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102 lines
2.8 KiB
C
102 lines
2.8 KiB
C
/* Complex hyperbole tangent for double.
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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 <complex.h>
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#include <fenv.h>
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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__complex__ double
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__ctanh (__complex__ double x)
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{
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__complex__ double res;
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if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
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{
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if (__isinf_ns (__real__ x))
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{
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__real__ res = __copysign (1.0, __real__ x);
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__imag__ res = __copysign (0.0, __imag__ x);
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}
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else if (__imag__ x == 0.0)
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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 = __nan ("");
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__imag__ res = __nan ("");
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if (__isinf_ns (__imag__ x))
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feraiseexcept (FE_INVALID);
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}
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}
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else
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{
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double sinix, cosix;
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double den;
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const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
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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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__sincos (__imag__ x, &sinix, &cosix);
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if (fabs (__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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double exp_2t = __ieee754_exp (2 * t);
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__real__ res = __copysign (1.0, __real__ x);
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__imag__ res = 4 * sinix * cosix;
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__real__ x = fabs (__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 /= __ieee754_exp (2 * __real__ x);
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}
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else
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{
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double sinhrx = __ieee754_sinh (__real__ x);
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double coshrx = __ieee754_cosh (__real__ x);
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den = sinhrx * sinhrx + 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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weak_alias (__ctanh, ctanh)
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#ifdef NO_LONG_DOUBLE
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strong_alias (__ctanh, __ctanhl)
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weak_alias (__ctanh, ctanhl)
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#endif
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