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/* Complex hyperbole tangent for long double. IBM extended format version.
Copyright (C) 1997-2014 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 <fenv.h>
#include <float.h>
#include <math.h>
#include <math_ldbl_opt.h>
#include <math_private.h>
/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */
static const long double ldbl_eps = 0x1p-106L;
__complex__ long double
__ctanhl (__complex__ long double x)
{
__complex__ long double res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinfl (__real__ x))
{
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = __copysignl (0.0L, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
#ifdef FE_INVALID
if (__isinfl (__imag__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
long double sinix, cosix;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
__sincosl (__imag__ x, &sinix, &cosix);
if (fabsl (__real__ x) > t)
{
/* Avoid intermediate overflow when the imaginary part of
the result may be subnormal. Ignoring negligible terms,
the real part is +/- 1, the imaginary part is
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
long double exp_2t = __ieee754_expl (2 * t);
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsl (__real__ x);
__real__ x -= t;
__imag__ res /= exp_2t;
if (__real__ x > t)
{
/* Underflow (original real part of x has absolute value
> 2t). */
__imag__ res /= exp_2t;
}
else
__imag__ res /= __ieee754_expl (2.0L * __real__ x);
}
else
{
long double sinhrx, coshrx;
if (fabs (__real__ x) > LDBL_MIN)
{
sinhrx = __ieee754_sinhl (__real__ x);
coshrx = __ieee754_coshl (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0L;
}
if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * (coshrx / den);
__imag__ res = sinix * (cosix / den);
}
/* __gcc_qmul does not respect -0.0 so we need the following fixup. */
if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
__real__ res = __real__ x;
if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
__imag__ res = __imag__ x;
}
return res;
}
long_double_symbol (libm, __ctanhl, ctanhl);
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