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 }
 495
 496 void test_gist_case(struct isl_ctx *ctx, const char *name)
 497 {
 498         char filename[PATH_MAX];
 499         FILE *input;
 500         int n;
 501         struct isl_basic_set *bset1, *bset2;
 502
 503         n = snprintf(filename, sizeof(filename),
 504                         "%s/test_inputs/%s.polylib", srcdir, name);
 505         assert(n < sizeof(filename));
 506         input = fopen(filename, "r");
 507         assert(input);
 508
 509         bset1 = isl_basic_set_read_from_file(ctx, input, 0);
 510         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 511
 512         bset1 = isl_basic_set_gist(bset1, bset2);
 513
 514         bset2 = isl_basic_set_read_from_file(ctx, input, 0);
 515
 516         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 517
 518         isl_basic_set_free(bset1);
 519         isl_basic_set_free(bset2);
 520
 521         fclose(input);
 522 }
 523
 524 void test_gist(struct isl_ctx *ctx)
 525 {
 526         test_gist_case(ctx, "gist1");
 527 }
 528
 529 void test_coalesce(struct isl_ctx *ctx)
 530 {
 531         struct isl_set *set, *set2;
 532         struct isl_map *map, *map2;
 533
 534         set = isl_set_read_from_str(ctx,
 535                 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
 536                        "y >= x & x >= 2 & 5 >= y }", -1);
 537         set = isl_set_coalesce(set);
 538         assert(set && set->n == 1);
 539         isl_set_free(set);
 540
 541         set = isl_set_read_from_str(ctx,
 542                 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
 543                        "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
 544         set = isl_set_coalesce(set);
 545         assert(set && set->n == 1);
 546         isl_set_free(set);
 547
 548         set = isl_set_read_from_str(ctx,
 549                 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
 550                        "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
 551         set = isl_set_coalesce(set);
 552         assert(set && set->n == 2);
 553         isl_set_free(set);
 554
 555         set = isl_set_read_from_str(ctx,
 556                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 557                        "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
 558         set = isl_set_coalesce(set);
 559         assert(set && set->n == 1);
 560         isl_set_free(set);
 561
 562         set = isl_set_read_from_str(ctx,
 563                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 564                        "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
 565         set = isl_set_coalesce(set);
 566         assert(set && set->n == 2);
 567         isl_set_free(set);
 568
 569         set = isl_set_read_from_str(ctx,
 570                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 571                        "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
 572         set = isl_set_coalesce(set);
 573         assert(set && set->n == 2);
 574         isl_set_free(set);
 575
 576         set = isl_set_read_from_str(ctx,
 577                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 578                        "y >= 0 & x = 6 & y <= 6}", -1);
 579         set = isl_set_coalesce(set);
 580         assert(set && set->n == 1);
 581         isl_set_free(set);
 582
 583         set = isl_set_read_from_str(ctx,
 584                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 585                        "y >= 0 & x = 7 & y <= 6}", -1);
 586         set = isl_set_coalesce(set);
 587         assert(set && set->n == 2);
 588         isl_set_free(set);
 589
 590         set = isl_set_read_from_str(ctx,
 591                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 592                        "y >= 0 & x = 6 & y <= 5}", -1);
 593         set = isl_set_coalesce(set);
 594         assert(set && set->n == 1);
 595         set2 = isl_set_read_from_str(ctx,
 596                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 597                        "y >= 0 & x = 6 & y <= 5}", -1);
 598         assert(isl_set_is_equal(set, set2));
 599         isl_set_free(set);
 600         isl_set_free(set2);
 601
 602         set = isl_set_read_from_str(ctx,
 603                 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
 604                        "y >= 0 & x = 6 & y <= 7}", -1);
 605         set = isl_set_coalesce(set);
 606         assert(set && set->n == 2);
 607         isl_set_free(set);
 608
 609         set = isl_set_read_from_str(ctx,
 610                 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
 611         set = isl_set_coalesce(set);
 612         assert(set && set->n == 1);
 613         set2 = isl_set_read_from_str(ctx,
 614                 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
 615         assert(isl_set_is_equal(set, set2));
 616         isl_set_free(set);
 617         isl_set_free(set2);
 618
 619         set = isl_set_read_from_str(ctx,
 620                 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
 621         set = isl_set_coalesce(set);
 622         set2 = isl_set_read_from_str(ctx,
 623                 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
 624         assert(isl_set_is_equal(set, set2));
 625         isl_set_free(set);
 626         isl_set_free(set2);
 627
 628         set = isl_set_read_from_str(ctx,
 629                 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
 630                                 "2 <= i and i <= n }", -1);
 631         set = isl_set_coalesce(set);
 632         assert(set && set->n == 1);
 633         set2 = isl_set_read_from_str(ctx,
 634                 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
 635                                 "2 <= i and i <= n }", -1);
 636         assert(isl_set_is_equal(set, set2));
 637         isl_set_free(set);
 638         isl_set_free(set2);
 639
 640         map = isl_map_read_from_str(ctx,
 641                 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 642                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 643                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 644                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
