1/* Return arc tangent of complex float type.
2   Copyright (C) 1997-2018 Free Software Foundation, Inc.
3   This file is part of the GNU C Library.
4   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
5
6   The GNU C Library is free software; you can redistribute it and/or
7   modify it under the terms of the GNU Lesser General Public
8   License as published by the Free Software Foundation; either
9   version 2.1 of the License, or (at your option) any later version.
10
11   The GNU C Library is distributed in the hope that it will be useful,
12   but WITHOUT ANY WARRANTY; without even the implied warranty of
13   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
14   Lesser General Public License for more details.
15
16   You should have received a copy of the GNU Lesser General Public
17   License along with the GNU C Library; if not, see
18   <http://www.gnu.org/licenses/>.  */
19
20#include "quadmath-imp.h"
21
22__complex128
23catanq (__complex128 x)
24{
25  __complex128 res;
26  int rcls = fpclassifyq (__real__ x);
27  int icls = fpclassifyq (__imag__ x);
28
29  if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
30    {
31      if (rcls == QUADFP_INFINITE)
32	{
33	  __real__ res = copysignq (M_PI_2q, __real__ x);
34	  __imag__ res = copysignq (0, __imag__ x);
35	}
36      else if (icls == QUADFP_INFINITE)
37	{
38	  if (rcls >= QUADFP_ZERO)
39	    __real__ res = copysignq (M_PI_2q, __real__ x);
40	  else
41	    __real__ res = nanq ("");
42	  __imag__ res = copysignq (0, __imag__ x);
43	}
44      else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE)
45	{
46	  __real__ res = nanq ("");
47	  __imag__ res = copysignq (0, __imag__ x);
48	}
49      else
50	{
51	  __real__ res = nanq ("");
52	  __imag__ res = nanq ("");
53	}
54    }
55  else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
56    {
57      res = x;
58    }
59  else
60    {
61      if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
62	  || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
63	{
64	  __real__ res = copysignq (M_PI_2q, __real__ x);
65	  if (fabsq (__real__ x) <= 1)
66	    __imag__ res = 1 / __imag__ x;
67	  else if (fabsq (__imag__ x) <= 1)
68	    __imag__ res = __imag__ x / __real__ x / __real__ x;
69	  else
70	    {
71	      __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
72	      __imag__ res = __imag__ x / h / h / 4;
73	    }
74	}
75      else
76	{
77	  __float128 den, absx, absy;
78
79	  absx = fabsq (__real__ x);
80	  absy = fabsq (__imag__ x);
81	  if (absx < absy)
82	    {
83	      __float128 t = absx;
84	      absx = absy;
85	      absy = t;
86	    }
87
88	  if (absy < FLT128_EPSILON / 2)
89	    {
90	      den = (1 - absx) * (1 + absx);
91	      if (den == 0)
92		den = 0;
93	    }
94	  else if (absx >= 1)
95	    den = (1 - absx) * (1 + absx) - absy * absy;
96	  else if (absx >= 0.75Q || absy >= 0.5Q)
97	    den = -__quadmath_x2y2m1q (absx, absy);
98	  else
99	    den = (1 - absx) * (1 + absx) - absy * absy;
100
101	  __real__ res = 0.5Q * atan2q (2 * __real__ x, den);
102
103	  if (fabsq (__imag__ x) == 1
104	      && fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON)
105	    __imag__ res = (copysignq (0.5Q, __imag__ x)
106			    * ((__float128) M_LN2q
107			       - logq (fabsq (__real__ x))));
108	  else
109	    {
110	      __float128 r2 = 0, num, f;
111
112	      if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_EPSILON)
113		r2 = __real__ x * __real__ x;
114
115	      num = __imag__ x + 1;
116	      num = r2 + num * num;
117
118	      den = __imag__ x - 1;
119	      den = r2 + den * den;
120
121	      f = num / den;
122	      if (f < 0.5Q)
123		__imag__ res = 0.25Q * logq (f);
124	      else
125		{
126		  num = 4 * __imag__ x;
127		  __imag__ res = 0.25Q * log1pq (num / den);
128		}
129	    }
130	}
131
132      math_check_force_underflow_complex (res);
133    }
134
135  return res;
136}
137