isl_test.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2010      INRIA Saclay
   4  * Copyright 2012-2013 Ecole Normale Superieure
   5  *
   6  * Use of this software is governed by the MIT license
   7  *
   8  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   9  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
  10  * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
  11  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
  12  * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  13  */
  14
  15 #include <assert.h>
  16 #include <stdio.h>
  17 #include <limits.h>
  18 #include <isl_ctx_private.h>
  19 #include <isl_map_private.h>
  20 #include <isl_aff_private.h>
  21 #include <isl/set.h>
  22 #include <isl/flow.h>
  23 #include <isl_constraint_private.h>
  24 #include <isl/polynomial.h>
  25 #include <isl/union_map.h>
  26 #include <isl_factorization.h>
  27 #include <isl/schedule.h>
  28 #include <isl_options_private.h>
  29 #include <isl/vertices.h>
  30 #include <isl/ast_build.h>
  31 #include <isl/val.h>
  32
  33 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
  34
  35 static char *srcdir;
  36
  37 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
  38         char *filename;
  39         int length;
  40         char *pattern = "%s/test_inputs/%s.%s";
  41
  42         length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
  43                 + strlen(suffix) + 1;
  44         filename = isl_alloc_array(ctx, char, length);
  45
  46         if (!filename)
  47                 return NULL;
  48
  49         sprintf(filename, pattern, srcdir, name, suffix);
  50
  51         return filename;
  52 }
  53
  54 void test_parse_map(isl_ctx *ctx, const char *str)
  55 {
  56         isl_map *map;
  57
  58         map = isl_map_read_from_str(ctx, str);
  59         assert(map);
  60         isl_map_free(map);
  61 }
  62
  63 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
  64 {
  65         isl_map *map, *map2;
  66         int equal;
  67
  68         map = isl_map_read_from_str(ctx, str);
  69         map2 = isl_map_read_from_str(ctx, str2);
  70         equal = isl_map_is_equal(map, map2);
  71         isl_map_free(map);
  72         isl_map_free(map2);
  73
  74         if (equal < 0)
  75                 return -1;
  76         if (!equal)
  77                 isl_die(ctx, isl_error_unknown, "maps not equal",
  78                         return -1);
  79
  80         return 0;
  81 }
  82
  83 void test_parse_pwqp(isl_ctx *ctx, const char *str)
  84 {
  85         isl_pw_qpolynomial *pwqp;
  86
  87         pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
  88         assert(pwqp);
  89         isl_pw_qpolynomial_free(pwqp);
  90 }
  91
  92 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
  93 {
  94         isl_pw_aff *pwaff;
  95
  96         pwaff = isl_pw_aff_read_from_str(ctx, str);
  97         assert(pwaff);
  98         isl_pw_aff_free(pwaff);
  99 }
 100
 101 int test_parse(struct isl_ctx *ctx)
 102 {
 103         isl_map *map, *map2;
 104         const char *str, *str2;
 105
 106         str = "{ [i] -> [-i] }";
 107         map = isl_map_read_from_str(ctx, str);
 108         assert(map);
 109         isl_map_free(map);
 110
 111         str = "{ A[i] -> L[([i/3])] }";
 112         map = isl_map_read_from_str(ctx, str);
 113         assert(map);
 114         isl_map_free(map);
 115
 116         test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
 117         test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
 118                                 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
 119
 120         str = "{ [x,y]  : [([x/2]+y)/3] >= 1 }";
 121         str2 = "{ [x, y] : 2y >= 6 - x }";
 122         if (test_parse_map_equal(ctx, str, str2) < 0)
 123                 return -1;
 124
 125         if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
 126                                       "{ [x,y] : x <= y, 2*y + 3 }") < 0)
 127                 return -1;
 128         str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
 129         if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
 130                                         str) < 0)
 131                 return -1;
 132
 133         str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
 134         map = isl_map_read_from_str(ctx, str);
 135         str = "{ [new, old] -> [o0, o1] : "
 136                "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
 137                "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
 138                "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
 139         map2 = isl_map_read_from_str(ctx, str);
 140         assert(isl_map_is_equal(map, map2));
 141         isl_map_free(map);
 142         isl_map_free(map2);
 143
 144         str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
 145         map = isl_map_read_from_str(ctx, str);
 146         str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
 147         map2 = isl_map_read_from_str(ctx, str);
 148         assert(isl_map_is_equal(map, map2));
 149         isl_map_free(map);
 150         isl_map_free(map2);
 151
 152         str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
 153         str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
 154         if (test_parse_map_equal(ctx, str, str2) < 0)
 155                 return -1;
 156
 157         str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
 158         str2 = "{ [i,j] -> [min(i,j)] }";
 159         if (test_parse_map_equal(ctx, str, str2) < 0)
 160                 return -1;
 161
 162         str = "{ [i,j] : i != j }";
 163         str2 = "{ [i,j] : i < j or i > j }";
 164         if (test_parse_map_equal(ctx, str, str2) < 0)
 165                 return -1;
 166
 167         str = "{ [i,j] : (i+1)*2 >= j }";
 168         str2 = "{ [i, j] : j <= 2 + 2i }";
 169         if (test_parse_map_equal(ctx, str, str2) < 0)
 170                 return -1;
 171
 172         str = "{ [i] -> [i > 0 ? 4 : 5] }";
 173         str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
 174         if (test_parse_map_equal(ctx, str, str2) < 0)
 175                 return -1;
 176
 177         str = "[N=2,M] -> { [i=[(M+N)/4]] }";
 178         str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
 179         if (test_parse_map_equal(ctx, str, str2) < 0)
 180                 return -1;
 181
 182         str = "{ [x] : x >= 0 }";
 183         str2 = "{ [x] : x-0 >= 0 }";
 184         if (test_parse_map_equal(ctx, str, str2) < 0)
 185                 return -1;
 186
 187         str = "{ [i] : ((i > 10)) }";
 188         str2 = "{ [i] : i >= 11 }";
 189         if (test_parse_map_equal(ctx, str, str2) < 0)
 190                 return -1;
 191
 192         str = "{ [i] -> [0] }";
 193         str2 = "{ [i] -> [0 * i] }";
 194         if (test_parse_map_equal(ctx, str, str2) < 0)
 195                 return -1;
 196
 197         test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
 198         test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
 199         test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
 200         test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
 201
 202         if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
 203                                       "{ [a] -> [b] : true }") < 0)
 204                 return -1;
 205
 206         if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
 207                                       "{ [i] : i <= 10 }") < 0)
 208                 return -1;
 209
 210         if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
 211                                       "[n] -> { [i] : i <= n }") < 0)
 212                 return -1;
 213
 214         if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
 215                 return -1;
 216
 217         if (test_parse_map_equal(ctx, "{ [i] : 2*floor(i/2) = i }",
 218                                       "{ [i] : exists a : i = 2 a }") < 0)
 219                 return -1;
 220
 221         if (test_parse_map_equal(ctx, "{ [a] -> [b] : a = 5 implies b = 5 }",
 222                                       "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
 223                 return -1;
 224
 225         if (test_parse_map_equal(ctx, "{ [a] -> [a - 1 : a > 0] }",
 226                                       "{ [a] -> [a - 1] : a > 0 }") < 0)
 227                 return -1;
 228         if (test_parse_map_equal(ctx,
 229             "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
 230             "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
 231                 return -1;
 232         if (test_parse_map_equal(ctx,
 233             "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
 234             "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
 235                 return -1;
 236         if (test_parse_map_equal(ctx,
 237             "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
 238             "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
 239                 return -1;
 240         if (test_parse_map_equal(ctx,
 241             "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
 242             "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
 243                 return -1;
 244         if (test_parse_map_equal(ctx,
 245             "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
 246             "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
 247                 return -1;
 248
 249         return 0;
 250 }
 251
 252 void test_read(struct isl_ctx *ctx)
 253 {
 254         char *filename;
 255         FILE *input;
 256         struct isl_basic_set *bset1, *bset2;
 257         const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
 258
 259         filename = get_filename(ctx, "set", "omega");
 260         assert(filename);
 261         input = fopen(filename, "r");
 262         assert(input);
 263
 264         bset1 = isl_basic_set_read_from_file(ctx, input);
 265         bset2 = isl_basic_set_read_from_str(ctx, str);
 266
 267         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 268
 269         isl_basic_set_free(bset1);
 270         isl_basic_set_free(bset2);
 271         free(filename);
 272
 273         fclose(input);
 274 }
 275
 276 void test_bounded(struct isl_ctx *ctx)
 277 {
 278         isl_set *set;
 279         int bounded;
 280
 281         set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
 282         bounded = isl_set_is_bounded(set);
 283         assert(bounded);
 284         isl_set_free(set);
 285
 286         set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
 287         bounded = isl_set_is_bounded(set);
 288         assert(!bounded);
 289         isl_set_free(set);
 290
 291         set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
 292         bounded = isl_set_is_bounded(set);
 293         assert(!bounded);
 294         isl_set_free(set);
 295 }
 296
 297 /* Construct the basic set { [i] : 5 <= i <= N } */
 298 void test_construction(struct isl_ctx *ctx)
 299 {
 300         isl_int v;
 301         isl_space *dim;
 302         isl_local_space *ls;
 303         struct isl_basic_set *bset;
 304         struct isl_constraint *c;
 305
 306         isl_int_init(v);
 307
 308         dim = isl_space_set_alloc(ctx, 1, 1);
 309         bset = isl_basic_set_universe(isl_space_copy(dim));
 310         ls = isl_local_space_from_space(dim);
 311
 312         c = isl_inequality_alloc(isl_local_space_copy(ls));
 313         isl_int_set_si(v, -1);
 314         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 315         isl_int_set_si(v, 1);
 316         isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
 317         bset = isl_basic_set_add_constraint(bset, c);
 318
 319         c = isl_inequality_alloc(isl_local_space_copy(ls));
 320         isl_int_set_si(v, 1);
 321         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 322         isl_int_set_si(v, -5);
 323         isl_constraint_set_constant(c, v);
 324         bset = isl_basic_set_add_constraint(bset, c);
 325
 326         isl_local_space_free(ls);
 327         isl_basic_set_free(bset);
 328
 329         isl_int_clear(v);
 330 }
 331
 332 void test_dim(struct isl_ctx *ctx)
 333 {
 334         const char *str;
 335         isl_map *map1, *map2;
 336
 337         map1 = isl_map_read_from_str(ctx,
 338             "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
 339         map1 = isl_map_add_dims(map1, isl_dim_in, 1);
 340         map2 = isl_map_read_from_str(ctx,
 341             "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
 342         assert(isl_map_is_equal(map1, map2));
 343         isl_map_free(map2);
 344
 345         map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
 346         map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
 347         assert(isl_map_is_equal(map1, map2));
 348
 349         isl_map_free(map1);
 350         isl_map_free(map2);
 351
 352         str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
 353         map1 = isl_map_read_from_str(ctx, str);
 354         str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
 355         map2 = isl_map_read_from_str(ctx, str);
 356         map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
 357         assert(isl_map_is_equal(map1, map2));
 358
 359         isl_map_free(map1);
 360         isl_map_free(map2);
 361 }
 362
 363 struct {
 364         __isl_give isl_val *(*op)(__isl_take isl_val *v);
 365         const char *arg;
 366         const char *res;
 367 } val_un_tests[] = {
 368         { &isl_val_neg, "0", "0" },
 369         { &isl_val_abs, "0", "0" },
 370         { &isl_val_2exp, "0", "1" },
 371         { &isl_val_floor, "0", "0" },
 372         { &isl_val_ceil, "0", "0" },
 373         { &isl_val_neg, "1", "-1" },
 374         { &isl_val_neg, "-1", "1" },
 375         { &isl_val_neg, "1/2", "-1/2" },
 376         { &isl_val_neg, "-1/2", "1/2" },
 377         { &isl_val_neg, "infty", "-infty" },
 378         { &isl_val_neg, "-infty", "infty" },
 379         { &isl_val_neg, "NaN", "NaN" },
 380         { &isl_val_abs, "1", "1" },
 381         { &isl_val_abs, "-1", "1" },
 382         { &isl_val_abs, "1/2", "1/2" },
 383         { &isl_val_abs, "-1/2", "1/2" },
 384         { &isl_val_abs, "infty", "infty" },
 385         { &isl_val_abs, "-infty", "infty" },
 386         { &isl_val_abs, "NaN", "NaN" },
 387         { &isl_val_floor, "1", "1" },
 388         { &isl_val_floor, "-1", "-1" },
 389         { &isl_val_floor, "1/2", "0" },
 390         { &isl_val_floor, "-1/2", "-1" },
 391         { &isl_val_floor, "infty", "infty" },
 392         { &isl_val_floor, "-infty", "-infty" },
 393         { &isl_val_floor, "NaN", "NaN" },
 394         { &isl_val_ceil, "1", "1" },
 395         { &isl_val_ceil, "-1", "-1" },
 396         { &isl_val_ceil, "1/2", "1" },
 397         { &isl_val_ceil, "-1/2", "0" },
 398         { &isl_val_ceil, "infty", "infty" },
 399         { &isl_val_ceil, "-infty", "-infty" },
 400         { &isl_val_ceil, "NaN", "NaN" },
 401         { &isl_val_2exp, "-3", "1/8" },
 402         { &isl_val_2exp, "-1", "1/2" },
 403         { &isl_val_2exp, "1", "2" },
 404         { &isl_val_2exp, "2", "4" },
 405         { &isl_val_2exp, "3", "8" },
 406 };
 407
 408 /* Perform some basic tests of unary operations on isl_val objects.
 409  */
 410 static int test_un_val(isl_ctx *ctx)
 411 {
 412         int i;
 413         isl_val *v, *res;
 414         __isl_give isl_val *(*fn)(__isl_take isl_val *v);
 415         int ok;
 416
 417         for (i = 0; i < ARRAY_SIZE(val_un_tests); ++i) {
 418                 v = isl_val_read_from_str(ctx, val_un_tests[i].arg);
 419                 res = isl_val_read_from_str(ctx, val_un_tests[i].res);
 420                 fn = val_un_tests[i].op;
 421                 v = fn(v);
 422                 if (isl_val_is_nan(res))
 423                         ok = isl_val_is_nan(v);
 424                 else
 425                         ok = isl_val_eq(v, res);
 426                 isl_val_free(v);
 427                 isl_val_free(res);
 428                 if (ok < 0)
 429                         return -1;
 430                 if (!ok)
 431                         isl_die(ctx, isl_error_unknown,
 432                                 "unexpected result", return -1);
 433         }
 434
 435         return 0;
 436 }
 437
 438 struct {
 439         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
 440                                 __isl_take isl_val *v2);
 441 } val_bin_op[] = {
 442         ['+'] = { &isl_val_add },
 443         ['-'] = { &isl_val_sub },
 444         ['*'] = { &isl_val_mul },
 445         ['/'] = { &isl_val_div },
 446         ['g'] = { &isl_val_gcd },
 447         ['m'] = { &isl_val_min },
 448         ['M'] = { &isl_val_max },
 449 };
 450
 451 struct {
 452         const char *arg1;
 453         unsigned char op;
 454         const char *arg2;
 455         const char *res;
 456 } val_bin_tests[] = {
 457         { "0", '+', "0", "0" },
 458         { "1", '+', "0", "1" },
 459         { "1", '+', "1", "2" },
 460         { "1", '-', "1", "0" },
 461         { "1", '*', "1", "1" },
 462         { "1", '/', "1", "1" },
 463         { "2", '*', "3", "6" },
 464         { "2", '*', "1/2", "1" },
 465         { "2", '*', "1/3", "2/3" },
 466         { "2/3", '*', "3/5", "2/5" },
 467         { "2/3", '*', "7/5", "14/15" },
 468         { "2", '/', "1/2", "4" },
 469         { "-2", '/', "-1/2", "4" },
 470         { "-2", '/', "1/2", "-4" },
 471         { "2", '/', "-1/2", "-4" },
 472         { "2", '/', "2", "1" },
 473         { "2", '/', "3", "2/3" },
 474         { "2/3", '/', "5/3", "2/5" },
 475         { "2/3", '/', "5/7", "14/15" },
 476         { "0", '/', "0", "NaN" },
 477         { "42", '/', "0", "NaN" },
 478         { "-42", '/', "0", "NaN" },
 479         { "infty", '/', "0", "NaN" },
 480         { "-infty", '/', "0", "NaN" },
 481         { "NaN", '/', "0", "NaN" },
 482         { "0", '/', "NaN", "NaN" },
 483         { "42", '/', "NaN", "NaN" },
 484         { "-42", '/', "NaN", "NaN" },
 485         { "infty", '/', "NaN", "NaN" },
 486         { "-infty", '/', "NaN", "NaN" },
 487         { "NaN", '/', "NaN", "NaN" },
 488         { "0", '/', "infty", "0" },
 489         { "42", '/', "infty", "0" },
 490         { "-42", '/', "infty", "0" },
 491         { "infty", '/', "infty", "NaN" },
 492         { "-infty", '/', "infty", "NaN" },
 493         { "NaN", '/', "infty", "NaN" },
 494         { "0", '/', "-infty", "0" },
 495         { "42", '/', "-infty", "0" },
 496         { "-42", '/', "-infty", "0" },
 497         { "infty", '/', "-infty", "NaN" },
 498         { "-infty", '/', "-infty", "NaN" },
 499         { "NaN", '/', "-infty", "NaN" },
 500         { "1", '-', "1/3", "2/3" },
 501         { "1/3", '+', "1/2", "5/6" },
 502         { "1/2", '+', "1/2", "1" },
 503         { "3/4", '-', "1/4", "1/2" },
 504         { "1/2", '-', "1/3", "1/6" },
 505         { "infty", '+', "42", "infty" },
 506         { "infty", '+', "infty", "infty" },
 507         { "42", '+', "infty", "infty" },
 508         { "infty", '-', "infty", "NaN" },
 509         { "infty", '*', "infty", "infty" },
 510         { "infty", '*', "-infty", "-infty" },
 511         { "-infty", '*', "infty", "-infty" },
 512         { "-infty", '*', "-infty", "infty" },
 513         { "0", '*', "infty", "NaN" },
 514         { "1", '*', "infty", "infty" },
 515         { "infty", '*', "0", "NaN" },
 516         { "infty", '*', "42", "infty" },
 517         { "42", '-', "infty", "-infty" },
 518         { "infty", '+', "-infty", "NaN" },
 519         { "4", 'g', "6", "2" },
 520         { "5", 'g', "6", "1" },
 521         { "42", 'm', "3", "3" },
 522         { "42", 'M', "3", "42" },
 523         { "3", 'm', "42", "3" },
 524         { "3", 'M', "42", "42" },
 525         { "42", 'm', "infty", "42" },
 526         { "42", 'M', "infty", "infty" },
 527         { "42", 'm', "-infty", "-infty" },
 528         { "42", 'M', "-infty", "42" },
 529         { "42", 'm', "NaN", "NaN" },
 530         { "42", 'M', "NaN", "NaN" },
 531         { "infty", 'm', "-infty", "-infty" },
 532         { "infty", 'M', "-infty", "infty" },
 533 };
 534
 535 /* Perform some basic tests of binary operations on isl_val objects.
