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<H2>
<BR>
2.1.4 Numeric Types 
</H2>

<P>
There are four numeric types: <i class="dfn">plain integers</i>, <i class="dfn">long integers</i>, 
<i class="dfn">floating point numbers</i>, and <i class="dfn">complex numbers</i>.
Plain integers (also just called <i class="dfn">integers</i>)
are implemented using <tt class="ctype">long</tt> in C, which gives them at least 32
bits of precision.  Long integers have unlimited precision.  Floating
point numbers are implemented using <tt class="ctype">double</tt> in C.  All bets on
their precision are off unless you happen to know the machine you are
working with.


<P>
Complex numbers have a real and imaginary part, which are both
implemented using <tt class="ctype">double</tt> in C.  To extract these parts from
a complex number <var>z</var>, use <code><var>z</var>.real</code> and <code><var>z</var>.imag</code>.  

<P>
Numbers are created by numeric literals or as the result of built-in
functions and operators.  Unadorned integer literals (including hex
and octal numbers) yield plain integers.  Integer literals with an
"<tt class="character">L</tt>" or "<tt class="character">l</tt>" suffix yield long integers
("<tt class="character">L</tt>" is preferred because "<tt class="samp">1l</tt>" looks too much like
eleven!).  Numeric literals containing a decimal point or an exponent
sign yield floating point numbers.  Appending "<tt class="character">j</tt>" or
"<tt class="character">J</tt>" to a numeric literal yields a complex number.


<P>
Python fully supports mixed arithmetic: when a binary arithmetic
operator has operands of different numeric types, the operand with the
``smaller'' type is converted to that of the other, where plain
integer is smaller than long integer is smaller than floating point is
smaller than complex.
Comparisons between numbers of mixed type use the same rule.<A NAME="tex2html3"
  HREF="#foot1414"><SUP>2.3</SUP></A> The functions <tt class="function">int()</tt>, <tt class="function">long()</tt>, <tt class="function">float()</tt>,
and <tt class="function">complex()</tt> can be used
to coerce numbers to a specific type.


<P>
All numeric types support the following operations, sorted by
ascending priority (operations in the same box have the same
priority; all numeric operations have a higher priority than
comparison operations):

<P>
<table border align="center" style="border-collapse: collapse">
  <thead>
    <tr>
      <th align="center"><b>Operation</b>&nbsp;</th>
      <th align="left"><b>Result</b>&nbsp;</th>
      <th align="center"><b>Notes</b>&nbsp;</th>
    </thead>
  <tbody valign='baseline'>
    <tr><td align="center" valign="baseline"><code><var>x</var> + <var>y</var></code></td>
        <td align="left">sum of <var>x</var> and <var>y</var></td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code><var>x</var> - <var>y</var></code></td>
        <td align="left">difference of <var>x</var> and <var>y</var></td>
        <td align="center">&nbsp;</td>
  
    <tr><td align="center" valign="baseline"><code><var>x</var> * <var>y</var></code></td>
        <td align="left">product of <var>x</var> and <var>y</var></td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code><var>x</var> / <var>y</var></code></td>
        <td align="left">quotient of <var>x</var> and <var>y</var></td>
        <td align="center">(1)</td>
    <tr><td align="center" valign="baseline"><code><var>x</var> % <var>y</var></code></td>
        <td align="left">remainder of <code><var>x</var> / <var>y</var></code></td>
        <td align="center">&nbsp;</td>
  
    <tr><td align="center" valign="baseline"><code>-<var>x</var></code></td>
        <td align="left"><var>x</var> negated</td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code>+<var>x</var></code></td>
        <td align="left"><var>x</var> unchanged</td>
        <td align="center">&nbsp;</td>
  
    <tr><td align="center" valign="baseline"><code>abs(<var>x</var>)</code></td>
        <td align="left">absolute value or magnitude of <var>x</var></td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code>int(<var>x</var>)</code></td>
        <td align="left"><var>x</var> converted to integer</td>
        <td align="center">(2)</td>
    <tr><td align="center" valign="baseline"><code>long(<var>x</var>)</code></td>
        <td align="left"><var>x</var> converted to long integer</td>
        <td align="center">(2)</td>
    <tr><td align="center" valign="baseline"><code>float(<var>x</var>)</code></td>
        <td align="left"><var>x</var> converted to floating point</td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code>complex(<var>re</var>,<var>im</var>)</code></td>
        <td align="left">a complex number with real part <var>re</var>, imaginary part <var>im</var>.  <var>im</var> defaults to zero.</td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code><var>c</var>.conjugate()</code></td>
        <td align="left">conjugate of the complex number <var>c</var></td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code>divmod(<var>x</var>, <var>y</var>)</code></td>
        <td align="left">the pair <code>(<var>x</var> / <var>y</var>, <var>x</var> % <var>y</var>)</code></td>
        <td align="center">(3)</td>
    <tr><td align="center" valign="baseline"><code>pow(<var>x</var>, <var>y</var>)</code></td>
        <td align="left"><var>x</var> to the power <var>y</var></td>
        <td align="center">&nbsp;</td>
    <tr><td align="center" valign="baseline"><code><var>x</var> ** <var>y</var></code></td>
        <td align="left"><var>x</var> to the power <var>y</var></td>
        <td align="center">&nbsp;</td></tbody>
</table>


<P>
Notes:
<DL>
<DT><STRONG>(1)</STRONG></DT>
<DD>For (plain or long) integer division, the result is an integer.
The result is always rounded towards minus infinity: 1/2 is 0, 
(-1)/2 is -1, 1/(-2) is -1, and (-1)/(-2) is 0.  Note that the result
is a long integer if either operand is a long integer, regardless of
the numeric value.


<P>
</DD>
<DT><STRONG>(2)</STRONG></DT>
<DD>Conversion from floating point to (long or plain) integer may round or
truncate as in C; see functions <tt class="function">floor()</tt> and
<tt class="function">ceil()</tt> in the <tt class='module'><a href="module-math.html" tppabs="http://www.python.org/doc/current/lib/module-math.html">math</a></tt> module
for well-defined conversions.


<P>
</DD>
<DT><STRONG>(3)</STRONG></DT>
<DD>See section <A href="built-in-funcs.html#built-in-funcs" tppabs="http://www.python.org/doc/current/lib/built-in-funcs.html#built-in-funcs">2.3</A>, ``Built-in Functions,'' for a full
description.

<P>
</DD>
</DL>

<P>
<BR><HR><H4>Footnotes</H4>
<DL>
<DT><A NAME="foot1414">... rule.</A><A NAME="foot1414"
 href="typesnumeric.html#tex2html3" tppabs="http://www.python.org/doc/current/lib/typesnumeric.html#tex2html3"><SUP>2.3</SUP></A>
<DD>
	As a consequence, the list <code>[1, 2]</code> is considered equal
        to <code>[1.0, 2.0]</code>, and similar for tuples.


</DL>
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<LI><A NAME="tex2html1025"
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