 645                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
 646                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
 647                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
 648                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
 649                 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 650                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 651                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 652                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
 653                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
 654                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
 655                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
 656                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
 657                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
 658                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
 659         map = isl_map_coalesce(map);
 660         map2 = isl_map_read_from_str(ctx,
 661                 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 662                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 663                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 664                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
 665                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
 666                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
 667                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
 668                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
 669                 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
 670                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
 671                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
 672                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
 673                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
 674                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
 675                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
 676                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
 677                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
 678                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
 679         assert(isl_map_is_equal(map, map2));
 680         isl_map_free(map);
 681         isl_map_free(map2);
 682 }
 683
 684 void test_closure(struct isl_ctx *ctx)
 685 {
 686         isl_set *dom;
 687         isl_map *up, *right;
 688         isl_map *map, *map2;
 689         int exact;
 690
 691         /* COCOA example 1 */
 692         map = isl_map_read_from_str(ctx,
 693                 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
 694                         "1 <= i and i < n and 1 <= j and j < n or "
 695                         "i2 = i + 1 and j2 = j - 1 and "
 696                         "1 <= i and i < n and 2 <= j and j <= n }", -1);
 697         map = isl_map_power(map, 1, &exact);
 698         assert(exact);
 699         isl_map_free(map);
 700
 701         /* COCOA example 1 */
 702         map = isl_map_read_from_str(ctx,
 703                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
 704                         "1 <= i and i < n and 1 <= j and j < n or "
 705                         "i2 = i + 1 and j2 = j - 1 and "
 706                         "1 <= i and i < n and 2 <= j and j <= n }", -1);
 707         map = isl_map_transitive_closure(map, &exact);
 708         assert(exact);
 709         map2 = isl_map_read_from_str(ctx,
 710                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
 711                         "1 <= i and i < n and 1 <= j and j <= n and "
 712                         "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
 713                         "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
 714                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
 715         assert(isl_map_is_equal(map, map2));
 716         isl_map_free(map2);
 717         isl_map_free(map);
 718
 719         map = isl_map_read_from_str(ctx,
 720                 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
 721                                      " 0 <= y and y <= n }", -1);
 722         map = isl_map_transitive_closure(map, &exact);
 723         map2 = isl_map_read_from_str(ctx,
 724                 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
 725                                      " 0 <= y and y <= n }", -1);
 726         assert(isl_map_is_equal(map, map2));
 727         isl_map_free(map2);
 728         isl_map_free(map);
 729
 730         /* COCOA example 2 */
 731         map = isl_map_read_from_str(ctx,
 732                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
 733                         "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
 734                         "i2 = i + 2 and j2 = j - 2 and "
 735                         "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
 736         map = isl_map_transitive_closure(map, &exact);
 737         assert(exact);
 738         map2 = isl_map_read_from_str(ctx,
 739                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
 740                         "1 <= i and i < n - 1 and 1 <= j and j <= n and "
 741                         "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
 742                         "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
 743                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
 744         assert(isl_map_is_equal(map, map2));
 745         isl_map_free(map);
 746         isl_map_free(map2);
 747
 748         /* COCOA Fig.2 left */
 749         map = isl_map_read_from_str(ctx,
 750                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
 751                         "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
 752                         "j <= n or "
 753                         "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
 754                         "j <= 2 i - 3 and j <= n - 2 or "
 755                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 756                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 757         map = isl_map_transitive_closure(map, &exact);
