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/* Return arc hyperbole cosine for double value.
Copyright (C) 1997-2013 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <complex.h>
#include <math.h>
#include <math_private.h>
__complex__ double
__cacosh (__complex__ double x)
{
__complex__ double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VAL;
if (rcls == FP_NAN)
__imag__ res = __nan ("");
else
__imag__ res = __copysign ((rcls == FP_INFINITE
? (__real__ x < 0.0
? M_PI - M_PI_4 : M_PI_4)
: M_PI_2), __imag__ x);
}
else if (rcls == FP_INFINITE)
{
__real__ res = HUGE_VAL;
if (icls >= FP_ZERO)
__imag__ res = __copysign (signbit (__real__ x) ? M_PI : 0.0,
__imag__ x);
else
__imag__ res = __nan ("");
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else if (rcls == FP_ZERO && icls == FP_ZERO)
{
__real__ res = 0.0;
__imag__ res = __copysign (M_PI_2, __imag__ x);
}
/* The factor 16 is just a guess. */
else if (16.0 * fabs (__imag__ x) < fabs (__real__ x))
{
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0 * __clog (__csqrt ((x + 1.0) / 2.0) + __csqrt ((x - 1.0) / 2.0));
if (signbit (__real__ res))
__real__ res = 0.0;
}
else
{
__complex__ double y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = __csqrt (y);
if (signbit (__real__ x))
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = __clog (y);
}
return res;
}
weak_alias (__cacosh, cacosh)
#ifdef NO_LONG_DOUBLE
strong_alias (__cacosh, __cacoshl)
weak_alias (__cacosh, cacoshl)
#endif
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