"""
Vectors with elements in GF(2).

AUTHOR:

- Martin Albrecht (2009-12): initial implementation
- Thomas Feulner (2012-11): added :meth:`Vector_mod2_dense.hamming_weight`

EXAMPLES::

    sage: VS = GF(2)^3
    sage: e = VS.random_element(); e
    (1, 0, 0)
    sage: f = VS.random_element(); f
    (0, 1, 1)
    sage: e + f
    (1, 1, 1)

TESTS::

    sage: w = vector(GF(2), [-1,0,0,0])
    sage: w.set_immutable()
    sage: isinstance(hash(w), int)
    True
"""

#*****************************************************************************
#       Copyright (C) 2009 Martin Albrecht <M.R.Albrecht@rhul.ac.uk>
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#                  http://www.gnu.org/licenses/
#*****************************************************************************
from __future__ import absolute_import

from sage.rings.finite_rings.integer_mod cimport IntegerMod_int, IntegerMod_abstract
from sage.rings.integer cimport Integer
from sage.rings.rational cimport Rational
from sage.structure.element cimport Element, ModuleElement, RingElement, Vector

cimport sage.modules.free_module_element as free_module_element
from .free_module_element import vector

from sage.libs.m4ri cimport *

cdef class Vector_mod2_dense(free_module_element.FreeModuleElement):
    cdef _new_c(self):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),3)
            sage: VS([0,0,1])
            (0, 0, 1)
            sage: type(_)
            <type 'sage.modules.vector_mod2_dense.Vector_mod2_dense'>
        """
        cdef Vector_mod2_dense y
        y = Vector_mod2_dense.__new__(Vector_mod2_dense)
        y._init(self._degree, self._parent)
        return y

    cdef bint is_dense_c(self):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),3)
            sage: VS([0,0,1]).is_dense()
            True
        """
        return 1

    cdef bint is_sparse_c(self):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),3)
            sage: VS([0,0,1]).is_sparse()
            False
        """
        return 0

    def __copy__(self):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10^4)
            sage: v = VS.random_element()
            sage: w = copy(v)
            sage: w == v
            True
            sage: v[:10]
            (1, 0, 0, 0, 1, 1, 1, 0, 0, 1)
            sage: w[:10]
            (1, 0, 0, 0, 1, 1, 1, 0, 0, 1)
        """
        cdef Vector_mod2_dense y = self._new_c()
        if self._degree:
            mzd_copy(y._entries, self._entries)
        return y

    cdef _init(self, Py_ssize_t degree, parent):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),3)
            sage: VS([0,0,1])
            (0, 0, 1)
            sage: type(_)
            <type 'sage.modules.vector_mod2_dense.Vector_mod2_dense'>
        """
        self._degree = degree
        self._parent = parent
        self._base_ring = parent.base_ring()
        self._entries = mzd_init(1, degree)
        if self._entries == NULL:
            raise MemoryError("Allocation of Vector_mod2_dense failed.")

    def __cinit__(self, parent=None, x=None, coerce=True, copy=True):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),3)
            sage: VS((0,0,1/3))
            (0, 0, 1)
            sage: type(_)
            <type 'sage.modules.vector_mod2_dense.Vector_mod2_dense'>
        """
        self._entries = NULL
        self._is_mutable = 1
        if not parent is None:
            self._init(parent.degree(), parent)

    def __init__(self, parent, x, coerce=True, copy=True):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),3)
            sage: VS((0,0,1/3))
            (0, 0, 1)
            sage: type(_)
            <type 'sage.modules.vector_mod2_dense.Vector_mod2_dense'>
            sage: VS((0,0,int(3)))
            (0, 0, 1)
            sage: VS((0,0,3))
            (0, 0, 1)
            sage: VS((0,0,GF(2)(1)))
            (0, 0, 1)

        TESTS:

        Check that ticket :trac:`8601` is fixed::

            sage: VS = VectorSpace(GF(2), 3)
            sage: VS((-1,-2,-3))
            (1, 0, 1)
            sage: V = VectorSpace(GF(2), 2)
            sage: V([1,3])
            (1, 1)
            sage: V([1,-3])
            (1, 1)

        Check integer overflow prior to :trac:`21746`::

            sage: VS = VectorSpace(GF(2),1)
            sage: VS([2**64])
            (0)
            sage: VS([3**100/5**100])
            (1)

        Check division error over rationals::

            sage: V = VectorSpace(GF(2), 2)
            sage: V([1/3, 3/4])
            Traceback (most recent call last):
            ...
            ZeroDivisionError: inverse does not exist

