isl_test.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include <assert.h>
  11 #include <stdio.h>
  12 #include <limits.h>
  13 #include <isl_ctx.h>
  14 #include <isl_set.h>
  15 #include <isl_flow.h>
  16 #include <isl_constraint.h>
  17
  18 static char *srcdir;
  19
  20 void test_read(struct isl_ctx *ctx)
  21 {
  22         char filename[PATH_MAX];
  23         FILE *input;
  24         int n;
  25         struct isl_basic_set *bset1, *bset2;
  26         const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
  27
  28         n = snprintf(filename, sizeof(filename),
  29                         "%s/test_inputs/set.omega", srcdir);
  30         assert(n < sizeof(filename));
  31         input = fopen(filename, "r");
  32         assert(input);
  33
  34         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
  35         bset2 = isl_basic_set_read_from_str(ctx, str, 0);
  36
  37         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
  38
  39         isl_basic_set_free(bset1);
  40         isl_basic_set_free(bset2);
  41
  42         fclose(input);
  43 }
  44
  45 void test_bounded(struct isl_ctx *ctx)
  46 {
  47         isl_set *set;
  48         int bounded;
  49
  50         set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
  51         bounded = isl_set_is_bounded(set);
  52         assert(bounded);
  53         isl_set_free(set);
  54
  55         set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
  56         bounded = isl_set_is_bounded(set);
  57         assert(!bounded);
  58         isl_set_free(set);
  59
  60         set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
  61         bounded = isl_set_is_bounded(set);
  62         assert(!bounded);
  63         isl_set_free(set);
  64 }
  65
  66 /* Construct the basic set { [i] : 5 <= i <= N } */
  67 void test_construction(struct isl_ctx *ctx)
  68 {
  69         isl_int v;
  70         struct isl_dim *dim;
  71         struct isl_basic_set *bset;
  72         struct isl_constraint *c;
  73
  74         isl_int_init(v);
  75
  76         dim = isl_dim_set_alloc(ctx, 1, 1);
  77         bset = isl_basic_set_universe(dim);
  78
  79         c = isl_inequality_alloc(isl_dim_copy(bset->dim));
  80         isl_int_set_si(v, -1);
  81         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
  82         isl_int_set_si(v, 1);
  83         isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
  84         bset = isl_basic_set_add_constraint(bset, c);
  85
  86         c = isl_inequality_alloc(isl_dim_copy(bset->dim));
  87         isl_int_set_si(v, 1);
  88         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
  89         isl_int_set_si(v, -5);
  90         isl_constraint_set_constant(c, v);
  91         bset = isl_basic_set_add_constraint(bset, c);
  92
  93         isl_basic_set_free(bset);
  94
  95         isl_int_clear(v);
  96 }
  97
  98 void test_dim(struct isl_ctx *ctx)
  99 {
 100         isl_map *map1, *map2;
 101
 102         map1 = isl_map_read_from_str(ctx,
 103             "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
 104         map1 = isl_map_add(map1, isl_dim_in, 1);
 105         map2 = isl_map_read_from_str(ctx,
 106             "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
 107         assert(isl_map_is_equal(map1, map2));
 108         isl_map_free(map2);
 109
 110         map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
 111         map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
 112         assert(isl_map_is_equal(map1, map2));
 113
 114         isl_map_free(map1);
 115         isl_map_free(map2);
 116 }
 117
 118 void test_div(struct isl_ctx *ctx)
 119 {
 120         isl_int v;
 121         int pos;
 122         struct isl_dim *dim;
 123         struct isl_div *div;
 124         struct isl_basic_set *bset;
 125         struct isl_constraint *c;
 126
 127         isl_int_init(v);
 128
 129         /* test 1 */
 130         dim = isl_dim_set_alloc(ctx, 0, 1);
 131         bset = isl_basic_set_universe(dim);
 132
 133         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 134         isl_int_set_si(v, -1);
 135         isl_constraint_set_constant(c, v);
 136         isl_int_set_si(v, 1);
 137         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 138         div = isl_div_alloc(isl_dim_copy(bset->dim));
 139         c = isl_constraint_add_div(c, div, &pos);
 140         isl_int_set_si(v, 3);
 141         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 142         bset = isl_basic_set_add_constraint(bset, c);
 143
 144         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 145         isl_int_set_si(v, 1);
 146         isl_constraint_set_constant(c, v);
 147         isl_int_set_si(v, -1);
 148         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 149         div = isl_div_alloc(isl_dim_copy(bset->dim));
 150         c = isl_constraint_add_div(c, div, &pos);
 151         isl_int_set_si(v, 3);
 152         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 153         bset = isl_basic_set_add_constraint(bset, c);
 154
 155         assert(bset->n_div == 1);
 156         isl_basic_set_free(bset);
 157
 158         /* test 2 */
 159         dim = isl_dim_set_alloc(ctx, 0, 1);
 160         bset = isl_basic_set_universe(dim);
 161
 162         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 163         isl_int_set_si(v, 1);
 164         isl_constraint_set_constant(c, v);
 165         isl_int_set_si(v, -1);
 166         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 167         div = isl_div_alloc(isl_dim_copy(bset->dim));
 168         c = isl_constraint_add_div(c, div, &pos);
 169         isl_int_set_si(v, 3);
