[OpenSPARC-T2-SAM] / sam-t2 / devtools / v9 / html / python / lib / module-math.html

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html>
<head>
<link rel="STYLESHEET" href="lib.css" type='text/css' />
<link rel="SHORTCUT ICON" href="../icons/pyfav.png" type="image/png" />
<link rel='start' href='../index.html' title='Python Documentation Index' />
<link rel="first" href="lib.html" title='Python Library Reference' />
<link rel='contents' href='contents.html' title="Contents" />
<link rel='index' href='genindex.html' title='Index' />
<link rel='last' href='about.html' title='About this document...' />
<link rel='help' href='about.html' title='About this document...' />
<link rel="next" href="module-cmath.html" />
<link rel="prev" href="module-decimal.html" />
<link rel="parent" href="misc.html" />
<link rel="next" href="module-cmath.html" />
<meta name='aesop' content='information' />
<title>5.7 math -- Mathematical functions</title>
</head>
<body>
<DIV CLASS="navigation">
<div id='top-navigation-panel' xml:id='top-navigation-panel'>
<table align="center" width="100%" cellpadding="0" cellspacing="2">
<tr>
<td class='online-navigation'><a rel="prev" title="5.6.8 Decimal FAQ"
  href="decimal-faq.html"><img src='../icons/previous.png'
  border='0' height='32'  alt='Previous Page' width='32' /></A></td>
<td class='online-navigation'><a rel="parent" title="5. Miscellaneous Services"
  href="misc.html"><img src='../icons/up.png'
  border='0' height='32'  alt='Up One Level' width='32' /></A></td>
<td class='online-navigation'><a rel="next" title="5.8 cmath  "
  href="module-cmath.html"><img src='../icons/next.png'
  border='0' height='32'  alt='Next Page' width='32' /></A></td>
<td align="center" width="100%">Python Library Reference</td>
<td class='online-navigation'><a rel="contents" title="Table of Contents"
  href="contents.html"><img src='../icons/contents.png'
  border='0' height='32'  alt='Contents' width='32' /></A></td>
<td class='online-navigation'><a href="modindex.html" title="Module Index"><img src='../icons/modules.png'
  border='0' height='32'  alt='Module Index' width='32' /></a></td>
<td class='online-navigation'><a rel="index" title="Index"
  href="genindex.html"><img src='../icons/index.png'
  border='0' height='32'  alt='Index' width='32' /></A></td>
</tr></table>
<div class='online-navigation'>
<b class="navlabel">Previous:</b>
<a class="sectref" rel="prev" href="decimal-faq.html">5.6.8 Decimal FAQ</A>
<b class="navlabel">Up:</b>
<a class="sectref" rel="parent" href="misc.html">5. Miscellaneous Services</A>
<b class="navlabel">Next:</b>
<a class="sectref" rel="next" href="module-cmath.html">5.8 cmath  </A>
</div>
<hr /></div>
</DIV>
<!--End of Navigation Panel-->

<H1><A NAME="SECTION007700000000000000000">
5.7 <tt class="module">math</tt> --
         Mathematical functions</A>
</H1>

<P>
<A NAME="module-math"></A>

<P>
This module is always available.  It provides access to the
mathematical functions defined by the C standard.

<P>
These functions cannot be used with complex numbers; use the functions
of the same name from the <tt class="module"><a href="module-cmath.html">cmath</a></tt> 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>
The following functions are provided by this module.  Except
when explicitly noted otherwise, all return values are floats.

