| File: | polly/lib/External/isl/isl_affine_hull.c |
| Warning: | line 513, column 6 Access to field 'sample' results in a dereference of a null pointer (loaded from variable 'bset') |
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| 1 | /* | |||
| 2 | * Copyright 2008-2009 Katholieke Universiteit Leuven | |||
| 3 | * Copyright 2010 INRIA Saclay | |||
| 4 | * Copyright 2012 Ecole Normale Superieure | |||
| 5 | * | |||
| 6 | * Use of this software is governed by the MIT license | |||
| 7 | * | |||
| 8 | * Written by Sven Verdoolaege, K.U.Leuven, Departement | |||
| 9 | * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium | |||
| 10 | * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite, | |||
| 11 | * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France | |||
| 12 | * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France | |||
| 13 | */ | |||
| 14 | ||||
| 15 | #include <isl_ctx_private.h> | |||
| 16 | #include <isl_map_private.h> | |||
| 17 | #include <isl_seq.h> | |||
| 18 | #include <isl/set.h> | |||
| 19 | #include <isl/lp.h> | |||
| 20 | #include <isl/map.h> | |||
| 21 | #include "isl_equalities.h" | |||
| 22 | #include "isl_sample.h" | |||
| 23 | #include "isl_tab.h" | |||
| 24 | #include <isl_mat_private.h> | |||
| 25 | #include <isl_vec_private.h> | |||
| 26 | ||||
| 27 | #include <bset_to_bmap.c> | |||
| 28 | #include <bset_from_bmap.c> | |||
| 29 | #include <set_to_map.c> | |||
| 30 | #include <set_from_map.c> | |||
| 31 | ||||
| 32 | __isl_give isl_basic_map *isl_basic_map_implicit_equalities( | |||
| 33 | __isl_take isl_basic_map *bmap) | |||
| 34 | { | |||
| 35 | struct isl_tab *tab; | |||
| 36 | ||||
| 37 | if (!bmap) | |||
| 38 | return bmap; | |||
| 39 | ||||
| 40 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | |||
| 41 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) | |||
| 42 | return bmap; | |||
| 43 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT)(!!(((bmap)->flags) & ((1 << 2))))) | |||
| 44 | return bmap; | |||
| 45 | if (bmap->n_ineq <= 1) | |||
| 46 | return bmap; | |||
| 47 | ||||
| 48 | tab = isl_tab_from_basic_map(bmap, 0); | |||
| 49 | if (isl_tab_detect_implicit_equalities(tab) < 0) | |||
| 50 | goto error; | |||
| 51 | bmap = isl_basic_map_update_from_tab(bmap, tab); | |||
| 52 | isl_tab_free(tab); | |||
| 53 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | |||
| 54 | ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT)(((bmap)->flags) |= ((1 << 2))); | |||
| 55 | return bmap; | |||
| 56 | error: | |||
| 57 | isl_tab_free(tab); | |||
| 58 | isl_basic_map_free(bmap); | |||
| 59 | return NULL((void*)0); | |||
| 60 | } | |||
| 61 | ||||
| 62 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_implicit_equalities( | |||
| 63 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 64 | { | |||
| 65 | return bset_from_bmap( | |||
| 66 | isl_basic_map_implicit_equalities(bset_to_bmap(bset))); | |||
| 67 | } | |||
| 68 | ||||
| 69 | /* Make eq[row][col] of both bmaps equal so we can add the row | |||
| 70 | * add the column to the common matrix. | |||
| 71 | * Note that because of the echelon form, the columns of row row | |||
| 72 | * after column col are zero. | |||
| 73 | */ | |||
| 74 | static void set_common_multiple( | |||
| 75 | struct isl_basic_setisl_basic_map *bset1, struct isl_basic_setisl_basic_map *bset2, | |||
| 76 | unsigned row, unsigned col) | |||
| 77 | { | |||
| 78 | isl_int m, c; | |||
| 79 | ||||
| 80 | if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col])(isl_sioimath_cmp(*(bset1->eq[row][col]), *(bset2->eq[row ][col])) == 0)) | |||
| 81 | return; | |||
| 82 | ||||
| 83 | isl_int_init(c)isl_sioimath_init((c)); | |||
| 84 | isl_int_init(m)isl_sioimath_init((m)); | |||
| 85 | isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col])isl_sioimath_lcm((m), *(bset1->eq[row][col]), *(bset2-> eq[row][col])); | |||
| 86 | isl_int_divexact(c, m, bset1->eq[row][col])isl_sioimath_tdiv_q((c), *(m), *(bset1->eq[row][col])); | |||
| 87 | isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1); | |||
| 88 | isl_int_divexact(c, m, bset2->eq[row][col])isl_sioimath_tdiv_q((c), *(m), *(bset2->eq[row][col])); | |||
| 89 | isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1); | |||
| 90 | isl_int_clear(c)isl_sioimath_clear((c)); | |||
| 91 | isl_int_clear(m)isl_sioimath_clear((m)); | |||
| 92 | } | |||
| 93 | ||||
| 94 | /* Delete a given equality, moving all the following equalities one up. | |||
| 95 | */ | |||
| 96 | static void delete_row(__isl_keep isl_basic_setisl_basic_map *bset, unsigned row) | |||
| 97 | { | |||
| 98 | isl_int *t; | |||
| 99 | int r; | |||
| 100 | ||||
| 101 | t = bset->eq[row]; | |||
| 102 | bset->n_eq--; | |||
| 103 | for (r = row; r < bset->n_eq; ++r) | |||
| 104 | bset->eq[r] = bset->eq[r+1]; | |||
| 105 | bset->eq[bset->n_eq] = t; | |||
| 106 | } | |||
| 107 | ||||
| 108 | /* Make first row entries in column col of bset1 identical to | |||
| 109 | * those of bset2, using the fact that entry bset1->eq[row][col]=a | |||
| 110 | * is non-zero. Initially, these elements of bset1 are all zero. | |||
| 111 | * For each row i < row, we set | |||
| 112 | * A[i] = a * A[i] + B[i][col] * A[row] | |||
| 113 | * B[i] = a * B[i] | |||
| 114 | * so that | |||
| 115 | * A[i][col] = B[i][col] = a * old(B[i][col]) | |||
| 116 | */ | |||
| 117 | static isl_stat construct_column( | |||
| 118 | __isl_keep isl_basic_setisl_basic_map *bset1, __isl_keep isl_basic_setisl_basic_map *bset2, | |||
| 119 | unsigned row, unsigned col) | |||
| 120 | { | |||
| 121 | int r; | |||
| 122 | isl_int a; | |||
| 123 | isl_int b; | |||
| 124 | isl_size total; | |||
| 125 | ||||
| 126 | total = isl_basic_set_dim(bset1, isl_dim_set); | |||
| 127 | if (total < 0) | |||
| 128 | return isl_stat_error; | |||
| 129 | ||||
| 130 | isl_int_init(a)isl_sioimath_init((a)); | |||
| 131 | isl_int_init(b)isl_sioimath_init((b)); | |||
| 132 | for (r = 0; r < row; ++r) { | |||
| 133 | if (isl_int_is_zero(bset2->eq[r][col])(isl_sioimath_sgn(*(bset2->eq[r][col])) == 0)) | |||
| 134 | continue; | |||
| 135 | isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col])isl_sioimath_gcd((b), *(bset2->eq[r][col]), *(bset1->eq [row][col])); | |||
| 136 | isl_int_divexact(a, bset1->eq[row][col], b)isl_sioimath_tdiv_q((a), *(bset1->eq[row][col]), *(b)); | |||
| 137 | isl_int_divexact(b, bset2->eq[r][col], b)isl_sioimath_tdiv_q((b), *(bset2->eq[r][col]), *(b)); | |||
| 138 | isl_seq_combine(bset1->eq[r], a, bset1->eq[r], | |||
| 139 | b, bset1->eq[row], 1 + total); | |||
| 140 | isl_seq_scale(bset2->eq[r], bset2->eq[r], a, 1 + total); | |||
| 141 | } | |||
| 142 | isl_int_clear(a)isl_sioimath_clear((a)); | |||
| 143 | isl_int_clear(b)isl_sioimath_clear((b)); | |||
| 144 | delete_row(bset1, row); | |||
| 145 | ||||
| 146 | return isl_stat_ok; | |||
| 147 | } | |||
| 148 | ||||
| 149 | /* Make first row entries in column col of bset1 identical to | |||
