log10</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.log10" title="Permalink to this definition">¶</a></dt>
<dd>Return the base-10 logarithm of <em>x</em>. This is usually more accurate
than <tt class="docutils literal"><span class="pre">log(x,</span> <span class="pre">10)</span></tt>.</dd></dl>
<dl class="function">
<dt id="math.pow">
<tt class="descclassname">math.</tt><tt class="descname">pow</tt><big>(</big><em>x</em>, <em>y</em><big>)</big><a class="headerlink" href="#math.pow" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <tt class="docutils literal"><span class="pre">x</span></tt> raised to the power <tt class="docutils literal"><span class="pre">y</span></tt>. Exceptional cases follow
Annex ‘F’ of the C99 standard as far as possible. In particular,
<tt class="docutils literal"><span class="pre">pow(1.0,</span> <span class="pre">x)</span></tt> and <tt class="docutils literal"><span class="pre">pow(x,</span> <span class="pre">0.0)</span></tt> always return <tt class="docutils literal"><span class="pre">1.0</span></tt>, even
when <tt class="docutils literal"><span class="pre">x</span></tt> is a zero or a NaN. If both <tt class="docutils literal"><span class="pre">x</span></tt> and <tt class="docutils literal"><span class="pre">y</span></tt> are finite,
<tt class="docutils literal"><span class="pre">x</span></tt> is negative, and <tt class="docutils literal"><span class="pre">y</span></tt> is not an integer then <tt class="docutils literal"><span class="pre">pow(x,</span> <span class="pre">y)</span></tt>
is undefined, and raises <a title="exceptions.ValueError" class="reference external" href="exceptions.html#exceptions.ValueError"><tt class="xref docutils literal"><span class="pre">ValueError</span></tt></a>.</p>
<p class="versionchanged">
<span class="versionmodified">Changed in version 2.6: </span>The outcome of <tt class="docutils literal"><span class="pre">1**nan</span></tt> and <tt class="docutils literal"><span class="pre">nan**0</span></tt> was undefined.</p>
</dd></dl>
<dl class="function">
<dt id="math.sqrt">
<tt class="descclassname">math.</tt><tt class="descname">sqrt</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.sqrt" title="Permalink to this definition">¶</a></dt>
<dd>Return the square root of <em>x</em>.</dd></dl>
</div>
<div class="section" id="trigonometric-functions">
<h2>10.2.3. Trigonometric functions<a class="headerlink" href="#trigonometric-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="math.acos">
<tt class="descclassname">math.</tt><tt class="descname">acos</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.acos" title="Permalink to this definition">¶</a></dt>
<dd>Return the arc cosine of <em>x</em>, in radians.</dd></dl>
<dl class="function">
<dt id="math.asin">
<tt class="descclassname">math.</tt><tt class="descname">asin</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.asin" title="Permalink to this definition">¶</a></dt>
<dd>Return the arc sine of <em>x</em>, in radians.</dd></dl>
<dl class="function">
<dt id="math.atan">
<tt class="descclassname">math.</tt><tt class="descname">atan</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.atan" title="Permalink to this definition">¶</a></dt>
<dd>Return the arc tangent of <em>x</em>, in radians.</dd></dl>
<dl class="function">
<dt id="math.atan2">
<tt class="descclassname">math.</tt><tt class="descname">atan2</tt><big>(</big><em>y</em>, <em>x</em><big>)</big><a class="headerlink" href="#math.atan2" title="Permalink to this definition">¶</a></dt>
<dd>Return <tt class="docutils literal"><span class="pre">atan(y</span> <span class="pre">/</span> <span class="pre">x)</span></tt>, in radians. The result is between <tt class="docutils literal"><span class="pre">-pi</span></tt> and <tt class="docutils literal"><span class="pre">pi</span></tt>.
The vector in the plane from the origin to point <tt class="docutils literal"><span class="pre">(x,</span> <span class="pre">y)</span></tt> makes this angle
with the positive X axis. The point of <a title="math.atan2" class="reference internal" href="#math.atan2"><tt class="xref docutils literal"><span class="pre">atan2()</span></tt></a> is that the signs of both
inputs are known to it, so it can compute the correct quadrant for the angle.
