1 /* Complex square root of long double value.
2 Copyright (C) 1997-2014 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.
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.
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.
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/>. */
23 #include <math_private.h>
26 __complex__ long double
27 __csqrtl (__complex__ long double x)
29 __complex__ long double res;
30 int rcls = fpclassify (__real__ x);
31 int icls = fpclassify (__imag__ x);
33 if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
35 if (icls == FP_INFINITE)
37 __real__ res = HUGE_VALL;
38 __imag__ res = __imag__ x;
40 else if (rcls == FP_INFINITE)
44 __real__ res = icls == FP_NAN ? __nanl ("") : 0;
45 __imag__ res = __copysignl (HUGE_VALL, __imag__ x);
49 __real__ res = __real__ x;
50 __imag__ res = (icls == FP_NAN
51 ? __nanl ("") : __copysignl (0.0, __imag__ x));
56 __real__ res = __nanl ("");
57 __imag__ res = __nanl ("");
62 if (__glibc_unlikely (icls == FP_ZERO))
67 __imag__ res = __copysignl (__ieee754_sqrtl (-__real__ x),
72 __real__ res = fabsl (__ieee754_sqrtl (__real__ x));
73 __imag__ res = __copysignl (0.0, __imag__ x);
76 else if (__glibc_unlikely (rcls == FP_ZERO))
79 if (fabsl (__imag__ x) >= 2.0L * LDBL_MIN)
80 r = __ieee754_sqrtl (0.5L * fabsl (__imag__ x));
82 r = 0.5L * __ieee754_sqrtl (2.0L * fabsl (__imag__ x));
85 __imag__ res = __copysignl (r, __imag__ x);
92 if (fabsl (__real__ x) > LDBL_MAX / 4.0L)
95 __real__ x = __scalbnl (__real__ x, -2 * scale);
96 __imag__ x = __scalbnl (__imag__ x, -2 * scale);
98 else if (fabsl (__imag__ x) > LDBL_MAX / 4.0L)
101 if (fabsl (__real__ x) >= 4.0L * LDBL_MIN)
102 __real__ x = __scalbnl (__real__ x, -2 * scale);
105 __imag__ x = __scalbnl (__imag__ x, -2 * scale);
107 else if (fabsl (__real__ x) < LDBL_MIN
108 && fabsl (__imag__ x) < LDBL_MIN)
110 scale = -(LDBL_MANT_DIG / 2);
111 __real__ x = __scalbnl (__real__ x, -2 * scale);
112 __imag__ x = __scalbnl (__imag__ x, -2 * scale);
115 d = __ieee754_hypotl (__real__ x, __imag__ x);
116 /* Use the identity 2 Re res Im res = Im x
117 to avoid cancellation error in d +/- Re x. */
120 r = __ieee754_sqrtl (0.5L * (d + __real__ x));
121 s = 0.5L * (__imag__ x / r);
125 s = __ieee754_sqrtl (0.5L * (d - __real__ x));
126 r = fabsl (0.5L * (__imag__ x / s));
131 r = __scalbnl (r, scale);
132 s = __scalbnl (s, scale);
136 __imag__ res = __copysignl (s, __imag__ x);
142 weak_alias (__csqrtl, csqrtl)