<P>
Number-theoretic and representation functions:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1250' xml:id='l2h-1250' class="function">ceil</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the ceiling of <var>x</var> as a float, the smallest integer value
greater than or equal to <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1251' xml:id='l2h-1251' class="function">fabs</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the absolute value of <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1252' xml:id='l2h-1252' class="function">floor</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the floor of <var>x</var> as a float, the largest integer value
less than or equal to <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1253' xml:id='l2h-1253' class="function">fmod</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
Return <code>fmod(<var>x</var>, <var>y</var>)</code>, as defined by the platform C library.
Note that the Python expression <code><var>x</var> % <var>y</var></code> may not return
the same result.  The intent of the C standard is that
<code>fmod(<var>x</var>, <var>y</var>)</code> be exactly (mathematically; to infinite
precision) equal to <code><var>x</var> - <var>n</var>*<var>y</var></code> for some integer
<var>n</var> such that the result has the same sign as <var>x</var> and
magnitude less than <code>abs(<var>y</var>)</code>.  Python's
<code><var>x</var> % <var>y</var></code> returns a result with the sign of
<var>y</var> instead, and may not be exactly computable for float arguments.
For example, <code>fmod(-1e-100, 1e100)</code> is <code>-1e-100</code>, but the
result of Python's <code>-1e-100 % 1e100</code> is <code>1e100-1e-100</code>, which
cannot be represented exactly as a float, and rounds to the surprising
<code>1e100</code>.  For this reason, function <tt class="function">fmod()</tt> is generally
preferred when working with floats, while Python's
<code><var>x</var> % <var>y</var></code> is preferred when working with integers.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1254' xml:id='l2h-1254' class="function">frexp</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the mantissa and exponent of <var>x</var> as the pair
<code>(<var>m</var>, <var>e</var>)</code>.  <var>m</var> is a float and <var>e</var> is an
integer such that <code><var>x</var> == <var>m</var> * 2**<var>e</var></code> exactly.
If <var>x</var> is zero, returns <code>(0.0, 0)</code>, otherwise
<code>0.5 &lt;= abs(<var>m</var>) &lt; 1</code>.  This is used to "pick apart" the
internal representation of a float in a portable way.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1255' xml:id='l2h-1255' class="function">ldexp</tt></b>(</nobr></td>
  <td><var>x, i</var>)</td></tr></table></dt>
<dd>
Return <code><var>x</var> * (2**<var>i</var>)</code>.  This is essentially the inverse of
function <tt class="function">frexp()</tt>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1256' xml:id='l2h-1256' class="function">modf</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the fractional and integer parts of <var>x</var>.  Both results
carry the sign of <var>x</var>, and both are floats.
</dl>

<P>
Note that <tt class="function">frexp()</tt> and <tt class="function">modf()</tt> 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>
For the <tt class="function">ceil()</tt>, <tt class="function">floor()</tt>, and <tt class="function">modf()</tt>
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 <var>x</var> with <code>abs(<var>x</var>) &gt;= 2**52</code>
necessarily has no fractional bits.

<P>
Power and logarithmic functions:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1257' xml:id='l2h-1257' class="function">exp</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return <code>e**<var>x</var></code>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1258' xml:id='l2h-1258' class="function">log</tt></b>(</nobr></td>
  <td><var>x</var><big>[</big><var>, base</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
Return the logarithm of <var>x</var> to the given <var>base</var>.
If the <var>base</var> is not specified, return the natural logarithm of <var>x</var>
(that is, the logarithm to base <em>e</em>).

<span class="versionnote">Changed in version 2.3:
<var>base</var> argument added.</span>

</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1259' xml:id='l2h-1259' class="function">log10</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the base-10 logarithm of <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1260' xml:id='l2h-1260' class="function">pow</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
Return <code><var>x</var>**<var>y</var></code>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1261' xml:id='l2h-1261' class="function">sqrt</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the square root of <var>x</var>.
</dl>

<P>
Trigonometric functions:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1262' xml:id='l2h-1262' class="function">acos</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the arc cosine of <var>x</var>, in radians.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1263' xml:id='l2h-1263' class="function">asin</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the arc sine of <var>x</var>, in radians.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1264' xml:id='l2h-1264' class="function">atan</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the arc tangent of <var>x</var>, in radians.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1265' xml:id='l2h-1265' class="function">atan2</tt></b>(</nobr></td>
  <td><var>y, x</var>)</td></tr></table></dt>
<dd>
Return <code>atan(<var>y</var> / <var>x</var>)</code>, in radians.
The result is between <code>-pi</code> and <code>pi</code>.
The vector in the plane from the origin to point <code>(<var>x</var>, <var>y</var>)</code>
makes this angle with the positive X axis.
The point of <tt class="function">atan2()</tt> is that the signs of both inputs are
known to it, so it can compute the correct quadrant for the angle.
For example, <code>atan(1</code>) and <code>atan2(1, 1)</code> are both <code>pi/4</code>,
but <code>atan2(-1, -1)</code> is <code>-3*pi/4</code>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1266' xml:id='l2h-1266' class="function">cos</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the cosine of <var>x</var> radians.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1267' xml:id='l2h-1267' class="function">hypot</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
Return the Euclidean norm, <code>sqrt(<var>x</var>*<var>x</var> + <var>y</var>*<var>y</var>)</code>.
This is the length of the vector from the origin to point
<code>(<var>x</var>, <var>y</var>)</code>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1268' xml:id='l2h-1268' class="function">sin</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the sine of <var>x</var> radians.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1269' xml:id='l2h-1269' class="function">tan</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the tangent of <var>x</var> radians.
</dl>

