lib/printf-frexp.c

   1 /* Split a double into fraction and mantissa, for hexadecimal printf.
   2    Copyright (C) 2007, 2009-2017 Free Software Foundation, Inc.
   3
   4    This program is free software: you can redistribute it and/or modify
   5    it under the terms of the GNU General Public License as published by
   6    the Free Software Foundation; either version 3 of the License, or
   7    (at your option) any later version.
   8
   9    This program is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12    GNU General Public License for more details.
  13
  14    You should have received a copy of the GNU General Public License
  15    along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
  16
  17 #if ! defined USE_LONG_DOUBLE
  18 # include <config.h>
  19 #endif
  20
  21 /* Specification.  */
  22 #ifdef USE_LONG_DOUBLE
  23 # include "printf-frexpl.h"
  24 #else
  25 # include "printf-frexp.h"
  26 #endif
  27
  28 #include <float.h>
  29 #include <math.h>
  30 #ifdef USE_LONG_DOUBLE
  31 # include "fpucw.h"
  32 #endif
  33
  34 /* This file assumes FLT_RADIX = 2.  If FLT_RADIX is a power of 2 greater
  35    than 2, or not even a power of 2, some rounding errors can occur, so that
  36    then the returned mantissa is only guaranteed to be <= 2.0, not < 2.0.  */
  37
  38 #ifdef USE_LONG_DOUBLE
  39 # define FUNC printf_frexpl
  40 # define DOUBLE long double
  41 # define MIN_EXP LDBL_MIN_EXP
  42 # if HAVE_FREXPL_IN_LIBC && HAVE_LDEXPL_IN_LIBC
  43 #  define USE_FREXP_LDEXP
  44 #  define FREXP frexpl
  45 #  define LDEXP ldexpl
  46 # endif
  47 # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
  48 # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
  49 # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
  50 # define L_(literal) literal##L
  51 #else
  52 # define FUNC printf_frexp
  53 # define DOUBLE double
  54 # define MIN_EXP DBL_MIN_EXP
  55 # if HAVE_FREXP_IN_LIBC && HAVE_LDEXP_IN_LIBC
  56 #  define USE_FREXP_LDEXP
  57 #  define FREXP frexp
  58 #  define LDEXP ldexp
  59 # endif
  60 # define DECL_ROUNDING
  61 # define BEGIN_ROUNDING()
  62 # define END_ROUNDING()
  63 # define L_(literal) literal
  64 #endif
  65
  66 DOUBLE
  67 FUNC (DOUBLE x, int *expptr)
  68 {
  69   int exponent;
  70   DECL_ROUNDING
  71
  72   BEGIN_ROUNDING ();
  73
  74 #ifdef USE_FREXP_LDEXP
  75   /* frexp and ldexp are usually faster than the loop below.  */
  76   x = FREXP (x, &exponent);
  77
  78   x = x + x;
  79   exponent -= 1;
  80
  81   if (exponent < MIN_EXP - 1)
  82     {
  83       x = LDEXP (x, exponent - (MIN_EXP - 1));
  84       exponent = MIN_EXP - 1;
  85     }
  86 #else
  87   {
  88     /* Since the exponent is an 'int', it fits in 64 bits.  Therefore the
  89        loops are executed no more than 64 times.  */
  90     DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
  91     DOUBLE powh[64]; /* powh[i] = 2^-2^i */
  92     int i;
  93
  94     exponent = 0;
  95     if (x >= L_(1.0))
  96       {
  97         /* A nonnegative exponent.  */
  98         {
  99           DOUBLE pow2_i; /* = pow2[i] */
 100           DOUBLE powh_i; /* = powh[i] */
 101
 102           /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
 103              x * 2^exponent = argument, x >= 1.0.  */
 104           for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
 105                ;
 106                i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
 107             {
 108               if (x >= pow2_i)
 109                 {
 110                   exponent += (1 << i);
 111                   x *= powh_i;
 112                 }
 113               else
 114                 break;
 115
 116               pow2[i] = pow2_i;
 117               powh[i] = powh_i;
 118             }
 119         }
 120         /* Here 1.0 <= x < 2^2^i.  */
 121       }
 122     else
 123       {
 124         /* A negative exponent.  */
 125         {
 126           DOUBLE pow2_i; /* = pow2[i] */
 127           DOUBLE powh_i; /* = powh[i] */
 128
 129           /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
 130              x * 2^exponent = argument, x < 1.0, exponent >= MIN_EXP - 1.  */
 131           for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
 132                ;
 133                i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
 134             {
 135               if (exponent - (1 << i) < MIN_EXP - 1)
 136                 break;
 137
 138               exponent -= (1 << i);
 139               x *= pow2_i;
 140               if (x >= L_(1.0))
 141                 break;
 142
 143               pow2[i] = pow2_i;
 144               powh[i] = powh_i;
 145             }
 146         }
 147         /* Here either x < 1.0 and exponent - 2^i < MIN_EXP - 1 <= exponent,
 148            or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
 149
 150         if (x < L_(1.0))
 151           /* Invariants: x * 2^exponent = argument, x < 1.0 and
 152              exponent - 2^i < MIN_EXP - 1 <= exponent.  */
 153           while (i > 0)
 154             {
 155               i--;
 156               if (exponent - (1 << i) >= MIN_EXP - 1)
 157                 {
 158                   exponent -= (1 << i);
 159                   x *= pow2[i];
 160                   if (x >= L_(1.0))
 161                     break;
 162                 }
 163             }
 164
 165         /* Here either x < 1.0 and exponent = MIN_EXP - 1,
 166            or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
 167       }
 168
 169     /* Invariants: x * 2^exponent = argument, and
 170        either x < 1.0 and exponent = MIN_EXP - 1,
 171        or 1.0 <= x < 2^2^i and exponent >= MIN_EXP - 1.  */
 172     while (i > 0)
 173       {
 174         i--;
 175         if (x >= pow2[i])
 176           {
 177             exponent += (1 << i);
 178             x *= powh[i];
 179           }
 180       }
 181     /* Here either x < 1.0 and exponent = MIN_EXP - 1,
 182        or 1.0 <= x < 2.0 and exponent >= MIN_EXP - 1.  */
 183   }
 184 #endif
 185
 186   END_ROUNDING ();
 187
 188   *expptr = exponent;
 189   return x;
 190 }