path: root/get_d.c

/* mpfr_get_d -- convert a multiple precision floating-point number
                 to a machine double precision float

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005 Free Software Foundation, Inc.

This file is part of the MPFR Library.

The 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 2.1 of the License, or (at your
option) any later version.

The 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 MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include <float.h>

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

/* "double" NaN and infinities are written as explicit bytes to be sure of
   getting what we want, and to be sure of not depending on libm.

   Could use 4-byte "float" values and let the code convert them, but it
   seems more direct to give exactly what we want.  Certainly for gcc 3.0.2
   on alphaev56-unknown-freebsd4.3 the NaN must be 8-bytes, since that
   compiler+system was seen incorrectly converting from a "float" NaN.  */

#if _GMP_IEEE_FLOATS

/* The "d" field guarantees alignment to a suitable boundary for a double.
   Could use a union instead, if we checked the compiler supports union
   initializers.  */
struct dbl_bytes {
  unsigned char b[8];
  double d;
};

#define MPFR_DBL_INFP  (* (const double *) dbl_infp.b)
#define MPFR_DBL_INFM  (* (const double *) dbl_infm.b)
#define MPFR_DBL_NAN   (* (const double *) dbl_nan.b)

#if HAVE_DOUBLE_IEEE_LITTLE_ENDIAN
static const struct dbl_bytes dbl_infp = 
  { { 0, 0, 0, 0, 0, 0, 0xF0, 0x7F }, 0.0 };
static const struct dbl_bytes dbl_infm = 
  { { 0, 0, 0, 0, 0, 0, 0xF0, 0xFF }, 0.0 };
static const struct dbl_bytes dbl_nan  = 
  { { 0, 0, 0, 0, 0, 0, 0xF8, 0x7F }, 0.0 };
#endif
#if HAVE_DOUBLE_IEEE_LITTLE_SWAPPED
static const struct dbl_bytes dbl_infp = 
  { { 0, 0, 0xF0, 0x7F, 0, 0, 0, 0 }, 0.0 };
static const struct dbl_bytes dbl_infm = 
  { { 0, 0, 0xF0, 0xFF, 0, 0, 0, 0 }, 0.0 };
static const struct dbl_bytes dbl_nan  = 
  { { 0, 0, 0xF8, 0x7F, 0, 0, 0, 0 }, 0.0 };
#endif
#if HAVE_DOUBLE_IEEE_BIG_ENDIAN
static const struct dbl_bytes dbl_infp = 
  { { 0x7F, 0xF0, 0, 0, 0, 0, 0, 0 }, 0.0 };
static const struct dbl_bytes dbl_infm = 
  { { 0xFF, 0xF0, 0, 0, 0, 0, 0, 0 }, 0.0 };
static const struct dbl_bytes dbl_nan  = 
  { { 0x7F, 0xF8, 0, 0, 0, 0, 0, 0 }, 0.0 };
#endif

#else /* _GMP_IEEE_FLOATS */

#define MPFR_DBL_INFP DBL_POS_INF
#define MPFR_DBL_INFM DBL_NEG_INF
#define MPFR_DBL_NAN DBL_NAN

#endif /* _GMP_IEEE_FLOATS */

 
/* multiplies 1/2 <= d <= 1 by 2^exp */
static double
mpfr_scale2 (double d, int exp)
{
#if _GMP_IEEE_FLOATS
  {
    union ieee_double_extract x;

    if (MPFR_UNLIKELY (d == 1.0))
      {
        d = 0.5;
        exp ++;
      }

    /* now 1/2 <= d < 1 */

    /* infinities and zeroes have already been checked */
    MPFR_ASSERTD (-1073 <= exp && exp <= 1025);

    x.d = d;
    if (MPFR_UNLIKELY (exp < -1021)) /* subnormal case */
      {
        x.s.exp += exp + 52;
        x.d *= DBL_EPSILON;
      }
    else /* normalized case */
      {
        x.s.exp += exp;
      }
    return x.d;
  }
#else /* _GMP_IEEE_FLOATS */
  {
    double factor;

    /* An overflow may occurs (example: 0.5*2^1024) */
    if (d < 1.0)
      {
	d += d;
	exp--;
      }
    /* Now 1.0 <= d < 2.0 */

    if (exp < 0)
      {
        factor = 0.5;
        exp = -exp;
      }
    else
      {
        factor = 2.0;
      }
    while (exp != 0)
      {
        if ((exp & 1) != 0)
          d *= factor;
        exp >>= 1;
        factor *= factor;
      }
    return d;
  }
#endif
}

/* Assumes IEEE-754 double precision; otherwise, only an approximated
   result will be returned, without any guaranty (and special cases
   such as NaN must be avoided if not supported). */

double
mpfr_get_d (mpfr_srcptr src, mp_rnd_t rnd_mode)
{
  double d;
  int negative;
  mp_exp_t e;

