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Numeric Types Emulators Inside DelphiVCL Library

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In DelphiVCL Library or Python in general, 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.

Table of Contents

object.__add__(self, other)

object.__sub__(self, other)

object.__mul__(self, other)

object.__matmul__(self, other)

object.__truediv__(self, other)

object.__floordiv__(self, other)

object.__mod__(self, other)

object.__divmod__(self, other)

object.__pow__(self, other[, modulo])

object.__lshift__(self, other)

object.__rshift__(self, other)

object.__and__(self, other)

object.__xor__(self, other)

object.__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, x.__add__(y) is called. The __divmod__() method should be the equivalent to using __floordiv__() and __mod__(); it should not be related to __truediv__(). 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.

object.__radd__(self, other)

object.__rsub__(self, other)

object.__rmul__(self, other)

object.__rmatmul__(self, other)

object.__rtruediv__(self, other)

object.__rfloordiv__(self, other)

object.__rmod__(self, other)

object.__rdivmod__(self, other)

object.__rpow__(self, other[, modulo])

object.__rlshift__(self, other)

object.__rrshift__(self, other)

object.__rand__(self, other)

object.__rxor__(self, other)

object.__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. 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 if x.__sub__(y) returns NotImplemented.

Note that ternary pow() will not try calling __rpow__() (the coercion rules would become too complicated).

Additional Note: If the right operand’s type is a subclass of the left operand’s type and that subclass provides a different implementation of 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.

object.__iadd__(self, other)

object.__isub__(self, other)

object.__imul__(self, other)

object.__imatmul__(self, other)

object.__itruediv__(self, other)

object.__ifloordiv__(self, other)

object.__imod__(self, other)

object.__ipow__(self, other[, modulo])

object.__ilshift__(self, other)

object.__irshift__(self, other)

object.__iand__(self, other)

object.__ixor__(self, other)

object.__ior__(self, other)

These methods are called to implement the augmented arithmetic assignments (+=, -=, *=, @=, /=, //=, %=, **=, <<=, >>=, &=, ^=, |=). 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 assignment falls back to the normal methods. For instance, if x is an instance of a class with an __iadd__() method, x += y is equivalent to x = x.__iadd__(y). Otherwise, x.__add__(y) and y.__radd__(x) are considered, as with the evaluation of x + y. In certain situations, the augmented assignment can result in unexpected errors (see Why does a_tuple[i] += [‘item’] raise an exception when the addition works?), but this behavior is part of the data model.

Additional Note: Due to a bug in the dispatching mechanism for **=, a class that defines __ipow__() but returns NotImplemented would fail to fall back to x.__pow__(y) and y.__rpow__(x). This bug is fixed in Python 3.10.





Called to implement the unary arithmetic operations (-, +, abs() and ~).




Called to implement the built-in functions complex(), int(), and float(). Should return a value of the appropriate type.


Called to implement operator.index(), and whenever Python needs to losslessly convert the numeric object to an integer object (such as in slicing, or the built-in bin(), hex() and oct() functions). The presence of this method indicates that the numeric object is an integer type. Must return an integer.

If __int__(), __float__() and __complex__() are not defined then corresponding built-in functions int(), float() and complex() fall back to __index__().

object.__round__(self[, ndigits])




Called to implement the built-in function round() and math functions trunc(), floor() and ceil(). Unless ndigits is passed to __round__() all these methods should return the value of the object truncated to an Integral (typically an int).

If __int__() is not defined then the built-in function int() falls back to __trunc__().


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