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/* Complex tangent function for double.
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 <math.h>
#include <math_private.h>
#include <float.h>
__complex__ double
__ctan (__complex__ double x)
{
__complex__ double res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_ns (__imag__ x))
{
__real__ res = __copysign (0.0, __real__ x);
__imag__ res = __copysign (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
if (__isinf_ns (__real__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
double sinrx, cosrx;
double den;
const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
int rcls = fpclassify (__real__ x);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincos (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0;
}
if (fabs (__imag__ x) > t)
{
/* Avoid intermediate overflow when the real part of the
result may be subnormal. Ignoring negligible terms, the
imaginary part is +/- 1, the real part is
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
double exp_2t = __ieee754_exp (2 * t);
__imag__ res = __copysign (1.0, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabs (__imag__ x);
__imag__ x -= t;
__real__ res /= exp_2t;
if (__imag__ x > t)
{
/* Underflow (original imaginary part of x has absolute
value > 2t). */
__real__ res /= exp_2t;
}
else
__real__ res /= __ieee754_exp (2 * __imag__ x);
}
else
{
double sinhix, coshix;
if (fabs (__imag__ x) > DBL_MIN)
{
sinhix = __ieee754_sinh (__imag__ x);
coshix = __ieee754_cosh (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0;
}
if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
}
return res;
}
weak_alias (__ctan, ctan)
#ifdef NO_LONG_DOUBLE
strong_alias (__ctan, __ctanl)
weak_alias (__ctan, ctanl)
#endif
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