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.

(`__add__``self, other`)(`__sub__``self, other`)(`__mul__``self, other`)(`__floordiv__``self, other`)(`__mod__``self, other`)(`__divmod__``self, other`)(`__pow__``self, other`[`, modulo`]`)`(`__lshift__``self, other`)(`__rshift__``self, other`)(`__and__``self, other`)(`__xor__``self, other`)(`__or__``self, other`)-
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,

is called. The`x`.__add__(`y`)`__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`

.

(`__div__``self, other`)(`__truediv__``self, other`)-
The division operator (
`/`

) is implemented by these methods. The`__truediv__()`method is used when`__future__.division`

is 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.

(`__radd__``self, other`)(`__rsub__``self, other`)(`__rmul__``self, other`)(`__rdiv__``self, other`)(`__rtruediv__``self, other`)(`__rfloordiv__``self, other`)(`__rmod__``self, other`)(`__rdivmod__``self, other`)(`__rpow__``self, other`)(`__rlshift__``self, other`)(`__rrshift__``self, other`)(`__rand__``self, other`)(`__rxor__``self, other`)(`__ror__``self, other`)-
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,

is called if`y`.__rsub__(`x`)

returns`x`.__sub__(`y`)`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.

(`__iadd__``self, other`)(`__isub__``self, other`)(`__imul__``self, other`)(`__idiv__``self, other`)(`__itruediv__``self, other`)(`__ifloordiv__``self, other`)(`__imod__``self, other`)(`__ipow__``self, other`[`, modulo`]`)`(`__ilshift__``self, other`)(`__irshift__``self, other`)(`__iand__``self, other`)(`__ixor__``self, other`)(`__ior__``self, other`)-
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,

is called. If`x`.__iadd__(`y`)`x`is an instance of a class that does not define a`__iadd__()`method,

and`x`.__add__(`y`)

are considered, as with the evaluation of`y`.__radd__(`x`)`x``+`

`y`.

(`__neg__``self`)(`__pos__``self`)(`__abs__``self`)(`__invert__``self`)-
Called to implement the unary arithmetic operations (
`-`

,`+`

,`abs()`and`~`

).

(`__complex__``self`)(`__int__``self`)(`__long__``self`)(`__float__``self`)-
Called to implement the built-in functions
`complex()`,`int()`,`long()`, and`float()`. Should return a value of the appropriate type.

(`__oct__``self`)(`__hex__``self`)-
Called to implement the built-in functions
`oct()`and`hex()`. Should return a string value.

(`__index__``self`)-
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.

(`__coerce__``self, other`)-
Called to implement ``mixed-mode'' numeric arithmetic. Should either
return a 2-tuple containing
`self`and`other`converted to a common numeric type, or`None`

if conversion is impossible. When the common type would be the type of`other`

, it is sufficient to return`None`

, 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`NotImplemented`

is equivalent to returning`None`

.

- ... types.
^{3.3} -
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.