 170         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 171         bset = isl_basic_set_add_constraint(bset, c);
 172
 173         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 174         isl_int_set_si(v, -1);
 175         isl_constraint_set_constant(c, v);
 176         isl_int_set_si(v, 1);
 177         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 178         div = isl_div_alloc(isl_dim_copy(bset->dim));
 179         c = isl_constraint_add_div(c, div, &pos);
 180         isl_int_set_si(v, 3);
 181         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 182         bset = isl_basic_set_add_constraint(bset, c);
 183
 184         assert(bset->n_div == 1);
 185         isl_basic_set_free(bset);
 186
 187         /* test 3 */
 188         dim = isl_dim_set_alloc(ctx, 0, 1);
 189         bset = isl_basic_set_universe(dim);
 190
 191         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 192         isl_int_set_si(v, 1);
 193         isl_constraint_set_constant(c, v);
 194         isl_int_set_si(v, -1);
 195         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 196         div = isl_div_alloc(isl_dim_copy(bset->dim));
 197         c = isl_constraint_add_div(c, div, &pos);
 198         isl_int_set_si(v, 3);
 199         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 200         bset = isl_basic_set_add_constraint(bset, c);
 201
 202         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 203         isl_int_set_si(v, -3);
 204         isl_constraint_set_constant(c, v);
 205         isl_int_set_si(v, 1);
 206         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 207         div = isl_div_alloc(isl_dim_copy(bset->dim));
 208         c = isl_constraint_add_div(c, div, &pos);
 209         isl_int_set_si(v, 4);
 210         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 211         bset = isl_basic_set_add_constraint(bset, c);
 212
 213         assert(bset->n_div == 1);
 214         isl_basic_set_free(bset);
 215
 216         /* test 4 */
 217         dim = isl_dim_set_alloc(ctx, 0, 1);
 218         bset = isl_basic_set_universe(dim);
 219
 220         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 221         isl_int_set_si(v, 2);
 222         isl_constraint_set_constant(c, v);
 223         isl_int_set_si(v, -1);
 224         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 225         div = isl_div_alloc(isl_dim_copy(bset->dim));
 226         c = isl_constraint_add_div(c, div, &pos);
 227         isl_int_set_si(v, 3);
 228         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 229         bset = isl_basic_set_add_constraint(bset, c);
 230
 231         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 232         isl_int_set_si(v, -1);
 233         isl_constraint_set_constant(c, v);
 234         isl_int_set_si(v, 1);
 235         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 236         div = isl_div_alloc(isl_dim_copy(bset->dim));
 237         c = isl_constraint_add_div(c, div, &pos);
 238         isl_int_set_si(v, 6);
 239         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 240         bset = isl_basic_set_add_constraint(bset, c);
 241
 242         assert(isl_basic_set_is_empty(bset));
 243         isl_basic_set_free(bset);
 244
 245         /* test 5 */
 246         dim = isl_dim_set_alloc(ctx, 0, 2);
 247         bset = isl_basic_set_universe(dim);
 248
 249         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 250         isl_int_set_si(v, -1);
 251         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 252         div = isl_div_alloc(isl_dim_copy(bset->dim));
 253         c = isl_constraint_add_div(c, div, &pos);
 254         isl_int_set_si(v, 3);
 255         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 256         bset = isl_basic_set_add_constraint(bset, c);
 257
 258         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 259         isl_int_set_si(v, 1);
 260         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 261         isl_int_set_si(v, -3);
 262         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 263         bset = isl_basic_set_add_constraint(bset, c);
 264
 265         assert(bset->n_div == 0);
 266         isl_basic_set_free(bset);
 267
 268         /* test 6 */
 269         dim = isl_dim_set_alloc(ctx, 0, 2);
 270         bset = isl_basic_set_universe(dim);
 271
 272         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 273         isl_int_set_si(v, -1);
 274         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 275         div = isl_div_alloc(isl_dim_copy(bset->dim));
 276         c = isl_constraint_add_div(c, div, &pos);
 277         isl_int_set_si(v, 6);
 278         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 279         bset = isl_basic_set_add_constraint(bset, c);
 280
 281         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 282         isl_int_set_si(v, 1);
 283         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 284         isl_int_set_si(v, -3);
 285         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 286         bset = isl_basic_set_add_constraint(bset, c);
 287
 288         assert(bset->n_div == 1);
 289         isl_basic_set_free(bset);
 290
 291         /* test 7 */
 292         /* This test is a bit tricky.  We set up an equality
 293          *              a + 3b + 3c = 6 e0
 294          * Normalization of divs creates _two_ divs
 295          *              a = 3 e0
 296          *              c - b - e0 = 2 e1
 297          * Afterwards e0 is removed again because it has coefficient -1
 298          * and we end up with the original equality and div again.
 299          * Perhaps we can avoid the introduction of this temporary div.
