niceSOFT/mpfr | Gitverse

src/set.c
199 строк6 KB
Vincent Lefèvre
03 янв 2018, 13:53
03 янв 2018, 13:532fce388
/* mpfr_set -- copy of a floating-point number

Copyright 1999, 2001-2018 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"

/* set a to abs(b) * signb: a=b when signb = SIGN(b), a=abs(b) when signb=1 */
MPFR_HOT_FUNCTION_ATTR int
mpfr_set4 (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode, int signb)
{
  /* Sign is ALWAYS copied */
  MPFR_SET_SIGN (a, signb);

  /* Exponent is also always copied since if the number is singular,
     the exponent field determined the number.
     Can't use MPFR_SET_EXP since the exponent may be singular */
  MPFR_EXP (a) = MPFR_EXP (b);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (b)))
    {
      /* MPFR_SET_NAN, MPFR_SET_ZERO and MPFR_SET_INF are useless
         since MPFR_EXP (a) = MPFR_EXP (b) does the job */
      if (MPFR_IS_NAN (b))
        MPFR_RET_NAN;
      else
        MPFR_RET (0);
    }
  else if (MPFR_PREC (b) == MPFR_PREC (a))
    {
      /* Same precision and b is not singular:
       * just copy the mantissa, and set the exponent and the sign
       * The result is exact. */
      MPN_COPY (MPFR_MANT (a), MPFR_MANT (b), MPFR_LIMB_SIZE (b));
      MPFR_RET (0);
    }
  else
    {
      int inex;

      /* Else Round B inside a */
      MPFR_RNDRAW (inex, a, MPFR_MANT (b), MPFR_PREC (b), rnd_mode, signb,
                   if (MPFR_UNLIKELY (++ MPFR_EXP (a) > __gmpfr_emax))
                     return mpfr_overflow (a, rnd_mode, signb)
                   );
      MPFR_RET (inex);
    }
}

/* Set a to b  */
#undef mpfr_set
int
mpfr_set (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
  return mpfr_set4 (a, b, rnd_mode, MPFR_SIGN (b));
}

/* Set a to |b| */
#undef mpfr_abs
int
mpfr_abs (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
  return mpfr_set4 (a, b, rnd_mode, MPFR_SIGN_POS);
}

/* Round (u, inex) into s with rounding mode rnd, where inex is the ternary
   value associated to u with the *same* rounding mode.
   Assumes PREC(u) = 2*PREC(s).
   The main algorithm is the following:
   rnd=RNDZ: inex2 = mpfr_set (s, u, rnd_mode); return inex2 | inex;
             (a negative value, if any, is preserved in inex2 | inex)
   rnd=RNDA: idem
   rnd=RNDN: inex2 = mpfr_set (s, u, rnd_mode);
             if (inex2) return inex2; else return inex; */
int
mpfr_set_1_2 (mpfr_ptr s, mpfr_srcptr u, mpfr_rnd_t rnd_mode, int inex)
{
  mpfr_prec_t p = MPFR_PREC(s);
  mpfr_prec_t sh = GMP_NUMB_BITS - p;
  mp_limb_t rb, sb;
  mp_limb_t *sp = MPFR_MANT(s);
  mp_limb_t *up = MPFR_MANT(u);
  mp_limb_t mask;
  int inex2;

  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u)))
    {
      mpfr_set (s, u, rnd_mode);
      return inex;
    }

  MPFR_ASSERTD(MPFR_PREC(u) == 2 * MPFR_PREC(s));

  if (MPFR_PREC(s) < GMP_NUMB_BITS)
    {
      mask = MPFR_LIMB_MASK(sh);

      if (MPFR_PREC(u) <= GMP_NUMB_BITS)
        {
          mp_limb_t u0 = up[0];

          /* it suffices to round (u0, inex) */
          rb = u0 & (MPFR_LIMB_ONE << (sh - 1));
          sb = (u0 & mask) ^ rb;
          sp[0] = u0 & ~mask;
        }
      else
        {
          mp_limb_t u1 = up[1];

          /* we need to round (u1, u0, inex) */
          mask = MPFR_LIMB_MASK(sh);
          rb = u1 & (MPFR_LIMB_ONE << (sh - 1));
          sb = ((u1 & mask) ^ rb) | up[0];
          sp[0] = u1 & ~mask;
        }

      inex2 = inex * MPFR_SIGN(u);
      MPFR_SIGN(s) = MPFR_SIGN(u);
      MPFR_EXP(s) = MPFR_EXP(u);

      /* in case inex2 > 0, the value of u is rounded away,
         thus we need to subtract something from (u0, rb, sb):
         (a) if sb is not zero, since the subtracted value is < 1, we can leave
         sb as it is;
         (b) if rb <> 0 and sb = 0: change to rb = 0 and sb = 1
         (c) if rb = sb = 0: change to rb = 1 and sb = 1, and subtract 1 */
      if (inex2 > 0)
        {
          if (rb && sb == 0)
            {
              rb = 0;
              sb = 1;
            }
        }
      else /* inex2 <= 0 */
        sb |= inex;

      /* now rb, sb are the round and sticky bits, together with the value of
         sp[0], except possibly in the case rb = sb = 0 and inex2 > 0 */
      if (rb == 0 && sb == 0)
        {
          if (inex2 <= 0)
            MPFR_RET(0);
          else /* inex2 > 0 can only occur for RNDN and RNDA:
                  RNDN: return sp[0] and inex
                  RNDA: return sp[0] and inex */
            MPFR_RET(inex);
        }
      else if (rnd_mode == MPFR_RNDN)
        {
          if (rb == 0 || (sb == 0 && (sp[0] & (MPFR_LIMB_ONE << sh)) == 0))
            goto truncate;
          else
            goto add_one_ulp;
        }
      else if (MPFR_IS_LIKE_RNDZ(rnd_mode, MPFR_IS_NEG(s)))
        {
        truncate:
          MPFR_RET(-MPFR_SIGN(s));
        }
      else /* round away from zero */
        {
        add_one_ulp:
          sp[0] += MPFR_LIMB_ONE << sh;
          if (MPFR_UNLIKELY(sp[0] == 0))
            {
              sp[0] = MPFR_LIMB_HIGHBIT;
              if (MPFR_EXP(s) + 1 <= __gmpfr_emax)
                MPFR_SET_EXP (s, MPFR_EXP(s) + 1);
              else /* overflow */
                return mpfr_overflow (s, rnd_mode, MPFR_SIGN(s));
            }
          MPFR_RET(MPFR_SIGN(s));
        }
    }

  /* general case PREC(s) >= GMP_NUMB_BITS */
  inex2 = mpfr_set (s, u, rnd_mode);
  return (rnd_mode != MPFR_RNDN) ? inex | inex2
    : (inex2) ? inex2 : inex;
}