EmbeddedPkg: Extend NvVarStoreFormattedLib LIBRARY_CLASS

[mirror_edk2.git] / AppPkg / Applications / Python / Python-2.7.10 / Lib / numbers.py

# Copyright 2007 Google, Inc. All Rights Reserved.\r
# Licensed to PSF under a Contributor Agreement.\r
\r
"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141.\r
\r
TODO: Fill out more detailed documentation on the operators."""\r
\r
from __future__ import division\r
from abc import ABCMeta, abstractmethod, abstractproperty\r
\r
__all__ = ["Number", "Complex", "Real", "Rational", "Integral"]\r
\r
class Number(object):\r
    """All numbers inherit from this class.\r
\r
    If you just want to check if an argument x is a number, without\r
    caring what kind, use isinstance(x, Number).\r
    """\r
    __metaclass__ = ABCMeta\r
    __slots__ = ()\r
\r
    # Concrete numeric types must provide their own hash implementation\r
    __hash__ = None\r
\r
\r
## Notes on Decimal\r
## ----------------\r
## Decimal has all of the methods specified by the Real abc, but it should\r
## not be registered as a Real because decimals do not interoperate with\r
## binary floats (i.e.  Decimal('3.14') + 2.71828 is undefined).  But,\r
## abstract reals are expected to interoperate (i.e. R1 + R2 should be\r
## expected to work if R1 and R2 are both Reals).\r
\r
class Complex(Number):\r
    """Complex defines the operations that work on the builtin complex type.\r
\r
    In short, those are: a conversion to complex, .real, .imag, +, -,\r
    *, /, abs(), .conjugate, ==, and !=.\r
\r
    If it is given heterogenous arguments, and doesn't have special\r
    knowledge about them, it should fall back to the builtin complex\r
    type as described below.\r
    """\r
\r
    __slots__ = ()\r
\r
    @abstractmethod\r
    def __complex__(self):\r
        """Return a builtin complex instance. Called for complex(self)."""\r
\r
    # Will be __bool__ in 3.0.\r
    def __nonzero__(self):\r
        """True if self != 0. Called for bool(self)."""\r
        return self != 0\r
\r
    @abstractproperty\r
    def real(self):\r
        """Retrieve the real component of this number.\r
\r
        This should subclass Real.\r
        """\r
        raise NotImplementedError\r
\r
    @abstractproperty\r
    def imag(self):\r
        """Retrieve the imaginary component of this number.\r
\r
        This should subclass Real.\r
        """\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __add__(self, other):\r
        """self + other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __radd__(self, other):\r
        """other + self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __neg__(self):\r
        """-self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __pos__(self):\r
        """+self"""\r
        raise NotImplementedError\r
\r
    def __sub__(self, other):\r
        """self - other"""\r
        return self + -other\r
\r
    def __rsub__(self, other):\r
        """other - self"""\r
        return -self + other\r
\r
    @abstractmethod\r
    def __mul__(self, other):\r
        """self * other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rmul__(self, other):\r
        """other * self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __div__(self, other):\r
        """self / other without __future__ division\r
\r
        May promote to float.\r
        """\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rdiv__(self, other):\r
        """other / self without __future__ division"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __truediv__(self, other):\r
        """self / other with __future__ division.\r
\r
        Should promote to float when necessary.\r
        """\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rtruediv__(self, other):\r
        """other / self with __future__ division"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __pow__(self, exponent):\r
        """self**exponent; should promote to float or complex when necessary."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rpow__(self, base):\r
        """base ** self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __abs__(self):\r
        """Returns the Real distance from 0. Called for abs(self)."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def conjugate(self):\r
        """(x+y*i).conjugate() returns (x-y*i)."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __eq__(self, other):\r
        """self == other"""\r
        raise NotImplementedError\r
\r
    def __ne__(self, other):\r
        """self != other"""\r
        # The default __ne__ doesn't negate __eq__ until 3.0.\r
        return not (self == other)\r
\r
Complex.register(complex)\r
\r
\r
class Real(Complex):\r
    """To Complex, Real adds the operations that work on real numbers.\r
\r
    In short, those are: a conversion to float, trunc(), divmod,\r
    %, <, <=, >, and >=.\r
\r
    Real also provides defaults for the derived operations.\r
    """\r
\r
    __slots__ = ()\r
\r
    @abstractmethod\r
    def __float__(self):\r
        """Any Real can be converted to a native float object.\r
\r
        Called for float(self)."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __trunc__(self):\r
        """trunc(self): Truncates self to an Integral.\r
\r
        Returns an Integral i such that:\r
          * i>0 iff self>0;\r
