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glibc/math/s_catanl.c
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/* Return arc tangent of complex long 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> | |
/* To avoid spurious overflows, use this definition to treat IBM long | |
double as approximating an IEEE-style format. */ | |
#if LDBL_MANT_DIG == 106 | |
# undef LDBL_EPSILON | |
# define LDBL_EPSILON 0x1p-106L | |
#endif | |
__complex__ long double | |
__catanl (__complex__ long double x) | |
{ | |
__complex__ long double 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 = __copysignl (M_PI_2l, __real__ x); | |
__imag__ res = __copysignl (0.0, __imag__ x); | |
} | |
else if (icls == FP_INFINITE) | |
{ | |
if (rcls >= FP_ZERO) | |
__real__ res = __copysignl (M_PI_2l, __real__ x); | |
else | |
__real__ res = __nanl (""); | |
__imag__ res = __copysignl (0.0, __imag__ x); | |
} | |
else if (icls == FP_ZERO || icls == FP_INFINITE) | |
{ | |
__real__ res = __nanl (""); | |
__imag__ res = __copysignl (0.0, __imag__ x); | |
} | |
else | |
{ | |
__real__ res = __nanl (""); | |
__imag__ res = __nanl (""); | |
} | |
} | |
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) | |
{ | |
res = x; | |
} | |
else | |
{ | |
if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON | |
|| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON) | |
{ | |
__real__ res = __copysignl (M_PI_2l, __real__ x); | |
if (fabsl (__real__ x) <= 1.0L) | |
__imag__ res = 1.0L / __imag__ x; | |
else if (fabsl (__imag__ x) <= 1.0L) | |
__imag__ res = __imag__ x / __real__ x / __real__ x; | |
else | |
{ | |
long double h = __ieee754_hypotl (__real__ x / 2.0L, | |
__imag__ x / 2.0L); | |
__imag__ res = __imag__ x / h / h / 4.0L; | |
} | |
} | |
else | |
{ | |
long double den, absx, absy; | |
absx = fabsl (__real__ x); | |
absy = fabsl (__imag__ x); | |
if (absx < absy) | |
{ | |
long double t = absx; | |
absx = absy; | |
absy = t; | |
} | |
if (absy < LDBL_EPSILON / 2.0L) | |
{ | |
den = (1.0L - absx) * (1.0L + absx); | |
if (den == -0.0L) | |
den = 0.0L; | |
} | |
else if (absx >= 1.0L) | |
den = (1.0L - absx) * (1.0L + absx) - absy * absy; | |
else if (absx >= 0.75L || absy >= 0.5L) | |
den = -__x2y2m1l (absx, absy); | |
else | |
den = (1.0L - absx) * (1.0L + absx) - absy * absy; | |
__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den); | |
if (fabsl (__imag__ x) == 1.0L | |
&& fabsl (__real__ x) < LDBL_EPSILON * LDBL_EPSILON) | |
__imag__ res = (__copysignl (0.5L, __imag__ x) | |
* (M_LN2l - __ieee754_logl (fabsl (__real__ x)))); | |
else | |
{ | |
long double r2 = 0.0L, num, f; | |
if (fabsl (__real__ x) >= LDBL_EPSILON * LDBL_EPSILON) | |
r2 = __real__ x * __real__ x; | |
num = __imag__ x + 1.0L; | |
num = r2 + num * num; | |
den = __imag__ x - 1.0L; | |
den = r2 + den * den; | |
f = num / den; | |
if (f < 0.5L) | |
__imag__ res = 0.25L * __ieee754_logl (f); | |
else | |
{ | |
num = 4.0L * __imag__ x; | |
__imag__ res = 0.25L * __log1pl (num / den); | |
} | |
} | |
} | |
math_check_force_underflow_complex (res); | |
} | |
return res; | |
} | |
weak_alias (__catanl, catanl) |