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

    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_sub_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_sub(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_neg(num, fmpq_numref(c));
         fmpz_set(den, fmpq_denref(c));
      } else if (len == 1)
         _fmpq_sub(num, den, num2, den2, fmpq_numref(c), fmpq_denref(c));
      else
      {
         /* fast path */
         if (fmpz_equal(fmpq_denref(c), den2))
         {
            fmpz_sub(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_submul(num, d2, fmpq_numref(c));

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

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