/* Complex tangent function for float. Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 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 <http://www.gnu.org/licenses/>. */ #include <complex.h> #include <fenv.h> #include <math.h> #include <math_private.h> #include <float.h> __complex__ float __ctanf (__complex__ float x) { __complex__ float res; if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0)) { if (__isinf_nsf (__imag__ x)) { __real__ res = __copysignf (0.0, __real__ x); __imag__ res = __copysignf (1.0, __imag__ x); } else if (__real__ x == 0.0) { res = x; } else { __real__ res = __nanf (""); __imag__ res = __nanf (""); if (__isinf_nsf (__real__ x)) feraiseexcept (FE_INVALID); } } else { float sinrx, cosrx; float den; const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2); /* 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). */ __sincosf (__real__ x, &sinrx, &cosrx); if (fabsf (__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). */ float exp_2t = __ieee754_expf (2 * t); __imag__ res = __copysignf (1.0, __imag__ x); __real__ res = 4 * sinrx * cosrx; __imag__ x = fabsf (__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_expf (2 * __imag__ x); } else { float sinhix = __ieee754_sinhf (__imag__ x); float coshix = __ieee754_coshf (__imag__ x); den = cosrx * cosrx + sinhix * sinhix; __real__ res = sinrx * cosrx / den; __imag__ res = sinhix * coshix / den; } } return res; } #ifndef __ctanf weak_alias (__ctanf, ctanf) #endif