re PR fortran/36158 (Transformational function BESSEL_YN(n1,n2,x) and BESSEL_JN missing)

2010-08-21  Tobias Burnus  <burnus@net-b.de>

        PR fortran/36158
        PR fortran/33197
        * intrinsic.c (add_sym): Init value attribute.
        (set_attr_value): New function.
        (add_functions) Use it and add JN/YN resolvers.
        * symbol.c (gfc_copy_formal_args_intr): Copy value attr.
        * intrinsic.h (gfc_resolve_bessel_n2): New prototype.
        * gfortran.h (gfc_intrinsic_arg): Add value attribute.
        * iresolve.c (gfc_resolve_bessel_n2): New function.
        * trans-intrinsic.c (gfc_get_symbol_for_expr): Create
        formal arg list.
        (gfc_conv_intrinsic_function,gfc_is_intrinsic_libcall):
        Add GFC_ISYM_JN2/GFC_ISYM_YN2 as case value.
        * simplify.c (): For YN set to -INF if previous values
        was -INF.
        * trans-expr.c (gfc_conv_procedure_call): Don't crash
        if sym->as is NULL.
        * iresolve.c (gfc_resolve_extends_type_of): Set the
        type of the dummy argument to the one of the actual.

2010-08-21  Tobias Burnus  <burnus@net-b.de>

        PR fortran/36158
        PR fortran/33197
        * m4/bessel.m4: Implement bessel_jn and bessel_yn.
        * gfortran.map: Add the generated bessel_jn_r{4,8,10,16}
        and bessel_yn_r{4,8,10,16}.
        * Makefile.am: Add bessel.m4.
        * Makefile.in: Regenerated.
        * generated/bessel_r4.c: Generated.
        * generated/bessel_r16.c: Generated.
        * generated/bessel_r8.c: Generated.
        * generated/bessel_r10.c: Generated.

2010-08-21  Tobias Burnus  <burnus@net-b.de>

        PR fortran/36158
        PR fortran/33197
        * gfortran.dg/bessel_6.f90: New.
        * gfortran.dg/bessel_7.f90: New.

