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Diffstat (limited to 'lib/python2.7/numbers.py')
| -rw-r--r-- | lib/python2.7/numbers.py | 391 |
1 files changed, 391 insertions, 0 deletions
diff --git a/lib/python2.7/numbers.py b/lib/python2.7/numbers.py new file mode 100644 index 0000000..bdc6dd6 --- /dev/null +++ b/lib/python2.7/numbers.py @@ -0,0 +1,391 @@ +# Copyright 2007 Google, Inc. All Rights Reserved. +# Licensed to PSF under a Contributor Agreement. + +"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141. + +TODO: Fill out more detailed documentation on the operators.""" + +from __future__ import division +from abc import ABCMeta, abstractmethod, abstractproperty + +__all__ = ["Number", "Complex", "Real", "Rational", "Integral"] + +class Number(object): + """All numbers inherit from this class. + + If you just want to check if an argument x is a number, without + caring what kind, use isinstance(x, Number). + """ + __metaclass__ = ABCMeta + __slots__ = () + + # Concrete numeric types must provide their own hash implementation + __hash__ = None + + +## Notes on Decimal +## ---------------- +## Decimal has all of the methods specified by the Real abc, but it should +## not be registered as a Real because decimals do not interoperate with +## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But, +## abstract reals are expected to interoperate (i.e. R1 + R2 should be +## expected to work if R1 and R2 are both Reals). + +class Complex(Number): + """Complex defines the operations that work on the builtin complex type. + + In short, those are: a conversion to complex, .real, .imag, +, -, + *, /, abs(), .conjugate, ==, and !=. + + If it is given heterogenous arguments, and doesn't have special + knowledge about them, it should fall back to the builtin complex + type as described below. + """ + + __slots__ = () + + @abstractmethod + def __complex__(self): + """Return a builtin complex instance. Called for complex(self).""" + + # Will be __bool__ in 3.0. + def __nonzero__(self): + """True if self != 0. Called for bool(self).""" + return self != 0 + + @abstractproperty + def real(self): + """Retrieve the real component of this number. + + This should subclass Real. + """ + raise NotImplementedError + + @abstractproperty + def imag(self): + """Retrieve the imaginary component of this number. + + This should subclass Real. + """ + raise NotImplementedError + + @abstractmethod + def __add__(self, other): + """self + other""" + raise NotImplementedError + + @abstractmethod + def __radd__(self, other): + """other + self""" + raise NotImplementedError + + @abstractmethod + def __neg__(self): + """-self""" + raise NotImplementedError + + @abstractmethod + def __pos__(self): + """+self""" + raise NotImplementedError + + def __sub__(self, other): + """self - other""" + return self + -other + + def __rsub__(self, other): + """other - self""" + return -self + other + + @abstractmethod + def __mul__(self, other): + """self * other""" + raise NotImplementedError + + @abstractmethod + def __rmul__(self, other): + """other * self""" + raise NotImplementedError + + @abstractmethod + def __div__(self, other): + """self / other without __future__ division + + May promote to float. + """ + raise NotImplementedError + + @abstractmethod + def __rdiv__(self, other): + """other / self without __future__ division""" + raise NotImplementedError + + @abstractmethod + def __truediv__(self, other): + """self / other with __future__ division. + + Should promote to float when necessary. + """ + raise NotImplementedError + + @abstractmethod + def __rtruediv__(self, other): + """other / self with __future__ division""" + raise NotImplementedError + + @abstractmethod + def __pow__(self, exponent): + """self**exponent; should promote to float or complex when necessary.""" + raise NotImplementedError + + @abstractmethod + def __rpow__(self, base): + """base ** self""" + raise NotImplementedError + + @abstractmethod + def __abs__(self): + """Returns the Real distance from 0. Called for abs(self).""" + raise NotImplementedError + + @abstractmethod + def conjugate(self): + """(x+y*i).conjugate() returns (x-y*i).""" + raise NotImplementedError + + @abstractmethod + def __eq__(self, other): + """self == other""" + raise NotImplementedError + + def __ne__(self, other): + """self != other""" + # The default __ne__ doesn't negate __eq__ until 3.0. + return not (self == other) + +Complex.register(complex) + + +class Real(Complex): + """To Complex, Real adds the operations that work on real numbers. + + In short, those are: a conversion to float, trunc(), divmod, + %, <, <=, >, and >=. + + Real also provides defaults for the derived operations. + """ + + __slots__ = () + + @abstractmethod + def __float__(self): + """Any Real can be converted to a native float object. + + Called