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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. | |
bfff8b1b | 4 | Copyright (C) 1997-2017 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 | |
19 | <http://www.gnu.org/licenses/>. */ | |
20 | ||
21 | #include <complex.h> | |
22 | #include <math.h> | |
23 | #include <math_private.h> | |
24 | #include <float.h> | |
25 | ||
26 | /* Return the complex inverse hyperbolic sine of finite nonzero Z, | |
27 | with the imaginary part of the result subtracted from pi/2 if ADJ | |
28 | is nonzero. */ | |
29 | ||
c50eee19 PM |
30 | CFLOAT |
31 | M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj) | |
ffb84f5e | 32 | { |
c50eee19 PM |
33 | CFLOAT res; |
34 | FLOAT rx, ix; | |
35 | CFLOAT y; | |
ffb84f5e PM |
36 | |
37 | /* Avoid cancellation by reducing to the first quadrant. */ | |
c50eee19 PM |
38 | rx = M_FABS (__real__ x); |
39 | ix = M_FABS (__imag__ x); | |
ffb84f5e | 40 | |
c50eee19 | 41 | if (rx >= 1 / M_EPSILON || ix >= 1 / M_EPSILON) |
ffb84f5e PM |
42 | { |
43 | /* For large x in the first quadrant, x + csqrt (1 + x * x) | |
44 | is sufficiently close to 2 * x to make no significant | |
45 | difference to the result; avoid possible overflow from | |
46 | the squaring and addition. */ | |
47 | __real__ y = rx; | |
48 | __imag__ y = ix; | |
49 | ||
50 | if (adj) | |
51 | { | |
c50eee19 PM |
52 | FLOAT t = __real__ y; |
53 | __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); | |
ffb84f5e PM |
54 | __imag__ y = t; |
55 | } | |
56 | ||
c50eee19 PM |
57 | res = M_SUF (__clog) (y); |
58 | __real__ res += (FLOAT) M_MLIT (M_LN2); | |
ffb84f5e | 59 | } |
c50eee19 | 60 | else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8) |
ffb84f5e | 61 | { |
c50eee19 | 62 | FLOAT s = M_HYPOT (1, rx); |
ffb84f5e | 63 | |
c50eee19 | 64 | __real__ res = M_LOG (rx + s); |
ffb84f5e | 65 | if (adj) |
c50eee19 | 66 | __imag__ res = M_ATAN2 (s, __imag__ x); |
ffb84f5e | 67 | else |
c50eee19 | 68 | __imag__ res = M_ATAN2 (ix, s); |
ffb84f5e | 69 | } |
c50eee19 | 70 | else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5)) |
ffb84f5e | 71 | { |
c50eee19 | 72 | FLOAT s = M_SQRT ((ix + 1) * (ix - 1)); |
ffb84f5e | 73 | |
c50eee19 | 74 | __real__ res = M_LOG (ix + s); |
ffb84f5e | 75 | if (adj) |
c50eee19 | 76 | __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
ffb84f5e | 77 | else |
c50eee19 | 78 | __imag__ res = M_ATAN2 (s, rx); |
ffb84f5e | 79 | } |
c50eee19 | 80 | else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5)) |
ffb84f5e | 81 | { |
c50eee19 | 82 | if (rx < M_EPSILON * M_EPSILON) |
ffb84f5e | 83 | { |
c50eee19 PM |
84 | FLOAT ix2m1 = (ix + 1) * (ix - 1); |
85 | FLOAT s = M_SQRT (ix2m1); | |
ffb84f5e | 86 | |
c50eee19 | 87 | __real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2; |
ffb84f5e | 88 | if (adj) |
c50eee19 | 89 | __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
ffb84f5e | 90 | else |
c50eee19 | 91 | __imag__ res = M_ATAN2 (s, rx); |
ffb84f5e PM |
92 | } |
93 | else | |
94 | { | |
c50eee19 PM |
95 | FLOAT ix2m1 = (ix + 1) * (ix - 1); |
96 | FLOAT rx2 = rx * rx; | |
97 | FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix); | |
98 | FLOAT d = M_SQRT (ix2m1 * ix2m1 + f); | |
99 | FLOAT dp = d + ix2m1; | |
100 | FLOAT dm = f / dp; | |
101 | FLOAT r1 = M_SQRT ((dm + rx2) / 2); | |
102 | FLOAT r2 = rx * ix / r1; | |
103 | ||
104 | __real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2; | |
ffb84f5e | 105 | if (adj) |
c50eee19 | 106 | __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x)); |
ffb84f5e | 107 | else |
