/*=============================================================================

    This file is part of Antic.

    Antic is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 2.1 of the License, or
    (at your option) any later version. See <http://www.gnu.org/licenses/>.

=============================================================================*/
/******************************************************************************

    Copyright (C) 2015 William Hart

******************************************************************************/

#include "nf_elem.h"

void nf_elem_add_fmpq(nf_elem_t a, const nf_elem_t b, const fmpq_t c, const nf_t nf)
{
   if (nf->flag & NF_LINEAR)
   {
      fmpz * den = LNF_ELEM_DENREF(a);
      fmpz * num = LNF_ELEM_NUMREF(a);
      const fmpz * const den2 = LNF_ELEM_DENREF(b);
      const fmpz * const num2 = LNF_ELEM_NUMREF(b);
	  
      _fmpq_add(num, den, num2, den2, fmpq_numref(c), fmpq_denref(c));
   }
   else if (nf->flag & NF_QUADRATIC)
   {
      fmpz * den = QNF_ELEM_DENREF(a);
      fmpz * num = QNF_ELEM_NUMREF(a);
      const fmpz * const den2 = QNF_ELEM_DENREF(b);
      const fmpz * const num2 = QNF_ELEM_NUMREF(b);
      slong len = 2;

      nf_elem_set(a, b, nf);

	    while (len != 0 && fmpz_is_zero(num2 + len - 1))
         len--;
	  
       if (len == 0)
       {
          fmpz_set(num, fmpq_numref(c));
          fmpz_set(den, fmpq_denref(c));
       } else if (len == 1)
          _fmpq_add(num, den, num2, den2, fmpq_numref(c), fmpq_denref(c));
       else
       {
          /* fast path */
          if (fmpz_equal(fmpq_denref(c), den))
          {
             fmpz_add(num, num2, fmpq_numref(c));
             fmpz_set(den, den2);
          } else /* slow path */
          {
             fmpz_t d1, d2, g;

             fmpz_init(d1);
             fmpz_init(d2);
             fmpz_init(g);

             fmpz_gcd(g, fmpq_denref(c), den);
             fmpz_divexact(d1, fmpq_denref(c), g);
             fmpz_divexact(d2, den, g);

             fmpz_mul(num + 1, num + 1, d1);
             fmpz_mul(num, num, d1);
             fmpz_mul(den, den, d1);

             fmpz_addmul(num, d2, fmpq_numref(c));

             fmpz_clear(g);
             fmpz_clear(d1);
             fmpz_clear(d2);
          }

          _fmpq_poly_canonicalise(num, den, 2);
       }
   } else
   {
      fmpq_poly_add_fmpq(NF_ELEM(a), NF_ELEM(b), c);
   }
}