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/* mpfr_get_d -- convert a multiple precision floating-point number
to a machine double precision float
Copyright 1999, 2000, 2001, 2002, 2003 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>
#ifndef NO_MATH_DEFS
#include <math.h>
#endif
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
#include "mpfr-math.h"
static double mpfr_scale2 _PROTO ((double, int));
#define IEEE_DBL_MANT_DIG 53
/* 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 (d == 1.0)
{
d = 0.5;
exp ++;
}
/* now 1/2 <= d < 1 */
/* infinities and zeroes have already been checked */
MPFR_ASSERTN(-1073 <= exp && exp <= 1025);
x.d = d;
if (exp < -1021) /* subnormal case */
{
x.s.exp += exp + 52;
x.d *= DBL_EPSILON;
}
else /* normalized case */
{
x.s.exp += exp;
}
return x.d;
}
#else
{
double factor;
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_d3 (mpfr_srcptr src, mp_exp_t e, mp_rnd_t rnd_mode)
{
double d;
int negative;
if (MPFR_IS_NAN(src))
return MPFR_DBL_NAN;
negative = MPFR_SIGN(src) < 0;
if (MPFR_IS_INF(src))
return negative ? MPFR_DBL_INFM : MPFR_DBL_INFP;
if (MPFR_IS_ZERO(src))
return negative ? -0.0 : 0.0;
/* the smallest normalized number is 2^(-1022)=0.1e-1021, and the smallest
subnormal is 2^(-1074)=0.1e-1073 */
if (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 (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_ptr tp;
int carry;
nbits = IEEE_DBL_MANT_DIG; /* 53 */
if (e < -1021) /* in the subnormal case, compute the exact number of
significant bits */
{
nbits += (1021 + e);
MPFR_ASSERTN(nbits >= 1);
}
np = (nbits - 1) / BITS_PER_MP_LIMB;
tp = (mp_ptr) (*__gmp_allocate_func) ((np + 1) * BYTES_PER_MP_LIMB);
carry = mpfr_round_raw (tp, MPFR_MANT(src), MPFR_PREC(src), negative,
nbits, rnd_mode, (int *) 0);
if (carry)
d = 1.0;
else
{
/* Warning: the rounding may still be incorrect in the rounding
to the nearest mode when the result is a subnormal because of
a double rounding (-> 53 bits -> final precision). */
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;
(*__gmp_free_func) (tp, (np + 1) * BYTES_PER_MP_LIMB);
}
return d;
}
/* Note: do not read the exponent if it has no meaning (avoid possible
traps on some implementations). */
double
mpfr_get_d (mpfr_srcptr src, mp_rnd_t rnd_mode)
{
return mpfr_get_d3 (src, MPFR_IS_FP(src) && MPFR_NOTZERO(src) ?
MPFR_EXP(src) : 0, rnd_mode);
}
double
mpfr_get_d1 (mpfr_srcptr src)
{
return mpfr_get_d3 (src, MPFR_IS_FP(src) && MPFR_NOTZERO(src) ?
MPFR_EXP(src) : 0, __gmpfr_default_rounding_mode);
}
double
mpfr_get_d_2exp (mp_exp_t *exp, mpfr_srcptr src, mp_rnd_t rnd_mode)
{
*exp = MPFR_EXP (src);
return mpfr_get_d3 (src, 0, rnd_mode);
}
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