other/s_common.F90
| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | submodule(m_common) s_common | ||
| 2 | contains | ||
| 3 | !> @brief Sort an array of integers using the quicksort algorithm | ||
| 4 | !> | ||
| 5 | !> @param [inout] array The array of integers to be sorted | ||
| 6 | !> @param [in] _(optional) inverse If true, sort in descending order; otherwise, ascending order (default: false) | ||
| 7 |
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1006 | module pure subroutine sort_int(array, inverse) |
| 8 | implicit none | ||
| 9 | |||
| 10 | integer, intent(inout) :: array(:) | ||
| 11 | logical, intent(in), optional :: inverse | ||
| 12 | |||
| 13 | 1006 | call quicksort_int(array, 1, size(array)) | |
| 14 |
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1006 | if (present(inverse)) then |
| 15 | ✗ | if (inverse) then | |
| 16 | ✗ | array = array(size(array):1:-1) | |
| 17 | end if | ||
| 18 | end if | ||
| 19 | |||
| 20 | contains | ||
| 21 | |||
| 22 |
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1894 | pure recursive subroutine quicksort_int(a, left, right) |
| 23 | integer, intent(inout) :: a(:) | ||
| 24 | integer, intent(in) :: left, right | ||
| 25 | integer :: i, j, pivot_idx, pivot, temp | ||
| 26 | |||
| 27 |
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1894 | if (left < right) then |
| 28 | 1894 | pivot_idx = left + (right - left) / 2 | |
| 29 | 1894 | pivot = a(pivot_idx) | |
| 30 | 1894 | i = left | |
| 31 | 1894 | j = right | |
| 32 | do | ||
| 33 |
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2091 | do while (a(i) < pivot) |
| 34 | 2091 | i = i + 1 | |
| 35 | end do | ||
| 36 |
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3746 | do while (a(j) > pivot) |
| 37 | 1826 | j = j - 1 | |
| 38 | end do | ||
| 39 |
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1920 | if (i <= j) then |
| 40 | temp = a(i) | ||
| 41 | 1915 | a(i) = a(j) | |
| 42 | 1915 | a(j) = temp | |
| 43 | 1915 | i = i + 1 | |
| 44 | 1915 | j = j - 1 | |
| 45 | end if | ||
| 46 |
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1920 | if (i > j) exit |
| 47 | end do | ||
| 48 |
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1894 | if (left < j) call quicksort_int(a, left, j) |
| 49 |
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1894 | if (i < right) call quicksort_int(a, i, right) |
| 50 | end if | ||
| 51 | 1894 | end subroutine quicksort_int | |
| 52 | |||
| 53 | end subroutine sort_int | ||
| 54 | |||
| 55 | !> @brief Sort an array of real numbers using the quicksort algorithm | ||
| 56 | !> | ||
| 57 | !> @param [inout] array The array of real numbers to be sorted | ||
| 58 | !> @param [in] _(optional) inverse If true, sort in descending order; otherwise, ascending order (default: false) | ||
| 59 | !> @param [in] _(optional) sort_fun A function to determine the sorting order | ||
| 60 |
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6 | module subroutine sort_real(array, inverse, sort_fun) |
| 61 | implicit none | ||
| 62 | |||
| 63 | real(wp), intent(inout) :: array(:) | ||
| 64 | logical, intent(in), optional :: inverse | ||
| 65 | procedure(user_function_1d_interface), optional :: sort_fun | ||
| 66 | |||
| 67 | 6 | call quicksort_real(array, 1, size(array)) | |
| 68 |
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6 | if (present(inverse)) then |
| 69 |
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1 | if (inverse) then |
| 70 |
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22 | array = array(size(array):1:-1) |
| 71 | end if | ||
| 72 | end if | ||
| 73 | |||
| 74 | contains | ||
| 75 | |||
| 76 |
