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/* Implementation of the BESSEL_JN and BESSEL_YN transformational
   function using a recurrence algorithm.
   Copyright 2010 Free Software Foundation, Inc.
   Contributed by Tobias Burnus <burnus@net-b.de>
 
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 3 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 General Public License for more details.
 
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
 
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */
 
#include "libgfortran.h"
#include <stdlib.h>
#include <assert.h>
 
 
 
#define MATHFUNC(funcname) funcname
 
#if defined (HAVE_GFC_REAL_8)
 
 
 
#if defined (HAVE_JN)
extern void bessel_jn_r8 (gfc_array_r8 * const restrict ret, int n1,
				     int n2, GFC_REAL_8 x);
export_proto(bessel_jn_r8);
 
void
bessel_jn_r8 (gfc_array_r8 * const restrict ret, int n1, int n2, GFC_REAL_8 x)
{
  int i;
  index_type stride;
 
  GFC_REAL_8 last1, last2, x2rev;
 
  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
 
  if (ret->data == NULL)
    {
      size_t size = n2 < n1 ? 0 : n2-n1+1; 
      GFC_DIMENSION_SET(ret->dim[0], 0, size-1, 1);
      ret->data = internal_malloc_size (sizeof (GFC_REAL_8) * size);
      ret->offset = 0;
    }
 
  if (unlikely (n2 < n1))
    return;
 
  if (unlikely (compile_options.bounds_check)
      && GFC_DESCRIPTOR_EXTENT(ret,0) != (n2-n1+1))
    runtime_error("Incorrect extent in return value of BESSEL_JN "
		  "(%ld vs. %ld)", (long int) n2-n1,
		  (long int) GFC_DESCRIPTOR_EXTENT(ret,0));
 
  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
 
  if (unlikely (x == 0))
    {
      ret->data[0] = 1;
      for (i = 1; i <= n2-n1; i++)
        ret->data[i*stride] = 0;
      return;
    }
 
  ret->data = ret->data;
  last1 = MATHFUNC(jn) (n2, x);
  ret->data[(n2-n1)*stride] = last1;
 
  if (n1 == n2)
    return;
 
  last2 = MATHFUNC(jn) (n2 - 1, x);
  ret->data[(n2-n1-1)*stride] = last2;
 
  if (n1 + 1 == n2)
    return;
 
  x2rev = GFC_REAL_8_LITERAL(2.)/x;
 
  for (i = n2-n1-2; i >= 0; i--)
    {
      ret->data[i*stride] = x2rev * (i+1+n1) * last2 - last1;
      last1 = last2;
      last2 = ret->data[i*stride];
    }
}
 
#endif
 
#if defined (HAVE_YN)
extern void bessel_yn_r8 (gfc_array_r8 * const restrict ret,
				     int n1, int n2, GFC_REAL_8 x);
export_proto(bessel_yn_r8);
 
void
bessel_yn_r8 (gfc_array_r8 * const restrict ret, int n1, int n2,
			 GFC_REAL_8 x)
{
  int i;
  index_type stride;
 
  GFC_REAL_8 last1, last2, x2rev;
 
  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
 
  if (ret->data == NULL)
    {
      size_t size = n2 < n1 ? 0 : n2-n1+1; 
      GFC_DIMENSION_SET(ret->dim[0], 0, size-1, 1);
      ret->data = internal_malloc_size (sizeof (GFC_REAL_8) * size);
      ret->offset = 0;
    }
 
  if (unlikely (n2 < n1))
    return;
 
  if (unlikely (compile_options.bounds_check)
      && GFC_DESCRIPTOR_EXTENT(ret,0) != (n2-n1+1))
    runtime_error("Incorrect extent in return value of BESSEL_JN "
		  "(%ld vs. %ld)", (long int) n2-n1,
		  (long int) GFC_DESCRIPTOR_EXTENT(ret,0));
 
  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
 
  if (unlikely (x == 0))
    {
      for (i = 0; i <= n2-n1; i++)
#if defined(GFC_REAL_8_INFINITY)
        ret->data[i*stride] = -GFC_REAL_8_INFINITY;
#else
        ret->data[i*stride] = -GFC_REAL_8_HUGE;
#endif
      return;
    }
 
  ret->data = ret->data;
  last1 = MATHFUNC(yn) (n1, x);
  ret->data[0] = last1;
 
  if (n1 == n2)
    return;
 
  last2 = MATHFUNC(yn) (n1 + 1, x);
  ret->data[1*stride] = last2;
 
  if (n1 + 1 == n2)
    return;
 
  x2rev = GFC_REAL_8_LITERAL(2.)/x;
 
  for (i = 2; i <= n1+n2; i++)
    {
#if defined(GFC_REAL_8_INFINITY)
      if (unlikely (last2 == -GFC_REAL_8_INFINITY))
	{
	  ret->data[i*stride] = -GFC_REAL_8_INFINITY;
	}
      else
#endif
	{
	  ret->data[i*stride] = x2rev * (i-1+n1) * last2 - last1;
	  last1 = last2;
	  last2 = ret->data[i*stride];
	}
    }
}
#endif
 
#endif