 536  */
 537 static int test_bin_val(isl_ctx *ctx)
 538 {
 539         int i;
 540         isl_val *v1, *v2, *res;
 541         __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
 542                                 __isl_take isl_val *v2);
 543         int ok;
 544
 545         for (i = 0; i < ARRAY_SIZE(val_bin_tests); ++i) {
 546                 v1 = isl_val_read_from_str(ctx, val_bin_tests[i].arg1);
 547                 v2 = isl_val_read_from_str(ctx, val_bin_tests[i].arg2);
 548                 res = isl_val_read_from_str(ctx, val_bin_tests[i].res);
 549                 fn = val_bin_op[val_bin_tests[i].op].fn;
 550                 v1 = fn(v1, v2);
 551                 if (isl_val_is_nan(res))
 552                         ok = isl_val_is_nan(v1);
 553                 else
 554                         ok = isl_val_eq(v1, res);
 555                 isl_val_free(v1);
 556                 isl_val_free(res);
 557                 if (ok < 0)
 558                         return -1;
 559                 if (!ok)
 560                         isl_die(ctx, isl_error_unknown,
 561                                 "unexpected result", return -1);
 562         }
 563
 564         return 0;
 565 }
 566
 567 /* Perform some basic tests on isl_val objects.
 568  */
 569 static int test_val(isl_ctx *ctx)
 570 {
 571         if (test_un_val(ctx) < 0)
 572                 return -1;
 573         if (test_bin_val(ctx) < 0)
 574                 return -1;
 575         return 0;
 576 }
 577
 578 static int test_div(isl_ctx *ctx)
 579 {
 580         unsigned n;
 581         const char *str;
 582         int empty;
 583         isl_int v;
 584         isl_space *dim;
 585         isl_set *set;
 586         isl_local_space *ls;
 587         struct isl_basic_set *bset;
 588         struct isl_constraint *c;
 589
 590         isl_int_init(v);
 591
 592         /* test 1 */
 593         dim = isl_space_set_alloc(ctx, 0, 3);
 594         bset = isl_basic_set_universe(isl_space_copy(dim));
 595         ls = isl_local_space_from_space(dim);
 596
 597         c = isl_equality_alloc(isl_local_space_copy(ls));
 598         isl_int_set_si(v, -1);
 599         isl_constraint_set_constant(c, v);
 600         isl_int_set_si(v, 1);
 601         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 602         isl_int_set_si(v, 3);
 603         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 604         bset = isl_basic_set_add_constraint(bset, c);
 605
 606         c = isl_equality_alloc(isl_local_space_copy(ls));
 607         isl_int_set_si(v, 1);
 608         isl_constraint_set_constant(c, v);
 609         isl_int_set_si(v, -1);
 610         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 611         isl_int_set_si(v, 3);
 612         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 613         bset = isl_basic_set_add_constraint(bset, c);
 614
 615         bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
 616
 617         assert(bset && bset->n_div == 1);
 618         isl_local_space_free(ls);
 619         isl_basic_set_free(bset);
 620
 621         /* test 2 */
 622         dim = isl_space_set_alloc(ctx, 0, 3);
 623         bset = isl_basic_set_universe(isl_space_copy(dim));
 624         ls = isl_local_space_from_space(dim);
 625
 626         c = isl_equality_alloc(isl_local_space_copy(ls));
 627         isl_int_set_si(v, 1);
 628         isl_constraint_set_constant(c, v);
 629         isl_int_set_si(v, -1);
 630         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 631         isl_int_set_si(v, 3);
 632         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 633         bset = isl_basic_set_add_constraint(bset, c);
 634
 635         c = isl_equality_alloc(isl_local_space_copy(ls));
 636         isl_int_set_si(v, -1);
 637         isl_constraint_set_constant(c, v);
 638         isl_int_set_si(v, 1);
 639         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 640         isl_int_set_si(v, 3);
 641         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 642         bset = isl_basic_set_add_constraint(bset, c);
 643
 644         bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
 645
 646         assert(bset && bset->n_div == 1);
 647         isl_local_space_free(ls);
 648         isl_basic_set_free(bset);
 649
 650         /* test 3 */
 651         dim = isl_space_set_alloc(ctx, 0, 3);
 652         bset = isl_basic_set_universe(isl_space_copy(dim));
 653         ls = isl_local_space_from_space(dim);
 654
 655         c = isl_equality_alloc(isl_local_space_copy(ls));
 656         isl_int_set_si(v, 1);
 657         isl_constraint_set_constant(c, v);
 658         isl_int_set_si(v, -1);
 659         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 660         isl_int_set_si(v, 3);
 661         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 662         bset = isl_basic_set_add_constraint(bset, c);
 663
 664         c = isl_equality_alloc(isl_local_space_copy(ls));
 665         isl_int_set_si(v, -3);
 666         isl_constraint_set_constant(c, v);
 667         isl_int_set_si(v, 1);
 668         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 669         isl_int_set_si(v, 4);
 670         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 671         bset = isl_basic_set_add_constraint(bset, c);
 672
 673         bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
 674
 675         assert(bset && bset->n_div == 1);
 676         isl_local_space_free(ls);
 677         isl_basic_set_free(bset);
 678
 679         /* test 4 */
 680         dim = isl_space_set_alloc(ctx, 0, 3);
 681         bset = isl_basic_set_universe(isl_space_copy(dim));
 682         ls = isl_local_space_from_space(dim);
 683
 684         c = isl_equality_alloc(isl_local_space_copy(ls));
 685         isl_int_set_si(v, 2);
 686         isl_constraint_set_constant(c, v);
 687         isl_int_set_si(v, -1);
 688         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 689         isl_int_set_si(v, 3);
 690         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 691         bset = isl_basic_set_add_constraint(bset, c);
 692
 693         c = isl_equality_alloc(isl_local_space_copy(ls));
 694         isl_int_set_si(v, -1);
 695         isl_constraint_set_constant(c, v);
 696         isl_int_set_si(v, 1);
 697         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 698         isl_int_set_si(v, 6);
 699         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 700         bset = isl_basic_set_add_constraint(bset, c);
 701
 702         bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
 703
 704         assert(isl_basic_set_is_empty(bset));
 705         isl_local_space_free(ls);
 706         isl_basic_set_free(bset);
 707
 708         /* test 5 */
 709         dim = isl_space_set_alloc(ctx, 0, 3);
 710         bset = isl_basic_set_universe(isl_space_copy(dim));
 711         ls = isl_local_space_from_space(dim);
 712
 713         c = isl_equality_alloc(isl_local_space_copy(ls));
 714         isl_int_set_si(v, -1);
 715         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 716         isl_int_set_si(v, 3);
 717         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 718         bset = isl_basic_set_add_constraint(bset, c);
 719
 720         c = isl_equality_alloc(isl_local_space_copy(ls));
 721         isl_int_set_si(v, 1);
 722         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 723         isl_int_set_si(v, -3);
 724         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 725         bset = isl_basic_set_add_constraint(bset, c);
 726
 727         bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
 728
 729         assert(bset && bset->n_div == 0);
 730         isl_basic_set_free(bset);
 731         isl_local_space_free(ls);
 732
 733         /* test 6 */
 734         dim = isl_space_set_alloc(ctx, 0, 3);
 735         bset = isl_basic_set_universe(isl_space_copy(dim));
 736         ls = isl_local_space_from_space(dim);
 737
 738         c = isl_equality_alloc(isl_local_space_copy(ls));
 739         isl_int_set_si(v, -1);
 740         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 741         isl_int_set_si(v, 6);
 742         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 743         bset = isl_basic_set_add_constraint(bset, c);
 744
 745         c = isl_equality_alloc(isl_local_space_copy(ls));
 746         isl_int_set_si(v, 1);
 747         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 748         isl_int_set_si(v, -3);
 749         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 750         bset = isl_basic_set_add_constraint(bset, c);
 751
 752         bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
 753
 754         assert(bset && bset->n_div == 1);
 755         isl_basic_set_free(bset);
 756         isl_local_space_free(ls);
 757
 758         /* test 7 */
 759         /* This test is a bit tricky.  We set up an equality
 760          *              a + 3b + 3c = 6 e0
 761          * Normalization of divs creates _two_ divs
 762          *              a = 3 e0
 763          *              c - b - e0 = 2 e1
 764          * Afterwards e0 is removed again because it has coefficient -1
 765          * and we end up with the original equality and div again.
 766          * Perhaps we can avoid the introduction of this temporary div.
 767          */
 768         dim = isl_space_set_alloc(ctx, 0, 4);
 769         bset = isl_basic_set_universe(isl_space_copy(dim));
 770         ls = isl_local_space_from_space(dim);
 771
 772         c = isl_equality_alloc(isl_local_space_copy(ls));
 773         isl_int_set_si(v, -1);
 774         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 775         isl_int_set_si(v, -3);
 776         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 777         isl_int_set_si(v, -3);
 778         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 779         isl_int_set_si(v, 6);
 780         isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
 781         bset = isl_basic_set_add_constraint(bset, c);
 782
 783         bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
 784
 785         /* Test disabled for now */
 786         /*
 787         assert(bset && bset->n_div == 1);
 788         */
 789         isl_local_space_free(ls);
 790         isl_basic_set_free(bset);
 791
 792         /* test 8 */
 793         dim = isl_space_set_alloc(ctx, 0, 5);
 794         bset = isl_basic_set_universe(isl_space_copy(dim));
 795         ls = isl_local_space_from_space(dim);
 796
 797         c = isl_equality_alloc(isl_local_space_copy(ls));
 798         isl_int_set_si(v, -1);
 799         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 800         isl_int_set_si(v, -3);
 801         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 802         isl_int_set_si(v, -3);
 803         isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
 804         isl_int_set_si(v, 6);
 805         isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
 806         bset = isl_basic_set_add_constraint(bset, c);
 807
 808         c = isl_equality_alloc(isl_local_space_copy(ls));
 809         isl_int_set_si(v, -1);
 810         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 811         isl_int_set_si(v, 1);
 812         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 813         isl_int_set_si(v, 1);
 814         isl_constraint_set_constant(c, v);
 815         bset = isl_basic_set_add_constraint(bset, c);
 816
 817         bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
 818
 819         /* Test disabled for now */
 820         /*
 821         assert(bset && bset->n_div == 1);
 822         */
 823         isl_local_space_free(ls);
 824         isl_basic_set_free(bset);
 825
 826         /* test 9 */
 827         dim = isl_space_set_alloc(ctx, 0, 4);
 828         bset = isl_basic_set_universe(isl_space_copy(dim));
 829         ls = isl_local_space_from_space(dim);
 830
 831         c = isl_equality_alloc(isl_local_space_copy(ls));
 832         isl_int_set_si(v, 1);
 833         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 834         isl_int_set_si(v, -1);
 835         isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
 836         isl_int_set_si(v, -2);
 837         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 838         bset = isl_basic_set_add_constraint(bset, c);
 839
 840         c = isl_equality_alloc(isl_local_space_copy(ls));
 841         isl_int_set_si(v, -1);
 842         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 843         isl_int_set_si(v, 3);
 844         isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
 845         isl_int_set_si(v, 2);
 846         isl_constraint_set_constant(c, v);
 847         bset = isl_basic_set_add_constraint(bset, c);
 848
 849         bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
 850
 851         bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
 852
 853         assert(!isl_basic_set_is_empty(bset));
 854
 855         isl_local_space_free(ls);
 856         isl_basic_set_free(bset);
 857
 858         /* test 10 */
 859         dim = isl_space_set_alloc(ctx, 0, 3);
 860         bset = isl_basic_set_universe(isl_space_copy(dim));
 861         ls = isl_local_space_from_space(dim);
 862
 863         c = isl_equality_alloc(isl_local_space_copy(ls));
 864         isl_int_set_si(v, 1);
 865         isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
 866         isl_int_set_si(v, -2);
 867         isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
 868         bset = isl_basic_set_add_constraint(bset, c);
 869
 870         bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
 871
 872         bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
 873
 874         isl_local_space_free(ls);
 875         isl_basic_set_free(bset);
 876
 877         isl_int_clear(v);
 878
 879         str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
 880             "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
 881         set = isl_set_read_from_str(ctx, str);
 882         set = isl_set_compute_divs(set);
 883         isl_set_free(set);
 884         if (!set)
 885                 return -1;
 886
 887         str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
 888         bset = isl_basic_set_read_from_str(ctx, str);
 889         n = isl_basic_set_dim(bset, isl_dim_div);
 890         isl_basic_set_free(bset);
 891         if (!bset)
 892                 return -1;
 893         if (n != 0)
 894                 isl_die(ctx, isl_error_unknown,
 895                         "expecting no existentials", return -1);
 896
 897         str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
 898         set = isl_set_read_from_str(ctx, str);
 899         set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
 900         set = isl_set_fix_si(set, isl_dim_set, 2, -3);
 901         empty = isl_set_is_empty(set);
 902         isl_set_free(set);
 903         if (empty < 0)
 904                 return -1;
 905         if (!empty)
 906                 isl_die(ctx, isl_error_unknown,
 907                         "result not as accurate as expected", return -1);
 908
 909         return 0;
 910 }
 911
 912 void test_application_case(struct isl_ctx *ctx, const char *name)
 913 {
 914         char *filename;
 915         FILE *input;
 916         struct isl_basic_set *bset1, *bset2;
 917         struct isl_basic_map *bmap;
 918
 919         filename = get_filename(ctx, name, "omega");
 920         assert(filename);
 921         input = fopen(filename, "r");
 922         assert(input);
 923
 924         bset1 = isl_basic_set_read_from_file(ctx, input);
 925         bmap = isl_basic_map_read_from_file(ctx, input);
 926
 927         bset1 = isl_basic_set_apply(bset1, bmap);
 928
 929         bset2 = isl_basic_set_read_from_file(ctx, input);
 930
 931         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 932
 933         isl_basic_set_free(bset1);
 934         isl_basic_set_free(bset2);
 935         free(filename);
 936
 937         fclose(input);
 938 }
 939
 940 void test_application(struct isl_ctx *ctx)
 941 {
 942         test_application_case(ctx, "application");
 943         test_application_case(ctx, "application2");
 944 }
 945
 946 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
 947 {
 948         char *filename;
 949         FILE *input;
 950         struct isl_basic_set *bset1, *bset2;
 951
 952         filename = get_filename(ctx, name, "polylib");
 953         assert(filename);
 954         input = fopen(filename, "r");
 955         assert(input);
 956
 957         bset1 = isl_basic_set_read_from_file(ctx, input);
 958         bset2 = isl_basic_set_read_from_file(ctx, input);
 959
 960         bset1 = isl_basic_set_affine_hull(bset1);
 961
 962         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
 963
 964         isl_basic_set_free(bset1);
 965         isl_basic_set_free(bset2);
 966         free(filename);
 967
 968         fclose(input);
 969 }
 970
 971 int test_affine_hull(struct isl_ctx *ctx)
 972 {
 973         const char *str;
 974         isl_set *set;
 975         isl_basic_set *bset, *bset2;
 976         int n;
 977         int subset;
 978
 979         test_affine_hull_case(ctx, "affine2");
 980         test_affine_hull_case(ctx, "affine");
 981         test_affine_hull_case(ctx, "affine3");
 982
 983         str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
 984                         "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
 985                         "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
 986                         "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
 987         set = isl_set_read_from_str(ctx, str);
 988         bset = isl_set_affine_hull(set);
 989         n = isl_basic_set_dim(bset, isl_dim_div);
 990         isl_basic_set_free(bset);
 991         if (n != 0)
 992                 isl_die(ctx, isl_error_unknown, "not expecting any divs",
 993                         return -1);
 994
 995         /* Check that isl_map_affine_hull is not confused by
 996          * the reordering of divs in isl_map_align_divs.