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1155 | recursive subroutine quicksort_real(a, left, right) |
| 77 | real(wp), intent(inout) :: a(:) | ||
| 78 | integer, intent(in) :: left, right | ||
| 79 | integer :: i, j, pivot_idx | ||
| 80 | real(wp) :: pivot, temp | ||
| 81 | real(wp) :: val_i, val_j | ||
| 82 | |||
| 83 |
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1155 | if (left < right) then |
| 84 | 1155 | pivot_idx = left + (right - left) / 2 | |
| 85 |
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1155 | if (present(sort_fun)) then |
| 86 | 387 | pivot = sort_fun(a(pivot_idx)) | |
| 87 | else | ||
| 88 | 768 | pivot = a(pivot_idx) | |
| 89 | end if | ||
| 90 | 1155 | i = left | |
| 91 | 1155 | j = right | |
| 92 | do | ||
| 93 |
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7088 | do while (i <= right) |
| 94 |
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7088 | if (present(sort_fun)) then |
| 95 | 2403 | val_i = sort_fun(a(i)) | |
| 96 | else | ||
| 97 | 4685 | val_i = a(i) | |
| 98 | end if | ||
| 99 |
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7088 | if (val_i >= pivot) exit |
| 100 | 7088 | i = i + 1 | |
| 101 | end do | ||
| 102 |
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7439 | do while (j >= left) |
| 103 |
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7439 | if (present(sort_fun)) then |
| 104 | 2522 | val_j = sort_fun(a(j)) | |
| 105 | else | ||
| 106 | 4917 | val_j = a(j) | |
| 107 | end if | ||
| 108 |
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7439 | if (val_j <= pivot) exit |
| 109 | 7439 | j = j - 1 | |
| 110 | end do | ||
| 111 |
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3246 | if (i <= j) then |
| 112 | 2980 | temp = a(i) | |
| 113 | 2980 | a(i) = a(j) | |
| 114 | 2980 | a(j) = temp | |
| 115 | 2980 | i = i + 1 | |
| 116 | 2980 | j = j - 1 | |
| 117 | end if | ||
| 118 |
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3246 | if (i > j) exit |
| 119 | end do | ||
| 120 |
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1155 | if (left < j) call quicksort_real(a, left, j) |
| 121 |
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1155 | if (i < right) call quicksort_real(a, i, right) |
| 122 | end if | ||
| 123 | 1155 | end subroutine quicksort_real | |
| 124 | |||
| 125 | end subroutine sort_real | ||
| 126 | |||
| 127 | !> @brief Compute a sort permutation of an array of real numbers (descending, high to low) | ||
| 128 | !> | ||
| 129 | !> @param [in] array The array of real numbers to rank | ||
| 130 | !> @param [out] perm The permutation indices such that array(perm) is sorted descending | ||
| 131 | !> @param [in] sort_fun _(optional)_ Applied to each element before comparison | ||
| 132 | ✗ | module subroutine sort_perm(array, perm, sort_fun) | |
| 133 | implicit none | ||
| 134 | |||
| 135 | real(wp), intent(in) :: array(:) | ||
| 136 | integer, intent(out) :: perm(:) | ||
| 137 | procedure(user_function_1d_interface), optional :: sort_fun | ||
| 138 | |||
| 139 | integer :: i, j, tmp | ||
| 140 | real(wp) :: key_i, key_j | ||
| 141 | |||
| 142 | ✗ | do i = 1, size(perm) | |
| 143 | ✗ | perm(i) = i | |
| 144 | end do | ||
| 145 | |||
| 146 | ! Insertion sort on perm, keyed by array values descending | ||
| 147 | ✗ | do i = 2, size(perm) | |
| 148 | ✗ | tmp = perm(i) | |
| 149 | ✗ | if (present(sort_fun)) then | |
| 150 | ✗ | key_i = sort_fun(array(tmp)) | |
| 151 | else | ||
| 152 | ✗ | key_i = array(tmp) | |
| 153 | end if | ||
| 154 | ✗ | j = i - 1 | |
| 155 | ✗ | do while (j >= 1) | |
| 156 | ✗ | if (present(sort_fun)) then | |
| 157 | ✗ | key_j = sort_fun(array(perm(j))) | |
| 158 | else | ||
| 159 | ✗ | key_j = array(perm(j)) | |