<P>
Angular conversion:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1270' xml:id='l2h-1270' class="function">degrees</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Converts angle <var>x</var> from radians to degrees.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1271' xml:id='l2h-1271' class="function">radians</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Converts angle <var>x</var> from degrees to radians.
</dl>

<P>
Hyperbolic functions:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1272' xml:id='l2h-1272' class="function">cosh</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the hyperbolic cosine of <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1273' xml:id='l2h-1273' class="function">sinh</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the hyperbolic sine of <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1274' xml:id='l2h-1274' class="function">tanh</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
Return the hyperbolic tangent of <var>x</var>.
</dl>

<P>
The module also defines two mathematical constants:

<P>
<dl><dt><b><tt id='l2h-1275' xml:id='l2h-1275'>pi</tt></b></dt>
<dd>
The mathematical constant <em>pi</em>.
</dd></dl>

<P>
<dl><dt><b><tt id='l2h-1276' xml:id='l2h-1276'>e</tt></b></dt>
<dd>
The mathematical constant <em>e</em>.
</dd></dl>

<P>
<div class="note"><b class="label">Note:</b>
The <tt class="module">math</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
  <code>math.log(0)</code> returns <code>-Inf</code> or raises <tt class="exception">ValueError</tt> or
  <tt class="exception">OverflowError</tt> isn't defined, and in
  cases where <code>math.log(0)</code> raises <tt class="exception">OverflowError</tt>,
  <code>math.log(0L)</code> may raise <tt class="exception">ValueError</tt> instead.
</div>

<P>
<div class="seealso">
  <p class="heading">See Also:</p>

  <dl compact="compact" class="seemodule">
    <dt>Module <b><tt class="module"><a href="module-cmath.html">cmath</a></tt>:</b>
    <dd>Complex number versions of many of these functions.
  </dl>
</div>