for float(self).""" + raise NotImplementedError + + @abstractmethod + def __trunc__(self): + """trunc(self): Truncates self to an Integral. + + Returns an Integral i such that: + * i>0 iff self>0; + * abs(i) <= abs(self); + * for any Integral j satisfying the first two conditions, + abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. + i.e. "truncate towards 0". + """ + raise NotImplementedError + + def __divmod__(self, other): + """divmod(self, other): The pair (self // other, self % other). + + Sometimes this can be computed faster than the pair of + operations. + """ + return (self // other, self % other) + + def __rdivmod__(self, other): + """divmod(other, self): The pair (self // other, self % other). + + Sometimes this can be computed faster than the pair of + operations. + """ + return (other // self, other % self) + + @abstractmethod + def __floordiv__(self, other): + """self // other: The floor() of self/other.""" + raise NotImplementedError + + @abstractmethod + def __rfloordiv__(self, other): + """other // self: The floor() of other/self.""" + raise NotImplementedError + + @abstractmethod + def __mod__(self, other): + """self % other""" + raise NotImplementedError + + @abstractmethod + def __rmod__(self, other): + """other % self""" + raise NotImplementedError + + @abstractmethod + def __lt__(self, other): + """self < other + + < on Reals defines a total ordering, except perhaps for NaN.""" + raise NotImplementedError + + @abstractmethod + def __le__(self, other): + """self <= other""" + raise NotImplementedError + + # Concrete implementations of Complex abstract methods. + def __complex__(self): + """complex(self) == complex(float(self), 0)""" + return complex(float(self)) + + @property + def real(self): + """Real numbers are their real component.""" + return +self + + @property + def imag(self): + """Real numbers have no imaginary component.""" + return 0 + + def conjugate(self): + """Conjugate is a no-op for Reals.""" + return +self + +Real.register(float) + + +class Rational(Real): + """.numerator and .denominator should be in lowest terms.""" + + __slots__ = () + + @abstractproperty + def numerator(self): + raise NotImplementedError + + @abstractproperty + def denominator(self): + raise NotImplementedError + + # Concrete implementation of Real's conversion to float. + def __float__(self): + """float(self) = self.numerator / self.denominator + + It's important that this conversion use the integer's "true" + division rather than casting one side to float before dividing + so that ratios of huge integers convert without overflowing. + + """ + return self.numerator / self.denominator + + +class Integral(Rational): + """Integral adds a conversion to long and the bit-string operations.""" + + __slots__ = () + + @abstractmethod + def __long__(self): + """long(self)""" + raise NotImplementedError + + def __index__(self): + """Called whenever an index is needed, such as in slicing""" + return long(self) + + @abstractmethod + def __pow__(self, exponent, modulus=None): + """self ** exponent % modulus, but maybe faster. + + Accept the modulus argument if you want to support the + 3-argument version of pow(). Raise a TypeError if exponent < 0 + or any argument isn't Integral. Otherwise, just implement the + 2-argument version described in Complex. + """ + raise NotImplementedError + + @abstractmethod + def __lshift__(self, other): + """self << other""" + raise NotImplementedError + + @abstractmethod + def __rlshift__(self, other): + """other << self""" + raise NotImplementedError + + @abstractmethod + def __rshift__(self, other): + """self >> other""" + raise NotImplementedError + + @abstractmethod + def __rrshift__(self, other): + """other >> self""" + raise NotImplementedError + + @abstractmethod + def __and__(self, other): + """self & other""" + raise NotImplementedError + + @abstractmethod + def __rand__(self, other): + """other & self""" + raise NotImplementedError + + @abstractmethod + def __xor__(self, other): + """self ^ other""" + raise NotImplementedError + + @abstractmethod + def __rxor__(self, other): + """other ^ self""" + raise NotImplementedError + + @abstractmethod + def __or__(self, other): + """self | other""" + raise NotImplementedError + + @abstractmethod + def __ror__(self, other): + """other | self""" + raise NotImplementedError + + @abstractmethod + def __invert__(self): + """~self""" + raise NotImplementedError + + # Concrete implementations of Rational and Real abstract methods. + def __float__(self): + """float(self) == float(long(self))""" + return float(long(self)) + + @property + def numerator(self): + """Integers are their own numerators.""" + return +self + + @property + def denominator(self): + """Integers have a denominator of 1.""" + return 1 + +Integral.register(int) +Integral.register(long) |