 300          */
 301         dim = isl_dim_set_alloc(ctx, 0, 3);
 302         bset = isl_basic_set_universe(dim);
 303
 304         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 305         isl_int_set_si(v, -1);
 306         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 307         isl_int_set_si(v, -3);
 308         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 309         isl_int_set_si(v, -3);
 310         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 311         div = isl_div_alloc(isl_dim_copy(bset->dim));
 312         c = isl_constraint_add_div(c, div, &pos);
 313         isl_int_set_si(v, 6);
 314         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 315         bset = isl_basic_set_add_constraint(bset, c);
 316
 317         /* Test disabled for now */
 318         /*
 319         assert(bset->n_div == 1);
 320         */
 321         isl_basic_set_free(bset);
 322
 323         /* test 8 */
 324         dim = isl_dim_set_alloc(ctx, 0, 4);
 325         bset = isl_basic_set_universe(dim);
 326
 327         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 328         isl_int_set_si(v, -1);
 329         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 330         isl_int_set_si(v, -3);
 331         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 332         isl_int_set_si(v, -3);
 333         isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
 334         div = isl_div_alloc(isl_dim_copy(bset->dim));
 335         c = isl_constraint_add_div(c, div, &pos);
 336         isl_int_set_si(v, 6);
 337         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 338         bset = isl_basic_set_add_constraint(bset, c);
 339
 340         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 341         isl_int_set_si(v, -1);
 342         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 343         isl_int_set_si(v, 1);
 344         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 345         isl_int_set_si(v, 1);
 346         isl_constraint_set_constant(c, v);
 347         bset = isl_basic_set_add_constraint(bset, c);
 348
 349         /* Test disabled for now */
 350         /*
 351         assert(bset->n_div == 1);
 352         */
 353         isl_basic_set_free(bset);
 354
 355         /* test 9 */
 356         dim = isl_dim_set_alloc(ctx, 0, 2);
 357         bset = isl_basic_set_universe(dim);
 358
 359         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 360         isl_int_set_si(v, 1);
 361         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 362         isl_int_set_si(v, -1);
 363         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 364         div = isl_div_alloc(isl_dim_copy(bset->dim));
 365         c = isl_constraint_add_div(c, div, &pos);
 366         isl_int_set_si(v, -2);
 367         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 368         bset = isl_basic_set_add_constraint(bset, c);
 369
 370         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 371         isl_int_set_si(v, -1);
 372         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 373         div = isl_div_alloc(isl_dim_copy(bset->dim));
 374         c = isl_constraint_add_div(c, div, &pos);
 375         isl_int_set_si(v, 3);
 376         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 377         isl_int_set_si(v, 2);
 378         isl_constraint_set_constant(c, v);
 379         bset = isl_basic_set_add_constraint(bset, c);
 380
 381         bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
 382
 383         assert(!isl_basic_set_is_empty(bset));
 384
 385         isl_basic_set_free(bset);
 386
 387         /* test 10 */
 388         dim = isl_dim_set_alloc(ctx, 0, 2);
 389         bset = isl_basic_set_universe(dim);
 390
 391         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 392         isl_int_set_si(v, 1);
 393         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 394         div = isl_div_alloc(isl_dim_copy(bset->dim));
 395         c = isl_constraint_add_div(c, div, &pos);
 396         isl_int_set_si(v, -2);
 397         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 398         bset = isl_basic_set_add_constraint(bset, c);
 399
 400         bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
 401
 402         isl_basic_set_free(bset);
 403
 404         isl_int_clear(v);
 405 }
 406
 407 void test_application_case(struct isl_ctx *ctx, const char *name)
 408 {
 409         char filename[PATH_MAX];
 410         FILE *input;
 411         int n;
 412         struct isl_basic_set *bset1, *bset2;
 413         struct isl_basic_map *bmap;
 414
 415         n = snprintf(filename, sizeof(filename),
 416                         "%s/test_inputs/%s.omega", srcdir, name);
 417         assert(n < sizeof(filename));
 418         input = fopen(filename, "r");
 419         assert(input);
 420
 421         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 422         bmap = isl_basic_map_read_from_file(ctx, input, 0);
 423
 424         bset1 = isl_basic_set_apply(bset1, bmap);
 425
 426         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 427
 428         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 429
 430         isl_basic_set_free(bset1);
 431         isl_basic_set_free(bset2);
 432
 433         fclose(input);
 434 }
 435
 436 void test_application(struct isl_ctx *ctx)
 437 {
 438         test_application_case(ctx, "application");
 439         test_application_case(ctx, "application2");
 440 }
 441
 442 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
 443 {
 444         char filename[PATH_MAX];
 445         FILE *input;
 446         int n;
 447         struct isl_basic_set *bset1, *bset2;
 448
 449         n = snprintf(filename, sizeof(filename),
 450                         "%s/test_inputs/%s.polylib", srcdir, name);
 451         assert(n < sizeof(filename));
 452         input = fopen(filename, "r");
 453         assert(input);
 454
 455         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 456         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 457
 458         bset1 = isl_basic_set_affine_hull(bset1);
 459
 460         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 461
 462         isl_basic_set_free(bset1);
 463         isl_basic_set_free(bset2);
 464
 465         fclose(input);
 466 }
 467
 468 void test_affine_hull(struct isl_ctx *ctx)
 469 {
 470         test_affine_hull_case(ctx, "affine2");
 471         test_affine_hull_case(ctx, "affine");
 472         test_affine_hull_case(ctx, "affine3");
 473 }
 474
 475 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
 476 {
 477         char filename[PATH_MAX];
 478         FILE *input;
 479         int n;
 480         struct isl_basic_set *bset1, *bset2;
 481         struct isl_set *set;
 482
 483         n = snprintf(filename, sizeof(filename),
 484                         "%s/test_inputs/%s.polylib", srcdir, name);
 485         assert(n < sizeof(filename));
 486         input = fopen(filename, "r");
 487         assert(input);
 488
 489         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 490         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 491
 492         set = isl_basic_set_union(bset1, bset2);
 493         bset1 = isl_set_convex_hull(set);
 494
 495         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 496
 497         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 498