<DIV CLASS="navigation">
<div class='online-navigation'>
<p></p><hr />
<table align="center" width="100%" cellpadding="0" cellspacing="2">
<tr>
<td class='online-navigation'><a rel="prev" title="5.6.8 Decimal FAQ"
  href="decimal-faq.html"><img src='../icons/previous.png'
  border='0' height='32'  alt='Previous Page' width='32' /></A></td>
<td class='online-navigation'><a rel="parent" title="5. Miscellaneous Services"
  href="misc.html"><img src='../icons/up.png'
  border='0' height='32'  alt='Up One Level' width='32' /></A></td>
<td class='online-navigation'><a rel="next" title="5.8 cmath  "
  href="module-cmath.html"><img src='../icons/next.png'
  border='0' height='32'  alt='Next Page' width='32' /></A></td>
<td align="center" width="100%">Python Library Reference</td>
<td class='online-navigation'><a rel="contents" title="Table of Contents"
  href="contents.html"><img src='../icons/contents.png'
  border='0' height='32'  alt='Contents' width='32' /></A></td>
<td class='online-navigation'><a href="modindex.html" title="Module Index"><img src='../icons/modules.png'
  border='0' height='32'  alt='Module Index' width='32' /></a></td>
<td class='online-navigation'><a rel="index" title="Index"
  href="genindex.html"><img src='../icons/index.png'
  border='0' height='32'  alt='Index' width='32' /></A></td>
</tr></table>
<div class='online-navigation'>
<b class="navlabel">Previous:</b>
<a class="sectref" rel="prev" href="decimal-faq.html">5.6.8 Decimal FAQ</A>
<b class="navlabel">Up:</b>
<a class="sectref" rel="parent" href="misc.html">5. Miscellaneous Services</A>
<b class="navlabel">Next:</b>
<a class="sectref" rel="next" href="module-cmath.html">5.8 cmath  </A>
</div>
</div>
<hr />
<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
</DIV>
<!--End of Navigation Panel-->
<ADDRESS>
See <i><a href="about.html">About this document...</a></i> for information on suggesting changes.
</ADDRESS>
</BODY>
</HTML>
Commit	Line	Data
920dae64 AT	1	<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
	2	<html>
	3	<head>
	4	<link rel="STYLESHEET" href="lib.css" type='text/css' />
	5	<link rel="SHORTCUT ICON" href="../icons/pyfav.png" type="image/png" />
	6	<link rel='start' href='../index.html' title='Python Documentation Index' />
	7	<link rel="first" href="lib.html" title='Python Library Reference' />
	8	<link rel='contents' href='contents.html' title="Contents" />
	9	<link rel='index' href='genindex.html' title='Index' />
	10	<link rel='last' href='about.html' title='About this document...' />
	11	<link rel='help' href='about.html' title='About this document...' />
	12	<link rel="next" href="module-cmath.html" />
	13	<link rel="prev" href="module-decimal.html" />
	14	<link rel="parent" href="misc.html" />
	15	<link rel="next" href="module-cmath.html" />
	16	<meta name='aesop' content='information' />
	17	<title>5.7 math -- Mathematical functions</title>
	18	</head>
	19	<body>
	20	<DIV CLASS="navigation">
	21	<div id='top-navigation-panel' xml:id='top-navigation-panel'>
	22	<table align="center" width="100%" cellpadding="0" cellspacing="2">
	23	<tr>
	24	<td class='online-navigation'><a rel="prev" title="5.6.8 Decimal FAQ"
	25	href="decimal-faq.html"><img src='../icons/previous.png'
	26	border='0' height='32' alt='Previous Page' width='32' /></A></td>
	27	<td class='online-navigation'><a rel="parent" title="5. Miscellaneous Services"
	28	href="misc.html"><img src='../icons/up.png'
	29	border='0' height='32' alt='Up One Level' width='32' /></A></td>
	30	<td class='online-navigation'><a rel="next" title="5.8 cmath "
	31	href="module-cmath.html"><img src='../icons/next.png'
	32	border='0' height='32' alt='Next Page' width='32' /></A></td>
	33	<td align="center" width="100%">Python Library Reference</td>
	34	<td class='online-navigation'><a rel="contents" title="Table of Contents"
	35	href="contents.html"><img src='../icons/contents.png'
	36	border='0' height='32' alt='Contents' width='32' /></A></td>
	37	<td class='online-navigation'><a href="modindex.html" title="Module Index"><img src='../icons/modules.png'
	38	border='0' height='32' alt='Module Index' width='32' /></a></td>