 997          */
 998         str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
 999                                 "32e0 = b and 32e1 = c); "
1000                 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1001         set = isl_set_read_from_str(ctx, str);
1002         bset = isl_set_affine_hull(set);
1003         isl_basic_set_free(bset);
1004         if (!bset)
1005                 return -1;
1006
1007         str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1008                         "32e2 = 31 + 31e0 }";
1009         set = isl_set_read_from_str(ctx, str);
1010         bset = isl_set_affine_hull(set);
1011         str = "{ [a] : exists e : a = 32 e }";
1012         bset2 = isl_basic_set_read_from_str(ctx, str);
1013         subset = isl_basic_set_is_subset(bset, bset2);
1014         isl_basic_set_free(bset);
1015         isl_basic_set_free(bset2);
1016         if (subset < 0)
1017                 return -1;
1018         if (!subset)
1019                 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
1020                         return -1);
1021
1022         return 0;
1023 }
1024
1025 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
1026 {
1027         char *filename;
1028         FILE *input;
1029         struct isl_basic_set *bset1, *bset2;
1030         struct isl_set *set;
1031
1032         filename = get_filename(ctx, name, "polylib");
1033         assert(filename);
1034         input = fopen(filename, "r");
1035         assert(input);
1036
1037         bset1 = isl_basic_set_read_from_file(ctx, input);
1038         bset2 = isl_basic_set_read_from_file(ctx, input);
1039
1040         set = isl_basic_set_union(bset1, bset2);
1041         bset1 = isl_set_convex_hull(set);
1042
1043         bset2 = isl_basic_set_read_from_file(ctx, input);
1044
1045         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1046
1047         isl_basic_set_free(bset1);
1048         isl_basic_set_free(bset2);
1049         free(filename);
1050
1051         fclose(input);
1052 }
1053
1054 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
1055 {
1056         const char *str1, *str2;
1057         isl_set *set1, *set2;
1058         int orig_convex = ctx->opt->convex;
1059         ctx->opt->convex = convex;
1060
1061         test_convex_hull_case(ctx, "convex0");
1062         test_convex_hull_case(ctx, "convex1");
1063         test_convex_hull_case(ctx, "convex2");
1064         test_convex_hull_case(ctx, "convex3");
1065         test_convex_hull_case(ctx, "convex4");
1066         test_convex_hull_case(ctx, "convex5");
1067         test_convex_hull_case(ctx, "convex6");
1068         test_convex_hull_case(ctx, "convex7");
1069         test_convex_hull_case(ctx, "convex8");
1070         test_convex_hull_case(ctx, "convex9");
1071         test_convex_hull_case(ctx, "convex10");
1072         test_convex_hull_case(ctx, "convex11");
1073         test_convex_hull_case(ctx, "convex12");
1074         test_convex_hull_case(ctx, "convex13");
1075         test_convex_hull_case(ctx, "convex14");
1076         test_convex_hull_case(ctx, "convex15");
1077
1078         str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1079                "(i0 = 1 and i1 = 0 and i2 = 1) or "
1080                "(i0 = 0 and i1 = 0 and i2 = 0) }";
1081         str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
1082         set1 = isl_set_read_from_str(ctx, str1);
1083         set2 = isl_set_read_from_str(ctx, str2);
1084         set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1085         assert(isl_set_is_equal(set1, set2));
1086         isl_set_free(set1);
1087         isl_set_free(set2);
1088
1089         ctx->opt->convex = orig_convex;
1090 }
1091
1092 void test_convex_hull(struct isl_ctx *ctx)
1093 {
1094         test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
1095         test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
1096 }
1097
1098 void test_gist_case(struct isl_ctx *ctx, const char *name)
1099 {
1100         char *filename;
1101         FILE *input;
1102         struct isl_basic_set *bset1, *bset2;
1103
1104         filename = get_filename(ctx, name, "polylib");
1105         assert(filename);
1106         input = fopen(filename, "r");
1107         assert(input);
1108
1109         bset1 = isl_basic_set_read_from_file(ctx, input);
1110         bset2 = isl_basic_set_read_from_file(ctx, input);
1111
1112         bset1 = isl_basic_set_gist(bset1, bset2);
1113
1114         bset2 = isl_basic_set_read_from_file(ctx, input);
1115
1116         assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1117
1118         isl_basic_set_free(bset1);
1119         isl_basic_set_free(bset2);
1120         free(filename);
1121
1122         fclose(input);
1123 }
1124
1125 static int test_gist(struct isl_ctx *ctx)
1126 {
1127         const char *str;
1128         isl_basic_set *bset1, *bset2;
1129         isl_map *map1, *map2;
1130
1131         test_gist_case(ctx, "gist1");
1132
1133         str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1134             "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1135             "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1136             "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1137             "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1138             "16e0 >= 16 + 16p6 + 15p10 and  p2 <= 15 and p3 >= 0 and "
1139             "p3 <= 31 and  p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1140             "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1141             "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1142         bset1 = isl_basic_set_read_from_str(ctx, str);
1143         str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1144             "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1145             "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1146             "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1147             "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1148             "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1149             "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1150             "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1151         bset2 = isl_basic_set_read_from_str(ctx, str);
1152         bset1 = isl_basic_set_gist(bset1, bset2);
1153         assert(bset1 && bset1->n_div == 0);
1154         isl_basic_set_free(bset1);
1155
1156         /* Check that the integer divisions of the second disjunct
1157          * do not spread to the first disjunct.
1158          */
1159         str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1160                 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1161                 "(exists (e0 = [(-1 + t1)/16], "
1162                         "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1163                         "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1164                         "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1165                         "o0 <= 4294967295 and t1 <= -1)) }";
1166         map1 = isl_map_read_from_str(ctx, str);
1167         str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1168         map2 = isl_map_read_from_str(ctx, str);
1169         map1 = isl_map_gist(map1, map2);
1170         if (!map1)
1171                 return -1;
1172         if (map1->n != 1)
1173                 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1174                         isl_map_free(map1); return -1);
1175         if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1176                 isl_die(ctx, isl_error_unknown, "expecting single div",
1177                         isl_map_free(map1); return -1);
1178         isl_map_free(map1);
1179
1180         return 0;
1181 }
1182
1183 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1184 {
1185         isl_set *set, *set2;
1186         int equal;
1187         int one;
1188
1189         set = isl_set_read_from_str(ctx, str);
1190         set = isl_set_coalesce(set);
1191         set2 = isl_set_read_from_str(ctx, str);
1192         equal = isl_set_is_equal(set, set2);
1193         one = set && set->n == 1;
1194         isl_set_free(set);
1195         isl_set_free(set2);
1196
1197         if (equal < 0)
1198                 return -1;
1199         if (!equal)
1200                 isl_die(ctx, isl_error_unknown,
1201                         "coalesced set not equal to input", return -1);
1202         if (check_one && !one)
1203                 isl_die(ctx, isl_error_unknown,
1204                         "coalesced set should not be a union", return -1);
1205
1206         return 0;
1207 }
1208
1209 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1210 {
1211         int r = 0;
1212         int bounded;
1213
1214         bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1215         isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1216
1217         if (test_coalesce_set(ctx,
1218                 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1219                         "-x - y + 1 >= 0 and -3 <= z <= 3;"
1220                 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1221                         "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1222                         "-10 <= y <= 0}", 1) < 0)
1223                 goto error;
1224         if (test_coalesce_set(ctx,
1225                 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1226                 goto error;
1227         if (test_coalesce_set(ctx,
1228                 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1229                 goto error;
1230
1231         if (0) {
1232 error:
1233                 r = -1;
1234         }
1235
1236         isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1237
1238         return r;
1239 }
1240
1241 /* Inputs for coalescing tests.
1242  * "str" is a string representation of the input set.
1243  * "single_disjunct" is set if we expect the result to consist of
1244  *      a single disjunct.
1245  */
1246 struct {
1247         int single_disjunct;
1248         const char *str;
1249 } coalesce_tests[] = {
1250         { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1251                        "y >= x & x >= 2 & 5 >= y }" },
1252         { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1253                        "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1254         { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1255                        "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1256         { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1257                        "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1258         { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1259                        "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1260         { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1261                        "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1262         { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1263         { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1264         { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1265         { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1266         { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1267         { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1268         { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1269         { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1270                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1271                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1272                 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1273                 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1274                 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1275                 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1276                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1277                 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1278                 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1279                 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1280                 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1281                 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1282                 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1283                 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1284                 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1285                 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1286                 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1287         { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1288               "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1289               "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1290               "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1291         { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1292           "[o0, o1, o2, o3, o4, o5, o6]] : "
1293           "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1294           "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1295           "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1296           "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1297           "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1298           "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1299           "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1300           "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1301           "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1302           "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1303           "o6 >= i3 + i6 - o3 and M >= 0 and "
1304           "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1305           "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1306         { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1307                 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1308                 "(o0 = 0 and M >= 2 and N >= 3) or "
1309                 "(M = 0 and o0 = 0 and N >= 3) }" },
1310         { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1311             "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1312             "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1313             "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1314         { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1315         { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1316         { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1317                 "(y = 3 and x = 1) }" },
1318         { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1319                 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1320                 "i1 <= M and i3 <= M and i4 <= M) or "
1321                 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1322                 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1323                 "i4 <= -1 + M) }" },
1324         { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1325                 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1326         { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1327         { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1328         { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1329         { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1330         { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1331         { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1332         { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1333         { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1334         { 0, "{ [a, b] : exists e : 2e = a and "
1335                     "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1336         { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1337                         "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1338                         "j >= 1 and j' <= i + j - i' and i >= 1; "
1339                 "[1, 1, 1, 1] }" },
1340         { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1341                  "[i,j] : exists a : j = 3a }" },
1342         { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1343                         "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1344                         "a >= 3) or "
1345                     "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1346                         "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1347         { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1348                                 "c <= 6 + 8a and a >= 3; "
1349                 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1350                                 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1351         { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1352                 "[x,0] : 3 <= x <= 4 }" },
1353         { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1354                 "[x,0] : 4 <= x <= 5 }" },
1355         { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1356                 "[x,0] : 3 <= x <= 5 }" },
1357         { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1358                 "[x,0] : 3 <= x <= 4 }" },
1359         { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1360                         "i1 <= 0; "
1361                 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1362 };
1363
1364 /* Test the functionality of isl_set_coalesce.
1365  * That is, check that the output is always equal to the input
1366  * and in some cases that the result consists of a single disjunct.
1367  */
1368 static int test_coalesce(struct isl_ctx *ctx)
1369 {
1370         int i;
1371
1372         for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1373                 const char *str = coalesce_tests[i].str;
1374                 int check_one = coalesce_tests[i].single_disjunct;
1375                 if (test_coalesce_set(ctx, str, check_one) < 0)
1376                         return -1;
1377         }
1378
1379         if (test_coalesce_unbounded_wrapping(ctx) < 0)
1380                 return -1;
1381
1382         return 0;
1383 }
1384
1385 void test_closure(struct isl_ctx *ctx)
1386 {
1387         const char *str;
1388         isl_set *dom;
1389         isl_map *up, *right;
1390         isl_map *map, *map2;
1391         int exact;
1392
1393         /* COCOA example 1 */
1394         map = isl_map_read_from_str(ctx,
1395                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1396                         "1 <= i and i < n and 1 <= j and j < n or "
1397                         "i2 = i + 1 and j2 = j - 1 and "
1398                         "1 <= i and i < n and 2 <= j and j <= n }");
1399         map = isl_map_power(map, &exact);
1400         assert(exact);
1401         isl_map_free(map);
1402
1403         /* COCOA example 1 */
1404         map = isl_map_read_from_str(ctx,
1405                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1406                         "1 <= i and i < n and 1 <= j and j < n or "
1407                         "i2 = i + 1 and j2 = j - 1 and "
1408                         "1 <= i and i < n and 2 <= j and j <= n }");
1409         map = isl_map_transitive_closure(map, &exact);
1410         assert(exact);
1411         map2 = isl_map_read_from_str(ctx,
1412                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1413                         "1 <= i and i < n and 1 <= j and j <= n and "
1414                         "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1415                         "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1416                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1417         assert(isl_map_is_equal(map, map2));
1418         isl_map_free(map2);
1419         isl_map_free(map);
1420
1421         map = isl_map_read_from_str(ctx,
1422                 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1423                                      " 0 <= y and y <= n }");
1424         map = isl_map_transitive_closure(map, &exact);
1425         map2 = isl_map_read_from_str(ctx,
1426                 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1427                                      " 0 <= y and y <= n }");
1428         assert(isl_map_is_equal(map, map2));
1429         isl_map_free(map2);
1430         isl_map_free(map);
1431
1432         /* COCOA example 2 */
1433         map = isl_map_read_from_str(ctx,
1434                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1435                         "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1436                         "i2 = i + 2 and j2 = j - 2 and "
1437                         "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1438         map = isl_map_transitive_closure(map, &exact);
1439         assert(exact);
1440         map2 = isl_map_read_from_str(ctx,
1441                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1442                         "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1443                         "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1444                         "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1445                         "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1446         assert(isl_map_is_equal(map, map2));
1447         isl_map_free(map);
1448         isl_map_free(map2);
1449
1450         /* COCOA Fig.2 left */
1451         map = isl_map_read_from_str(ctx,
1452                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1453                         "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1454                         "j <= n or "
1455                         "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1456                         "j <= 2 i - 3 and j <= n - 2 or "
1457                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1458                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1459         map = isl_map_transitive_closure(map, &exact);
1460         assert(exact);
1461         isl_map_free(map);
1462
1463         /* COCOA Fig.2 right */
1464         map = isl_map_read_from_str(ctx,
1465                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1466                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1467                         "j <= n or "
1468                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1469                         "j <= 2 i - 4 and j <= n - 3 or "
1470                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1471                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1472         map = isl_map_power(map, &exact);
1473         assert(exact);
1474         isl_map_free(map);
1475
1476         /* COCOA Fig.2 right */
1477         map = isl_map_read_from_str(ctx,
1478                 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1479                         "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1480                         "j <= n or "
1481                         "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1482                         "j <= 2 i - 4 and j <= n - 3 or "
1483                         "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1484                         "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1485         map = isl_map_transitive_closure(map, &exact);
1486         assert(exact);
1487         map2 = isl_map_read_from_str(ctx,
1488                 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1489                         "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1490                         "j <= n and 3 + i + 2 j <= 3 n and "
1491                         "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1492                         "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1493                         "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1494                         "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1495                         "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1496         assert(isl_map_is_equal(map, map2));
1497         isl_map_free(map2);
1498         isl_map_free(map);
1499
1500         /* COCOA Fig.1 right */
1501         dom = isl_set_read_from_str(ctx,
1502                 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1503                         "2 x - 3 y + 3 >= 0 }");
1504         right = isl_map_read_from_str(ctx,
1505                 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1506         up = isl_map_read_from_str(ctx,
1507                 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1508         right = isl_map_intersect_domain(right, isl_set_copy(dom));
1509         right = isl_map_intersect_range(right, isl_set_copy(dom));
1510         up = isl_map_intersect_domain(up, isl_set_copy(dom));
1511         up = isl_map_intersect_range(up, dom);
1512         map = isl_map_union(up, right);
1513         map = isl_map_transitive_closure(map, &exact);
1514         assert(exact);
1515         map2 = isl_map_read_from_str(ctx,
1516                 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1517                 "  [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1518         assert(isl_map_is_equal(map, map2));
1519         isl_map_free(map2);
1520         isl_map_free(map);
1521
1522         /* COCOA Theorem 1 counter example */
1523         map = isl_map_read_from_str(ctx,
1524                 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1525                         "i2 = 1 and j2 = j or "
1526                         "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1527         map = isl_map_transitive_closure(map, &exact);
1528         assert(exact);
1529         isl_map_free(map);
1530
1531         map = isl_map_read_from_str(ctx,
1532                 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1533                         "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1534                         "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1535                         "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1536         map = isl_map_transitive_closure(map, &exact);
1537         assert(exact);
1538         isl_map_free(map);
1539
1540         /* Kelly et al 1996, fig 12 */
1541         map = isl_map_read_from_str(ctx,
1542                 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1543                         "1 <= i,j,j+1 <= n or "
1544                         "j = n and j2 = 1 and i2 = i + 1 and "
1545                         "1 <= i,i+1 <= n }");
1546         map = isl_map_transitive_closure(map, &exact);
1547         assert(exact);
1548         map2 = isl_map_read_from_str(ctx,
1549                 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1550                         "1 <= i <= n and i = i2 or "
1551                         "1 <= i < i2 <= n and 1 <= j <= n and "
1552                         "1 <= j2 <= n }");
1553         assert(isl_map_is_equal(map, map2));
1554         isl_map_free(map2);
1555         isl_map_free(map);
1556
1557         /* Omega's closure4 */
1558         map = isl_map_read_from_str(ctx,
1559                 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1560                         "1 <= x,y <= 10 or "
1561                         "x2 = x + 1 and y2 = y and "
1562                         "1 <= x <= 20 && 5 <= y <= 15 }");
1563         map = isl_map_transitive_closure(map, &exact);
1564         assert(exact);
1565         isl_map_free(map);
1566
1567         map = isl_map_read_from_str(ctx,
1568                 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1569         map = isl_map_transitive_closure(map, &exact);
1570         assert(!exact);
1571         map2 = isl_map_read_from_str(ctx,
1572                 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1573         assert(isl_map_is_equal(map, map2));
1574         isl_map_free(map);
1575         isl_map_free(map2);
1576
1577         str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1578             "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1579             "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1580             "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1581         map = isl_map_read_from_str(ctx, str);
1582         map = isl_map_transitive_closure(map, &exact);
1583         assert(exact);
1584         map2 = isl_map_read_from_str(ctx, str);
1585         assert(isl_map_is_equal(map, map2));
1586         isl_map_free(map);
1587         isl_map_free(map2);
1588
1589         str = "{[0] -> [1]; [2] -> [3]}";
1590         map = isl_map_read_from_str(ctx, str);
1591         map = isl_map_transitive_closure(map, &exact);
1592         assert(exact);
1593         map2 = isl_map_read_from_str(ctx, str);
1594         assert(isl_map_is_equal(map, map2));
1595         isl_map_free(map);
1596         isl_map_free(map2);
1597
1598         str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1599             "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1600             "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1601             "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1602             "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1603             "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1604             "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1605             "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1606             "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1607             "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1608             "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1609             "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1610             "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1611             "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1612             "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1613             "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1614             "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1615             "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1616             "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1617             "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1618         map = isl_map_read_from_str(ctx, str);
1619         map = isl_map_transitive_closure(map, NULL);
1620         assert(map);
1621         isl_map_free(map);
1622 }
1623
1624 void test_lex(struct isl_ctx *ctx)
1625 {
1626         isl_space *dim;
1627         isl_map *map;
1628
1629         dim = isl_space_set_alloc(ctx, 0, 0);
1630         map = isl_map_lex_le(dim);
1631         assert(!isl_map_is_empty(map));
1632         isl_map_free(map);
1633 }
1634
1635 static int test_lexmin(struct isl_ctx *ctx)
