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_constraint.h>
  16
  17 static char *srcdir;
  18
  19 void test_read(struct isl_ctx *ctx)
  20 {
  21         char filename[PATH_MAX];
  22         FILE *input;
  23         int n;
  24         struct isl_basic_set *bset1, *bset2;
  25         const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
  26
  27         n = snprintf(filename, sizeof(filename),
  28                         "%s/test_inputs/set.omega", srcdir);
  29         assert(n < sizeof(filename));
  30         input = fopen(filename, "r");
  31         assert(input);
  32
  33         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
  34         bset2 = isl_basic_set_read_from_str(ctx, str, 0);
  35
  36         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
  37
  38         isl_basic_set_free(bset1);
  39         isl_basic_set_free(bset2);
  40
  41         fclose(input);
  42 }
  43
  44 /* Construct the basic set { [i] : 5 <= i <= N } */
  45 void test_construction(struct isl_ctx *ctx)
  46 {
  47         isl_int v;
  48         struct isl_dim *dim;
  49         struct isl_basic_set *bset;
  50         struct isl_constraint *c;
  51
  52         isl_int_init(v);
  53
  54         dim = isl_dim_set_alloc(ctx, 1, 1);
  55         bset = isl_basic_set_universe(dim);
  56
  57         c = isl_inequality_alloc(isl_dim_copy(bset->dim));
  58         isl_int_set_si(v, -1);
  59         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
  60         isl_int_set_si(v, 1);
  61         isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
  62         bset = isl_basic_set_add_constraint(bset, c);
  63
  64         c = isl_inequality_alloc(isl_dim_copy(bset->dim));
  65         isl_int_set_si(v, 1);
  66         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
  67         isl_int_set_si(v, -5);
  68         isl_constraint_set_constant(c, v);
  69         bset = isl_basic_set_add_constraint(bset, c);
  70
  71         isl_basic_set_free(bset);
  72
  73         isl_int_clear(v);
  74 }
  75
  76 void test_dim(struct isl_ctx *ctx)
  77 {
  78         isl_map *map1, *map2;
  79
  80         map1 = isl_map_read_from_str(ctx,
  81             "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
  82         map1 = isl_map_add(map1, isl_dim_in, 1);
  83         map2 = isl_map_read_from_str(ctx,
  84             "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
  85         assert(isl_map_is_equal(map1, map2));
  86         isl_map_free(map2);
  87
  88         map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
  89         map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
  90         assert(isl_map_is_equal(map1, map2));
  91
  92         isl_map_free(map1);
  93         isl_map_free(map2);
  94 }
  95
  96 void test_div(struct isl_ctx *ctx)
  97 {
  98         isl_int v;
  99         int pos;
 100         struct isl_dim *dim;
 101         struct isl_div *div;
 102         struct isl_basic_set *bset;
 103         struct isl_constraint *c;
 104
 105         isl_int_init(v);
 106
 107         /* test 1 */
 108         dim = isl_dim_set_alloc(ctx, 0, 1);
 109         bset = isl_basic_set_universe(dim);
 110
 111         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 112         isl_int_set_si(v, -1);
 113         isl_constraint_set_constant(c, v);
 114         isl_int_set_si(v, 1);
 115         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 116         div = isl_div_alloc(isl_dim_copy(bset->dim));
 117         c = isl_constraint_add_div(c, div, &pos);
 118         isl_int_set_si(v, 3);
 119         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 120         bset = isl_basic_set_add_constraint(bset, c);
 121
 122         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 123         isl_int_set_si(v, 1);
 124         isl_constraint_set_constant(c, v);
 125         isl_int_set_si(v, -1);
 126         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 127         div = isl_div_alloc(isl_dim_copy(bset->dim));
 128         c = isl_constraint_add_div(c, div, &pos);
 129         isl_int_set_si(v, 3);
 130         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 131         bset = isl_basic_set_add_constraint(bset, c);
 132
 133         assert(bset->n_div == 1);
 134         isl_basic_set_free(bset);
 135
 136         /* test 2 */
 137         dim = isl_dim_set_alloc(ctx, 0, 1);
 138         bset = isl_basic_set_universe(dim);
 139
 140         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 141         isl_int_set_si(v, 1);
 142         isl_constraint_set_constant(c, v);
 143         isl_int_set_si(v, -1);
 144         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 145         div = isl_div_alloc(isl_dim_copy(bset->dim));
 146         c = isl_constraint_add_div(c, div, &pos);
 147         isl_int_set_si(v, 3);
 148         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 149         bset = isl_basic_set_add_constraint(bset, c);
 150
 151         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 152         isl_int_set_si(v, -1);
 153         isl_constraint_set_constant(c, v);
 154         isl_int_set_si(v, 1);
 155         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 156         div = isl_div_alloc(isl_dim_copy(bset->dim));
