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c50eee19 PM |
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. | |
2b778ceb | 4 | Copyright (C) 1997-2021 Free Software Foundation, Inc. |
ffb84f5e PM |
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 | |
5a82c748 | 19 | <https://www.gnu.org/licenses/>. */ |
ffb84f5e PM |
20 | |
21 | #include <complex.h> | |
22 | #include <math.h> | |
23 | #include <math_private.h> | |
8f5b00d3 | 24 | #include <math-underflow.h> |
ffb84f5e PM |
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 | ||
c50eee19 PM |
31 | CFLOAT |
32 | M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj) | |
ffb84f5e | 33 | { |
c50eee19 PM |
34 | CFLOAT res; |
35 | FLOAT rx, ix; | |
36 | CFLOAT y; | |
ffb84f5e PM |
37 | |
38 | /* Avoid cancellation by reducing to the first quadrant. */ | |
c50eee19 PM |
39 | rx = M_FABS (__real__ x); |
40 | ix = M_FABS (__imag__ x); | |
ffb84f5e | 41 | |
c50eee19 | 42 | if (rx >= 1 / M_EPSILON || ix >= 1 / M_EPSILON) |
ffb84f5e PM |
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 | { | |
c50eee19 PM |
53 | FLOAT t = __real__ y; |
54 | __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); | |
ffb84f5e PM |
55 | __imag__ y = t; |
56 | } | |
57 | ||
c50eee19 PM |
58 | res = M_SUF (__clog) (y); |
59 | __real__ res += (FLOAT) M_MLIT (M_LN2); | |
ffb84f5e | 60 | } |
c50eee19 | 61 | else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8) |
ffb84f5e | 62 | { |
c50eee19 | 63 | FLOAT s = M_HYPOT (1, rx); |
ffb84f5e | 64 | |
c50eee19 | 65 | __real__ res = M_LOG (rx + s); |
ffb84f5e | 66 | if (adj) |
c50eee19 | 67 | __imag__ res = M_ATAN2 (s, __imag__ x); |
ffb84f5e | 68 | else |
c50eee19 | 69 | __imag__ res = M_ATAN2 (ix, s); |
ffb84f5e | 70 | } |
c50eee19 | 71 | else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5)) |
ffb84f5e | 72 | { |
c50eee19 | 73 | FLOAT s = M_SQRT ((ix + 1) * (ix - 1)); |
ffb84f5e | 74 | |
c50eee19 | 75 | __real__ res = M_LOG (ix + s); |
ffb84f5e | 76 | if (adj) |
c50eee19 | 77 | __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
ffb84f5e | 78 | else |
c50eee19 | 79 | __imag__ res = M_ATAN2 (s, rx); |
ffb84f5e | 80 | } |
c50eee19 | 81 | else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5)) |
ffb84f5e | 82 | { |
c50eee19 | 83 | if (rx < M_EPSILON * M_EPSILON) |
ffb84f5e | 84 | { |
c50eee19 PM |
85 | FLOAT ix2m1 = (ix + 1) * (ix - 1); |
86 | FLOAT s = M_SQRT (ix2m1); | |
ffb84f5e | 87 | |
c50eee19 | 88 | __real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2; |
ffb84f5e | 89 | if (adj) |
c50eee19 | 90 | __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
ffb84f5e | 91 | else |
c50eee19 | 92 | __imag__ res = M_ATAN2 (s, rx); |
ffb84f5e PM |
93 | } |
94 | else | |
95 | { | |
c50eee19 PM |
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; | |
ffb84f5e | 106 | if (adj) |
c50eee19 | 107 | __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x)); |
ffb84f5e | 108 | else |
c50eee19 | 109 | __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
ffb84f5e PM |
110 | } |
111 | } | |
