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      1 /* mpfr_scale2 -- multiply a double float by 2^exp
      2 
      3 Copyright 1999-2023 Free Software Foundation, Inc.
      4 Contributed by the AriC and Caramba 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 https://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 DBL_EPSILON */
     24 #include "mpfr-impl.h"
     25 
     26 /* Note: we could use the ldexp function, but since we want not to depend on
     27    math.h, we write our own implementation. */
     28 
     29 /* multiplies 1/2 <= d <= 1 by 2^exp */
     30 double
     31 mpfr_scale2 (double d, int exp)
     32 {
     33 #if _MPFR_IEEE_FLOATS
     34   {
     35     union mpfr_ieee_double_extract x;
     36 
     37     if (MPFR_UNLIKELY (d == 1.0))
     38       {
     39         d = 0.5;
     40         exp ++;
     41       }
     42 
     43     /* now 1/2 <= d < 1 */
     44 
     45     /* infinities and zeroes have already been checked */
     46     MPFR_ASSERTD (-1073 <= exp && exp <= 1025);
     47 
     48     x.d = d;
     49     if (MPFR_UNLIKELY (exp < -1021)) /* subnormal case */
     50       {
     51         x.s.exp += exp + 52;
     52         x.d *= DBL_EPSILON;
     53       }
     54     else /* normalized case */
     55       {
     56         x.s.exp += exp;
     57       }
     58     return x.d;
     59   }
     60 #else /* _MPFR_IEEE_FLOATS */
     61   {
     62     double factor;
     63 
     64     /* An overflow may occurs (example: 0.5*2^1024) */
     65     if (d < 1.0)
     66       {
     67         d += d;
     68         exp--;
     69       }
     70     /* Now 1.0 <= d < 2.0 */
     71 
     72     if (exp < 0)
     73       {
     74         factor = 0.5;
     75         exp = -exp;
     76       }
     77     else
     78       {
     79         factor = 2.0;
     80       }
     81     while (exp != 0)
     82       {
     83         if ((exp & 1) != 0)
     84           d *= factor;
     85         exp >>= 1;
     86         factor *= factor;
     87       }
     88     return d;
     89   }
     90 #endif /* _MPFR_IEEE_FLOATS */
     91 }
     92