From-SVN: r163440

4 files changed, 732 insertions, 0 deletions

diff --git a/libgfortran/generated/bessel_r10.c b/libgfortran/generated/bessel_r10.c
new file mode 100644
index 0000000..579de84
--- /dev/null
+++ b/libgfortran/generated/bessel_r10.c
@@ -0,0 +1,183 @@
+/* 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>
+
+
+#if defined (HAVE_GFC_REAL_10)
+
+
+
+#if defined (HAVE_JNL)
+extern void bessel_jn_r10 (gfc_array_r10 * const restrict ret, int n1,
+				     int n2, GFC_REAL_10 x);
+export_proto(bessel_jn_r10);
+
+void
+bessel_jn_r10 (gfc_array_r10 * const restrict ret, int n1, int n2, GFC_REAL_10 x)
+{
+  int i;
+  index_type stride;
+
+  GFC_REAL_10 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_10) * 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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0L))
+    {
+      ret->data[0] = 1.0L;
+      for (i = 1; i <= n2-n1; i++)
+        ret->data[i*stride] = 0.0L;
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = jnl (n2, x);
+  ret->data[(n2-n1)*stride] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = jnl (n2 - 1, x);
+  ret->data[(n2-n1-1)*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0L/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_YNL)
+extern void bessel_yn_r10 (gfc_array_r10 * const restrict ret,
+				     int n1, int n2, GFC_REAL_10 x);
+export_proto(bessel_yn_r10);
+
+void
+bessel_yn_r10 (gfc_array_r10 * const restrict ret, int n1, int n2,
+			 GFC_REAL_10 x)
+{
+  int i;
+  index_type stride;
+
+  GFC_REAL_10 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_10) * 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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0L))
+    {
+      for (i = 0; i <= n2-n1; i++)
+#if defined(GFC_REAL_10_INFINITY)
+        ret->data[i*stride] = -GFC_REAL_10_INFINITY;
+#else
+        ret->data[i*stride] = -GFC_REAL_10_HUGE;
+#endif
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = ynl (n1, x);
+  ret->data[0] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = ynl (n1 + 1, x);
+  ret->data[1*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0L/x;
+
+  for (i = 2; i <= n1+n2; i++)
+    {
+#if defined(GFC_REAL_10_INFINITY)
+      if (unlikely (last2 == -GFC_REAL_10_INFINITY))
+	{
+	  ret->data[i*stride] = -GFC_REAL_10_INFINITY;
+	}
+      else
+#endif
+	{
+	  ret->data[i*stride] = x2rev * (i-1+n1) * last2 - last1;
+	  last1 = last2;
+	  last2 = ret->data[i*stride];
+	}
+    }
+}
+#endif
+
+#endif
+
diff --git a/libgfortran/generated/bessel_r16.c b/libgfortran/generated/bessel_r16.c
new file mode 100644
index 0000000..a3ef181
--- /dev/null
+++ b/libgfortran/generated/bessel_r16.c
@@ -0,0 +1,183 @@
+/* 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>
+
+
+#if defined (HAVE_GFC_REAL_16)
+
+
+
+#if defined (HAVE_JNL)
+extern void bessel_jn_r16 (gfc_array_r16 * const restrict ret, int n1,
+				     int n2, GFC_REAL_16 x);
+export_proto(bessel_jn_r16);
+
+void
+bessel_jn_r16 (gfc_array_r16 * const restrict ret, int n1, int n2, GFC_REAL_16 x)
+{
+  int i;
+  index_type stride;
+
+  GFC_REAL_16 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_16) * 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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0L))
+    {
+      ret->data[0] = 1.0L;
+      for (i = 1; i <= n2-n1; i++)
+        ret->data[i*stride] = 0.0L;
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = jnl (n2, x);
+  ret->data[(n2-n1)*stride] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = jnl (n2 - 1, x);
+  ret->data[(n2-n1-1)*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0L/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_YNL)
+extern void bessel_yn_r16 (gfc_array_r16 * const restrict ret,
+				     int n1, int n2, GFC_REAL_16 x);
+export_proto(bessel_yn_r16);
+
+void
+bessel_yn_r16 (gfc_array_r16 * const restrict ret, int n1, int n2,
+			 GFC_REAL_16 x)
+{
+  int i;
+  index_type stride;
+
+  GFC_REAL_16 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_16) * 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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0L))
+    {
+      for (i = 0; i <= n2-n1; i++)
+#if defined(GFC_REAL_16_INFINITY)
+        ret->data[i*stride] = -GFC_REAL_16_INFINITY;
+#else
+        ret->data[i*stride] = -GFC_REAL_16_HUGE;
+#endif
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = ynl (n1, x);
+  ret->data[0] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = ynl (n1 + 1, x);
+  ret->data[1*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0L/x;
+
+  for (i = 2; i <= n1+n2; i++)
+    {
+#if defined(GFC_REAL_16_INFINITY)
+      if (unlikely (last2 == -GFC_REAL_16_INFINITY))
+	{
+	  ret->data[i*stride] = -GFC_REAL_16_INFINITY;
+	}
+      else
+#endif
+	{
+	  ret->data[i*stride] = x2rev * (i-1+n1) * last2 - last1;
+	  last1 = last2;
+	  last2 = ret->data[i*stride];
+	}
+    }
+}
+#endif
+
+#endif
+
diff --git a/libgfortran/generated/bessel_r4.c b/libgfortran/generated/bessel_r4.c
new file mode 100644
index 0000000..961c67c
--- /dev/null
+++ b/libgfortran/generated/bessel_r4.c
@@ -0,0 +1,183 @@
+/* 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>
+
+
+#if defined (HAVE_GFC_REAL_4)
+
+
+
+#if defined (HAVE_JNF)
+extern void bessel_jn_r4 (gfc_array_r4 * const restrict ret, int n1,
+				     int n2, GFC_REAL_4 x);
+export_proto(bessel_jn_r4);
+
+void
+bessel_jn_r4 (gfc_array_r4 * const restrict ret, int n1, int n2, GFC_REAL_4 x)
+{
+  int i;
+  index_type stride;
+
+  GFC_REAL_4 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_4) * 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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0F))
+    {
+      ret->data[0] = 1.0F;
+      for (i = 1; i <= n2-n1; i++)
+        ret->data[i*stride] = 0.0F;
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = jnf (n2, x);
+  ret->data[(n2-n1)*stride] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = jnf (n2 - 1, x);
+  ret->data[(n2-n1-1)*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0F/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_YNF)
+extern void bessel_yn_r4 (gfc_array_r4 * const restrict ret,
+				     int n1, int n2, GFC_REAL_4 x);
+export_proto(bessel_yn_r4);
+
+void
+bessel_yn_r4 (gfc_array_r4 * const restrict ret, int n1, int n2,
+			 GFC_REAL_4 x)
+{
+  int i;
+  index_type stride;
+
+  GFC_REAL_4 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_4) * 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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0F))
+    {
+      for (i = 0; i <= n2-n1; i++)
+#if defined(GFC_REAL_4_INFINITY)
+        ret->data[i*stride] = -GFC_REAL_4_INFINITY;
+#else
+        ret->data[i*stride] = -GFC_REAL_4_HUGE;
+#endif
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = ynf (n1, x);
+  ret->data[0] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = ynf (n1 + 1, x);
+  ret->data[1*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0F/x;
+
+  for (i = 2; i <= n1+n2; i++)
+    {
+#if defined(GFC_REAL_4_INFINITY)
+      if (unlikely (last2 == -GFC_REAL_4_INFINITY))
+	{
+	  ret->data[i*stride] = -GFC_REAL_4_INFINITY;
+	}
+      else
+#endif
+	{
+	  ret->data[i*stride] = x2rev * (i-1+n1) * last2 - last1;
+	  last1 = last2;
+	  last2 = ret->data[i*stride];
+	}
+    }
+}
+#endif
+
+#endif
+
diff --git a/libgfortran/generated/bessel_r8.c b/libgfortran/generated/bessel_r8.c
new file mode 100644
index 0000000..c896ae4
--- /dev/null
+++ b/libgfortran/generated/bessel_r8.c
@@ -0,0 +1,183 @@
+/* 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>
+
+
+#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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0))
+    {
+      ret->data[0] = 1.0;
+      for (i = 1; i <= n2-n1; i++)
+        ret->data[i*stride] = 0.0;
+      return;
+    }
+
+  ret->data = ret->data;
+  last1 = jn (n2, x);
+  ret->data[(n2-n1)*stride] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = jn (n2 - 1, x);
+  ret->data[(n2-n1-1)*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0/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,
+		  GFC_DESCRIPTOR_EXTENT(ret,0));
+
+  stride = GFC_DESCRIPTOR_STRIDE(ret,0);
+
+  if (unlikely (x == 0.0))
+    {
+      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 = yn (n1, x);
+  ret->data[0] = last1;
+
+  if (n1 == n2)
+    return;
+
+  last2 = yn (n1 + 1, x);
+  ret->data[1*stride] = last2;
+
+  if (n1 + 1 == n2)
+    return;
+
+  x2rev = 2.0/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
+