	39	<td class='online-navigation'><a rel="index" title="Index"
	40	href="genindex.html"><img src='../icons/index.png'
	41	border='0' height='32' alt='Index' width='32' /></A></td>
	42	</tr></table>
	43	<div class='online-navigation'>
	44	<b class="navlabel">Previous:</b>
	45	<a class="sectref" rel="prev" href="decimal-faq.html">5.6.8 Decimal FAQ</A>
	46	<b class="navlabel">Up:</b>
	47	<a class="sectref" rel="parent" href="misc.html">5. Miscellaneous Services</A>
	48	<b class="navlabel">Next:</b>
	49	<a class="sectref" rel="next" href="module-cmath.html">5.8 cmath </A>
	50	</div>
	51	<hr /></div>
	52	</DIV>
	53	<!--End of Navigation Panel-->
	54
	55	<H1><A NAME="SECTION007700000000000000000">
	56	5.7 <tt class="module">math</tt> --
	57	Mathematical functions</A>
	58	</H1>
	59
	60	<P>
	61	<A NAME="module-math"></A>
	62
	63	<P>
	64	This module is always available. It provides access to the
65	mathematical functions defined by the C standard.
66
67	<P>
68	These functions cannot be used with complex numbers; use the functions
69	of the same name from the <tt class="module"><a href="module-cmath.html">cmath</a></tt> module if you require
70	support for complex numbers. The distinction between functions which
71	support complex numbers and those which don't is made since most users
72	do not want to learn quite as much mathematics as required to
73	understand complex numbers. Receiving an exception instead of a
74	complex result allows earlier detection of the unexpected complex
75	number used as a parameter, so that the programmer can determine how
76	and why it was generated in the first place.
77
78	<P>
79	The following functions are provided by this module. Except
80	when explicitly noted otherwise, all return values are floats.
81
82	<P>
83	Number-theoretic and representation functions:
84
85	<P>
86	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
87	<td><nobr><b><tt id='l2h-1250' xml:id='l2h-1250' class="function">ceil</tt></b>(</nobr></td>
88	<td><var>x</var>)</td></tr></table></dt>
89	<dd>
90	Return the ceiling of <var>x</var> as a float, the smallest integer value
91	greater than or equal to <var>x</var>.
92	</dl>
93
94	<P>
95	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
96	<td><nobr><b><tt id='l2h-1251' xml:id='l2h-1251' class="function">fabs</tt></b>(</nobr></td>
97	<td><var>x</var>)</td></tr></table></dt>
98	<dd>
99	Return the absolute value of <var>x</var>.
100	</dl>
101
102	<P>
103	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
104	<td><nobr><b><tt id='l2h-1252' xml:id='l2h-1252' class="function">floor</tt></b>(</nobr></td>
105	<td><var>x</var>)</td></tr></table></dt>
106	<dd>
107	Return the floor of <var>x</var> as a float, the largest integer value
108	less than or equal to <var>x</var>.
109	</dl>
110
111	<P>
112	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
113	<td><nobr><b><tt id='l2h-1253' xml:id='l2h-1253' class="function">fmod</tt></b>(</nobr></td>
114	<td><var>x, y</var>)</td></tr></table></dt>
115	<dd>
116	Return <code>fmod(<var>x</var>, <var>y</var>)</code>, as defined by the platform C library.
117	Note that the Python expression <code><var>x</var> % <var>y</var></code> may not return
118	the same result. The intent of the C standard is that
119	<code>fmod(<var>x</var>, <var>y</var>)</code> be exactly (mathematically; to infinite
120	precision) equal to <code><var>x</var> - <var>n</var>*<var>y</var></code> for some integer
121	<var>n</var> such that the result has the same sign as <var>x</var> and
122	magnitude less than <code>abs(<var>y</var>)</code>. Python's
123	<code><var>x</var> % <var>y</var></code> returns a result with the sign of
124	<var>y</var> instead, and may not be exactly computable for float arguments.
125	For example, <code>fmod(-1e-100, 1e100)</code> is <code>-1e-100</code>, but the
126	result of Python's <code>-1e-100 % 1e100</code> is <code>1e100-1e-100</code>, which
127	cannot be represented exactly as a float, and rounds to the surprising
128	<code>1e100</code>. For this reason, function <tt class="function">fmod()</tt> is generally
