1 /* Split a double into fraction and mantissa.
2 Copyright (C) 2007-2023 Free Software Foundation, Inc.
3
4 This file is free software: you can redistribute it and/or modify
5 it under the terms of the GNU Lesser General Public License as
6 published by the Free Software Foundation; either version 2.1 of the
7 License, or (at your option) any later version.
8
9 This file 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 <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
57 DOUBLE
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 }