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1 | /* Complex square root of double value. |
2 | Copyright (C) 1997-2016 Free Software Foundation, Inc. | |
3 | This file is part of the GNU C Library. | |
4 | Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>. | |
5 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. | |
6 | ||
7 | The GNU C Library is free software; you can redistribute it and/or | |
8 | modify it under the terms of the GNU Lesser General Public | |
9 | License as published by the Free Software Foundation; either | |
10 | version 2.1 of the License, or (at your option) any later version. | |
11 | ||
12 | The GNU C Library is distributed in the hope that it will be useful, | |
13 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
15 | Lesser General Public License for more details. | |
16 | ||
17 | You should have received a copy of the GNU Lesser General Public | |
18 | License along with the GNU C Library; if not, see | |
19 | <http://www.gnu.org/licenses/>. */ | |
20 | ||
21 | #include <complex.h> | |
22 | #include <math.h> | |
23 | #include <math_private.h> | |
24 | #include <float.h> | |
25 | ||
26 | __complex__ double | |
27 | __csqrt (__complex__ double x) | |
28 | { | |
29 | __complex__ double res; | |
30 | int rcls = fpclassify (__real__ x); | |
31 | int icls = fpclassify (__imag__ x); | |
32 | ||
33 | if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) | |
34 | { | |
35 | if (icls == FP_INFINITE) | |
36 | { | |
37 | __real__ res = HUGE_VAL; | |
38 | __imag__ res = __imag__ x; | |
39 | } | |
40 | else if (rcls == FP_INFINITE) | |
41 | { | |
42 | if (__real__ x < 0.0) | |
43 | { | |
44 | __real__ res = icls == FP_NAN ? __nan ("") : 0; | |
45 | __imag__ res = __copysign (HUGE_VAL, __imag__ x); | |
46 | } | |
47 | else | |
48 | { | |
49 | __real__ res = __real__ x; | |
50 | __imag__ res = (icls == FP_NAN | |
51 | ? __nan ("") : __copysign (0.0, __imag__ x)); | |
52 | } | |
53 | } | |
54 | else | |
55 | { | |
56 | __real__ res = __nan (""); | |
57 | __imag__ res = __nan (""); | |
58 | } | |
59 | } | |
60 | else | |
61 | { | |
62 | if (__glibc_unlikely (icls == FP_ZERO)) | |
63 | { | |
64 | if (__real__ x < 0.0) | |
65 | { | |
66 | __real__ res = 0.0; | |
67 | __imag__ res = __copysign (__ieee754_sqrt (-__real__ x), | |
68 | __imag__ x); | |
69 | } | |
70 | else | |
71 | { | |
72 | __real__ res = fabs (__ieee754_sqrt (__real__ x)); | |
73 | __imag__ res = __copysign (0.0, __imag__ x); | |
74 | } | |
75 | } | |
76 | else if (__glibc_unlikely (rcls == FP_ZERO)) | |
77 | { | |
78 | double r; | |
79 | if (fabs (__imag__ x) >= 2.0 * DBL_MIN) | |
80 | r = __ieee754_sqrt (0.5 * fabs (__imag__ x)); | |
81 | else | |
82 | r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x)); | |
83 | ||
84 | __real__ res = r; | |
85 | __imag__ res = __copysign (r, __imag__ x); | |
86 | } | |
87 | else | |
88 | { | |
89 | double d, r, s; | |
90 | int scale = 0; | |
91 | ||
92 | if (fabs (__real__ x) > DBL_MAX / 4.0) | |
93 | { | |
94 | scale = 1; | |
95 | __real__ x = __scalbn (__real__ x, -2 * scale); | |
96 | __imag__ x = __scalbn (__imag__ x, -2 * scale); | |
97 | } | |
98 | else if (fabs (__imag__ x) > DBL_MAX / 4.0) | |
99 | { | |
100 | scale = 1; | |
101 | if (fabs (__real__ x) >= 4.0 * DBL_MIN) | |
102 | __real__ x = __scalbn (__real__ x, -2 * scale); | |
103 | else | |
104 | __real__ x = 0.0; | |
105 | __imag__ x = __scalbn (__imag__ x, -2 * scale); | |
106 | } | |
107 | else if (fabs (__real__ x) < 2.0 * DBL_MIN | |
108 | && fabs (__imag__ x) < 2.0 * DBL_MIN) | |
109 | { | |
110 | scale = -((DBL_MANT_DIG + 1) / 2); | |
111 | __real__ x = __scalbn (__real__ x, -2 * scale); | |
112 | __imag__ x = __scalbn (__imag__ x, -2 * scale); | |
113 | } | |
114 | ||
115 | d = __ieee754_hypot (__real__ x, __imag__ x); | |
116 | /* Use the identity 2 Re res Im res = Im x | |
117 | to avoid cancellation error in d +/- Re x. */ | |
118 | if (__real__ x > 0) | |
119 | { | |
120 | r = __ieee754_sqrt (0.5 * (d + __real__ x)); | |
121 | if (scale == 1 && fabs (__imag__ x) < 1.0) | |
122 | { | |
123 | /* Avoid possible intermediate underflow. */ | |
124 | s = __imag__ x / r; | |
125 | r = __scalbn (r, scale); | |
126 | scale = 0; | |
127 | } | |
128 | else | |
129 | s = 0.5 * (__imag__ x / r); | |
130 | } | |
131 | else | |
132 | { | |
133 | s = __ieee754_sqrt (0.5 * (d - __real__ x)); | |
134 | if (scale == 1 && fabs (__imag__ x) < 1.0) | |
135 | { | |
136 | /* Avoid possible intermediate underflow. */ | |
137 | r = fabs (__imag__ x / s); | |
138 | s = __scalbn (s, scale); | |
139 | scale = 0; | |
140 | } | |
141 | else | |
142 | r = fabs (0.5 * (__imag__ x / s)); | |
143 | } | |
144 | ||
145 | if (scale) | |
146 | { | |
147 | r = __scalbn (r, scale); | |
148 | s = __scalbn (s, scale); | |
149 | } | |
150 | ||
151 | math_check_force_underflow (r); | |
152 | math_check_force_underflow (s); | |
153 | ||
154 | __real__ res = r; | |
155 | __imag__ res = __copysign (s, __imag__ x); | |
156 | } | |
157 | } | |
158 | ||
159 | return res; | |
160 | } | |
161 | weak_alias (__csqrt, csqrt) | |
162 | #ifdef NO_LONG_DOUBLE | |
163 | strong_alias (__csqrt, __csqrtl) | |
164 | weak_alias (__csqrt, csqrtl) | |
165 | #endif |