153 lines
4.1 KiB
C
153 lines
4.1 KiB
C
/* Return arc tangent of complex long double value.
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Copyright (C) 1997-2013 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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/* To avoid spurious overflows, use this definition to treat IBM long
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double as approximating an IEEE-style format. */
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#if LDBL_MANT_DIG == 106
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# undef LDBL_EPSILON
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# define LDBL_EPSILON 0x1p-106L
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#endif
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__complex__ long double
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__catanl (__complex__ long double x)
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{
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__complex__ long 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 (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
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{
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if (rcls == FP_INFINITE)
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{
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__real__ res = __copysignl (M_PI_2l, __real__ x);
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__imag__ res = __copysignl (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 = __copysignl (M_PI_2l, __real__ x);
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else
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__real__ res = __nanl ("");
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__imag__ res = __copysignl (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 = __nanl ("");
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__imag__ res = __copysignl (0.0, __imag__ x);
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}
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else
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{
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__real__ res = __nanl ("");
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__imag__ res = __nanl ("");
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}
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}
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else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
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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 (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
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|| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
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{
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__real__ res = __copysignl (M_PI_2l, __real__ x);
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if (fabsl (__real__ x) <= 1.0L)
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__imag__ res = 1.0L / __imag__ x;
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else if (fabsl (__imag__ x) <= 1.0L)
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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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long double h = __ieee754_hypotl (__real__ x / 2.0L,
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__imag__ x / 2.0L);
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__imag__ res = __imag__ x / h / h / 4.0L;
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}
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}
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else
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{
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long double den, absx, absy;
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absx = fabsl (__real__ x);
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absy = fabsl (__imag__ x);
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if (absx < absy)
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{
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long 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 < LDBL_EPSILON / 2.0L)
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den = (1.0L - absx) * (1.0L + absx);
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else if (absx >= 1.0L)
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den = (1.0L - absx) * (1.0L + absx) - absy * absy;
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else if (absx >= 0.75L || absy >= 0.5L)
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den = -__x2y2m1l (absx, absy);
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else
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den = (1.0L - absx) * (1.0L + absx) - absy * absy;
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__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
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if (fabsl (__imag__ x) == 1.0L
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&& fabsl (__real__ x) < LDBL_EPSILON * LDBL_EPSILON)
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__imag__ res = (__copysignl (0.5L, __imag__ x)
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* (M_LN2l - __ieee754_logl (fabsl (__real__ x))));
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else
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{
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long double r2 = 0.0L, num, f;
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if (fabsl (__real__ x) >= LDBL_EPSILON * LDBL_EPSILON)
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r2 = __real__ x * __real__ x;
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num = __imag__ x + 1.0L;
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num = r2 + num * num;
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den = __imag__ x - 1.0L;
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den = r2 + den * den;
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f = num / den;
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if (f < 0.5L)
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__imag__ res = 0.25L * __ieee754_logl (f);
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else
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{
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num = 4.0L * __imag__ x;
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__imag__ res = 0.25L * __log1pl (num / den);
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}
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}
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}
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if (fabsl (__real__ res) < LDBL_MIN)
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{
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volatile long double force_underflow = __real__ res * __real__ res;
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(void) force_underflow;
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}
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if (fabsl (__imag__ res) < LDBL_MIN)
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{
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volatile long double force_underflow = __imag__ res * __imag__ res;
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(void) force_underflow;
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}
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}
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return res;
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}
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weak_alias (__catanl, catanl)
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