140 lines
3.0 KiB
C
140 lines
3.0 KiB
C
/* Complex exponential functions
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Copyright 2002, 2004 Free Software Foundation, Inc.
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Contributed by Paul Brook <paul@nowt.org>
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This file is part of the GNU Fortran 95 runtime library (libgfor).
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Libgfortran 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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Libgfortran 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
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GNU 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 libgfor; see the file COPYING.LIB. If not,
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write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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Boston, MA 02111-1307, USA. */
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#include <math.h>
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#include "libgfortran.h"
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/* z = a + ib */
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/* Absolute value. */
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GFC_REAL_8
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cabs (GFC_COMPLEX_8 z)
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{
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return hypot (REALPART (z), IMAGPART (z));
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}
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/* Complex argument. The angle made with the +ve real axis. Range 0-2pi. */
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GFC_REAL_8
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carg (GFC_COMPLEX_8 z)
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{
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GFC_REAL_8 arg;
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arg = atan2 (IMAGPART (z), REALPART (z));
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if (arg < 0)
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return arg + 2 * M_PI;
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else
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return arg;
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}
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/* exp(z) = exp(a)*(cos(b) + isin(b)) */
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GFC_COMPLEX_8
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cexp (GFC_COMPLEX_8 z)
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{
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GFC_REAL_8 a;
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GFC_REAL_8 b;
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GFC_COMPLEX_8 v;
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a = REALPART (z);
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b = IMAGPART (z);
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COMPLEX_ASSIGN (v, cos (b), sin (b));
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return exp (a) * v;
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}
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/* log(z) = log (cabs(z)) + i*carg(z) */
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GFC_COMPLEX_8
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clog (GFC_COMPLEX_8 z)
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{
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GFC_COMPLEX_8 v;
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COMPLEX_ASSIGN (v, log (cabs (z)), carg (z));
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return v;
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}
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/* log10(z) = log10 (cabs(z)) + i*carg(z) */
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GFC_COMPLEX_8
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clog10 (GFC_COMPLEX_8 z)
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{
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GFC_COMPLEX_8 v;
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COMPLEX_ASSIGN (v, log10 (cabs (z)), carg (z));
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return v;
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}
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/* pow(base, power) = cexp (power * clog (base)) */
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GFC_COMPLEX_8
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cpow (GFC_COMPLEX_8 base, GFC_COMPLEX_8 power)
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{
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return cexp (power * clog (base));
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}
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/* sqrt(z). Algorithm pulled from glibc. */
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GFC_COMPLEX_8
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csqrt (GFC_COMPLEX_8 z)
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{
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GFC_REAL_8 re;
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GFC_REAL_8 im;
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GFC_COMPLEX_8 v;
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re = REALPART (z);
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im = IMAGPART (z);
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if (im == 0.0)
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{
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if (re < 0.0)
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{
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COMPLEX_ASSIGN (v, 0.0, copysign (sqrt (-re), im));
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}
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else
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{
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COMPLEX_ASSIGN (v, fabs (sqrt (re)),
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copysign (0.0, im));
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}
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}
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else if (re == 0.0)
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{
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GFC_REAL_8 r;
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r = sqrt (0.5 * fabs (im));
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COMPLEX_ASSIGN (v, copysign (r, im), r);
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}
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else
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{
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GFC_REAL_8 d, r, s;
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d = hypot (re, im);
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/* Use the identity 2 Re res Im res = Im x
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to avoid cancellation error in d +/- Re x. */
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if (re > 0)
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{
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r = sqrt (0.5 * d + 0.5 * re);
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s = (0.5 * im) / r;
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}
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else
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{
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s = sqrt (0.5 * d - 0.5 * re);
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r = fabs ((0.5 * im) / s);
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}
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COMPLEX_ASSIGN (v, r, copysign (s, im));
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}
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return v;
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}
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