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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 -pi-pi. */
GFC_REAL_8
carg (GFC_COMPLEX_8 z)
{
GFC_REAL_8 arg;
return atan2 (IMAGPART (z), REALPART (z));
}
/* 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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