c50eee19 | 112 | else if (ix == 1 && rx < M_LIT (0.5)) |
ffb84f5e | 113 | { |
c50eee19 | 114 | if (rx < M_EPSILON / 8) |
ffb84f5e | 115 | { |
c50eee19 | 116 | __real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2; |
ffb84f5e | 117 | if (adj) |
c50eee19 | 118 | __imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x)); |
ffb84f5e | 119 | else |
c50eee19 | 120 | __imag__ res = M_ATAN2 (1, M_SQRT (rx)); |
ffb84f5e PM |
121 | } |
122 | else | |
123 | { | |
c50eee19 PM |
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); | |
ffb84f5e | 127 | |
c50eee19 | 128 | __real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2; |
ffb84f5e | 129 | if (adj) |
c50eee19 | 130 | __imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x)); |
ffb84f5e | 131 | else |
c50eee19 | 132 | __imag__ res = M_ATAN2 (1 + s2, rx + s1); |
ffb84f5e PM |
133 | } |
134 | } | |
c50eee19 | 135 | else if (ix < 1 && rx < M_LIT (0.5)) |
ffb84f5e | 136 | { |
c50eee19 | 137 | if (ix >= M_EPSILON) |
ffb84f5e | 138 | { |
c50eee19 | 139 | if (rx < M_EPSILON * M_EPSILON) |
ffb84f5e | 140 | { |
c50eee19 PM |
141 | FLOAT onemix2 = (1 + ix) * (1 - ix); |
142 | FLOAT s = M_SQRT (onemix2); | |
ffb84f5e | 143 | |
c50eee19 | 144 | __real__ res = M_LOG1P (2 * rx / s) / 2; |
ffb84f5e | 145 | if (adj) |
c50eee19 | 146 | __imag__ res = M_ATAN2 (s, __imag__ x); |
ffb84f5e | 147 | else |
c50eee19 | 148 | __imag__ res = M_ATAN2 (ix, s); |
ffb84f5e PM |
149 | } |
150 | else | |
151 | { | |
c50eee19 PM |
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; | |
ffb84f5e | 162 | if (adj) |
c50eee19 PM |
163 | __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, |
164 | __imag__ x)); | |
ffb84f5e | 165 | else |
c50eee19 | 166 | __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
ffb84f5e PM |
167 | } |
168 | } | |
169 | else | |
170 | { | |
c50eee19 | 171 | FLOAT s = M_HYPOT (1, rx); |
ffb84f5e | 172 | |
c50eee19 | 173 | __real__ res = M_LOG1P (2 * rx * (rx + s)) / 2; |
ffb84f5e | 174 | if (adj) |
c50eee19 | 175 | __imag__ res = M_ATAN2 (s, __imag__ x); |
ffb84f5e | 176 | else |
c50eee19 | 177 | __imag__ res = M_ATAN2 (ix, s); |
ffb84f5e PM |
178 | } |
179 | math_check_force_underflow_nonneg (__real__ res); | |
180 | } | |
181 | else | |
182 | { | |
c50eee19 PM |
183 | __real__ y = (rx - ix) * (rx + ix) + 1; |
184 | __imag__ y = 2 * rx * ix; | |
ffb84f5e | 185 | |
c50eee19 | 186 | y = M_SUF (__csqrt) (y); |
ffb84f5e PM |
187 | |
188 | __real__ y += rx; | |
189 | __imag__ y += ix; | |
190 | ||
191 | if (adj) | |
192 | { | |
c50eee19 PM |
193 | FLOAT t = __real__ y; |
194 | __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); | |
ffb84f5e PM |
195 | __imag__ y = t; |
196 | } | |
197 | ||
c50eee19 | 198 | res = M_SUF (__clog) (y); |
ffb84f5e PM |
199 | } |
200 | ||
201 | /* Give results the correct sign for the original argument. */ | |
c50eee19 PM |
202 | __real__ res = M_COPYSIGN (__real__ res, __real__ x); |
203 | __imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x)); | |
ffb84f5e PM |
204 | |
205 | return res; | |
206 | } |