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 *sched;
2432         int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2433
2434         D = isl_union_set_read_from_str(ctx, d);
2435         W = isl_union_map_read_from_str(ctx, w);
2436         R = isl_union_map_read_from_str(ctx, r);
2437         S = isl_union_map_read_from_str(ctx, s);
2438
2439         W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2440         R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2441
2442         empty = isl_union_map_empty(isl_union_map_get_space(S));
2443         isl_union_map_compute_flow(isl_union_map_copy(R),
2444                                    isl_union_map_copy(W), empty,
2445                                    isl_union_map_copy(S),
2446                                    &dep_raw, NULL, NULL, NULL);
2447         isl_union_map_compute_flow(isl_union_map_copy(W),
2448                                    isl_union_map_copy(W),
2449                                    isl_union_map_copy(R),
2450                                    isl_union_map_copy(S),
2451                                    &dep_waw, &dep_war, NULL, NULL);
2452
2453         dep = isl_union_map_union(dep_waw, dep_war);
2454         dep = isl_union_map_union(dep, dep_raw);
2455         validity = isl_union_map_copy(dep);
2456         proximity = isl_union_map_copy(dep);
2457
2458         sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2459                                                validity, proximity);
2460         schedule = isl_schedule_get_map(sched);
2461         isl_schedule_free(sched);
2462         isl_union_map_free(W);
2463         isl_union_map_free(R);
2464         isl_union_map_free(S);
2465
2466         is_injection = 1;
2467         isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2468
2469         domain = isl_union_map_domain(isl_union_map_copy(schedule));
2470         is_complete = isl_union_set_is_subset(D, domain);
2471         isl_union_set_free(D);
2472         isl_union_set_free(domain);
2473
2474         test = isl_union_map_reverse(isl_union_map_copy(schedule));
2475         test = isl_union_map_apply_range(test, dep);
2476         test = isl_union_map_apply_range(test, schedule);
2477
2478         delta = isl_union_map_deltas(test);
2479         if (isl_union_set_n_set(delta) == 0) {
2480                 is_tilable = 1;
2481                 is_parallel = 1;
2482                 is_nonneg = 1;
2483                 isl_union_set_free(delta);
2484         } else {
2485                 delta_set = isl_set_from_union_set(delta);
2486
2487                 slice = isl_set_universe(isl_set_get_space(delta_set));
2488                 for (i = 0; i < tilable; ++i)
2489                         slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2490                 is_tilable = isl_set_is_subset(delta_set, slice);
2491                 isl_set_free(slice);
2492
2493                 slice = isl_set_universe(isl_set_get_space(delta_set));
2494                 for (i = 0; i < parallel; ++i)
2495                         slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2496                 is_parallel = isl_set_is_subset(delta_set, slice);
2497                 isl_set_free(slice);
2498
2499                 origin = isl_set_universe(isl_set_get_space(delta_set));
2500                 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2501                         origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2502
2503                 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2504                 delta_set = isl_set_lexmin(delta_set);
2505
2506                 is_nonneg = isl_set_is_equal(delta_set, origin);
2507
2508                 isl_set_free(origin);
2509                 isl_set_free(delta_set);
2510         }
2511
2512         if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2513             is_injection < 0 || is_complete < 0)
2514                 return -1;
2515         if (!is_complete)
2516                 isl_die(ctx, isl_error_unknown,
2517                         "generated schedule incomplete", return -1);
2518         if (!is_injection)
2519                 isl_die(ctx, isl_error_unknown,
2520                         "generated schedule not injective on each statement",
2521                         return -1);
2522         if (!is_nonneg)
2523                 isl_die(ctx, isl_error_unknown,
2524                         "negative dependences in generated schedule",
2525                         return -1);
2526         if (!is_tilable)
2527                 isl_die(ctx, isl_error_unknown,
2528                         "generated schedule not as tilable as expected",
2529                         return -1);
2530         if (!is_parallel)
2531                 isl_die(ctx, isl_error_unknown,
2532                         "generated schedule not as parallel as expected",
2533                         return -1);
2534
2535         return 0;
2536 }
2537
2538 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2539         const char *domain, const char *validity, const char *proximity)
2540 {
2541         isl_union_set *dom;
2542         isl_union_map *dep;
2543         isl_union_map *prox;
2544         isl_schedule *schedule;
2545         isl_union_map *sched;
2546
2547         dom = isl_union_set_read_from_str(ctx, domain);
2548         dep = isl_union_map_read_from_str(ctx, validity);
2549         prox = isl_union_map_read_from_str(ctx, proximity);
2550         schedule = isl_union_set_compute_schedule(dom, dep, prox);
2551         sched = isl_schedule_get_map(schedule);
2552         isl_schedule_free(schedule);
2553
2554         return sched;
2555 }
2556
2557 /* Check that a schedule can be constructed on the given domain
2558  * with the given validity and proximity constraints.