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
    {
      if (MPFR_IS_NAN (src))
	return MPFR_DBL_NAN;

      negative = MPFR_IS_NEG (src);
      
      if (MPFR_IS_INF (src))
	return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP;
      
      MPFR_ASSERTD (MPFR_IS_ZERO(src));
      return negative ? -0.0 : 0.0;
    }
  
  e = MPFR_GET_EXP (src);
  negative = MPFR_IS_NEG (src);
  
  /* the smallest normalized number is 2^(-1022)=0.1e-1021, and the smallest
     subnormal is 2^(-1074)=0.1e-1073 */
  if (MPFR_UNLIKELY (e < -1073))
    {
      /* Note: Avoid using a constant expression DBL_MIN * DBL_EPSILON
         as this gives 0 instead of the correct result with gcc on some
         Alpha machines. */
      d = negative ?
        (rnd_mode == GMP_RNDD ||
         (rnd_mode == GMP_RNDN && mpfr_cmp_si_2exp(src, -1, -1075) < 0)
         ? -DBL_MIN : -0.0) :
        (rnd_mode == GMP_RNDU ||
         (rnd_mode == GMP_RNDN && mpfr_cmp_si_2exp(src, 1, -1075) > 0)
         ? DBL_MIN : 0.0);
      if (d != 0.0)
        d *= DBL_EPSILON;
    }
  /* the largest normalized number is 2^1024*(1-2^(-53))=0.111...111e1024 */
  else if (MPFR_UNLIKELY (e > 1024))
    {
      d = negative ?
        (rnd_mode == GMP_RNDZ || rnd_mode == GMP_RNDU ?
         -DBL_MAX : MPFR_DBL_INFM) :
        (rnd_mode == GMP_RNDZ || rnd_mode == GMP_RNDD ?
         DBL_MAX : MPFR_DBL_INFP);
    }
  else
    {
      int nbits;
      mp_size_t np, i;
      mp_limb_t tp[ MPFR_LIMBS_PER_DOUBLE ];
      int carry;

      nbits = IEEE_DBL_MANT_DIG; /* 53 */
      if (MPFR_UNLIKELY (e < -1021))
	/*In the subnormal case, compute the exact number of significant bits*/
        {
          nbits += (1021 + e);
          MPFR_ASSERTD (nbits >= 1);
        }
      np = (nbits + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
      MPFR_ASSERTD ( np <= MPFR_LIMBS_PER_DOUBLE );
      carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative,
				nbits, rnd_mode);
      if (MPFR_UNLIKELY(carry))
        d = 1.0;
      else
        {
          /* The following computations are exact thanks to the previous
             mpfr_round_raw. */
          d = (double) tp[0] / MP_BASE_AS_DOUBLE;
          for (i = 1 ; i < np ; i++)
            d = (d + tp[i]) / MP_BASE_AS_DOUBLE;
          /* d is the mantissa (between 1/2 and 1) of the argument rounded
             to 53 bits */
        }
      d = mpfr_scale2 (d, e);
      if (negative)
        d = -d;
    }

  return d;
}

#undef mpfr_get_d1
double
mpfr_get_d1 (mpfr_srcptr src)
{
  return mpfr_get_d (src, __gmpfr_default_rounding_mode);
}

double
mpfr_get_d_2exp (long *expptr, mpfr_srcptr src, mp_rnd_t rnd_mode)
{
  double ret;
  mp_exp_t exp;
  mpfr_t tmp;

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
    {
      int negative;
      *expptr = 0;
      if (MPFR_IS_NAN (src))
        return MPFR_DBL_NAN;
      negative = MPFR_IS_NEG (src);
      if (MPFR_IS_INF (src))
        return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP;
      MPFR_ASSERTD (MPFR_IS_ZERO(src));
      return negative ? -0.0 : 0.0;
    }

  tmp[0] = *src;        /* Hack copy mpfr_t */
  MPFR_SET_EXP (tmp, 0);
  ret = mpfr_get_d (tmp, rnd_mode);

  if (MPFR_IS_PURE_FP(src))
    {
      exp = MPFR_GET_EXP (src);

      /* rounding can give 1.0, adjust back to 0.5 <= abs(ret) < 1.0 */
      if (ret == 1.0)
        {
          ret = 0.5;
          exp++;
        }
      else if (ret == -1.0)
        {
          ret = -0.5;
          exp++;
        }

      MPFR_ASSERTN ((ret >= 0.5 && ret < 1.0)
                    || (ret <= -0.5 && ret > -1.0));
      MPFR_ASSERTN (exp >= LONG_MIN && exp <= LONG_MAX);
    }
  else
    exp = 0;

  *expptr = exp;
  return ret;
}