 157         c = isl_constraint_add_div(c, div, &pos);
 158         isl_int_set_si(v, 3);
 159         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 160         bset = isl_basic_set_add_constraint(bset, c);
 161
 162         assert(bset->n_div == 1);
 163         isl_basic_set_free(bset);
 164
 165         /* test 3 */
 166         dim = isl_dim_set_alloc(ctx, 0, 1);
 167         bset = isl_basic_set_universe(dim);
 168
 169         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 170         isl_int_set_si(v, 1);
 171         isl_constraint_set_constant(c, v);
 172         isl_int_set_si(v, -1);
 173         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 174         div = isl_div_alloc(isl_dim_copy(bset->dim));
 175         c = isl_constraint_add_div(c, div, &pos);
 176         isl_int_set_si(v, 3);
 177         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 178         bset = isl_basic_set_add_constraint(bset, c);
 179
 180         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 181         isl_int_set_si(v, -3);
 182         isl_constraint_set_constant(c, v);
 183         isl_int_set_si(v, 1);
 184         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 185         div = isl_div_alloc(isl_dim_copy(bset->dim));
 186         c = isl_constraint_add_div(c, div, &pos);
 187         isl_int_set_si(v, 4);
 188         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 189         bset = isl_basic_set_add_constraint(bset, c);
 190
 191         assert(bset->n_div == 1);
 192         isl_basic_set_free(bset);
 193
 194         /* test 4 */
 195         dim = isl_dim_set_alloc(ctx, 0, 1);
 196         bset = isl_basic_set_universe(dim);
 197
 198         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 199         isl_int_set_si(v, 2);
 200         isl_constraint_set_constant(c, v);
 201         isl_int_set_si(v, -1);
 202         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 203         div = isl_div_alloc(isl_dim_copy(bset->dim));
 204         c = isl_constraint_add_div(c, div, &pos);
 205         isl_int_set_si(v, 3);
 206         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 207         bset = isl_basic_set_add_constraint(bset, c);
 208
 209         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 210         isl_int_set_si(v, -1);
 211         isl_constraint_set_constant(c, v);
 212         isl_int_set_si(v, 1);
 213         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 214         div = isl_div_alloc(isl_dim_copy(bset->dim));
 215         c = isl_constraint_add_div(c, div, &pos);
 216         isl_int_set_si(v, 6);
 217         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 218         bset = isl_basic_set_add_constraint(bset, c);
 219
 220         assert(isl_basic_set_is_empty(bset));
 221         isl_basic_set_free(bset);
 222
 223         /* test 5 */
 224         dim = isl_dim_set_alloc(ctx, 0, 2);
 225         bset = isl_basic_set_universe(dim);
 226
 227         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 228         isl_int_set_si(v, -1);
 229         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 230         div = isl_div_alloc(isl_dim_copy(bset->dim));
 231         c = isl_constraint_add_div(c, div, &pos);
 232         isl_int_set_si(v, 3);
 233         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 234         bset = isl_basic_set_add_constraint(bset, c);
 235
 236         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 237         isl_int_set_si(v, 1);
 238         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 239         isl_int_set_si(v, -3);
 240         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 241         bset = isl_basic_set_add_constraint(bset, c);
 242
 243         assert(bset->n_div == 0);
 244         isl_basic_set_free(bset);
 245
 246         /* test 6 */
 247         dim = isl_dim_set_alloc(ctx, 0, 2);
 248         bset = isl_basic_set_universe(dim);
 249
 250         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 251         isl_int_set_si(v, -1);
 252         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 253         div = isl_div_alloc(isl_dim_copy(bset->dim));
 254         c = isl_constraint_add_div(c, div, &pos);
 255         isl_int_set_si(v, 6);
 256         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 257         bset = isl_basic_set_add_constraint(bset, c);
 258
 259         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 260         isl_int_set_si(v, 1);
 261         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 262         isl_int_set_si(v, -3);
 263         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 264         bset = isl_basic_set_add_constraint(bset, c);
 265
 266         assert(bset->n_div == 1);
 267         isl_basic_set_free(bset);
 268
 269         /* test 7 */
 270         /* This test is a bit tricky.  We set up an equality
 271          *              a + 3b + 3c = 6 e0
 272          * Normalization of divs creates _two_ divs
 273          *              a = 3 e0
 274          *              c - b - e0 = 2 e1
 275          * Afterwards e0 is removed again because it has coefficient -1
 276          * and we end up with the original equality and div again.
