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 /* Complex tangent function for double. Copyright (C) 1997-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see . */ #include #include #include #include #include __complex__ double __ctan (__complex__ double x) { __complex__ double res; if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0)) { if (__isinf_ns (__imag__ x)) { __real__ res = __copysign (0.0, __real__ x); __imag__ res = __copysign (1.0, __imag__ x); } else if (__real__ x == 0.0) { res = x; } else { __real__ res = __nan (""); __imag__ res = __nan (""); if (__isinf_ns (__real__ x)) feraiseexcept (FE_INVALID); } } else { double sinrx, cosrx; double den; const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); int rcls = fpclassify (__real__ x); /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ if (__builtin_expect (rcls != FP_SUBNORMAL, 1)) { __sincos (__real__ x, &sinrx, &cosrx); } else { sinrx = __real__ x; cosrx = 1.0; } if (fabs (__imag__ x) > t) { /* Avoid intermediate overflow when the real part of the result may be subnormal. Ignoring negligible terms, the imaginary part is +/- 1, the real part is sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ double exp_2t = __ieee754_exp (2 * t); __imag__ res = __copysign (1.0, __imag__ x); __real__ res = 4 * sinrx * cosrx; __imag__ x = fabs (__imag__ x); __imag__ x -= t; __real__ res /= exp_2t; if (__imag__ x > t) { /* Underflow (original imaginary part of x has absolute value > 2t). */ __real__ res /= exp_2t; } else __real__ res /= __ieee754_exp (2 * __imag__ x); } else { double sinhix, coshix; if (fabs (__imag__ x) > DBL_MIN) { sinhix = __ieee754_sinh (__imag__ x); coshix = __ieee754_cosh (__imag__ x); } else { sinhix = __imag__ x; coshix = 1.0; } if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON) den = cosrx * cosrx + sinhix * sinhix; else den = cosrx * cosrx; __real__ res = sinrx * cosrx / den; __imag__ res = sinhix * coshix / den; } } return res; } weak_alias (__ctan, ctan) #ifdef NO_LONG_DOUBLE strong_alias (__ctan, __ctanl) weak_alias (__ctan, ctanl) #endif