2559  */
2560 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2561         const char *validity, const char *proximity)
2562 {
2563         isl_union_map *sched;
2564
2565         sched = compute_schedule(ctx, domain, validity, proximity);
2566         if (!sched)
2567                 return -1;
2568
2569         isl_union_map_free(sched);
2570         return 0;
2571 }
2572
2573 int test_special_schedule(isl_ctx *ctx, const char *domain,
2574         const char *validity, const char *proximity, const char *expected_sched)
2575 {
2576         isl_union_map *sched1, *sched2;
2577         int equal;
2578
2579         sched1 = compute_schedule(ctx, domain, validity, proximity);
2580         sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2581
2582         equal = isl_union_map_is_equal(sched1, sched2);
2583         isl_union_map_free(sched1);
2584         isl_union_map_free(sched2);
2585
2586         if (equal < 0)
2587                 return -1;
2588         if (!equal)
2589                 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2590                         return -1);
2591
2592         return 0;
2593 }
2594
2595 /* Check that the schedule map is properly padded, even after being
2596  * reconstructed from the band forest.
2597  */
2598 static int test_padded_schedule(isl_ctx *ctx)
2599 {
2600         const char *str;
2601         isl_union_set *D;
2602         isl_union_map *validity, *proximity;
2603         isl_schedule *sched;
2604         isl_union_map *map1, *map2;
2605         isl_band_list *list;
2606         int equal;
2607
2608         str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2609         D = isl_union_set_read_from_str(ctx, str);
2610         validity = isl_union_map_empty(isl_union_set_get_space(D));
2611         proximity = isl_union_map_copy(validity);
2612         sched = isl_union_set_compute_schedule(D, validity, proximity);
2613         map1 = isl_schedule_get_map(sched);
2614         list = isl_schedule_get_band_forest(sched);
2615         isl_band_list_free(list);
2616         map2 = isl_schedule_get_map(sched);
2617         isl_schedule_free(sched);
2618         equal = isl_union_map_is_equal(map1, map2);
2619         isl_union_map_free(map1);
2620         isl_union_map_free(map2);
2621
2622         if (equal < 0)
2623                 return -1;
2624         if (!equal)
2625                 isl_die(ctx, isl_error_unknown,
2626                         "reconstructed schedule map not the same as original",
2627                         return -1);
2628
2629         return 0;
2630 }
2631
2632 int test_schedule(isl_ctx *ctx)
2633 {
2634         const char *D, *W, *R, *V, *P, *S;
2635
2636         /* Handle resulting schedule with zero bands. */
2637         if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2638                 return -1;
2639
2640         /* Jacobi */
2641         D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2642         W = "{ S1[t,i] -> a[t,i] }";
2643         R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2644                 "S1[t,i] -> a[t-1,i+1] }";
2645         S = "{ S1[t,i] -> [t,i] }";
2646         if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2647                 return -1;
2648
2649         /* Fig. 5 of CC2008 */
2650         D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2651                                 "j <= -1 + N }";
2652         W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2653                                 "j >= 2 and j <= -1 + N }";
2654         R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2655                                 "j >= 2 and j <= -1 + N; "
2656                     "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2657                                 "j >= 2 and j <= -1 + N }";
2658         S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2659         if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2660                 return -1;
2661
2662         D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2663         W = "{ S1[i] -> a[i] }";
2664         R = "{ S2[i] -> a[i+1] }";
2665         S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2666         if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2667                 return -1;
2668
2669         D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2670         W = "{ S1[i] -> a[i] }";
2671         R = "{ S2[i] -> a[9-i] }";
2672         S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2673         if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2674                 return -1;
2675
2676         D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2677         W = "{ S1[i] -> a[i] }";
2678         R = "[N] -> { S2[i] -> a[N-1-i] }";
2679         S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2680         if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2681                 return -1;
2682
2683         D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2684         W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2685         R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2686         S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2687         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2688                 return -1;
2689
2690         D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2691         W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2692         R = "{ S2[i,j] -> a[i-1,j] }";
2693         S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2694         if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2695                 return -1;
2696
2697         D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2698         W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2699         R = "{ S2[i,j] -> a[i,j-1] }";
2700         S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2701         if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2702                 return -1;
2703
2704         D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2705         W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2706                     "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2707         R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2708         S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2709                     "S_0[] -> [0, 0, 0] }";
2710         if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2711                 return -1;
2712         ctx->opt->schedule_parametric = 0;
2713         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2714                 return -1;
2715         ctx->opt->schedule_parametric = 1;
2716
2717         D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2718                     "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2719         W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2720         R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2721                     "S4[i] -> a[i,N] }";
2722         S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2723                 "S4[i] -> [4,i,0] }";
2724         if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2725                 return -1;
2726
2727         D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2728         W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2729                                         "j <= N }";
2730         R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2731                                         "j <= N; "
2732                     "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2733                                         "j <= N }";
2734         S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2735         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2736                 return -1;
2737
2738         D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2739                     " S_2[t] : t >= 0 and t <= -1 + N; "
2740                     " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2741                                 "i <= -1 + N }";
2742         W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2743                     " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2744                     " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2745                                                 "i >= 0 and i <= -1 + N }";
2746         R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2747                                             "i >= 0 and i <= -1 + N; "
2748                     " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2749         S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2750                     " S_0[t] -> [0, t, 0] }";
2751