 277          * Perhaps we can avoid the introduction of this temporary div.
 278          */
 279         dim = isl_dim_set_alloc(ctx, 0, 3);
 280         bset = isl_basic_set_universe(dim);
 281
 282         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 283         isl_int_set_si(v, -1);
 284         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 285         isl_int_set_si(v, -3);
 286         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 287         isl_int_set_si(v, -3);
 288         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 289         div = isl_div_alloc(isl_dim_copy(bset->dim));
 290         c = isl_constraint_add_div(c, div, &pos);
 291         isl_int_set_si(v, 6);
 292         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 293         bset = isl_basic_set_add_constraint(bset, c);
 294
 295         assert(bset->n_div == 1);
 296         isl_basic_set_free(bset);
 297
 298         /* test 8 */
 299         dim = isl_dim_set_alloc(ctx, 0, 4);
 300         bset = isl_basic_set_universe(dim);
 301
 302         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 303         isl_int_set_si(v, -1);
 304         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 305         isl_int_set_si(v, -3);
 306         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 307         isl_int_set_si(v, -3);
 308         isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
 309         div = isl_div_alloc(isl_dim_copy(bset->dim));
 310         c = isl_constraint_add_div(c, div, &pos);
 311         isl_int_set_si(v, 6);
 312         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 313         bset = isl_basic_set_add_constraint(bset, c);
 314
 315         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 316         isl_int_set_si(v, -1);
 317         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 318         isl_int_set_si(v, 1);
 319         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 320         isl_int_set_si(v, 1);
 321         isl_constraint_set_constant(c, v);
 322         bset = isl_basic_set_add_constraint(bset, c);
 323
 324         assert(bset->n_div == 1);
 325         isl_basic_set_free(bset);
 326
 327         /* test 9 */
 328         dim = isl_dim_set_alloc(ctx, 0, 2);
 329         bset = isl_basic_set_universe(dim);
 330
 331         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 332         isl_int_set_si(v, 1);
 333         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 334         isl_int_set_si(v, -1);
 335         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 336         div = isl_div_alloc(isl_dim_copy(bset->dim));
 337         c = isl_constraint_add_div(c, div, &pos);
 338         isl_int_set_si(v, -2);
 339         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 340         bset = isl_basic_set_add_constraint(bset, c);
 341
 342         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 343         isl_int_set_si(v, -1);
 344         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 345         div = isl_div_alloc(isl_dim_copy(bset->dim));
 346         c = isl_constraint_add_div(c, div, &pos);
 347         isl_int_set_si(v, 3);
 348         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 349         isl_int_set_si(v, 2);
 350         isl_constraint_set_constant(c, v);
 351         bset = isl_basic_set_add_constraint(bset, c);
 352
 353         bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
 354
 355         assert(!isl_basic_set_is_empty(bset));
 356
 357         isl_basic_set_free(bset);
 358
 359         /* test 10 */
 360         dim = isl_dim_set_alloc(ctx, 0, 2);
 361         bset = isl_basic_set_universe(dim);
 362
 363         c = isl_equality_alloc(isl_dim_copy(bset->dim));
 364         isl_int_set_si(v, 1);
 365         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 366         div = isl_div_alloc(isl_dim_copy(bset->dim));
 367         c = isl_constraint_add_div(c, div, &pos);
 368         isl_int_set_si(v, -2);
 369         isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
 370         bset = isl_basic_set_add_constraint(bset, c);
 371
 372         bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
 373
 374         isl_basic_set_free(bset);
 375
 376         isl_int_clear(v);
 377 }
 378
 379 void test_application_case(struct isl_ctx *ctx, const char *name)
 380 {
 381         char filename[PATH_MAX];
 382         FILE *input;
 383         int n;
 384         struct isl_basic_set *bset1, *bset2;
 385         struct isl_basic_map *bmap;
 386
 387         n = snprintf(filename, sizeof(filename),
 388                         "%s/test_inputs/%s.omega", srcdir, name);
 389         assert(n < sizeof(filename));
 390         input = fopen(filename, "r");
 391         assert(input);
 392
 393         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 394         bmap = isl_basic_map_read_from_file(ctx, input, 0);
 395
 396         bset1 = isl_basic_set_apply(bset1, bmap);
 397
 398         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 399
 400         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 401
 402         isl_basic_set_free(bset1);
 403         isl_basic_set_free(bset2);
 404
 405         fclose(input);
 406 }
 407
 408 void test_application(struct isl_ctx *ctx)
 409 {
 410         test_application_case(ctx, "application");
 411         test_application_case(ctx, "application2");
 412 }
 413
 414 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
 415 {
 416         char filename[PATH_MAX];
 417         FILE *input;
 418         int n;
 419         struct isl_basic_set *bset1, *bset2;
 420
 421         n = snprintf(filename, sizeof(filename),
