1 /* Return arc hyperbole sine for float value, with the imaginary part
2 of the result possibly adjusted for use in computing other
4 Copyright (C) 1997-2013 Free Software Foundation, Inc.
5 This file is part of the GNU C Library.
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.
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.
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/>. */
23 #include <math_private.h>
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
31 __kernel_casinhf (__complex__ float x, int adj)
33 __complex__ float res;
37 /* Avoid cancellation by reducing to the first quadrant. */
38 rx = fabsf (__real__ x);
39 ix = fabsf (__imag__ x);
41 if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
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. */
53 __real__ y = __copysignf (__imag__ y, __imag__ x);
58 __real__ res += (float) M_LN2;
60 else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
62 float s = __ieee754_hypotf (1.0f, rx);
64 __real__ res = __ieee754_logf (rx + s);
66 __imag__ res = __ieee754_atan2f (s, __imag__ x);
68 __imag__ res = __ieee754_atan2f (ix, s);
70 else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
72 float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
74 __real__ res = __ieee754_logf (ix + s);
76 __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
78 __imag__ res = __ieee754_atan2f (s, rx);
80 else if (ix > 1.0f && ix < 1.5f && rx < 0.5f)
82 if (rx < FLT_EPSILON * FLT_EPSILON)
84 float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
85 float s = __ieee754_sqrtf (ix2m1);
87 __real__ res = __log1pf (2.0f * (ix2m1 + ix * s)) / 2.0f;
89 __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
91 __imag__ res = __ieee754_atan2f (s, rx);
95 float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
97 float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
98 float d = __ieee754_sqrtf (ix2m1 * ix2m1 + f);
101 float r1 = __ieee754_sqrtf ((dm + rx2) / 2.0f);
102 float r2 = rx * ix / r1;
105 = __log1pf (rx2 + dp + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
107 __imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2,
110 __imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
113 else if (ix == 1.0f && rx < 0.5f)
115 if (rx < FLT_EPSILON / 8.0f)
117 __real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f;
119 __imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx),
120 __copysignf (1.0f, __imag__ x));
122 __imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx));
126 float d = rx * __ieee754_sqrtf (4.0f + rx * rx);
127 float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f);
128 float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f);
130 __real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f;
132 __imag__ res = __ieee754_atan2f (rx + s1,
133 __copysignf (1.0f + s2,
136 __imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1);
139 else if (ix < 1.0f && rx < 0.5f)
141 if (ix >= FLT_EPSILON)
143 if (rx < FLT_EPSILON * FLT_EPSILON)
145 float onemix2 = (1.0f + ix) * (1.0f - ix);
146 float s = __ieee754_sqrtf (onemix2);
148 __real__ res = __log1pf (2.0f * rx / s) / 2.0f;
150 __imag__ res = __ieee754_atan2f (s, __imag__ x);
152 __imag__ res = __ieee754_atan2f (ix, s);
156 float onemix2 = (1.0f + ix) * (1.0f - ix);
158 float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
159 float d = __ieee754_sqrtf (onemix2 * onemix2 + f);
160 float dp = d + onemix2;
162 float r1 = __ieee754_sqrtf ((dp + rx2) / 2.0f);
163 float r2 = rx * ix / r1;
166 = __log1pf (rx2 + dm + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
168 __imag__ res = __ieee754_atan2f (rx + r1,
169 __copysignf (ix + r2,
172 __imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
177 float s = __ieee754_hypotf (1.0f, rx);
179 __real__ res = __log1pf (2.0f * rx * (rx + s)) / 2.0f;
181 __imag__ res = __ieee754_atan2f (s, __imag__ x);
183 __imag__ res = __ieee754_atan2f (ix, s);
185 if (__real__ res < FLT_MIN)
187 volatile float force_underflow = __real__ res * __real__ res;
188 (void) force_underflow;
193 __real__ y = (rx - ix) * (rx + ix) + 1.0f;
194 __imag__ y = 2.0f * rx * ix;
203 float t = __real__ y;
204 __real__ y = __copysignf (__imag__ y, __imag__ x);
211 /* Give results the correct sign for the original argument. */
212 __real__ res = __copysignf (__real__ res, __real__ x);
213 __imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));