| 150 | * those of bset2, using only these entries of the two matrices. | |||
| 151 | * Let t be the last row with different entries. | |||
| 152 | * For each row i < t, we set | |||
| 153 | * A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t] | |||
| 154 | * B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t] | |||
| 155 | * so that | |||
| 156 | * A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col]) | |||
| 157 | */ | |||
| 158 | static isl_bool transform_column( | |||
| 159 | __isl_keep isl_basic_setisl_basic_map *bset1, __isl_keep isl_basic_setisl_basic_map *bset2, | |||
| 160 | unsigned row, unsigned col) | |||
| 161 | { | |||
| 162 | int i, t; | |||
| 163 | isl_int a, b, g; | |||
| 164 | isl_size total; | |||
| 165 | ||||
| 166 | for (t = row-1; t >= 0; --t) | |||
| 167 | if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col])(isl_sioimath_cmp(*(bset1->eq[t][col]), *(bset2->eq[t][ col])) != 0)) | |||
| 168 | break; | |||
| 169 | if (t < 0) | |||
| 170 | return isl_bool_false; | |||
| 171 | ||||
| 172 | total = isl_basic_set_dim(bset1, isl_dim_set); | |||
| 173 | if (total < 0) | |||
| 174 | return isl_bool_error; | |||
| 175 | isl_int_init(a)isl_sioimath_init((a)); | |||
| 176 | isl_int_init(b)isl_sioimath_init((b)); | |||
| 177 | isl_int_init(g)isl_sioimath_init((g)); | |||
| 178 | isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col])isl_sioimath_sub((b), *(bset1->eq[t][col]), *(bset2->eq [t][col])); | |||
| 179 | for (i = 0; i < t; ++i) { | |||
| 180 | isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col])isl_sioimath_sub((a), *(bset2->eq[i][col]), *(bset1->eq [i][col])); | |||
| 181 | isl_int_gcd(g, a, b)isl_sioimath_gcd((g), *(a), *(b)); | |||
| 182 | isl_int_divexact(a, a, g)isl_sioimath_tdiv_q((a), *(a), *(g)); | |||
| 183 | isl_int_divexact(g, b, g)isl_sioimath_tdiv_q((g), *(b), *(g)); | |||
| 184 | isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t], | |||
| 185 | 1 + total); | |||
| 186 | isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t], | |||
| 187 | 1 + total); | |||
| 188 | } | |||
| 189 | isl_int_clear(a)isl_sioimath_clear((a)); | |||
| 190 | isl_int_clear(b)isl_sioimath_clear((b)); | |||
| 191 | isl_int_clear(g)isl_sioimath_clear((g)); | |||
| 192 | delete_row(bset1, t); | |||
| 193 | delete_row(bset2, t); | |||
| 194 | return isl_bool_true; | |||
| 195 | } | |||
| 196 | ||||
| 197 | /* The implementation is based on Section 5.2 of Michael Karr, | |||
| 198 | * "Affine Relationships Among Variables of a Program", | |||
| 199 | * except that the echelon form we use starts from the last column | |||
| 200 | * and that we are dealing with integer coefficients. | |||
| 201 | */ | |||
| 202 | static __isl_give isl_basic_setisl_basic_map *affine_hull( | |||
| 203 | __isl_take isl_basic_setisl_basic_map *bset1, __isl_take isl_basic_setisl_basic_map *bset2) | |||
| 204 | { | |||
| 205 | isl_size dim; | |||
| 206 | unsigned total; | |||
| 207 | int col; | |||
| 208 | int row; | |||
| 209 | ||||
| 210 | dim = isl_basic_set_dim(bset1, isl_dim_set); | |||
| 211 | if (dim < 0 || !bset2) | |||
| 212 | goto error; | |||
| 213 | ||||
| 214 | total = 1 + dim; | |||
| 215 | ||||
| 216 | row = 0; | |||
| 217 | for (col = total-1; col >= 0; --col) { | |||
| 218 | int is_zero1 = row >= bset1->n_eq || | |||
| 219 | isl_int_is_zero(bset1->eq[row][col])(isl_sioimath_sgn(*(bset1->eq[row][col])) == 0); | |||
| 220 | int is_zero2 = row >= bset2->n_eq || | |||
| 221 | isl_int_is_zero(bset2->eq[row][col])(isl_sioimath_sgn(*(bset2->eq[row][col])) == 0); | |||
| 222 | if (!is_zero1 && !is_zero2) { | |||
| 223 | set_common_multiple(bset1, bset2, row, col); | |||
| 224 | ++row; | |||
| 225 | } else if (!is_zero1 && is_zero2) { | |||
| 226 | if (construct_column(bset1, bset2, row, col) < 0) | |||
| 227 | goto error; | |||
| 228 | } else if (is_zero1 && !is_zero2) { | |||
| 229 | if (construct_column(bset2, bset1, row, col) < 0) | |||
| 230 | goto error; | |||
| 231 | } else { | |||
| 232 | isl_bool transform; | |||
| 233 | ||||
| 234 | transform = transform_column(bset1, bset2, row, col); | |||
| 235 | if (transform < 0) | |||
| 236 | goto error; | |||
| 237 | if (transform) | |||
| 238 | --row; | |||
| 239 | } | |||
| 240 | } | |||
| 241 | isl_assert(bset1->ctx, row == bset1->n_eq, goto error)do { if (row == bset1->n_eq) break; do { isl_handle_error( bset1->ctx, isl_error_unknown, "Assertion \"" "row == bset1->n_eq" "\" failed", "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_affine_hull.c" , 241); goto error; } while (0); } while (0); | |||
| 242 | isl_basic_set_free(bset2); | |||
| 243 | bset1 = isl_basic_set_normalize_constraints(bset1); | |||
| 244 | return bset1; | |||
| 245 | error: | |||
| 246 | isl_basic_set_free(bset1); | |||
| 247 | isl_basic_set_free(bset2); | |||
| 248 | return NULL((void*)0); | |||
| 249 | } | |||
| 250 | ||||
| 251 | /* Find an integer point in the set represented by "tab" | |||
| 252 | * that lies outside of the equality "eq" e(x) = 0. | |||
| 253 | * If "up" is true, look for a point satisfying e(x) - 1 >= 0. | |||
| 254 | * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1). | |||
| 255 | * The point, if found, is returned. | |||
| 256 | * If no point can be found, a zero-length vector is returned. | |||
| 257 | * | |||
| 258 | * Before solving an ILP problem, we first check if simply | |||
| 259 | * adding the normal of the constraint to one of the known | |||
| 260 | * integer points in the basic set represented by "tab" | |||
| 261 | * yields another point inside the basic set. | |||
| 262 | * | |||
| 263 | * The caller of this function ensures that the tableau is bounded or | |||
| 264 | * that tab->basis and tab->n_unbounded have been set appropriately. | |||
| 265 | */ | |||
| 266 | static __isl_give isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, | |||
| 267 | int up) | |||
| 268 | { | |||
| 269 | struct isl_ctx *ctx; | |||
| 270 | struct isl_vec *sample = NULL((void*)0); | |||
| 271 | struct isl_tab_undo *snap; | |||
| 272 | unsigned dim; | |||
| 273 | ||||
| 274 | if (!tab) | |||
| 275 | return NULL((void*)0); | |||
| 276 | ctx = tab->mat->ctx; | |||
| 277 | ||||
| 278 | dim = tab->n_var; | |||
| 279 | sample = isl_vec_alloc(ctx, 1 + dim); | |||
| 280 | if (!sample) | |||
| 281 | return NULL((void*)0); | |||
| 282 | isl_int_set_si(sample->el[0], 1)isl_sioimath_set_si((sample->el[0]), 1); | |||
| 283 | isl_seq_combine(sample->el + 1, | |||
| 284 | ctx->one, tab->bmap->sample->el + 1, | |||
| 285 | up ? ctx->one : ctx->negone, eq + 1, dim); | |||
| 286 | if (isl_basic_map_contains(tab->bmap, sample)) | |||
| 287 | return sample; | |||
| 288 | isl_vec_free(sample); | |||
| 289 | sample = NULL((void*)0); | |||
| 290 | ||||
| 291 | snap = isl_tab_snap(tab); | |||
| 292 | ||||
| 293 | if (!up) | |||
| 294 | isl_seq_neg(eq, eq, 1 + dim); | |||
| 295 | isl_int_sub_ui(eq[0], eq[0], 1)isl_sioimath_sub_ui((eq[0]), *(eq[0]), 1); | |||
