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<title>3.3.7 Emulating numeric types</title>
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<H2><A NAME="SECTION005370000000000000000"></A><A NAME="numeric-types"></A>
<BR>
3.3.7 Emulating numeric types
</H2>

<P>
The following methods can be defined to emulate numeric objects.
Methods corresponding to operations that are not supported by the
particular kind of number implemented (e.g., bitwise operations for
non-integral numbers) should be left undefined.

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-240' xml:id='l2h-240' class="method">__add__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-241' xml:id='l2h-241' class="method">__sub__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-242' xml:id='l2h-242' class="method">__mul__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-243' xml:id='l2h-243' class="method">__floordiv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-244' xml:id='l2h-244' class="method">__mod__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-245' xml:id='l2h-245' class="method">__divmod__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-246' xml:id='l2h-246' class="method">__pow__</tt></b>(</nobr></td>
  <td><var>self, other</var><big>[</big><var>, modulo</var><big>]</big><var></var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-247' xml:id='l2h-247' class="method">__lshift__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-248' xml:id='l2h-248' class="method">__rshift__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-249' xml:id='l2h-249' class="method">__and__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-250' xml:id='l2h-250' class="method">__xor__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-251' xml:id='l2h-251' class="method">__or__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>These methods are
called to implement the binary arithmetic operations (<code>+</code>,
<code>-</code>, <code>*</code>, <code>//</code>, <code>%</code>,
<tt class="function">divmod()</tt><a id='l2h-252' xml:id='l2h-252'></a>,
<tt class="function">pow()</tt><a id='l2h-253' xml:id='l2h-253'></a>, <code>**</code>, <code>&lt;</code><code>&lt;</code>,
<code>&gt;</code><code>&gt;</code>, <code>&amp;</code>, <code>^</code>, <code>|</code>).  For instance, to
evaluate the expression <var>x</var><code>+</code><var>y</var>, where <var>x</var> is an
instance of a class that has an <tt class="method">__add__()</tt> method,
<code><var>x</var>.__add__(<var>y</var>)</code> is called.  The <tt class="method">__divmod__()</tt>
method should be the equivalent to using <tt class="method">__floordiv__()</tt> and
<tt class="method">__mod__()</tt>; it should not be related to <tt class="method">__truediv__()</tt>
(described below).  Note that
<tt class="method">__pow__()</tt> should be defined to accept an optional third
argument if the ternary version of the built-in
<tt class="function">pow()</tt><a id='l2h-254' xml:id='l2h-254'></a> function is to be supported.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-255' xml:id='l2h-255' class="method">__div__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-256' xml:id='l2h-256' class="method">__truediv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>The division operator (<code>/</code>) is implemented by these methods.  The
<tt class="method">__truediv__()</tt> method is used when <code>__future__.division</code>
is in effect, otherwise <tt class="method">__div__()</tt> is used.  If only one of
these two methods is defined, the object will not support division in
the alternate context; <tt class="exception">TypeError</tt> will be raised instead.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-257' xml:id='l2h-257' class="method">__radd__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-258' xml:id='l2h-258' class="method">__rsub__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-259' xml:id='l2h-259' class="method">__rmul__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-260' xml:id='l2h-260' class="method">__rdiv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-261' xml:id='l2h-261' class="method">__rtruediv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-262' xml:id='l2h-262' class="method">__rfloordiv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>	     
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-263' xml:id='l2h-263' class="method">__rmod__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-264' xml:id='l2h-264' class="method">__rdivmod__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-265' xml:id='l2h-265' class="method">__rpow__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-266' xml:id='l2h-266' class="method">__rlshift__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-267' xml:id='l2h-267' class="method">__rrshift__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-268' xml:id='l2h-268' class="method">__rand__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-269' xml:id='l2h-269' class="method">__rxor__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-270' xml:id='l2h-270' class="method">__ror__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>These methods are
called to implement the binary arithmetic operations (<code>+</code>,
<code>-</code>, <code>*</code>, <code>/</code>, <code>%</code>,
<tt class="function">divmod()</tt><a id='l2h-271' xml:id='l2h-271'></a>,
<tt class="function">pow()</tt><a id='l2h-272' xml:id='l2h-272'></a>, <code>**</code>, <code>&lt;</code><code>&lt;</code>,
<code>&gt;</code><code>&gt;</code>, <code>&amp;</code>, <code>^</code>, <code>|</code>) with reflected
(swapped) operands.  These functions are only called if the left
operand does not support the corresponding operation.  For instance,
to evaluate the expression <var>x</var><code>-</code><var>y</var>, where <var>y</var> is an
