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1 /* Split a double into fraction and mantissa.
2    Copyright (C) 2007-2012 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 /* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and
18    Bruno Haible <bruno@clisp.org>, 2007.  */
19 
20 #if ! defined USE_LONG_DOUBLE
21 # include <config.h>
22 #endif
23 
24 /* Specification.  */
25 #include <math.h>
26 
27 #include <float.h>
28 #ifdef USE_LONG_DOUBLE
29 # include "isnanl-nolibm.h"
30 # include "fpucw.h"
31 #else
32 # include "isnand-nolibm.h"
33 #endif
34 
35 /* This file assumes FLT_RADIX = 2.  If FLT_RADIX is a power of 2 greater
36    than 2, or not even a power of 2, some rounding errors can occur, so that
37    then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0.  */
38 
39 #ifdef USE_LONG_DOUBLE
40 # define FUNC frexpl
41 # define DOUBLE long double
42 # define ISNAN isnanl
43 # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING
44 # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING ()
45 # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING ()
46 # define L_(literal) literal##L
47 #else
48 # define FUNC frexp
49 # define DOUBLE double
50 # define ISNAN isnand
51 # define DECL_ROUNDING
52 # define BEGIN_ROUNDING()
53 # define END_ROUNDING()
54 # define L_(literal) literal
55 #endif
56 
57 DOUBLE
FUNC(DOUBLE x,int * expptr)58 FUNC (DOUBLE x, int *expptr)
59 {
60   int sign;
61   int exponent;
62   DECL_ROUNDING
63 
64   /* Test for NaN, infinity, and zero.  */
65   if (ISNAN (x) || x + x == x)
66     {
67       *expptr = 0;
68       return x;
69     }
70 
71   sign = 0;
72   if (x < 0)
73     {
74       x = - x;
75       sign = -1;
76     }
77 
78   BEGIN_ROUNDING ();
79 
80   {
81     /* Since the exponent is an 'int', it fits in 64 bits.  Therefore the
82        loops are executed no more than 64 times.  */
83     DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
84     DOUBLE powh[64]; /* powh[i] = 2^-2^i */
85     int i;
86 
87     exponent = 0;
88     if (x >= L_(1.0))
89       {
90         /* A positive exponent.  */
91         DOUBLE pow2_i; /* = pow2[i] */
92         DOUBLE powh_i; /* = powh[i] */
93 
94         /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
95            x * 2^exponent = argument, x >= 1.0.  */
96         for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
97              ;
98              i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
99           {
100             if (x >= pow2_i)
101               {
102                 exponent += (1 << i);
103                 x *= powh_i;
104               }
105             else
106               break;
107 
108             pow2[i] = pow2_i;
109             powh[i] = powh_i;
110           }
111         /* Avoid making x too small, as it could become a denormalized
112            number and thus lose precision.  */
113         while (i > 0 && x < pow2[i - 1])
114           {
115             i--;
116             powh_i = powh[i];
117           }
118         exponent += (1 << i);
119         x *= powh_i;
120         /* Here 2^-2^i <= x < 1.0.  */
121       }
122     else
123       {
124         /* A negative or zero exponent.  */
125         DOUBLE pow2_i; /* = pow2[i] */
126         DOUBLE powh_i; /* = powh[i] */
127 
128         /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
129            x * 2^exponent = argument, x < 1.0.  */
130         for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
131              ;
132              i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
133           {
134             if (x < powh_i)
135               {
136                 exponent -= (1 << i);
137                 x *= pow2_i;
138               }
139             else
140               break;
141 
142             pow2[i] = pow2_i;
143             powh[i] = powh_i;
144           }
145         /* Here 2^-2^i <= x < 1.0.  */
146       }
147 
148     /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0.  */
149     while (i > 0)
150       {
151         i--;
152         if (x < powh[i])
153           {
154             exponent -= (1 << i);
155             x *= pow2[i];
156           }
157       }
158     /* Here 0.5 <= x < 1.0.  */
159   }
160 
161   if (sign < 0)
162     x = - x;
163 
164   END_ROUNDING ();
165 
166   *expptr = exponent;
167   return x;
168 }
169