import functools
import numbers

from . import islhelper

from .islhelper import mainctx, libisl
from .linexprs import Expression, Constant
from .domains import Domain


__all__ = [
    'Polyhedron',
    'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
    'Empty', 'Universe',
]


class Polyhedron(Domain):

    __slots__ = (
        '_equalities',
        '_inequalities',
        '_constraints',
        '_symbols',
        '_dimension',
    )

    def __new__(cls, equalities=None, inequalities=None):
        if isinstance(equalities, str):
            if inequalities is not None:
                raise TypeError('too many arguments')
            return cls.fromstring(equalities)
        elif isinstance(equalities, Polyhedron):
            if inequalities is not None:
                raise TypeError('too many arguments')
            return equalities
        elif isinstance(equalities, Domain):
            if inequalities is not None:
                raise TypeError('too many arguments')
            return equalities.polyhedral_hull()
        if equalities is None:
            equalities = []
        else:
            for i, equality in enumerate(equalities):
                if not isinstance(equality, Expression):
                    raise TypeError('equalities must be linear expressions')
                equalities[i] = equality._toint()
        if inequalities is None:
            inequalities = []
        else:
            for i, inequality in enumerate(inequalities):
                if not isinstance(inequality, Expression):
                    raise TypeError('inequalities must be linear expressions')
                inequalities[i] = inequality._toint()
        symbols = cls._xsymbols(equalities + inequalities)
        islbset = cls._toislbasicset(equalities, inequalities, symbols)
        return cls._fromislbasicset(islbset, symbols)

    @property
    def equalities(self):
        return self._equalities

    @property
    def inequalities(self):
        return self._inequalities

    @property
    def constraints(self):
        return self._constraints

    @property
    def polyhedra(self):
        return self,

    def disjoint(self):
        return self

    def isuniverse(self):
        islbset = self._toislbasicset(self.equalities, self.inequalities,
            self.symbols)
        universe = bool(libisl.isl_basic_set_is_universe(islbset))
        libisl.isl_basic_set_free(islbset)
        return universe

    def polyhedral_hull(self):
        return self

    @classmethod
    def _fromislbasicset(cls, islbset, symbols):
        islconstraints = islhelper.isl_basic_set_constraints(islbset)
        equalities = []
        inequalities = []
        for islconstraint in islconstraints:
            constant = libisl.isl_constraint_get_constant_val(islconstraint)
            constant = islhelper.isl_val_to_int(constant)
            coefficients = {}
            for index, symbol in enumerate(symbols):
                coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint, libisl.isl_dim_set, index)
                coefficient = islhelper.isl_val_to_int(coefficient)
                if coefficient != 0:
                    coefficients[symbol] = coefficient
            expression = Expression(coefficients, constant)
            if libisl.isl_constraint_is_equality(islconstraint):
                equalities.append(expression)
            else:
                inequalities.append(expression)
        libisl.isl_basic_set_free(islbset)
        self = object().__new__(Polyhedron)
        self._equalities = tuple(equalities)
        self._inequalities = tuple(inequalities)
        self._constraints = tuple(equalities + inequalities)
        self._symbols = cls._xsymbols(self._constraints)
        self._dimension = len(self._symbols)
        return self