129	preferred when working with floats, while Python's
130	<code><var>x</var> % <var>y</var></code> is preferred when working with integers.
131	</dl>
132
133	<P>
134	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
135	<td><nobr><b><tt id='l2h-1254' xml:id='l2h-1254' class="function">frexp</tt></b>(</nobr></td>
136	<td><var>x</var>)</td></tr></table></dt>
137	<dd>
138	Return the mantissa and exponent of <var>x</var> as the pair
139	<code>(<var>m</var>, <var>e</var>)</code>. <var>m</var> is a float and <var>e</var> is an
140	integer such that <code><var>x</var> == <var>m</var> * 2**<var>e</var></code> exactly.
141	If <var>x</var> is zero, returns <code>(0.0, 0)</code>, otherwise
142	<code>0.5 <= abs(<var>m</var>) < 1</code>. This is used to "pick apart" the
143	internal representation of a float in a portable way.
144	</dl>
145
146	<P>
147	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
148	<td><nobr><b><tt id='l2h-1255' xml:id='l2h-1255' class="function">ldexp</tt></b>(</nobr></td>
149	<td><var>x, i</var>)</td></tr></table></dt>
150	<dd>
151	Return <code><var>x</var> * (2**<var>i</var>)</code>. This is essentially the inverse of
152	function <tt class="function">frexp()</tt>.
153	</dl>
154
155	<P>
156	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
157	<td><nobr><b><tt id='l2h-1256' xml:id='l2h-1256' class="function">modf</tt></b>(</nobr></td>
158	<td><var>x</var>)</td></tr></table></dt>
159	<dd>
160	Return the fractional and integer parts of <var>x</var>. Both results
161	carry the sign of <var>x</var>, and both are floats.
162	</dl>
163
164	<P>
165	Note that <tt class="function">frexp()</tt> and <tt class="function">modf()</tt> have a different
166	call/return pattern than their C equivalents: they take a single
167	argument and return a pair of values, rather than returning their
168	second return value through an `output parameter' (there is no such
169	thing in Python).
170
171	<P>
172	For the <tt class="function">ceil()</tt>, <tt class="function">floor()</tt>, and <tt class="function">modf()</tt>
173	functions, note that <em>all</em> floating-point numbers of sufficiently
174	large magnitude are exact integers. Python floats typically carry no more
175	than 53 bits of precision (the same as the platform C double type), in
176	which case any float <var>x</var> with <code>abs(<var>x</var>) >= 2**52</code>
177	necessarily has no fractional bits.
178
179	<P>
180	Power and logarithmic functions:
181
182	<P>
183	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
184	<td><nobr><b><tt id='l2h-1257' xml:id='l2h-1257' class="function">exp</tt></b>(</nobr></td>
185	<td><var>x</var>)</td></tr></table></dt>
186	<dd>
187	Return <code>e**<var>x</var></code>.
188	</dl>
189
190	<P>
191	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
192	<td><nobr><b><tt id='l2h-1258' xml:id='l2h-1258' class="function">log</tt></b>(</nobr></td>
193	<td><var>x</var><big>[</big><var>, base</var><big>]</big><var></var>)</td></tr></table></dt>
194	<dd>
195	Return the logarithm of <var>x</var> to the given <var>base</var>.
196	If the <var>base</var> is not specified, return the natural logarithm of <var>x</var>
197	(that is, the logarithm to base <em>e</em>).
198
199	<span class="versionnote">Changed in version 2.3:
200	<var>base</var> argument added.</span>
201
202	</dl>
203
204	<P>
205	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
206	<td><nobr><b><tt id='l2h-1259' xml:id='l2h-1259' class="function">log10</tt></b>(</nobr></td>
207	<td><var>x</var>)</td></tr></table></dt>
208	<dd>
209	Return the base-10 logarithm of <var>x</var>.
210	</dl>
211
212	<P>
213	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
214	<td><nobr><b><tt id='l2h-1260' xml:id='l2h-1260' class="function">pow</tt></b>(</nobr></td>
215	<td><var>x, y</var>)</td></tr></table></dt>
216	<dd>
217	Return <code><var>x</var>**<var>y</var></code>.
218	</dl>
219
220	<P>
221	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
222	<td><nobr><b><tt id='l2h-1261' xml:id='l2h-1261' class="function">sqrt</tt></b>(</nobr></td>
223	<td><var>x</var>)</td></tr></table></dt>
224	<dd>
