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 |
166 | |