2752         if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2753                 return -1;
2754         ctx->opt->schedule_parametric = 0;
2755         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2756                 return -1;
2757         ctx->opt->schedule_parametric = 1;
2758
2759         D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2760         S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2761         if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2762                 return -1;
2763
2764         D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2765             "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2766         W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2767                                             "j >= 0 and j <= -1 + N; "
2768                         "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2769         R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2770                                             "j >= 0 and j <= -1 + N; "
2771                         "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2772         S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2773         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2774                 return -1;
2775
2776         D = "{ S_0[i] : i >= 0 }";
2777         W = "{ S_0[i] -> a[i] : i >= 0 }";
2778         R = "{ S_0[i] -> a[0] : i >= 0 }";
2779         S = "{ S_0[i] -> [0, i, 0] }";
2780         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2781                 return -1;
2782
2783         D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2784         W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2785         R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2786         S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2787         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2788                 return -1;
2789
2790         D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2791                                 "k <= -1 + n and k >= 0 }";
2792         W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "                                                  "k <= -1 + n and k >= 0 }";
2793         R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2794                                         "k <= -1 + n and k >= 0; "
2795                     "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2796                                         "k <= -1 + n and k >= 0; "
2797                     "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2798                                         "k <= -1 + n and k >= 0 }";
2799         S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2800         ctx->opt->schedule_outer_zero_distance = 1;
2801         if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2802                 return -1;
2803         ctx->opt->schedule_outer_zero_distance = 0;
2804
2805         D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2806                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2807                 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2808              "Stmt_for_body24[i0, i1, 1, 0]:"
2809                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2810              "Stmt_for_body7[i0, i1, i2]:"
2811                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2812                 "i2 <= 7 }";
2813
2814         V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2815                 "Stmt_for_body24[1, i1, i2, i3]:"
2816                 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2817                 "i2 >= 1;"
2818              "Stmt_for_body24[0, i1, i2, i3] -> "
2819                 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2820                 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2821                 "i3 >= 0;"
2822               "Stmt_for_body24[0, i1, i2, i3] ->"
2823                 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2824                 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2825               "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2826                 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2827                 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2828                 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2829               "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2830                 "i1 <= 6 and i1 >= 0;"
2831               "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2832               "Stmt_for_body7[i0, i1, i2] -> "
2833                 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2834                 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2835                 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2836               "Stmt_for_body7[i0, i1, i2] -> "
2837                 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2838                 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2839                 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2840         P = V;
2841         S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2842                 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2843             "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2844
2845         if (test_special_schedule(ctx, D, V, P, S) < 0)
2846                 return -1;
2847
2848         D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2849         V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2850                                            "j >= 1 and j <= 7;"
2851                 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2852                                              "j >= 1 and j <= 8 }";
2853         P = "{ }";
2854         S = "{ S_0[i, j] -> [i + j, j] }";
2855         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2856         if (test_special_schedule(ctx, D, V, P, S) < 0)
2857                 return -1;
2858         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2859
2860         /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2861         D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2862                                  "j >= 0 and j <= -1 + i }";
2863         V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2864                                         "i <= -1 + N and j >= 0;"
2865                      "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2866                                         "i <= -2 + N }";
2867         P = "{ }";
2868         S = "{ S_0[i, j] -> [i, j] }";
2869         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2870         if (test_special_schedule(ctx, D, V, P, S) < 0)
2871                 return -1;
2872         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2873
2874         /* Test both algorithms on a case with only proximity dependences. */
2875         D = "{ S[i,j] : 0 <= i <= 10 }";
2876         V = "{ }";
2877         P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2878         S = "{ S[i, j] -> [j, i] }";
2879         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2880         if (test_special_schedule(ctx, D, V, P, S) < 0)
2881                 return -1;
2882         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2883         if (test_special_schedule(ctx, D, V, P, S) < 0)
2884                 return -1;
2885
2886         D = "{ A[a]; B[] }";
2887         V = "{}";
2888         P = "{ A[a] -> B[] }";
2889         if (test_has_schedule(ctx, D, V, P) < 0)
2890                 return -1;
2891
2892         if (test_padded_schedule(ctx) < 0)
2893                 return -1;
2894
2895         /* Check that check for progress is not confused by rational
2896          * solution.
2897          */
2898         D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
2899         V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
2900                                                         "i0 <= -2 + N; "
2901                         "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
2902                                 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
2903         P = "{}";
2904         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2905         if (test_has_schedule(ctx, D, V, P) < 0)
2906                 return -1;
2907         ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2908
2909         return 0;
2910 }
2911
2912 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2913 {
2914         isl_union_map *umap;
2915         int test;
2916
2917         umap = isl_union_map_read_from_str(ctx, str);
2918         test = isl_union_map_plain_is_injective(umap);