1636 {
1637         int equal;
1638         const char *str;
1639         isl_basic_map *bmap;
1640         isl_map *map, *map2;
1641         isl_set *set;
1642         isl_set *set2;
1643         isl_pw_multi_aff *pma;
1644
1645         str = "[p0, p1] -> { [] -> [] : "
1646             "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1647             "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1648             "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1649             "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1650             "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1651             "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1652             "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1653             "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1654             "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1655             "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1656             "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1657         map = isl_map_read_from_str(ctx, str);
1658         map = isl_map_lexmin(map);
1659         isl_map_free(map);
1660
1661         str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1662             "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1663         set = isl_set_read_from_str(ctx, str);
1664         set = isl_set_lexmax(set);
1665         str = "[C] -> { [obj,a,b,c] : C = 8 }";
1666         set2 = isl_set_read_from_str(ctx, str);
1667         set = isl_set_intersect(set, set2);
1668         assert(!isl_set_is_empty(set));
1669         isl_set_free(set);
1670
1671         str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1672         map = isl_map_read_from_str(ctx, str);
1673         map = isl_map_lexmin(map);
1674         str = "{ [x] -> [5] : 6 <= x <= 8; "
1675                 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1676         map2 = isl_map_read_from_str(ctx, str);
1677         assert(isl_map_is_equal(map, map2));
1678         isl_map_free(map);
1679         isl_map_free(map2);
1680
1681         str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1682         map = isl_map_read_from_str(ctx, str);
1683         map2 = isl_map_copy(map);
1684         map = isl_map_lexmin(map);
1685         assert(isl_map_is_equal(map, map2));
1686         isl_map_free(map);
1687         isl_map_free(map2);
1688
1689         str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1690         map = isl_map_read_from_str(ctx, str);
1691         map = isl_map_lexmin(map);
1692         str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1693                 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1694                 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1695                 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1696         map2 = isl_map_read_from_str(ctx, str);
1697         assert(isl_map_is_equal(map, map2));
1698         isl_map_free(map);
1699         isl_map_free(map2);
1700
1701         str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1702                                 " 8i' <= i and 8i' >= -7 + i }";
1703         bmap = isl_basic_map_read_from_str(ctx, str);
1704         pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1705         map2 = isl_map_from_pw_multi_aff(pma);
1706         map = isl_map_from_basic_map(bmap);
1707         assert(isl_map_is_equal(map, map2));
1708         isl_map_free(map);
1709         isl_map_free(map2);
1710
1711         str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1712         map = isl_map_read_from_str(ctx, str);
1713         map = isl_map_lexmin(map);
1714         str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1715         map2 = isl_map_read_from_str(ctx, str);
1716         assert(isl_map_is_equal(map, map2));
1717         isl_map_free(map);
1718         isl_map_free(map2);
1719
1720         /* Check that empty pieces are properly combined. */
1721         str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1722                 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1723                 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1724         map = isl_map_read_from_str(ctx, str);
1725         map = isl_map_lexmin(map);
1726         str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1727                 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1728                 "x >= 4 }";
1729         map2 = isl_map_read_from_str(ctx, str);
1730         assert(isl_map_is_equal(map, map2));
1731         isl_map_free(map);
1732         isl_map_free(map2);
1733
1734         str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1735                                 " 8i' <= i and 8i' >= -7 + i }";
1736         set = isl_set_read_from_str(ctx, str);
1737         pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1738         set2 = isl_set_from_pw_multi_aff(pma);
1739         equal = isl_set_is_equal(set, set2);
1740         isl_set_free(set);
1741         isl_set_free(set2);
1742         if (equal < 0)
1743                 return -1;
1744         if (!equal)
1745                 isl_die(ctx, isl_error_unknown,
1746                         "unexpected difference between set and "
1747                         "piecewise affine expression", return -1);
1748
1749         return 0;
1750 }
1751
1752 struct must_may {
1753         isl_map *must;
1754         isl_map *may;
1755 };
1756
1757 static int collect_must_may(__isl_take isl_map *dep, int must,
1758         void *dep_user, void *user)
1759 {
1760         struct must_may *mm = (struct must_may *)user;
1761
1762         if (must)
1763                 mm->must = isl_map_union(mm->must, dep);
1764         else
1765                 mm->may = isl_map_union(mm->may, dep);
1766
1767         return 0;
1768 }
1769
1770 static int common_space(void *first, void *second)
1771 {
1772         int depth = *(int *)first;
1773         return 2 * depth;
1774 }
1775
1776 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1777 {
1778         isl_map *map2;
1779         int equal;
1780
1781         if (!map)
1782                 return -1;
1783
1784         map2 = isl_map_read_from_str(map->ctx, str);
1785         equal = isl_map_is_equal(map, map2);
1786         isl_map_free(map2);
1787
1788         return equal;
1789 }
1790
1791 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1792 {
1793         int equal;
1794
1795         equal = map_is_equal(map, str);
1796         if (equal < 0)
1797                 return -1;
1798         if (!equal)
1799                 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1800                         "result not as expected", return -1);
1801         return 0;
1802 }
1803
1804 void test_dep(struct isl_ctx *ctx)
1805 {
1806         const char *str;
1807         isl_space *dim;
1808         isl_map *map;
1809         isl_access_info *ai;
1810         isl_flow *flow;
1811         int depth;
1812         struct must_may mm;
1813
1814         depth = 3;
1815
1816         str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1817         map = isl_map_read_from_str(ctx, str);
1818         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1819
1820         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1821         map = isl_map_read_from_str(ctx, str);
1822         ai = isl_access_info_add_source(ai, map, 1, &depth);
1823
1824         str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1825         map = isl_map_read_from_str(ctx, str);
1826         ai = isl_access_info_add_source(ai, map, 1, &depth);
1827
1828         flow = isl_access_info_compute_flow(ai);
1829         dim = isl_space_alloc(ctx, 0, 3, 3);
1830         mm.must = isl_map_empty(isl_space_copy(dim));
1831         mm.may = isl_map_empty(dim);
1832
1833         isl_flow_foreach(flow, collect_must_may, &mm);
1834
1835         str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1836               "  [1,10,0] -> [2,5,0] }";
1837         assert(map_is_equal(mm.must, str));
1838         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1839         assert(map_is_equal(mm.may, str));
1840
1841         isl_map_free(mm.must);
1842         isl_map_free(mm.may);
1843         isl_flow_free(flow);
1844
1845
1846         str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1847         map = isl_map_read_from_str(ctx, str);
1848         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1849
1850         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1851         map = isl_map_read_from_str(ctx, str);
1852         ai = isl_access_info_add_source(ai, map, 1, &depth);
1853
1854         str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1855         map = isl_map_read_from_str(ctx, str);
1856         ai = isl_access_info_add_source(ai, map, 0, &depth);
1857
1858         flow = isl_access_info_compute_flow(ai);
1859         dim = isl_space_alloc(ctx, 0, 3, 3);
1860         mm.must = isl_map_empty(isl_space_copy(dim));
1861         mm.may = isl_map_empty(dim);
1862
1863         isl_flow_foreach(flow, collect_must_may, &mm);
1864
1865         str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1866         assert(map_is_equal(mm.must, str));
1867         str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1868         assert(map_is_equal(mm.may, str));
1869
1870         isl_map_free(mm.must);
1871         isl_map_free(mm.may);
1872         isl_flow_free(flow);
1873
1874
1875         str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1876         map = isl_map_read_from_str(ctx, str);
1877         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1878
1879         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1880         map = isl_map_read_from_str(ctx, str);
1881         ai = isl_access_info_add_source(ai, map, 0, &depth);
1882
1883         str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1884         map = isl_map_read_from_str(ctx, str);
1885         ai = isl_access_info_add_source(ai, map, 0, &depth);
1886
1887         flow = isl_access_info_compute_flow(ai);
1888         dim = isl_space_alloc(ctx, 0, 3, 3);
1889         mm.must = isl_map_empty(isl_space_copy(dim));
1890         mm.may = isl_map_empty(dim);
1891
1892         isl_flow_foreach(flow, collect_must_may, &mm);
1893
1894         str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1895               "  [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1896         assert(map_is_equal(mm.may, str));
1897         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1898         assert(map_is_equal(mm.must, str));
1899
1900         isl_map_free(mm.must);
1901         isl_map_free(mm.may);
1902         isl_flow_free(flow);
1903
1904
1905         str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1906         map = isl_map_read_from_str(ctx, str);
1907         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1908
1909         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1910         map = isl_map_read_from_str(ctx, str);
1911         ai = isl_access_info_add_source(ai, map, 0, &depth);
1912
1913         str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1914         map = isl_map_read_from_str(ctx, str);
1915         ai = isl_access_info_add_source(ai, map, 0, &depth);
1916
1917         flow = isl_access_info_compute_flow(ai);
1918         dim = isl_space_alloc(ctx, 0, 3, 3);
1919         mm.must = isl_map_empty(isl_space_copy(dim));
1920         mm.may = isl_map_empty(dim);
1921
1922         isl_flow_foreach(flow, collect_must_may, &mm);
1923
1924         str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1925               "  [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1926         assert(map_is_equal(mm.may, str));
1927         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1928         assert(map_is_equal(mm.must, str));
1929
1930         isl_map_free(mm.must);
1931         isl_map_free(mm.may);
1932         isl_flow_free(flow);
1933
1934
1935         str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1936         map = isl_map_read_from_str(ctx, str);
1937         ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1938
1939         str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1940         map = isl_map_read_from_str(ctx, str);
1941         ai = isl_access_info_add_source(ai, map, 0, &depth);
1942
1943         str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1944         map = isl_map_read_from_str(ctx, str);
1945         ai = isl_access_info_add_source(ai, map, 0, &depth);
1946
1947         flow = isl_access_info_compute_flow(ai);
1948         dim = isl_space_alloc(ctx, 0, 3, 3);
1949         mm.must = isl_map_empty(isl_space_copy(dim));
1950         mm.may = isl_map_empty(dim);
1951
1952         isl_flow_foreach(flow, collect_must_may, &mm);
1953
1954         str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1955               "  [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1956         assert(map_is_equal(mm.may, str));
1957         str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1958         assert(map_is_equal(mm.must, str));
1959
1960         isl_map_free(mm.must);
1961         isl_map_free(mm.may);
1962         isl_flow_free(flow);
1963
1964
1965         depth = 5;
1966
1967         str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1968         map = isl_map_read_from_str(ctx, str);
1969         ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1970
1971         str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1972         map = isl_map_read_from_str(ctx, str);
1973         ai = isl_access_info_add_source(ai, map, 1, &depth);
1974
1975         flow = isl_access_info_compute_flow(ai);
1976         dim = isl_space_alloc(ctx, 0, 5, 5);
1977         mm.must = isl_map_empty(isl_space_copy(dim));
1978         mm.may = isl_map_empty(dim);
1979
1980         isl_flow_foreach(flow, collect_must_may, &mm);
1981
1982         str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1983         assert(map_is_equal(mm.must, str));
1984         str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1985         assert(map_is_equal(mm.may, str));
1986
1987         isl_map_free(mm.must);
1988         isl_map_free(mm.may);
1989         isl_flow_free(flow);
1990 }
1991
1992 int test_sv(isl_ctx *ctx)
1993 {
1994         const char *str;
1995         isl_map *map;
1996         isl_union_map *umap;
1997         int sv;
1998
1999         str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
2000         map = isl_map_read_from_str(ctx, str);
2001         sv = isl_map_is_single_valued(map);
2002         isl_map_free(map);
2003         if (sv < 0)
2004                 return -1;
2005         if (!sv)
2006                 isl_die(ctx, isl_error_internal,
2007                         "map not detected as single valued", return -1);
2008
2009         str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
2010         map = isl_map_read_from_str(ctx, str);
2011         sv = isl_map_is_single_valued(map);
2012         isl_map_free(map);
2013         if (sv < 0)
2014                 return -1;
2015         if (sv)
2016                 isl_die(ctx, isl_error_internal,
2017                         "map detected as single valued", return -1);
2018
2019         str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
2020         umap = isl_union_map_read_from_str(ctx, str);
2021         sv = isl_union_map_is_single_valued(umap);
2022         isl_union_map_free(umap);
2023         if (sv < 0)
2024                 return -1;
2025         if (!sv)
2026                 isl_die(ctx, isl_error_internal,
2027                         "map not detected as single valued", return -1);
2028
2029         str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
2030         umap = isl_union_map_read_from_str(ctx, str);
2031         sv = isl_union_map_is_single_valued(umap);
2032         isl_union_map_free(umap);
2033         if (sv < 0)
2034                 return -1;
2035         if (sv)
2036                 isl_die(ctx, isl_error_internal,
2037                         "map detected as single valued", return -1);
2038
2039         return 0;
2040 }
2041
2042 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
2043 {
2044         isl_map *map;
2045
2046         map = isl_map_read_from_str(ctx, str);
2047         if (bijective)
2048                 assert(isl_map_is_bijective(map));
2049         else
2050                 assert(!isl_map_is_bijective(map));
2051         isl_map_free(map);
2052 }
2053
2054 void test_bijective(struct isl_ctx *ctx)
2055 {
2056         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
2057         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2058         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2059         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2060         test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
2061         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
2062         test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
2063         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2064         test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
2065         test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
2066         test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
2067         test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
2068         test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2069 }
2070
2071 static int test_pwqp(struct isl_ctx *ctx)
2072 {
2073         const char *str;
2074         isl_set *set;
2075         isl_pw_qpolynomial *pwqp1, *pwqp2;
2076         int equal;
2077
2078         str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2079         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2080
2081         pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2082                                                 isl_dim_in, 1, 1);
2083
2084         str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2085         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2086
2087         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2088
2089         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2090
2091         isl_pw_qpolynomial_free(pwqp1);
2092
2093         str = "{ [i] -> i }";
2094         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2095         str = "{ [k] : exists a : k = 2a }";
2096         set = isl_set_read_from_str(ctx, str);
2097         pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2098         str = "{ [i] -> i }";
2099         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2100
2101         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2102
2103         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2104
2105         isl_pw_qpolynomial_free(pwqp1);
2106
2107         str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
2108         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2109         str = "{ [10] }";
2110         set = isl_set_read_from_str(ctx, str);
2111         pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2112         str = "{ [i] -> 16 }";
2113         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2114
2115         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2116
2117         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2118
2119         isl_pw_qpolynomial_free(pwqp1);
2120
2121         str = "{ [i] -> ([(i)/2]) }";
2122         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2123         str = "{ [k] : exists a : k = 2a+1 }";
2124         set = isl_set_read_from_str(ctx, str);
2125         pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2126         str = "{ [i] -> -1/2 + 1/2 * i }";
2127         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2128
2129         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2130
2131         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2132
2133         isl_pw_qpolynomial_free(pwqp1);
2134
2135         str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2136         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2137         str = "{ [i] -> ([(2 * [i/2])/5]) }";
2138         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2139
2140         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2141
2142         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2143
2144         isl_pw_qpolynomial_free(pwqp1);
2145
2146         str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2147         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2148         str = "{ [x] -> x }";
2149         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2150
2151         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2152
2153         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2154
2155         isl_pw_qpolynomial_free(pwqp1);
2156
2157         str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2158         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2159         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2160         pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2161         pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2162         assert(isl_pw_qpolynomial_is_zero(pwqp1));
2163         isl_pw_qpolynomial_free(pwqp1);
2164
2165         str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2166         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2167         str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2168         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2169         set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2170         pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2171         equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2172         isl_pw_qpolynomial_free(pwqp1);
2173         isl_pw_qpolynomial_free(pwqp2);
2174         if (equal < 0)
2175                 return -1;
2176         if (!equal)
2177                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2178
2179         str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2180         pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2181         str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2182         pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2183         pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2184                                                 isl_val_one(ctx));
2185         equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2186         isl_pw_qpolynomial_free(pwqp1);
2187         isl_pw_qpolynomial_free(pwqp2);
2188         if (equal < 0)
2189                 return -1;
2190         if (!equal)
2191                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2192
2193         return 0;
2194 }
2195
2196 void test_split_periods(isl_ctx *ctx)
2197 {
2198         const char *str;
2199         isl_pw_qpolynomial *pwqp;
2200
2201         str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2202                 "U + 2V + 3 >= 0 and - U -2V  >= 0 and - U + 10 >= 0 and "
2203                 "U  >= 0; [U,V] -> U^2 : U >= 100 }";
2204         pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2205
2206         pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2207         assert(pwqp);
2208
2209         isl_pw_qpolynomial_free(pwqp);
2210 }
2211
2212 void test_union(isl_ctx *ctx)
2213 {
2214         const char *str;
2215         isl_union_set *uset1, *uset2;
2216         isl_union_map *umap1, *umap2;
2217
2218         str = "{ [i] : 0 <= i <= 1 }";
2219         uset1 = isl_union_set_read_from_str(ctx, str);
2220         str = "{ [1] -> [0] }";
2221         umap1 = isl_union_map_read_from_str(ctx, str);
2222
2223         umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2224         assert(isl_union_map_is_equal(umap1, umap2));
2225
2226         isl_union_map_free(umap1);
2227         isl_union_map_free(umap2);
2228
2229         str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2230         umap1 = isl_union_map_read_from_str(ctx, str);
2231         str = "{ A[i]; B[i] }";
2232         uset1 = isl_union_set_read_from_str(ctx, str);
2233
2234         uset2 = isl_union_map_domain(umap1);
2235
2236         assert(isl_union_set_is_equal(uset1, uset2));
2237
2238         isl_union_set_free(uset1);
2239         isl_union_set_free(uset2);
2240 }
2241
2242 void test_bound(isl_ctx *ctx)
2243 {
2244         const char *str;
2245         isl_pw_qpolynomial *pwqp;
2246         isl_pw_qpolynomial_fold *pwf;
2247
2248         str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2249         pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2250         pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2251         assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
2252         isl_pw_qpolynomial_fold_free(pwf);
2253
2254         str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2255         pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2256         pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2257         assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2258         isl_pw_qpolynomial_fold_free(pwf);
2259 }
2260
2261 void test_lift(isl_ctx *ctx)
2262 {
2263         const char *str;
2264         isl_basic_map *bmap;
2265         isl_basic_set *bset;
2266
2267         str = "{ [i0] : exists e0 : i0 = 4e0 }";
2268         bset = isl_basic_set_read_from_str(ctx, str);
2269         bset = isl_basic_set_lift(bset);
2270         bmap = isl_basic_map_from_range(bset);
2271         bset = isl_basic_map_domain(bmap);
2272         isl_basic_set_free(bset);
2273 }
2274
2275 struct {
2276         const char *set1;
2277         const char *set2;
2278         int subset;
2279 } subset_tests[] = {
2280         { "{ [112, 0] }",
2281           "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2282                 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2283                 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2284         { "{ [65] }",
2285           "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2286                 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2287                 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2288                     "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2289                     "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2290                     "256e0 <= 255i and 256e0 >= -255 + 255i and "
2291                     "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2292                     "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2293                     "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2294         { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2295         { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2296         { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2297         { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2298 };
2299
2300 static int test_subset(isl_ctx *ctx)
2301 {
2302         int i;
2303         isl_set *set1, *set2;
2304         int subset;
2305
2306         for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2307                 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2308                 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2309                 subset = isl_set_is_subset(set1, set2);
2310                 isl_set_free(set1);
2311                 isl_set_free(set2);
2312                 if (subset < 0)
2313                         return -1;
2314                 if (subset != subset_tests[i].subset)
2315                         isl_die(ctx, isl_error_unknown,
2316                                 "incorrect subset result", return -1);
2317         }
2318
2319         return 0;
2320 }
2321
2322 struct {
2323         const char *minuend;
2324         const char *subtrahend;
2325         const char *difference;
2326 } subtract_domain_tests[] = {
2327         { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2328         { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2329         { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2330 };
2331
2332 static int test_subtract(isl_ctx *ctx)
2333 {
2334         int i;
2335         isl_union_map *umap1, *umap2;
2336         isl_union_set *uset;
2337         int equal;
2338
2339         for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2340                 umap1 = isl_union_map_read_from_str(ctx,
2341                                 subtract_domain_tests[i].minuend);
2342                 uset = isl_union_set_read_from_str(ctx,
2343                                 subtract_domain_tests[i].subtrahend);
2344                 umap2 = isl_union_map_read_from_str(ctx,
2345                                 subtract_domain_tests[i].difference);
2346                 umap1 = isl_union_map_subtract_domain(umap1, uset);
2347                 equal = isl_union_map_is_equal(umap1, umap2);
2348                 isl_union_map_free(umap1);
2349                 isl_union_map_free(umap2);
2350                 if (equal < 0)
2351                         return -1;
2352                 if (!equal)
2353                         isl_die(ctx, isl_error_unknown,
2354                                 "incorrect subtract domain result", return -1);
2355         }
2356
2357         return 0;
2358 }
2359
2360 int test_factorize(isl_ctx *ctx)
2361 {
2362         const char *str;
2363         isl_basic_set *bset;
2364         isl_factorizer *f;
2365
2366         str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2367             "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2368             "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2369             "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2370             "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2371             "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2372             "3i5 >= -2i0 - i2 + 3i4 }";
2373         bset = isl_basic_set_read_from_str(ctx, str);
2374         f = isl_basic_set_factorizer(bset);
2375         isl_basic_set_free(bset);
2376         isl_factorizer_free(f);
2377         if (!f)
2378                 isl_die(ctx, isl_error_unknown,
2379                         "failed to construct factorizer", return -1);
2380
2381         str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2382             "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2383             "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2384             "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2385             "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2386             "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2387             "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2388             "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2389             "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2390             "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2391         bset = isl_basic_set_read_from_str(ctx, str);
2392         f = isl_basic_set_factorizer(bset);
2393         isl_basic_set_free(bset);
