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144 lines
3.7 KiB
C
144 lines
3.7 KiB
C
/* Return arc tangent of complex double value.
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Copyright (C) 1997-2016 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <complex.h>
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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__complex__ double
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__catan (__complex__ double x)
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{
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__complex__ double res;
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int rcls = fpclassify (__real__ x);
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int icls = fpclassify (__imag__ x);
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if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
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{
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if (rcls == FP_INFINITE)
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{
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__real__ res = __copysign (M_PI_2, __real__ x);
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__imag__ res = __copysign (0.0, __imag__ x);
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}
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else if (icls == FP_INFINITE)
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{
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if (rcls >= FP_ZERO)
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__real__ res = __copysign (M_PI_2, __real__ x);
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else
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__real__ res = __nan ("");
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__imag__ res = __copysign (0.0, __imag__ x);
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}
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else if (icls == FP_ZERO || icls == FP_INFINITE)
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{
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__real__ res = __nan ("");
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__imag__ res = __copysign (0.0, __imag__ x);
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}
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else
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{
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__real__ res = __nan ("");
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__imag__ res = __nan ("");
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}
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}
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else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
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{
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res = x;
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}
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else
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{
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if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
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|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
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{
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__real__ res = __copysign (M_PI_2, __real__ x);
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if (fabs (__real__ x) <= 1.0)
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__imag__ res = 1.0 / __imag__ x;
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else if (fabs (__imag__ x) <= 1.0)
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__imag__ res = __imag__ x / __real__ x / __real__ x;
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else
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{
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double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
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__imag__ res = __imag__ x / h / h / 4.0;
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}
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}
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else
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{
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double den, absx, absy;
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absx = fabs (__real__ x);
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absy = fabs (__imag__ x);
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if (absx < absy)
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{
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double t = absx;
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absx = absy;
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absy = t;
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}
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if (absy < DBL_EPSILON / 2.0)
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{
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den = (1.0 - absx) * (1.0 + absx);
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if (den == -0.0)
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den = 0.0;
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}
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else if (absx >= 1.0)
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den = (1.0 - absx) * (1.0 + absx) - absy * absy;
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else if (absx >= 0.75 || absy >= 0.5)
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den = -__x2y2m1 (absx, absy);
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else
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den = (1.0 - absx) * (1.0 + absx) - absy * absy;
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__real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
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if (fabs (__imag__ x) == 1.0
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&& fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON)
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__imag__ res = (__copysign (0.5, __imag__ x)
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* (M_LN2 - __ieee754_log (fabs (__real__ x))));
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else
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{
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double r2 = 0.0, num, f;
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if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON)
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r2 = __real__ x * __real__ x;
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num = __imag__ x + 1.0;
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num = r2 + num * num;
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den = __imag__ x - 1.0;
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den = r2 + den * den;
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f = num / den;
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if (f < 0.5)
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__imag__ res = 0.25 * __ieee754_log (f);
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else
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{
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num = 4.0 * __imag__ x;
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__imag__ res = 0.25 * __log1p (num / den);
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}
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}
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}
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math_check_force_underflow_complex (res);
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}
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return res;
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}
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weak_alias (__catan, catan)
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#ifdef NO_LONG_DOUBLE
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strong_alias (__catan, __catanl)
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weak_alias (__catan, catanl)
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#endif
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