| 160 | end if | ||
| 161 | ✗ | if (key_j >= key_i) exit | |
| 162 | ✗ | perm(j + 1) = perm(j) | |
| 163 | ✗ | j = j - 1 | |
| 164 | end do | ||
| 165 | ✗ | perm(j + 1) = tmp | |
| 166 | end do | ||
| 167 | ✗ | end subroutine sort_perm | |
| 168 | |||
| 169 | !> @brief Compute the union of two sets of integers | ||
| 170 | !> | ||
| 171 | !> @param [out] union The resulting union of the two sets | ||
| 172 | !> @param [in] set1 The first set of integers | ||
| 173 | !> @param [in] set2 The second set of integers | ||
| 174 |
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1 | module subroutine set_union(union, set1, set2) |
| 175 | implicit none | ||
| 176 | |||
| 177 | integer, allocatable, intent(out) :: union(:) | ||
| 178 | integer, intent(in) :: set1(0:), set2(0:) | ||
| 179 | |||
| 180 | 1 | integer, allocatable :: temp(:) | |
| 181 | integer :: nr_duplicates, i | ||
| 182 | |||
| 183 | ! 1: append, 2: sort, 3: remove duplicates | ||
| 184 | |||
| 185 |
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1 | if (size(set1) == 0 .and. size(set2) == 0) then |
| 186 | ✗ | allocate (union(0:-1)) | |
| 187 | return | ||
| 188 | end if | ||
| 189 | |||
| 190 |
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3 | allocate (temp(0:size(set1) + size(set2) - 1)) |
| 191 |
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7 | temp(0:size(set1) - 1) = set1 |
| 192 |
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7 | temp(size(set1):size(set1) + size(set2) - 1) = set2 |
| 193 | |||
| 194 | 1 | call sort(temp) | |
| 195 | |||
| 196 | nr_duplicates = 0 | ||
| 197 |
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12 | do i = 0, size(temp) - 2 |
| 198 |
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12 | if (temp(i) == temp(i + 1)) then |
| 199 | 3 | nr_duplicates = nr_duplicates + 1 | |
| 200 | end if | ||
| 201 | end do | ||
| 202 | |||
| 203 |
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3 | allocate (union(0:size(temp) - nr_duplicates - 1)) |
| 204 | |||
| 205 | nr_duplicates = 0 | ||
| 206 | 1 | union(0) = temp(0) | |
| 207 |
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12 | do i = 1, size(temp) - 1 |
| 208 |
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12 | if (temp(i - 1) == temp(i)) then |
| 209 | 3 | nr_duplicates = nr_duplicates + 1 | |
| 210 | else | ||
| 211 | 8 | union(i - nr_duplicates) = temp(i) | |
| 212 | end if | ||
| 213 | end do | ||
| 214 | |||
| 215 | 1 | deallocate (temp) | |
| 216 | end subroutine set_union | ||
| 217 | |||
| 218 | 11 | module pure subroutine prime_factors(n, factors) | |
| 219 | implicit none | ||
| 220 | |||
| 221 | integer, intent(in) :: n | ||
| 222 | integer, allocatable, intent(out) :: factors(:) | ||
| 223 | |||
| 224 | integer :: num, divisor, count, i | ||
| 225 | |||
| 226 | ! Handle edge cases | ||
| 227 |
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11 | if (n <= 1) then |
| 228 |
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2 | allocate (factors(0)) |
| 229 | 2 | return | |
| 230 | end if | ||
| 231 | |||
| 232 | ! Count the number of prime factors | ||
| 233 | num = n | ||
| 234 | count = 0 | ||
| 235 | |||
| 236 | ! Count factors of 2 | ||
| 237 |
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25 | do while (mod(num, 2) == 0) |
| 238 | 16 | count = count + 1 | |
| 239 | 16 | num = num / 2 | |
| 240 | end do | ||
| 241 | |||
| 242 | ! Count odd factors | ||
| 243 | divisor = 3 | ||
| 244 |
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17 | do while (divisor * divisor <= num) |
| 245 |
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13 | do while (mod(num, divisor) == 0) |
| 246 | 5 | count = count + 1 | |