2394         isl_factorizer_free(f);
2395         if (!f)
2396                 isl_die(ctx, isl_error_unknown,
2397                         "failed to construct factorizer", return -1);
2398
2399         return 0;
2400 }
2401
2402 static int check_injective(__isl_take isl_map *map, void *user)
2403 {
2404         int *injective = user;
2405
2406         *injective = isl_map_is_injective(map);
2407         isl_map_free(map);
2408
2409         if (*injective < 0 || !*injective)
2410                 return -1;
2411
2412         return 0;
2413 }
2414
2415 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2416         const char *r, const char *s, int tilable, int parallel)
2417 {
2418         int i;
2419         isl_union_set *D;
2420         isl_union_map *W, *R, *S;
2421         isl_union_map *empty;
2422         isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2423         isl_union_map *validity, *proximity;
2424         isl_union_map *schedule;
2425         isl_union_map *test;
2426         isl_union_set *delta;
2427         isl_union_set *domain;
2428         isl_set *delta_set;
2429         isl_set *slice;
2430         isl_set *origin;
2431         isl_schedule_constraints *sc;
2432         isl_schedule *sched;
2433         int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2434
2435         D = isl_union_set_read_from_str(ctx, d);
2436         W = isl_union_map_read_from_str(ctx, w);
2437         R = isl_union_map_read_from_str(ctx, r);
2438         S = isl_union_map_read_from_str(ctx, s);
2439
2440         W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2441         R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2442
2443         empty = isl_union_map_empty(isl_union_map_get_space(S));
2444         isl_union_map_compute_flow(isl_union_map_copy(R),
2445                                    isl_union_map_copy(W), empty,
2446                                    isl_union_map_copy(S),
2447                                    &dep_raw, NULL, NULL, NULL);
2448         isl_union_map_compute_flow(isl_union_map_copy(W),
2449                                    isl_union_map_copy(W),
2450                                    isl_union_map_copy(R),
2451                                    isl_union_map_copy(S),
2452                                    &dep_waw, &dep_war, NULL, NULL);
2453
2454         dep = isl_union_map_union(dep_waw, dep_war);
2455         dep = isl_union_map_union(dep, dep_raw);
2456         validity = isl_union_map_copy(dep);
2457         proximity = isl_union_map_copy(dep);
2458
2459         sc = isl_schedule_constraints_on_domain(isl_union_set_copy(D));
2460         sc = isl_schedule_constraints_set_validity(sc, validity);
2461         sc = isl_schedule_constraints_set_proximity(sc, proximity);
2462         sched = isl_schedule_constraints_compute_schedule(sc);
2463         schedule = isl_schedule_get_map(sched);
2464         isl_schedule_free(sched);
2465         isl_union_map_free(W);
2466         isl_union_map_free(R);
2467         isl_union_map_free(S);
2468
2469         is_injection = 1;
2470         isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2471
2472         domain = isl_union_map_domain(isl_union_map_copy(schedule));
2473         is_complete = isl_union_set_is_subset(D, domain);
2474         isl_union_set_free(D);
2475         isl_union_set_free(domain);
2476
2477         test = isl_union_map_reverse(isl_union_map_copy(schedule));
2478         test = isl_union_map_apply_range(test, dep);
2479         test = isl_union_map_apply_range(test, schedule);
2480
2481         delta = isl_union_map_deltas(test);
2482         if (isl_union_set_n_set(delta) == 0) {
2483                 is_tilable = 1;
2484                 is_parallel = 1;
2485                 is_nonneg = 1;
2486                 isl_union_set_free(delta);
2487         } else {
2488                 delta_set = isl_set_from_union_set(delta);
2489
2490                 slice = isl_set_universe(isl_set_get_space(delta_set));
2491                 for (i = 0; i < tilable; ++i)
2492                         slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2493                 is_tilable = isl_set_is_subset(delta_set, slice);
2494                 isl_set_free(slice);
2495
2496                 slice = isl_set_universe(isl_set_get_space(delta_set));
2497                 for (i = 0; i < parallel; ++i)
2498                         slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2499                 is_parallel = isl_set_is_subset(delta_set, slice);
2500                 isl_set_free(slice);
2501
2502                 origin = isl_set_universe(isl_set_get_space(delta_set));
2503                 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2504                         origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2505
2506                 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2507                 delta_set = isl_set_lexmin(delta_set);
2508
2509                 is_nonneg = isl_set_is_equal(delta_set, origin);
2510
2511                 isl_set_free(origin);
2512                 isl_set_free(delta_set);
2513         }
2514
2515         if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2516             is_injection < 0 || is_complete < 0)
2517                 return -1;
2518         if (!is_complete)
2519                 isl_die(ctx, isl_error_unknown,
2520                         "generated schedule incomplete", return -1);
2521         if (!is_injection)
2522                 isl_die(ctx, isl_error_unknown,
2523                         "generated schedule not injective on each statement",
2524                         return -1);
2525         if (!is_nonneg)
2526                 isl_die(ctx, isl_error_unknown,
2527                         "negative dependences in generated schedule",
2528                         return -1);
2529         if (!is_tilable)
2530                 isl_die(ctx, isl_error_unknown,
2531                         "generated schedule not as tilable as expected",
2532                         return -1);
2533         if (!is_parallel)
2534                 isl_die(ctx, isl_error_unknown,
2535                         "generated schedule not as parallel as expected",
2536                         return -1);
2537
2538         return 0;
2539 }
2540
2541 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2542         const char *domain, const char *validity, const char *proximity)
2543 {
2544         isl_union_set *dom;
2545         isl_union_map *dep;
2546         isl_union_map *prox;
2547         isl_schedule_constraints *sc;
2548         isl_schedule *schedule;
2549         isl_union_map *sched;
2550
2551         dom = isl_union_set_read_from_str(ctx, domain);
2552         dep = isl_union_map_read_from_str(ctx, validity);
2553         prox = isl_union_map_read_from_str(ctx, proximity);
2554         sc = isl_schedule_constraints_on_domain(dom);
2555         sc = isl_schedule_constraints_set_validity(sc, dep);
2556         sc = isl_schedule_constraints_set_proximity(sc, prox);
2557         schedule = isl_schedule_constraints_compute_schedule(sc);
2558         sched = isl_schedule_get_map(schedule);
2559         isl_schedule_free(schedule);
2560
2561         return sched;
2562 }
2563
2564 /* Check that a schedule can be constructed on the given domain
2565  * with the given validity and proximity constraints.
2566  */
2567 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2568         const char *validity, const char *proximity)
2569 {
2570         isl_union_map *sched;
2571
2572         sched = compute_schedule(ctx, domain, validity, proximity);
2573         if (!sched)
2574                 return -1;
2575
2576         isl_union_map_free(sched);
2577         return 0;
2578 }
2579
2580 int test_special_schedule(isl_ctx *ctx, const char *domain,
2581         const char *validity, const char *proximity, const char *expected_sched)
2582 {
2583         isl_union_map *sched1, *sched2;
2584         int equal;
2585
2586         sched1 = compute_schedule(ctx, domain, validity, proximity);
2587         sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2588
2589         equal = isl_union_map_is_equal(sched1, sched2);
2590         isl_union_map_free(sched1);
2591         isl_union_map_free(sched2);
2592
2593         if (equal < 0)
2594                 return -1;
2595         if (!equal)
2596                 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2597                         return -1);
2598
2599         return 0;
2600 }
2601
2602 /* Check that the schedule map is properly padded, even after being
2603  * reconstructed from the band forest.
2604  */
2605 static int test_padded_schedule(isl_ctx *ctx)
2606 {
2607         const char *str;
2608         isl_union_set *D;
2609         isl_union_map *validity, *proximity;
2610         isl_schedule_constraints *sc;
2611         isl_schedule *sched;
2612         isl_union_map *map1, *map2;
2613         isl_band_list *list;
2614         int equal;
2615
2616         str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2617         D = isl_union_set_read_from_str(ctx, str);
2618         validity = isl_union_map_empty(isl_union_set_get_space(D));
2619         proximity = isl_union_map_copy(validity);
2620         sc = isl_schedule_constraints_on_domain(D);
2621         sc = isl_schedule_constraints_set_validity(sc, validity);
2622         sc = isl_schedule_constraints_set_proximity(sc, proximity);
2623         sched = isl_schedule_constraints_compute_schedule(sc);
2624         map1 = isl_schedule_get_map(sched);
2625         list = isl_schedule_get_band_forest(sched);
2626         isl_band_list_free(list);
2627         map2 = isl_schedule_get_map(sched);
2628         isl_schedule_free(sched);
2629         equal = isl_union_map_is_equal(map1, map2);
2630         isl_union_map_free(map1);
2631         isl_union_map_free(map2);
2632
2633         if (equal < 0)
2634                 return -1;
2635         if (!equal)
2636                 isl_die(ctx, isl_error_unknown,
2637                         "reconstructed schedule map not the same as original",
2638                         return -1);
2639
2640         return 0;
2641 }
2642
2643 /* Input for testing of schedule construction based on
2644  * conditional constraints.
2645  *
2646  * domain is the iteration domain
2647  * flow are the flow dependences, which determine the validity and
2648  *      proximity constraints
2649  * condition are the conditions on the conditional validity constraints
2650  * conditional_validity are the conditional validity constraints
2651  * outer_band_n is the expected number of members in the outer band
2652  */
2653 struct {
2654         const char *domain;
2655         const char *flow;
2656         const char *condition;
2657         const char *conditional_validity;
2658         int outer_band_n;
2659 } live_range_tests[] = {
2660         /* Contrived example that illustrates that we need to keep
2661          * track of tagged condition dependences and
2662          * tagged conditional validity dependences
2663          * in isl_sched_edge separately.
2664          * In particular, the conditional validity constraints on A
2665          * cannot be satisfied,
2666          * but they can be ignored because there are no corresponding
2667          * condition constraints.  However, we do have an additional
2668          * conditional validity constraint that maps to the same
2669          * dependence relation
2670          * as the condition constraint on B.  If we did not make a distinction
2671          * between tagged condition and tagged conditional validity
2672          * dependences, then we
2673          * could end up treating this shared dependence as an condition
2674          * constraint on A, forcing a localization of the conditions,
2675          * which is impossible.
2676          */
2677         { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2678           "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2679           "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2680           "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2681             "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2682             "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2683           1
2684         },
2685         /* TACO 2013 Fig. 7 */
2686         { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2687           "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2688                    "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2689           "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2690                    "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2691                                 "0 <= i < n and 0 <= j < n - 1 }",
2692           "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2693                                 "0 <= i < n and 0 <= j < j' < n;"
2694                    "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2695                                 "0 <= i < i' < n and 0 <= j,j' < n;"
2696                    "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2697                                 "0 <= i,j,j' < n and j < j' }",
2698             2
2699         },
2700         /* TACO 2013 Fig. 7, without tags */
2701         { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2702           "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2703                    "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2704           "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2705                    "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2706           "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2707                    "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2708                    "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2709            1
2710         },
2711         /* TACO 2013 Fig. 12 */
2712         { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2713             "S3[i,3] : 0 <= i <= 1 }",
2714           "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2715             "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2716             "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2717           "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2718             "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2719             "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2720           "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2721             "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2722             "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2723             "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2724             "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2725            1
2726         }
2727 };
2728
2729 /* Test schedule construction based on conditional constraints.
2730  * In particular, check the number of members in the outer band
2731  * as an indication of whether tiling is possible or not.
2732  */
2733 static int test_conditional_schedule_constraints(isl_ctx *ctx)
2734 {
2735         int i;
2736         isl_union_set *domain;
2737         isl_union_map *condition;
2738         isl_union_map *flow;
2739         isl_union_map *validity;
2740         isl_schedule_constraints *sc;
2741         isl_schedule *schedule;
2742         isl_band_list *list;
2743         isl_band *band;
2744         int n_member;
2745
2746         for (i = 0; i < ARRAY_SIZE(live_range_tests); ++i) {
2747                 domain = isl_union_set_read_from_str(ctx,
2748                                 live_range_tests[i].domain);
2749                 flow = isl_union_map_read_from_str(ctx,
2750                                 live_range_tests[i].flow);
2751                 condition = isl_union_map_read_from_str(ctx,
2752                                 live_range_tests[i].condition);
2753                 validity = isl_union_map_read_from_str(ctx,
2754                                 live_range_tests[i].conditional_validity);
2755                 sc = isl_schedule_constraints_on_domain(domain);
2756                 sc = isl_schedule_constraints_set_validity(sc,
2757                                 isl_union_map_copy(flow));
2758                 sc = isl_schedule_constraints_set_proximity(sc, flow);
2759                 sc = isl_schedule_constraints_set_conditional_validity(sc,
2760                                 condition, validity);
2761                 schedule = isl_schedule_constraints_compute_schedule(sc);
2762                 list = isl_schedule_get_band_forest(schedule);
2763                 band = isl_band_list_get_band(list, 0);
2764                 n_member = isl_band_n_member(band);
2765                 isl_band_free(band);
2766                 isl_band_list_free(list);
2767                 isl_schedule_free(schedule);
2768
2769                 if (!schedule)
2770                         return -1;
2771                 if (n_member != live_range_tests[i].outer_band_n)
2772                         isl_die(ctx, isl_error_unknown,
2773                                 "unexpected number of members in outer band",
2774                                 return -1);
2775         }
2776         return 0;
2777 }
2778
2779 int test_schedule(isl_ctx *ctx)
2780 {
2781         const char *D, *W, *R, *V, *P, *S;
2782
2783         /* Handle resulting schedule with zero bands. */
2784         if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2785                 return -1;
2786
2787         /* Jacobi */
2788         D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2789         W = "{ S1[t,i] -> a[t,i] }";
2790         R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2791                 "S1[t,i] -> a[t-1,i+1] }";
2792         S = "{ S1[t,i] -> [t,i] }";
2793         if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2794                 return -1;
2795
2796         /* Fig. 5 of CC2008 */
2797         D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2798                                 "j <= -1 + N }";
2799         W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2800                                 "j >= 2 and j <= -1 + N }";
2801         R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2802                                 "j >= 2 and j <= -1 + N; "
2803                     "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2804                                 "j >= 2 and j <= -1 + N }";
2805         S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2806         if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2807                 return -1;
2808
2809         D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2810         W = "{ S1[i] -> a[i] }";
2811         R = "{ S2[i] -> a[i+1] }";
2812         S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2813         if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2814                 return -1;
2815
2816         D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2817         W = "{ S1[i] -> a[i] }";
2818         R = "{ S2[i] -> a[9-i] }";
2819         S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2820         if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2821                 return -1;
2822
2823         D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2824         W = "{ S1[i] -> a[i] }";
2825         R = "[N] -> { S2[i] -> a[N-1-i] }";
2826         S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2827         if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2828                 return -1;
2829
2830         D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2831         W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2832         R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2833         S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2834         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2835                 return -1;
2836
2837         D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2838         W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2839         R = "{ S2[i,j] -> a[i-1,j] }";
2840         S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2841         if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2842                 return -1;
2843
2844         D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2845         W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2846         R = "{ S2[i,j] -> a[i,j-1] }";
2847         S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2848         if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2849                 return -1;
2850
2851         D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2852         W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2853                     "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2854         R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2855         S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2856                     "S_0[] -> [0, 0, 0] }";
2857         if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2858                 return -1;
2859         ctx->opt->schedule_parametric = 0;
2860         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2861                 return -1;
2862         ctx->opt->schedule_parametric = 1;
2863
2864         D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2865                     "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2866         W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2867         R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2868                     "S4[i] -> a[i,N] }";
2869         S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2870                 "S4[i] -> [4,i,0] }";
2871         if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2872                 return -1;
2873
2874         D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2875         W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2876                                         "j <= N }";
2877         R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2878                                         "j <= N; "
2879                     "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2880                                         "j <= N }";
2881         S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2882         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2883                 return -1;
2884
2885         D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2886                     " S_2[t] : t >= 0 and t <= -1 + N; "
2887                     " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2888                                 "i <= -1 + N }";
2889         W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2890                     " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2891                     " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2892                                                 "i >= 0 and i <= -1 + N }";
2893         R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2894                                             "i >= 0 and i <= -1 + N; "
2895                     " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2896         S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2897                     " S_0[t] -> [0, t, 0] }";
2898
2899         if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2900                 return -1;
2901         ctx->opt->schedule_parametric = 0;
2902         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2903                 return -1;
2904         ctx->opt->schedule_parametric = 1;
2905
2906         D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2907         S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2908         if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2909                 return -1;
2910
2911         D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2912             "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2913         W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2914                                             "j >= 0 and j <= -1 + N; "
2915                         "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2916         R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2917                                             "j >= 0 and j <= -1 + N; "
2918                         "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2919         S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2920         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2921                 return -1;
2922
2923         D = "{ S_0[i] : i >= 0 }";
2924         W = "{ S_0[i] -> a[i] : i >= 0 }";
2925         R = "{ S_0[i] -> a[0] : i >= 0 }";
2926         S = "{ S_0[i] -> [0, i, 0] }";
2927         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2928                 return -1;
2929
2930         D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2931         W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2932         R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2933         S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2934         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2935                 return -1;
2936
2937         D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2938                                 "k <= -1 + n and k >= 0 }";
2939         W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "                                                  "k <= -1 + n and k >= 0 }";
2940         R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2941                                         "k <= -1 + n and k >= 0; "
2942                     "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2943                                         "k <= -1 + n and k >= 0; "
2944                     "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2945                                         "k <= -1 + n and k >= 0 }";
2946         S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2947         ctx->opt->schedule_outer_zero_distance = 1;
2948         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2949                 return -1;
2950         ctx->opt->schedule_outer_zero_distance = 0;
2951
2952         D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2953                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2954                 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2955              "Stmt_for_body24[i0, i1, 1, 0]:"
2956                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2957              "Stmt_for_body7[i0, i1, i2]:"
2958                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2959                 "i2 <= 7 }";
2960
2961         V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2962                 "Stmt_for_body24[1, i1, i2, i3]:"
2963                 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2964                 "i2 >= 1;"
2965              "Stmt_for_body24[0, i1, i2, i3] -> "
2966                 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2967                 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2968                 "i3 >= 0;"
2969               "Stmt_for_body24[0, i1, i2, i3] ->"
2970                 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2971                 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2972               "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2973                 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2974                 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2975                 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2976               "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2977                 "i1 <= 6 and i1 >= 0;"
2978               "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2979               "Stmt_for_body7[i0, i1, i2] -> "
2980                 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2981                 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2982                 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2983               "Stmt_for_body7[i0, i1, i2] -> "
2984                 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2985                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2986                 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2987         P = V;
2988         S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2989                 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2990             "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2991
2992         if (test_special_schedule(ctx, D, V, P, S) < 0)
2993                 return -1;
2994
2995         D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2996         V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2997                                            "j >= 1 and j <= 7;"
2998                 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2999                                              "j >= 1 and j <= 8 }";
3000         P = "{ }";
3001         S = "{ S_0[i, j] -> [i + j, j] }";
3002         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3003         if (test_special_schedule(ctx, D, V, P, S) < 0)
3004                 return -1;
3005         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3006
3007         /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3008         D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3009                                  "j >= 0 and j <= -1 + i }";
3010         V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3011                                         "i <= -1 + N and j >= 0;"
3012                      "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3013                                         "i <= -2 + N }";
3014         P = "{ }";
3015         S = "{ S_0[i, j] -> [i, j] }";
3016         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3017         if (test_special_schedule(ctx, D, V, P, S) < 0)
3018                 return -1;
3019         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3020
3021         /* Test both algorithms on a case with only proximity dependences. */
3022         D = "{ S[i,j] : 0 <= i <= 10 }";
3023         V = "{ }";
3024         P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3025         S = "{ S[i, j] -> [j, i] }";
3026         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3027         if (test_special_schedule(ctx, D, V, P, S) < 0)
3028                 return -1;
3029         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3030         if (test_special_schedule(ctx, D, V, P, S) < 0)
3031                 return -1;
3032
3033         D = "{ A[a]; B[] }";
3034         V = "{}";
3035         P = "{ A[a] -> B[] }";
3036         if (test_has_schedule(ctx, D, V, P) < 0)
3037                 return -1;
3038
3039         if (test_padded_schedule(ctx) < 0)
3040                 return -1;
3041
3042         /* Check that check for progress is not confused by rational
3043          * solution.
