lib/frexp.c

   1 /* Split a double into fraction and mantissa.
   2    Copyright (C) 2007-2011 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 Lesser 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 Lesser General Public License for more details.
  13
  14    You should have received a copy of the GNU Lesser General Public License
  15    along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
  16
  17 /* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and
  18    Bruno Haible <bruno@clisp.org>, 2007.  */
  19
  20 #include <config.h>
  21
  22 /* Specification.  */
  23 #include <math.h>
  24
  25 #include <float.h>
  26 #ifdef USE_LONG_DOUBLE
  27 # include "isnanl-nolibm.h"
  28 # include "fpucw.h"
  29 #else
  30 # include "isnand-nolibm.h"
  31 #endif
  32
  33 /* This file assumes FLT_RADIX = 2.  If FLT_RADIX is a power of 2 greater
  34    than 2, or not even a power of 2, some rounding errors can occur, so that
  35    then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0.  */
  36
  37 #ifdef USE_LONG_DOUBLE
  38 # define FUNC frexpl
  39 # define DOUBLE long double
  40 # define ISNAN isnanl
  41 # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
  42 # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
  43 # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
  44 # define L_(literal) literal##L
  45 #else
  46 # define FUNC frexp
  47 # define DOUBLE double
  48 # define ISNAN isnand
  49 # define DECL_ROUNDING
  50 # define BEGIN_ROUNDING()
  51 # define END_ROUNDING()
  52 # define L_(literal) literal
  53 #endif
  54
  55 DOUBLE
  56 FUNC (DOUBLE x, int *expptr)
  57 {
  58   int sign;
  59   int exponent;
  60   DECL_ROUNDING
  61
  62   /* Test for NaN, infinity, and zero.  */
  63   if (ISNAN (x) || x + x == x)
  64     {
  65       *expptr = 0;
  66       return x;
  67     }
  68
  69   sign = 0;
  70   if (x < 0)
  71     {
  72       x = - x;
  73       sign = -1;
  74     }
  75
  76   BEGIN_ROUNDING ();
  77
  78   {
  79     /* Since the exponent is an 'int', it fits in 64 bits.  Therefore the
  80        loops are executed no more than 64 times.  */
  81     DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
  82     DOUBLE powh[64]; /* powh[i] = 2^-2^i */
  83     int i;
  84
  85     exponent = 0;
  86     if (x >= L_(1.0))
  87       {
  88         /* A positive exponent.  */
  89         DOUBLE pow2_i; /* = pow2[i] */
  90         DOUBLE powh_i; /* = powh[i] */
  91
  92         /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
  93            x * 2^exponent = argument, x >= 1.0.  */
  94         for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
  95              ;
  96              i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
  97           {
  98             if (x >= pow2_i)
  99               {
 100                 exponent += (1 << i);
 101                 x *= powh_i;
 102               }
 103             else
 104               break;
 105
 106             pow2[i] = pow2_i;
 107             powh[i] = powh_i;
 108           }
 109         /* Avoid making x too small, as it could become a denormalized
 110            number and thus lose precision.  */
 111         while (i > 0 && x < pow2[i - 1])
 112           {
 113             i--;
 114             powh_i = powh[i];
 115           }
 116         exponent += (1 << i);
 117         x *= powh_i;
 118         /* Here 2^-2^i <= x < 1.0.  */
 119       }
 120     else
 121       {
 122         /* A negative or zero exponent.  */
 123         DOUBLE pow2_i; /* = pow2[i] */
 124         DOUBLE powh_i; /* = powh[i] */
 125
 126         /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
 127            x * 2^exponent = argument, x < 1.0.  */
 128         for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
 129              ;
 130              i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
 131           {
 132             if (x < powh_i)
 133               {
 134                 exponent -= (1 << i);
 135                 x *= pow2_i;
 136               }
 137             else
 138               break;
 139
 140             pow2[i] = pow2_i;
 141             powh[i] = powh_i;
 142           }
 143         /* Here 2^-2^i <= x < 1.0.  */
 144       }
 145
 146     /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0.  */
 147     while (i > 0)
 148       {
 149         i--;
 150         if (x < powh[i])
 151           {
 152             exponent -= (1 << i);
 153             x *= pow2[i];
 154           }
 155       }
 156     /* Here 0.5 <= x < 1.0.  */
 157   }
 158
 159   if (sign < 0)
 160     x = - x;
 161
 162   END_ROUNDING ();
 163
 164   *expptr = exponent;
 165   return x;
 166 }