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122 lines
3.4 KiB
C
122 lines
3.4 KiB
C
/* Complex tangent function 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 <math.h>
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#include <math_ldbl_opt.h>
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#include <float.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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__ctanl (__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 (__imag__ x))
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{
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__real__ res = __copysignl (0.0, __real__ x);
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__imag__ res = __copysignl (1.0, __imag__ x);
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}
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else if (__real__ 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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if (__isinf_nsl (__real__ 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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long double sinrx, cosrx;
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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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/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
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= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
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__sincosl (__real__ x, &sinrx, &cosrx);
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if (fabsl (__imag__ x) > t)
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{
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/* Avoid intermediate overflow when the real part of the
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result may be subnormal. Ignoring negligible terms, the
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imaginary part is +/- 1, the real part is
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sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
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long double exp_2t = __ieee754_expl (2 * t);
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__imag__ res = __copysignl (1.0L, __imag__ x);
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__real__ res = 4 * sinrx * cosrx;
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__imag__ x = fabsl (__imag__ x);
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__imag__ x -= t;
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__real__ res /= exp_2t;
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if (__imag__ x > t)
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{
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/* Underflow (original imaginary part of x has absolute
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value > 2t). */
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__real__ res /= exp_2t;
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}
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else
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__real__ res /= __ieee754_expl (2.0L * __imag__ x);
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}
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else
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{
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long double sinhix, coshix;
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if (fabsl (__imag__ x) > LDBL_MIN)
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{
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sinhix = __ieee754_sinhl (__imag__ x);
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coshix = __ieee754_coshl (__imag__ x);
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}
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else
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{
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sinhix = __imag__ x;
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coshix = 1.0L;
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}
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if (fabsl (sinhix) > fabsl (cosrx) * ldbl_eps)
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den = cosrx * cosrx + sinhix * sinhix;
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else
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den = cosrx * cosrx;
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__real__ res = sinrx * (cosrx / den);
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__imag__ res = sinhix * (coshix / 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, __ctanl, ctanl);
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