        Check zero initialization::

            sage: for _ in range(1,100):
            ....:     assert VectorSpace(GF(2), randint(1,5000))(0).is_zero()
            sage: (GF(2)**5)(1)
            Traceback (most recent call last):
            ...
            TypeError: can't initialize vector from nonzero non-list
            sage: (GF(2)**0).zero_vector()
            ()
        """
        cdef Py_ssize_t i
        if isinstance(x, (list, tuple)):
            if len(x) != self._degree:
                raise TypeError("x must be a list of the right length")
            for i in range(len(x)):
                xi = x[i]
                if isinstance(xi, (IntegerMod_int, int, long, Integer)):
                    # the if/else statement is because in some compilers, (-1)%2 is -1
                    mzd_write_bit(self._entries, 0, i, 1 if xi%2 else 0)
                elif isinstance(xi, Rational):
                    if not (xi.denominator() % 2):
                        raise ZeroDivisionError("inverse does not exist")
                    mzd_write_bit(self._entries, 0, i, 1 if (xi.numerator() % 2) else 0)
                else:
                    mzd_write_bit(self._entries, 0, i, xi%2)
        elif x != 0:
            raise TypeError("can't initialize vector from nonzero non-list")
        elif self._degree:
            mzd_set_ui(self._entries, 0)

    def __dealloc__(self):
        """
        EXAMPLES::

        sage: VS = VectorSpace(GF(2),10^3)
        sage: import gc
        sage: for i in range(10):
        ....:     v = VS.random_element()
        ....:     del v
        ....:     _ = gc.collect()
        """
        if self._entries:
            mzd_free(self._entries)

    cpdef int _cmp_(left, right) except -2:
        """
        EXAMPLES::
            sage: v = vector(GF(2), [0,0,0,0])
            sage: v == 0
            True
            sage: v == 1
            False
            sage: v == v
            True
            sage: w = vector(GF(2), [1,0,0,0])
            sage: w < v
            False
            sage: w > v
            True
            sage: w = vector(GF(2), [-1,0,0,0])
            sage: w == w
            True
        """
        if left._degree == 0:
            return 0
        return mzd_cmp(left._entries, (<Vector_mod2_dense>right)._entries)

    cdef get_unsafe(self, Py_ssize_t i):
        """
        EXAMPLES::

            sage: v = vector(GF(2), [1,2,3]); v
            (1, 0, 1)
            sage: v[0]
            1
            sage: v[2]
            1
            sage: v[-2]
            0
            sage: v[0:2]
            (1, 0)
        """
        return self._base_ring(mzd_read_bit(self._entries, 0, i))

    cdef int set_unsafe(self, Py_ssize_t i, value) except -1:
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),4)
            sage: v = VS.random_element(); v
            (1, 0, 0, 0)
            sage: v[0] = 0; v
            (0, 0, 0, 0)
            sage: v[1:3] = [1, 1]; v
            (0, 1, 1, 0)
            sage: v[4] = 0
            Traceback (most recent call last):
            ...
            IndexError: vector index out of range
        """
        mzd_write_bit(self._entries, 0, i, value)


    def __reduce__(self):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10^4)
            sage: e = VS.random_element()
            sage: loads(dumps(e)) == e
            True
        """
        return unpickle_v0, (self._parent, self.list(), self._degree, self._is_mutable)

    cpdef _add_(self, right):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS([0,0,1,1,0,0,1,1,0,0])
            sage: f = VS([0,1,0,1,0,1,0,1,0,1])
            sage: e + f #indirect doctest
            (0, 1, 1, 0, 0, 1, 1, 0, 0, 1)
        """
        cdef Vector_mod2_dense z = self._new_c()
        if self._degree:
            mzd_add(z._entries, self._entries, (<Vector_mod2_dense>right)._entries)
        return z

    cpdef _sub_(self, right):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS([0,0,1,1,0,0,1,1,0,0])
            sage: f = VS([0,1,0,1,0,1,0,1,0,1])
            sage: e - f #indirect doctest
            (0, 1, 1, 0, 0, 1, 1, 0, 0, 1)
        """
        cdef Vector_mod2_dense z = self._new_c()
        if self._degree:
            mzd_add(z._entries, self._entries, (<Vector_mod2_dense>right)._entries)
        return z

    cpdef int hamming_weight(self):
        """
        Return the number of positions ``i`` such that ``self[i] != 0``.

