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dd36ce77 MW |
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 | } |