import math
import sys

class Infinity:
    """
    Class representing infinity and minus infinity
    """
    def __init__(self, negated = False):
        self.negated = negated

    def __neg__(self):
        return Infinity(not self.negated)

    def __le__(self, other):
        if isinstance(other, Infinity) and (not other.negated or other.negated == self.negated): return True
        return self.negated

    def __ge__(self, other):
        if isinstance(other, Infinity) and (other.negated or other.negated == self.negated): return True
        return not self.negated

    def __lt__(self, other):
        if isinstance(other, Infinity) and other.negated: return False
        return self.negated

    def __gt__(self, other):
        if isinstance(other, Infinity) and not other.negated: return False
        return not self.negated

    def __eq__(self, other):
        if sys.version_info[1] >= 5:
            return (isinstance(other, Infinity) and other.negated == self.negated) or (not self.negated and other == math.inf)
        else:
            return (isinstance(other, Infinity) and other.negated == self.negated)

    def __add__(self, other):
        return self

    def __radd__(self, other):
        return self

    def __sub__(self, other):
        return self

    def __rsub__(self, other):
        return self

    def __mul__(self, other):
        if other < 0:
            return -self
        return self

    def __rmul__(self, other):
        if other < 0:
            return -self
        return self

    def __div__(self, other):
        if other < 0:
            return - self
        return self

    def __rdiv__(self, other):
        return 0

    def __str__(self):
        return "-infty" if self.negated else "infty"

    def __repr__(self):
        return "-pycarl.inf" if self.negated else "pycarl.inf"

    def __hash__(self):
        return 42 if self.negated else 23