    @classmethod
    def _toislbasicset(cls, equalities, inequalities, symbols):
        dimension = len(symbols)
        indices = {symbol: index for index, symbol in enumerate(symbols)}
        islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
        islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
        islls = libisl.isl_local_space_from_space(islsp)
        for equality in equalities:
            isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
            for symbol, coefficient in equality.coefficients():
                islval = str(coefficient).encode()
                islval = libisl.isl_val_read_from_str(mainctx, islval)
                index = indices[symbol]
                isleq = libisl.isl_constraint_set_coefficient_val(isleq,
                    libisl.isl_dim_set, index, islval)
            if equality.constant != 0:
                islval = str(equality.constant).encode()
                islval = libisl.isl_val_read_from_str(mainctx, islval)
                isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
            islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
        for inequality in inequalities:
            islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
            for symbol, coefficient in inequality.coefficients():
                islval = str(coefficient).encode()
                islval = libisl.isl_val_read_from_str(mainctx, islval)
                index = indices[symbol]
                islin = libisl.isl_constraint_set_coefficient_val(islin,
                    libisl.isl_dim_set, index, islval)
            if inequality.constant != 0:
                islval = str(inequality.constant).encode()
                islval = libisl.isl_val_read_from_str(mainctx, islval)
                islin = libisl.isl_constraint_set_constant_val(islin, islval)
            islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
        return islbset

    @classmethod
    def fromstring(cls, string):
        domain = Domain.fromstring(string)
        if not isinstance(domain, Polyhedron):
            raise ValueError('non-polyhedral expression: {!r}'.format(string))
        return domain

    def __repr__(self):
        if self.isempty():
            return 'Empty'
        elif self.isuniverse():
            return 'Universe'
        else:
            strings = []
            for equality in self.equalities:
                strings.append('Eq({}, 0)'.format(equality))
            for inequality in self.inequalities:
                strings.append('Ge({}, 0)'.format(inequality))
            if len(strings) == 1:
                return strings[0]
            else:
                return 'And({})'.format(', '.join(strings))

    @classmethod
    def _fromsympy(cls, expr):
        import sympy
        equalities = []
        inequalities = []
        if expr.func == sympy.And:
            for arg in expr.args:
                arg_eqs, arg_ins = cls._fromsympy(arg)
                equalities.extend(arg_eqs)
                inequalities.extend(arg_ins)
        elif expr.func == sympy.Eq:
            expr = Expression.fromsympy(expr.args[0] - expr.args[1])
            equalities.append(expr)
        else:
            if expr.func == sympy.Lt:
                expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
            elif expr.func == sympy.Le:
                expr = Expression.fromsympy(expr.args[1] - expr.args[0])
            elif expr.func == sympy.Ge:
                expr = Expression.fromsympy(expr.args[0] - expr.args[1])
            elif expr.func == sympy.Gt:
                expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
            else:
                raise ValueError('non-polyhedral expression: {!r}'.format(expr))
            inequalities.append(expr)
        return equalities, inequalities

    @classmethod
    def fromsympy(cls, expr):
        import sympy
        equalities, inequalities = cls._fromsympy(expr)
        return cls(equalities, inequalities)

    def tosympy(self):
        import sympy
        constraints = []
        for equality in self.equalities:
            constraints.append(sympy.Eq(equality.tosympy(), 0))
        for inequality in self.inequalities:
            constraints.append(sympy.Ge(inequality.tosympy(), 0))
        return sympy.And(*constraints)


def _polymorphic(func):
    @functools.wraps(func)
    def wrapper(left, right):
        if isinstance(left, numbers.Rational):
            left = Constant(left)
        elif not isinstance(left, Expression):
            raise TypeError('left must be a a rational number '
                'or a linear expression')
        if isinstance(right, numbers.Rational):
            right = Constant(right)
        elif not isinstance(right, Expression):
            raise TypeError('right must be a a rational number '
                'or a linear expression')
        return func(left, right)
    return wrapper

@_polymorphic
def Lt(left, right):
    return Polyhedron([], [right - left - 1])

@_polymorphic
def Le(left, right):
    return Polyhedron([], [right - left])

@_polymorphic
def Eq(left, right):
    return Polyhedron([left - right], [])

@_polymorphic
def Ne(left, right):
    return ~Eq(left, right)

@_polymorphic
def Gt(left, right):
    return Polyhedron([], [left - right - 1])

@_polymorphic
def Ge(left, right):
    return Polyhedron([], [left - right])


Empty = Eq(1, 0)

Universe = Polyhedron([])