| 247 | 5 | num = num / divisor | |
| 248 | end do | ||
| 249 | 8 | divisor = divisor + 2 | |
| 250 | end do | ||
| 251 | |||
| 252 | ! If num > 1, then it's a prime factor | ||
| 253 |
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9 | if (num > 1) then |
| 254 | 5 | count = count + 1 | |
| 255 | end if | ||
| 256 | |||
| 257 | ! Allocate the array | ||
| 258 |
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27 | allocate (factors(count)) |
| 259 | |||
| 260 | ! Fill the array with prime factors | ||
| 261 | num = n | ||
| 262 | i = 1 | ||
| 263 | |||
| 264 | ! Extract factors of 2 | ||
| 265 |
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25 | do while (mod(num, 2) == 0) |
| 266 | 16 | factors(i) = 2 | |
| 267 | 16 | i = i + 1 | |
| 268 | 16 | num = num / 2 | |
| 269 | end do | ||
| 270 | |||
| 271 | ! Extract odd factors | ||
| 272 | divisor = 3 | ||
| 273 |
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17 | do while (divisor * divisor <= num) |
| 274 |
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13 | do while (mod(num, divisor) == 0) |
| 275 | 5 | factors(i) = divisor | |
| 276 | 5 | i = i + 1 | |
| 277 | 5 | num = num / divisor | |
| 278 | end do | ||
| 279 | 8 | divisor = divisor + 2 | |
| 280 | end do | ||
| 281 | |||
| 282 | ! If num > 1, then it's a prime factor | ||
| 283 |
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9 | if (num > 1) then |
| 284 | 5 | factors(i) = num | |
| 285 | end if | ||
| 286 | |||
| 287 | end subroutine prime_factors | ||
| 288 | |||
| 289 | !> @brief Split an integer into two factors that are as close as possible | ||
| 290 | !> | ||
| 291 | !> Given an integer N, find n1 and n2 such that N = n1 * n2 and |n1 - n2| is minimized. | ||
| 292 | !> The result satisfies n1 <= n2. | ||
| 293 | !> | ||
| 294 | !> @param[in] n The integer to split | ||
| 295 | !> @param[out] n1 The smaller factor | ||
| 296 | !> @param[out] n2 The larger factor | ||
| 297 | 3835 | module pure subroutine balanced_split_2(n, n1, n2) | |
| 298 | implicit none | ||
| 299 | |||
| 300 | integer, intent(in) :: n | ||
| 301 | integer, intent(out) :: n1, n2 | ||
| 302 | |||
| 303 | integer :: i, sqrt_n | ||
| 304 | |||
| 305 | ! Handle edge cases | ||
| 306 |
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3835 | if (n <= 0) then |
| 307 | ✗ | n1 = 1 | |
| 308 | ✗ | n2 = n | |
| 309 | ✗ | return | |
| 310 | end if | ||
| 311 | |||
| 312 |
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3835 | if (n == 1) then |
| 313 | 3 | n1 = 1 | |
| 314 | 3 | n2 = 1 | |
| 315 | 3 | return | |
| 316 | end if | ||
| 317 | |||
| 318 | ! Start from sqrt(n) and work downward to find the largest divisor <= sqrt(n) | ||
| 319 | 3832 | sqrt_n = int(sqrt(real(n))) | |
| 320 | |||
| 321 |
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35439 | do i = sqrt_n, 1, -1 |
| 322 |
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35439 | if (mod(n, i) == 0) then |
| 323 | 3832 | n1 = i | |
| 324 | 3832 | n2 = n / i | |
| 325 | 3832 | return | |
| 326 | end if | ||
| 327 | end do | ||
| 328 | |||
| 329 | ! Should never reach here, but as a fallback | ||
| 330 | ✗ | n1 = 1 | |
| 331 | ✗ | n2 = n | |
| 332 | |||
| 333 | end subroutine balanced_split_2 | ||
| 334 | |||
| 335 | !> @brief Split an integer into three factors that are as close as possible | ||
| 336 | !> | ||
| 337 | !> Given an integer N, find n1, n2, and n3 such that N = n1 * n2 * n3 and the factors are as balanced as possible. | ||
| 338 | !> The result satisfies n1 <= n2 <= n3. | ||
| 339 | !> | ||
| 340 | !> @param[in] n The integer to split | ||
| 341 | !> @param[out] n1 The smallest factor | ||
| 342 | !> @param[out] n2 The middle factor | ||
