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glibc/math/s_catanh.c
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/* Return arc hyperbole tangent for double value. | |
Copyright (C) 1997-2016 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> | |
__complex__ double | |
__catanh (__complex__ double x) | |
{ | |
__complex__ double res; | |
int rcls = fpclassify (__real__ x); | |
int icls = fpclassify (__imag__ x); | |
if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) | |
{ | |
if (icls == FP_INFINITE) | |
{ | |
__real__ res = __copysign (0.0, __real__ x); | |
__imag__ res = __copysign (M_PI_2, __imag__ x); | |
} | |
else if (rcls == FP_INFINITE || rcls == FP_ZERO) | |
{ | |
__real__ res = __copysign (0.0, __real__ x); | |
if (icls >= FP_ZERO) | |
__imag__ res = __copysign (M_PI_2, __imag__ x); | |
else | |
__imag__ res = __nan (""); | |
} | |
else | |
{ | |
__real__ res = __nan (""); | |
__imag__ res = __nan (""); | |
} | |
} | |
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) | |
{ | |
res = x; | |
} | |
else | |
{ | |
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON | |
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON) | |
{ | |
__imag__ res = __copysign (M_PI_2, __imag__ x); | |
if (fabs (__imag__ x) <= 1.0) | |
__real__ res = 1.0 / __real__ x; | |
else if (fabs (__real__ x) <= 1.0) | |
__real__ res = __real__ x / __imag__ x / __imag__ x; | |
else | |
{ | |
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0); | |
__real__ res = __real__ x / h / h / 4.0; | |
} | |
} | |
else | |
{ | |
if (fabs (__real__ x) == 1.0 | |
&& fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON) | |
__real__ res = (__copysign (0.5, __real__ x) | |
* (M_LN2 - __ieee754_log (fabs (__imag__ x)))); | |
else | |
{ | |
double i2 = 0.0; | |
if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON) | |
i2 = __imag__ x * __imag__ x; | |
double num = 1.0 + __real__ x; | |
num = i2 + num * num; | |
double den = 1.0 - __real__ x; | |
den = i2 + den * den; | |
double f = num / den; | |
if (f < 0.5) | |
__real__ res = 0.25 * __ieee754_log (f); | |
else | |
{ | |
num = 4.0 * __real__ x; | |
__real__ res = 0.25 * __log1p (num / den); | |
} | |
} | |
double absx, absy, den; | |
absx = fabs (__real__ x); | |
absy = fabs (__imag__ x); | |
if (absx < absy) | |
{ | |
double t = absx; | |
absx = absy; | |
absy = t; | |
} | |
if (absy < DBL_EPSILON / 2.0) | |
{ | |
den = (1.0 - absx) * (1.0 + absx); | |
if (den == -0.0) | |
den = 0.0; | |
} | |
else if (absx >= 1.0) | |
den = (1.0 - absx) * (1.0 + absx) - absy * absy; | |
else if (absx >= 0.75 || absy >= 0.5) | |
den = -__x2y2m1 (absx, absy); | |
else | |
den = (1.0 - absx) * (1.0 + absx) - absy * absy; | |
__imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den); | |
} | |
math_check_force_underflow_complex (res); | |
} | |
return res; | |
} | |
weak_alias (__catanh, catanh) | |
#ifdef NO_LONG_DOUBLE | |
strong_alias (__catanh, __catanhl) | |
weak_alias (__catanh, catanhl) | |
#endif |