from __future__ import print_function, division

from sympy.core.singleton import S
from sympy.core.function import Function
from sympy.core import Add
from sympy.core.evalf import get_integer_part, PrecisionExhausted
from sympy.core.numbers import Integer
from sympy.core.relational import Gt, Lt, Ge, Le
from sympy.core.symbol import Symbol


###############################################################################
######################### FLOOR and CEILING FUNCTIONS #########################
###############################################################################


class RoundFunction(Function):
    """The base class for rounding functions."""

    @classmethod
    def eval(cls, arg):
        from sympy import im
        if arg.is_integer or arg.is_finite is False:
            return arg
        if arg.is_imaginary or (S.ImaginaryUnit*arg).is_real:
            i = im(arg)
            if not i.has(S.ImaginaryUnit):
                return cls(i)*S.ImaginaryUnit
            return cls(arg, evaluate=False)

        v = cls._eval_number(arg)
        if v is not None:
            return v

        # Integral, numerical, symbolic part
        ipart = npart = spart = S.Zero

        # Extract integral (or complex integral) terms
        terms = Add.make_args(arg)

        for t in terms:
            if t.is_integer or (t.is_imaginary and im(t).is_integer):
                ipart += t
            elif t.has(Symbol):
                spart += t
            else:
                npart += t

        if not (npart or spart):
            return ipart

        # Evaluate npart numerically if independent of spart
        if npart and (
            not spart or
            npart.is_real and (spart.is_imaginary or (S.ImaginaryUnit*spart).is_real) or
                npart.is_imaginary and spart.is_real):
            try:
                r, i = get_integer_part(
                    npart, cls._dir, {}, return_ints=True)
                ipart += Integer(r) + Integer(i)*S.ImaginaryUnit
                npart = S.Zero
            except (PrecisionExhausted, NotImplementedError):
                pass

        spart += npart
        if not spart:
            return ipart
        elif spart.is_imaginary or (S.ImaginaryUnit*spart).is_real:
            return ipart + cls(im(spart), evaluate=False)*S.ImaginaryUnit
        else:
            return ipart + cls(spart, evaluate=False)

    def _eval_is_finite(self):
        return self.args[0].is_finite

    def _eval_is_real(self):
        return self.args[0].is_real

    def _eval_is_integer(self):
        return self.args[0].is_real


class floor(RoundFunction):
    """
    Floor is a univariate function which returns the largest integer
    value not greater than its argument. This implementation
    generalizes floor to complex numbers by taking the floor of the
    real and imaginary parts separately.

    Examples
    ========

    >>> from sympy import floor, E, I, S, Float, Rational
    >>> floor(17)
    17
    >>> floor(Rational(23, 10))
    2
    >>> floor(2*E)
    5
    >>> floor(-Float(0.567))
    -1
    >>> floor(-I/2)
    -I
    >>> floor(S(5)/2 + 5*I/2)
    2 + 2*I

    See Also
    ========

    sympy.functions.elementary.integers.ceiling

    References
    ==========

    .. [1] "Concrete mathematics" by Graham, pp. 87
    .. [2] http://mathworld.wolfram.com/FloorFunction.html

    """
    _dir = -1

    @classmethod
    def _eval_number(cls, arg):
        if arg.is_Number:
            return arg.floor()
        elif any(isinstance(i, j)
                for i in (arg, -arg) for j in (floor, ceiling)):
            return arg
        if arg.is_NumberSymbol:
            return arg.approximation_interval(Integer)[0]

    def _eval_nseries(self, x, n, logx):
        r = self.subs(x, 0)
        args = self.args[0]
        args0 = args.subs(x, 0)
        if args0 == r:
            direction = (args - args0).leadterm(x)[0]
            if direction.is_positive:
                return r
            else:
                return r - 1
        else:
            return r

    def _eval_rewrite_as_ceiling(self, arg):
        return -ceiling(-arg)

    def _eval_rewrite_as_frac(self, arg):
        return arg - frac(arg)

    def _eval_Eq(self, other):
        if isinstance(self, floor):
            if (self.rewrite(ceiling) == other) or \
                    (self.rewrite(frac) == other):
                return S.true

    def __le__(self, other):
        if self.args[0] == other and other.is_real:
            return S.true
        return Le(self, other, evaluate=False)

    def __gt__(self, other):
        if self.args[0] == other and other.is_real:
            return S.false
        return Gt(self, other, evaluate=False)


class ceiling(RoundFunction):
    """
    Ceiling is a univariate function which returns the smallest integer
    value not less than its argument. This implementation
    generalizes ceiling to complex numbers by taking the ceiling of the
    real and imaginary parts separately.

