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1# Copyright 2007 Google, Inc. All Rights Reserved.2# Licensed to PSF under a Contributor Agreement.3 4"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141.5 6TODO: Fill out more detailed documentation on the operators."""7 8from abc import ABCMeta, abstractmethod9 10__all__ = ["Number", "Complex", "Real", "Rational", "Integral"]11 12class Number(metaclass=ABCMeta):13    """All numbers inherit from this class.14 15    If you just want to check if an argument x is a number, without16    caring what kind, use isinstance(x, Number).17    """18    __slots__ = ()19 20    # Concrete numeric types must provide their own hash implementation21    __hash__ = None22 23 24## Notes on Decimal25## ----------------26## Decimal has all of the methods specified by the Real abc, but it should27## not be registered as a Real because decimals do not interoperate with28## binary floats (i.e.  Decimal('3.14') + 2.71828 is undefined).  But,29## abstract reals are expected to interoperate (i.e. R1 + R2 should be30## expected to work if R1 and R2 are both Reals).31 32class Complex(Number):33    """Complex defines the operations that work on the builtin complex type.34 35    In short, those are: a conversion to complex, .real, .imag, +, -,36    *, /, **, abs(), .conjugate, ==, and !=.37 38    If it is given heterogeneous arguments, and doesn't have special39    knowledge about them, it should fall back to the builtin complex40    type as described below.41    """42 43    __slots__ = ()44 45    @abstractmethod46    def __complex__(self):47        """Return a builtin complex instance. Called for complex(self)."""48 49    def __bool__(self):50        """True if self != 0. Called for bool(self)."""51        return self != 052 53    @property54    @abstractmethod55    def real(self):56        """Retrieve the real component of this number.57 58        This should subclass Real.59        """60        raise NotImplementedError61 62    @property63    @abstractmethod64    def imag(self):65        """Retrieve the imaginary component of this number.66 67        This should subclass Real.68        """69        raise NotImplementedError70 71    @abstractmethod72    def __add__(self, other):73        """self + other"""74        raise NotImplementedError75 76    @abstractmethod77    def __radd__(self, other):78        """other + self"""79        raise NotImplementedError80 81    @abstractmethod82    def __neg__(self):83        """-self"""84        raise NotImplementedError85 86    @abstractmethod87    def __pos__(self):88        """+self"""89        raise NotImplementedError90 91    def __sub__(self, other):92        """self - other"""93        return self + -other94 95    def __rsub__(self, other):96        """other - self"""97        return -self + other98 99    @abstractmethod100    def __mul__(self, other):101        """self * other"""102        raise NotImplementedError103 104    @abstractmethod105    def __rmul__(self, other):106        """other * self"""107        raise NotImplementedError108 109    @abstractmethod110    def __truediv__(self, other):111        """self / other: Should promote to float when necessary."""112        raise NotImplementedError113 114    @abstractmethod115    def __rtruediv__(self, other):116        """other / self"""117        raise NotImplementedError118 119    @abstractmethod120    def __pow__(self, exponent):121        """self**exponent; should promote to float or complex when necessary."""122        raise NotImplementedError123 124    @abstractmethod125    def __rpow__(self, base):126        """base ** self"""127        raise NotImplementedError128 129    @abstractmethod130    def __abs__(self):131        """Returns the Real distance from 0. Called for abs(self)."""132        raise NotImplementedError133 134    @abstractmethod135    def conjugate(self):136        """(x+y*i).conjugate() returns (x-y*i)."""137        raise NotImplementedError138 139    @abstractmethod140    def __eq__(self, other):141        """self == other"""142        raise NotImplementedError143 144Complex.register(complex)145 146 147class Real(Complex):148    """To Complex, Real adds the operations that work on real numbers.149 150    In short, those are: a conversion to float, trunc(), divmod,151    %, <, <=, >, and >=.152 153    Real also provides defaults for the derived operations.154    """155 156    __slots__ = ()157 158    @abstractmethod159    def __float__(self):160        """Any Real can be converted to a native float object.161 162        Called for float(self)."""163        raise NotImplementedError164 165    @abstractmethod166    def __trunc__(self):167        """trunc(self): Truncates self to an Integral.168 169        Returns an Integral i such that:170          * i>0 iff self>0;171          * abs(i) <= abs(self);172          * for any Integral j satisfying the first two conditions,173            abs(i) >= abs(j) [i.e. i has "maximal" abs among those].174        i.e. "truncate towards 0".175        """176        raise NotImplementedError177 178    @abstractmethod179    def __floor__(self):180        """Finds the greatest Integral <= self."""181        raise NotImplementedError182 183    @abstractmethod184    def __ceil__(self):185        """Finds the least Integral >= self."""186        raise NotImplementedError187 188    @abstractmethod189    def __round__(self, ndigits=None):190        """Rounds self to ndigits decimal places, defaulting to 0.191 192        If ndigits is omitted or None, returns an Integral, otherwise193        returns