225	Return the square root of <var>x</var>.
226	</dl>
227
228	<P>
229	Trigonometric functions:
230
231	<P>
232	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
233	<td><nobr><b><tt id='l2h-1262' xml:id='l2h-1262' class="function">acos</tt></b>(</nobr></td>
234	<td><var>x</var>)</td></tr></table></dt>
235	<dd>
236	Return the arc cosine of <var>x</var>, in radians.
237	</dl>
238
239	<P>
240	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
241	<td><nobr><b><tt id='l2h-1263' xml:id='l2h-1263' class="function">asin</tt></b>(</nobr></td>
242	<td><var>x</var>)</td></tr></table></dt>
243	<dd>
244	Return the arc sine of <var>x</var>, in radians.
245	</dl>
246
247	<P>
248	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
249	<td><nobr><b><tt id='l2h-1264' xml:id='l2h-1264' class="function">atan</tt></b>(</nobr></td>
250	<td><var>x</var>)</td></tr></table></dt>
251	<dd>
252	Return the arc tangent of <var>x</var>, in radians.
253	</dl>
254
255	<P>
256	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
257	<td><nobr><b><tt id='l2h-1265' xml:id='l2h-1265' class="function">atan2</tt></b>(</nobr></td>
258	<td><var>y, x</var>)</td></tr></table></dt>
259	<dd>
260	Return <code>atan(<var>y</var> / <var>x</var>)</code>, in radians.
261	The result is between <code>-pi</code> and <code>pi</code>.
262	The vector in the plane from the origin to point <code>(<var>x</var>, <var>y</var>)</code>
263	makes this angle with the positive X axis.
264	The point of <tt class="function">atan2()</tt> is that the signs of both inputs are
265	known to it, so it can compute the correct quadrant for the angle.
266	For example, <code>atan(1</code>) and <code>atan2(1, 1)</code> are both <code>pi/4</code>,
267	but <code>atan2(-1, -1)</code> is <code>-3*pi/4</code>.
268	</dl>
269
270	<P>
271	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
272	<td><nobr><b><tt id='l2h-1266' xml:id='l2h-1266' class="function">cos</tt></b>(</nobr></td>
273	<td><var>x</var>)</td></tr></table></dt>
274	<dd>
275	Return the cosine of <var>x</var> radians.
276	</dl>
277
278	<P>
279	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
280	<td><nobr><b><tt id='l2h-1267' xml:id='l2h-1267' class="function">hypot</tt></b>(</nobr></td>
281	<td><var>x, y</var>)</td></tr></table></dt>
282	<dd>
283	Return the Euclidean norm, <code>sqrt(<var>x</var><var>x</var> + <var>y</var><var>y</var>)</code>.
284	This is the length of the vector from the origin to point
285	<code>(<var>x</var>, <var>y</var>)</code>.
286	</dl>
287
288	<P>
289	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
290	<td><nobr><b><tt id='l2h-1268' xml:id='l2h-1268' class="function">sin</tt></b>(</nobr></td>
291	<td><var>x</var>)</td></tr></table></dt>
292	<dd>
293	Return the sine of <var>x</var> radians.
294	</dl>
295
296	<P>
297	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
298	<td><nobr><b><tt id='l2h-1269' xml:id='l2h-1269' class="function">tan</tt></b>(</nobr></td>
299	<td><var>x</var>)</td></tr></table></dt>
300	<dd>
301	Return the tangent of <var>x</var> radians.
302	</dl>
303
304	<P>
305	Angular conversion:
306
307	<P>
308	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
309	<td><nobr><b><tt id='l2h-1270' xml:id='l2h-1270' class="function">degrees</tt></b>(</nobr></td>
310	<td><var>x</var>)</td></tr></table></dt>
311	<dd>
312	Converts angle <var>x</var> from radians to degrees.
313	</dl>
314
315	<P>
316	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
317	<td><nobr><b><tt id='l2h-1271' xml:id='l2h-1271' class="function">radians</tt></b>(</nobr></td>
318	<td><var>x</var>)</td></tr></table></dt>
319	<dd>
320	Converts angle <var>x</var> from degrees to radians.
321	</dl>
322
323	<P>
324	Hyperbolic functions:
325
326	<P>
327	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
328	<td><nobr><b><tt id='l2h-1272' xml:id='l2h-1272' class="function">cosh</tt></b>(</nobr></td>
329	<td><var>x</var>)</td></tr></table></dt>
330	<dd>
331	Return the hyperbolic cosine of <var>x</var>.
332	</dl>
333
334	<P>
335	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
336	<td><nobr><b><tt id='l2h-1273' xml:id='l2h-1273' class="function">sinh</tt></b>(</nobr></td>
