/* Complex hyperbolic tangent for float types. Copyright (C) 1997-2017 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 CFLOAT M_DECL_FUNC (__ctanh) (CFLOAT x) { CFLOAT res; if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) { if (isinf (__real__ x)) { __real__ res = M_COPYSIGN (1, __real__ x); if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1) { FLOAT sinix, cosix; M_SINCOS (__imag__ x, &sinix, &cosix); __imag__ res = M_COPYSIGN (0, sinix * cosix); } else __imag__ res = M_COPYSIGN (0, __imag__ x); } else if (__imag__ x == 0) { res = x; } else { if (__real__ x == 0) __real__ res = __real__ x; else __real__ res = M_NAN; __imag__ res = M_NAN; if (isinf (__imag__ x)) feraiseexcept (FE_INVALID); } } else { FLOAT sinix, cosix; FLOAT den; const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2); /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ if (__glibc_likely (M_FABS (__imag__ x) > M_MIN)) { M_SINCOS (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1; } if (M_FABS (__real__ x) > t) { /* Avoid intermediate overflow when the imaginary part of the result may be subnormal. Ignoring negligible terms, the real part is +/- 1, the imaginary part is sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ FLOAT exp_2t = M_EXP (2 * t); __real__ res = M_COPYSIGN (1, __real__ x); __imag__ res = 4 * sinix * cosix; __real__ x = M_FABS (__real__ x); __real__ x -= t; __imag__ res /= exp_2t; if (__real__ x > t) { /* Underflow (original real part of x has absolute value > 2t). */ __imag__ res /= exp_2t; } else __imag__ res /= M_EXP (2 * __real__ x); } else { FLOAT sinhrx, coshrx; if (M_FABS (__real__ x) > M_MIN) { sinhrx = M_SINH (__real__ x); coshrx = M_COSH (__real__ x); } else { sinhrx = __real__ x; coshrx = 1; } if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON) den = sinhrx * sinhrx + cosix * cosix; else den = cosix * cosix; __real__ res = sinhrx * coshrx / den; __imag__ res = sinix * cosix / den; } math_check_force_underflow_complex (res); } return res; } declare_mgen_alias (__ctanh, ctanh)