          * abs(i) <= abs(self);\r
          * for any Integral j satisfying the first two conditions,\r
            abs(i) >= abs(j) [i.e. i has "maximal" abs among those].\r
        i.e. "truncate towards 0".\r
        """\r
        raise NotImplementedError\r
\r
    def __divmod__(self, other):\r
        """divmod(self, other): The pair (self // other, self % other).\r
\r
        Sometimes this can be computed faster than the pair of\r
        operations.\r
        """\r
        return (self // other, self % other)\r
\r
    def __rdivmod__(self, other):\r
        """divmod(other, self): The pair (self // other, self % other).\r
\r
        Sometimes this can be computed faster than the pair of\r
        operations.\r
        """\r
        return (other // self, other % self)\r
\r
    @abstractmethod\r
    def __floordiv__(self, other):\r
        """self // other: The floor() of self/other."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rfloordiv__(self, other):\r
        """other // self: The floor() of other/self."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __mod__(self, other):\r
        """self % other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rmod__(self, other):\r
        """other % self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __lt__(self, other):\r
        """self < other\r
\r
        < on Reals defines a total ordering, except perhaps for NaN."""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __le__(self, other):\r
        """self <= other"""\r
        raise NotImplementedError\r
\r
    # Concrete implementations of Complex abstract methods.\r
    def __complex__(self):\r
        """complex(self) == complex(float(self), 0)"""\r
        return complex(float(self))\r
\r
    @property\r
    def real(self):\r
        """Real numbers are their real component."""\r
        return +self\r
\r
    @property\r
    def imag(self):\r
        """Real numbers have no imaginary component."""\r
        return 0\r
\r
    def conjugate(self):\r
        """Conjugate is a no-op for Reals."""\r
        return +self\r
\r
Real.register(float)\r
\r
\r
class Rational(Real):\r
    """.numerator and .denominator should be in lowest terms."""\r
\r
    __slots__ = ()\r
\r
    @abstractproperty\r
    def numerator(self):\r
        raise NotImplementedError\r
\r
    @abstractproperty\r
    def denominator(self):\r
        raise NotImplementedError\r
\r
    # Concrete implementation of Real's conversion to float.\r
    def __float__(self):\r
        """float(self) = self.numerator / self.denominator\r
\r
        It's important that this conversion use the integer's "true"\r
        division rather than casting one side to float before dividing\r
        so that ratios of huge integers convert without overflowing.\r
\r
        """\r
        return self.numerator / self.denominator\r
\r
\r
class Integral(Rational):\r
    """Integral adds a conversion to long and the bit-string operations."""\r
\r
    __slots__ = ()\r
\r
    @abstractmethod\r
    def __long__(self):\r
        """long(self)"""\r
        raise NotImplementedError\r
\r
    def __index__(self):\r
        """Called whenever an index is needed, such as in slicing"""\r
        return long(self)\r
\r
    @abstractmethod\r
    def __pow__(self, exponent, modulus=None):\r
        """self ** exponent % modulus, but maybe faster.\r
\r
        Accept the modulus argument if you want to support the\r
        3-argument version of pow(). Raise a TypeError if exponent < 0\r
        or any argument isn't Integral. Otherwise, just implement the\r
        2-argument version described in Complex.\r
        """\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __lshift__(self, other):\r
        """self << other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rlshift__(self, other):\r
        """other << self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rshift__(self, other):\r
        """self >> other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rrshift__(self, other):\r
        """other >> self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __and__(self, other):\r
        """self & other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rand__(self, other):\r
        """other & self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __xor__(self, other):\r
        """self ^ other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __rxor__(self, other):\r
        """other ^ self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __or__(self, other):\r
        """self | other"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __ror__(self, other):\r
        """other | self"""\r
        raise NotImplementedError\r
\r
    @abstractmethod\r
    def __invert__(self):\r
        """~self"""\r
        raise NotImplementedError\r
\r
    # Concrete implementations of Rational and Real abstract methods.\r
    def __float__(self):\r
        """float(self) == float(long(self))"""\r
        return float(long(self))\r
\r
    @property\r
    def numerator(self):\r
        """Integers are their own numerators."""\r
        return +self\r
\r
    @property\r
    def denominator(self):\r
        """Integers have a denominator of 1."""\r
        return 1\r
\r
Integral.register(int)\r
Integral.register(long)\r