cexp.m4   [plain text]

`/* 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"'

include(`mtype.m4')dnl

/* z = a + ib  */
/* Absolute value.  */
real_type
cabs`'q (complex_type z)
{
  return hypot`'q (REALPART (z), IMAGPART (z));
}

/* Complex argument.  The angle made with the +ve real axis.  Range 0-2pi.  */
real_type
carg`'q (complex_type z)
{
  real_type arg;

  arg = atan2`'q (IMAGPART (z), REALPART (z));
  if (arg < 0)
    return arg + 2 * M_PI;
  else
    return arg;
}

/* exp(z) = exp(a)*(cos(b) + isin(b))  */
complex_type
cexp`'q (complex_type z)
{
  real_type a;
  real_type b;
  complex_type v;

  a = REALPART (z);
  b = IMAGPART (z);
  COMPLEX_ASSIGN (v, cos`'q (b), sin`'q (b));
  return exp`'q (a) * v;
}

/* log(z) = log (cabs(z)) + i*carg(z)  */
complex_type
clog`'q (complex_type z)
{
  complex_type v;

  COMPLEX_ASSIGN (v, log`'q (cabs`'q (z)), carg`'q (z));
  return v;
}

/* log10(z) = log10 (cabs(z)) + i*carg(z)  */
complex_type
clog10`'q (complex_type z)
{
  complex_type v;

  COMPLEX_ASSIGN (v, log10`'q (cabs`'q (z)), carg`'q (z));
  return v;
}

/* pow(base, power) = cexp (power * clog (base))  */
complex_type
cpow`'q (complex_type base, complex_type power)
{
  return cexp`'q (power * clog`'q (base));
}

/* sqrt(z).  Algorithm pulled from glibc.  */
complex_type
csqrt`'q (complex_type z)
{
  real_type re;
  real_type im;
  complex_type v;

  re = REALPART (z);
  im = IMAGPART (z);
  if (im == 0.0)
    {
      if (re < 0.0)
        {
          COMPLEX_ASSIGN (v, 0.0, copysign`'q (sqrt`'q (-re), im));
        }
      else
        {
          COMPLEX_ASSIGN (v, fabs`'q (sqrt (re)),
                          copysign`'q (0.0, im));
        }
    }
  else if (re == 0.0)
    {
      real_type r;

      r = sqrt`'q (0.5 * fabs (im));

      COMPLEX_ASSIGN (v, copysign`'q (r, im), r);
    }
  else
    {
      real_type d, r, s;

      d = hypot`'q (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`'q (0.5 * d + 0.5 * re);
          s = (0.5 * im) / r;
        }
      else
        {
          s = sqrt`'q (0.5 * d - 0.5 * re);
          r = fabs`'q ((0.5 * im) / s);
        }

      COMPLEX_ASSIGN (v, r, copysign`'q (s, im));
    }
  return v;
}