337	<td><var>x</var>)</td></tr></table></dt>
338	<dd>
339	Return the hyperbolic sine of <var>x</var>.
340	</dl>
341
342	<P>
343	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
344	<td><nobr><b><tt id='l2h-1274' xml:id='l2h-1274' class="function">tanh</tt></b>(</nobr></td>
345	<td><var>x</var>)</td></tr></table></dt>
346	<dd>
347	Return the hyperbolic tangent of <var>x</var>.
348	</dl>
349
350	<P>
351	The module also defines two mathematical constants:
352
353	<P>
354	<dl><dt><b><tt id='l2h-1275' xml:id='l2h-1275'>pi</tt></b></dt>
355	<dd>
356	The mathematical constant <em>pi</em>.
357	</dd></dl>
358
359	<P>
360	<dl><dt><b><tt id='l2h-1276' xml:id='l2h-1276'>e</tt></b></dt>
361	<dd>
362	The mathematical constant <em>e</em>.
363	</dd></dl>
364
365	<P>
366	<div class="note"><b class="label">Note:</b>
367	The <tt class="module">math</tt> module consists mostly of thin wrappers around
368	the platform C math library functions. Behavior in exceptional cases is
369	loosely specified by the C standards, and Python inherits much of its
370	math-function error-reporting behavior from the platform C
371	implementation. As a result,
372	the specific exceptions raised in error cases (and even whether some
373	arguments are considered to be exceptional at all) are not defined in any
374	useful cross-platform or cross-release way. For example, whether
375	<code>math.log(0)</code> returns <code>-Inf</code> or raises <tt class="exception">ValueError</tt> or
376	<tt class="exception">OverflowError</tt> isn't defined, and in
377	cases where <code>math.log(0)</code> raises <tt class="exception">OverflowError</tt>,
378	<code>math.log(0L)</code> may raise <tt class="exception">ValueError</tt> instead.
379	</div>
380
381	<P>
382	<div class="seealso">
383	<p class="heading">See Also:</p>
384
385	<dl compact="compact" class="seemodule">
386	<dt>Module <b><tt class="module"><a href="module-cmath.html">cmath</a></tt>:</b>
387	<dd>Complex number versions of many of these functions.
388	</dl>
389	</div>
390
391	<DIV CLASS="navigation">
392	<div class='online-navigation'>
393	<p></p><hr />
394	<table align="center" width="100%" cellpadding="0" cellspacing="2">
395	<tr>
396	<td class='online-navigation'><a rel="prev" title="5.6.8 Decimal FAQ"
397	href="decimal-faq.html"><img src='../icons/previous.png'
398	border='0' height='32' alt='Previous Page' width='32' /></A></td>
399	<td class='online-navigation'><a rel="parent" title="5. Miscellaneous Services"
400	href="misc.html"><img src='../icons/up.png'
401	border='0' height='32' alt='Up One Level' width='32' /></A></td>
402	<td class='online-navigation'><a rel="next" title="5.8 cmath "
403	href="module-cmath.html"><img src='../icons/next.png'
404	border='0' height='32' alt='Next Page' width='32' /></A></td>
405	<td align="center" width="100%">Python Library Reference</td>
406	<td class='online-navigation'><a rel="contents" title="Table of Contents"
407	href="contents.html"><img src='../icons/contents.png'
408	border='0' height='32' alt='Contents' width='32' /></A></td>
409	<td class='online-navigation'><a href="modindex.html" title="Module Index"><img src='../icons/modules.png'
410	border='0' height='32' alt='Module Index' width='32' /></a></td>
411	<td class='online-navigation'><a rel="index" title="Index"
412	href="genindex.html"><img src='../icons/index.png'
413	border='0' height='32' alt='Index' width='32' /></A></td>
414	</tr></table>
415	<div class='online-navigation'>
416	<b class="navlabel">Previous:</b>
417	<a class="sectref" rel="prev" href="decimal-faq.html">5.6.8 Decimal FAQ</A>
418	<b class="navlabel">Up:</b>
419	<a class="sectref" rel="parent" href="misc.html">5. Miscellaneous Services</A>
420	<b class="navlabel">Next:</b>
421	<a class="sectref" rel="next" href="module-cmath.html">5.8 cmath </A>
422	</div>
423	</div>
424	<hr />
425	<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
426	</DIV>
427	<!--End of Navigation Panel-->
428	<ADDRESS>
429	See <i><a href="about.html">About this document...</a></i> for information on suggesting changes.
430	</ADDRESS>
431	</BODY>
432	</HTML>