/* mpfr_frac -- Fractional part of a floating-point number.

Copyright 2002, 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
Contributed by the AriC and Caramel projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */


#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

/* Optimization note: it is not a good idea to call mpfr_integer_p,
   as some cases will take longer (the number may be parsed twice). */

int
mpfr_frac (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  mpfr_exp_t re, ue;
  mpfr_prec_t uq;
  mp_size_t un, tn, t0;
  mp_limb_t *up, *tp, k;
  int sh;
  mpfr_t tmp;
  mpfr_ptr t;
  int inex;
  MPFR_SAVE_EXPO_DECL (expo);

  /* Special cases */
  if (MPFR_UNLIKELY(MPFR_IS_NAN(u)))
    {
      MPFR_SET_NAN(r);
      MPFR_RET_NAN;
    }
  else if (MPFR_UNLIKELY(MPFR_IS_INF(u) || mpfr_integer_p (u)))
    {
      MPFR_SET_SAME_SIGN(r, u);
      MPFR_SET_ZERO(r);
      MPFR_RET(0);  /* zero is exact */
    }

  ue = MPFR_GET_EXP (u);
  if (ue <= 0)  /* |u| < 1 */
    return mpfr_set (r, u, rnd_mode);

  /* Now |u| >= 1, meaning that an overflow is not possible. */

  uq = MPFR_PREC(u);
  un = (uq - 1) / GMP_NUMB_BITS;  /* index of most significant limb */
  un -= (mp_size_t) (ue / GMP_NUMB_BITS);
  /* now the index of the MSL containing bits of the fractional part */

  up = MPFR_MANT(u);
  sh = ue % GMP_NUMB_BITS;
  k = up[un] << sh;
  /* the first bit of the fractional part is the MSB of k */

  if (k != 0)
    {
      int cnt;

      count_leading_zeros(cnt, k);
      /* first bit 1 of the fractional part -> MSB of the number */
      re = -cnt;
      sh += cnt;
      MPFR_ASSERTN (sh < GMP_NUMB_BITS);
      k <<= cnt;
    }
  else
    {
      re = sh - GMP_NUMB_BITS;
      /* searching for the first bit 1 (exists since u isn't an integer) */
      while (up[--un] == 0)
        re -= GMP_NUMB_BITS;
      MPFR_ASSERTN(un >= 0);
      k = up[un];
      count_leading_zeros(sh, k);
      re -= sh;
      k <<= sh;
    }
  /* The exponent of r will be re */
  /* un: index of the limb of u that contains the first bit 1 of the FP */

  t = (mp_size_t) (MPFR_PREC(r) - 1) / GMP_NUMB_BITS < un ?
    (mpfr_init2 (tmp, (un + 1) * GMP_NUMB_BITS), tmp) : r;
  /* t has enough precision to contain the fractional part of u */
  /* If we use a temporary variable, we take the non-significant bits
     of u into account, because of the mpn_lshift below. */
  MPFR_SET_SAME_SIGN(t, u);

  /* Put the fractional part of u into t */
  tn = (MPFR_PREC(t) - 1) / GMP_NUMB_BITS;
  MPFR_ASSERTN(tn >= un);
  t0 = tn - un;
  tp = MPFR_MANT(t);
  if (sh == 0)
    MPN_COPY_DECR(tp + t0, up, un + 1);
  else /* warning: un may be 0 here */
    tp[tn] = k | ((un) ? mpn_lshift (tp + t0, up, un, sh) : (mp_limb_t) 0);
  if (t0 > 0)
    MPN_ZERO(tp, t0);

  MPFR_SAVE_EXPO_MARK (expo);

  if (t != r)
    { /* t is tmp */
      MPFR_EXP (t) = 0;  /* should be re, but not necessarily in the range */
      inex = mpfr_set (r, t, rnd_mode);  /* no underflow */
      mpfr_clear (t);
      MPFR_EXP (r) += re;
    }
  else
    { /* There may be remaining non-significant bits in t (= r). */
      int carry;

      MPFR_EXP (r) = re;
      carry = mpfr_round_raw (tp, tp,
                              (mpfr_prec_t) (tn + 1) * GMP_NUMB_BITS,
                              MPFR_IS_NEG (r), MPFR_PREC (r), rnd_mode,
                              &inex);
      if (carry)
        {
          tp[tn] = MPFR_LIMB_HIGHBIT;
          MPFR_EXP (r) ++;
        }
    }

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (r, inex, rnd_mode);
}