For example, <tt class="docutils literal"><span class="pre">atan(1</span></tt>) and <tt class="docutils literal"><span class="pre">atan2(1,</span> <span class="pre">1)</span></tt> are both <tt class="docutils literal"><span class="pre">pi/4</span></tt>, but <tt class="docutils literal"><span class="pre">atan2(-1,</span>
<span class="pre">-1)</span></tt> is <tt class="docutils literal"><span class="pre">-3*pi/4</span></tt>.</dd></dl>
<dl class="function">
<dt id="math.cos">
<tt class="descclassname">math.</tt><tt class="descname">cos</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.cos" title="Permalink to this definition">¶</a></dt>
<dd>Return the cosine of <em>x</em> radians.</dd></dl>
<dl class="function">
<dt id="math.hypot">
<tt class="descclassname">math.</tt><tt class="descname">hypot</tt><big>(</big><em>x</em>, <em>y</em><big>)</big><a class="headerlink" href="#math.hypot" title="Permalink to this definition">¶</a></dt>
<dd>Return the Euclidean norm, <tt class="docutils literal"><span class="pre">sqrt(x*x</span> <span class="pre">+</span> <span class="pre">y*y)</span></tt>. This is the length of the vector
from the origin to point <tt class="docutils literal"><span class="pre">(x,</span> <span class="pre">y)</span></tt>.</dd></dl>
<dl class="function">
<dt id="math.sin">
<tt class="descclassname">math.</tt><tt class="descname">sin</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.sin" title="Permalink to this definition">¶</a></dt>
<dd>Return the sine of <em>x</em> radians.</dd></dl>
<dl class="function">
<dt id="math.tan">
<tt class="descclassname">math.</tt><tt class="descname">tan</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.tan" title="Permalink to this definition">¶</a></dt>
<dd>Return the tangent of <em>x</em> radians.</dd></dl>
</div>
<div class="section" id="angular-conversion">
<h2>10.2.4. Angular conversion<a class="headerlink" href="#angular-conversion" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="math.degrees">
<tt class="descclassname">math.</tt><tt class="descname">degrees</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.degrees" title="Permalink to this definition">¶</a></dt>
<dd>Converts angle <em>x</em> from radians to degrees.</dd></dl>
<dl class="function">
<dt id="math.radians">
<tt class="descclassname">math.</tt><tt class="descname">radians</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.radians" title="Permalink to this definition">¶</a></dt>
<dd>Converts angle <em>x</em> from degrees to radians.</dd></dl>
</div>
<div class="section" id="hyperbolic-functions">
<h2>10.2.5. Hyperbolic functions<a class="headerlink" href="#hyperbolic-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="math.acosh">
<tt class="descclassname">math.</tt><tt class="descname">acosh</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.acosh" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the inverse hyperbolic cosine of <em>x</em>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.asinh">
<tt class="descclassname">math.</tt><tt class="descname">asinh</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.asinh" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the inverse hyperbolic sine of <em>x</em>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.atanh">
<tt class="descclassname">math.</tt><tt class="descname">atanh</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.atanh" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the inverse hyperbolic tangent of <em>x</em>.</p>
<p class="versionadded">
<span class="versionmodified">New in version 2.6.</span></p>
</dd></dl>
<dl class="function">
<dt id="math.cosh">
<tt class="descclassname">math.</tt><tt class="descname">cosh</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.cosh" title="Permalink to this definition">¶</a></dt>
<dd>Return the hyperbolic cosine of <em>x</em>.</dd></dl>
<dl class="function">
<dt id="math.sinh">
<tt class="descclassname">math.</tt><tt class="descname">sinh</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.sinh" title="Permalink to this definition">¶</a></dt>
<dd>Return the hyperbolic sine of <em>x</em>.</dd></dl>
<dl class="function">
<dt id="math.tanh">
<tt class="descclassname">math.</tt><tt class="descname">tanh</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#math.tanh" title="Permalink to this definition">¶</a></dt>
<dd>Return the hyperbolic tangent of <em>x</em>.</dd></dl>
</div>
<div class="section" id="constants">
<h2>10.2.6. Constants<a class="headerlink" href="#constants" title="Permalink to this headline">¶</a></h2>
<dl class="data">
