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