libgfortran/generated/exp_c8.c

   1 /* Complex exponential functions
   2    Copyright 2002, 2004 Free Software Foundation, Inc.
   3    Contributed by Paul Brook <paul@nowt.org>
   4
   5 This file is part of the GNU Fortran 95 runtime library (libgfortran).
   6
   7 Libgfortran is free software; you can redistribute it and/or
   8 modify it under the terms of the GNU General Public
   9 License as published by the Free Software Foundation; either
  10 version 2 of the License, or (at your option) any later version.
  11
  12 In addition to the permissions in the GNU General Public License, the
  13 Free Software Foundation gives you unlimited permission to link the
  14 compiled version of this file into combinations with other programs,
  15 and to distribute those combinations without any restriction coming
  16 from the use of this file.  (The General Public License restrictions
  17 do apply in other respects; for example, they cover modification of
  18 the file, and distribution when not linked into a combine
  19 executable.)
  20
  21 Libgfortran is distributed in the hope that it will be useful,
  22 but WITHOUT ANY WARRANTY; without even the implied warranty of
  23 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  24 GNU General Public License for more details.
  25
  26 You should have received a copy of the GNU General Public
  27 License along with libgfortran; see the file COPYING.  If not,
  28 write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  29 Boston, MA 02111-1307, USA.  */
  30 #include <math.h>
  31 #include "libgfortran.h"
  32
  33
  34 /* z = a + ib  */
  35 /* Absolute value.  */
  36 GFC_REAL_8
  37 cabs (GFC_COMPLEX_8 z)
  38 {
  39   return hypot (REALPART (z), IMAGPART (z));
  40 }
  41
  42 /* Complex argument.  The angle made with the +ve real axis.
  43    Range -pi-pi.  */
  44 GFC_REAL_8
  45 carg (GFC_COMPLEX_8 z)
  46 {
  47   GFC_REAL_8 arg;
  48
  49   return atan2 (IMAGPART (z), REALPART (z));
  50 }
  51
  52 /* exp(z) = exp(a)*(cos(b) + isin(b))  */
  53 GFC_COMPLEX_8
  54 cexp (GFC_COMPLEX_8 z)
  55 {
  56   GFC_REAL_8 a;
  57   GFC_REAL_8 b;
  58   GFC_COMPLEX_8 v;
  59
  60   a = REALPART (z);
  61   b = IMAGPART (z);
  62   COMPLEX_ASSIGN (v, cos (b), sin (b));
  63   return exp (a) * v;
  64 }
  65
  66 /* log(z) = log (cabs(z)) + i*carg(z)  */
  67 GFC_COMPLEX_8
  68 clog (GFC_COMPLEX_8 z)
  69 {
  70   GFC_COMPLEX_8 v;
  71
  72   COMPLEX_ASSIGN (v, log (cabs (z)), carg (z));
  73   return v;
  74 }
  75
  76 /* log10(z) = log10 (cabs(z)) + i*carg(z)  */
  77 GFC_COMPLEX_8
  78 clog10 (GFC_COMPLEX_8 z)
  79 {
  80   GFC_COMPLEX_8 v;
  81
  82   COMPLEX_ASSIGN (v, log10 (cabs (z)), carg (z));
  83   return v;
  84 }
  85
  86 /* pow(base, power) = cexp (power * clog (base))  */
  87 GFC_COMPLEX_8
  88 cpow (GFC_COMPLEX_8 base, GFC_COMPLEX_8 power)
  89 {
  90   return cexp (power * clog (base));
  91 }
  92
  93 /* sqrt(z).  Algorithm pulled from glibc.  */
  94 GFC_COMPLEX_8
  95 csqrt (GFC_COMPLEX_8 z)
  96 {
  97   GFC_REAL_8 re;
  98   GFC_REAL_8 im;
  99   GFC_COMPLEX_8 v;
 100
 101   re = REALPART (z);
 102   im = IMAGPART (z);
 103   if (im == 0.0)
 104     {
 105       if (re < 0.0)
 106         {
 107           COMPLEX_ASSIGN (v, 0.0, copysign (sqrt (-re), im));
 108         }
 109       else
 110         {
 111           COMPLEX_ASSIGN (v, fabs (sqrt (re)),
 112                           copysign (0.0, im));
 113         }
 114     }
 115   else if (re == 0.0)
 116     {
 117       GFC_REAL_8 r;
 118
 119       r = sqrt (0.5 * fabs (im));
 120
 121       COMPLEX_ASSIGN (v, copysign (r, im), r);
 122     }
 123   else
 124     {
 125       GFC_REAL_8 d, r, s;
 126
 127       d = hypot (re, im);
 128       /* Use the identity   2  Re res  Im res = Im x
 129          to avoid cancellation error in  d +/- Re x.  */
 130       if (re > 0)
 131         {
 132           r = sqrt (0.5 * d + 0.5 * re);
 133           s = (0.5 * im) / r;
 134         }
 135       else
 136         {
 137           s = sqrt (0.5 * d - 0.5 * re);
 138           r = fabs ((0.5 * im) / s);
 139         }
 140
 141       COMPLEX_ASSIGN (v, r, copysign (s, im));
 142     }
 143   return v;
 144 }
 145