 499         isl_basic_set_free(bset1);
 500         isl_basic_set_free(bset2);
 501
 502         fclose(input);
 503 }
 504
 505 void test_convex_hull(struct isl_ctx *ctx)
 506 {
 507         const char *str1, *str2;
 508         isl_set *set1, *set2;
 509
 510         test_convex_hull_case(ctx, "convex0");
 511         test_convex_hull_case(ctx, "convex1");
 512         test_convex_hull_case(ctx, "convex2");
 513         test_convex_hull_case(ctx, "convex3");
 514         test_convex_hull_case(ctx, "convex4");
 515         test_convex_hull_case(ctx, "convex5");
 516         test_convex_hull_case(ctx, "convex6");
 517         test_convex_hull_case(ctx, "convex7");
 518         test_convex_hull_case(ctx, "convex8");
 519         test_convex_hull_case(ctx, "convex9");
 520         test_convex_hull_case(ctx, "convex10");
 521         test_convex_hull_case(ctx, "convex11");
 522         test_convex_hull_case(ctx, "convex12");
 523         test_convex_hull_case(ctx, "convex13");
 524         test_convex_hull_case(ctx, "convex14");
 525         test_convex_hull_case(ctx, "convex15");
 526
 527         str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
 528                "(i0 = 1 and i1 = 0 and i2 = 1) or "
 529                "(i0 = 0 and i1 = 0 and i2 = 0) }";
 530         str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
 531         set1 = isl_set_read_from_str(ctx, str1, -1);
 532         set2 = isl_set_read_from_str(ctx, str2, -1);
 533         set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
 534         assert(isl_set_is_equal(set1, set2));
 535         isl_set_free(set1);
 536         isl_set_free(set2);
 537 }
 538
 539 void test_gist_case(struct isl_ctx *ctx, const char *name)
 540 {
 541         char filename[PATH_MAX];
 542         FILE *input;
 543         int n;
 544         struct isl_basic_set *bset1, *bset2;
 545
 546         n = snprintf(filename, sizeof(filename),
 547                         "%s/test_inputs/%s.polylib", srcdir, name);
 548         assert(n < sizeof(filename));
 549         input = fopen(filename, "r");
 550         assert(input);
 551
 552         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 553         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 554
 555         bset1 = isl_basic_set_gist(bset1, bset2);
 556
 557         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 558
 559         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 560
 561         isl_basic_set_free(bset1);
 562         isl_basic_set_free(bset2);
 563
 564         fclose(input);
 565 }
 566
 567 void test_gist(struct isl_ctx *ctx)
 568 {
 569         test_gist_case(ctx, "gist1");
 570 }
 571
 572 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
 573 {
 574         isl_set *set, *set2;
 575
 576         set = isl_set_read_from_str(ctx, str, -1);
 577         set = isl_set_coalesce(set);
 578         set2 = isl_set_read_from_str(ctx, str, -1);
 579         assert(isl_set_is_equal(set, set2));
 580         if (check_one)
 581                 assert(set && set->n == 1);
 582         isl_set_free(set);
 583         isl_set_free(set2);
 584 }
 585
 586 void test_coalesce(struct isl_ctx *ctx)
 587 {
 588         const char *str;
 589         struct isl_set *set, *set2;
 590         struct isl_map *map, *map2;
 591
 592         set = isl_set_read_from_str(ctx,
 593                 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
 594                        "y >= x & x >= 2 & 5 >= y }", -1);
 595         set = isl_set_coalesce(set);
 596         assert(set && set->n == 1);
 597         isl_set_free(set);
 598
 599         set = isl_set_read_from_str(ctx,
 600                 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
 601                        "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
 602         set = isl_set_coalesce(set);
 603         assert(set && set->n == 1);
 604         isl_set_free(set);
 605
 606         set = isl_set_read_from_str(ctx,
 607                 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
 608                        "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
 609         set = isl_set_coalesce(set);
 610         assert(set && set->n == 2);
 611         isl_set_free(set);
 612
 613         set = isl_set_read_from_str(ctx,
 614                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 615                        "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
 616         set = isl_set_coalesce(set);
 617         assert(set && set->n == 1);
 618         isl_set_free(set);
 619
 620         set = isl_set_read_from_str(ctx,
 621                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 622                        "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
 623         set = isl_set_coalesce(set);
 624         assert(set && set->n == 2);
 625         isl_set_free(set);
 626
 627         set = isl_set_read_from_str(ctx,
 628                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 629                        "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
 630         set = isl_set_coalesce(set);
 631         assert(set && set->n == 2);
 632         isl_set_free(set);
 633
 634         set = isl_set_read_from_str(ctx,
 635                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 636                        "y >= 0 & x = 6 & y <= 6}", -1);
 637         set = isl_set_coalesce(set);
 638         assert(set && set->n == 1);
 639         isl_set_free(set);
 640
 641         set = isl_set_read_from_str(ctx,
 642                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 643                        "y >= 0 & x = 7 & y <= 6}", -1);
 644         set = isl_set_coalesce(set);
 645         assert(set && set->n == 2);
 646         isl_set_free(set);
 647
 648         set = isl_set_read_from_str(ctx,
 649                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 650                        "y >= 0 & x = 6 & y <= 5}", -1);
 651         set = isl_set_coalesce(set);
 652         assert(set && set->n == 1);
 653         set2 = isl_set_read_from_str(ctx,
 654                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 655                        "y >= 0 & x = 6 & y <= 5}", -1);
 656         assert(isl_set_is_equal(set, set2));
 657         isl_set_free(set);
 658         isl_set_free(set2);
 659
 660         set = isl_set_read_from_str(ctx,
 661                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 662                        "y >= 0 & x = 6 & y <= 7}", -1);
 663         set = isl_set_coalesce(set);
 664         assert(set && set->n == 2);
 665         isl_set_free(set);
 666
 667         set = isl_set_read_from_str(ctx,
 668                 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
 669         set = isl_set_coalesce(set);
 670         assert(set && set->n == 1);
 671         set2 = isl_set_read_from_str(ctx,
 672                 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
 673         assert(isl_set_is_equal(set, set2));
 674         isl_set_free(set);
 675         isl_set_free(set2);
 676
 677         set = isl_set_read_from_str(ctx,
 678                 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
 679         set = isl_set_coalesce(set);
 680         set2 = isl_set_read_from_str(ctx,
 681                 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
 682         assert(isl_set_is_equal(set, set2));