    Examples
    ========

    >>> from sympy import ceiling, E, I, S, Float, Rational
    >>> ceiling(17)
    17
    >>> ceiling(Rational(23, 10))
    3
    >>> ceiling(2*E)
    6
    >>> ceiling(-Float(0.567))
    0
    >>> ceiling(I/2)
    I
    >>> ceiling(S(5)/2 + 5*I/2)
    3 + 3*I

    See Also
    ========

    sympy.functions.elementary.integers.floor

    References
    ==========

    .. [1] "Concrete mathematics" by Graham, pp. 87
    .. [2] http://mathworld.wolfram.com/CeilingFunction.html

    """
    _dir = 1

    @classmethod
    def _eval_number(cls, arg):
        if arg.is_Number:
            return arg.ceiling()
        elif any(isinstance(i, j)
                for i in (arg, -arg) for j in (floor, ceiling)):
            return arg
        if arg.is_NumberSymbol:
            return arg.approximation_interval(Integer)[1]

    def _eval_nseries(self, x, n, logx):
        r = self.subs(x, 0)
        args = self.args[0]
        args0 = args.subs(x, 0)
        if args0 == r:
            direction = (args - args0).leadterm(x)[0]
            if direction.is_positive:
                return r + 1
            else:
                return r
        else:
            return r

    def _eval_rewrite_as_floor(self, arg):
        return -floor(-arg)

    def _eval_rewrite_as_frac(self, arg):
        return arg + frac(-arg)

    def _eval_Eq(self, other):
        if isinstance(self, ceiling):
            if (self.rewrite(floor) == other) or \
                    (self.rewrite(frac) == other):
                return S.true

    def __lt__(self, other):
        if self.args[0] == other and other.is_real:
            return S.false
        return Lt(self, other, evaluate=False)

    def __ge__(self, other):
        if self.args[0] == other and other.is_real:
            return S.true
        return Ge(self, other, evaluate=False)


class frac(Function):
    r"""Represents the fractional part of x

    For real numbers it is defined [1]_ as

    .. math::
        x - \lfloor{x}\rfloor

    Examples
    ========

    >>> from sympy import Symbol, frac, Rational, floor, ceiling, I
    >>> frac(Rational(4, 3))
    1/3
    >>> frac(-Rational(4, 3))
    2/3

    returns zero for integer arguments

    >>> n = Symbol('n', integer=True)
    >>> frac(n)
    0

    rewrite as floor

    >>> x = Symbol('x')
    >>> frac(x).rewrite(floor)
    x - floor(x)

    for complex arguments

    >>> r = Symbol('r', real=True)
    >>> t = Symbol('t', real=True)
    >>> frac(t + I*r)
    I*frac(r) + frac(t)

    See Also
    ========

    sympy.functions.elementary.integers.floor
    sympy.functions.elementary.integers.ceiling

    References
    ===========

    .. [1] http://en.wikipedia.org/wiki/Fractional_part
    .. [2] http://mathworld.wolfram.com/FractionalPart.html

    """
    @classmethod
    def eval(cls, arg):
        from sympy import AccumBounds, im

        def _eval(arg):
            if arg is S.Infinity or arg is S.NegativeInfinity:
                return AccumBounds(0, 1)
            if arg.is_integer:
                return S.Zero
            if arg.is_number:
                if arg is S.NaN:
                    return S.NaN
                elif arg is S.ComplexInfinity:
                    return None
                else:
                    return arg - floor(arg)
            return cls(arg, evaluate=False)

        terms = Add.make_args(arg)
        real, imag = S.Zero, S.Zero
        for t in terms:
            # Two checks are needed for complex arguments
            # see issue-7649 for details
            if t.is_imaginary or (S.ImaginaryUnit*t).is_real:
                i = im(t)
                if not i.has(S.ImaginaryUnit):
                    imag += i
                else:
                    real += t
            else:
                real += t

        real = _eval(real)
        imag = _eval(imag)
        return real + S.ImaginaryUnit*imag

    def _eval_rewrite_as_floor(self, arg):
        return arg - floor(arg)

    def _eval_rewrite_as_ceiling(self, arg):
        return arg + ceiling(-arg)

    def _eval_Eq(self, other):
        if isinstance(self, frac):
            if (self.rewrite(floor) == other) or \
                    (self.rewrite(ceiling) == other):
                return S.true