1*627f7eb2Smrg /* Return arc hyperbolic tangent for a complex float type.
2*627f7eb2Smrg Copyright (C) 1997-2018 Free Software Foundation, Inc.
3*627f7eb2Smrg This file is part of the GNU C Library.
4*627f7eb2Smrg Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
5*627f7eb2Smrg
6*627f7eb2Smrg The GNU C Library is free software; you can redistribute it and/or
7*627f7eb2Smrg modify it under the terms of the GNU Lesser General Public
8*627f7eb2Smrg License as published by the Free Software Foundation; either
9*627f7eb2Smrg version 2.1 of the License, or (at your option) any later version.
10*627f7eb2Smrg
11*627f7eb2Smrg The GNU C Library is distributed in the hope that it will be useful,
12*627f7eb2Smrg but WITHOUT ANY WARRANTY; without even the implied warranty of
13*627f7eb2Smrg MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14*627f7eb2Smrg Lesser General Public License for more details.
15*627f7eb2Smrg
16*627f7eb2Smrg You should have received a copy of the GNU Lesser General Public
17*627f7eb2Smrg License along with the GNU C Library; if not, see
18*627f7eb2Smrg <http://www.gnu.org/licenses/>. */
19*627f7eb2Smrg
20*627f7eb2Smrg #include "quadmath-imp.h"
21*627f7eb2Smrg
22*627f7eb2Smrg __complex128
catanhq(__complex128 x)23*627f7eb2Smrg catanhq (__complex128 x)
24*627f7eb2Smrg {
25*627f7eb2Smrg __complex128 res;
26*627f7eb2Smrg int rcls = fpclassifyq (__real__ x);
27*627f7eb2Smrg int icls = fpclassifyq (__imag__ x);
28*627f7eb2Smrg
29*627f7eb2Smrg if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
30*627f7eb2Smrg {
31*627f7eb2Smrg if (icls == QUADFP_INFINITE)
32*627f7eb2Smrg {
33*627f7eb2Smrg __real__ res = copysignq (0, __real__ x);
34*627f7eb2Smrg __imag__ res = copysignq (M_PI_2q, __imag__ x);
35*627f7eb2Smrg }
36*627f7eb2Smrg else if (rcls == QUADFP_INFINITE || rcls == QUADFP_ZERO)
37*627f7eb2Smrg {
38*627f7eb2Smrg __real__ res = copysignq (0, __real__ x);
39*627f7eb2Smrg if (icls >= QUADFP_ZERO)
40*627f7eb2Smrg __imag__ res = copysignq (M_PI_2q, __imag__ x);
41*627f7eb2Smrg else
42*627f7eb2Smrg __imag__ res = nanq ("");
43*627f7eb2Smrg }
44*627f7eb2Smrg else
45*627f7eb2Smrg {
46*627f7eb2Smrg __real__ res = nanq ("");
47*627f7eb2Smrg __imag__ res = nanq ("");
48*627f7eb2Smrg }
49*627f7eb2Smrg }
50*627f7eb2Smrg else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
51*627f7eb2Smrg {
52*627f7eb2Smrg res = x;
53*627f7eb2Smrg }
54*627f7eb2Smrg else
55*627f7eb2Smrg {
56*627f7eb2Smrg if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
57*627f7eb2Smrg || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
58*627f7eb2Smrg {
59*627f7eb2Smrg __imag__ res = copysignq (M_PI_2q, __imag__ x);
60*627f7eb2Smrg if (fabsq (__imag__ x) <= 1)
61*627f7eb2Smrg __real__ res = 1 / __real__ x;
62*627f7eb2Smrg else if (fabsq (__real__ x) <= 1)
63*627f7eb2Smrg __real__ res = __real__ x / __imag__ x / __imag__ x;
64*627f7eb2Smrg else
65*627f7eb2Smrg {
66*627f7eb2Smrg __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
67*627f7eb2Smrg __real__ res = __real__ x / h / h / 4;
68*627f7eb2Smrg }
69*627f7eb2Smrg }
70*627f7eb2Smrg else
71*627f7eb2Smrg {
72*627f7eb2Smrg if (fabsq (__real__ x) == 1
73*627f7eb2Smrg && fabsq (__imag__ x) < FLT128_EPSILON * FLT128_EPSILON)
74*627f7eb2Smrg __real__ res = (copysignq (0.5Q, __real__ x)
75*627f7eb2Smrg * ((__float128) M_LN2q
76*627f7eb2Smrg - logq (fabsq (__imag__ x))));
77*627f7eb2Smrg else
78*627f7eb2Smrg {
79*627f7eb2Smrg __float128 i2 = 0;
80*627f7eb2Smrg if (fabsq (__imag__ x) >= FLT128_EPSILON * FLT128_EPSILON)
81*627f7eb2Smrg i2 = __imag__ x * __imag__ x;
82*627f7eb2Smrg
83*627f7eb2Smrg __float128 num = 1 + __real__ x;
84*627f7eb2Smrg num = i2 + num * num;
85*627f7eb2Smrg
86*627f7eb2Smrg __float128 den = 1 - __real__ x;
87*627f7eb2Smrg den = i2 + den * den;
88*627f7eb2Smrg
89*627f7eb2Smrg __float128 f = num / den;
90*627f7eb2Smrg if (f < 0.5Q)
91*627f7eb2Smrg __real__ res = 0.25Q * logq (f);
92*627f7eb2Smrg else
93*627f7eb2Smrg {
94*627f7eb2Smrg num = 4 * __real__ x;
95*627f7eb2Smrg __real__ res = 0.25Q * log1pq (num / den);
96*627f7eb2Smrg }
97*627f7eb2Smrg }
98*627f7eb2Smrg
99*627f7eb2Smrg __float128 absx, absy, den;
100*627f7eb2Smrg
101*627f7eb2Smrg absx = fabsq (__real__ x);
102*627f7eb2Smrg absy = fabsq (__imag__ x);
103*627f7eb2Smrg if (absx < absy)
104*627f7eb2Smrg {
105*627f7eb2Smrg __float128 t = absx;
106*627f7eb2Smrg absx = absy;
107*627f7eb2Smrg absy = t;
108*627f7eb2Smrg }
109*627f7eb2Smrg
110*627f7eb2Smrg if (absy < FLT128_EPSILON / 2)
111*627f7eb2Smrg {
112*627f7eb2Smrg den = (1 - absx) * (1 + absx);
113*627f7eb2Smrg if (den == 0)
114*627f7eb2Smrg den = 0;
115*627f7eb2Smrg }
116*627f7eb2Smrg else if (absx >= 1)
117*627f7eb2Smrg den = (1 - absx) * (1 + absx) - absy * absy;
118*627f7eb2Smrg else if (absx >= 0.75Q || absy >= 0.5Q)
119*627f7eb2Smrg den = -__quadmath_x2y2m1q (absx, absy);
120*627f7eb2Smrg else
121*627f7eb2Smrg den = (1 - absx) * (1 + absx) - absy * absy;
122*627f7eb2Smrg
123*627f7eb2Smrg __imag__ res = 0.5Q * atan2q (2 * __imag__ x, den);
124*627f7eb2Smrg }
125*627f7eb2Smrg
126*627f7eb2Smrg math_check_force_underflow_complex (res);
127*627f7eb2Smrg }
128*627f7eb2Smrg
129*627f7eb2Smrg return res;
130*627f7eb2Smrg }
131