 422                         "%s/test_inputs/%s.polylib", srcdir, name);
 423         assert(n < sizeof(filename));
 424         input = fopen(filename, "r");
 425         assert(input);
 426
 427         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 428         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 429
 430         bset1 = isl_basic_set_affine_hull(bset1);
 431
 432         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 433
 434         isl_basic_set_free(bset1);
 435         isl_basic_set_free(bset2);
 436
 437         fclose(input);
 438 }
 439
 440 void test_affine_hull(struct isl_ctx *ctx)
 441 {
 442         test_affine_hull_case(ctx, "affine2");
 443         test_affine_hull_case(ctx, "affine");
 444         test_affine_hull_case(ctx, "affine3");
 445 }
 446
 447 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
 448 {
 449         char filename[PATH_MAX];
 450         FILE *input;
 451         int n;
 452         struct isl_basic_set *bset1, *bset2;
 453         struct isl_set *set;
 454
 455         n = snprintf(filename, sizeof(filename),
 456                         "%s/test_inputs/%s.polylib", srcdir, name);
 457         assert(n < sizeof(filename));
 458         input = fopen(filename, "r");
 459         assert(input);
 460
 461         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 462         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 463
 464         set = isl_basic_set_union(bset1, bset2);
 465         bset1 = isl_set_convex_hull(set);
 466
 467         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 468
 469         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 470
 471         isl_basic_set_free(bset1);
 472         isl_basic_set_free(bset2);
 473
 474         fclose(input);
 475 }
 476
 477 void test_convex_hull(struct isl_ctx *ctx)
 478 {
 479         test_convex_hull_case(ctx, "convex0");
 480         test_convex_hull_case(ctx, "convex1");
 481         test_convex_hull_case(ctx, "convex2");
 482         test_convex_hull_case(ctx, "convex3");
 483         test_convex_hull_case(ctx, "convex4");
 484         test_convex_hull_case(ctx, "convex5");
 485         test_convex_hull_case(ctx, "convex6");
 486         test_convex_hull_case(ctx, "convex7");
 487         test_convex_hull_case(ctx, "convex8");
 488         test_convex_hull_case(ctx, "convex9");
 489         test_convex_hull_case(ctx, "convex10");
 490         test_convex_hull_case(ctx, "convex11");
 491         test_convex_hull_case(ctx, "convex12");
 492         test_convex_hull_case(ctx, "convex13");
 493         test_convex_hull_case(ctx, "convex14");
 494         test_convex_hull_case(ctx, "convex15");
 495 }
 496
 497 void test_gist_case(struct isl_ctx *ctx, const char *name)
 498 {
 499         char filename[PATH_MAX];
 500         FILE *input;
 501         int n;
 502         struct isl_basic_set *bset1, *bset2;
 503
 504         n = snprintf(filename, sizeof(filename),
 505                         "%s/test_inputs/%s.polylib", srcdir, name);
 506         assert(n < sizeof(filename));
 507         input = fopen(filename, "r");
 508         assert(input);
 509
 510         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 511         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 512
 513         bset1 = isl_basic_set_gist(bset1, bset2);
 514
 515         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 516
 517         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 518
 519         isl_basic_set_free(bset1);
 520         isl_basic_set_free(bset2);
 521
 522         fclose(input);
 523 }
 524
 525 void test_gist(struct isl_ctx *ctx)
 526 {
 527         test_gist_case(ctx, "gist1");
 528 }
 529
 530 void test_coalesce(struct isl_ctx *ctx)
 531 {
 532         const char *str;
 533         struct isl_set *set, *set2;
 534         struct isl_map *map, *map2;
 535
 536         set = isl_set_read_from_str(ctx,
 537                 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
 538                        "y >= x & x >= 2 & 5 >= y }", -1);
 539         set = isl_set_coalesce(set);
 540         assert(set && set->n == 1);
 541         isl_set_free(set);
 542
 543         set = isl_set_read_from_str(ctx,
 544                 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
 545                        "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
 546         set = isl_set_coalesce(set);
 547         assert(set && set->n == 1);
 548         isl_set_free(set);
 549
 550         set = isl_set_read_from_str(ctx,
 551                 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
 552                        "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
 553         set = isl_set_coalesce(set);
 554         assert(set && set->n == 2);
 555         isl_set_free(set);
 556
 557         set = isl_set_read_from_str(ctx,
 558                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 559                        "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
 560         set = isl_set_coalesce(set);
 561         assert(set && set->n == 1);
 562         isl_set_free(set);
 563
 564         set = isl_set_read_from_str(ctx,
 565                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 566                        "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
 567         set = isl_set_coalesce(set);
 568         assert(set && set->n == 2);
 569         isl_set_free(set);
 570
 571         set = isl_set_read_from_str(ctx,
 572                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 573                        "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
 574         set = isl_set_coalesce(set);
 575         assert(set && set->n == 2);