| 296 | ||||
| 297 | if (isl_tab_extend_cons(tab, 1) < 0) | |||
| 298 | goto error; | |||
| 299 | if (isl_tab_add_ineq(tab, eq) < 0) | |||
| 300 | goto error; | |||
| 301 | ||||
| 302 | sample = isl_tab_sample(tab); | |||
| 303 | ||||
| 304 | isl_int_add_ui(eq[0], eq[0], 1)isl_sioimath_add_ui((eq[0]), *(eq[0]), 1); | |||
| 305 | if (!up) | |||
| 306 | isl_seq_neg(eq, eq, 1 + dim); | |||
| 307 | ||||
| 308 | if (sample && isl_tab_rollback(tab, snap) < 0) | |||
| 309 | goto error; | |||
| 310 | ||||
| 311 | return sample; | |||
| 312 | error: | |||
| 313 | isl_vec_free(sample); | |||
| 314 | return NULL((void*)0); | |||
| 315 | } | |||
| 316 | ||||
| 317 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_recession_cone( | |||
| 318 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 319 | { | |||
| 320 | int i; | |||
| 321 | isl_bool empty; | |||
| 322 | ||||
| 323 | empty = isl_basic_set_plain_is_empty(bset); | |||
| 324 | if (empty < 0) | |||
| 325 | return isl_basic_set_free(bset); | |||
| 326 | if (empty) | |||
| 327 | return bset; | |||
| 328 | ||||
| 329 | bset = isl_basic_set_cow(bset); | |||
| 330 | if (isl_basic_set_check_no_locals(bset) < 0) | |||
| 331 | return isl_basic_set_free(bset); | |||
| 332 | ||||
| 333 | for (i = 0; i < bset->n_eq; ++i) | |||
| 334 | isl_int_set_si(bset->eq[i][0], 0)isl_sioimath_set_si((bset->eq[i][0]), 0); | |||
| 335 | ||||
| 336 | for (i = 0; i < bset->n_ineq; ++i) | |||
| 337 | isl_int_set_si(bset->ineq[i][0], 0)isl_sioimath_set_si((bset->ineq[i][0]), 0); | |||
| 338 | ||||
| 339 | ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT)(((bset)->flags) &= ~((1 << 2))); | |||
| 340 | return isl_basic_set_implicit_equalities(bset); | |||
| 341 | } | |||
| 342 | ||||
| 343 | /* Move "sample" to a point that is one up (or down) from the original | |||
| 344 | * point in dimension "pos". | |||
| 345 | */ | |||
| 346 | static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up) | |||
| 347 | { | |||
| 348 | if (up) | |||
| 349 | isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1)isl_sioimath_add_ui((sample->el[1 + pos]), *(sample->el [1 + pos]), 1); | |||
| 350 | else | |||
| 351 | isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1)isl_sioimath_sub_ui((sample->el[1 + pos]), *(sample->el [1 + pos]), 1); | |||
| 352 | } | |||
| 353 | ||||
| 354 | /* Check if any points that are adjacent to "sample" also belong to "bset". | |||
| 355 | * If so, add them to "hull" and return the updated hull. | |||
| 356 | * | |||
| 357 | * Before checking whether and adjacent point belongs to "bset", we first | |||
| 358 | * check whether it already belongs to "hull" as this test is typically | |||
| 359 | * much cheaper. | |||
| 360 | */ | |||
| 361 | static __isl_give isl_basic_setisl_basic_map *add_adjacent_points( | |||
| 362 | __isl_take isl_basic_setisl_basic_map *hull, __isl_take isl_vec *sample, | |||
| 363 | __isl_keep isl_basic_setisl_basic_map *bset) | |||
| 364 | { | |||
| 365 | int i, up; | |||
| 366 | isl_size dim; | |||
| 367 | ||||
| 368 | dim = isl_basic_set_dim(hull, isl_dim_set); | |||
| 369 | if (!sample || dim < 0) | |||
| 370 | goto error; | |||
| 371 | ||||
| 372 | for (i = 0; i < dim; ++i) { | |||
| 373 | for (up = 0; up <= 1; ++up) { | |||
| 374 | int contains; | |||
| 375 | isl_basic_setisl_basic_map *point; | |||
| 376 | ||||
| 377 | adjacent_point(sample, i, up); | |||
| 378 | contains = isl_basic_set_contains(hull, sample); | |||
| 379 | if (contains < 0) | |||
| 380 | goto error; | |||
| 381 | if (contains) { | |||
| 382 | adjacent_point(sample, i, !up); | |||
| 383 | continue; | |||
| 384 | } | |||
| 385 | contains = isl_basic_set_contains(bset, sample); | |||
| 386 | if (contains < 0) | |||
| 387 | goto error; | |||
| 388 | if (contains) { | |||
| 389 | point = isl_basic_set_from_vec( | |||
| 390 | isl_vec_copy(sample)); | |||
| 391 | hull = affine_hull(hull, point); | |||
| 392 | } | |||
| 393 | adjacent_point(sample, i, !up); | |||
| 394 | if (contains) | |||
| 395 | break; | |||
| 396 | } | |||
| 397 | } | |||
| 398 | ||||
| 399 | isl_vec_free(sample); | |||
| 400 | ||||
| 401 | return hull; | |||
| 402 | error: | |||
| 403 | isl_vec_free(sample); | |||
| 404 | isl_basic_set_free(hull); | |||
| 405 | return NULL((void*)0); | |||
| 406 | } | |||
| 407 | ||||
| 408 | /* Extend an initial (under-)approximation of the affine hull of basic | |||
| 409 | * set represented by the tableau "tab" | |||
| 410 | * by looking for points that do not satisfy one of the equalities | |||
| 411 | * in the current approximation and adding them to that approximation | |||
| 412 | * until no such points can be found any more. | |||
| 413 | * | |||
| 414 | * The caller of this function ensures that "tab" is bounded or | |||
| 415 | * that tab->basis and tab->n_unbounded have been set appropriately. | |||
| 416 | * | |||
| 417 | * "bset" may be either NULL or the basic set represented by "tab". | |||
| 418 | * If "bset" is not NULL, we check for any point we find if any | |||
| 419 | * of its adjacent points also belong to "bset". | |||
| 420 | */ | |||
| 421 | static __isl_give isl_basic_setisl_basic_map *extend_affine_hull(struct isl_tab *tab, | |||
| 422 | __isl_take isl_basic_setisl_basic_map *hull, __isl_keep isl_basic_setisl_basic_map *bset) | |||
| 423 | { | |||
| 424 | int i, j; | |||
| 425 | unsigned dim; | |||
| 426 | ||||
| 427 | if (!tab || !hull) | |||
| 428 | goto error; | |||
| 429 | ||||
| 430 | dim = tab->n_var; | |||
| 431 | ||||
| 432 | if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0) | |||
| 433 | goto error; | |||
| 434 | ||||
| 435 | for (i = 0; i < dim; ++i) { | |||
| 436 | struct isl_vec *sample; | |||
| 437 | struct isl_basic_setisl_basic_map *point; | |||
| 438 | for (j = 0; j < hull->n_eq; ++j) { | |||
| 439 | sample = outside_point(tab, hull->eq[j], 1); | |||
| 440 | if (!sample) | |||
| 441 | goto error; | |||
| 442 | if (sample->size > 0) | |||
| 443 | break; | |||
| 444 | isl_vec_free(sample); | |||
| 445 | sample = outside_point(tab, hull->eq[j], 0); | |||
| 446 | if (!sample) | |||
| 447 | goto error; | |||
| 448 | if (sample->size > 0) | |||
| 449 | break; | |||
| 450 | isl_vec_free(sample); | |||
| 451 | ||||
| 452 | if (isl_tab_add_eq(tab, hull->eq[j]) < 0) | |||
| 453 | goto error; | |||
| 454 | } | |||
| 455 | if (j == hull->n_eq) | |||
| 456 | break; | |||
| 457 | if (tab->samples && | |||
| 458 | isl_tab_add_sample(tab, isl_vec_copy(sample)) < 0) | |||
| 459 | hull = isl_basic_set_free(hull); | |||
| 460 | if (bset) | |||
| 461 | hull = add_adjacent_points(hull, isl_vec_copy(sample), | |||
| 462 | bset); | |||
| 463 | point = isl_basic_set_from_vec(sample); | |||
| 464 | hull = affine_hull(hull, point); | |||
| 465 | if (!hull) | |||
| 466 | return NULL((void*)0); | |||
| 467 | } | |||
| 468 | ||||
| 469 | return hull; | |||
| 470 | error: | |||
| 471 | isl_basic_set_free(hull); | |||
| 472 | return NULL((void*)0); | |||
