1/* Complex square root of a float type.
2 Copyright (C) 1997-2020 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 <https://www.gnu.org/licenses/>. */
20
21#include <complex.h>
22#include <math.h>
23#include <math_private.h>
24#include <math-underflow.h>
25#include <float.h>
26
27CFLOAT
28M_DECL_FUNC (__csqrt) (CFLOAT x)
29{
30 CFLOAT res;
31 int rcls = fpclassify (__real__ x);
32 int icls = fpclassify (__imag__ x);
33
34 if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
35 {
36 if (icls == FP_INFINITE)
37 {
38 __real__ res = M_HUGE_VAL;
39 __imag__ res = __imag__ x;
40 }
41 else if (rcls == FP_INFINITE)
42 {
43 if (__real__ x < 0)
44 {
45 __real__ res = icls == FP_NAN ? M_NAN : 0;
46 __imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
47 }
48 else
49 {
50 __real__ res = __real__ x;
51 __imag__ res = (icls == FP_NAN
52 ? M_NAN : M_COPYSIGN (0, __imag__ x));
53 }
54 }
55 else
56 {
57 __real__ res = M_NAN;
58 __imag__ res = M_NAN;
59 }
60 }
61 else
62 {
63 if (__glibc_unlikely (icls == FP_ZERO))
64 {
65 if (__real__ x < 0)
66 {
67 __real__ res = 0;
68 __imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);
69 }
70 else
71 {
72 __real__ res = M_FABS (M_SQRT (__real__ x));
73 __imag__ res = M_COPYSIGN (0, __imag__ x);
74 }
75 }
76 else if (__glibc_unlikely (rcls == FP_ZERO))
77 {
78 FLOAT r;
79 if (M_FABS (__imag__ x) >= 2 * M_MIN)
80 r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));
81 else
82 r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));
83
84 __real__ res = r;
85 __imag__ res = M_COPYSIGN (r, __imag__ x);
86 }
87 else
88 {
89 FLOAT d, r, s;
90 int scale = 0;
91
92 if (M_FABS (__real__ x) > M_MAX / 4)
93 {
94 scale = 1;
95 __real__ x = M_SCALBN (__real__ x, -2 * scale);
96 __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
97 }
98 else if (M_FABS (__imag__ x) > M_MAX / 4)
99 {
100 scale = 1;
101 if (M_FABS (__real__ x) >= 4 * M_MIN)
102 __real__ x = M_SCALBN (__real__ x, -2 * scale);
103 else
104 __real__ x = 0;
105 __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
106 }
107 else if (M_FABS (__real__ x) < 2 * M_MIN
108 && M_FABS (__imag__ x) < 2 * M_MIN)
109 {
110 scale = -((M_MANT_DIG + 1) / 2);
111 __real__ x = M_SCALBN (__real__ x, -2 * scale);
112 __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
113 }
114
115 d = M_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 = M_SQRT (M_LIT (0.5) * (d + __real__ x));
121 if (scale == 1 && M_FABS (__imag__ x) < 1)
122 {
123 /* Avoid possible intermediate underflow. */
124 s = __imag__ x / r;
125 r = M_SCALBN (r, scale);
126 scale = 0;
127 }
128 else
129 s = M_LIT (0.5) * (__imag__ x / r);
130 }
131 else
132 {
133 s = M_SQRT (M_LIT (0.5) * (d - __real__ x));
134 if (scale == 1 && M_FABS (__imag__ x) < 1)
135 {
136 /* Avoid possible intermediate underflow. */
137 r = M_FABS (__imag__ x / s);
138 s = M_SCALBN (s, scale);
139 scale = 0;
140 }
141 else
142 r = M_FABS (M_LIT (0.5) * (__imag__ x / s));
143 }
144
145 if (scale)
146 {
147 r = M_SCALBN (r, scale);
148 s = M_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 = M_COPYSIGN (s, __imag__ x);
156 }
157 }
158
159 return res;
160}
161declare_mgen_alias (__csqrt, csqrt)
162