| /* Return arc tangent of complex float type. |
| Copyright (C) 1997-2018 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 <math.h> |
| #include <math_private.h> |
| #include <float.h> |
| |
| CFLOAT |
| M_DECL_FUNC (__catan) (CFLOAT x) |
| { |
| CFLOAT res; |
| int rcls = fpclassify (__real__ x); |
| int icls = fpclassify (__imag__ x); |
| |
| if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) |
| { |
| if (rcls == FP_INFINITE) |
| { |
| __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
| __imag__ res = M_COPYSIGN (0, __imag__ x); |
| } |
| else if (icls == FP_INFINITE) |
| { |
| if (rcls >= FP_ZERO) |
| __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
| else |
| __real__ res = M_NAN; |
| __imag__ res = M_COPYSIGN (0, __imag__ x); |
| } |
| else if (icls == FP_ZERO || icls == FP_INFINITE) |
| { |
| __real__ res = M_NAN; |
| __imag__ res = M_COPYSIGN (0, __imag__ x); |
| } |
| else |
| { |
| __real__ res = M_NAN; |
| __imag__ res = M_NAN; |
| } |
| } |
| else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
| { |
| res = x; |
| } |
| else |
| { |
| if (M_FABS (__real__ x) >= 16 / M_EPSILON |
| || M_FABS (__imag__ x) >= 16 / M_EPSILON) |
| { |
| __real__ res = M_COPYSIGN (M_MLIT (M_PI_2), __real__ x); |
| if (M_FABS (__real__ x) <= 1) |
| __imag__ res = 1 / __imag__ x; |
| else if (M_FABS (__imag__ x) <= 1) |
| __imag__ res = __imag__ x / __real__ x / __real__ x; |
| else |
| { |
| FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2); |
| __imag__ res = __imag__ x / h / h / 4; |
| } |
| } |
| else |
| { |
| FLOAT den, absx, absy; |
| |
| absx = M_FABS (__real__ x); |
| absy = M_FABS (__imag__ x); |
| if (absx < absy) |
| { |
| FLOAT t = absx; |
| absx = absy; |
| absy = t; |
| } |
| |
| if (absy < M_EPSILON / 2) |
| { |
| den = (1 - absx) * (1 + absx); |
| if (den == 0) |
| den = 0; |
| } |
| else if (absx >= 1) |
| den = (1 - absx) * (1 + absx) - absy * absy; |
| else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5)) |
| den = -M_SUF (__x2y2m1) (absx, absy); |
| else |
| den = (1 - absx) * (1 + absx) - absy * absy; |
| |
| __real__ res = M_LIT (0.5) * M_ATAN2 (2 * __real__ x, den); |
| |
| if (M_FABS (__imag__ x) == 1 |
| && M_FABS (__real__ x) < M_EPSILON * M_EPSILON) |
| __imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x) |
| * ((FLOAT) M_MLIT (M_LN2) |
| - M_LOG (M_FABS (__real__ x)))); |
| else |
| { |
| FLOAT r2 = 0, num, f; |
| |
| if (M_FABS (__real__ x) >= M_EPSILON * M_EPSILON) |
| r2 = __real__ x * __real__ x; |
| |
| num = __imag__ x + 1; |
| num = r2 + num * num; |
| |
| den = __imag__ x - 1; |
| den = r2 + den * den; |
| |
| f = num / den; |
| if (f < M_LIT (0.5)) |
| __imag__ res = M_LIT (0.25) * M_LOG (f); |
| else |
| { |
| num = 4 * __imag__ x; |
| __imag__ res = M_LIT (0.25) * M_LOG1P (num / den); |
| } |
| } |
| } |
| |
| math_check_force_underflow_complex (res); |
| } |
| |
| return res; |
| } |
| |
| declare_mgen_alias (__catan, catan) |