xref: /netbsd-src/external/gpl3/gcc.old/dist/libquadmath/math/catanhq.c (revision 627f7eb200a4419d89b531d55fccd2ee3ffdcde0)
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