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88b48903 | 1 | /* Split a double into fraction and mantissa. |
4a626d0a | 2 | Copyright (C) 2007-2015 Free Software Foundation, Inc. |
88b48903 WN |
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 | |
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 | } |