| 473 | } | |||
| 474 | ||||
| 475 | /* Construct an initial underapproximation of the hull of "bset" | |||
| 476 | * from "sample" and any of its adjacent points that also belong to "bset". | |||
| 477 | */ | |||
| 478 | static __isl_give isl_basic_setisl_basic_map *initialize_hull(__isl_keep isl_basic_setisl_basic_map *bset, | |||
| 479 | __isl_take isl_vec *sample) | |||
| 480 | { | |||
| 481 | isl_basic_setisl_basic_map *hull; | |||
| 482 | ||||
| 483 | hull = isl_basic_set_from_vec(isl_vec_copy(sample)); | |||
| 484 | hull = add_adjacent_points(hull, sample, bset); | |||
| 485 | ||||
| 486 | return hull; | |||
| 487 | } | |||
| 488 | ||||
| 489 | /* Look for all equalities satisfied by the integer points in bset, | |||
| 490 | * which is assumed to be bounded. | |||
| 491 | * | |||
| 492 | * The equalities are obtained by successively looking for | |||
| 493 | * a point that is affinely independent of the points found so far. | |||
| 494 | * In particular, for each equality satisfied by the points so far, | |||
| 495 | * we check if there is any point on a hyperplane parallel to the | |||
| 496 | * corresponding hyperplane shifted by at least one (in either direction). | |||
| 497 | */ | |||
| 498 | static __isl_give isl_basic_setisl_basic_map *uset_affine_hull_bounded( | |||
| 499 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 500 | { | |||
| 501 | struct isl_vec *sample = NULL((void*)0); | |||
| 502 | struct isl_basic_setisl_basic_map *hull; | |||
| 503 | struct isl_tab *tab = NULL((void*)0); | |||
| 504 | isl_size dim; | |||
| 505 | ||||
| 506 | if (isl_basic_set_plain_is_empty(bset)) | |||
| 507 | return bset; | |||
| 508 | ||||
| 509 | dim = isl_basic_set_dim(bset, isl_dim_set); | |||
| 510 | if (dim < 0) | |||
| 511 | return isl_basic_set_free(bset); | |||
| 512 | ||||
| 513 | if (bset->sample && bset->sample->size == 1 + dim) { | |||
| ||||
| 514 | int contains = isl_basic_set_contains(bset, bset->sample); | |||
| 515 | if (contains < 0) | |||
| 516 | goto error; | |||
| 517 | if (contains) { | |||
| 518 | if (dim == 0) | |||
| 519 | return bset; | |||
| 520 | sample = isl_vec_copy(bset->sample); | |||
| 521 | } else { | |||
| 522 | isl_vec_free(bset->sample); | |||
| 523 | bset->sample = NULL((void*)0); | |||
| 524 | } | |||
| 525 | } | |||
| 526 | ||||
| 527 | tab = isl_tab_from_basic_set(bset, 1); | |||
| 528 | if (!tab) | |||
| 529 | goto error; | |||
| 530 | if (tab->empty) { | |||
| 531 | isl_tab_free(tab); | |||
| 532 | isl_vec_free(sample); | |||
| 533 | return isl_basic_set_set_to_empty(bset); | |||
| 534 | } | |||
| 535 | ||||
| 536 | if (!sample) { | |||
| 537 | struct isl_tab_undo *snap; | |||
| 538 | snap = isl_tab_snap(tab); | |||
| 539 | sample = isl_tab_sample(tab); | |||
| 540 | if (isl_tab_rollback(tab, snap) < 0) | |||
| 541 | goto error; | |||
| 542 | isl_vec_free(tab->bmap->sample); | |||
| 543 | tab->bmap->sample = isl_vec_copy(sample); | |||
| 544 | } | |||
| 545 | ||||
| 546 | if (!sample) | |||
| 547 | goto error; | |||
| 548 | if (sample->size == 0) { | |||
| 549 | isl_tab_free(tab); | |||
| 550 | isl_vec_free(sample); | |||
| 551 | return isl_basic_set_set_to_empty(bset); | |||
| 552 | } | |||
| 553 | ||||
| 554 | hull = initialize_hull(bset, sample); | |||
| 555 | ||||
| 556 | hull = extend_affine_hull(tab, hull, bset); | |||
| 557 | isl_basic_set_free(bset); | |||
| 558 | isl_tab_free(tab); | |||
| 559 | ||||
| 560 | return hull; | |||
| 561 | error: | |||
| 562 | isl_vec_free(sample); | |||
| 563 | isl_tab_free(tab); | |||
| 564 | isl_basic_set_free(bset); | |||
| 565 | return NULL((void*)0); | |||
| 566 | } | |||
| 567 | ||||
| 568 | /* Given an unbounded tableau and an integer point satisfying the tableau, | |||
| 569 | * construct an initial affine hull containing the recession cone | |||
| 570 | * shifted to the given point. | |||
| 571 | * | |||
| 572 | * The unbounded directions are taken from the last rows of the basis, | |||
| 573 | * which is assumed to have been initialized appropriately. | |||
| 574 | */ | |||
| 575 | static __isl_give isl_basic_setisl_basic_map *initial_hull(struct isl_tab *tab, | |||
| 576 | __isl_take isl_vec *vec) | |||
| 577 | { | |||
| 578 | int i; | |||
| 579 | int k; | |||
| 580 | struct isl_basic_setisl_basic_map *bset = NULL((void*)0); | |||
| 581 | struct isl_ctx *ctx; | |||
| 582 | isl_size dim; | |||
| 583 | ||||
| 584 | if (!vec || !tab) | |||
| 585 | return NULL((void*)0); | |||
| 586 | ctx = vec->ctx; | |||
| 587 | isl_assert(ctx, vec->size != 0, goto error)do { if (vec->size != 0) break; do { isl_handle_error(ctx, isl_error_unknown, "Assertion \"" "vec->size != 0" "\" failed" , "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_affine_hull.c" , 587); goto error; } while (0); } while (0); | |||
| 588 | ||||
| 589 | bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0); | |||
| 590 | dim = isl_basic_set_dim(bset, isl_dim_set); | |||
| 591 | if (dim < 0) | |||
| 592 | goto error; | |||
| 593 | dim -= tab->n_unbounded; | |||
| 594 | for (i = 0; i < dim; ++i) { | |||
| 595 | k = isl_basic_set_alloc_equality(bset); | |||
| 596 | if (k < 0) | |||
| 597 | goto error; | |||
| 598 | isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1, | |||
| 599 | vec->size - 1); | |||
| 600 | isl_seq_inner_product(bset->eq[k] + 1, vec->el +1, | |||
| 601 | vec->size - 1, &bset->eq[k][0]); | |||
| 602 | isl_int_neg(bset->eq[k][0], bset->eq[k][0])isl_sioimath_neg((bset->eq[k][0]), *(bset->eq[k][0])); | |||
| 603 | } | |||
| 604 | bset->sample = vec; | |||
| 605 | bset = isl_basic_set_gauss(bset, NULL((void*)0)); | |||
| 606 | ||||
| 607 | return bset; | |||
| 608 | error: | |||
| 609 | isl_basic_set_free(bset); | |||
| 610 | isl_vec_free(vec); | |||
| 611 | return NULL((void*)0); | |||
| 612 | } | |||
| 613 | ||||
| 614 | /* Given a tableau of a set and a tableau of the corresponding | |||
| 615 | * recession cone, detect and add all equalities to the tableau. | |||
| 616 | * If the tableau is bounded, then we can simply keep the | |||
| 617 | * tableau in its state after the return from extend_affine_hull. | |||
| 618 | * However, if the tableau is unbounded, then | |||
| 619 | * isl_tab_set_initial_basis_with_cone will add some additional | |||
| 620 | * constraints to the tableau that have to be removed again. | |||
| 621 | * In this case, we therefore rollback to the state before | |||
| 622 | * any constraints were added and then add the equalities back in. | |||
| 623 | */ | |||
| 624 | struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab, | |||
| 625 | struct isl_tab *tab_cone) | |||
| 626 | { | |||
| 627 | int j; | |||
| 628 | struct isl_vec *sample; | |||
| 629 | struct isl_basic_setisl_basic_map *hull = NULL((void*)0); | |||
| 630 | struct isl_tab_undo *snap; | |||
| 631 | ||||
| 632 | if (!tab || !tab_cone) | |||
| 633 | goto error; | |||
| 634 | ||||
| 635 | snap = isl_tab_snap(tab); | |||
| 636 | ||||
