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<title>3.3.7 Emulating numeric types
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<H2><A NAME=
"SECTION005370000000000000000"></A><A NAME=
"numeric-types"></A>
3.3.7 Emulating numeric types
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.
<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>
<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>
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><</code><code><</code>,
<code>></code><code>></code>,
<code>&</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><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>
<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><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>
<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>
<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>
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><</code><code><</code>,
<code>></code><code>></code>,
<code>&</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
<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>
<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>
<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><</code><code><=
</code>,
<code>></code><code>>=
</code>,
<code>&=
</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><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>
<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><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>
<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
<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>
<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><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>
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>.
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