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126 lines
3.5 KiB
C
126 lines
3.5 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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__complex__ double
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__clog (__complex__ double x)
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{
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__complex__ 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_PI : 0.0;
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__imag__ result = __copysign (__imag__ result, __imag__ x);
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/* Yes, the following line raises an exception. */
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__real__ result = -1.0 / fabs (__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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double absx = fabs (__real__ x), absy = fabs (__imag__ x);
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int scale = 0;
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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 (absx > DBL_MAX / 2.0)
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{
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scale = -1;
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absx = __scalbn (absx, scale);
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absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
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}
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else if (absx < DBL_MIN && absy < DBL_MIN)
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{
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scale = DBL_MANT_DIG;
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absx = __scalbn (absx, scale);
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absy = __scalbn (absy, scale);
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}
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if (absx == 1.0 && scale == 0)
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{
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double absy2 = absy * absy;
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if (absy2 <= DBL_MIN * 2.0)
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{
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#if __FLT_EVAL_METHOD__ == 0
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__real__ result = absy2 / 2.0 - absy2 * absy2 / 4.0;
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#else
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volatile double force_underflow = absy2 * absy2 / 4.0;
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__real__ result = absy2 / 2.0 - force_underflow;
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#endif
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}
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else
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__real__ result = __log1p (absy2) / 2.0;
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}
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else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
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{
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double d2m1 = (absx - 1.0) * (absx + 1.0);
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if (absy >= DBL_EPSILON)
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d2m1 += absy * absy;
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__real__ result = __log1p (d2m1) / 2.0;
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}
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else if (absx < 1.0
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&& absx >= 0.75
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&& absy < DBL_EPSILON / 2.0
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&& scale == 0)
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{
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double d2m1 = (absx - 1.0) * (absx + 1.0);
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__real__ result = __log1p (d2m1) / 2.0;
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}
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else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0)
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{
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double d2m1 = __x2y2m1 (absx, absy);
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__real__ result = __log1p (d2m1) / 2.0;
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}
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else
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{
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double d = __ieee754_hypot (absx, absy);
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__real__ result = __ieee754_log (d) - scale * M_LN2;
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}
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__imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
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}
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else
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{
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__imag__ result = __nan ("");
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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_VAL;
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else
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__real__ result = __nan ("");
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}
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return result;
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}
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weak_alias (__clog, clog)
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#ifdef NO_LONG_DOUBLE
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strong_alias (__clog, __clogl)
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weak_alias (__clog, clogl)
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#endif
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