| 343 | !> @param[out] n3 The largest factor | ||
| 344 | 1006 | module pure subroutine balanced_split_3(n, n1, n2, n3) | |
| 345 | implicit none | ||
| 346 | |||
| 347 | integer, intent(in) :: n | ||
| 348 | integer, intent(out) :: n1, n2, n3 | ||
| 349 | |||
| 350 | integer :: i, cbrt_n, temp_n2, temp_n3 | ||
| 351 | integer :: best_n1, best_n2, best_n3 | ||
| 352 | integer :: max_diff, current_max_diff | ||
| 353 | |||
| 354 | integer :: nlist(3) | ||
| 355 | |||
| 356 | ! Handle edge cases | ||
| 357 |
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|
1006 | if (n <= 0) then |
| 358 | ✗ | n1 = 1 | |
| 359 | ✗ | n2 = 1 | |
| 360 | ✗ | n3 = n | |
| 361 | 2 | return | |
| 362 | end if | ||
| 363 | |||
| 364 |
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1006 | if (n == 1) then |
| 365 | 2 | n1 = 1 | |
| 366 | 2 | n2 = 1 | |
| 367 | 2 | n3 = 1 | |
| 368 | 2 | return | |
| 369 | end if | ||
| 370 | |||
| 371 | ! Start from cbrt(n) and search for the most balanced factorization | ||
| 372 | 1004 | cbrt_n = int(real(n)**(1.0 / 3.0)) + 1 | |
| 373 | best_n1 = 1 | ||
| 374 | best_n2 = 1 | ||
| 375 | best_n3 = n | ||
| 376 | 1004 | max_diff = n - 1 | |
| 377 | |||
| 378 |
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9004 | do i = cbrt_n, 1, -1 |
| 379 |
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9004 | if (mod(n, i) == 0) then |
| 380 | ! i is a divisor, now split n/i into two balanced factors | ||
| 381 | 2701 | call balanced_split(n / i, temp_n2, temp_n3) | |
| 382 | |||
| 383 | ! Check if this is more balanced | ||
| 384 | 2701 | current_max_diff = max(temp_n3 - i, temp_n3 - temp_n2, temp_n2 - i) | |
| 385 | |||
| 386 |
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2701 | if (current_max_diff < max_diff) then |
| 387 | best_n1 = i | ||
| 388 | best_n2 = temp_n2 | ||
| 389 | best_n3 = temp_n3 | ||
| 390 | max_diff = current_max_diff | ||
| 391 | end if | ||
| 392 | end if | ||
| 393 | end do | ||
| 394 | |||
| 395 | ! Sort the results to ensure n1 <= n2 <= n3 | ||
| 396 |
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4016 | nlist = [best_n1, best_n2, best_n3] |
| 397 | 1004 | call sort_int(nlist) | |
| 398 | 1004 | n1 = nlist(1) | |
| 399 | 1004 | n2 = nlist(2) | |
| 400 | 1004 | n3 = nlist(3) | |
| 401 | |||
| 402 | end subroutine balanced_split_3 | ||
| 403 | |||
| 404 | 91 | module real(wp) function brent(fun, xa_in, xb_in, x_tol, max_iter, fa_in, fb_in, success) result(xsol) | |
| 405 | implicit none | ||
| 406 | |||
| 407 | procedure(user_function_1d_interface) :: fun | ||
| 408 | real(wp), intent(in) :: xa_in, xb_in, x_tol | ||
| 409 | integer, intent(in) :: max_iter | ||
| 410 | real(wp), intent(in), optional :: fa_in, fb_in | ||
| 411 | logical, intent(out), optional :: success | ||
| 412 | |||
| 413 | ! Local variables | ||
| 414 | real(wp) :: xa, xb, fa, fb, fc, xc, xd, xe, xm, p, q, r, s | ||
| 415 | real(wp) :: toler | ||
| 416 | integer :: iter, flag | ||
| 417 | |||
| 418 | |||
| 419 | |||
| 420 | iter = 0 | ||
| 421 | |||
| 422 | 91 | xa = xa_in | |
| 423 | 91 | xb = xb_in | |
| 424 |
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91 | if (present(fa_in)) then |
| 425 | ✗ | fa = fa_in | |
| 426 | else | ||
| 427 | 91 | fa = fun(xa) | |
| 428 | iter = iter + 1 | ||
| 429 | endif | ||
| 430 |
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91 | if (present(fb_in)) then |
| 431 | ✗ | fb = fb_in | |
| 432 | else | ||
| 433 | 91 | fb = fun(xb) | |
| 434 | 91 | iter = iter + 1 | |
| 435 | endif | ||
| 436 | |||
| 437 | flag = 1 ! 1: continue, 0: converged, -1: some problem | ||
| 438 |
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91 | if (fa == 0) then |