 576         isl_set_free(set);
 577
 578         set = isl_set_read_from_str(ctx,
 579                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 580                        "y >= 0 & x = 6 & y <= 6}", -1);
 581         set = isl_set_coalesce(set);
 582         assert(set && set->n == 1);
 583         isl_set_free(set);
 584
 585         set = isl_set_read_from_str(ctx,
 586                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 587                        "y >= 0 & x = 7 & y <= 6}", -1);
 588         set = isl_set_coalesce(set);
 589         assert(set && set->n == 2);
 590         isl_set_free(set);
 591
 592         set = isl_set_read_from_str(ctx,
 593                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 594                        "y >= 0 & x = 6 & y <= 5}", -1);
 595         set = isl_set_coalesce(set);
 596         assert(set && set->n == 1);
 597         set2 = isl_set_read_from_str(ctx,
 598                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 599                        "y >= 0 & x = 6 & y <= 5}", -1);
 600         assert(isl_set_is_equal(set, set2));
 601         isl_set_free(set);
 602         isl_set_free(set2);
 603
 604         set = isl_set_read_from_str(ctx,
 605                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 606                        "y >= 0 & x = 6 & y <= 7}", -1);
 607         set = isl_set_coalesce(set);
 608         assert(set && set->n == 2);
 609         isl_set_free(set);
 610
 611         set = isl_set_read_from_str(ctx,
 612                 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
 613         set = isl_set_coalesce(set);
 614         assert(set && set->n == 1);
 615         set2 = isl_set_read_from_str(ctx,
 616                 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
 617         assert(isl_set_is_equal(set, set2));
 618         isl_set_free(set);
 619         isl_set_free(set2);
 620
 621         set = isl_set_read_from_str(ctx,
 622                 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
 623         set = isl_set_coalesce(set);
 624         set2 = isl_set_read_from_str(ctx,
 625                 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
 626         assert(isl_set_is_equal(set, set2));
 627         isl_set_free(set);
 628         isl_set_free(set2);
 629
 630         set = isl_set_read_from_str(ctx,
 631                 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
 632                                 "2 <= i and i <= n }", -1);
 633         set = isl_set_coalesce(set);
 634         assert(set && set->n == 1);
 635         set2 = isl_set_read_from_str(ctx,
 636                 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
 637                                 "2 <= i and i <= n }", -1);
 638         assert(isl_set_is_equal(set, set2));
 639         isl_set_free(set);
 640         isl_set_free(set2);
 641
 642         map = isl_map_read_from_str(ctx,
 643                 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 644                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 645                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 646                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
 647                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
 648                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
 649                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
 650                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
 651                 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 652                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 653                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 654                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
 655                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
 656                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
 657                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
 658                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
 659                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
 660                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
 661         map = isl_map_coalesce(map);
 662         map2 = isl_map_read_from_str(ctx,
 663                 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 664                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 665                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 666                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
 667                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
 668                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
 669                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
 670                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
 671                 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 672                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 673                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 674                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
 675                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
 676                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
 677                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
 678                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
 679                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
 680                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
 681         assert(isl_map_is_equal(map, map2));