2919         isl_union_map_free(umap);
2920         if (test < 0)
2921                 return -1;
2922         if (test == injective)
2923                 return 0;
2924         if (injective)
2925                 isl_die(ctx, isl_error_unknown,
2926                         "map not detected as injective", return -1);
2927         else
2928                 isl_die(ctx, isl_error_unknown,
2929                         "map detected as injective", return -1);
2930 }
2931
2932 int test_injective(isl_ctx *ctx)
2933 {
2934         const char *str;
2935
2936         if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2937                 return -1;
2938         if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2939                 return -1;
2940         if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2941                 return -1;
2942         if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2943                 return -1;
2944         if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2945                 return -1;
2946         if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2947                 return -1;
2948         if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2949                 return -1;
2950         if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2951                 return -1;
2952
2953         str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2954         if (test_plain_injective(ctx, str, 1))
2955                 return -1;
2956         str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2957         if (test_plain_injective(ctx, str, 0))
2958                 return -1;
2959
2960         return 0;
2961 }
2962
2963 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2964 {
2965         isl_aff *aff2;
2966         int equal;
2967
2968         if (!aff)
2969                 return -1;
2970
2971         aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2972         equal = isl_aff_plain_is_equal(aff, aff2);
2973         isl_aff_free(aff2);
2974
2975         return equal;
2976 }
2977
2978 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2979 {
2980         int equal;
2981
2982         equal = aff_plain_is_equal(aff, str);
2983         if (equal < 0)
2984                 return -1;
2985         if (!equal)
2986                 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2987                         "result not as expected", return -1);
2988         return 0;
2989 }
2990
2991 int test_aff(isl_ctx *ctx)
2992 {
2993         const char *str;
2994         isl_set *set;
2995         isl_space *space;
2996         isl_local_space *ls;
2997         isl_aff *aff;
2998         int zero, equal;
2999
3000         space = isl_space_set_alloc(ctx, 0, 1);
3001         ls = isl_local_space_from_space(space);
3002         aff = isl_aff_zero_on_domain(ls);
3003
3004         aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3005         aff = isl_aff_scale_down_ui(aff, 3);
3006         aff = isl_aff_floor(aff);
3007         aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3008         aff = isl_aff_scale_down_ui(aff, 2);
3009         aff = isl_aff_floor(aff);
3010         aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3011
3012         str = "{ [10] }";
3013         set = isl_set_read_from_str(ctx, str);
3014         aff = isl_aff_gist(aff, set);
3015
3016         aff = isl_aff_add_constant_si(aff, -16);
3017         zero = isl_aff_plain_is_zero(aff);
3018         isl_aff_free(aff);
3019
3020         if (zero < 0)
3021                 return -1;
3022         if (!zero)
3023                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3024
3025         aff = isl_aff_read_from_str(ctx, "{ [-1] }");
3026         aff = isl_aff_scale_down_ui(aff, 64);
3027         aff = isl_aff_floor(aff);
3028         equal = aff_check_plain_equal(aff, "{ [-1] }");
3029         isl_aff_free(aff);
3030         if (equal < 0)
3031                 return -1;
3032
3033         return 0;
3034 }
3035
3036 int test_dim_max(isl_ctx *ctx)
3037 {
3038         int equal;
3039         const char *str;
3040         isl_set *set1, *set2;
3041         isl_set *set;
3042         isl_map *map;
3043         isl_pw_aff *pwaff;
3044
3045         str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3046         set = isl_set_read_from_str(ctx, str);
3047         pwaff = isl_set_dim_max(set, 0);
3048         set1 = isl_set_from_pw_aff(pwaff);
3049         str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3050         set2 = isl_set_read_from_str(ctx, str);
3051         equal = isl_set_is_equal(set1, set2);
3052         isl_set_free(set1);
3053         isl_set_free(set2);
3054         if (equal < 0)
3055                 return -1;
3056         if (!equal)
3057                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3058
3059         str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3060         set = isl_set_read_from_str(ctx, str);
3061         pwaff = isl_set_dim_max(set, 0);
3062         set1 = isl_set_from_pw_aff(pwaff);
3063         str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3064         set2 = isl_set_read_from_str(ctx, str);
3065         equal = isl_set_is_equal(set1, set2);
3066         isl_set_free(set1);
3067         isl_set_free(set2);
3068         if (equal < 0)
3069                 return -1;
3070         if (!equal)
3071                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3072
3073         str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3074         set = isl_set_read_from_str(ctx, str);
3075         pwaff = isl_set_dim_max(set, 0);
3076         set1 = isl_set_from_pw_aff(pwaff);
3077         str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3078         set2 = isl_set_read_from_str(ctx, str);
3079         equal = isl_set_is_equal(set1, set2);
3080         isl_set_free(set1);
3081         isl_set_free(set2);
3082         if (equal < 0)
3083                 return -1;
3084         if (!equal)
3085                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3086
3087         str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3088                         "0 <= i < N and 0 <= j < M }";
3089         map = isl_map_read_from_str(ctx, str);
3090         set = isl_map_range(map);
3091
3092         pwaff = isl_set_dim_max(isl_set_copy(set), 0);
3093         set1 = isl_set_from_pw_aff(pwaff);
3094         str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3095         set2 = isl_set_read_from_str(ctx, str);
3096         equal = isl_set_is_equal(set1, set2);
3097         isl_set_free(set1);
3098         isl_set_free(set2);
3099
3100         pwaff = isl_set_dim_max(isl_set_copy(set), 3);
3101         set1 = isl_set_from_pw_aff(pwaff);
3102         str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3103         set2 = isl_set_read_from_str(ctx, str);
3104         if (equal >= 0 && equal)
3105                 equal = isl_set_is_equal(set1, set2);
3106         isl_set_free(set1);
3107         isl_set_free(set2);
3108
3109         isl_set_free(set);
3110
3111         if (equal < 0)
3112                 return -1;
3113         if (!equal)
3114                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3115
3116         /* Check that solutions are properly merged. */
3117         str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
3118                                 "c <= -1 + n - 4a - 2b and c >= -2b and "
3119                                 "4a >= -4 + n and c >= 0 }";
3120         set = isl_set_read_from_str(ctx, str);
3121         pwaff = isl_set_dim_min(set, 2);
3122         set1 = isl_set_from_pw_aff(pwaff);
3123         str = "[n] -> { [(0)] : n >= 1 }";
3124         set2 = isl_set_read_from_str(ctx, str);
3125         equal = isl_set_is_equal(set1, set2);
3126         isl_set_free(set1);
3127         isl_set_free(set2);
3128
3129         if (equal < 0)
3130                 return -1;
3131         if (!equal)
3132                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3133
3134         return 0;
3135 }
3136
3137 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3138  */
3139 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
3140         const char *str)
3141 {
3142         isl_ctx *ctx;
3143         isl_pw_multi_aff *pma2;
3144         int equal;
3145
3146         if (!pma)
3147                 return -1;
3148
3149         ctx = isl_pw_multi_aff_get_ctx(pma);
3150         pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3151         equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
3152         isl_pw_multi_aff_free(pma2);
3153
3154         return equal;
3155 }
3156
3157 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3158  * represented by "str".