 683         isl_set_free(set);
 684         isl_set_free(set2);
 685
 686         set = isl_set_read_from_str(ctx,
 687                 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
 688                                 "2 <= i and i <= n }", -1);
 689         set = isl_set_coalesce(set);
 690         assert(set && set->n == 1);
 691         set2 = isl_set_read_from_str(ctx,
 692                 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
 693                                 "2 <= i and i <= n }", -1);
 694         assert(isl_set_is_equal(set, set2));
 695         isl_set_free(set);
 696         isl_set_free(set2);
 697
 698         map = isl_map_read_from_str(ctx,
 699                 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 700                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 701                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 702                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
 703                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
 704                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
 705                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
 706                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
 707                 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 708                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 709                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 710                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
 711                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
 712                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
 713                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
 714                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
 715                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
 716                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
 717         map = isl_map_coalesce(map);
 718         map2 = isl_map_read_from_str(ctx,
 719                 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 720                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 721                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 722                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
 723                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
 724                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
 725                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
 726                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
 727                 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 728                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 729                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 730                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
 731                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
 732                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
 733                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
 734                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
 735                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
 736                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
 737         assert(isl_map_is_equal(map, map2));
 738         isl_map_free(map);
 739         isl_map_free(map2);
 740
 741         str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
 742               "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
 743               "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
 744               "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
 745         map = isl_map_read_from_str(ctx, str, -1);
 746         map = isl_map_coalesce(map);
 747         map2 = isl_map_read_from_str(ctx, str, -1);
 748         assert(isl_map_is_equal(map, map2));
 749         isl_map_free(map);
 750         isl_map_free(map2);
 751
 752         str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
 753           "[o0, o1, o2, o3, o4, o5, o6] : "
 754           "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
 755           "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
 756           "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
 757           "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
 758           "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
 759           "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
 760           "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
 761           "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
 762           "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
 763           "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
 764           "o6 >= i3 + i6 - o3 and M >= 0 and "
 765           "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
 766           "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
 767         map = isl_map_read_from_str(ctx, str, -1);
 768         map = isl_map_coalesce(map);
 769         map2 = isl_map_read_from_str(ctx, str, -1);
 770         assert(isl_map_is_equal(map, map2));
 771         isl_map_free(map);
 772         isl_map_free(map2);
 773
 774         str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
 775                 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
 776                 "(o0 = 0 and M >= 2 and N >= 3) or "
 777                 "(M = 0 and o0 = 0 and N >= 3) }";
 778         map = isl_map_read_from_str(ctx, str, -1);
 779         map = isl_map_coalesce(map);
 780         map2 = isl_map_read_from_str(ctx, str, -1);
 781         assert(isl_map_is_equal(map, map2));
 782         isl_map_free(map);
 783         isl_map_free(map2);
 784
 785         str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
 786                 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
 787                 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
 788                 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
 789         map = isl_map_read_from_str(ctx, str, -1);
 790         map = isl_map_coalesce(map);
 791         map2 = isl_map_read_from_str(ctx, str, -1);
 792         assert(isl_map_is_equal(map, map2));
 793         isl_map_free(map);
 794         isl_map_free(map2);
 795
 796         test_coalesce_set(ctx,
 797                 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
 798                                 "(i1 = M and M >= 1) }", 0);
 799         test_coalesce_set(ctx,
 800                 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
 801         test_coalesce_set(ctx,
 802                 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
 803                 "(y = 3 and x = 1) }", 1);
 804         test_coalesce_set(ctx,
 805                 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
 806                 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
 807                 "i1 <= M and i3 <= M and i4 <= M) or "
 808                 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
 809                 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
 810                 "i4 <= -1 + M) }", 1);
 811         test_coalesce_set(ctx,
