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from typing import Tuple as tTuple

from sympy.core.basic import Basic
from sympy.core.expr import Expr

from sympy.core import Add, S
from sympy.core.evalf import get_integer_part, PrecisionExhausted
from sympy.core.function import Function
from sympy.core.logic import fuzzy_or
from sympy.core.numbers import Integer
from sympy.core.relational import Gt, Lt, Ge, Le, Relational, is_eq
from sympy.core.symbol import Symbol
from sympy.core.sympify import _sympify
from sympy.functions.elementary.complexes import im, re
from sympy.multipledispatch import dispatch

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

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

args: tTuple[Expr]

@classmethod
    def eval(cls, arg):
        v = cls._eval_number(arg)
        if v is not None:
            return v

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)

# 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
        elif isinstance(spart, (floor, ceiling)):
            return ipart + spart
        else:
            return ipart + cls(spart, evaluate=False)

@classmethod
    def _eval_number(cls, arg):
        raise NotImplementedError()

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] https://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_as_leading_term(self, x, logx=None, cdir=0):
        from sympy.calculus.accumulationbounds import AccumBounds
        arg = self.args[0]
        arg0 = arg.subs(x, 0)
        r = self.subs(x, 0)
        if arg0 is S.NaN or isinstance(arg0, AccumBounds):
            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
            r = floor(arg0)
        if arg0.is_finite:
            if arg0 == r:
                ndir = arg.dir(x, cdir=cdir)
                return r - 1 if ndir.is_negative else r
            else:
                return r
        return arg.as_leading_term(x, logx=logx, cdir=cdir)

def _eval_nseries(self, x, n, logx, cdir=0):
        arg = self.args[0]
        arg0 = arg.subs(x, 0)
        r = self.subs(x, 0)
        if arg0 is S.NaN:
            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
            r = floor(arg0)
        if arg0.is_infinite:
            from sympy.calculus.accumulationbounds import AccumBounds
            from sympy.series.order import Order
            s = arg._eval_nseries(x, n, logx, cdir)
            o = Order(1, (x, 0)) if n <= 0 else AccumBounds(-1, 0)
            return s + o
        if arg0 == r:
            ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1)
            return r - 1 if ndir.is_negative else r
        else:
            return r

def _eval_is_negative(self):
        return self.args[0].is_negative

def _eval_is_nonnegative(self):
        return self.args[0].is_nonnegative

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

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

def __le__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] < other + 1
            if other.is_number and other.is_real:
                return self.args[0] < ceiling(other)
        if self.args[0] == other and other.is_real:
            return S.true
        if other is S.Infinity and self.is_finite:
            return S.true

return Le(self, other, evaluate=False)

def __ge__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] >= other
            if other.is_number and other.is_real:
                return self.args[0] >= ceiling(other)
        if self.args[0] == other and other.is_real:
            return S.false
        if other is S.NegativeInfinity and self.is_finite:
            return S.true

return Ge(self, other, evaluate=False)

def __gt__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] >= other + 1
            if other.is_number and other.is_real:
                return self.args[0] >= ceiling(other)
        if self.args[0] == other and other.is_real:
            return S.false
        if other is S.NegativeInfinity and self.is_finite:
            return S.true

return Gt(self, other, evaluate=False)

def __lt__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] < other
            if other.is_number and other.is_real:
                return self.args[0] < ceiling(other)
        if self.args[0] == other and other.is_real:
            return S.false
        if other is S.Infinity and self.is_finite:
            return S.true

return Lt(self, other, evaluate=False)

@dispatch(floor, Expr)
def _eval_is_eq(lhs, rhs): # noqa:F811
   return is_eq(lhs.rewrite(ceiling), rhs) or \
        is_eq(lhs.rewrite(frac),rhs)

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] https://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_as_leading_term(self, x, logx=None, cdir=0):
        from sympy.calculus.accumulationbounds import AccumBounds
        arg = self.args[0]
        arg0 = arg.subs(x, 0)
        r = self.subs(x, 0)
        if arg0 is S.NaN or isinstance(arg0, AccumBounds):
            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
            r = ceiling(arg0)
        if arg0.is_finite:
            if arg0 == r:
                ndir = arg.dir(x, cdir=cdir)
                return r if ndir.is_negative else r + 1
            else:
                return r
        return arg.as_leading_term(x, logx=logx, cdir=cdir)

def _eval_nseries(self, x, n, logx, cdir=0):
        arg = self.args[0]
        arg0 = arg.subs(x, 0)
        r = self.subs(x, 0)
        if arg0 is S.NaN:
            arg0 = arg.limit(x, 0, dir='-' if re(cdir).is_negative else '+')
            r = ceiling(arg0)
        if arg0.is_infinite:
            from sympy.calculus.accumulationbounds import AccumBounds
            from sympy.series.order import Order
            s = arg._eval_nseries(x, n, logx, cdir)
            o = Order(1, (x, 0)) if n <= 0 else AccumBounds(0, 1)
            return s + o
        if arg0 == r:
            ndir = arg.dir(x, cdir=cdir if cdir != 0 else 1)
            return r if ndir.is_negative else r + 1
        else:
            return r

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

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

def _eval_is_positive(self):
        return self.args[0].is_positive

def _eval_is_nonpositive(self):
        return self.args[0].is_nonpositive

def __lt__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] <= other - 1
            if other.is_number and other.is_real:
                return self.args[0] <= floor(other)
        if self.args[0] == other and other.is_real:
            return S.false
        if other is S.Infinity and self.is_finite:
            return S.true

return Lt(self, other, evaluate=False)

def __gt__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] > other
            if other.is_number and other.is_real:
                return self.args[0] > floor(other)
        if self.args[0] == other and other.is_real:
            return S.false
        if other is S.NegativeInfinity and self.is_finite:
            return S.true

return Gt(self, other, evaluate=False)

def __ge__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] > other - 1
            if other.is_number and other.is_real:
                return self.args[0] > floor(other)
        if self.args[0] == other and other.is_real:
            return S.true
        if other is S.NegativeInfinity and self.is_finite:
            return S.true

return Ge(self, other, evaluate=False)

def __le__(self, other):
        other = S(other)
        if self.args[0].is_real:
            if other.is_integer:
                return self.args[0] <= other
            if other.is_number and other.is_real:
                return self.args[0] <= floor(other)
        if self.args[0] == other and other.is_real:
            return S.false
        if other is S.Infinity and self.is_finite:
            return S.true

return Le(self, other, evaluate=False)

@dispatch(ceiling, Basic)  # type:ignore
def _eval_is_eq(lhs, rhs): # noqa:F811
    return is_eq(lhs.rewrite(floor), rhs) or is_eq(lhs.rewrite(frac),rhs)

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

For real numbers it is defined [1]_ as

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

Examples
    ========

>>> from sympy import Symbol, frac, Rational, floor, 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)