3159  */
3160 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
3161         const char *str)
3162 {
3163         int equal;
3164
3165         equal = pw_multi_aff_plain_is_equal(pma, str);
3166         if (equal < 0)
3167                 return -1;
3168         if (!equal)
3169                 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
3170                         "result not as expected", return -1);
3171         return 0;
3172 }
3173
3174 /* Basic test for isl_pw_multi_aff_product.
3175  *
3176  * Check that multiple pieces are properly handled.
3177  */
3178 static int test_product_pma(isl_ctx *ctx)
3179 {
3180         int equal;
3181         const char *str;
3182         isl_pw_multi_aff *pma1, *pma2;
3183
3184         str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3185         pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3186         str = "{ C[] -> D[] }";
3187         pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3188         pma1 = isl_pw_multi_aff_product(pma1, pma2);
3189         str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3190                 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3191         equal = pw_multi_aff_check_plain_equal(pma1, str);
3192         isl_pw_multi_aff_free(pma1);
3193         if (equal < 0)
3194                 return -1;
3195
3196         return 0;
3197 }
3198
3199 int test_product(isl_ctx *ctx)
3200 {
3201         const char *str;
3202         isl_set *set;
3203         isl_union_set *uset1, *uset2;
3204         int ok;
3205
3206         str = "{ A[i] }";
3207         set = isl_set_read_from_str(ctx, str);
3208         set = isl_set_product(set, isl_set_copy(set));
3209         ok = isl_set_is_wrapping(set);
3210         isl_set_free(set);
3211         if (ok < 0)
3212                 return -1;
3213         if (!ok)
3214                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3215
3216         str = "{ [] }";
3217         uset1 = isl_union_set_read_from_str(ctx, str);
3218         uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
3219         str = "{ [[] -> []] }";
3220         uset2 = isl_union_set_read_from_str(ctx, str);
3221         ok = isl_union_set_is_equal(uset1, uset2);
3222         isl_union_set_free(uset1);
3223         isl_union_set_free(uset2);
3224         if (ok < 0)
3225                 return -1;
3226         if (!ok)
3227                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3228
3229         if (test_product_pma(ctx) < 0)
3230                 return -1;
3231
3232         return 0;
3233 }
3234
3235 int test_equal(isl_ctx *ctx)
3236 {
3237         const char *str;
3238         isl_set *set, *set2;
3239         int equal;
3240
3241         str = "{ S_6[i] }";
3242         set = isl_set_read_from_str(ctx, str);
3243         str = "{ S_7[i] }";
3244         set2 = isl_set_read_from_str(ctx, str);
3245         equal = isl_set_is_equal(set, set2);
3246         isl_set_free(set);
3247         isl_set_free(set2);
3248         if (equal < 0)
3249                 return -1;
3250         if (equal)
3251                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3252
3253         return 0;
3254 }
3255
3256 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
3257         enum isl_dim_type type, unsigned pos, int fixed)
3258 {
3259         int test;
3260
3261         test = isl_map_plain_is_fixed(map, type, pos, NULL);
3262         isl_map_free(map);
3263         if (test < 0)
3264                 return -1;
3265         if (test == fixed)
3266                 return 0;
3267         if (fixed)
3268                 isl_die(ctx, isl_error_unknown,
3269                         "map not detected as fixed", return -1);
3270         else
3271                 isl_die(ctx, isl_error_unknown,
3272                         "map detected as fixed", return -1);
3273 }
3274
3275 int test_fixed(isl_ctx *ctx)
3276 {
3277         const char *str;
3278         isl_map *map;
3279
3280         str = "{ [i] -> [i] }";
3281         map = isl_map_read_from_str(ctx, str);
3282         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
3283                 return -1;
3284         str = "{ [i] -> [1] }";
3285         map = isl_map_read_from_str(ctx, str);
3286         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3287                 return -1;
3288         str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3289         map = isl_map_read_from_str(ctx, str);
3290         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3291                 return -1;
3292         map = isl_map_read_from_str(ctx, str);
3293         map = isl_map_neg(map);
3294         if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3295                 return -1;
3296
3297         return 0;
3298 }
3299
3300 int test_vertices(isl_ctx *ctx)
3301 {
3302         const char *str;
3303         isl_basic_set *bset;
3304         isl_vertices *vertices;
3305
3306         str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
3307         bset = isl_basic_set_read_from_str(ctx, str);
3308         vertices = isl_basic_set_compute_vertices(bset);
3309         isl_basic_set_free(bset);
3310         isl_vertices_free(vertices);
3311         if (!vertices)
3312                 return -1;
3313
3314         str = "{ A[t, i] : t = 14 and i = 1 }";
3315         bset = isl_basic_set_read_from_str(ctx, str);
3316         vertices = isl_basic_set_compute_vertices(bset);
3317         isl_basic_set_free(bset);
3318         isl_vertices_free(vertices);
3319         if (!vertices)
3320                 return -1;
3321
3322         return 0;
3323 }
3324
3325 int test_union_pw(isl_ctx *ctx)
3326 {
3327         int equal;
3328         const char *str;
3329         isl_union_set *uset;
3330         isl_union_pw_qpolynomial *upwqp1, *upwqp2;
3331
3332         str = "{ [x] -> x^2 }";
3333         upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
3334         upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
3335         uset = isl_union_pw_qpolynomial_domain(upwqp1);
3336         upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
3337         upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
3338         equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
3339         isl_union_pw_qpolynomial_free(upwqp1);
3340         isl_union_pw_qpolynomial_free(upwqp2);
3341         if (equal < 0)
3342                 return -1;
3343         if (!equal)
3344                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3345
3346         return 0;
3347 }
3348
3349 int test_output(isl_ctx *ctx)
3350 {
3351         char *s;
3352         const char *str;