        EXAMPLES::

            sage: vector(GF(2), [1,1,0]).hamming_weight()
            2
        """
        cdef int i
        cdef int res = 0
        for i from 0 <= i < self._entries.width:
            res += Integer(self._entries.rows[0][i]).popcount()
        return res


    cpdef _dot_product_(self, Vector right):
        """
        EXAMPLES::
           sage: VS = VectorSpace(GF(2),3)
           sage: v = VS([1,1,1]); w = VS([0,0,0])
           sage: v * w, w * v #indirect doctest
           (0, 0)
           sage: v = VS([1,1,1]); w = VS([0,1,0])
           sage: v * w, w * v
           (1, 1)
           sage: v = VS([1,1,1]); w = VS([0,1,1])
           sage: v * w, w * v
           (0, 0)
           sage: v = VS([1,1,1]); w = VS([1,1,1])
           sage: v * w, w * v
           (1, 1)

           sage: VS = VectorSpace(GF(2),10^4)
           sage: v = VS(0); w = VS(0)
           sage: v[1337] = 1; w[1337] = 1
           sage: v * w, w * v
           (1, 1)
           sage: v[9881] = 1; w[9881] = 1
           sage: v * w, w * v
           (0, 0)
           sage: v[5172] = 1; w[6178] = 1
           sage: v * w, w * v
           (0, 0)
        """
        cdef Py_ssize_t i
        cdef IntegerMod_int n
        cdef Vector_mod2_dense r = right
        cdef m4ri_word tmp = 0
        n =  IntegerMod_int.__new__(IntegerMod_int)
        IntegerMod_abstract.__init__(n, self.base_ring())
        n.ivalue = 0

        for i from 0 <= i < self._entries.width:
            tmp ^= self._entries.rows[0][i] & r._entries.rows[0][i]

        for i in range(64):
            n.ivalue ^= <int>(tmp & 1)
            tmp = tmp >> 1

        return n

    cpdef _pairwise_product_(self, Vector right):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS.random_element(); e
            (1, 0, 0, 0, 1, 1, 1, 0, 0, 1)
            sage: f = VS.random_element(); f
            (1, 1, 0, 1, 1, 1, 0, 0, 0, 1)
            sage: e.pairwise_product(f) #indirect doctest
            (1, 0, 0, 0, 1, 1, 0, 0, 0, 1)
        """
        cdef Vector_mod2_dense z, r
        r = right
        z = self._new_c()
        cdef Py_ssize_t i
        for i from 0 <= i < self._entries.width:
            z._entries.rows[0][i] = (self._entries.rows[0][i] & r._entries.rows[0][i])
        return z

    cpdef _lmul_(self, Element left):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS.random_element(); e
            (1, 0, 0, 0, 1, 1, 1, 0, 0, 1)
            sage: 0 * e
            (0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
            sage: 1 * e
            (1, 0, 0, 0, 1, 1, 1, 0, 0, 1)
            sage: 2 * e #indirect doctest
            (0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

        ::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS.random_element(); e
            (1, 1, 0, 1, 1, 1, 0, 0, 0, 1)
            sage: e * 0 #indirect doctest
            (0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
            sage: e * 1
            (1, 1, 0, 1, 1, 1, 0, 0, 0, 1)
            sage: e * 2
            (0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
        """
        cdef IntegerMod_int a

        if left:
            return self.__copy__()
        else:
            return self._new_c()

    cpdef _neg_(self):
        """
        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS.random_element()
            sage: -e == e
            True
        """
        return self.__copy__()

    def list(self, copy=True):
        """
        Return a list of entries in ``self``.

        INPUT:

        - ``copy`` - always ``True``

        EXAMPLES::

            sage: VS = VectorSpace(GF(2),10)
            sage: e = VS.random_element(); e
            (1, 0, 0, 0, 1, 1, 1, 0, 0, 1)
            sage: e.list()
            [1, 0, 0, 0, 1, 1, 1, 0, 0, 1]
        """
        cdef Py_ssize_t d = self._degree
        cdef Py_ssize_t i
        cdef list v = [0]*d
        K = self.base_ring()
        z = K.zero()
        o = K.one()
        cdef list switch = [z,o]
        for i in range(d):
            v[i] = switch[mzd_read_bit(self._entries, 0, i)]
        return v

def unpickle_v0(parent, entries, degree, is_mutable):
    """
    EXAMPLES::

        sage: from sage.modules.vector_mod2_dense import unpickle_v0
        sage: VS = VectorSpace(GF(2),10)
        sage: unpickle_v0(VS, [0,1,2,3,4,5,6,7,8,9], 10, 0)
        (0, 1, 0, 1, 0, 1, 0, 1, 0, 1)
    """
    # If you think you want to change this function, don't.
    cdef Vector_mod2_dense v
    v = Vector_mod2_dense.__new__(Vector_mod2_dense)
    v._init(degree, parent)
    cdef int xi

    for i from 0 <= i < degree:
        if isinstance(entries[i], IntegerMod_int) or isinstance(entries[i], int) or isinstance(entries[i], Integer):
            xi = entries[i]
            mzd_write_bit(v._entries, 0, i, xi%2)
        else:
            mzd_write_bit(v._entries, 0, i, entries[i]%2)
    v._is_mutable = int(is_mutable)
    return v