| 637 | isl_mat_free(tab->basis); | |||
| 638 | tab->basis = NULL((void*)0); | |||
| 639 | ||||
| 640 | isl_assert(tab->mat->ctx, tab->bmap, goto error)do { if (tab->bmap) break; do { isl_handle_error(tab->mat ->ctx, isl_error_unknown, "Assertion \"" "tab->bmap" "\" failed" , "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_affine_hull.c" , 640); goto error; } while (0); } while (0); | |||
| 641 | isl_assert(tab->mat->ctx, tab->samples, goto error)do { if (tab->samples) break; do { isl_handle_error(tab-> mat->ctx, isl_error_unknown, "Assertion \"" "tab->samples" "\" failed", "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_affine_hull.c" , 641); goto error; } while (0); } while (0); | |||
| 642 | isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error)do { if (tab->samples->n_col == 1 + tab->n_var) break ; do { isl_handle_error(tab->mat->ctx, isl_error_unknown , "Assertion \"" "tab->samples->n_col == 1 + tab->n_var" "\" failed", "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_affine_hull.c" , 642); goto error; } while (0); } while (0); | |||
| 643 | isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error)do { if (tab->n_sample > tab->n_outside) break; do { isl_handle_error(tab->mat->ctx, isl_error_unknown, "Assertion \"" "tab->n_sample > tab->n_outside" "\" failed", "/build/llvm-toolchain-snapshot-14~++20210828111110+16086d47c0d0/polly/lib/External/isl/isl_affine_hull.c" , 643); goto error; } while (0); } while (0); | |||
| 644 | ||||
| 645 | if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0) | |||
| 646 | goto error; | |||
| 647 | ||||
| 648 | sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var); | |||
| 649 | if (!sample) | |||
| 650 | goto error; | |||
| 651 | ||||
| 652 | isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size); | |||
| 653 | ||||
| 654 | isl_vec_free(tab->bmap->sample); | |||
| 655 | tab->bmap->sample = isl_vec_copy(sample); | |||
| 656 | ||||
| 657 | if (tab->n_unbounded == 0) | |||
| 658 | hull = isl_basic_set_from_vec(isl_vec_copy(sample)); | |||
| 659 | else | |||
| 660 | hull = initial_hull(tab, isl_vec_copy(sample)); | |||
| 661 | ||||
| 662 | for (j = tab->n_outside + 1; j < tab->n_sample; ++j) { | |||
| 663 | isl_seq_cpy(sample->el, tab->samples->row[j], sample->size); | |||
| 664 | hull = affine_hull(hull, | |||
| 665 | isl_basic_set_from_vec(isl_vec_copy(sample))); | |||
| 666 | } | |||
| 667 | ||||
| 668 | isl_vec_free(sample); | |||
| 669 | ||||
| 670 | hull = extend_affine_hull(tab, hull, NULL((void*)0)); | |||
| 671 | if (!hull) | |||
| 672 | goto error; | |||
| 673 | ||||
| 674 | if (tab->n_unbounded == 0) { | |||
| 675 | isl_basic_set_free(hull); | |||
| 676 | return tab; | |||
| 677 | } | |||
| 678 | ||||
| 679 | if (isl_tab_rollback(tab, snap) < 0) | |||
| 680 | goto error; | |||
| 681 | ||||
| 682 | if (hull->n_eq > tab->n_zero) { | |||
| 683 | for (j = 0; j < hull->n_eq; ++j) { | |||
| 684 | isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var); | |||
| 685 | if (isl_tab_add_eq(tab, hull->eq[j]) < 0) | |||
| 686 | goto error; | |||
| 687 | } | |||
| 688 | } | |||
| 689 | ||||
| 690 | isl_basic_set_free(hull); | |||
| 691 | ||||
| 692 | return tab; | |||
| 693 | error: | |||
| 694 | isl_basic_set_free(hull); | |||
| 695 | isl_tab_free(tab); | |||
| 696 | return NULL((void*)0); | |||
| 697 | } | |||
| 698 | ||||
| 699 | /* Compute the affine hull of "bset", where "cone" is the recession cone | |||
| 700 | * of "bset". | |||
| 701 | * | |||
| 702 | * We first compute a unimodular transformation that puts the unbounded | |||
| 703 | * directions in the last dimensions. In particular, we take a transformation | |||
| 704 | * that maps all equalities to equalities (in HNF) on the first dimensions. | |||
| 705 | * Let x be the original dimensions and y the transformed, with y_1 bounded | |||
| 706 | * and y_2 unbounded. | |||
| 707 | * | |||
| 708 | * [ y_1 ] [ y_1 ] [ Q_1 ] | |||
| 709 | * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x | |||
| 710 | * | |||
| 711 | * Let's call the input basic set S. We compute S' = preimage(S, U) | |||
| 712 | * and drop the final dimensions including any constraints involving them. | |||
| 713 | * This results in set S''. | |||
| 714 | * Then we compute the affine hull A'' of S''. | |||
| 715 | * Let F y_1 >= g be the constraint system of A''. In the transformed | |||
| 716 | * space the y_2 are unbounded, so we can add them back without any constraints, | |||
| 717 | * resulting in | |||
| 718 | * | |||
| 719 | * [ y_1 ] | |||
| 720 | * [ F 0 ] [ y_2 ] >= g | |||
| 721 | * or | |||
| 722 | * [ Q_1 ] | |||
| 723 | * [ F 0 ] [ Q_2 ] x >= g | |||
| 724 | * or | |||
| 725 | * F Q_1 x >= g | |||
| 726 | * | |||
| 727 | * The affine hull in the original space is then obtained as | |||
| 728 | * A = preimage(A'', Q_1). | |||
| 729 | */ | |||
| 730 | static __isl_give isl_basic_setisl_basic_map *affine_hull_with_cone( | |||
| 731 | __isl_take isl_basic_setisl_basic_map *bset, __isl_take isl_basic_setisl_basic_map *cone) | |||
| 732 | { | |||
| 733 | isl_size total; | |||
| 734 | unsigned cone_dim; | |||
| 735 | struct isl_basic_setisl_basic_map *hull; | |||
| 736 | struct isl_mat *M, *U, *Q; | |||
| 737 | ||||
| 738 | total = isl_basic_set_dim(cone, isl_dim_all); | |||
| 739 | if (!bset || total < 0) | |||
| ||||
| 740 | goto error; | |||
| 741 | ||||
| 742 | cone_dim = total - cone->n_eq; | |||
| 743 | ||||
| 744 | M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total); | |||
| 745 | M = isl_mat_left_hermite(M, 0, &U, &Q); | |||
| 746 | if (!M) | |||
| 747 | goto error; | |||
| 748 | isl_mat_free(M); | |||
| 749 | ||||
| 750 | U = isl_mat_lin_to_aff(U); | |||
| 751 | bset = isl_basic_set_preimage(bset, isl_mat_copy(U)); | |||
| 752 | ||||
| 753 | bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim, | |||
| 754 | cone_dim); | |||
| 755 | bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim); | |||
| 756 | ||||
| 757 | Q = isl_mat_lin_to_aff(Q); | |||
| 758 | Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim); | |||
| 759 | ||||
| 760 | if (bset && bset->sample && bset->sample->size == 1 + total) | |||
| 761 | bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample); | |||
| 762 | ||||
| 763 | hull = uset_affine_hull_bounded(bset); | |||
| 764 | ||||
| 765 | if (!hull) { | |||
| 766 | isl_mat_free(Q); | |||
| 767 | isl_mat_free(U); | |||
| 768 | } else { | |||
| 769 | struct isl_vec *sample = isl_vec_copy(hull->sample); | |||
| 770 | U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim); | |||
| 771 | if (sample && sample->size > 0) | |||
| 772 | sample = isl_mat_vec_product(U, sample); | |||
| 773 | else | |||
| 774 | isl_mat_free(U); | |||
| 775 | hull = isl_basic_set_preimage(hull, Q); | |||
| 776 | if (hull) { | |||
| 777 | isl_vec_free(hull->sample); | |||
| 778 | hull->sample = sample; | |||
| 779 | } else | |||
| 780 | isl_vec_free(sample); | |||
| 781 | } | |||
| 782 | ||||
