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      1 `/* Implementation of the BESSEL_JN and BESSEL_YN transformational
      2    function using a recurrence algorithm.
      3    Copyright (C) 2010-2022 Free Software Foundation, Inc.
      4    Contributed by Tobias Burnus <burnus (a] net-b.de>
      5 
      6 This file is part of the GNU Fortran runtime library (libgfortran).
      7 
      8 Libgfortran is free software; you can redistribute it and/or
      9 modify it under the terms of the GNU General Public
     10 License as published by the Free Software Foundation; either
     11 version 3 of the License, or (at your option) any later version.
     12 
     13 Libgfortran is distributed in the hope that it will be useful,
     14 but WITHOUT ANY WARRANTY; without even the implied warranty of
     15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     16 GNU General Public License for more details.
     17 
     18 Under Section 7 of GPL version 3, you are granted additional
     19 permissions described in the GCC Runtime Library Exception, version
     20 3.1, as published by the Free Software Foundation.
     21 
     22 You should have received a copy of the GNU General Public License and
     23 a copy of the GCC Runtime Library Exception along with this program;
     24 see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
     25 <http://www.gnu.org/licenses/>.  */
     26 
     27 #include "libgfortran.h"'
     28 
     29 include(iparm.m4)dnl
     30 include(`mtype.m4')dnl
     31 
     32 mathfunc_macro
     33 
     34 `#if defined (HAVE_'rtype_name`)
     35 
     36 
     37 
     38 #if 'hasmathfunc(jn)`
     39 extern void bessel_jn_r'rtype_kind` ('rtype` * const restrict ret, int n1,
     40 				     int n2, 'rtype_name` x);
     41 export_proto(bessel_jn_r'rtype_kind`);
     42 
     43 void
     44 bessel_jn_r'rtype_kind` ('rtype` * const restrict ret, int n1, int n2, 'rtype_name` x)
     45 {
     46   int i;
     47   index_type stride;
     48 
     49   'rtype_name` last1, last2, x2rev;
     50 
     51   stride = GFC_DESCRIPTOR_STRIDE(ret,0);
     52 
     53   if (ret->base_addr == NULL)
     54     {
     55       size_t size = n2 < n1 ? 0 : n2-n1+1; 
     56       GFC_DIMENSION_SET(ret->dim[0], 0, size-1, 1);
     57       ret->base_addr = xmallocarray (size, sizeof ('rtype_name`));
     58       ret->offset = 0;
     59     }
     60 
     61   if (unlikely (n2 < n1))
     62     return;
     63 
     64   if (unlikely (compile_options.bounds_check)
     65       && GFC_DESCRIPTOR_EXTENT(ret,0) != (n2-n1+1))
     66     runtime_error("Incorrect extent in return value of BESSEL_JN "
     67 		  "(%ld vs. %ld)", (long int) n2-n1,
     68 		  (long int) GFC_DESCRIPTOR_EXTENT(ret,0));
     69 
     70   stride = GFC_DESCRIPTOR_STRIDE(ret,0);
     71 
     72   if (unlikely (x == 0))
     73     {
     74       ret->base_addr[0] = 1;
     75       for (i = 1; i <= n2-n1; i++)
     76         ret->base_addr[i*stride] = 0;
     77       return;
     78     }
     79 
     80   last1 = MATHFUNC(jn) (n2, x);
     81   ret->base_addr[(n2-n1)*stride] = last1;
     82 
     83   if (n1 == n2)
     84     return;
     85 
     86   last2 = MATHFUNC(jn) (n2 - 1, x);
     87   ret->base_addr[(n2-n1-1)*stride] = last2;
     88 
     89   if (n1 + 1 == n2)
     90     return;
     91 
     92   x2rev = GFC_REAL_'rtype_kind`_LITERAL(2.)/x;
     93 
     94   for (i = n2-n1-2; i >= 0; i--)
     95     {
     96       ret->base_addr[i*stride] = x2rev * (i+1+n1) * last2 - last1;
     97       last1 = last2;
     98       last2 = ret->base_addr[i*stride];
     99     }
    100 }
    101 
    102 #endif
    103 
    104 #if 'hasmathfunc(yn)`
    105 extern void bessel_yn_r'rtype_kind` ('rtype` * const restrict ret,
    106 				     int n1, int n2, 'rtype_name` x);
    107 export_proto(bessel_yn_r'rtype_kind`);
    108 
    109 void
    110 bessel_yn_r'rtype_kind` ('rtype` * const restrict ret, int n1, int n2,
    111 			 'rtype_name` x)
    112 {
    113   int i;
    114   index_type stride;
    115 
    116   'rtype_name` last1, last2, x2rev;
    117 
    118   stride = GFC_DESCRIPTOR_STRIDE(ret,0);
    119 
    120   if (ret->base_addr == NULL)
    121     {
    122       size_t size = n2 < n1 ? 0 : n2-n1+1; 
    123       GFC_DIMENSION_SET(ret->dim[0], 0, size-1, 1);
    124       ret->base_addr = xmallocarray (size, sizeof ('rtype_name`));
    125       ret->offset = 0;
    126     }
    127 
    128   if (unlikely (n2 < n1))
    129     return;
    130 
    131   if (unlikely (compile_options.bounds_check)
    132       && GFC_DESCRIPTOR_EXTENT(ret,0) != (n2-n1+1))
    133     runtime_error("Incorrect extent in return value of BESSEL_JN "
    134 		  "(%ld vs. %ld)", (long int) n2-n1,
    135 		  (long int) GFC_DESCRIPTOR_EXTENT(ret,0));
    136 
    137   stride = GFC_DESCRIPTOR_STRIDE(ret,0);
    138 
    139   if (unlikely (x == 0))
    140     {
    141       for (i = 0; i <= n2-n1; i++)
    142 #if defined('rtype_name`_INFINITY)
    143         ret->base_addr[i*stride] = -'rtype_name`_INFINITY;
    144 #else
    145         ret->base_addr[i*stride] = -'rtype_name`_HUGE;
    146 #endif
    147       return;
    148     }
    149 
    150   last1 = MATHFUNC(yn) (n1, x);
    151   ret->base_addr[0] = last1;
    152 
    153   if (n1 == n2)
    154     return;
    155 
    156   last2 = MATHFUNC(yn) (n1 + 1, x);
    157   ret->base_addr[1*stride] = last2;
    158 
    159   if (n1 + 1 == n2)
    160     return;
    161 
    162   x2rev = GFC_REAL_'rtype_kind`_LITERAL(2.)/x;
    163 
    164   for (i = 2; i <= n2 - n1; i++)
    165     {
    166 #if defined('rtype_name`_INFINITY)
    167       if (unlikely (last2 == -'rtype_name`_INFINITY))
    168 	{
    169 	  ret->base_addr[i*stride] = -'rtype_name`_INFINITY;
    170 	}
    171       else
    172 #endif
    173 	{
    174 	  ret->base_addr[i*stride] = x2rev * (i-1+n1) * last2 - last1;
    175 	  last1 = last2;
    176 	  last2 = ret->base_addr[i*stride];
    177 	}
    178     }
    179 }
    180 #endif
    181 
    182 #endif'
    183 
    184