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/* mpfr_get_flt -- convert a mpfr_t to a machine single precision float
Copyright 2009 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> /* for FLT_MIN */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
#include "ieee_floats.h"
#define FLT_NEG_ZERO ((float) DBL_NEG_ZERO)
#define MPFR_FLT_INFM ((float) MPFR_DBL_INFM)
#define MPFR_FLT_INFP ((float) MPFR_DBL_INFP)
float
mpfr_get_flt (mpfr_srcptr src, mpfr_rnd_t rnd_mode)
{
int negative;
mp_exp_t e;
float d;
/* in case of NaN, +Inf, -Inf, +0, -0, the conversion from double to float
is exact */
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
return (float) mpfr_get_d (src, rnd_mode);
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 positive normal float number is 2^(-126) = 0.5*2^(-125),
and the smallest positive subnormal number is 2^(-149) = 0.5*2^(-148) */
if (MPFR_UNLIKELY (e < -148))
{
/* |src| < 2^(-149), i.e., |src| is smaller than the smallest positive
subnormal number.
In round-to-nearest mode, 2^(-150) is rounded to zero.
*/
d = negative ?
(rnd_mode == MPFR_RNDD ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, -1, -150) < 0)
? -FLT_MIN : FLT_NEG_ZERO) :
(rnd_mode == MPFR_RNDU ||
(rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, 1, -150) > 0)
? FLT_MIN : 0.0);
if (d != 0.0) /* we multiply FLT_MIN = 2^(-126) by FLT_EPSILON = 2^(-23)
to get +-2^(-149) */
d *= FLT_EPSILON;
}
/* the largest normal number is 2^128*(1-2^(-24)) = 0.111...111e128 */
else if (MPFR_UNLIKELY (e > 128))
{
d = negative ?
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ?
-FLT_MAX : MPFR_FLT_INFM) :
(rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ?
FLT_MAX : MPFR_FLT_INFP);
}
else /* -148 <= e <= 127 */
{
int nbits;
mp_size_t np, i;
mp_limb_t tp[MPFR_LIMBS_PER_FLT];
int carry;
double dd;
nbits = IEEE_FLT_MANT_DIG; /* 24 */
if (MPFR_UNLIKELY (e < -125))
/*In the subnormal case, compute the exact number of significant bits*/
{
nbits += (125 + e);
MPFR_ASSERTD (nbits >= 1);
}
np = (nbits + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
MPFR_ASSERTD(np <= MPFR_LIMBS_PER_FLT);
carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative,
nbits, rnd_mode);
/* we perform the reconstruction using the 'double' type here,
knowing the result is exactly representable as 'float' */
if (MPFR_UNLIKELY(carry))
dd = 1.0;
else
{
/* The following computations are exact thanks to the previous
mpfr_round_raw. */
dd = (double) tp[0] / MP_BASE_AS_DOUBLE;
for (i = 1 ; i < np ; i++)
dd = (dd + tp[i]) / MP_BASE_AS_DOUBLE;
/* dd is the mantissa (between 1/2 and 1) of the argument rounded
to 24 bits */
}
dd = mpfr_scale2 (dd, e);
if (negative)
dd = -dd;
/* convert (exacly) to float */
d = (float) dd;
}
return d;
}
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