| 783 | isl_basic_set_free(cone); | |||
| 784 | ||||
| 785 | return hull; | |||
| 786 | error: | |||
| 787 | isl_basic_set_free(bset); | |||
| 788 | isl_basic_set_free(cone); | |||
| 789 | return NULL((void*)0); | |||
| 790 | } | |||
| 791 | ||||
| 792 | /* Look for all equalities satisfied by the integer points in bset, | |||
| 793 | * which is assumed not to have any explicit equalities. | |||
| 794 | * | |||
| 795 | * The equalities are obtained by successively looking for | |||
| 796 | * a point that is affinely independent of the points found so far. | |||
| 797 | * In particular, for each equality satisfied by the points so far, | |||
| 798 | * we check if there is any point on a hyperplane parallel to the | |||
| 799 | * corresponding hyperplane shifted by at least one (in either direction). | |||
| 800 | * | |||
| 801 | * Before looking for any outside points, we first compute the recession | |||
| 802 | * cone. The directions of this recession cone will always be part | |||
| 803 | * of the affine hull, so there is no need for looking for any points | |||
| 804 | * in these directions. | |||
| 805 | * In particular, if the recession cone is full-dimensional, then | |||
| 806 | * the affine hull is simply the whole universe. | |||
| 807 | */ | |||
| 808 | static __isl_give isl_basic_setisl_basic_map *uset_affine_hull( | |||
| 809 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 810 | { | |||
| 811 | struct isl_basic_setisl_basic_map *cone; | |||
| 812 | isl_size total; | |||
| 813 | ||||
| 814 | if (isl_basic_set_plain_is_empty(bset)) | |||
| 815 | return bset; | |||
| 816 | ||||
| 817 | cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset)); | |||
| 818 | if (!cone) | |||
| 819 | goto error; | |||
| 820 | if (cone->n_eq == 0) { | |||
| 821 | isl_space *space; | |||
| 822 | space = isl_basic_set_get_space(bset); | |||
| 823 | isl_basic_set_free(cone); | |||
| 824 | isl_basic_set_free(bset); | |||
| 825 | return isl_basic_set_universe(space); | |||
| 826 | } | |||
| 827 | ||||
| 828 | total = isl_basic_set_dim(cone, isl_dim_all); | |||
| 829 | if (total < 0) | |||
| 830 | bset = isl_basic_set_free(bset); | |||
| 831 | if (cone->n_eq < total) | |||
| 832 | return affine_hull_with_cone(bset, cone); | |||
| 833 | ||||
| 834 | isl_basic_set_free(cone); | |||
| 835 | return uset_affine_hull_bounded(bset); | |||
| 836 | error: | |||
| 837 | isl_basic_set_free(bset); | |||
| 838 | return NULL((void*)0); | |||
| 839 | } | |||
| 840 | ||||
| 841 | /* Look for all equalities satisfied by the integer points in bmap | |||
| 842 | * that are independent of the equalities already explicitly available | |||
| 843 | * in bmap. | |||
| 844 | * | |||
| 845 | * We first remove all equalities already explicitly available, | |||
| 846 | * then look for additional equalities in the reduced space | |||
| 847 | * and then transform the result to the original space. | |||
| 848 | * The original equalities are _not_ added to this set. This is | |||
| 849 | * the responsibility of the calling function. | |||
| 850 | * The resulting basic set has all meaning about the dimensions removed. | |||
| 851 | * In particular, dimensions that correspond to existential variables | |||
| 852 | * in bmap and that are found to be fixed are not removed. | |||
| 853 | */ | |||
| 854 | static __isl_give isl_basic_setisl_basic_map *equalities_in_underlying_set( | |||
| 855 | __isl_take isl_basic_map *bmap) | |||
| 856 | { | |||
| 857 | struct isl_mat *T1 = NULL((void*)0); | |||
| 858 | struct isl_mat *T2 = NULL((void*)0); | |||
| 859 | struct isl_basic_setisl_basic_map *bset = NULL((void*)0); | |||
| 860 | struct isl_basic_setisl_basic_map *hull = NULL((void*)0); | |||
| 861 | ||||
| 862 | bset = isl_basic_map_underlying_set(bmap); | |||
| 863 | if (!bset) | |||
| 864 | return NULL((void*)0); | |||
| 865 | if (bset->n_eq) | |||
| 866 | bset = isl_basic_set_remove_equalities(bset, &T1, &T2); | |||
| 867 | if (!bset) | |||
| 868 | goto error; | |||
| 869 | ||||
| 870 | hull = uset_affine_hull(bset); | |||
| 871 | if (!T2) | |||
| 872 | return hull; | |||
| 873 | ||||
| 874 | if (!hull) { | |||
| 875 | isl_mat_free(T1); | |||
| 876 | isl_mat_free(T2); | |||
| 877 | } else { | |||
| 878 | struct isl_vec *sample = isl_vec_copy(hull->sample); | |||
| 879 | if (sample && sample->size > 0) | |||
| 880 | sample = isl_mat_vec_product(T1, sample); | |||
| 881 | else | |||
| 882 | isl_mat_free(T1); | |||
| 883 | hull = isl_basic_set_preimage(hull, T2); | |||
| 884 | if (hull) { | |||
| 885 | isl_vec_free(hull->sample); | |||
| 886 | hull->sample = sample; | |||
| 887 | } else | |||
| 888 | isl_vec_free(sample); | |||
| 889 | } | |||
| 890 | ||||
| 891 | return hull; | |||
| 892 | error: | |||
| 893 | isl_mat_free(T1); | |||
| 894 | isl_mat_free(T2); | |||
| 895 | isl_basic_set_free(bset); | |||
| 896 | isl_basic_set_free(hull); | |||
| 897 | return NULL((void*)0); | |||
| 898 | } | |||
| 899 | ||||
| 900 | /* Detect and make explicit all equalities satisfied by the (integer) | |||
| 901 | * points in bmap. | |||
| 902 | */ | |||
| 903 | __isl_give isl_basic_map *isl_basic_map_detect_equalities( | |||
| 904 | __isl_take isl_basic_map *bmap) | |||
| 905 | { | |||
| 906 | int i, j; | |||
| 907 | isl_size total; | |||
| 908 | struct isl_basic_setisl_basic_map *hull = NULL((void*)0); | |||
| 909 | ||||
| 910 | if (!bmap) | |||
| 911 | return NULL((void*)0); | |||
| 912 | if (bmap->n_ineq == 0) | |||
| 913 | return bmap; | |||
| 914 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)(!!(((bmap)->flags) & ((1 << 1))))) | |||
| 915 | return bmap; | |||
| 916 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES)(!!(((bmap)->flags) & ((1 << 7))))) | |||
| 917 | return bmap; | |||
| 918 | if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)(!!(((bmap)->flags) & ((1 << 4))))) | |||
| 919 | return isl_basic_map_implicit_equalities(bmap); | |||
| 920 | ||||
| 921 | hull = equalities_in_underlying_set(isl_basic_map_copy(bmap)); | |||
| 922 | if (!hull) | |||
| 923 | goto error; | |||
| 924 | if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)(!!(((hull)->flags) & ((1 << 1))))) { | |||
| 925 | isl_basic_set_free(hull); | |||
| 926 | return isl_basic_map_set_to_empty(bmap); | |||
| 927 | } | |||
| 928 | bmap = isl_basic_map_extend(bmap, 0, hull->n_eq, 0); | |||
| 929 | total = isl_basic_set_dim(hull, isl_dim_all); | |||
| 930 | if (total < 0) | |||
| 931 | goto error; | |||
| 932 | for (i = 0; i < hull->n_eq; ++i) { | |||
| 933 | j = isl_basic_map_alloc_equality(bmap); | |||
| 934 | if (j < 0) | |||
| 935 | goto error; | |||
| 936 | isl_seq_cpy(bmap->eq[j], hull->eq[i], 1 + total); | |||
| 937 | } | |||
| 938 | isl_vec_free(bmap->sample); | |||
| 939 | bmap->sample = isl_vec_copy(hull->sample); | |||
| 940 | isl_basic_set_free(hull); | |||
| 941 | ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES)(((bmap)->flags) |= ((1 << 2) | (1 << 7))); | |||