3044          */
3045         D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3046         V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3047                                                         "i0 <= -2 + N; "
3048                         "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3049                                 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3050         P = "{}";
3051         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3052         if (test_has_schedule(ctx, D, V, P) < 0)
3053                 return -1;
3054         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3055
3056         if (test_conditional_schedule_constraints(ctx) < 0)
3057                 return -1;
3058
3059         return 0;
3060 }
3061
3062 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
3063 {
3064         isl_union_map *umap;
3065         int test;
3066
3067         umap = isl_union_map_read_from_str(ctx, str);
3068         test = isl_union_map_plain_is_injective(umap);
3069         isl_union_map_free(umap);
3070         if (test < 0)
3071                 return -1;
3072         if (test == injective)
3073                 return 0;
3074         if (injective)
3075                 isl_die(ctx, isl_error_unknown,
3076                         "map not detected as injective", return -1);
3077         else
3078                 isl_die(ctx, isl_error_unknown,
3079                         "map detected as injective", return -1);
3080 }
3081
3082 int test_injective(isl_ctx *ctx)
3083 {
3084         const char *str;
3085
3086         if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3087                 return -1;
3088         if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
3089                 return -1;
3090         if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
3091                 return -1;
3092         if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
3093                 return -1;
3094         if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3095                 return -1;
3096         if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3097                 return -1;
3098         if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3099                 return -1;
3100         if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3101                 return -1;
3102
3103         str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3104         if (test_plain_injective(ctx, str, 1))
3105                 return -1;
3106         str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3107         if (test_plain_injective(ctx, str, 0))
3108                 return -1;
3109
3110         return 0;
3111 }
3112
3113 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
3114 {
3115         isl_aff *aff2;
3116         int equal;
3117
3118         if (!aff)
3119                 return -1;
3120
3121         aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
3122         equal = isl_aff_plain_is_equal(aff, aff2);
3123         isl_aff_free(aff2);
3124
3125         return equal;
3126 }
3127
3128 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
3129 {
3130         int equal;
3131
3132         equal = aff_plain_is_equal(aff, str);
3133         if (equal < 0)
3134                 return -1;
3135         if (!equal)
3136                 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
3137                         "result not as expected", return -1);
3138         return 0;
3139 }
3140
3141 int test_aff(isl_ctx *ctx)
3142 {
3143         const char *str;
3144         isl_set *set;
3145         isl_space *space;
3146         isl_local_space *ls;
3147         isl_aff *aff;
3148         int zero, equal;
3149
3150         space = isl_space_set_alloc(ctx, 0, 1);
3151         ls = isl_local_space_from_space(space);
3152         aff = isl_aff_zero_on_domain(ls);
3153
3154         aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3155         aff = isl_aff_scale_down_ui(aff, 3);
3156         aff = isl_aff_floor(aff);
3157         aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3158         aff = isl_aff_scale_down_ui(aff, 2);
3159         aff = isl_aff_floor(aff);
3160         aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3161
3162         str = "{ [10] }";
3163         set = isl_set_read_from_str(ctx, str);
3164         aff = isl_aff_gist(aff, set);
3165
3166         aff = isl_aff_add_constant_si(aff, -16);
3167         zero = isl_aff_plain_is_zero(aff);
3168         isl_aff_free(aff);
3169
3170         if (zero < 0)
3171                 return -1;
3172         if (!zero)
3173                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3174
3175         aff = isl_aff_read_from_str(ctx, "{ [-1] }");
3176         aff = isl_aff_scale_down_ui(aff, 64);
3177         aff = isl_aff_floor(aff);
3178         equal = aff_check_plain_equal(aff, "{ [-1] }");
3179         isl_aff_free(aff);
3180         if (equal < 0)
3181                 return -1;
3182
3183         return 0;
3184 }
3185
3186 int test_dim_max(isl_ctx *ctx)
3187 {
3188         int equal;
3189         const char *str;
3190         isl_set *set1, *set2;
3191         isl_set *set;
3192         isl_map *map;
3193         isl_pw_aff *pwaff;
3194
3195         str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3196         set = isl_set_read_from_str(ctx, str);
3197         pwaff = isl_set_dim_max(set, 0);
3198         set1 = isl_set_from_pw_aff(pwaff);
3199         str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3200         set2 = isl_set_read_from_str(ctx, str);
3201         equal = isl_set_is_equal(set1, set2);
3202         isl_set_free(set1);
3203         isl_set_free(set2);
3204         if (equal < 0)
3205                 return -1;
3206         if (!equal)
3207                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3208
3209         str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3210         set = isl_set_read_from_str(ctx, str);
3211         pwaff = isl_set_dim_max(set, 0);
3212         set1 = isl_set_from_pw_aff(pwaff);
3213         str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3214         set2 = isl_set_read_from_str(ctx, str);
3215         equal = isl_set_is_equal(set1, set2);
3216         isl_set_free(set1);
3217         isl_set_free(set2);
3218         if (equal < 0)
3219                 return -1;
3220         if (!equal)
3221                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3222
3223         str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3224         set = isl_set_read_from_str(ctx, str);
3225         pwaff = isl_set_dim_max(set, 0);
3226         set1 = isl_set_from_pw_aff(pwaff);
3227         str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3228         set2 = isl_set_read_from_str(ctx, str);
3229         equal = isl_set_is_equal(set1, set2);
3230         isl_set_free(set1);
3231         isl_set_free(set2);
3232         if (equal < 0)
3233                 return -1;
3234         if (!equal)
3235                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3236
3237         str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3238                         "0 <= i < N and 0 <= j < M }";
3239         map = isl_map_read_from_str(ctx, str);
3240         set = isl_map_range(map);
3241
3242         pwaff = isl_set_dim_max(isl_set_copy(set), 0);
3243         set1 = isl_set_from_pw_aff(pwaff);
3244         str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3245         set2 = isl_set_read_from_str(ctx, str);
3246         equal = isl_set_is_equal(set1, set2);
3247         isl_set_free(set1);
3248         isl_set_free(set2);
3249
3250         pwaff = isl_set_dim_max(isl_set_copy(set), 3);
3251         set1 = isl_set_from_pw_aff(pwaff);
3252         str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3253         set2 = isl_set_read_from_str(ctx, str);
3254         if (equal >= 0 && equal)
3255                 equal = isl_set_is_equal(set1, set2);
3256         isl_set_free(set1);
3257         isl_set_free(set2);
3258
3259         isl_set_free(set);
3260
3261         if (equal < 0)
3262                 return -1;
3263         if (!equal)
3264                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3265
3266         /* Check that solutions are properly merged. */
3267         str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
3268                                 "c <= -1 + n - 4a - 2b and c >= -2b and "
3269                                 "4a >= -4 + n and c >= 0 }";
3270         set = isl_set_read_from_str(ctx, str);
3271         pwaff = isl_set_dim_min(set, 2);
3272         set1 = isl_set_from_pw_aff(pwaff);
3273         str = "[n] -> { [(0)] : n >= 1 }";
3274         set2 = isl_set_read_from_str(ctx, str);
3275         equal = isl_set_is_equal(set1, set2);
3276         isl_set_free(set1);
3277         isl_set_free(set2);
3278
3279         if (equal < 0)
3280                 return -1;
3281         if (!equal)
3282                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3283
3284         return 0;
3285 }
3286
3287 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3288  */
3289 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
3290         const char *str)
3291 {
3292         isl_ctx *ctx;
3293         isl_pw_multi_aff *pma2;
3294         int equal;
3295
3296         if (!pma)
3297                 return -1;
3298
3299         ctx = isl_pw_multi_aff_get_ctx(pma);
3300         pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3301         equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
3302         isl_pw_multi_aff_free(pma2);
3303
3304         return equal;
3305 }
3306
3307 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3308  * represented by "str".
3309  */
3310 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
3311         const char *str)
3312 {
3313         int equal;
3314
3315         equal = pw_multi_aff_plain_is_equal(pma, str);
3316         if (equal < 0)
3317                 return -1;
3318         if (!equal)
3319                 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
3320                         "result not as expected", return -1);
3321         return 0;
3322 }
3323
3324 /* Basic test for isl_pw_multi_aff_product.
3325  *
3326  * Check that multiple pieces are properly handled.
3327  */
3328 static int test_product_pma(isl_ctx *ctx)
3329 {
3330         int equal;
3331         const char *str;
3332         isl_pw_multi_aff *pma1, *pma2;
3333
3334         str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3335         pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3336         str = "{ C[] -> D[] }";
3337         pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3338         pma1 = isl_pw_multi_aff_product(pma1, pma2);
3339         str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3340                 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3341         equal = pw_multi_aff_check_plain_equal(pma1, str);
3342         isl_pw_multi_aff_free(pma1);
3343         if (equal < 0)
3344                 return -1;
3345
3346         return 0;
3347 }
3348
3349 int test_product(isl_ctx *ctx)
3350 {
3351         const char *str;
3352         isl_set *set;
3353         isl_union_set *uset1, *uset2;
3354         int ok;
3355
3356         str = "{ A[i] }";
3357         set = isl_set_read_from_str(ctx, str);
3358         set = isl_set_product(set, isl_set_copy(set));
3359         ok = isl_set_is_wrapping(set);
3360         isl_set_free(set);
3361         if (ok < 0)
3362                 return -1;
3363         if (!ok)
3364                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3365
3366         str = "{ [] }";
3367         uset1 = isl_union_set_read_from_str(ctx, str);
3368         uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
3369         str = "{ [[] -> []] }";
3370         uset2 = isl_union_set_read_from_str(ctx, str);
3371         ok = isl_union_set_is_equal(uset1, uset2);
3372         isl_union_set_free(uset1);
3373         isl_union_set_free(uset2);
3374         if (ok < 0)
3375                 return -1;
3376         if (!ok)
3377                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3378
3379         if (test_product_pma(ctx) < 0)
3380                 return -1;
3381
3382         return 0;
3383 }
3384
3385 int test_equal(isl_ctx *ctx)
3386 {
3387         const char *str;
3388         isl_set *set, *set2;
3389         int equal;
3390
3391         str = "{ S_6[i] }";
3392         set = isl_set_read_from_str(ctx, str);
3393         str = "{ S_7[i] }";
3394         set2 = isl_set_read_from_str(ctx, str);
3395         equal = isl_set_is_equal(set, set2);
3396         isl_set_free(set);
3397         isl_set_free(set2);
3398         if (equal < 0)
3399                 return -1;
3400         if (equal)
3401                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3402
3403         return 0;
3404 }
3405
3406 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
3407         enum isl_dim_type type, unsigned pos, int fixed)
3408 {
3409         int test;
3410
3411         test = isl_map_plain_is_fixed(map, type, pos, NULL);
3412         isl_map_free(map);
3413         if (test < 0)
3414                 return -1;
3415         if (test == fixed)
3416                 return 0;
3417         if (fixed)
3418                 isl_die(ctx, isl_error_unknown,
3419                         "map not detected as fixed", return -1);
3420         else
3421                 isl_die(ctx, isl_error_unknown,
3422                         "map detected as fixed", return -1);
3423 }
3424
3425 int test_fixed(isl_ctx *ctx)
3426 {
3427         const char *str;
3428         isl_map *map;
3429
3430         str = "{ [i] -> [i] }";
3431         map = isl_map_read_from_str(ctx, str);
3432         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
3433                 return -1;
3434         str = "{ [i] -> [1] }";
3435         map = isl_map_read_from_str(ctx, str);
3436         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3437                 return -1;
3438         str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3439         map = isl_map_read_from_str(ctx, str);
3440         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3441                 return -1;
3442         map = isl_map_read_from_str(ctx, str);
3443         map = isl_map_neg(map);
3444         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3445                 return -1;
3446
3447         return 0;
3448 }
3449
3450 int test_vertices(isl_ctx *ctx)
3451 {
3452         const char *str;
3453         isl_basic_set *bset;
3454         isl_vertices *vertices;
3455
3456         str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
3457         bset = isl_basic_set_read_from_str(ctx, str);
3458         vertices = isl_basic_set_compute_vertices(bset);
3459         isl_basic_set_free(bset);
3460         isl_vertices_free(vertices);
3461         if (!vertices)
3462                 return -1;
3463
3464         str = "{ A[t, i] : t = 14 and i = 1 }";
3465         bset = isl_basic_set_read_from_str(ctx, str);
3466         vertices = isl_basic_set_compute_vertices(bset);
3467         isl_basic_set_free(bset);
3468         isl_vertices_free(vertices);
3469         if (!vertices)
3470                 return -1;
3471
3472         return 0;
3473 }
3474
3475 int test_union_pw(isl_ctx *ctx)
3476 {
3477         int equal;
3478         const char *str;
3479         isl_union_set *uset;
3480         isl_union_pw_qpolynomial *upwqp1, *upwqp2;
3481
3482         str = "{ [x] -> x^2 }";
3483         upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
3484         upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
3485         uset = isl_union_pw_qpolynomial_domain(upwqp1);
3486         upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
3487         upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
3488         equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
3489         isl_union_pw_qpolynomial_free(upwqp1);
3490         isl_union_pw_qpolynomial_free(upwqp2);
3491         if (equal < 0)
3492                 return -1;
3493         if (!equal)
3494                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3495
3496         return 0;
3497 }
3498
3499 int test_output(isl_ctx *ctx)
3500 {
3501         char *s;
3502         const char *str;
3503         isl_pw_aff *pa;
3504         isl_printer *p;
3505         int equal;
3506
3507         str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3508         pa = isl_pw_aff_read_from_str(ctx, str);
3509
3510         p = isl_printer_to_str(ctx);
3511         p = isl_printer_set_output_format(p, ISL_FORMAT_C);
3512         p = isl_printer_print_pw_aff(p, pa);
3513         s = isl_printer_get_str(p);
3514         isl_printer_free(p);
3515         isl_pw_aff_free(pa);
3516         if (!s)
3517                 equal = -1;
3518         else
3519                 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
3520         free(s);
3521         if (equal < 0)
3522                 return -1;
3523         if (!equal)
3524                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3525
3526         return 0;
3527 }
3528
3529 int test_sample(isl_ctx *ctx)
3530 {
3531         const char *str;
3532         isl_basic_set *bset1, *bset2;
3533         int empty, subset;
3534
3535         str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3536             "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3537             "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3538             "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3539             "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3540             "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3541             "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3542             "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3543             "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3544             "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3545             "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3546             "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3547                 "d - 1073741821e and "
3548             "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3549             "3j >= 1 - a + b + 2e and "
3550             "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3551             "3i <= 4 - a + 4b - e and "
3552             "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3553             "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3554             "c <= -1 + a and 3i >= -2 - a + 3e and "
3555             "1073741822e <= 1073741823 - a + 1073741822b + c and "
3556             "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3557             "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3558             "1073741823e >= 1 + 1073741823b - d and "
3559             "3i >= 1073741823b + c - 1073741823e - f and "
3560             "3i >= 1 + 2b + e + 3g }";
3561         bset1 = isl_basic_set_read_from_str(ctx, str);
3562         bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3563         empty = isl_basic_set_is_empty(bset2);
3564         subset = isl_basic_set_is_subset(bset2, bset1);
3565         isl_basic_set_free(bset1);
3566         isl_basic_set_free(bset2);
3567         if (empty < 0 || subset < 0)
3568                 return -1;
3569         if (empty)
3570                 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3571         if (!subset)
3572                 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3573
3574         return 0;
3575 }
3576
3577 int test_fixed_power(isl_ctx *ctx)
3578 {
3579         const char *str;
3580         isl_map *map;
3581         isl_int exp;
3582         int equal;
3583
3584         isl_int_init(exp);
3585         str = "{ [i] -> [i + 1] }";
3586         map = isl_map_read_from_str(ctx, str);
3587         isl_int_set_si(exp, 23);
3588         map = isl_map_fixed_power(map, exp);
3589         equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3590         isl_int_clear(exp);
3591         isl_map_free(map);
3592         if (equal < 0)
3593                 return -1;
3594
3595         return 0;
3596 }
3597
3598 int test_slice(isl_ctx *ctx)
3599 {
3600         const char *str;
3601         isl_map *map;
3602         int equal;
3603
3604         str = "{ [i] -> [j] }";
3605         map = isl_map_read_from_str(ctx, str);
3606         map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3607         equal = map_check_equal(map, "{ [i] -> [i] }");
3608         isl_map_free(map);
3609         if (equal < 0)
3610                 return -1;
3611
3612         str = "{ [i] -> [j] }";
3613         map = isl_map_read_from_str(ctx, str);
3614         map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3615         equal = map_check_equal(map, "{ [i] -> [j] }");
3616         isl_map_free(map);
3617         if (equal < 0)
3618                 return -1;
3619
3620         str = "{ [i] -> [j] }";
3621         map = isl_map_read_from_str(ctx, str);
3622         map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3623         equal = map_check_equal(map, "{ [i] -> [-i] }");
3624         isl_map_free(map);
3625         if (equal < 0)
3626                 return -1;
3627
3628         str = "{ [i] -> [j] }";
3629         map = isl_map_read_from_str(ctx, str);
3630         map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3631         equal = map_check_equal(map, "{ [0] -> [j] }");
3632         isl_map_free(map);
3633         if (equal < 0)
3634                 return -1;
3635
3636         str = "{ [i] -> [j] }";
3637         map = isl_map_read_from_str(ctx, str);
3638         map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3639         equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3640         isl_map_free(map);
3641         if (equal < 0)
3642                 return -1;
3643
3644         str = "{ [i] -> [j] }";
3645         map = isl_map_read_from_str(ctx, str);
3646         map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3647         equal = map_check_equal(map, "{ [i] -> [j] : false }");
3648         isl_map_free(map);
3649         if (equal < 0)
3650                 return -1;
3651
3652         return 0;
3653 }
3654
3655 int test_eliminate(isl_ctx *ctx)
3656 {
3657         const char *str;
3658         isl_map *map;
3659         int equal;
3660
3661         str = "{ [i] -> [j] : i = 2j }";
3662         map = isl_map_read_from_str(ctx, str);
3663         map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3664         equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3665         isl_map_free(map);
3666         if (equal < 0)
3667                 return -1;
3668
3669         return 0;
3670 }
3671
3672 /* Check that isl_set_dim_residue_class detects that the values of j
3673  * in the set below are all odd and that it does not detect any spurious
3674  * strides.
