source/libs/mpfr/mpfr-3.1.3/src/get_flt.c

   1 /* mpfr_get_flt -- convert a mpfr_t to a machine single precision float
   2
   3 Copyright 2009-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  22
  23 #include <float.h>     /* for FLT_MIN */
  24
  25 #define MPFR_NEED_LONGLONG_H
  26 #include "mpfr-impl.h"
  27
  28 #include "ieee_floats.h"
  29
  30 #define FLT_NEG_ZERO ((float) DBL_NEG_ZERO)
  31 #define MPFR_FLT_INFM ((float) MPFR_DBL_INFM)
  32 #define MPFR_FLT_INFP ((float) MPFR_DBL_INFP)
  33
  34 float
  35 mpfr_get_flt (mpfr_srcptr src, mpfr_rnd_t rnd_mode)
  36 {
  37   int negative;
  38   mpfr_exp_t e;
  39   float d;
  40
  41   /* in case of NaN, +Inf, -Inf, +0, -0, the conversion from double to float
  42      is exact */
  43   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
  44     return (float) mpfr_get_d (src, rnd_mode);
  45
  46   e = MPFR_GET_EXP (src);
  47   negative = MPFR_IS_NEG (src);
  48
  49   if (MPFR_UNLIKELY(rnd_mode == MPFR_RNDA))
  50     rnd_mode = negative ? MPFR_RNDD : MPFR_RNDU;
  51
  52   /* the smallest positive normal float number is 2^(-126) = 0.5*2^(-125),
  53      and the smallest positive subnormal number is 2^(-149) = 0.5*2^(-148) */
  54   if (MPFR_UNLIKELY (e < -148))
  55     {
  56       /* |src| < 2^(-149), i.e., |src| is smaller than the smallest positive
  57          subnormal number.
  58          In round-to-nearest mode, 2^(-150) is rounded to zero.
  59       */
  60       d = negative ?
  61         (rnd_mode == MPFR_RNDD ||
  62          (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, -1, -150) < 0)
  63          ? -FLT_MIN : FLT_NEG_ZERO) :
  64         (rnd_mode == MPFR_RNDU ||
  65          (rnd_mode == MPFR_RNDN && mpfr_cmp_si_2exp (src, 1, -150) > 0)
  66          ? FLT_MIN : 0.0);
  67       if (d != 0.0) /* we multiply FLT_MIN = 2^(-126) by FLT_EPSILON = 2^(-23)
  68                        to get +-2^(-149) */
  69         d *= FLT_EPSILON;
  70     }
  71   /* the largest normal number is 2^128*(1-2^(-24)) = 0.111...111e128 */
  72   else if (MPFR_UNLIKELY (e > 128))
  73     {
  74       d = negative ?
  75         (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDU ?
  76          -FLT_MAX : MPFR_FLT_INFM) :
  77         (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD ?
  78          FLT_MAX : MPFR_FLT_INFP);
  79     }
  80   else /* -148 <= e <= 127 */
  81     {
  82       int nbits;
  83       mp_size_t np, i;
  84       mp_limb_t tp[MPFR_LIMBS_PER_FLT];
  85       int carry;
  86       double dd;
  87
  88       nbits = IEEE_FLT_MANT_DIG; /* 24 */
  89       if (MPFR_UNLIKELY (e < -125))
  90         /*In the subnormal case, compute the exact number of significant bits*/
  91         {
  92           nbits += (125 + e);
  93           MPFR_ASSERTD (nbits >= 1);
  94         }
  95       np = MPFR_PREC2LIMBS (nbits);
  96       MPFR_ASSERTD(np <= MPFR_LIMBS_PER_FLT);
  97       carry = mpfr_round_raw_4 (tp, MPFR_MANT(src), MPFR_PREC(src), negative,
  98                                 nbits, rnd_mode);
  99       /* we perform the reconstruction using the 'double' type here,
 100          knowing the result is exactly representable as 'float' */
 101       if (MPFR_UNLIKELY(carry))
 102         dd = 1.0;
 103       else
 104         {
 105           /* The following computations are exact thanks to the previous
 106              mpfr_round_raw. */
 107           dd = (double) tp[0] / MP_BASE_AS_DOUBLE;
 108           for (i = 1 ; i < np ; i++)
 109             dd = (dd + tp[i]) / MP_BASE_AS_DOUBLE;
 110           /* dd is the mantissa (between 1/2 and 1) of the argument rounded
 111              to 24 bits */
 112         }
 113       dd = mpfr_scale2 (dd, e);
 114       if (negative)
 115         dd = -dd;
 116
 117       /* convert (exacly) to float */
 118       d = (float) dd;
 119     }
 120
 121   return d;
 122 }
 123