 812                 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
 813                 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
 814         test_coalesce_set(ctx,
 815                 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
 816                         "-x - y + 1 >= 0 and -3 <= z <= 3;"
 817                 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
 818                         "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
 819         test_coalesce_set(ctx,
 820                 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
 821 }
 822
 823 void test_closure(struct isl_ctx *ctx)
 824 {
 825         const char *str;
 826         isl_set *dom;
 827         isl_map *up, *right;
 828         isl_map *map, *map2;
 829         int exact;
 830
 831         /* COCOA example 1 */
 832         map = isl_map_read_from_str(ctx,
 833                 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
 834                         "1 <= i and i < n and 1 <= j and j < n or "
 835                         "i2 = i + 1 and j2 = j - 1 and "
 836                         "1 <= i and i < n and 2 <= j and j <= n }", -1);
 837         map = isl_map_power(map, 1, &exact);
 838         assert(exact);
 839         isl_map_free(map);
 840
 841         /* COCOA example 1 */
 842         map = isl_map_read_from_str(ctx,
 843                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
 844                         "1 <= i and i < n and 1 <= j and j < n or "
 845                         "i2 = i + 1 and j2 = j - 1 and "
 846                         "1 <= i and i < n and 2 <= j and j <= n }", -1);
 847         map = isl_map_transitive_closure(map, &exact);
 848         assert(exact);
 849         map2 = isl_map_read_from_str(ctx,
 850                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
 851                         "1 <= i and i < n and 1 <= j and j <= n and "
 852                         "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
 853                         "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
 854                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
 855         assert(isl_map_is_equal(map, map2));
 856         isl_map_free(map2);
 857         isl_map_free(map);
 858
 859         map = isl_map_read_from_str(ctx,
 860                 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
 861                                      " 0 <= y and y <= n }", -1);
 862         map = isl_map_transitive_closure(map, &exact);
 863         map2 = isl_map_read_from_str(ctx,
 864                 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
 865                                      " 0 <= y and y <= n }", -1);
 866         assert(isl_map_is_equal(map, map2));
 867         isl_map_free(map2);
 868         isl_map_free(map);
 869
 870         /* COCOA example 2 */
 871         map = isl_map_read_from_str(ctx,
 872                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
 873                         "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
 874                         "i2 = i + 2 and j2 = j - 2 and "
 875                         "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
 876         map = isl_map_transitive_closure(map, &exact);
 877         assert(exact);
 878         map2 = isl_map_read_from_str(ctx,
 879                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
 880                         "1 <= i and i < n - 1 and 1 <= j and j <= n and "
 881                         "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
 882                         "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
 883                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
 884         assert(isl_map_is_equal(map, map2));
 885         isl_map_free(map);
 886         isl_map_free(map2);
 887
 888         /* COCOA Fig.2 left */
 889         map = isl_map_read_from_str(ctx,
 890                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
 891                         "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
 892                         "j <= n or "
 893                         "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
 894                         "j <= 2 i - 3 and j <= n - 2 or "
 895                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 896                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 897         map = isl_map_transitive_closure(map, &exact);
 898         assert(exact);
 899         isl_map_free(map);
 900
 901         /* COCOA Fig.2 right */
 902         map = isl_map_read_from_str(ctx,
 903                 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
 904                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
 905                         "j <= n or "
 906                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
 907                         "j <= 2 i - 4 and j <= n - 3 or "
 908                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 909                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 910         map = isl_map_power(map, 1, &exact);
 911         assert(exact);
 912         isl_map_free(map);
 913
 914         /* COCOA Fig.2 right */
 915         map = isl_map_read_from_str(ctx,
 916                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
 917                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
 918                         "j <= n or "
 919                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
 920                         "j <= 2 i - 4 and j <= n - 3 or "
 921                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 922                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 923         map = isl_map_transitive_closure(map, &exact);
 924         assert(exact);
 925         map2 = isl_map_read_from_str(ctx,
 926                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
 927                         "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
 928                         "j <= n and 3 + i + 2 j <= 3 n and "
 929                         "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
 930                         "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
 931                         "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
 932                         "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
 933                         "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
 934         assert(isl_map_is_equal(map, map2));
 935         isl_map_free(map2);
 936         isl_map_free(map);
 937
 938         /* COCOA Fig.1 right */
 939         dom = isl_set_read_from_str(ctx,
 940                 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
 941                         "2 x - 3 y + 3 >= 0 }", -1);
 942         right = isl_map_read_from_str(ctx,
 943                 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
 944         up = isl_map_read_from_str(ctx,
 945                 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
 946         right = isl_map_intersect_domain(right, isl_set_copy(dom));
 947         right = isl_map_intersect_range(right, isl_set_copy(dom));
 948         up = isl_map_intersect_domain(up, isl_set_copy(dom));
 949         up = isl_map_intersect_range(up, dom);
 950         map = isl_map_union(up, right);