3353         isl_pw_aff *pa;
3354         isl_printer *p;
3355         int equal;
3356
3357         str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3358         pa = isl_pw_aff_read_from_str(ctx, str);
3359
3360         p = isl_printer_to_str(ctx);
3361         p = isl_printer_set_output_format(p, ISL_FORMAT_C);
3362         p = isl_printer_print_pw_aff(p, pa);
3363         s = isl_printer_get_str(p);
3364         isl_printer_free(p);
3365         isl_pw_aff_free(pa);
3366         if (!s)
3367                 equal = -1;
3368         else
3369                 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
3370         free(s);
3371         if (equal < 0)
3372                 return -1;
3373         if (!equal)
3374                 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3375
3376         return 0;
3377 }
3378
3379 int test_sample(isl_ctx *ctx)
3380 {
3381         const char *str;
3382         isl_basic_set *bset1, *bset2;
3383         int empty, subset;
3384
3385         str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3386             "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3387             "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3388             "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3389             "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3390             "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3391             "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3392             "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3393             "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3394             "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3395             "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3396             "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3397                 "d - 1073741821e and "
3398             "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3399             "3j >= 1 - a + b + 2e and "
3400             "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3401             "3i <= 4 - a + 4b - e and "
3402             "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3403             "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3404             "c <= -1 + a and 3i >= -2 - a + 3e and "
3405             "1073741822e <= 1073741823 - a + 1073741822b + c and "
3406             "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3407             "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3408             "1073741823e >= 1 + 1073741823b - d and "
3409             "3i >= 1073741823b + c - 1073741823e - f and "
3410             "3i >= 1 + 2b + e + 3g }";
3411         bset1 = isl_basic_set_read_from_str(ctx, str);
3412         bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3413         empty = isl_basic_set_is_empty(bset2);
3414         subset = isl_basic_set_is_subset(bset2, bset1);
3415         isl_basic_set_free(bset1);
3416         isl_basic_set_free(bset2);
3417         if (empty < 0 || subset < 0)
3418                 return -1;
3419         if (empty)
3420                 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3421         if (!subset)
3422                 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3423
3424         return 0;
3425 }
3426
3427 int test_fixed_power(isl_ctx *ctx)
3428 {
3429         const char *str;
3430         isl_map *map;
3431         isl_int exp;
3432         int equal;
3433
3434         isl_int_init(exp);
3435         str = "{ [i] -> [i + 1] }";
3436         map = isl_map_read_from_str(ctx, str);
3437         isl_int_set_si(exp, 23);
3438         map = isl_map_fixed_power(map, exp);
3439         equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3440         isl_int_clear(exp);
3441         isl_map_free(map);
3442         if (equal < 0)
3443                 return -1;
3444
3445         return 0;
3446 }
3447
3448 int test_slice(isl_ctx *ctx)
3449 {
3450         const char *str;
3451         isl_map *map;
3452         int equal;
3453
3454         str = "{ [i] -> [j] }";
3455         map = isl_map_read_from_str(ctx, str);
3456         map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3457         equal = map_check_equal(map, "{ [i] -> [i] }");
3458         isl_map_free(map);
3459         if (equal < 0)
3460                 return -1;
3461
3462         str = "{ [i] -> [j] }";
3463         map = isl_map_read_from_str(ctx, str);
3464         map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3465         equal = map_check_equal(map, "{ [i] -> [j] }");
3466         isl_map_free(map);
3467         if (equal < 0)
3468                 return -1;
3469
3470         str = "{ [i] -> [j] }";
3471         map = isl_map_read_from_str(ctx, str);
3472         map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3473         equal = map_check_equal(map, "{ [i] -> [-i] }");
3474         isl_map_free(map);
3475         if (equal < 0)
3476                 return -1;
3477
3478         str = "{ [i] -> [j] }";
3479         map = isl_map_read_from_str(ctx, str);
3480         map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3481         equal = map_check_equal(map, "{ [0] -> [j] }");
3482         isl_map_free(map);
3483         if (equal < 0)
3484                 return -1;
3485
3486         str = "{ [i] -> [j] }";
3487         map = isl_map_read_from_str(ctx, str);
3488         map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3489         equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3490         isl_map_free(map);
3491         if (equal < 0)
3492                 return -1;
3493
3494         str = "{ [i] -> [j] }";
3495         map = isl_map_read_from_str(ctx, str);
3496         map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3497         equal = map_check_equal(map, "{ [i] -> [j] : false }");
3498         isl_map_free(map);
3499         if (equal < 0)
3500                 return -1;
3501
3502         return 0;
3503 }
3504
3505 int test_eliminate(isl_ctx *ctx)
3506 {
3507         const char *str;
3508         isl_map *map;
3509         int equal;
3510
3511         str = "{ [i] -> [j] : i = 2j }";
3512         map = isl_map_read_from_str(ctx, str);
3513         map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3514         equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3515         isl_map_free(map);
3516         if (equal < 0)
3517                 return -1;
3518
3519         return 0;
3520 }
3521
3522 /* Check that isl_set_dim_residue_class detects that the values of j
3523  * in the set below are all odd and that it does not detect any spurious
3524  * strides.
