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121 lines
3.1 KiB
C
121 lines
3.1 KiB
C
/* Complex hyperbole tangent for __float128.
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Copyright (C) 1997-2012 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include "quadmath-imp.h"
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#ifdef HAVE_FENV_H
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# include <fenv.h>
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#endif
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__complex128
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ctanhq (__complex128 x)
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{
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__complex128 res;
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if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
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{
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if (__quadmath_isinf_nsq (__real__ x))
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{
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__real__ res = copysignq (1.0Q, __real__ x);
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__imag__ res = copysignq (0.0Q, __imag__ x);
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}
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else if (__imag__ x == 0.0Q)
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{
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res = x;
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}
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else
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{
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__real__ res = nanq ("");
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__imag__ res = nanq ("");
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#ifdef HAVE_FENV_H
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if (__quadmath_isinf_nsq (__imag__ x))
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feraiseexcept (FE_INVALID);
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#endif
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}
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}
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else
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{
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__float128 sinix, cosix;
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__float128 den;
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const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
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int icls = fpclassifyq (__imag__ x);
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/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
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= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
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if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
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{
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sincosq (__imag__ x, &sinix, &cosix);
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}
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else
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{
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sinix = __imag__ x;
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cosix = 1.0Q;
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}
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if (fabsq (__real__ x) > t)
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{
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/* Avoid intermediate overflow when the imaginary part of
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the result may be subnormal. Ignoring negligible terms,
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the real part is +/- 1, the imaginary part is
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sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
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__float128 exp_2t = expq (2 * t);
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__real__ res = copysignq (1.0, __real__ x);
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__imag__ res = 4 * sinix * cosix;
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__real__ x = fabsq (__real__ x);
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__real__ x -= t;
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__imag__ res /= exp_2t;
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if (__real__ x > t)
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{
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/* Underflow (original real part of x has absolute value
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> 2t). */
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__imag__ res /= exp_2t;
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}
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else
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__imag__ res /= expq (2 * __real__ x);
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}
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else
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{
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__float128 sinhrx, coshrx;
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if (fabsq (__real__ x) > FLT128_MIN)
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{
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sinhrx = sinhq (__real__ x);
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coshrx = coshq (__real__ x);
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}
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else
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{
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sinhrx = __real__ x;
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coshrx = 1.0Q;
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}
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if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
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den = sinhrx * sinhrx + cosix * cosix;
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else
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den = cosix * cosix;
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__real__ res = sinhrx * coshrx / den;
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__imag__ res = sinix * cosix / den;
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}
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}
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return res;
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}
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