<dt id="math.pi">
<tt class="descclassname">math.</tt><tt class="descname">pi</tt><a class="headerlink" href="#math.pi" title="Permalink to this definition">¶</a></dt>
<dd>The mathematical constant <em>pi</em>.</dd></dl>
<dl class="data">
<dt id="math.e">
<tt class="descclassname">math.</tt><tt class="descname">e</tt><a class="headerlink" href="#math.e" title="Permalink to this definition">¶</a></dt>
<dd>The mathematical constant <em>e</em>.</dd></dl>
<div class="impl-detail compound">
<p class="compound-first"><strong>CPython implementation detail:</strong> The <tt class="xref docutils literal"><span class="pre">math</span></tt> module consists mostly of thin wrappers around the platform C
math library functions. Behavior in exceptional cases is loosely specified
by the C standards, and Python inherits much of its math-function
error-reporting behavior from the platform C implementation. As a result,
the specific exceptions raised in error cases (and even whether some
arguments are considered to be exceptional at all) are not defined in any
useful cross-platform or cross-release way. For example, whether
<tt class="docutils literal"><span class="pre">math.log(0)</span></tt> returns <tt class="docutils literal"><span class="pre">-Inf</span></tt> or raises <a title="exceptions.ValueError" class="reference external" href="exceptions.html#exceptions.ValueError"><tt class="xref docutils literal"><span class="pre">ValueError</span></tt></a> or
<a title="exceptions.OverflowError" class="reference external" href="exceptions.html#exceptions.OverflowError"><tt class="xref docutils literal"><span class="pre">OverflowError</span></tt></a> isn’t defined, and in cases where <tt class="docutils literal"><span class="pre">math.log(0)</span></tt> raises
<a title="exceptions.OverflowError" class="reference external" href="exceptions.html#exceptions.OverflowError"><tt class="xref docutils literal"><span class="pre">OverflowError</span></tt></a>, <tt class="docutils literal"><span class="pre">math.log(0L)</span></tt> may raise <a title="exceptions.ValueError" class="reference external" href="exceptions.html#exceptions.ValueError"><tt class="xref docutils literal"><span class="pre">ValueError</span></tt></a> instead.</p>
<p class="compound-middle">All functions return a quiet <em>NaN</em> if at least one of the args is <em>NaN</em>.
Signaling <em>NaN</em>s raise an exception. The exception type still depends on the
platform and libm implementation. It’s usually <a title="exceptions.ValueError" class="reference external" href="exceptions.html#exceptions.ValueError"><tt class="xref docutils literal"><span class="pre">ValueError</span></tt></a> for <em>EDOM</em>
and <a title="exceptions.OverflowError" class="reference external" href="exceptions.html#exceptions.OverflowError"><tt class="xref docutils literal"><span class="pre">OverflowError</span></tt></a> for errno <em>ERANGE</em>.</p>
<p class="compound-last versionchanged">
<span class="versionmodified">Changed in version 2.6: </span>In earlier versions of Python the outcome of an operation with NaN as
input depended on platform and libm implementation.</p>
</div>
<div class="admonition-see-also admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt>Module <a title="Mathematical functions for complex numbers." class="reference external" href="cmath.html#module-cmath"><tt class="xref docutils literal"><span class="pre">cmath</span></tt></a></dt>
<dd>Complex number versions of many of these functions.</dd>
</dl>
</div>
</div>
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</div>
</div>
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<h3><a href="../contents.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference external" href="#">10.2. <tt class="docutils literal"><span class="pre">math</span></tt> — Mathematical functions</a><ul>
<li><a class="reference external" href="#number-theoretic-and-representation-functions">10.2.1. Number-theoretic and representation functions</a></li>
<li><a class="reference external" href="#power-and-logarithmic-functions">10.2.2. Power and logarithmic functions</a></li>
<li><a class="reference external" href="#trigonometric-functions">10.2.3. Trigonometric functions</a></li>
<li><a class="reference external" href="#angular-conversion">10.2.4. Angular conversion</a></li>
<li><a class="reference external" href="#hyperbolic-functions">10.2.5. Hyperbolic functions</a></li>
<li><a class="reference external" href="#constants">10.2.6. Constants</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
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