122 lines
3.6 KiB
C
122 lines
3.6 KiB
C
/* Compute complex natural logarithm.
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Copyright (C) 1997-2014 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 underflows, 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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__clogl (__complex__ long double x)
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{
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__complex__ long double result;
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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_ZERO && icls == FP_ZERO))
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{
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/* Real and imaginary part are 0.0. */
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__imag__ result = signbit (__real__ x) ? M_PIl : 0.0;
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__imag__ result = __copysignl (__imag__ result, __imag__ x);
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/* Yes, the following line raises an exception. */
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__real__ result = -1.0 / fabsl (__real__ x);
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}
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else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
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{
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/* Neither real nor imaginary part is NaN. */
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long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
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int scale = 0;
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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 (absx > LDBL_MAX / 2.0L)
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{
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scale = -1;
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absx = __scalbnl (absx, scale);
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absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
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}
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else if (absx < LDBL_MIN && absy < LDBL_MIN)
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{
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scale = LDBL_MANT_DIG;
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absx = __scalbnl (absx, scale);
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absy = __scalbnl (absy, scale);
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}
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if (absx == 1.0L && scale == 0)
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{
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long double absy2 = absy * absy;
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if (absy2 <= LDBL_MIN * 2.0L)
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__real__ result = absy2 / 2.0L - absy2 * absy2 / 4.0L;
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else
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__real__ result = __log1pl (absy2) / 2.0L;
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}
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else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
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{
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long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
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if (absy >= LDBL_EPSILON)
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d2m1 += absy * absy;
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__real__ result = __log1pl (d2m1) / 2.0L;
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}
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else if (absx < 1.0L
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&& absx >= 0.75L
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&& absy < LDBL_EPSILON / 2.0L
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&& scale == 0)
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{
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long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
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__real__ result = __log1pl (d2m1) / 2.0L;
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}
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else if (absx < 1.0L && (absx >= 0.75L || absy >= 0.5L) && scale == 0)
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{
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long double d2m1 = __x2y2m1l (absx, absy);
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__real__ result = __log1pl (d2m1) / 2.0L;
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}
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else
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{
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long double d = __ieee754_hypotl (absx, absy);
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__real__ result = __ieee754_logl (d) - scale * M_LN2l;
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}
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__imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
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}
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else
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{
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__imag__ result = __nanl ("");
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if (rcls == FP_INFINITE || icls == FP_INFINITE)
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/* Real or imaginary part is infinite. */
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__real__ result = HUGE_VALL;
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else
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__real__ result = __nanl ("");
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}
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return result;
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}
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weak_alias (__clogl, clogl)
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