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/* mpfr_get_flt -- convert a mpfr_t to a machine single precision float
Copyright 2009-2021 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
https://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;
mpfr_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)))
{
/* for NaN, we don't propagate the sign bit */
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;
/* FIXME: The code below assumes the IEEE-754 binary32 format
with subnormal support. Fix it by converting to double, then
to float, and in case of binary radix (for which we want
correct rounding), handle double-rounding issues somewhere
in the code? */
/* 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_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 (1 <= nbits && nbits < 24);
}
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
{
#if MPFR_LIMBS_PER_FLT == 1
dd = (double) tp[0] / MP_BASE_AS_DOUBLE;
#else
mp_size_t np, i;
np = MPFR_PREC2LIMBS (nbits);
MPFR_ASSERTD(np <= MPFR_LIMBS_PER_FLT);
/* 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 */
#endif
}
dd = mpfr_scale2 (dd, e);
if (negative)
dd = -dd;
/* convert (exactly) to float */
d = (float) dd;
}
return d;
}
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