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1 /* Implementation of the BESSEL_JN and BESSEL_YN transformational
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2 function using a recurrence algorithm.
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145
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3 Copyright (C) 2010-2020 Free Software Foundation, Inc.
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111
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4 Contributed by Tobias Burnus <burnus@net-b.de>
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5
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6 This file is part of the GNU Fortran runtime library (libgfortran).
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7
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8 Libgfortran is free software; you can redistribute it and/or
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9 modify it under the terms of the GNU General Public
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10 License as published by the Free Software Foundation; either
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11 version 3 of the License, or (at your option) any later version.
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12
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13 Libgfortran is distributed in the hope that it will be useful,
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14 but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 GNU General Public License for more details.
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17
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18 Under Section 7 of GPL version 3, you are granted additional
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19 permissions described in the GCC Runtime Library Exception, version
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20 3.1, as published by the Free Software Foundation.
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21
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22 You should have received a copy of the GNU General Public License and
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23 a copy of the GCC Runtime Library Exception along with this program;
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24 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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25 <http://www.gnu.org/licenses/>. */
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26
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27 #include "libgfortran.h"
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28
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29
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30
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31 #if defined(GFC_REAL_16_IS_FLOAT128)
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32 #define MATHFUNC(funcname) funcname ## q
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33 #else
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34 #define MATHFUNC(funcname) funcname ## l
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35 #endif
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36
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37 #if defined (HAVE_GFC_REAL_16)
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38
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39
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40
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41 #if (defined(GFC_REAL_16_IS_FLOAT128) || defined(HAVE_JNL))
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42 extern void bessel_jn_r16 (gfc_array_r16 * const restrict ret, int n1,
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43 int n2, GFC_REAL_16 x);
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44 export_proto(bessel_jn_r16);
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45
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46 void
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47 bessel_jn_r16 (gfc_array_r16 * const restrict ret, int n1, int n2, GFC_REAL_16 x)
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48 {
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49 int i;
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50 index_type stride;
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51
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52 GFC_REAL_16 last1, last2, x2rev;
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53
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54 stride = GFC_DESCRIPTOR_STRIDE(ret,0);
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55
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56 if (ret->base_addr == NULL)
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57 {
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58 size_t size = n2 < n1 ? 0 : n2-n1+1;
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59 GFC_DIMENSION_SET(ret->dim[0], 0, size-1, 1);
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60 ret->base_addr = xmallocarray (size, sizeof (GFC_REAL_16));
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61 ret->offset = 0;
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62 }
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63
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64 if (unlikely (n2 < n1))
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65 return;
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66
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67 if (unlikely (compile_options.bounds_check)
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68 && GFC_DESCRIPTOR_EXTENT(ret,0) != (n2-n1+1))
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69 runtime_error("Incorrect extent in return value of BESSEL_JN "
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70 "(%ld vs. %ld)", (long int) n2-n1,
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71 (long int) GFC_DESCRIPTOR_EXTENT(ret,0));
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72
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73 stride = GFC_DESCRIPTOR_STRIDE(ret,0);
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74
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75 if (unlikely (x == 0))
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76 {
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77 ret->base_addr[0] = 1;
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78 for (i = 1; i <= n2-n1; i++)
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79 ret->base_addr[i*stride] = 0;
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80 return;
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81 }
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82
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83 last1 = MATHFUNC(jn) (n2, x);
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84 ret->base_addr[(n2-n1)*stride] = last1;
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85
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86 if (n1 == n2)
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87 return;
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88
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89 last2 = MATHFUNC(jn) (n2 - 1, x);
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90 ret->base_addr[(n2-n1-1)*stride] = last2;
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91
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92 if (n1 + 1 == n2)
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93 return;
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94
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95 x2rev = GFC_REAL_16_LITERAL(2.)/x;
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96
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97 for (i = n2-n1-2; i >= 0; i--)
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98 {
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99 ret->base_addr[i*stride] = x2rev * (i+1+n1) * last2 - last1;
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100 last1 = last2;
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101 last2 = ret->base_addr[i*stride];
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102 }
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103 }
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104
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105 #endif
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106
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107 #if (defined(GFC_REAL_16_IS_FLOAT128) || defined(HAVE_YNL))
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108 extern void bessel_yn_r16 (gfc_array_r16 * const restrict ret,
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109 int n1, int n2, GFC_REAL_16 x);
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110 export_proto(bessel_yn_r16);
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111
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112 void
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113 bessel_yn_r16 (gfc_array_r16 * const restrict ret, int n1, int n2,
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114 GFC_REAL_16 x)
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115 {
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116 int i;
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117 index_type stride;
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118
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119 GFC_REAL_16 last1, last2, x2rev;
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120
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121 stride = GFC_DESCRIPTOR_STRIDE(ret,0);
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122
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123 if (ret->base_addr == NULL)
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124 {
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125 size_t size = n2 < n1 ? 0 : n2-n1+1;
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126 GFC_DIMENSION_SET(ret->dim[0], 0, size-1, 1);
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127 ret->base_addr = xmallocarray (size, sizeof (GFC_REAL_16));
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128 ret->offset = 0;
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129 }
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130
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131 if (unlikely (n2 < n1))
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132 return;
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133
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134 if (unlikely (compile_options.bounds_check)
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135 && GFC_DESCRIPTOR_EXTENT(ret,0) != (n2-n1+1))
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136 runtime_error("Incorrect extent in return value of BESSEL_JN "
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137 "(%ld vs. %ld)", (long int) n2-n1,
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138 (long int) GFC_DESCRIPTOR_EXTENT(ret,0));
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139
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140 stride = GFC_DESCRIPTOR_STRIDE(ret,0);
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141
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142 if (unlikely (x == 0))
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143 {
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144 for (i = 0; i <= n2-n1; i++)
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145 #if defined(GFC_REAL_16_INFINITY)
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146 ret->base_addr[i*stride] = -GFC_REAL_16_INFINITY;
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147 #else
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148 ret->base_addr[i*stride] = -GFC_REAL_16_HUGE;
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149 #endif
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150 return;
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151 }
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152
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153 last1 = MATHFUNC(yn) (n1, x);
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154 ret->base_addr[0] = last1;
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155
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156 if (n1 == n2)
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157 return;
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158
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159 last2 = MATHFUNC(yn) (n1 + 1, x);
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160 ret->base_addr[1*stride] = last2;
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161
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162 if (n1 + 1 == n2)
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163 return;
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164
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165 x2rev = GFC_REAL_16_LITERAL(2.)/x;
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166
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167 for (i = 2; i <= n2 - n1; i++)
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168 {
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169 #if defined(GFC_REAL_16_INFINITY)
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170 if (unlikely (last2 == -GFC_REAL_16_INFINITY))
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171 {
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172 ret->base_addr[i*stride] = -GFC_REAL_16_INFINITY;
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173 }
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174 else
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175 #endif
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176 {
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177 ret->base_addr[i*stride] = x2rev * (i-1+n1) * last2 - last1;
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178 last1 = last2;
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179 last2 = ret->base_addr[i*stride];
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180 }
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181 }
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182 }
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183 #endif
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184
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185 #endif
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186
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