| 942 | bmap = isl_basic_map_simplify(bmap); | |||
| 943 | return isl_basic_map_finalize(bmap); | |||
| 944 | error: | |||
| 945 | isl_basic_set_free(hull); | |||
| 946 | isl_basic_map_free(bmap); | |||
| 947 | return NULL((void*)0); | |||
| 948 | } | |||
| 949 | ||||
| 950 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_detect_equalities( | |||
| 951 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 952 | { | |||
| 953 | return bset_from_bmap( | |||
| 954 | isl_basic_map_detect_equalities(bset_to_bmap(bset))); | |||
| 955 | } | |||
| 956 | ||||
| 957 | __isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map) | |||
| 958 | { | |||
| 959 | return isl_map_inline_foreach_basic_map(map, | |||
| 960 | &isl_basic_map_detect_equalities); | |||
| 961 | } | |||
| 962 | ||||
| 963 | __isl_give isl_setisl_map *isl_set_detect_equalities(__isl_take isl_setisl_map *set) | |||
| 964 | { | |||
| 965 | return set_from_map(isl_map_detect_equalities(set_to_map(set))); | |||
| 966 | } | |||
| 967 | ||||
| 968 | /* Return the superset of "bmap" described by the equalities | |||
| 969 | * satisfied by "bmap" that are already known. | |||
| 970 | */ | |||
| 971 | __isl_give isl_basic_map *isl_basic_map_plain_affine_hull( | |||
| 972 | __isl_take isl_basic_map *bmap) | |||
| 973 | { | |||
| 974 | bmap = isl_basic_map_cow(bmap); | |||
| 975 | if (bmap) | |||
| 976 | isl_basic_map_free_inequality(bmap, bmap->n_ineq); | |||
| 977 | bmap = isl_basic_map_finalize(bmap); | |||
| 978 | return bmap; | |||
| 979 | } | |||
| 980 | ||||
| 981 | /* Return the superset of "bset" described by the equalities | |||
| 982 | * satisfied by "bset" that are already known. | |||
| 983 | */ | |||
| 984 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_plain_affine_hull( | |||
| 985 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 986 | { | |||
| 987 | return isl_basic_map_plain_affine_hull(bset); | |||
| 988 | } | |||
| 989 | ||||
| 990 | /* After computing the rational affine hull (by detecting the implicit | |||
| 991 | * equalities), we compute the additional equalities satisfied by | |||
| 992 | * the integer points (if any) and add the original equalities back in. | |||
| 993 | */ | |||
| 994 | __isl_give isl_basic_map *isl_basic_map_affine_hull( | |||
| 995 | __isl_take isl_basic_map *bmap) | |||
| 996 | { | |||
| 997 | bmap = isl_basic_map_detect_equalities(bmap); | |||
| 998 | bmap = isl_basic_map_plain_affine_hull(bmap); | |||
| 999 | return bmap; | |||
| 1000 | } | |||
| 1001 | ||||
| 1002 | __isl_give isl_basic_setisl_basic_map *isl_basic_set_affine_hull( | |||
| 1003 | __isl_take isl_basic_setisl_basic_map *bset) | |||
| 1004 | { | |||
| 1005 | return bset_from_bmap(isl_basic_map_affine_hull(bset_to_bmap(bset))); | |||
| 1006 | } | |||
| 1007 | ||||
| 1008 | /* Given a rational affine matrix "M", add stride constraints to "bmap" | |||
| 1009 | * that ensure that | |||
| 1010 | * | |||
| 1011 | * M(x) | |||
| 1012 | * | |||
| 1013 | * is an integer vector. The variables x include all the variables | |||
| 1014 | * of "bmap" except the unknown divs. | |||
| 1015 | * | |||
| 1016 | * If d is the common denominator of M, then we need to impose that | |||
| 1017 | * | |||
| 1018 | * d M(x) = 0 mod d | |||
| 1019 | * | |||
| 1020 | * or | |||
| 1021 | * | |||
| 1022 | * exists alpha : d M(x) = d alpha | |||
| 1023 | * | |||
| 1024 | * This function is similar to add_strides in isl_morph.c | |||
| 1025 | */ | |||
| 1026 | static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap, | |||
| 1027 | __isl_keep isl_mat *M, int n_known) | |||
| 1028 | { | |||
| 1029 | int i, div, k; | |||
| 1030 | isl_int gcd; | |||
| 1031 | ||||
| 1032 | if (isl_int_is_one(M->row[0][0])(isl_sioimath_cmp_si(*(M->row[0][0]), 1) == 0)) | |||
| 1033 | return bmap; | |||
| 1034 | ||||
| 1035 | bmap = isl_basic_map_extend(bmap, M->n_row - 1, M->n_row - 1, 0); | |||
| 1036 | ||||
| 1037 | isl_int_init(gcd)isl_sioimath_init((gcd)); | |||
| 1038 | for (i = 1; i < M->n_row; ++i) { | |||
| 1039 | isl_seq_gcd(M->row[i], M->n_col, &gcd); | |||
| 1040 | if (isl_int_is_divisible_by(gcd, M->row[0][0])isl_sioimath_is_divisible_by(*(gcd), *(M->row[0][0]))) | |||
| 1041 | continue; | |||
| 1042 | div = isl_basic_map_alloc_div(bmap); | |||
| 1043 | if (div < 0) | |||
| 1044 | goto error; | |||
| 1045 | isl_int_set_si(bmap->div[div][0], 0)isl_sioimath_set_si((bmap->div[div][0]), 0); | |||
| 1046 | k = isl_basic_map_alloc_equality(bmap); | |||
| 1047 | if (k < 0) | |||
| 1048 | goto error; | |||
| 1049 | isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col); | |||
| 1050 | isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known); | |||
| 1051 | isl_int_set(bmap->eq[k][M->n_col - n_known + div],isl_sioimath_set((bmap->eq[k][M->n_col - n_known + div] ), *(M->row[0][0])) | |||
| 1052 | M->row[0][0])isl_sioimath_set((bmap->eq[k][M->n_col - n_known + div] ), *(M->row[0][0])); | |||
| 1053 | } | |||
| 1054 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | |||
| 1055 | ||||
| 1056 | return bmap; | |||
| 1057 | error: | |||
| 1058 | isl_int_clear(gcd)isl_sioimath_clear((gcd)); | |||
| 1059 | isl_basic_map_free(bmap); | |||
| 1060 | return NULL((void*)0); | |||
| 1061 | } | |||
| 1062 | ||||
| 1063 | /* If there are any equalities that involve (multiple) unknown divs, | |||
| 1064 | * then extract the stride information encoded by those equalities | |||
| 1065 | * and make it explicitly available in "bmap". | |||
| 1066 | * | |||
| 1067 | * We first sort the divs so that the unknown divs appear last and | |||
| 1068 | * then we count how many equalities involve these divs. | |||
| 1069 | * | |||
| 1070 | * Let these equalities be of the form | |||
| 1071 | * | |||
| 1072 | * A(x) + B y = 0 | |||
| 1073 | * | |||
| 1074 | * where y represents the unknown divs and x the remaining variables. | |||
| 1075 | * Let [H 0] be the Hermite Normal Form of B, i.e., | |||
| 1076 | * | |||
| 1077 | * B = [H 0] Q | |||
| 1078 | * | |||
| 1079 | * Then x is a solution of the equalities iff | |||
| 1080 | * | |||
| 1081 | * H^-1 A(x) (= - [I 0] Q y) | |||
| 1082 | * | |||
| 1083 | * is an integer vector. Let d be the common denominator of H^-1. | |||
| 1084 | * We impose | |||
| 1085 | * | |||
| 1086 | * d H^-1 A(x) = d alpha | |||
| 1087 | * | |||
| 1088 | * in add_strides, with alpha fresh existentially quantified variables. | |||
| 1089 | */ | |||
| 1090 | static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit( | |||
| 1091 | __isl_take isl_basic_map *bmap) | |||
| 1092 | { | |||
| 1093 | isl_bool known; | |||
| 1094 | int n_known; | |||
| 1095 | int n, n_col; | |||
| 1096 | isl_size v_div; | |||
| 1097 | isl_ctx *ctx; | |||
| 1098 | isl_mat *A, *B, *M; | |||
| 1099 | ||||
| 1100 | known = isl_basic_map_divs_known(bmap); | |||
| 1101 | if (known < 0) | |||
| 1102 | return isl_basic_map_free(bmap); | |||
| 1103 | if (known) | |||
| 1104 | return bmap; | |||
