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/* Complex hyperbole tangent for float.
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 <fenv.h>
#include <math.h>
#include <math_private.h>
#include <float.h>
__complex__ float
__ctanhf (__complex__ float x)
{
__complex__ float res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_nsf (__real__ x))
{
__real__ res = __copysignf (1.0, __real__ x);
__imag__ res = __copysignf (0.0, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
if (__isinf_nsf (__imag__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
float sinix, cosix;
float den;
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
/* 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). */
if (__builtin_expect (fpclassify(__imag__ x) != FP_SUBNORMAL, 1))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (fabsf (__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). */
float exp_2t = __ieee754_expf (2 * t);
__real__ res = __copysignf (1.0, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsf (__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_expf (2 * __real__ x);
}
else
{
float sinhrx, coshrx;
if (fabsf (__real__ x) > FLT_MIN)
{
sinhrx = __ieee754_sinhf (__real__ x);
coshrx = __ieee754_coshf (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0f;
}
if (fabsf (sinhrx) > fabsf (cosix) * FLT_EPSILON)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
}
return res;
}
#ifndef __ctanhf
weak_alias (__ctanhf, ctanhf)
#endif
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