a Real. Rounds half toward even.194        """195        raise NotImplementedError196 197    def __divmod__(self, other):198        """divmod(self, other): The pair (self // other, self % other).199 200        Sometimes this can be computed faster than the pair of201        operations.202        """203        return (self // other, self % other)204 205    def __rdivmod__(self, other):206        """divmod(other, self): The pair (self // other, self % other).207 208        Sometimes this can be computed faster than the pair of209        operations.210        """211        return (other // self, other % self)212 213    @abstractmethod214    def __floordiv__(self, other):215        """self // other: The floor() of self/other."""216        raise NotImplementedError217 218    @abstractmethod219    def __rfloordiv__(self, other):220        """other // self: The floor() of other/self."""221        raise NotImplementedError222 223    @abstractmethod224    def __mod__(self, other):225        """self % other"""226        raise NotImplementedError227 228    @abstractmethod229    def __rmod__(self, other):230        """other % self"""231        raise NotImplementedError232 233    @abstractmethod234    def __lt__(self, other):235        """self < other236 237        < on Reals defines a total ordering, except perhaps for NaN."""238        raise NotImplementedError239 240    @abstractmethod241    def __le__(self, other):242        """self <= other"""243        raise NotImplementedError244 245    # Concrete implementations of Complex abstract methods.246    def __complex__(self):247        """complex(self) == complex(float(self), 0)"""248        return complex(float(self))249 250    @property251    def real(self):252        """Real numbers are their real component."""253        return +self254 255    @property256    def imag(self):257        """Real numbers have no imaginary component."""258        return 0259 260    def conjugate(self):261        """Conjugate is a no-op for Reals."""262        return +self263 264Real.register(float)265 266 267class Rational(Real):268    """.numerator and .denominator should be in lowest terms."""269 270    __slots__ = ()271 272    @property273    @abstractmethod274    def numerator(self):275        raise NotImplementedError276 277    @property278    @abstractmethod279    def denominator(self):280        raise NotImplementedError281 282    # Concrete implementation of Real's conversion to float.283    def __float__(self):284        """float(self) = self.numerator / self.denominator285 286        It's important that this conversion use the integer's "true"287        division rather than casting one side to float before dividing288        so that ratios of huge integers convert without overflowing.289 290        """291        return self.numerator / self.denominator292 293 294class Integral(Rational):295    """Integral adds methods that work on integral numbers.296 297    In short, these are conversion to int, pow with modulus, and the298    bit-string operations.299    """300 301    __slots__ = ()302 303    @abstractmethod304    def __int__(self):305        """int(self)"""306        raise NotImplementedError307 308    def __index__(self):309        """Called whenever an index is needed, such as in slicing"""310        return int(self)311 312    @abstractmethod313    def __pow__(self, exponent, modulus=None):314        """self ** exponent % modulus, but maybe faster.315 316        Accept the modulus argument if you want to support the317        3-argument version of pow(). Raise a TypeError if exponent < 0318        or any argument isn't Integral. Otherwise, just implement the319        2-argument version described in Complex.320        """321        raise NotImplementedError322 323    @abstractmethod324    def __lshift__(self, other):325        """self << other"""326        raise NotImplementedError327 328    @abstractmethod329    def __rlshift__(self, other):330        """other << self"""331        raise NotImplementedError332 333    @abstractmethod334    def __rshift__(self, other):335        """self >> other"""336        raise NotImplementedError337 338    @abstractmethod339    def __rrshift__(self, other):340        """other >> self"""341        raise NotImplementedError342 343    @abstractmethod344    def __and__(self, other):345        """self & other"""346        raise NotImplementedError347 348    @abstractmethod349    def __rand__(self, other):350        """other & self"""351        raise NotImplementedError352 353    @abstractmethod354    def __xor__(self, other):355        """self ^ other"""356        raise NotImplementedError357 358    @abstractmethod359    def __rxor__(self, other):360        """other ^ self"""361        raise NotImplementedError362 363    @abstractmethod364    def __or__(self, other):365        """self | other"""366        raise NotImplementedError367 368    @abstractmethod369    def __ror__(self, other):370        """other | self"""371        raise NotImplementedError372 373    @abstractmethod374    def __invert__(self):375        """~self"""376        raise NotImplementedError377 378    # Concrete implementations of Rational and Real abstract methods.379    def __float__(self):380        """float(self) == float(int(self))"""381        return float(int(self))382 383    @property384    def numerator(self):385        """Integers are their own numerators."""386        return +self387 388    @property389    def denominator(self):390        """Integers have a denominator of 1."""391        return 1392 393Integral.register(int)394