path: root/src/round_prec.c

/* mpfr_round_raw_generic, mpfr_round_raw2, mpfr_round_raw, mpfr_prec_round,
   mpfr_can_round, mpfr_can_round_raw -- various rounding functions

Copyright 1999-2016 Free Software Foundation, Inc.
Contributed by the AriC and Caramba 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. */

#include "mpfr-impl.h"

#define mpfr_round_raw_generic mpfr_round_raw
#define flag 0
#define use_inexp 1
#include "round_raw_generic.c"

#define mpfr_round_raw_generic mpfr_round_raw_2
#define flag 1
#define use_inexp 0
#include "round_raw_generic.c"

/* Seems to be unused. Remove comment to implement it.
#define mpfr_round_raw_generic mpfr_round_raw_3
#define flag 1
#define use_inexp 1
#include "round_raw_generic.c"
*/

#define mpfr_round_raw_generic mpfr_round_raw_4
#define flag 0
#define use_inexp 0
#include "round_raw_generic.c"

int
mpfr_prec_round (mpfr_ptr x, mpfr_prec_t prec, mpfr_rnd_t rnd_mode)
{
  mp_limb_t *tmp, *xp;
  int carry, inexact;
  mpfr_prec_t nw, ow;
  MPFR_TMP_DECL(marker);

  MPFR_ASSERTN(prec >= MPFR_PREC_MIN && prec <= MPFR_PREC_MAX);

  nw = MPFR_PREC2LIMBS (prec); /* needed allocated limbs */

  /* check if x has enough allocated space for the significand */
  /* Get the number of limbs from the precision.
     (Compatible with all allocation methods) */
  ow = MPFR_LIMB_SIZE (x);
  if (nw > ow)
    {
      /* FIXME: Variable can't be created using custom allocation,
         MPFR_DECL_INIT or GROUP_ALLOC: How to detect? */
      ow = MPFR_GET_ALLOC_SIZE(x);
      if (nw > ow)
       {
         /* Realloc significand */
         mpfr_limb_ptr tmpx = (mpfr_limb_ptr) (*__gmp_reallocate_func)
           (MPFR_GET_REAL_PTR(x), MPFR_MALLOC_SIZE(ow), MPFR_MALLOC_SIZE(nw));
         MPFR_SET_MANT_PTR(x, tmpx); /* mant ptr must be set
                                        before alloc size */
         MPFR_SET_ALLOC_SIZE(x, nw); /* new number of allocated limbs */
       }
    }

  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
    {
      MPFR_PREC(x) = prec; /* Special value: need to set prec */
      if (MPFR_IS_NAN(x))
        MPFR_RET_NAN;
      MPFR_ASSERTD(MPFR_IS_INF(x) || MPFR_IS_ZERO(x));
      return 0; /* infinity and zero are exact */
    }

  /* x is a non-zero real number */

  MPFR_TMP_MARK(marker);
  tmp = MPFR_TMP_LIMBS_ALLOC (nw);
  xp = MPFR_MANT(x);
  carry = mpfr_round_raw (tmp, xp, MPFR_PREC(x), MPFR_IS_NEG(x),
                          prec, rnd_mode, &inexact);
  MPFR_PREC(x) = prec;

  if (MPFR_UNLIKELY(carry))
    {
      mpfr_exp_t exp = MPFR_EXP (x);

      if (MPFR_UNLIKELY(exp == __gmpfr_emax))
        (void) mpfr_overflow(x, rnd_mode, MPFR_SIGN(x));
      else
        {
          MPFR_ASSERTD (exp < __gmpfr_emax);
          MPFR_SET_EXP (x, exp + 1);
          xp[nw - 1] = MPFR_LIMB_HIGHBIT;
          if (nw - 1 > 0)
            MPN_ZERO(xp, nw - 1);
        }
    }
  else
    MPN_COPY(xp, tmp, nw);

  MPFR_TMP_FREE(marker);
  return inexact;
}

/* assumption: GMP_NUMB_BITS is a power of 2 */

/* assuming b is an approximation to x in direction rnd1 with error at
   most 2^(MPFR_EXP(b)-err), returns 1 if one is able to round exactly
   x to precision prec with direction rnd2, and 0 otherwise.

   Side effects: none.
*/

int
mpfr_can_round (mpfr_srcptr b, mpfr_exp_t err, mpfr_rnd_t rnd1,
                mpfr_rnd_t rnd2, mpfr_prec_t prec)
{
  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(b)))
    return 0; /* We cannot round if Zero, Nan or Inf */
  else
    return mpfr_can_round_raw (MPFR_MANT(b), MPFR_LIMB_SIZE(b),
                               MPFR_SIGN(b), err, rnd1, rnd2, prec);
}

int
mpfr_can_round_raw (const mp_limb_t *bp, mp_size_t bn, int neg, mpfr_exp_t err0,
                    mpfr_rnd_t rnd1, mpfr_rnd_t rnd2, mpfr_prec_t prec)
{
  mpfr_prec_t err, prec0 = prec;
  mp_size_t k, k1, tn;
  int s, s1;
  mp_limb_t cc, cc2;
  mp_limb_t *tmp;
  MPFR_TMP_DECL(marker);

  MPFR_ASSERTD(bp[bn - 1] & MPFR_LIMB_HIGHBIT);

  if (MPFR_UNLIKELY(err0 < 0 || (mpfr_uexp_t) err0 <= prec))
    return 0;  /* can't round */

  MPFR_ASSERT_SIGN(neg);
  neg = MPFR_IS_NEG_SIGN(neg);

