1 | /* Return arc hyperbolic sine for a complex float type, with the |
2 | imaginary part of the result possibly adjusted for use in |
3 | computing other functions. |
4 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
5 | This file is part of the GNU C Library. |
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 | |
27 | /* Return the complex inverse hyperbolic sine of finite nonzero Z, |
28 | with the imaginary part of the result subtracted from pi/2 if ADJ |
29 | is nonzero. */ |
30 | |
31 | CFLOAT |
32 | M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj) |
33 | { |
34 | CFLOAT res; |
35 | FLOAT rx, ix; |
36 | CFLOAT y; |
37 | |
38 | /* Avoid cancellation by reducing to the first quadrant. */ |
39 | rx = M_FABS (__real__ x); |
40 | ix = M_FABS (__imag__ x); |
41 | |
42 | if (rx >= 1 / M_EPSILON || ix >= 1 / M_EPSILON) |
43 | { |
44 | /* For large x in the first quadrant, x + csqrt (1 + x * x) |
45 | is sufficiently close to 2 * x to make no significant |
46 | difference to the result; avoid possible overflow from |
47 | the squaring and addition. */ |
48 | __real__ y = rx; |
49 | __imag__ y = ix; |
50 | |
51 | if (adj) |
52 | { |
53 | FLOAT t = __real__ y; |
54 | __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); |
55 | __imag__ y = t; |
56 | } |
57 | |
58 | res = M_SUF (__clog) (y); |
59 | __real__ res += M_MLIT (M_LN2); |
60 | } |
61 | else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8) |
62 | { |
63 | FLOAT s = M_HYPOT (1, rx); |
64 | |
65 | __real__ res = M_LOG (rx + s); |
66 | if (adj) |
67 | __imag__ res = M_ATAN2 (s, __imag__ x); |
68 | else |
69 | __imag__ res = M_ATAN2 (ix, s); |
70 | } |
71 | else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5)) |
72 | { |
73 | FLOAT s = M_SQRT ((ix + 1) * (ix - 1)); |
74 | |
75 | __real__ res = M_LOG (ix + s); |
76 | if (adj) |
77 | __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
78 | else |
79 | __imag__ res = M_ATAN2 (s, rx); |
80 | } |
81 | else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5)) |
82 | { |
83 | if (rx < M_EPSILON * M_EPSILON) |
84 | { |
85 | FLOAT ix2m1 = (ix + 1) * (ix - 1); |
86 | FLOAT s = M_SQRT (ix2m1); |
87 | |
88 | __real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2; |
89 | if (adj) |
90 | __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
91 | else |
92 | __imag__ res = M_ATAN2 (s, rx); |
93 | } |
94 | else |
95 | { |
96 | FLOAT ix2m1 = (ix + 1) * (ix - 1); |
97 | FLOAT rx2 = rx * rx; |
98 | FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix); |
99 | FLOAT d = M_SQRT (ix2m1 * ix2m1 + f); |
100 | FLOAT dp = d + ix2m1; |
101 | FLOAT dm = f / dp; |
102 | FLOAT r1 = M_SQRT ((dm + rx2) / 2); |
103 | FLOAT r2 = rx * ix / r1; |
104 | |
105 | __real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2; |
106 | if (adj) |
107 | __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x)); |
108 | else |
109 | __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
110 | } |
111 | } |
112 | else if (ix == 1 && rx < M_LIT (0.5)) |
113 | { |
114 | if (rx < M_EPSILON / 8) |
115 | { |
116 | __real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2; |
117 | if (adj) |
118 | __imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x)); |
119 | else |
120 | __imag__ res = M_ATAN2 (1, M_SQRT (rx)); |
121 | } |
122 | else |
123 | { |
124 | FLOAT d = rx * M_SQRT (4 + rx * rx); |
125 | FLOAT s1 = M_SQRT ((d + rx * rx) / 2); |
126 | FLOAT s2 = M_SQRT ((d - rx * rx) / 2); |
127 | |
128 | __real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2; |
129 | if (adj) |
130 | __imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x)); |
131 | else |
132 | __imag__ res = M_ATAN2 (1 + s2, rx + s1); |
133 | } |
134 | } |
135 | else if (ix < 1 && rx < M_LIT (0.5)) |
136 | { |
137 | if (ix >= M_EPSILON) |
138 | { |
139 | if (rx < M_EPSILON * M_EPSILON) |
140 | { |
141 | FLOAT onemix2 = (1 + ix) * (1 - ix); |
142 | FLOAT s = M_SQRT (onemix2); |
143 | |
144 | __real__ res = M_LOG1P (2 * rx / s) / 2; |
145 | if (adj) |
146 | __imag__ res = M_ATAN2 (s, __imag__ x); |
147 | else |
148 | __imag__ res = M_ATAN2 (ix, s); |
149 | } |
150 | else |
151 | { |
152 | FLOAT onemix2 = (1 + ix) * (1 - ix); |
153 | FLOAT rx2 = rx * rx; |
154 | FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix); |
155 | FLOAT d = M_SQRT (onemix2 * onemix2 + f); |
156 | FLOAT dp = d + onemix2; |
157 | FLOAT dm = f / dp; |
158 | FLOAT r1 = M_SQRT ((dp + rx2) / 2); |
159 | FLOAT r2 = rx * ix / r1; |
160 | |
161 | __real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2; |
162 | if (adj) |
163 | __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, |
164 | __imag__ x)); |
165 | else |
166 | __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
167 | } |
168 | } |
169 | else |
170 | { |
171 | FLOAT s = M_HYPOT (1, rx); |
172 | |
173 | __real__ res = M_LOG1P (2 * rx * (rx + s)) / 2; |
174 | if (adj) |
175 | __imag__ res = M_ATAN2 (s, __imag__ x); |
176 | else |
177 | __imag__ res = M_ATAN2 (ix, s); |
178 | } |
179 | math_check_force_underflow_nonneg (__real__ res); |
180 | } |
181 | else |
182 | { |
183 | __real__ y = (rx - ix) * (rx + ix) + 1; |
184 | __imag__ y = 2 * rx * ix; |
185 | |
186 | y = M_SUF (__csqrt) (y); |
187 | |
188 | __real__ y += rx; |
189 | __imag__ y += ix; |
190 | |
191 | if (adj) |
192 | { |
193 | FLOAT t = __real__ y; |
194 | __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); |
195 | __imag__ y = t; |
196 | } |
197 | |
198 | res = M_SUF (__clog) (y); |
199 | } |
200 | |
201 | /* Give results the correct sign for the original argument. */ |
202 | __real__ res = M_COPYSIGN (__real__ res, __real__ x); |
203 | __imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x)); |
204 | |
205 | return res; |
206 | } |
207 | |