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122 lines
3.5 KiB
C
122 lines
3.5 KiB
C
/* Complex hyperbole tangent for long double. IBM extended format version.
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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 <float.h>
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#include <math.h>
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#include <math_ldbl_opt.h>
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#include <math_private.h>
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/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */
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static const long double ldbl_eps = 0x1p-106L;
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__complex__ long double
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__ctanhl (__complex__ long double x)
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{
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__complex__ long double res;
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if (!isfinite (__real__ x) || !isfinite (__imag__ x))
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{
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if (__isinfl (__real__ x))
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{
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__real__ res = __copysignl (1.0L, __real__ x);
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__imag__ res = __copysignl (0.0L, __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 = __nanl ("");
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__imag__ res = __nanl ("");
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#ifdef FE_INVALID
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if (__isinfl (__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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long double sinix, cosix;
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long double den;
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const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
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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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__sincosl (__imag__ x, &sinix, &cosix);
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if (fabsl (__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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long double exp_2t = __ieee754_expl (2 * t);
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__real__ res = __copysignl (1.0L, __real__ x);
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__imag__ res = 4 * sinix * cosix;
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__real__ x = fabsl (__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_expl (2.0L * __real__ x);
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}
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else
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{
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long double sinhrx, coshrx;
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if (fabs (__real__ x) > LDBL_MIN)
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{
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sinhrx = __ieee754_sinhl (__real__ x);
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coshrx = __ieee754_coshl (__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 = 1.0L;
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}
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if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
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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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/* __gcc_qmul does not respect -0.0 so we need the following fixup. */
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if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
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__real__ res = __real__ x;
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if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
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__imag__ res = __imag__ x;
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}
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return res;
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}
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long_double_symbol (libm, __ctanhl, ctanhl);
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