1/*
2 This Software is provided under the Zope Public License (ZPL) Version 2.1.
3
4 Copyright (c) 2009, 2010 by the mingw-w64 project
5
6 See the AUTHORS file for the list of contributors to the mingw-w64 project.
7
8 This license has been certified as open source. It has also been designated
9 as GPL compatible by the Free Software Foundation (FSF).
10
11 Redistribution and use in source and binary forms, with or without
12 modification, are permitted provided that the following conditions are met:
13
14 1. Redistributions in source code must retain the accompanying copyright
15 notice, this list of conditions, and the following disclaimer.
16 2. Redistributions in binary form must reproduce the accompanying
17 copyright notice, this list of conditions, and the following disclaimer
18 in the documentation and/or other materials provided with the
19 distribution.
20 3. Names of the copyright holders must not be used to endorse or promote
21 products derived from this software without prior written permission
22 from the copyright holders.
23 4. The right to distribute this software or to use it for any purpose does
24 not give you the right to use Servicemarks (sm) or Trademarks (tm) of
25 the copyright holders. Use of them is covered by separate agreement
26 with the copyright holders.
27 5. If any files are modified, you must cause the modified files to carry
28 prominent notices stating that you changed the files and the date of
29 any change.
30
31 Disclaimer
32
33 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY EXPRESSED
34 OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
35 OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
36 EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT,
37 INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
38 LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
39 OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
40 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
41 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
42 EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
43*/
44
45__FLT_TYPE __complex__ __cdecl
46__FLT_ABI(catanh) (__FLT_TYPE __complex__ z)
47{
48 __complex__ __FLT_TYPE ret;
49 __FLT_TYPE i2, n, d;
50 int r_class = fpclassify (__real__ z);
51 int i_class = fpclassify (__imag__ z);
52
53 if (r_class == FP_INFINITE || r_class == FP_NAN || i_class == FP_INFINITE || i_class == FP_NAN)
54 {
55 if (i_class == FP_INFINITE)
56 {
57 __real__ ret = __FLT_ABI(copysign) (__FLT_CST(0.0), __real__ z);
58 __imag__ ret = __FLT_ABI(copysign) (__FLT_PI_2, __imag__ z);
59 return ret;
60 }
61
62 if (r_class == FP_INFINITE || r_class == FP_ZERO)
63 {
64 __real__ ret = __FLT_ABI(copysign) (__FLT_CST(0.0), __real__ z);
65 __imag__ ret = ((i_class != FP_NAN && i_class != FP_INFINITE)
66 ? __FLT_ABI(copysign) (__FLT_PI_2, __imag__ z) : __FLT_NAN);
67 return ret;
68 }
69
70 __real__ ret = __FLT_NAN;
71 __imag__ ret = __FLT_NAN;
72 return ret;
73 }
74
75 if (r_class == FP_ZERO && i_class == FP_ZERO)
76 return z;
77
78 /* catanh(z) = 1/2 * clog(1+z) - 1/2 * clog(1-z) = 1/2 * clog((1+z)/(1-z)) */
79
80 /* Use identity clog(c) = 1/2*log(|c|^2) + i*arg(c) to calculate real and
81 imaginary parts separately. */
82
83 /* real part */
84 /* |c|^2 = (Im(z)^2 + (1+Re(z))^2)/(Im(z)^2 + (1-Re(z))^2) */
85 i2 = __imag__ z * __imag__ z;
86
87 if (__FLT_ABI(fabs) (__real__ z) <= __FLT_EPSILON)
88 {
89 /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + O(Re(z)^2) (Taylor series) */
90 __real__ ret = __FLT_CST(0.25) *
91 __FLT_ABI(log1p) (__FLT_CST(4.0)*(__real__ z) / (__FLT_CST(1.0) + i2));
92 }
93 else if ((__real__ z)*(__real__ z) <= __FLT_EPSILON)
94 {
95 /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + 8*Re(z)^2/(1+Im(z)^2)^2 + O(Re(z)^3) (Taylor series) */
96 d = __real__ z / (__FLT_CST(1.0) + i2);
97 __real__ ret = __FLT_CST(0.25) *
98 __FLT_ABI(log1p) (__FLT_CST(4.0) * d * (__FLT_CST(1.0) + __FLT_CST(2.0) * d));
99 }
100 else
101 {
102 n = __FLT_CST(1.0) + __real__ z;
103 n = i2 + n * n;
104
105 d = __FLT_CST(1.0) - __real__ z;
106 d = i2 + d * d;
107
108 __real__ ret = __FLT_CST(0.25) * (__FLT_ABI(log) (n) - __FLT_ABI(log) (d));
109 }
110
111 /* imaginary part */
112 /* z = (1 - Re(z)^2 - Im(z)^2 + 2i * Im(z) / ((1-Re(z))^2 + Im(z)^2) */
113 d = __FLT_CST(1.0) - __real__ z * __real__ z - i2;
114
115 __imag__ ret = __FLT_CST(0.5) * __FLT_ABI(atan2) (__FLT_CST(2.0) * __imag__ z, d);
116
117 return ret;
118}