c50eee19 | 108 | __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
ffb84f5e PM |
109 | } |
110 | } | |
c50eee19 | 111 | else if (ix == 1 && rx < M_LIT (0.5)) |
ffb84f5e | 112 | { |
c50eee19 | 113 | if (rx < M_EPSILON / 8) |
ffb84f5e | 114 | { |
c50eee19 | 115 | __real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2; |
ffb84f5e | 116 | if (adj) |
c50eee19 | 117 | __imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x)); |
ffb84f5e | 118 | else |
c50eee19 | 119 | __imag__ res = M_ATAN2 (1, M_SQRT (rx)); |
ffb84f5e PM |
120 | } |
121 | else | |
122 | { | |
c50eee19 PM |
123 | FLOAT d = rx * M_SQRT (4 + rx * rx); |
124 | FLOAT s1 = M_SQRT ((d + rx * rx) / 2); | |
125 | FLOAT s2 = M_SQRT ((d - rx * rx) / 2); | |
ffb84f5e | 126 | |
c50eee19 | 127 | __real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2; |
ffb84f5e | 128 | if (adj) |
c50eee19 | 129 | __imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x)); |
ffb84f5e | 130 | else |
c50eee19 | 131 | __imag__ res = M_ATAN2 (1 + s2, rx + s1); |
ffb84f5e PM |
132 | } |
133 | } | |
c50eee19 | 134 | else if (ix < 1 && rx < M_LIT (0.5)) |
ffb84f5e | 135 | { |
c50eee19 | 136 | if (ix >= M_EPSILON) |
ffb84f5e | 137 | { |
c50eee19 | 138 | if (rx < M_EPSILON * M_EPSILON) |
ffb84f5e | 139 | { |
c50eee19 PM |
140 | FLOAT onemix2 = (1 + ix) * (1 - ix); |
141 | FLOAT s = M_SQRT (onemix2); | |
ffb84f5e | 142 | |
c50eee19 | 143 | __real__ res = M_LOG1P (2 * rx / s) / 2; |
ffb84f5e | 144 | if (adj) |
c50eee19 | 145 | __imag__ res = M_ATAN2 (s, __imag__ x); |
ffb84f5e | 146 | else |
c50eee19 | 147 | __imag__ res = M_ATAN2 (ix, s); |
ffb84f5e PM |
148 | } |
149 | else | |
150 | { | |
c50eee19 PM |
151 | FLOAT onemix2 = (1 + ix) * (1 - ix); |
152 | FLOAT rx2 = rx * rx; | |
153 | FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix); | |
154 | FLOAT d = M_SQRT (onemix2 * onemix2 + f); | |
155 | FLOAT dp = d + onemix2; | |
156 | FLOAT dm = f / dp; | |
157 | FLOAT r1 = M_SQRT ((dp + rx2) / 2); | |
158 | FLOAT r2 = rx * ix / r1; | |
159 | ||
160 | __real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2; | |
ffb84f5e | 161 | if (adj) |
c50eee19 PM |
162 | __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, |
163 | __imag__ x)); | |
ffb84f5e | 164 | else |
c50eee19 | 165 | __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
ffb84f5e PM |
166 | } |
167 | } | |
168 | else | |
169 | { | |
c50eee19 | 170 | FLOAT s = M_HYPOT (1, rx); |
ffb84f5e | 171 | |
c50eee19 | 172 | __real__ res = M_LOG1P (2 * rx * (rx + s)) / 2; |
ffb84f5e | 173 | if (adj) |
c50eee19 | 174 | __imag__ res = M_ATAN2 (s, __imag__ x); |
ffb84f5e | 175 | else |
c50eee19 | 176 | __imag__ res = M_ATAN2 (ix, s); |
ffb84f5e PM |
177 | } |
178 | math_check_force_underflow_nonneg (__real__ res); | |
179 | } | |
180 | else | |
181 | { | |
c50eee19 PM |
182 | __real__ y = (rx - ix) * (rx + ix) + 1; |
183 | __imag__ y = 2 * rx * ix; | |
ffb84f5e | 184 | |
c50eee19 | 185 | y = M_SUF (__csqrt) (y); |
ffb84f5e PM |
186 | |
187 | __real__ y += rx; | |
188 | __imag__ y += ix; | |
189 | ||
190 | if (adj) | |
191 | { | |
c50eee19 PM |
192 | FLOAT t = __real__ y; |
193 | __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); | |
ffb84f5e PM |
194 | __imag__ y = t; |
195 | } | |
196 | ||
c50eee19 | 197 | res = M_SUF (__clog) (y); |
ffb84f5e PM |
198 | } |
199 | ||
200 | /* Give results the correct sign for the original argument. */ | |
c50eee19 PM |
201 | __real__ res = M_COPYSIGN (__real__ res, __real__ x); |
202 | __imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x)); | |
ffb84f5e PM |
203 | |
204 | return res; | |
205 | } |