3675  */
3676 static int test_residue_class(isl_ctx *ctx)
3677 {
3678         const char *str;
3679         isl_set *set;
3680         isl_int m, r;
3681         int res;
3682
3683         str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3684                 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3685         set = isl_set_read_from_str(ctx, str);
3686         isl_int_init(m);
3687         isl_int_init(r);
3688         res = isl_set_dim_residue_class(set, 1, &m, &r);
3689         if (res >= 0 &&
3690             (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3691                 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3692                         res = -1);
3693         isl_int_clear(r);
3694         isl_int_clear(m);
3695         isl_set_free(set);
3696
3697         return res;
3698 }
3699
3700 int test_align_parameters(isl_ctx *ctx)
3701 {
3702         const char *str;
3703         isl_space *space;
3704         isl_multi_aff *ma1, *ma2;
3705         int equal;
3706
3707         str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3708         ma1 = isl_multi_aff_read_from_str(ctx, str);
3709
3710         space = isl_space_params_alloc(ctx, 1);
3711         space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3712         ma1 = isl_multi_aff_align_params(ma1, space);
3713
3714         str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3715         ma2 = isl_multi_aff_read_from_str(ctx, str);
3716
3717         equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3718
3719         isl_multi_aff_free(ma1);
3720         isl_multi_aff_free(ma2);
3721
3722         if (equal < 0)
3723                 return -1;
3724         if (!equal)
3725                 isl_die(ctx, isl_error_unknown,
3726                         "result not as expected", return -1);
3727
3728         return 0;
3729 }
3730
3731 static int test_list(isl_ctx *ctx)
3732 {
3733         isl_id *a, *b, *c, *d, *id;
3734         isl_id_list *list;
3735         int ok;
3736
3737         a = isl_id_alloc(ctx, "a", NULL);
3738         b = isl_id_alloc(ctx, "b", NULL);
3739         c = isl_id_alloc(ctx, "c", NULL);
3740         d = isl_id_alloc(ctx, "d", NULL);
3741
3742         list = isl_id_list_alloc(ctx, 4);
3743         list = isl_id_list_add(list, a);
3744         list = isl_id_list_add(list, b);
3745         list = isl_id_list_add(list, c);
3746         list = isl_id_list_add(list, d);
3747         list = isl_id_list_drop(list, 1, 1);
3748
3749         if (isl_id_list_n_id(list) != 3) {
3750                 isl_id_list_free(list);
3751                 isl_die(ctx, isl_error_unknown,
3752                         "unexpected number of elements in list", return -1);
3753         }
3754
3755         id = isl_id_list_get_id(list, 0);
3756         ok = id == a;
3757         isl_id_free(id);
3758         id = isl_id_list_get_id(list, 1);
3759         ok = ok && id == c;
3760         isl_id_free(id);
3761         id = isl_id_list_get_id(list, 2);
3762         ok = ok && id == d;
3763         isl_id_free(id);
3764
3765         isl_id_list_free(list);
3766
3767         if (!ok)
3768                 isl_die(ctx, isl_error_unknown,
3769                         "unexpected elements in list", return -1);
3770
3771         return 0;
3772 }
3773
3774 const char *set_conversion_tests[] = {
3775         "[N] -> { [i] : N - 1 <= 2 i <= N }",
3776         "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3777         "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3778         "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3779 };
3780
3781 /* Check that converting from isl_set to isl_pw_multi_aff and back
3782  * to isl_set produces the original isl_set.
3783  */
3784 static int test_set_conversion(isl_ctx *ctx)
3785 {
3786         int i;
3787         const char *str;
3788         isl_set *set1, *set2;
3789         isl_pw_multi_aff *pma;
3790         int equal;
3791
3792         for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3793                 str = set_conversion_tests[i];
3794                 set1 = isl_set_read_from_str(ctx, str);
3795                 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3796                 set2 = isl_set_from_pw_multi_aff(pma);
3797                 equal = isl_set_is_equal(set1, set2);
3798                 isl_set_free(set1);
3799                 isl_set_free(set2);
3800
3801                 if (equal < 0)
3802                         return -1;
3803                 if (!equal)
3804                         isl_die(ctx, isl_error_unknown, "bad conversion",
3805                                 return -1);
3806         }
3807
3808         return 0;
3809 }
3810
3811 /* Check that converting from isl_map to isl_pw_multi_aff and back
3812  * to isl_map produces the original isl_map.
3813  */
3814 static int test_map_conversion(isl_ctx *ctx)
3815 {
3816         const char *str;
3817         isl_map *map1, *map2;
3818         isl_pw_multi_aff *pma;
3819         int equal;
3820
3821         str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
3822                 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3823                 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3824                 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3825                 "9e <= -2 - 2a) }";
3826         map1 = isl_map_read_from_str(ctx, str);
3827         pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
3828         map2 = isl_map_from_pw_multi_aff(pma);
3829         equal = isl_map_is_equal(map1, map2);
3830         isl_map_free(map1);
3831         isl_map_free(map2);
3832
3833         if (equal < 0)
3834                 return -1;
3835         if (!equal)
3836                 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
3837
3838         return 0;
3839 }
3840
3841 static int test_conversion(isl_ctx *ctx)
3842 {
3843         if (test_set_conversion(ctx) < 0)
3844                 return -1;
3845         if (test_map_conversion(ctx) < 0)
3846                 return -1;
3847         return 0;
3848 }
3849
3850 /* Check that isl_basic_map_curry does not modify input.
3851  */
3852 static int test_curry(isl_ctx *ctx)
3853 {
3854         const char *str;
3855         isl_basic_map *bmap1, *bmap2;
3856         int equal;
3857
3858         str = "{ [A[] -> B[]] -> C[] }";
3859         bmap1 = isl_basic_map_read_from_str(ctx, str);
3860         bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
3861         equal = isl_basic_map_is_equal(bmap1, bmap2);
3862         isl_basic_map_free(bmap1);
3863         isl_basic_map_free(bmap2);
3864
3865         if (equal < 0)
3866                 return -1;
3867         if (equal)
3868                 isl_die(ctx, isl_error_unknown,
3869                         "curried map should not be equal to original",
3870                         return -1);
3871
3872         return 0;
3873 }
3874
3875 struct {
3876         const char *set;
3877         const char *ma;
3878         const char *res;
3879 } preimage_tests[] = {
3880         { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3881           "{ A[j,i] -> B[i,j] }",
3882           "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3883         { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3884           "{ A[a,b] -> B[a/2,b/6] }",
3885           "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3886         { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3887           "{ A[a,b] -> B[a/2,b/6] }",
3888           "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3889                     "exists i,j : a = 2 i and b = 6 j }" },
3890         { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3891           "[n] -> { : 0 <= n <= 100 }" },
3892         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3893           "{ A[a] -> B[2a] }",
3894           "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3895         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3896           "{ A[a] -> B[([a/2])] }",
3897           "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3898         { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3899           "{ A[a] -> B[a,a,a/3] }",
3900           "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3901         { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3902           "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3903 };
3904
3905 static int test_preimage_basic_set(isl_ctx *ctx)
3906 {
3907         int i;
3908         isl_basic_set *bset1, *bset2;
3909         isl_multi_aff *ma;
3910         int equal;
3911
3912         for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3913                 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3914                 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3915                 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3916                 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3917                 equal = isl_basic_set_is_equal(bset1, bset2);
3918                 isl_basic_set_free(bset1);
3919                 isl_basic_set_free(bset2);
3920                 if (equal < 0)
3921                         return -1;
3922                 if (!equal)
3923                         isl_die(ctx, isl_error_unknown, "bad preimage",
3924                                 return -1);
3925         }
3926
3927         return 0;
3928 }
3929
3930 struct {
3931         const char *map;
3932         const char *ma;
3933         const char *res;
3934 } preimage_domain_tests[] = {
3935         { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
3936           "{ A[j,i] -> B[i,j] }",
3937           "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
3938         { "{ B[i] -> C[i]; D[i] -> E[i] }",
3939           "{ A[i] -> B[i + 1] }",
3940           "{ A[i] -> C[i + 1] }" },
3941         { "{ B[i] -> C[i]; B[i] -> E[i] }",
3942           "{ A[i] -> B[i + 1] }",
3943           "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
3944         { "{ B[i] -> C[([i/2])] }",
3945           "{ A[i] -> B[2i] }",
3946           "{ A[i] -> C[i] }" },
3947         { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
3948           "{ A[i] -> B[([i/5]), ([i/7])] }",
3949           "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
3950         { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
3951           "[N] -> { A[] -> B[([N/5])] }",
3952           "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
3953         { "{ B[i] -> C[i] : exists a : i = 5 a }",
3954           "{ A[i] -> B[2i] }",
3955           "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
3956         { "{ B[i] -> C[i] : exists a : i = 2 a; "
3957             "B[i] -> D[i] : exists a : i = 2 a + 1 }",
3958           "{ A[i] -> B[2i] }",
3959           "{ A[i] -> C[2i] }" },
3960 };
3961
3962 static int test_preimage_union_map(isl_ctx *ctx)
3963 {
3964         int i;
3965         isl_union_map *umap1, *umap2;
3966         isl_multi_aff *ma;
3967         int equal;
3968
3969         for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
3970                 umap1 = isl_union_map_read_from_str(ctx,
3971                                                 preimage_domain_tests[i].map);
3972                 ma = isl_multi_aff_read_from_str(ctx,
3973                                                 preimage_domain_tests[i].ma);
3974                 umap2 = isl_union_map_read_from_str(ctx,
3975                                                 preimage_domain_tests[i].res);
3976                 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
3977                 equal = isl_union_map_is_equal(umap1, umap2);
3978                 isl_union_map_free(umap1);
3979                 isl_union_map_free(umap2);
3980                 if (equal < 0)
3981                         return -1;
3982                 if (!equal)
3983                         isl_die(ctx, isl_error_unknown, "bad preimage",
3984                                 return -1);
3985         }
3986
3987         return 0;
3988 }
3989
3990 static int test_preimage(isl_ctx *ctx)
3991 {
3992         if (test_preimage_basic_set(ctx) < 0)
3993                 return -1;
3994         if (test_preimage_union_map(ctx) < 0)
3995                 return -1;
3996
3997         return 0;
3998 }
3999
4000 struct {
4001         const char *ma1;
4002         const char *ma;
4003         const char *res;
4004 } pullback_tests[] = {
4005         { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4006           "{ A[a,b] -> C[b + 2a] }" },
4007         { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4008         { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4009         { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4010           "{ A[a] -> C[(a)/6] }" },
4011         { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4012         { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4013           "{ A[a] -> C[(2a)/3] }" },
4014         { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4015         { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4016           "{ A[i,j] -> C[i + j, i + j] }"},
4017         { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4018         { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4019           "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4020 };
4021
4022 static int test_pullback(isl_ctx *ctx)
4023 {
4024         int i;
4025         isl_multi_aff *ma1, *ma2;
4026         isl_multi_aff *ma;
4027         int equal;
4028
4029         for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
4030                 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
4031                 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
4032                 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
4033                 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
4034                 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4035                 isl_multi_aff_free(ma1);
4036                 isl_multi_aff_free(ma2);
4037                 if (equal < 0)
4038                         return -1;
4039                 if (!equal)
4040                         isl_die(ctx, isl_error_unknown, "bad pullback",
4041                                 return -1);
4042         }
4043
4044         return 0;
4045 }
4046
4047 /* Check that negation is printed correctly.
4048  */
4049 static int test_ast(isl_ctx *ctx)
4050 {
4051         isl_ast_expr *expr, *expr1, *expr2, *expr3;
4052         char *str;
4053         int ok;
4054
4055         expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4056         expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4057         expr = isl_ast_expr_add(expr1, expr2);
4058         expr = isl_ast_expr_neg(expr);
4059         str = isl_ast_expr_to_str(expr);
4060         ok = str ? !strcmp(str, "-(A + B)") : -1;
4061         free(str);
4062         isl_ast_expr_free(expr);
4063
4064         if (ok < 0)
4065                 return -1;
4066         if (!ok)
4067                 isl_die(ctx, isl_error_unknown,
4068                         "isl_ast_expr printed incorrectly", return -1);
4069
4070         expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4071         expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4072         expr = isl_ast_expr_add(expr1, expr2);
4073         expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
4074         expr = isl_ast_expr_sub(expr3, expr);
4075         str = isl_ast_expr_to_str(expr);
4076         ok = str ? !strcmp(str, "C - (A + B)") : -1;
4077         free(str);
4078         isl_ast_expr_free(expr);
4079
4080         if (ok < 0)
4081                 return -1;
4082         if (!ok)
4083                 isl_die(ctx, isl_error_unknown,
4084                         "isl_ast_expr printed incorrectly", return -1);
4085
4086         return 0;
4087 }
4088
4089 /* Internal data structure for before_for and after_for callbacks.
4090  *
4091  * depth is the current depth
4092  * before is the number of times before_for has been called
4093  * after is the number of times after_for has been called
4094  */
4095 struct isl_test_codegen_data {
4096         int depth;
4097         int before;
4098         int after;
4099 };
4100
4101 /* This function is called before each for loop in the AST generated
4102  * from test_ast_gen1.
4103  *
4104  * Increment the number of calls and the depth.
4105  * Check that the space returned by isl_ast_build_get_schedule_space
4106  * matches the target space of the schedule returned by
4107  * isl_ast_build_get_schedule.
4108  * Return an isl_id that is checked by the corresponding call
4109  * to after_for.
