1 | /* Complex square root of a float type. |
2 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <complex.h> |
20 | #include <math.h> |
21 | #include <math_private.h> |
22 | #include <math-underflow.h> |
23 | #include <float.h> |
24 | |
25 | CFLOAT |
26 | M_DECL_FUNC (__csqrt) (CFLOAT x) |
27 | { |
28 | CFLOAT res; |
29 | int rcls = fpclassify (__real__ x); |
30 | int icls = fpclassify (__imag__ x); |
31 | |
32 | if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) |
33 | { |
34 | if (icls == FP_INFINITE) |
35 | { |
36 | __real__ res = M_HUGE_VAL; |
37 | __imag__ res = __imag__ x; |
38 | } |
39 | else if (rcls == FP_INFINITE) |
40 | { |
41 | if (__real__ x < 0) |
42 | { |
43 | __real__ res = icls == FP_NAN ? M_NAN : 0; |
44 | __imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x); |
45 | } |
46 | else |
47 | { |
48 | __real__ res = __real__ x; |
49 | __imag__ res = (icls == FP_NAN |
50 | ? M_NAN : M_COPYSIGN (0, __imag__ x)); |
51 | } |
52 | } |
53 | else |
54 | { |
55 | __real__ res = M_NAN; |
56 | __imag__ res = M_NAN; |
57 | } |
58 | } |
59 | else |
60 | { |
61 | if (__glibc_unlikely (icls == FP_ZERO)) |
62 | { |
63 | if (__real__ x < 0) |
64 | { |
65 | __real__ res = 0; |
66 | __imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x); |
67 | } |
68 | else |
69 | { |
70 | __real__ res = M_FABS (M_SQRT (__real__ x)); |
71 | __imag__ res = M_COPYSIGN (0, __imag__ x); |
72 | } |
73 | } |
74 | else if (__glibc_unlikely (rcls == FP_ZERO)) |
75 | { |
76 | FLOAT r; |
77 | if (M_FABS (__imag__ x) >= 2 * M_MIN) |
78 | r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x)); |
79 | else |
80 | r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x)); |
81 | |
82 | __real__ res = r; |
83 | __imag__ res = M_COPYSIGN (r, __imag__ x); |
84 | } |
85 | else |
86 | { |
87 | FLOAT d, r, s; |
88 | int scale = 0; |
89 | |
90 | if (M_FABS (__real__ x) > M_MAX / 4) |
91 | { |
92 | scale = 1; |
93 | __real__ x = M_SCALBN (__real__ x, -2 * scale); |
94 | __imag__ x = M_SCALBN (__imag__ x, -2 * scale); |
95 | } |
96 | else if (M_FABS (__imag__ x) > M_MAX / 4) |
97 | { |
98 | scale = 1; |
99 | if (M_FABS (__real__ x) >= 4 * M_MIN) |
100 | __real__ x = M_SCALBN (__real__ x, -2 * scale); |
101 | else |
102 | __real__ x = 0; |
103 | __imag__ x = M_SCALBN (__imag__ x, -2 * scale); |
104 | } |
105 | else if (M_FABS (__real__ x) < 2 * M_MIN |
106 | && M_FABS (__imag__ x) < 2 * M_MIN) |
107 | { |
108 | scale = -((M_MANT_DIG + 1) / 2); |
109 | __real__ x = M_SCALBN (__real__ x, -2 * scale); |
110 | __imag__ x = M_SCALBN (__imag__ x, -2 * scale); |
111 | } |
112 | |
113 | d = M_HYPOT (__real__ x, __imag__ x); |
114 | /* Use the identity 2 Re res Im res = Im x |
115 | to avoid cancellation error in d +/- Re x. */ |
116 | if (__real__ x > 0) |
117 | { |
118 | r = M_SQRT (M_LIT (0.5) * (d + __real__ x)); |
119 | if (scale == 1 && M_FABS (__imag__ x) < 1) |
120 | { |
121 | /* Avoid possible intermediate underflow. */ |
122 | s = __imag__ x / r; |
123 | r = M_SCALBN (r, scale); |
124 | scale = 0; |
125 | } |
126 | else |
127 | s = M_LIT (0.5) * (__imag__ x / r); |
128 | } |
129 | else |
130 | { |
131 | s = M_SQRT (M_LIT (0.5) * (d - __real__ x)); |
132 | if (scale == 1 && M_FABS (__imag__ x) < 1) |
133 | { |
134 | /* Avoid possible intermediate underflow. */ |
135 | r = M_FABS (__imag__ x / s); |
136 | s = M_SCALBN (s, scale); |
137 | scale = 0; |
138 | } |
139 | else |
140 | r = M_FABS (M_LIT (0.5) * (__imag__ x / s)); |
141 | } |
142 | |
143 | if (scale) |
144 | { |
145 | r = M_SCALBN (r, scale); |
146 | s = M_SCALBN (s, scale); |
147 | } |
148 | |
149 | math_check_force_underflow (r); |
150 | math_check_force_underflow (s); |
151 | |
152 | __real__ res = r; |
153 | __imag__ res = M_COPYSIGN (s, __imag__ x); |
154 | } |
155 | } |
156 | |
157 | return res; |
158 | } |
159 | declare_mgen_alias (__csqrt, csqrt) |
160 | |