3525  */
3526 static int test_residue_class(isl_ctx *ctx)
3527 {
3528         const char *str;
3529         isl_set *set;
3530         isl_int m, r;
3531         int res;
3532
3533         str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3534                 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3535         set = isl_set_read_from_str(ctx, str);
3536         isl_int_init(m);
3537         isl_int_init(r);
3538         res = isl_set_dim_residue_class(set, 1, &m, &r);
3539         if (res >= 0 &&
3540             (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3541                 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3542                         res = -1);
3543         isl_int_clear(r);
3544         isl_int_clear(m);
3545         isl_set_free(set);
3546
3547         return res;
3548 }
3549
3550 int test_align_parameters(isl_ctx *ctx)
3551 {
3552         const char *str;
3553         isl_space *space;
3554         isl_multi_aff *ma1, *ma2;
3555         int equal;
3556
3557         str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3558         ma1 = isl_multi_aff_read_from_str(ctx, str);
3559
3560         space = isl_space_params_alloc(ctx, 1);
3561         space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3562         ma1 = isl_multi_aff_align_params(ma1, space);
3563
3564         str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3565         ma2 = isl_multi_aff_read_from_str(ctx, str);
3566
3567         equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3568
3569         isl_multi_aff_free(ma1);
3570         isl_multi_aff_free(ma2);
3571
3572         if (equal < 0)
3573                 return -1;
3574         if (!equal)
3575                 isl_die(ctx, isl_error_unknown,
3576                         "result not as expected", return -1);
3577
3578         return 0;
3579 }
3580
3581 static int test_list(isl_ctx *ctx)
3582 {
3583         isl_id *a, *b, *c, *d, *id;
3584         isl_id_list *list;
3585         int ok;
3586
3587         a = isl_id_alloc(ctx, "a", NULL);
3588         b = isl_id_alloc(ctx, "b", NULL);
3589         c = isl_id_alloc(ctx, "c", NULL);
3590         d = isl_id_alloc(ctx, "d", NULL);
3591
3592         list = isl_id_list_alloc(ctx, 4);
3593         list = isl_id_list_add(list, a);
3594         list = isl_id_list_add(list, b);
3595         list = isl_id_list_add(list, c);
3596         list = isl_id_list_add(list, d);
3597         list = isl_id_list_drop(list, 1, 1);
3598
3599         if (isl_id_list_n_id(list) != 3) {
3600                 isl_id_list_free(list);
3601                 isl_die(ctx, isl_error_unknown,
3602                         "unexpected number of elements in list", return -1);
3603         }
3604
3605         id = isl_id_list_get_id(list, 0);
3606         ok = id == a;
3607         isl_id_free(id);
3608         id = isl_id_list_get_id(list, 1);
3609         ok = ok && id == c;
3610         isl_id_free(id);
3611         id = isl_id_list_get_id(list, 2);
3612         ok = ok && id == d;
3613         isl_id_free(id);
3614
3615         isl_id_list_free(list);
3616
3617         if (!ok)
3618                 isl_die(ctx, isl_error_unknown,
3619                         "unexpected elements in list", return -1);
3620
3621         return 0;
3622 }
3623
3624 const char *set_conversion_tests[] = {
3625         "[N] -> { [i] : N - 1 <= 2 i <= N }",
3626         "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3627         "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3628         "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3629 };
3630
3631 /* Check that converting from isl_set to isl_pw_multi_aff and back
3632  * to isl_set produces the original isl_set.
3633  */
3634 static int test_set_conversion(isl_ctx *ctx)
3635 {
3636         int i;
3637         const char *str;
3638         isl_set *set1, *set2;
3639         isl_pw_multi_aff *pma;
3640         int equal;
3641
3642         for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3643                 str = set_conversion_tests[i];
3644                 set1 = isl_set_read_from_str(ctx, str);
3645                 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3646                 set2 = isl_set_from_pw_multi_aff(pma);
3647                 equal = isl_set_is_equal(set1, set2);
3648                 isl_set_free(set1);
3649                 isl_set_free(set2);
3650
3651                 if (equal < 0)
3652                         return -1;
3653                 if (!equal)
3654                         isl_die(ctx, isl_error_unknown, "bad conversion",
3655                                 return -1);
3656         }
3657
3658         return 0;
3659 }
3660
3661 /* Check that converting from isl_map to isl_pw_multi_aff and back
3662  * to isl_map produces the original isl_map.