4110  */
4111 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
4112         void *user)
4113 {
4114         struct isl_test_codegen_data *data = user;
4115         isl_ctx *ctx;
4116         isl_space *space;
4117         isl_union_map *schedule;
4118         isl_union_set *uset;
4119         isl_set *set;
4120         int empty;
4121         char name[] = "d0";
4122
4123         ctx = isl_ast_build_get_ctx(build);
4124
4125         if (data->before >= 3)
4126                 isl_die(ctx, isl_error_unknown,
4127                         "unexpected number of for nodes", return NULL);
4128         if (data->depth >= 2)
4129                 isl_die(ctx, isl_error_unknown,
4130                         "unexpected depth", return NULL);
4131
4132         snprintf(name, sizeof(name), "d%d", data->depth);
4133         data->before++;
4134         data->depth++;
4135
4136         schedule = isl_ast_build_get_schedule(build);
4137         uset = isl_union_map_range(schedule);
4138         if (!uset)
4139                 return NULL;
4140         if (isl_union_set_n_set(uset) != 1) {
4141                 isl_union_set_free(uset);
4142                 isl_die(ctx, isl_error_unknown,
4143                         "expecting single range space", return NULL);
4144         }
4145
4146         space = isl_ast_build_get_schedule_space(build);
4147         set = isl_union_set_extract_set(uset, space);
4148         isl_union_set_free(uset);
4149         empty = isl_set_is_empty(set);
4150         isl_set_free(set);
4151
4152         if (empty < 0)
4153                 return NULL;
4154         if (empty)
4155                 isl_die(ctx, isl_error_unknown,
4156                         "spaces don't match", return NULL);
4157
4158         return isl_id_alloc(ctx, name, NULL);
4159 }
4160
4161 /* This function is called after each for loop in the AST generated
4162  * from test_ast_gen1.
4163  *
4164  * Increment the number of calls and decrement the depth.
4165  * Check that the annotation attached to the node matches
4166  * the isl_id returned by the corresponding call to before_for.
4167  */
4168 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
4169         __isl_keep isl_ast_build *build, void *user)
4170 {
4171         struct isl_test_codegen_data *data = user;
4172         isl_id *id;
4173         const char *name;
4174         int valid;
4175
4176         data->after++;
4177         data->depth--;
4178
4179         if (data->after > data->before)
4180                 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4181                         "mismatch in number of for nodes",
4182                         return isl_ast_node_free(node));
4183
4184         id = isl_ast_node_get_annotation(node);
4185         if (!id)
4186                 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4187                         "missing annotation", return isl_ast_node_free(node));
4188
4189         name = isl_id_get_name(id);
4190         valid = name && atoi(name + 1) == data->depth;
4191         isl_id_free(id);
4192
4193         if (!valid)
4194                 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4195                         "wrong annotation", return isl_ast_node_free(node));
4196
4197         return node;
4198 }
4199
4200 /* Check that the before_each_for and after_each_for callbacks
4201  * are called for each for loop in the generated code,
4202  * that they are called in the right order and that the isl_id
4203  * returned from the before_each_for callback is attached to
4204  * the isl_ast_node passed to the corresponding after_each_for call.
4205  */
4206 static int test_ast_gen1(isl_ctx *ctx)
4207 {
4208         const char *str;
4209         isl_set *set;
4210         isl_union_map *schedule;
4211         isl_ast_build *build;
4212         isl_ast_node *tree;
4213         struct isl_test_codegen_data data;
4214
4215         str = "[N] -> { : N >= 10 }";
4216         set = isl_set_read_from_str(ctx, str);
4217         str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4218                     "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4219         schedule = isl_union_map_read_from_str(ctx, str);
4220
4221         data.before = 0;
4222         data.after = 0;
4223         data.depth = 0;
4224         build = isl_ast_build_from_context(set);
4225         build = isl_ast_build_set_before_each_for(build,
4226                         &before_for, &data);
4227         build = isl_ast_build_set_after_each_for(build,
4228                         &after_for, &data);
4229         tree = isl_ast_build_ast_from_schedule(build, schedule);
4230         isl_ast_build_free(build);
4231         if (!tree)
4232                 return -1;
4233
4234         isl_ast_node_free(tree);
4235
4236         if (data.before != 3 || data.after != 3)
4237                 isl_die(ctx, isl_error_unknown,
4238                         "unexpected number of for nodes", return -1);
4239
4240         return 0;
4241 }
4242
4243 /* Check that the AST generator handles domains that are integrally disjoint
4244  * but not ratinoally disjoint.
4245  */
4246 static int test_ast_gen2(isl_ctx *ctx)
4247 {
4248         const char *str;
4249         isl_set *set;
4250         isl_union_map *schedule;
4251         isl_union_map *options;
4252         isl_ast_build *build;
4253         isl_ast_node *tree;
4254
4255         str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4256         schedule = isl_union_map_read_from_str(ctx, str);
4257         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4258         build = isl_ast_build_from_context(set);
4259
4260         str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4261         options = isl_union_map_read_from_str(ctx, str);
4262         build = isl_ast_build_set_options(build, options);
4263         tree = isl_ast_build_ast_from_schedule(build, schedule);
4264         isl_ast_build_free(build);
4265         if (!tree)
4266                 return -1;
4267         isl_ast_node_free(tree);
4268
4269         return 0;
4270 }
4271
4272 /* Increment *user on each call.
4273  */
4274 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
4275         __isl_keep isl_ast_build *build, void *user)
4276 {
4277         int *n = user;
4278
4279         (*n)++;
4280
4281         return node;
4282 }
4283
4284 /* Test that unrolling tries to minimize the number of instances.
4285  * In particular, for the schedule given below, make sure it generates
4286  * 3 nodes (rather than 101).
4287  */
4288 static int test_ast_gen3(isl_ctx *ctx)
4289 {
4290         const char *str;
4291         isl_set *set;
4292         isl_union_map *schedule;
4293         isl_union_map *options;
4294         isl_ast_build *build;
4295         isl_ast_node *tree;
4296         int n_domain = 0;
4297
4298         str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4299         schedule = isl_union_map_read_from_str(ctx, str);
4300         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4301
4302         str = "{ [i] -> unroll[0] }";
4303         options = isl_union_map_read_from_str(ctx, str);
4304
4305         build = isl_ast_build_from_context(set);
4306         build = isl_ast_build_set_options(build, options);
4307         build = isl_ast_build_set_at_each_domain(build,
4308                         &count_domains, &n_domain);
4309         tree = isl_ast_build_ast_from_schedule(build, schedule);
4310         isl_ast_build_free(build);
4311         if (!tree)
4312                 return -1;
4313
4314         isl_ast_node_free(tree);
4315
4316         if (n_domain != 3)
4317                 isl_die(ctx, isl_error_unknown,
4318                         "unexpected number of for nodes", return -1);
4319
4320         return 0;
4321 }
4322
4323 /* Check that if the ast_build_exploit_nested_bounds options is set,
4324  * we do not get an outer if node in the generated AST,
4325  * while we do get such an outer if node if the options is not set.
4326  */
4327 static int test_ast_gen4(isl_ctx *ctx)
4328 {
4329         const char *str;
4330         isl_set *set;
4331         isl_union_map *schedule;
4332         isl_ast_build *build;
4333         isl_ast_node *tree;
4334         enum isl_ast_node_type type;
4335         int enb;
4336
4337         enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
4338         str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4339
4340         isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
4341
4342         schedule = isl_union_map_read_from_str(ctx, str);
4343         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4344         build = isl_ast_build_from_context(set);
4345         tree = isl_ast_build_ast_from_schedule(build, schedule);
4346         isl_ast_build_free(build);
4347         if (!tree)
4348                 return -1;
4349
4350         type = isl_ast_node_get_type(tree);
4351         isl_ast_node_free(tree);
4352
4353         if (type == isl_ast_node_if)
4354                 isl_die(ctx, isl_error_unknown,
4355                         "not expecting if node", return -1);
4356
4357         isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
4358
4359         schedule = isl_union_map_read_from_str(ctx, str);
4360         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4361         build = isl_ast_build_from_context(set);
4362         tree = isl_ast_build_ast_from_schedule(build, schedule);
4363         isl_ast_build_free(build);
4364         if (!tree)
4365                 return -1;
4366
4367         type = isl_ast_node_get_type(tree);
4368         isl_ast_node_free(tree);
4369
4370         if (type != isl_ast_node_if)
4371                 isl_die(ctx, isl_error_unknown,
4372                         "expecting if node", return -1);
4373
4374         isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
4375
4376         return 0;
4377 }
4378
4379 /* This function is called for each leaf in the AST generated
4380  * from test_ast_gen5.
4381  *
4382  * We finalize the AST generation by extending the outer schedule
4383  * with a zero-dimensional schedule.  If this results in any for loops,
4384  * then this means that we did not pass along enough information
4385  * about the outer schedule to the inner AST generation.
4386  */
4387 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
4388         void *user)
4389 {
4390         isl_union_map *schedule, *extra;
4391         isl_ast_node *tree;
4392
4393         schedule = isl_ast_build_get_schedule(build);
4394         extra = isl_union_map_copy(schedule);
4395         extra = isl_union_map_from_domain(isl_union_map_domain(extra));
4396         schedule = isl_union_map_range_product(schedule, extra);
4397         tree = isl_ast_build_ast_from_schedule(build, schedule);
4398         isl_ast_build_free(build);
4399
4400         if (!tree)
4401                 return NULL;
4402
4403         if (isl_ast_node_get_type(tree) == isl_ast_node_for)
4404                 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
4405                         "code should not contain any for loop",
4406                         return isl_ast_node_free(tree));
4407
4408         return tree;
4409 }
4410
4411 /* Check that we do not lose any information when going back and
4412  * forth between internal and external schedule.
4413  *
4414  * In particular, we create an AST where we unroll the only
4415  * non-constant dimension in the schedule.  We therefore do
4416  * not expect any for loops in the AST.  However, older versions
4417  * of isl would not pass along enough information about the outer
4418  * schedule when performing an inner code generation from a create_leaf
4419  * callback, resulting in the inner code generation producing a for loop.
4420  */
4421 static int test_ast_gen5(isl_ctx *ctx)
4422 {
4423         const char *str;
4424         isl_set *set;
4425         isl_union_map *schedule, *options;
4426         isl_ast_build *build;
4427         isl_ast_node *tree;
4428
4429         str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4430         schedule = isl_union_map_read_from_str(ctx, str);
4431
4432         str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4433                                 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4434         options = isl_union_map_read_from_str(ctx, str);
4435
4436         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4437         build = isl_ast_build_from_context(set);
4438         build = isl_ast_build_set_options(build, options);
4439         build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
4440         tree = isl_ast_build_ast_from_schedule(build, schedule);
4441         isl_ast_build_free(build);
4442         isl_ast_node_free(tree);
4443         if (!tree)
4444                 return -1;
4445
4446         return 0;
4447 }
4448
4449 static int test_ast_gen(isl_ctx *ctx)
4450 {
4451         if (test_ast_gen1(ctx) < 0)
4452                 return -1;
4453         if (test_ast_gen2(ctx) < 0)
4454                 return -1;
4455         if (test_ast_gen3(ctx) < 0)
4456                 return -1;
4457         if (test_ast_gen4(ctx) < 0)
4458                 return -1;
4459         if (test_ast_gen5(ctx) < 0)
4460                 return -1;
4461         return 0;
4462 }
4463
4464 /* Check if dropping output dimensions from an isl_pw_multi_aff
4465  * works properly.
4466  */
4467 static int test_pw_multi_aff(isl_ctx *ctx)
4468 {
4469         const char *str;
4470         isl_pw_multi_aff *pma1, *pma2;
4471         int equal;
4472
4473         str = "{ [i,j] -> [i+j, 4i-j] }";
4474         pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4475         str = "{ [i,j] -> [4i-j] }";
4476         pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4477
4478         pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
4479
4480         equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
4481
4482         isl_pw_multi_aff_free(pma1);
4483         isl_pw_multi_aff_free(pma2);
4484         if (equal < 0)
4485                 return -1;
4486         if (!equal)
4487                 isl_die(ctx, isl_error_unknown,
4488                         "expressions not equal", return -1);
4489
4490         return 0;
4491 }
4492
4493 /* Check that we can properly parse multi piecewise affine expressions
4494  * where the piecewise affine expressions have different domains.
4495  */
4496 static int test_multi_pw_aff(isl_ctx *ctx)
4497 {
4498         const char *str;
4499         isl_set *dom, *dom2;
4500         isl_multi_pw_aff *mpa1, *mpa2;
4501         isl_pw_aff *pa;
4502         int equal;
4503         int equal_domain;
4504
4505         mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
4506         dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
4507         mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
4508         mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
4509         mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
4510         str = "{ [i] -> [(i : i > 0), 2i] }";
4511         mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
4512
4513         equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
4514
4515         pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
4516         dom = isl_pw_aff_domain(pa);
4517         pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
4518         dom2 = isl_pw_aff_domain(pa);
4519         equal_domain = isl_set_is_equal(dom, dom2);
4520
4521         isl_set_free(dom);
4522         isl_set_free(dom2);
4523         isl_multi_pw_aff_free(mpa1);
4524         isl_multi_pw_aff_free(mpa2);
4525
4526         if (equal < 0)
4527                 return -1;
4528         if (!equal)
4529                 isl_die(ctx, isl_error_unknown,
4530                         "expressions not equal", return -1);
4531
4532         if (equal_domain < 0)
4533                 return -1;
4534         if (equal_domain)
4535                 isl_die(ctx, isl_error_unknown,
4536                         "domains unexpectedly equal", return -1);
4537
4538         return 0;
4539 }
4540
4541 /* This is a regression test for a bug where isl_basic_map_simplify
4542  * would end up in an infinite loop.  In particular, we construct
4543  * an empty basic set that is not obviously empty.
4544  * isl_basic_set_is_empty marks the basic set as empty.
4545  * After projecting out i3, the variable can be dropped completely,
4546  * but isl_basic_map_simplify refrains from doing so if the basic set
4547  * is empty and would end up in an infinite loop if it didn't test
4548  * explicitly for empty basic maps in the outer loop.
4549  */
4550 static int test_simplify(isl_ctx *ctx)
4551 {
4552         const char *str;
4553         isl_basic_set *bset;
4554         int empty;
4555
4556         str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4557                 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4558                 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4559                 "i3 >= i2 }";
4560         bset = isl_basic_set_read_from_str(ctx, str);
4561         empty = isl_basic_set_is_empty(bset);
4562         bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
4563         isl_basic_set_free(bset);
4564         if (!bset)
4565                 return -1;
4566         if (!empty)
4567                 isl_die(ctx, isl_error_unknown,
4568                         "basic set should be empty", return -1);
4569
4570         return 0;
4571 }
4572
4573 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4574  * with gbr context would fail to disable the use of the shifted tableau
4575  * when transferring equalities for the input to the context, resulting
4576  * in invalid sample values.
4577  */
4578 static int test_partial_lexmin(isl_ctx *ctx)
4579 {
4580         const char *str;
4581         isl_basic_set *bset;
4582         isl_basic_map *bmap;
4583         isl_map *map;
4584
4585         str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
4586         bmap = isl_basic_map_read_from_str(ctx, str);
4587         str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
4588         bset = isl_basic_set_read_from_str(ctx, str);
4589         map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
4590         isl_map_free(map);
4591
4592         if (!map)
4593                 return -1;
4594
4595         return 0;
4596 }
4597
4598 /* Check that the variable compression performed on the existentially
4599  * quantified variables inside isl_basic_set_compute_divs is not confused
4600  * by the implicit equalities among the parameters.
4601  */
4602 static int test_compute_divs(isl_ctx *ctx)
4603 {
4604         const char *str;
4605         isl_basic_set *bset;
4606         isl_set *set;
4607
4608         str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4609                 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4610                 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4611                 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4612         bset = isl_basic_set_read_from_str(ctx, str);
4613         set = isl_basic_set_compute_divs(bset);
4614         isl_set_free(set);
4615         if (!set)
4616                 return -1;
4617
4618         return 0;
4619 }
4620
4621 struct {
4622         const char *name;
4623         int (*fn)(isl_ctx *ctx);
4624 } tests [] = {
4625         { "val", &test_val },
4626         { "compute divs", &test_compute_divs },
4627         { "partial lexmin", &test_partial_lexmin },
4628         { "simplify", &test_simplify },
4629         { "curry", &test_curry },
4630         { "piecewise multi affine expressions", &test_pw_multi_aff },
4631         { "multi piecewise affine expressions", &test_multi_pw_aff },
4632         { "conversion", &test_conversion },
4633         { "list", &test_list },
4634         { "align parameters", &test_align_parameters },
4635         { "preimage", &test_preimage },
4636         { "pullback", &test_pullback },
4637         { "AST", &test_ast },
4638         { "AST generation", &test_ast_gen },
4639         { "eliminate", &test_eliminate },
4640         { "residue class", &test_residue_class },
4641         { "div", &test_div },
4642         { "slice", &test_slice },
4643         { "fixed power", &test_fixed_power },
4644         { "sample", &test_sample },
4645         { "output", &test_output },
4646         { "vertices", &test_vertices },
4647         { "fixed", &test_fixed },
4648         { "equal", &test_equal },
4649         { "product", &test_product },
4650         { "dim_max", &test_dim_max },
4651         { "affine", &test_aff },
4652         { "injective", &test_injective },
4653         { "schedule", &test_schedule },
4654         { "union_pw", &test_union_pw },
4655         { "parse", &test_parse },
4656         { "single-valued", &test_sv },
4657         { "affine hull", &test_affine_hull },
4658         { "coalesce", &test_coalesce },
4659         { "factorize", &test_factorize },
4660         { "subset", &test_subset },
4661         { "subtract", &test_subtract },
4662         { "lexmin", &test_lexmin },
4663         { "gist", &test_gist },
4664         { "piecewise quasi-polynomials", &test_pwqp },
4665 };
4666
4667 int main()
4668 {
4669         int i;
4670         struct isl_ctx *ctx;
4671
4672         srcdir = getenv("srcdir");
4673         assert(srcdir);
4674
4675         ctx = isl_ctx_alloc();
4676         for (i = 0; i < ARRAY_SIZE(tests); ++i) {
4677                 printf("%s\n", tests[i].name);
4678                 if (tests[i].fn(ctx) < 0)
4679                         goto error;
4680         }
4681         test_lift(ctx);
4682         test_bound(ctx);
4683         test_union(ctx);
4684         test_split_periods(ctx);
4685         test_lex(ctx);
4686         test_bijective(ctx);
4687         test_dep(ctx);
4688         test_read(ctx);
4689         test_bounded(ctx);
4690         test_construction(ctx);
4691         test_dim(ctx);
4692         test_application(ctx);
4693         test_convex_hull(ctx);
4694         test_closure(ctx);
4695         isl_ctx_free(ctx);
4696         return 0;
4697 error:
4698         isl_ctx_free(ctx);
4699         return -1;
4700 }