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+/* Complex exponential functions
+ Copyright 2002, 2004 Free Software Foundation, Inc.
+ Contributed by Paul Brook <paul@nowt.org>
+
+This file is part of the GNU Fortran 95 runtime library (libgfor).
+
+Libgfortran is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+Libgfortran is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with libgfor; see the file COPYING.LIB. If not,
+write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+Boston, MA 02111-1307, USA. */
+#include <math.h>
+#include "libgfortran.h"
+
+
+/* z = a + ib */
+/* Absolute value. */
+GFC_REAL_8
+cabs (GFC_COMPLEX_8 z)
+{
+ return hypot (REALPART (z), IMAGPART (z));
+}
+
+/* Complex argument. The angle made with the +ve real axis. Range 0-2pi. */
+GFC_REAL_8
+carg (GFC_COMPLEX_8 z)
+{
+ GFC_REAL_8 arg;
+
+ arg = atan2 (IMAGPART (z), REALPART (z));
+ if (arg < 0)
+ return arg + 2 * M_PI;
+ else
+ return arg;
+}
+
+/* exp(z) = exp(a)*(cos(b) + isin(b)) */
+GFC_COMPLEX_8
+cexp (GFC_COMPLEX_8 z)
+{
+ GFC_REAL_8 a;
+ GFC_REAL_8 b;
+ GFC_COMPLEX_8 v;
+
+ a = REALPART (z);
+ b = IMAGPART (z);
+ COMPLEX_ASSIGN (v, cos (b), sin (b));
+ return exp (a) * v;
+}
+
+/* log(z) = log (cabs(z)) + i*carg(z) */
+GFC_COMPLEX_8
+clog (GFC_COMPLEX_8 z)
+{
+ GFC_COMPLEX_8 v;
+
+ COMPLEX_ASSIGN (v, log (cabs (z)), carg (z));
+ return v;
+}
+
+/* log10(z) = log10 (cabs(z)) + i*carg(z) */
+GFC_COMPLEX_8
+clog10 (GFC_COMPLEX_8 z)
+{
+ GFC_COMPLEX_8 v;
+
+ COMPLEX_ASSIGN (v, log10 (cabs (z)), carg (z));
+ return v;
+}
+
+/* pow(base, power) = cexp (power * clog (base)) */
+GFC_COMPLEX_8
+cpow (GFC_COMPLEX_8 base, GFC_COMPLEX_8 power)
+{
+ return cexp (power * clog (base));
+}
+
+/* sqrt(z). Algorithm pulled from glibc. */
+GFC_COMPLEX_8
+csqrt (GFC_COMPLEX_8 z)
+{
+ GFC_REAL_8 re;
+ GFC_REAL_8 im;
+ GFC_COMPLEX_8 v;
+
+ re = REALPART (z);
+ im = IMAGPART (z);
+ if (im == 0.0)
+ {
+ if (re < 0.0)
+ {
+ COMPLEX_ASSIGN (v, 0.0, copysign (sqrt (-re), im));
+ }
+ else
+ {
+ COMPLEX_ASSIGN (v, fabs (sqrt (re)),
+ copysign (0.0, im));
+ }
+ }
+ else if (re == 0.0)
+ {
+ GFC_REAL_8 r;
+
+ r = sqrt (0.5 * fabs (im));
+
+ COMPLEX_ASSIGN (v, copysign (r, im), r);
+ }
+ else
+ {
+ GFC_REAL_8 d, r, s;
+
+ d = hypot (re, im);
+ /* Use the identity 2 Re res Im res = Im x
+ to avoid cancellation error in d +/- Re x. */
+ if (re > 0)
+ {
+ r = sqrt (0.5 * d + 0.5 * re);
+ s = (0.5 * im) / r;
+ }
+ else
+ {
+ s = sqrt (0.5 * d - 0.5 * re);
+ r = fabs ((0.5 * im) / s);
+ }
+
+ COMPLEX_ASSIGN (v, r, copysign (s, im));
+ }
+ return v;
+}
+
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