1/* Complex square root of a float type.
2   Copyright (C) 1997-2018 Free Software Foundation, Inc.
3   This file is part of the GNU C Library.
4   Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
5   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
6
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.
11
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.
16
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/>.  */
20
21#include "quadmath-imp.h"
22
23__complex128
24csqrtq (__complex128 x)
25{
26  __complex128 res;
27  int rcls = fpclassifyq (__real__ x);
28  int icls = fpclassifyq (__imag__ x);
29
30  if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
31    {
32      if (icls == QUADFP_INFINITE)
33	{
34	  __real__ res = HUGE_VALQ;
35	  __imag__ res = __imag__ x;
36	}
37      else if (rcls == QUADFP_INFINITE)
38	{
39	  if (__real__ x < 0)
40	    {
41	      __real__ res = icls == QUADFP_NAN ? nanq ("") : 0;
42	      __imag__ res = copysignq (HUGE_VALQ, __imag__ x);
43	    }
44	  else
45	    {
46	      __real__ res = __real__ x;
47	      __imag__ res = (icls == QUADFP_NAN
48			      ? nanq ("") : copysignq (0, __imag__ x));
49	    }
50	}
51      else
52	{
53	  __real__ res = nanq ("");
54	  __imag__ res = nanq ("");
55	}
56    }
57  else
58    {
59      if (__glibc_unlikely (icls == QUADFP_ZERO))
60	{
61	  if (__real__ x < 0)
62	    {
63	      __real__ res = 0;
64	      __imag__ res = copysignq (sqrtq (-__real__ x), __imag__ x);
65	    }
66	  else
67	    {
68	      __real__ res = fabsq (sqrtq (__real__ x));
69	      __imag__ res = copysignq (0, __imag__ x);
70	    }
71	}
72      else if (__glibc_unlikely (rcls == QUADFP_ZERO))
73	{
74	  __float128 r;
75	  if (fabsq (__imag__ x) >= 2 * FLT128_MIN)
76	    r = sqrtq (0.5Q * fabsq (__imag__ x));
77	  else
78	    r = 0.5Q * sqrtq (2 * fabsq (__imag__ x));
79
80	  __real__ res = r;
81	  __imag__ res = copysignq (r, __imag__ x);
82	}
83      else
84	{
85	  __float128 d, r, s;
86	  int scale = 0;
87
88	  if (fabsq (__real__ x) > FLT128_MAX / 4)
89	    {
90	      scale = 1;
91	      __real__ x = scalbnq (__real__ x, -2 * scale);
92	      __imag__ x = scalbnq (__imag__ x, -2 * scale);
93	    }
94	  else if (fabsq (__imag__ x) > FLT128_MAX / 4)
95	    {
96	      scale = 1;
97	      if (fabsq (__real__ x) >= 4 * FLT128_MIN)
98		__real__ x = scalbnq (__real__ x, -2 * scale);
99	      else
100		__real__ x = 0;
101	      __imag__ x = scalbnq (__imag__ x, -2 * scale);
102	    }
103	  else if (fabsq (__real__ x) < 2 * FLT128_MIN
104		   && fabsq (__imag__ x) < 2 * FLT128_MIN)
105	    {
106	      scale = -((FLT128_MANT_DIG + 1) / 2);
107	      __real__ x = scalbnq (__real__ x, -2 * scale);
108	      __imag__ x = scalbnq (__imag__ x, -2 * scale);
109	    }
110
111	  d = hypotq (__real__ x, __imag__ x);
112	  /* Use the identity   2  Re res  Im res = Im x
113	     to avoid cancellation error in  d +/- Re x.  */
114	  if (__real__ x > 0)
115	    {
116	      r = sqrtq (0.5Q * (d + __real__ x));
117	      if (scale == 1 && fabsq (__imag__ x) < 1)
118		{
119		  /* Avoid possible intermediate underflow.  */
120		  s = __imag__ x / r;
121		  r = scalbnq (r, scale);
122		  scale = 0;
123		}
124	      else
125		s = 0.5Q * (__imag__ x / r);
126	    }
127	  else
128	    {
129	      s = sqrtq (0.5Q * (d - __real__ x));
130	      if (scale == 1 && fabsq (__imag__ x) < 1)
131		{
132		  /* Avoid possible intermediate underflow.  */
133		  r = fabsq (__imag__ x / s);
134		  s = scalbnq (s, scale);
135		  scale = 0;
136		}
137	      else
138		r = fabsq (0.5Q * (__imag__ x / s));
139	    }
140
141	  if (scale)
142	    {
143	      r = scalbnq (r, scale);
144	      s = scalbnq (s, scale);
145	    }
146
147	  math_check_force_underflow (r);
148	  math_check_force_underflow (s);
149
150	  __real__ res = r;
151	  __imag__ res = copysignq (s, __imag__ x);
152	}
153    }
154
155  return res;
156}
157