| 1105 | bmap = isl_basic_map_sort_divs(bmap); | |||
| 1106 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | |||
| 1107 | if (!bmap) | |||
| 1108 | return NULL((void*)0); | |||
| 1109 | ||||
| 1110 | for (n_known = 0; n_known < bmap->n_div; ++n_known) | |||
| 1111 | if (isl_int_is_zero(bmap->div[n_known][0])(isl_sioimath_sgn(*(bmap->div[n_known][0])) == 0)) | |||
| 1112 | break; | |||
| 1113 | v_div = isl_basic_map_var_offset(bmap, isl_dim_div); | |||
| 1114 | if (v_div < 0) | |||
| 1115 | return isl_basic_map_free(bmap); | |||
| 1116 | for (n = 0; n < bmap->n_eq; ++n) | |||
| 1117 | if (isl_seq_first_non_zero(bmap->eq[n] + 1 + v_div + n_known, | |||
| 1118 | bmap->n_div - n_known) == -1) | |||
| 1119 | break; | |||
| 1120 | if (n == 0) | |||
| 1121 | return bmap; | |||
| 1122 | ctx = isl_basic_map_get_ctx(bmap); | |||
| 1123 | B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + v_div + n_known); | |||
| 1124 | n_col = bmap->n_div - n_known; | |||
| 1125 | A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + v_div + n_known, n_col); | |||
| 1126 | A = isl_mat_left_hermite(A, 0, NULL((void*)0), NULL((void*)0)); | |||
| 1127 | A = isl_mat_drop_cols(A, n, n_col - n); | |||
| 1128 | A = isl_mat_lin_to_aff(A); | |||
| 1129 | A = isl_mat_right_inverse(A); | |||
| 1130 | B = isl_mat_insert_zero_rows(B, 0, 1); | |||
| 1131 | B = isl_mat_set_element_si(B, 0, 0, 1); | |||
| 1132 | M = isl_mat_product(A, B); | |||
| 1133 | if (!M) | |||
| 1134 | return isl_basic_map_free(bmap); | |||
| 1135 | bmap = add_strides(bmap, M, n_known); | |||
| 1136 | bmap = isl_basic_map_gauss(bmap, NULL((void*)0)); | |||
| 1137 | isl_mat_free(M); | |||
| 1138 | ||||
| 1139 | return bmap; | |||
| 1140 | } | |||
| 1141 | ||||
| 1142 | /* Compute the affine hull of each basic map in "map" separately | |||
| 1143 | * and make all stride information explicit so that we can remove | |||
| 1144 | * all unknown divs without losing this information. | |||
| 1145 | * The result is also guaranteed to be gaussed. | |||
| 1146 | * | |||
| 1147 | * In simple cases where a div is determined by an equality, | |||
| 1148 | * calling isl_basic_map_gauss is enough to make the stride information | |||
| 1149 | * explicit, as it will derive an explicit representation for the div | |||
| 1150 | * from the equality. If, however, the stride information | |||
| 1151 | * is encoded through multiple unknown divs then we need to make | |||
| 1152 | * some extra effort in isl_basic_map_make_strides_explicit. | |||
| 1153 | */ | |||
| 1154 | static __isl_give isl_map *isl_map_local_affine_hull(__isl_take isl_map *map) | |||
| 1155 | { | |||
| 1156 | int i; | |||
| 1157 | ||||
| 1158 | map = isl_map_cow(map); | |||
| 1159 | if (!map) | |||
| 1160 | return NULL((void*)0); | |||
| 1161 | ||||
| 1162 | for (i = 0; i < map->n; ++i) { | |||
| 1163 | map->p[i] = isl_basic_map_affine_hull(map->p[i]); | |||
| 1164 | map->p[i] = isl_basic_map_gauss(map->p[i], NULL((void*)0)); | |||
| 1165 | map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]); | |||
| 1166 | if (!map->p[i]) | |||
| 1167 | return isl_map_free(map); | |||
| 1168 | } | |||
| 1169 | ||||
| 1170 | return map; | |||
| 1171 | } | |||
| 1172 | ||||
| 1173 | static __isl_give isl_setisl_map *isl_set_local_affine_hull(__isl_take isl_setisl_map *set) | |||
| 1174 | { | |||
| 1175 | return isl_map_local_affine_hull(set); | |||
| 1176 | } | |||
| 1177 | ||||
| 1178 | /* Return an empty basic map living in the same space as "map". | |||
| 1179 | */ | |||
| 1180 | static __isl_give isl_basic_map *replace_map_by_empty_basic_map( | |||
| 1181 | __isl_take isl_map *map) | |||
| 1182 | { | |||
| 1183 | isl_space *space; | |||
| 1184 | ||||
| 1185 | space = isl_map_get_space(map); | |||
| 1186 | isl_map_free(map); | |||
| 1187 | return isl_basic_map_empty(space); | |||
| 1188 | } | |||
| 1189 | ||||
| 1190 | /* Compute the affine hull of "map". | |||
| 1191 | * | |||
| 1192 | * We first compute the affine hull of each basic map separately. | |||
| 1193 | * Then we align the divs and recompute the affine hulls of the basic | |||
| 1194 | * maps since some of them may now have extra divs. | |||
| 1195 | * In order to avoid performing parametric integer programming to | |||
| 1196 | * compute explicit expressions for the divs, possible leading to | |||
| 1197 | * an explosion in the number of basic maps, we first drop all unknown | |||
| 1198 | * divs before aligning the divs. Note that isl_map_local_affine_hull tries | |||
| 1199 | * to make sure that all stride information is explicitly available | |||
| 1200 | * in terms of known divs. This involves calling isl_basic_set_gauss, | |||
| 1201 | * which is also needed because affine_hull assumes its input has been gaussed, | |||
| 1202 | * while isl_map_affine_hull may be called on input that has not been gaussed, | |||
| 1203 | * in particular from initial_facet_constraint. | |||
| 1204 | * Similarly, align_divs may reorder some divs so that we need to | |||
| 1205 | * gauss the result again. | |||
| 1206 | * Finally, we combine the individual affine hulls into a single | |||
| 1207 | * affine hull. | |||
| 1208 | */ | |||
| 1209 | __isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map) | |||
| 1210 | { | |||
| 1211 | struct isl_basic_map *model = NULL((void*)0); | |||
| 1212 | struct isl_basic_map *hull = NULL((void*)0); | |||
| 1213 | struct isl_setisl_map *set; | |||
| 1214 | isl_basic_setisl_basic_map *bset; | |||
| 1215 | ||||
| 1216 | map = isl_map_detect_equalities(map); | |||
| 1217 | map = isl_map_local_affine_hull(map); | |||
| 1218 | map = isl_map_remove_empty_parts(map); | |||
| 1219 | map = isl_map_remove_unknown_divs(map); | |||
| 1220 | map = isl_map_align_divs_internal(map); | |||
| 1221 | ||||
| 1222 | if (!map) | |||
| 1223 | return NULL((void*)0); | |||
| 1224 | ||||
| 1225 | if (map->n == 0) | |||
| 1226 | return replace_map_by_empty_basic_map(map); | |||
| 1227 | ||||
| 1228 | model = isl_basic_map_copy(map->p[0]); | |||
| 1229 | set = isl_map_underlying_set(map); | |||
| 1230 | set = isl_set_cow(set); | |||
| 1231 | set = isl_set_local_affine_hull(set); | |||
| 1232 | if (!set) | |||
| 1233 | goto error; | |||
| 1234 | ||||
| 1235 | while (set->n > 1) | |||
| 1236 | set->p[0] = affine_hull(set->p[0], set->p[--set->n]); | |||
| 1237 | ||||
| 1238 | bset = isl_basic_set_copy(set->p[0]); | |||
| 1239 | hull = isl_basic_map_overlying_set(bset, model); | |||
| 1240 | isl_set_free(set); | |||
| 1241 | hull = isl_basic_map_simplify(hull); | |||
| 1242 | return isl_basic_map_finalize(hull); | |||
| 1243 | error: | |||
| 1244 | isl_basic_map_free(model); | |||
| 1245 | isl_set_free(set); | |||
| 1246 | return NULL((void*)0); | |||
| 1247 | } | |||
| 1248 | ||||
| 1249 | __isl_give isl_basic_setisl_basic_map *isl_set_affine_hull(__isl_take isl_setisl_map *set) | |||
| 1250 | { | |||
| 1251 | return bset_from_bmap(isl_map_affine_hull(set_to_map(set))); | |||
| 1252 | } |