instance of a class that has an <tt class="method">__rsub__()</tt> method,
<code><var>y</var>.__rsub__(<var>x</var>)</code> is called.  Note that ternary
<tt class="function">pow()</tt><a id='l2h-273' xml:id='l2h-273'></a> will not try calling
<tt class="method">__rpow__()</tt> (the coercion rules would become too
complicated).
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-274' xml:id='l2h-274' class="method">__iadd__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-275' xml:id='l2h-275' class="method">__isub__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-276' xml:id='l2h-276' class="method">__imul__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-277' xml:id='l2h-277' class="method">__idiv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-278' xml:id='l2h-278' class="method">__itruediv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-279' xml:id='l2h-279' class="method">__ifloordiv__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-280' xml:id='l2h-280' class="method">__imod__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>		     
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-281' xml:id='l2h-281' class="method">__ipow__</tt></b>(</nobr></td>
  <td><var>self, other</var><big>[</big><var>, modulo</var><big>]</big><var></var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-282' xml:id='l2h-282' class="method">__ilshift__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-283' xml:id='l2h-283' class="method">__irshift__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-284' xml:id='l2h-284' class="method">__iand__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-285' xml:id='l2h-285' class="method">__ixor__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-286' xml:id='l2h-286' class="method">__ior__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>These methods are called to implement the augmented arithmetic
operations (<code>+=</code>, <code>-=</code>, <code>*=</code>, <code>/=</code>, <code>%=</code>,
<code>**=</code>, <code>&lt;</code><code>&lt;=</code>, <code>&gt;</code><code>&gt;=</code>, <code>&amp;=</code>,
<code>^=</code>, <code>|=</code>).  These methods should attempt to do the
operation in-place (modifying <var>self</var>) and return the result (which
could be, but does not have to be, <var>self</var>).  If a specific method
is not defined, the augmented operation falls back to the normal
methods.  For instance, to evaluate the expression
<var>x</var><code>+=</code><var>y</var>, where <var>x</var> is an instance of a class that
has an <tt class="method">__iadd__()</tt> method, <code><var>x</var>.__iadd__(<var>y</var>)</code> is
called.  If <var>x</var> is an instance of a class that does not define a
<tt class="method">__iadd__()</tt> method, <code><var>x</var>.__add__(<var>y</var>)</code> and
<code><var>y</var>.__radd__(<var>x</var>)</code> are considered, as with the
evaluation of <var>x</var><code>+</code><var>y</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-287' xml:id='l2h-287' class="method">__neg__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-288' xml:id='l2h-288' class="method">__pos__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-289' xml:id='l2h-289' class="method">__abs__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-290' xml:id='l2h-290' class="method">__invert__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd>Called to implement the unary arithmetic operations (<code>-</code>,
<code>+</code>, <tt class="function">abs()</tt><a id='l2h-291' xml:id='l2h-291'></a> and <code>~</code>).
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-292' xml:id='l2h-292' class="method">__complex__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-293' xml:id='l2h-293' class="method">__int__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-294' xml:id='l2h-294' class="method">__long__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-295' xml:id='l2h-295' class="method">__float__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd>Called to implement the built-in functions
<tt class="function">complex()</tt><a id='l2h-296' xml:id='l2h-296'></a>,
<tt class="function">int()</tt><a id='l2h-297' xml:id='l2h-297'></a>, <tt class="function">long()</tt><a id='l2h-298' xml:id='l2h-298'></a>,
and <tt class="function">float()</tt><a id='l2h-299' xml:id='l2h-299'></a>.  Should return a value of
the appropriate type.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-300' xml:id='l2h-300' class="method">__oct__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd>
<dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-301' xml:id='l2h-301' class="method">__hex__</tt></b>(</nobr></td>
  <td><var>self</var>)</td></tr></table></dt>
<dd>Called to implement the built-in functions
<tt class="function">oct()</tt><a id='l2h-302' xml:id='l2h-302'></a> and
<tt class="function">hex()</tt><a id='l2h-303' xml:id='l2h-303'></a>.  Should return a string value.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-304' xml:id='l2h-304' class="method">__coerce__</tt></b>(</nobr></td>
  <td><var>self, other</var>)</td></tr></table></dt>
<dd>
Called to implement ``mixed-mode'' numeric arithmetic.  Should either
return a 2-tuple containing <var>self</var> and <var>other</var> converted to
a common numeric type, or <code>None</code> if conversion is impossible.  When
the common type would be the type of <code>other</code>, it is sufficient to
return <code>None</code>, since the interpreter will also ask the other
object to attempt a coercion (but sometimes, if the implementation of
the other type cannot be changed, it is useful to do the conversion to
the other type here).  A return value of <code>NotImplemented</code> is
equivalent to returning <code>None</code>.
</dl>

<P>

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<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
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