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/* mpfr_get_d, mpfr_get_d_2exp -- convert a multiple precision floating-point
number to a machine double precision float
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao 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 <float.h>
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
#include "ieee_floats.h"
/* 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, mpfr_rnd_t rnd_mode)
{
double d;
int negative;
mpfr_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 ? DBL_NEG_ZERO : 0.0;
}
e = MPFR_GET_EXP (src);
negative = MPFR_IS_NEG (src);
if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA))
rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU;
/* 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 == MPFR_RNDD ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp(src, -1, -1075) < 0)
? -DBL_MIN : DBL_NEG_ZERO) :
(rnd_mode == MPFR_RNDU ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp(src, 1, -1075) > 0)
? DBL_MIN : 0.0);
if (d != 0.0) /* we multiply DBL_MIN = 2^(-1022) by DBL_EPSILON = 2^(-52)
to get +-2^(-1074) */
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 == MPFR_RNDZ || rnd_mode == MPFR_RNDU ?
-DBL_MAX : MPFR_DBL_INFM) :
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_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 + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
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, mpfr_rnd_t rnd_mode)
{
double ret;
mpfr_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 ? DBL_NEG_ZERO : 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;
}
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