  /* Transform RNDD and RNDU to Zero / Away */
  MPFR_ASSERTD((neg == 0) || (neg == 1));
  if (rnd1 != MPFR_RNDN)
    rnd1 = MPFR_IS_LIKE_RNDZ(rnd1, neg) ? MPFR_RNDZ : MPFR_RNDA;
  if (rnd2 != MPFR_RNDN)
    rnd2 = MPFR_IS_LIKE_RNDZ(rnd2, neg) ? MPFR_RNDZ : MPFR_RNDA;

  if (MPFR_UNLIKELY (prec > (mpfr_prec_t) bn * GMP_NUMB_BITS))
    { /* Then prec < PREC(b): we can round:
         (i) in rounding to the nearest iff err0 >= prec + 2
         (ii) in directed rounding mode iff rnd1 is compatible with rnd2
              and err0 >= prec + 1, unless b = 2^k and rnd1=rnd2=RNDA in
              which case we need err0 >= prec + 2. */
      if (rnd2 == MPFR_RNDN)
        return (mpfr_uexp_t) err0 - 2 >= prec;
      else
        return (rnd1 == rnd2) && (mpfr_uexp_t) err0 - 2 >= prec;
    }

  /* if the error is smaller than ulp(b), then anyway it will propagate
     up to ulp(b) */
  err = ((mpfr_uexp_t) err0 > (mpfr_prec_t) bn * GMP_NUMB_BITS) ?
    (mpfr_prec_t) bn * GMP_NUMB_BITS : (mpfr_prec_t) err0;

  /* warning: if k = m*GMP_NUMB_BITS, consider limb m-1 and not m */
  k = (err - 1) / GMP_NUMB_BITS;
  MPFR_UNSIGNED_MINUS_MODULO(s, err);
  /* the error corresponds to bit s in limb k, the most significant limb
     being limb 0; in memory, limb k is bp[bn-1-k]. */

  k1 = (prec - 1) / GMP_NUMB_BITS;
  MPFR_UNSIGNED_MINUS_MODULO(s1, prec);
  /* the least significant bit is bit s1 in limb k1 */

  /* We don't need to consider the k1 most significant limbs.
     They will be considered later only to detect when subtracting
     the error bound yields a change of binade.
     Warning! The number with updated bn may no longer be normalized. */
  k -= k1;
  bn -= k1;
  prec -= (mpfr_prec_t) k1 * GMP_NUMB_BITS;

  /* We can decide of the correct rounding if rnd2(b-eps) and rnd2(b+eps)
     give the same result to the target precision 'prec', i.e., if when
     adding or subtracting (1 << s) in bp[bn-1-k], it does not change the
     rounding in direction 'rnd2' at ulp-position bp[bn-1] >> s1, taking also
     into account the possible change of binade. */
  MPFR_TMP_MARK(marker);
  tn = bn;
  k++; /* since we work with k+1 everywhere */
  tmp = MPFR_TMP_LIMBS_ALLOC (tn);
  if (bn > k)
    MPN_COPY (tmp, bp, bn - k);

  MPFR_ASSERTD (k > 0);

  switch (rnd1)
    {
    case MPFR_RNDZ:
      /* Round to Zero */
      cc = (bp[bn - 1] >> s1) & 1;
      /* mpfr_round_raw2 returns 1 if one should add 1 at ulp(b,prec),
         and 0 otherwise */
      cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec);
      /* cc is the new value of bit s1 in bp[bn-1] after rounding 'rnd2' */

      /* now round b + 2^(MPFR_EXP(b)-err) */
      mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
      /* if there was a carry here, then necessarily bit s1 of bp[bn-1]
         changed, thus we surely cannot round for directed rounding, but this
         will be detected below, with cc2 != cc */
      break;
    case MPFR_RNDN:
      /* Round to nearest */

      /* first round b+2^(MPFR_EXP(b)-err) */
      mpn_add_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
      /* same remark as above in case a carry occurs in mpn_add_1() */
      cc = (tmp[bn - 1] >> s1) & 1; /* gives 0 when cc=1 */
      cc ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);
      /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */

    subtract_eps:
      /* now round b-2^(MPFR_EXP(b)-err) */
      cc2 = mpn_sub_1 (tmp + bn - k, bp + bn - k, k, MPFR_LIMB_ONE << s);
      /* propagate the potential borrow up to the most significant limb
         (it cannot propagate further since the most significant limb is
         at least MPFR_LIMB_HIGHBIT) */
      for (tn = 0; tn + 1 < k1 && (cc2 != 0); tn ++)
        cc2 = bp[bn + tn] == 0;
      /* We have an exponent decrease when either:
           (i) k1 = 0 and tmp[bn-1] < MPFR_LIMB_HIGHBIT
           (ii) k1 > 0 and cc <> 0 and bp[bn + tn] = MPFR_LIMB_HIGHBIT
                (then necessarily tn = k1-1).
         Then for directed rounding we cannot round,
         and for rounding to nearest we cannot round when err = prec + 1.
      */
      if (((k1 == 0 && tmp[bn - 1] < MPFR_LIMB_HIGHBIT) ||
           (k1 != 0 && cc2 != 0 && bp[bn + tn] == MPFR_LIMB_HIGHBIT)) &&
          (rnd2 != MPFR_RNDN || err0 == prec0 + 1))
        {
          MPFR_TMP_FREE(marker);
          return 0;
        }
      break;
    default:
      /* Round away */
      cc = (bp[bn - 1] >> s1) & 1;
      cc ^= mpfr_round_raw2 (bp, bn, neg, rnd2, prec);
      /* cc is the new value of bit s1 in bp[bn-1]+eps after rounding 'rnd2' */

      goto subtract_eps;
    }

  cc2 = (tmp[bn - 1] >> s1) & 1;
  cc2 ^= mpfr_round_raw2 (tmp, bn, neg, rnd2, prec);

  MPFR_TMP_FREE(marker);
  return cc == cc2;
}