#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#
# Copyright © 2017 lafrite <lafrite@Poivre>
#
# Distributed under terms of the MIT license.

"""
Adding MO
"""

from ..tree import Tree
from ..MO.mo import MO, MOnumber
from ..MO.fraction import MOFraction
from .exceptions import AddError
from .arithmetic import lcm
from .type_filter import args_are


def add(left, right):
    """ Perform the addition of left and right

    :param left: left MO
    :param right: right MO
    :returns: Tree or MO

    >>> a = MOnumber(4)
    >>> b = MOnumber(6)
    >>> add(a, b)
    <MOnumber 10>
    >>> b = MOnumber(0)
    >>> add(a, b)
    <MOnumber 4>

    """
    if left.value == 0:
        return right
    elif right.value ==  0:
        return left

    return ADDFUNCTIONS[(type(left), type(right))](left, right)

@args_are(MOnumber, MOnumber)
def monumber_monumber(left, right):
    """ Adding 2 monumbers

    :param left: left MOnumber
    :param right: right MOnumber
    :returns: MONumber

    >>> a = MOnumber(4)
    >>> b = MOnumber(6)
    >>> monumber_monumber(a, b)
    <MOnumber 10>

    """
    return MO.factory(left.value + right.value)

@args_are(MOnumber, MOFraction)
def monumber_mofraction(left, right):
    """ Adding a monumber and a mofraction

    :param left: a monumber
    :param right: a mofraction
    :returns: Tree with the number converted into a mofraction

    >>> a = MOnumber(4)
    >>> b = MOFraction(6, 5)
    >>> print(monumber_mofraction(a, b))
    +
     > /
     | > 4
     | > 1
     > /
     | > 6
     | > 5
    """
    left_fraction = MOFraction(left, MOnumber(1))
    return Tree("+", left_fraction, right)

@args_are(MOFraction, MOnumber)
def mofraction_monumber(left, right):
    """ Adding a monumber and a mofraction

    :param left: a mofraction
    :param right: a monumber
    :returns: Tree with the number converted into a mofraction

    >>> a = MOFraction(6, 5)
    >>> b = MOnumber(4)
    >>> print(mofraction_monumber(a, b))
    +
     > /
     | > 6
     | > 5
     > /
     | > 4
     | > 1
    """
    right_fraction = MOFraction(right, MOnumber(1))
    return Tree("+", left, right_fraction)

@args_are(MOFraction, MOFraction)
def mofraction_mofraction(left, right):
    """ Adding two mofractions

    :param left: a mofraction
    :param right: a mofraction
    :returns: Tree 

    >>> a = MOFraction(1, 5)
    >>> b = MOFraction(4, 5)
    >>> print(mofraction_mofraction(a, b))
    /
     > +
     | > 1
     | > 4
     > 5
    >>> a = MOFraction(1, 5, True)
    >>> b = MOFraction(4, 5)
    >>> print(mofraction_mofraction(a, b))
    /
     > +
     | > -
     | | > None
     | | > 1
     | > 4
     > 5
    >>> a = MOFraction(1, 5)
    >>> b = MOFraction(4, 5, True)
    >>> print(mofraction_mofraction(a, b))
    /
     > +
     | > 1
     | > -
     | | > None
     | | > 4
     > 5
    >>> a = MOFraction(1, 2)
    >>> b = MOFraction(1, 4)
    >>> print(mofraction_mofraction(a, b))
    +
     > /
     | > *
     | | > 1
     | | > 2
     | > *
     | | > 2
     | | > 2
     > /
     | > 1
     | > 4
    >>> a = MOFraction(1, 2)
    >>> b = MOFraction(1, 5)
    >>> print(mofraction_mofraction(a, b))
    +
     > /
     | > *
     | | > 1
     | | > 5
     | > *
     | | > 2
     | | > 5
     > /
     | > *
     | | > 1
     | | > 2
     | > *
     | | > 5
     | | > 2
    """
    if left.denominator == right.denominator:
        num = Tree("+", left.numerator, right.numerator)
        return Tree("/", num, left.denominator)

    denom_lcm = lcm(left.denominator, right.denominator)

    if left.denominator == denom_lcm:
        left_frac = left
    else:
        multiply_by = denom_lcm // left.denominator
        left_num = Tree("*", left.numerator, MO.factory(multiply_by))
        left_denom = Tree("*", left.denominator, MO.factory(multiply_by))
        left_frac = Tree("/", left_num, left_denom)

    if right.denominator == denom_lcm:
        right_frac = right
    else:
        multiply_by = denom_lcm // right.denominator
        right_num = Tree("*", right.numerator, MO.factory(multiply_by))
        right_denom = Tree("*", right.denominator, MO.factory(multiply_by))
        right_frac = Tree("/", right_num, right_denom)

    return Tree("+", left_frac, right_frac)

# TODO: Faire un décorateur pour un enregistrement automatique |dim. mars 11 18:24:32 EAT 2018
ADDFUNCTIONS = {
    (MOnumber, MOnumber): monumber_monumber,
    (MOnumber, MOFraction): monumber_mofraction,
    (MOFraction, MOnumber): mofraction_monumber,
    (MOFraction, MOFraction): mofraction_mofraction,
    }

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