 682         isl_map_free(map);
 683         isl_map_free(map2);
 684
 685         str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
 686               "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
 687               "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
 688               "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
 689         map = isl_map_read_from_str(ctx, str, -1);
 690         map = isl_map_coalesce(map);
 691         map2 = isl_map_read_from_str(ctx, str, -1);
 692         assert(isl_map_is_equal(map, map2));
 693         isl_map_free(map);
 694         isl_map_free(map2);
 695 }
 696
 697 void test_closure(struct isl_ctx *ctx)
 698 {
 699         const char *str;
 700         isl_set *dom;
 701         isl_map *up, *right;
 702         isl_map *map, *map2;
 703         int exact;
 704
 705         /* COCOA example 1 */
 706         map = isl_map_read_from_str(ctx,
 707                 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
 708                         "1 <= i and i < n and 1 <= j and j < n or "
 709                         "i2 = i + 1 and j2 = j - 1 and "
 710                         "1 <= i and i < n and 2 <= j and j <= n }", -1);
 711         map = isl_map_power(map, 1, &exact);
 712         assert(exact);
 713         isl_map_free(map);
 714
 715         /* COCOA example 1 */
 716         map = isl_map_read_from_str(ctx,
 717                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
 718                         "1 <= i and i < n and 1 <= j and j < n or "
 719                         "i2 = i + 1 and j2 = j - 1 and "
 720                         "1 <= i and i < n and 2 <= j and j <= n }", -1);
 721         map = isl_map_transitive_closure(map, &exact);
 722         assert(exact);
 723         map2 = isl_map_read_from_str(ctx,
 724                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
 725                         "1 <= i and i < n and 1 <= j and j <= n and "
 726                         "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
 727                         "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
 728                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
 729         assert(isl_map_is_equal(map, map2));
 730         isl_map_free(map2);
 731         isl_map_free(map);
 732
 733         map = isl_map_read_from_str(ctx,
 734                 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
 735                                      " 0 <= y and y <= n }", -1);
 736         map = isl_map_transitive_closure(map, &exact);
 737         map2 = isl_map_read_from_str(ctx,
 738                 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
 739                                      " 0 <= y and y <= n }", -1);
 740         assert(isl_map_is_equal(map, map2));
 741         isl_map_free(map2);
 742         isl_map_free(map);
 743
 744         /* COCOA example 2 */
 745         map = isl_map_read_from_str(ctx,
 746                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
 747                         "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
 748                         "i2 = i + 2 and j2 = j - 2 and "
 749                         "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
 750         map = isl_map_transitive_closure(map, &exact);
 751         assert(exact);
 752         map2 = isl_map_read_from_str(ctx,
 753                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
 754                         "1 <= i and i < n - 1 and 1 <= j and j <= n and "
 755                         "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
 756                         "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
 757                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
 758         assert(isl_map_is_equal(map, map2));
 759         isl_map_free(map);
 760         isl_map_free(map2);
 761
 762         /* COCOA Fig.2 left */
 763         map = isl_map_read_from_str(ctx,
 764                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
 765                         "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
 766                         "j <= n or "
 767                         "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
 768                         "j <= 2 i - 3 and j <= n - 2 or "
 769                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 770                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 771         map = isl_map_transitive_closure(map, &exact);
 772         assert(exact);
 773         isl_map_free(map);
 774
 775         /* COCOA Fig.2 right */
 776         map = isl_map_read_from_str(ctx,
 777                 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
 778                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
 779                         "j <= n or "
 780                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
 781                         "j <= 2 i - 4 and j <= n - 3 or "
 782                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 783                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 784         map = isl_map_power(map, 1, &exact);
 785         assert(exact);
 786         isl_map_free(map);
 787
 788         /* COCOA Fig.2 right */
 789         map = isl_map_read_from_str(ctx,
 790                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
 791                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
 792                         "j <= n or "
 793                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
 794                         "j <= 2 i - 4 and j <= n - 3 or "