 951         map = isl_map_transitive_closure(map, &exact);
 952         assert(exact);
 953         map2 = isl_map_read_from_str(ctx,
 954                 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
 955                 "  [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
 956         assert(isl_map_is_equal(map, map2));
 957         isl_map_free(map2);
 958         isl_map_free(map);
 959
 960         /* COCOA Theorem 1 counter example */
 961         map = isl_map_read_from_str(ctx,
 962                 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
 963                         "i2 = 1 and j2 = j or "
 964                         "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
 965         map = isl_map_transitive_closure(map, &exact);
 966         assert(exact);
 967         isl_map_free(map);
 968
 969         map = isl_map_read_from_str(ctx,
 970                 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
 971                         "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
 972                         "i2 = i + 1 and 3 <= j2 - j <= 4 and "
 973                         "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
 974         map = isl_map_transitive_closure(map, &exact);
 975         assert(exact);
 976         isl_map_free(map);
 977
 978         /* Kelly et al 1996, fig 12 */
 979         map = isl_map_read_from_str(ctx,
 980                 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
 981                         "1 <= i,j,j+1 <= n or "
 982                         "j = n and j2 = 1 and i2 = i + 1 and "
 983                         "1 <= i,i+1 <= n }", -1);
 984         map = isl_map_transitive_closure(map, &exact);
 985         assert(exact);
 986         map2 = isl_map_read_from_str(ctx,
 987                 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
 988                         "1 <= i <= n and i = i2 or "
 989                         "1 <= i < i2 <= n and 1 <= j <= n and "
 990                         "1 <= j2 <= n }", -1);
 991         assert(isl_map_is_equal(map, map2));
 992         isl_map_free(map2);
 993         isl_map_free(map);
 994
 995         /* Omega's closure4 */
 996         map = isl_map_read_from_str(ctx,
 997                 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
 998                         "1 <= x,y <= 10 or "
 999                         "x2 = x + 1 and y2 = y and "
1000                         "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1001         map = isl_map_transitive_closure(map, &exact);
1002         assert(exact);
1003         isl_map_free(map);
1004
1005         map = isl_map_read_from_str(ctx,
1006                 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1007         map = isl_map_transitive_closure(map, &exact);
1008         assert(!exact);
1009         map2 = isl_map_read_from_str(ctx,
1010                 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1011         assert(isl_map_is_equal(map, map2));
1012         isl_map_free(map);
1013         isl_map_free(map2);
1014
1015         str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1016             "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1017             "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1018             "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1019         map = isl_map_read_from_str(ctx, str, -1);
1020         map = isl_map_transitive_closure(map, &exact);
1021         assert(exact);
1022         map2 = isl_map_read_from_str(ctx, str, -1);
1023         assert(isl_map_is_equal(map, map2));
1024         isl_map_free(map);
1025         isl_map_free(map2);
1026
1027         str = "{[0] -> [1]; [2] -> [3]}";
1028         map = isl_map_read_from_str(ctx, str, -1);
1029         map = isl_map_transitive_closure(map, &exact);
1030         assert(exact);
1031         map2 = isl_map_read_from_str(ctx, str, -1);
1032         assert(isl_map_is_equal(map, map2));
1033         isl_map_free(map);
1034         isl_map_free(map2);
1035 }
1036
1037 void test_lexmin(struct isl_ctx *ctx)
1038 {
1039         const char *str;
1040         isl_map *map;
1041
1042         str = "[p0, p1] -> { [] -> [] : "
1043             "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1044             "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1045             "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1046             "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1047             "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1048             "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1049             "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1050             "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1051             "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1052             "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1053             "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1054         map = isl_map_read_from_str(ctx, str, -1);
1055         map = isl_map_lexmin(map);
1056         isl_map_free(map);
1057 }
1058
1059 struct must_may {
1060         isl_map *must;
1061         isl_map *may;
1062 };
1063
1064 static int collect_must_may(__isl_take isl_map *dep, int must,
1065         void *dep_user, void *user)
1066 {
1067         struct must_may *mm = (struct must_may *)user;
1068
1069         if (must)
1070                 mm->must = isl_map_union(mm->must, dep);
1071         else
1072                 mm->may = isl_map_union(mm->may, dep);
1073
1074         return 0;
1075 }
1076
1077 static int common_space(void *first, void *second)
1078 {
1079         int depth = *(int *)first;
1080         return 2 * depth;
1081 }
1082
1083 int map_is_equal(__isl_keep isl_map *map, const char *str)
1084 {
1085         isl_map *map2;
1086         int equal;
1087
1088         map2 = isl_map_read_from_str(map->ctx, str, -1);
1089         equal = isl_map_is_equal(map, map2);
1090         isl_map_free(map2);
1091
1092         return equal;
1093 }
1094
1095 void test_dep(struct isl_ctx *ctx)
1096 {
1097         const char *str;
1098         isl_dim *dim;
1099         isl_map *map;
1100         isl_access_info *ai;
1101         isl_flow *flow;
1102         int depth;
1103         struct must_may mm;
1104
1105         depth = 3;
1106
1107         str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1108         map = isl_map_read_from_str(ctx, str, -1);
1109         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1110
1111         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1112         map = isl_map_read_from_str(ctx, str, -1);
1113         ai = isl_access_info_add_source(ai, map, 1, &depth);
1114
1115         str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1116         map = isl_map_read_from_str(ctx, str, -1);
1117         ai = isl_access_info_add_source(ai, map, 1, &depth);
1118
1119         flow = isl_access_info_compute_flow(ai);
1120         dim = isl_dim_alloc(ctx, 0, 3, 3);
1121         mm.must = isl_map_empty(isl_dim_copy(dim));
1122         mm.may = isl_map_empty(dim);
1123
1124         isl_flow_foreach(flow, collect_must_may, &mm);
1125
1126         str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1127               "  [1,10,0] -> [2,5,0] }";
1128         assert(map_is_equal(mm.must, str));
1129         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1130         assert(map_is_equal(mm.may, str));
