1/* Split a double into fraction and mantissa.
2   Copyright (C) 2007-2020 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 <https://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
57DOUBLE
58FUNC (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