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131 lines
3.3 KiB
C
131 lines
3.3 KiB
C
/* Complex hyperbolic tangent for float types.
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Copyright (C) 1997-2019 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 <math-underflow.h>
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#include <float.h>
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CFLOAT
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M_DECL_FUNC (__ctanh) (CFLOAT x)
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{
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CFLOAT res;
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if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
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{
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if (isinf (__real__ x))
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{
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__real__ res = M_COPYSIGN (1, __real__ x);
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if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
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{
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FLOAT sinix, cosix;
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M_SINCOS (__imag__ x, &sinix, &cosix);
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__imag__ res = M_COPYSIGN (0, sinix * cosix);
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}
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else
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__imag__ res = M_COPYSIGN (0, __imag__ x);
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}
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else if (__imag__ x == 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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if (__real__ x == 0)
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__real__ res = __real__ x;
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else
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__real__ res = M_NAN;
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__imag__ res = M_NAN;
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if (isinf (__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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FLOAT sinix, cosix;
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FLOAT den;
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const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (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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if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
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{
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M_SINCOS (__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;
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}
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if (M_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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FLOAT exp_2t = M_EXP (2 * t);
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__real__ res = M_COPYSIGN (1, __real__ x);
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__imag__ res = 4 * sinix * cosix;
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__real__ x = M_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 /= M_EXP (2 * __real__ x);
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}
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else
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{
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FLOAT sinhrx, coshrx;
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if (M_FABS (__real__ x) > M_MIN)
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{
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sinhrx = M_SINH (__real__ x);
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coshrx = M_COSH (__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;
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}
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if (M_FABS (sinhrx) > M_FABS (cosix) * M_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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math_check_force_underflow_complex (res);
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}
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return res;
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}
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declare_mgen_alias (__ctanh, ctanh)
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