1131
1132         isl_map_free(mm.must);
1133         isl_map_free(mm.may);
1134         isl_flow_free(flow);
1135
1136
1137         str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1138         map = isl_map_read_from_str(ctx, str, -1);
1139         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1140
1141         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1142         map = isl_map_read_from_str(ctx, str, -1);
1143         ai = isl_access_info_add_source(ai, map, 1, &depth);
1144
1145         str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1146         map = isl_map_read_from_str(ctx, str, -1);
1147         ai = isl_access_info_add_source(ai, map, 0, &depth);
1148
1149         flow = isl_access_info_compute_flow(ai);
1150         dim = isl_dim_alloc(ctx, 0, 3, 3);
1151         mm.must = isl_map_empty(isl_dim_copy(dim));
1152         mm.may = isl_map_empty(dim);
1153
1154         isl_flow_foreach(flow, collect_must_may, &mm);
1155
1156         str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1157         assert(map_is_equal(mm.must, str));
1158         str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1159         assert(map_is_equal(mm.may, str));
1160
1161         isl_map_free(mm.must);
1162         isl_map_free(mm.may);
1163         isl_flow_free(flow);
1164
1165
1166         str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1167         map = isl_map_read_from_str(ctx, str, -1);
1168         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1169
1170         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1171         map = isl_map_read_from_str(ctx, str, -1);
1172         ai = isl_access_info_add_source(ai, map, 0, &depth);
1173
1174         str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1175         map = isl_map_read_from_str(ctx, str, -1);
1176         ai = isl_access_info_add_source(ai, map, 0, &depth);
1177
1178         flow = isl_access_info_compute_flow(ai);
1179         dim = isl_dim_alloc(ctx, 0, 3, 3);
1180         mm.must = isl_map_empty(isl_dim_copy(dim));
1181         mm.may = isl_map_empty(dim);
1182
1183         isl_flow_foreach(flow, collect_must_may, &mm);
1184
1185         str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1186               "  [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1187         assert(map_is_equal(mm.may, str));
1188         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1189         assert(map_is_equal(mm.must, str));
1190
1191         isl_map_free(mm.must);
1192         isl_map_free(mm.may);
1193         isl_flow_free(flow);
1194
1195
1196         str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1197         map = isl_map_read_from_str(ctx, str, -1);
1198         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1199
1200         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1201         map = isl_map_read_from_str(ctx, str, -1);
1202         ai = isl_access_info_add_source(ai, map, 0, &depth);
1203
1204         str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1205         map = isl_map_read_from_str(ctx, str, -1);
1206         ai = isl_access_info_add_source(ai, map, 0, &depth);
1207
1208         flow = isl_access_info_compute_flow(ai);
1209         dim = isl_dim_alloc(ctx, 0, 3, 3);
1210         mm.must = isl_map_empty(isl_dim_copy(dim));
1211         mm.may = isl_map_empty(dim);
1212
1213         isl_flow_foreach(flow, collect_must_may, &mm);
1214
1215         str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1216               "  [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1217         assert(map_is_equal(mm.may, str));
1218         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1219         assert(map_is_equal(mm.must, str));
1220
1221         isl_map_free(mm.must);
1222         isl_map_free(mm.may);
1223         isl_flow_free(flow);
1224
1225
1226         str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1227         map = isl_map_read_from_str(ctx, str, -1);
1228         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1229
1230         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1231         map = isl_map_read_from_str(ctx, str, -1);
1232         ai = isl_access_info_add_source(ai, map, 0, &depth);
1233
1234         str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1235         map = isl_map_read_from_str(ctx, str, -1);
1236         ai = isl_access_info_add_source(ai, map, 0, &depth);
1237
1238         flow = isl_access_info_compute_flow(ai);
1239         dim = isl_dim_alloc(ctx, 0, 3, 3);
1240         mm.must = isl_map_empty(isl_dim_copy(dim));
1241         mm.may = isl_map_empty(dim);
1242
1243         isl_flow_foreach(flow, collect_must_may, &mm);
1244
1245         str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1246               "  [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1247         assert(map_is_equal(mm.may, str));
1248         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1249         assert(map_is_equal(mm.must, str));
1250
1251         isl_map_free(mm.must);
1252         isl_map_free(mm.may);
1253         isl_flow_free(flow);
1254
1255
1256         depth = 5;
1257
1258         str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1259         map = isl_map_read_from_str(ctx, str, -1);
1260         ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1261
1262         str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1263         map = isl_map_read_from_str(ctx, str, -1);
1264         ai = isl_access_info_add_source(ai, map, 1, &depth);
1265
1266         flow = isl_access_info_compute_flow(ai);
1267         dim = isl_dim_alloc(ctx, 0, 5, 5);
1268         mm.must = isl_map_empty(isl_dim_copy(dim));
1269         mm.may = isl_map_empty(dim);
1270
1271         isl_flow_foreach(flow, collect_must_may, &mm);
1272
1273         str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1274         assert(map_is_equal(mm.must, str));
1275         str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1276         assert(map_is_equal(mm.may, str));
1277
1278         isl_map_free(mm.must);
1279         isl_map_free(mm.may);
1280         isl_flow_free(flow);
1281 }
1282
1283 void test_sv(struct isl_ctx *ctx)
1284 {
1285         const char *str;
1286         isl_map *map;
1287
1288         str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1289         map = isl_map_read_from_str(ctx, str, -1);
1290         assert(isl_map_is_single_valued(map));
1291         isl_map_free(map);
1292
1293         str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1294         map = isl_map_read_from_str(ctx, str, -1);
1295         assert(!isl_map_is_single_valued(map));
1296         isl_map_free(map);
1297 }
1298
1299 int main()
1300 {
1301         struct isl_ctx *ctx;
1302
1303         srcdir = getenv("srcdir");
1304         assert(srcdir);
1305
1306         ctx = isl_ctx_alloc();
1307         test_sv(ctx);
1308         test_dep(ctx);
1309         test_read(ctx);
1310         test_bounded(ctx);
1311         test_construction(ctx);
1312         test_dim(ctx);
1313         test_div(ctx);
1314         test_application(ctx);
1315         test_affine_hull(ctx);
1316         test_convex_hull(ctx);
1317         test_gist(ctx);
1318         test_coalesce(ctx);
1319         test_closure(ctx);
1320         test_lexmin(ctx);
1321         isl_ctx_free(ctx);
1322         return 0;
1323 }