3.4.7 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.
- These methods are
called to implement the binary arithmetic operations (
+,-,*,//,%, divmod(), pow(),**,<<,>>,&,^,|). For instance, to evaluate the expression x+y, where x is an instance of a class that has an __add__() method,x.__add__(y)is called. The __divmod__() method should be the equivalent to using __floordiv__() and __mod__(); it should not be related to __truediv__() (described below). Note that __pow__() should be defined to accept an optional third argument if the ternary version of the built-in pow() function is to be supported.If one of those methods does not support the operation with the supplied arguments, it should return
NotImplemented.
- The division operator (
/) is implemented by these methods. The __truediv__() method is used when__future__.divisionis in effect, otherwise __div__() is used. If only one of these two methods is defined, the object will not support division in the alternate context; TypeError will be raised instead.
- These methods are
called to implement the binary arithmetic operations (
+,-,*,/,%, divmod(), pow(),**,<<,>>,&,^,|) with reflected (swapped) operands. These functions are only called if the left operand does not support the corresponding operation and the operands are of different types.3.3 For instance, to evaluate the expression x-y, where y is an instance of a class that has an __rsub__() method,y.__rsub__(x)is called ifx.__sub__(y)returns NotImplemented.Note that ternary pow() will not try calling __rpow__() (the coercion rules would become too complicated).
Note: If the right operand's type is a subclass of the left operand's type and that subclass provides the reflected method for the operation, this method will be called before the left operand's non-reflected method. This behavior allows subclasses to override their ancestors' operations.
- These methods are called to implement the augmented arithmetic
operations (
+=,-=,*=,/=,%=,**=,<<=,>>=,&=,^=,|=). These methods should attempt to do the operation in-place (modifying self) and return the result (which could be, but does not have to be, self). If a specific method is not defined, the augmented operation falls back to the normal methods. For instance, to evaluate the expression x+=y, where x is an instance of a class that has an __iadd__() method,x.__iadd__(y)is called. If x is an instance of a class that does not define a __iadd__() method,x.__add__(y)andy.__radd__(x)are considered, as with the evaluation of x+y.
- Called to implement the built-in functions complex(), int(), long(), and float(). Should return a value of the appropriate type.
- Called to implement operator.index(). Also called whenever Python needs an integer object (such as in slicing). Must return an integer (int or long). New in version 2.5.
-
Called to implement ``mixed-mode'' numeric arithmetic. Should either
return a 2-tuple containing self and other converted to
a common numeric type, or
Noneif conversion is impossible. When the common type would be the type ofother, it is sufficient to returnNone, 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 ofNotImplementedis equivalent to returningNone.
Footnotes
- For operands of the same type, it is assumed that if the non-reflected method (such as __add__()) fails the operation is not supported, which is why the reflected method is not called.
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Release 2.5, documentation updated on 19th September, 2006.