| 439 | xsol = xa | ||
| 440 | flag = 0 | ||
| 441 |
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91 | elseif (fb == 0) then |
| 442 | xsol = xb | ||
| 443 | flag = 0 | ||
| 444 |
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91 | elseif (fa * fb > 0) then |
| 445 | xsol = 0 | ||
| 446 | flag = -1 | ||
| 447 | endif | ||
| 448 | |||
| 449 | xc = xa; fc = fa | ||
| 450 | 91 | xd = xb - xa; xe = xd | |
| 451 | |||
| 452 |
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537 | do while (flag == 1 .and. fb /= 0 .and. xa /= xb) |
| 453 | |||
| 454 | ! Ensure that b is the best result so far, a is the previous | ||
| 455 | ! value of b, and c is on the opposite side of the zero from b. | ||
| 456 |
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516 | if (fb * fc > 0) then |
| 457 | xc = xa; fc = fa | ||
| 458 | 268 | xd = xb - xa; xe = xd | |
| 459 | endif | ||
| 460 |
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516 | if (abs(fc) < abs(fb)) then |
| 461 | 157 | xa = xb; xb = xc; xc = xa | |
| 462 | fa = fb; fb = fc; fc = fa | ||
| 463 | endif | ||
| 464 | |||
| 465 | ! Convergence test and possible exit | ||
| 466 | 516 | xm = 0.5*(xc - xb) | |
| 467 | |||
| 468 | 516 | toler = x_tol | |
| 469 |
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516 | if ((abs(xm) <= toler) .or. (fb == 0.0)) then |
| 470 | flag = 0 | ||
| 471 | exit | ||
| 472 |
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446 | elseif (iter == max_iter) then |
| 473 | flag = -1 | ||
| 474 | exit | ||
| 475 | endif | ||
| 476 | |||
| 477 | ! Choose bisection or interpolation | ||
| 478 |
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446 | if ((abs(xe) < toler) .or. (abs(fa) <= abs(fb))) then |
| 479 | ! Bisection | ||
| 480 | xd = xm; xe = xm | ||
| 481 | else | ||
| 482 | ! Interpolation | ||
| 483 | 446 | s = fb/fa; | |
| 484 |
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446 | if (xa == xc) then |
| 485 | ! Linear interpolation | ||
| 486 | 268 | p = 2*xm*s | |
| 487 | 268 | q = 1 - s | |
| 488 | else | ||
| 489 | ! Inverse quadratic interpolation | ||
| 490 | 178 | q = fa/fc | |
| 491 | 178 | r = fb/fc | |
| 492 | 178 | p = s*(2*xm*q*(q - r) - (xb - xa)*(r - 1)) | |
| 493 | 178 | q = (q - 1)*(r - 1)*(s - 1) | |
| 494 | endif | ||
| 495 |
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446 | if (p > 0) then |
| 496 | 276 | q = -q | |
| 497 | else | ||
| 498 | 170 | p = -p | |
| 499 | endif | ||
| 500 | ! Is interpolated point acceptable | ||
| 501 |
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446 | if ((2*p < 3*xm*q - abs(toler*q)) .and. (p < abs(0.5*xe*q))) then |
| 502 | 390 | xe = xd; xd = p/q | |
| 503 | else | ||
| 504 | xd = xm; xe = xm | ||
| 505 | endif | ||
| 506 | endif ! Interpolation | ||
| 507 | |||
| 508 | ! Next point | ||
| 509 | 446 | xa = xb | |
| 510 | fa = fb | ||
| 511 |
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446 | if (abs(xd) > toler) then |
| 512 | 376 | xb = xb + xd | |
| 513 |
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70 | elseif (xb > xc) then |
| 514 | 33 | xb = xb - toler | |
| 515 | else | ||
| 516 | 37 | xb = xb + toler | |
| 517 | endif | ||
| 518 | 446 | fb = fun(xb) | |
| 519 | 446 | iter = iter + 1 | |
| 520 | |||
| 521 | end do | ||
| 522 | |||
| 523 | 91 | xsol = xb | |
| 524 | |||
| 525 |
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91 | if (flag == 1 .and. (fb == 0 .or. xa == xb)) then |
| 526 | flag = 0 | ||
| 527 | end if | ||
| 528 | |||
| 529 |
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91 | if (present(success)) success = flag == 0 |
| 530 | |||
| 531 | 91 | end function | |
| 532 | |||
| 533 | end submodule | ||
| 534 |