 795                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 796                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 797         map = isl_map_transitive_closure(map, &exact);
 798         assert(exact);
 799         map2 = isl_map_read_from_str(ctx,
 800                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
 801                         "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
 802                         "j <= n and 3 + i + 2 j <= 3 n and "
 803                         "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
 804                         "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
 805                         "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
 806                         "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
 807                         "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
 808         assert(isl_map_is_equal(map, map2));
 809         isl_map_free(map2);
 810         isl_map_free(map);
 811
 812         /* COCOA Fig.1 right */
 813         dom = isl_set_read_from_str(ctx,
 814                 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
 815                         "2 x - 3 y + 3 >= 0 }", -1);
 816         right = isl_map_read_from_str(ctx,
 817                 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
 818         up = isl_map_read_from_str(ctx,
 819                 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
 820         right = isl_map_intersect_domain(right, isl_set_copy(dom));
 821         right = isl_map_intersect_range(right, isl_set_copy(dom));
 822         up = isl_map_intersect_domain(up, isl_set_copy(dom));
 823         up = isl_map_intersect_range(up, dom);
 824         map = isl_map_union(up, right);
 825         map = isl_map_transitive_closure(map, &exact);
 826         assert(!exact);
 827         isl_map_free(map);
 828
 829         /* COCOA Theorem 1 counter example */
 830         map = isl_map_read_from_str(ctx,
 831                 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
 832                         "i2 = 1 and j2 = j or "
 833                         "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
 834         map = isl_map_transitive_closure(map, &exact);
 835         assert(exact);
 836         isl_map_free(map);
 837
 838         map = isl_map_read_from_str(ctx,
 839                 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
 840                         "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
 841                         "i2 = i + 1 and 3 <= j2 - j <= 4 and "
 842                         "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
 843         map = isl_map_transitive_closure(map, &exact);
 844         assert(exact);
 845         isl_map_free(map);
 846
 847         /* Kelly et al 1996, fig 12 */
 848         map = isl_map_read_from_str(ctx,
 849                 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
 850                         "1 <= i,j,j+1 <= n or "
 851                         "j = n and j2 = 1 and i2 = i + 1 and "
 852                         "1 <= i,i+1 <= n }", -1);
 853         map = isl_map_transitive_closure(map, &exact);
 854         assert(exact);
 855         map2 = isl_map_read_from_str(ctx,
 856                 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
 857                         "1 <= i <= n and i = i2 or "
 858                         "1 <= i < i2 <= n and 1 <= j <= n and "
 859                         "1 <= j2 <= n }", -1);
 860         assert(isl_map_is_equal(map, map2));
 861         isl_map_free(map2);
 862         isl_map_free(map);
 863
 864         /* Omega's closure4 */
 865         map = isl_map_read_from_str(ctx,
 866                 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
 867                         "1 <= x,y <= 10 or "
 868                         "x2 = x + 1 and y2 = y and "
 869                         "1 <= x <= 20 && 5 <= y <= 15 }", -1);
 870         map = isl_map_transitive_closure(map, &exact);
 871         assert(exact);
 872         isl_map_free(map);
 873
 874         map = isl_map_read_from_str(ctx,
 875                 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
 876         map = isl_map_transitive_closure(map, &exact);
 877         assert(!exact);
 878         map2 = isl_map_read_from_str(ctx,
 879                 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
 880         assert(isl_map_is_equal(map, map2));
 881         isl_map_free(map);
 882         isl_map_free(map2);
 883
 884         str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
 885             "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
 886             "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
 887             "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
 888         map = isl_map_read_from_str(ctx, str, -1);
 889         map = isl_map_transitive_closure(map, &exact);
 890         assert(exact);
 891         map2 = isl_map_read_from_str(ctx, str, -1);
 892         assert(isl_map_is_equal(map, map2));
 893         isl_map_free(map);
 894         isl_map_free(map2);
 895 }
 896
 897 int main()
 898 {
 899         struct isl_ctx *ctx;
 900
 901         srcdir = getenv("srcdir");
 902         assert(srcdir);
 903
 904         ctx = isl_ctx_alloc();
 905         test_read(ctx);
 906         test_construction(ctx);
 907         test_dim(ctx);
 908         test_div(ctx);
 909         test_application(ctx);
 910         test_affine_hull(ctx);
 911         test_convex_hull(ctx);
 912         test_gist(ctx);
 913         test_coalesce(ctx);
 914         test_closure(ctx);
 915         isl_ctx_free(ctx);
 916         return 0;
 917 }