1/* Complex square root of __float128 value.
2 Copyright (C) 1997-2012 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 "quadmath-imp.h"
22
23#ifdef HAVE_FENV_H
24# include <fenv.h>
25#endif
26
27
28__complex128
29csqrtq (__complex128 x)
30{
31 __complex128 res;
32 int rcls = fpclassifyq (__real__ x);
33 int icls = fpclassifyq (__imag__ x);
34
35 if (__builtin_expect (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE, 0))
36 {
37 if (icls == QUADFP_INFINITE)
38 {
39 __real__ res = HUGE_VALQ;
40 __imag__ res = __imag__ x;
41 }
42 else if (rcls == QUADFP_INFINITE)
43 {
44 if (__real__ x < 0.0Q)
45 {
46 __real__ res = icls == QUADFP_NAN ? nanq ("") : 0;
47 __imag__ res = copysignq (HUGE_VALQ, __imag__ x);
48 }
49 else
50 {
51 __real__ res = __real__ x;
52 __imag__ res = (icls == QUADFP_NAN
53 ? nanq ("") : copysignq (0.0Q, __imag__ x));
54 }
55 }
56 else
57 {
58 __real__ res = nanq ("");
59 __imag__ res = nanq ("");
60 }
61 }
62 else
63 {
64 if (__builtin_expect (icls == QUADFP_ZERO, 0))
65 {
66 if (__real__ x < 0.0Q)
67 {
68 __real__ res = 0.0Q;
69 __imag__ res = copysignq (sqrtq (-__real__ x),
70 __imag__ x);
71 }
72 else
73 {
74 __real__ res = fabsq (sqrtq (__real__ x));
75 __imag__ res = copysignq (0.0Q, __imag__ x);
76 }
77 }
78 else if (__builtin_expect (rcls == QUADFP_ZERO, 0))
79 {
80 __float128 r;
81 if (fabsq (__imag__ x) >= 2.0Q * FLT128_MIN)
82 r = sqrtq (0.5Q * fabsq (__imag__ x));
83 else
84 r = 0.5Q * sqrtq (2.0Q * fabsq (__imag__ x));
85
86 __real__ res = r;
87 __imag__ res = copysignq (r, __imag__ x);
88 }
89 else
90 {
91 __float128 d, r, s;
92 int scale = 0;
93
94 if (fabsq (__real__ x) > FLT128_MAX / 4.0Q)
95 {
96 scale = 1;
97 __real__ x = scalbnq (__real__ x, -2 * scale);
98 __imag__ x = scalbnq (__imag__ x, -2 * scale);
99 }
100 else if (fabsq (__imag__ x) > FLT128_MAX / 4.0Q)
101 {
102 scale = 1;
103 if (fabsq (__real__ x) >= 4.0Q * FLT128_MIN)
104 __real__ x = scalbnq (__real__ x, -2 * scale);
105 else
106 __real__ x = 0.0Q;
107 __imag__ x = scalbnq (__imag__ x, -2 * scale);
108 }
109 else if (fabsq (__real__ x) < FLT128_MIN
110 && fabsq (__imag__ x) < FLT128_MIN)
111 {
112 scale = -(FLT128_MANT_DIG / 2);
113 __real__ x = scalbnq (__real__ x, -2 * scale);
114 __imag__ x = scalbnq (__imag__ x, -2 * scale);
115 }
116
117 d = hypotq (__real__ x, __imag__ x);
118 /* Use the identity 2 Re res Im res = Im x
119 to avoid cancellation error in d +/- Re x. */
120 if (__real__ x > 0)
121 {
122 r = sqrtq (0.5Q * (d + __real__ x));
123 s = 0.5Q * (__imag__ x / r);
124 }
125 else
126 {
127 s = sqrtq (0.5Q * (d - __real__ x));
128 r = fabsq (0.5Q * (__imag__ x / s));
129 }
130
131 if (scale)
132 {
133 r = scalbnq (r, scale);
134 s = scalbnq (s, scale);
135 }
136
137 __real__ res = r;
138 __imag__ res = copysignq (s, __imag__ x);
139 }
140 }
141
142 return res;
143}
144