 758         assert(exact);
 759         isl_map_free(map);
 760
 761         /* COCOA Fig.2 right */
 762         map = isl_map_read_from_str(ctx,
 763                 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
 764                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
 765                         "j <= n or "
 766                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
 767                         "j <= 2 i - 4 and j <= n - 3 or "
 768                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 769                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 770         map = isl_map_power(map, 1, &exact);
 771         assert(exact);
 772         isl_map_free(map);
 773
 774         /* COCOA Fig.2 right */
 775         map = isl_map_read_from_str(ctx,
 776                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
 777                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
 778                         "j <= n or "
 779                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
 780                         "j <= 2 i - 4 and j <= n - 3 or "
 781                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
 782                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
 783         map = isl_map_transitive_closure(map, &exact);
 784         assert(exact);
 785         map2 = isl_map_read_from_str(ctx,
 786                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
 787                         "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
 788                         "j <= n and 3 + i + 2 j <= 3 n and "
 789                         "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
 790                         "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
 791                         "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
 792                         "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
 793                         "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
 794         assert(isl_map_is_equal(map, map2));
 795         isl_map_free(map2);
 796         isl_map_free(map);
 797
 798         /* COCOA Fig.1 right */
 799         dom = isl_set_read_from_str(ctx,
 800                 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
 801                         "2 x - 3 y + 3 >= 0 }", -1);
 802         right = isl_map_read_from_str(ctx,
 803                 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
 804         up = isl_map_read_from_str(ctx,
 805                 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
 806         right = isl_map_intersect_domain(right, isl_set_copy(dom));
 807         right = isl_map_intersect_range(right, isl_set_copy(dom));
 808         up = isl_map_intersect_domain(up, isl_set_copy(dom));
 809         up = isl_map_intersect_range(up, dom);
 810         map = isl_map_union(up, right);
 811         map = isl_map_transitive_closure(map, &exact);
 812         assert(!exact);
 813         isl_map_free(map);
 814
 815         /* COCOA Theorem 1 counter example */
 816         map = isl_map_read_from_str(ctx,
 817                 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
 818                         "i2 = 1 and j2 = j or "
 819                         "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
 820         map = isl_map_transitive_closure(map, &exact);
 821         assert(exact);
 822         isl_map_free(map);
 823
 824         map = isl_map_read_from_str(ctx,
 825                 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
 826                         "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
 827                         "i2 = i + 1 and 3 <= j2 - j <= 4 and "
 828                         "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
 829         map = isl_map_transitive_closure(map, &exact);
 830         assert(exact);
 831         isl_map_free(map);
 832
 833         /* Kelly et al 1996, fig 12 */
 834         map = isl_map_read_from_str(ctx,
 835                 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
 836                         "1 <= i,j,j+1 <= n or "
 837                         "j = n and j2 = 1 and i2 = i + 1 and "
 838                         "1 <= i,i+1 <= n }", -1);
 839         map = isl_map_transitive_closure(map, &exact);
 840         assert(exact);
 841         map2 = isl_map_read_from_str(ctx,
 842                 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
 843                         "1 <= i <= n and i = i2 or "
 844                         "1 <= i < i2 <= n and 1 <= j <= n and "
 845                         "1 <= j2 <= n }", -1);
 846         assert(isl_map_is_equal(map, map2));
 847         isl_map_free(map2);
 848         isl_map_free(map);
 849
 850         /* Omega's closure4 */
 851         map = isl_map_read_from_str(ctx,
 852                 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
 853                         "1 <= x,y <= 10 or "
 854                         "x2 = x + 1 and y2 = y and "
 855                         "1 <= x <= 20 && 5 <= y <= 15 }", -1);
 856         map = isl_map_transitive_closure(map, &exact);
 857         assert(exact);
 858         isl_map_free(map);
 859
 860         map = isl_map_read_from_str(ctx,
 861                 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
 862         map = isl_map_transitive_closure(map, &exact);
 863         assert(!exact);
 864         map2 = isl_map_read_from_str(ctx,
 865                 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
 866         assert(isl_map_is_equal(map, map2));
 867         isl_map_free(map);
 868         isl_map_free(map2);
 869 }
 870
 871 int main()
 872 {
 873         struct isl_ctx *ctx;
 874
 875         srcdir = getenv("srcdir");
 876         assert(srcdir);
 877
 878         ctx = isl_ctx_alloc();
 879         test_read(ctx);
 880         test_construction(ctx);
 881         test_dim(ctx);
 882         test_div(ctx);
 883         test_application(ctx);
 884         test_affine_hull(ctx);
 885         test_convex_hull(ctx);
 886         test_gist(ctx);
 887         test_coalesce(ctx);
 888         test_closure(ctx);
 889         isl_ctx_free(ctx);
 890         return 0;
 891 }