gcc/libgfortran/intrinsics/erfc_scaled_inc.c

/* Implementation of the ERFC_SCALED intrinsic, to be included by erfc_scaled.c
   Copyright (c) 2008 Free Software Foundation, Inc.

This file is part of the GNU Fortran runtime library (libgfortran).

Libgfortran is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public
License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.

In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file.  (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)

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 General Public License for more details.

You should have received a copy of the GNU General Public
License along with libgfortran; see the file COPYING.  If not,
write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.  */

/* This implementation of ERFC_SCALED is based on the netlib algorithm
   available at http://www.netlib.org/specfun/erf  */

#define TYPE KIND_SUFFIX(GFC_REAL_,KIND)
#define CONCAT(x,y) x ## y
#define KIND_SUFFIX(x,y) CONCAT(x,y)

#if (KIND == 4)
# define EXP(x) expf(x)
# define TRUNC(x) truncf(x)
#elif (KIND == 8)
# define EXP(x) exp(x)
# define TRUNC(x) trunc(x)
#else
# define EXP(x) expl(x)
# define TRUNC(x) truncl(x)
#endif

extern TYPE KIND_SUFFIX(erfc_scaled_r,KIND) (TYPE);
export_proto(KIND_SUFFIX(erfc_scaled_r,KIND));

TYPE
KIND_SUFFIX(erfc_scaled_r,KIND) (TYPE x)
{
  /* The main computation evaluates near-minimax approximations
     from "Rational Chebyshev approximations for the error function"
     by W. J. Cody, Math. Comp., 1969, PP. 631-638.  This
     transportable program uses rational functions that theoretically
     approximate  erf(x)  and  erfc(x)  to at least 18 significant
     decimal digits.  The accuracy achieved depends on the arithmetic
     system, the compiler, the intrinsic functions, and proper
     selection of the machine-dependent constants.  */

  int i;
  TYPE del, res, xden, xnum, y, ysq;

#if (KIND == 4)
  static TYPE xneg = -9.382, xsmall = 5.96e-8,
	      xbig = 9.194, xhuge = 2.90e+3, xmax = 4.79e+37;
#else
  static TYPE xneg = -26.628, xsmall = 1.11e-16,
	      xbig = 26.543, xhuge = 6.71e+7, xmax = 2.53e+307;
#endif

#define SQRPI ((TYPE) 0.56418958354775628695L)
#define THRESH ((TYPE) 0.46875L)

  static TYPE a[5] = { 3.16112374387056560l, 113.864154151050156l,
    377.485237685302021l, 3209.37758913846947l, 0.185777706184603153l };

  static TYPE b[4] = { 23.6012909523441209l, 244.024637934444173l,
    1282.61652607737228l, 2844.23683343917062l };

  static TYPE c[9] = { 0.564188496988670089l, 8.88314979438837594l,
    66.1191906371416295l, 298.635138197400131l, 881.952221241769090l,
    1712.04761263407058l, 2051.07837782607147l, 1230.33935479799725l,
    2.15311535474403846e-8l };

  static TYPE d[8] = { 15.7449261107098347l, 117.693950891312499l,
    537.181101862009858l, 1621.38957456669019l, 3290.79923573345963l,
    4362.61909014324716l, 3439.36767414372164l, 1230.33935480374942l };

  static TYPE p[6] = { 0.305326634961232344l, 0.360344899949804439l,
    0.125781726111229246l, 0.0160837851487422766l,
    0.000658749161529837803l, 0.0163153871373020978l };

  static TYPE q[5] = { 2.56852019228982242l, 1.87295284992346047l,
    0.527905102951428412l, 0.0605183413124413191l,
    0.00233520497626869185l };

  y = (x > 0 ? x : -x);
  if (y <= THRESH)
    {
      ysq = 0;
      if (y > xsmall)
	ysq = y * y;
      xnum = a[4]*ysq;
      xden = ysq;
      for (i = 0; i <= 2; i++)
	{
          xnum = (xnum + a[i]) * ysq;
          xden = (xden + b[i]) * ysq;
	}
      res = x * (xnum + a[3]) / (xden + b[3]);
      res = 1 - res;
      res = EXP(ysq) * res;
      return res;
    }
  else if (y <= 4)
    {
      xnum = c[8]*y;
      xden = y;
      for (i = 0; i <= 6; i++)
	{
	  xnum = (xnum + c[i]) * y;
	  xden = (xden + d[i]) * y;
	}
      res = (xnum + c[7]) / (xden + d[7]);
    }
  else
    {
      res = 0;
      if (y >= xbig)
	{
          if (y >= xmax)
	    goto finish;
          if (y >= xhuge)
	    {
	      res = SQRPI / y;
	      goto finish;
	    }
	}
      ysq = ((TYPE) 1) / (y * y);
      xnum = p[5]*ysq;
      xden = ysq;
      for (i = 0; i <= 3; i++)
	{
          xnum = (xnum + p[i]) * ysq;
          xden = (xden + q[i]) * ysq;
	}
      res = ysq *(xnum + p[4]) / (xden + q[4]);
      res = (SQRPI -  res) / y;
    }

finish:
  if (x < 0)
    {
      if (x < xneg)
	res = __builtin_inf ();
      else
	{
	  ysq = TRUNC (x*((TYPE) 16))/((TYPE) 16);
	  del = (x-ysq)*(x+ysq);
	  y = EXP(ysq*ysq) * EXP(del);
	  res = (y+y) - res;
	}
    }
  return res;
}

#undef EXP
#undef TRUNC

#undef CONCAT
#undef TYPE
#undef KIND_SUFFIX