3663  */
3664 static int test_map_conversion(isl_ctx *ctx)
3665 {
3666         const char *str;
3667         isl_map *map1, *map2;
3668         isl_pw_multi_aff *pma;
3669         int equal;
3670
3671         str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
3672                 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3673                 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3674                 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3675                 "9e <= -2 - 2a) }";
3676         map1 = isl_map_read_from_str(ctx, str);
3677         pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
3678         map2 = isl_map_from_pw_multi_aff(pma);
3679         equal = isl_map_is_equal(map1, map2);
3680         isl_map_free(map1);
3681         isl_map_free(map2);
3682
3683         if (equal < 0)
3684                 return -1;
3685         if (!equal)
3686                 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
3687
3688         return 0;
3689 }
3690
3691 static int test_conversion(isl_ctx *ctx)
3692 {
3693         if (test_set_conversion(ctx) < 0)
3694                 return -1;
3695         if (test_map_conversion(ctx) < 0)
3696                 return -1;
3697         return 0;
3698 }
3699
3700 /* Check that isl_basic_map_curry does not modify input.
3701  */
3702 static int test_curry(isl_ctx *ctx)
3703 {
3704         const char *str;
3705         isl_basic_map *bmap1, *bmap2;
3706         int equal;
3707
3708         str = "{ [A[] -> B[]] -> C[] }";
3709         bmap1 = isl_basic_map_read_from_str(ctx, str);
3710         bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
3711         equal = isl_basic_map_is_equal(bmap1, bmap2);
3712         isl_basic_map_free(bmap1);
3713         isl_basic_map_free(bmap2);
3714
3715         if (equal < 0)
3716                 return -1;
3717         if (equal)
3718                 isl_die(ctx, isl_error_unknown,
3719                         "curried map should not be equal to original",
3720                         return -1);
3721
3722         return 0;
3723 }
3724
3725 struct {
3726         const char *set;
3727         const char *ma;
3728         const char *res;
3729 } preimage_tests[] = {
3730         { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3731           "{ A[j,i] -> B[i,j] }",
3732           "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3733         { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3734           "{ A[a,b] -> B[a/2,b/6] }",
3735           "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3736         { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3737           "{ A[a,b] -> B[a/2,b/6] }",
3738           "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3739                     "exists i,j : a = 2 i and b = 6 j }" },
3740         { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3741           "[n] -> { : 0 <= n <= 100 }" },
3742         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3743           "{ A[a] -> B[2a] }",
3744           "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3745         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3746           "{ A[a] -> B[([a/2])] }",
3747           "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3748         { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3749           "{ A[a] -> B[a,a,a/3] }",
3750           "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3751         { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3752           "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3753 };
3754
3755 static int test_preimage_basic_set(isl_ctx *ctx)
3756 {
3757         int i;
3758         isl_basic_set *bset1, *bset2;
3759         isl_multi_aff *ma;
3760         int equal;
3761
3762         for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3763                 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3764                 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3765                 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3766                 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3767                 equal = isl_basic_set_is_equal(bset1, bset2);
3768                 isl_basic_set_free(bset1);
3769                 isl_basic_set_free(bset2);
3770                 if (equal < 0)
3771                         return -1;
3772                 if (!equal)
3773                         isl_die(ctx, isl_error_unknown, "bad preimage",
3774                                 return -1);
3775         }
3776
3777         return 0;
3778 }
3779
3780 struct {
3781         const char *map;
3782         const char *ma;
3783         const char *res;
3784 } preimage_domain_tests[] = {
3785         { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
3786           "{ A[j,i] -> B[i,j] }",
3787           "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
3788         { "{ B[i] -> C[i]; D[i] -> E[i] }",
3789           "{ A[i] -> B[i + 1] }",
3790           "{ A[i] -> C[i + 1] }" },
3791         { "{ B[i] -> C[i]; B[i] -> E[i] }",
3792           "{ A[i] -> B[i + 1] }",
3793           "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
3794         { "{ B[i] -> C[([i/2])] }",
3795           "{ A[i] -> B[2i] }",
3796           "{ A[i] -> C[i] }" },
3797         { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
3798           "{ A[i] -> B[([i/5]), ([i/7])] }",
3799           "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
3800         { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
3801           "[N] -> { A[] -> B[([N/5])] }",
3802           "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
3803         { "{ B[i] -> C[i] : exists a : i = 5 a }",
3804           "{ A[i] -> B[2i] }",
3805           "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
3806         { "{ B[i] -> C[i] : exists a : i = 2 a; "
3807             "B[i] -> D[i] : exists a : i = 2 a + 1 }",
3808           "{ A[i] -> B[2i] }",
3809           "{ A[i] -> C[2i] }" },
3810 };
3811
3812 static int test_preimage_union_map(isl_ctx *ctx)
3813 {
3814         int i;
3815         isl_union_map *umap1, *umap2;
3816         isl_multi_aff *ma;
3817         int equal;
3818
3819         for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
3820                 umap1 = isl_union_map_read_from_str(ctx,
3821                                                 preimage_domain_tests[i].map);
3822                 ma = isl_multi_aff_read_from_str(ctx,
3823                                                 preimage_domain_tests[i].ma);
3824                 umap2 = isl_union_map_read_from_str(ctx,
3825                                                 preimage_domain_tests[i].res);
3826                 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
3827                 equal = isl_union_map_is_equal(umap1, umap2);
3828                 isl_union_map_free(umap1);
3829                 isl_union_map_free(umap2);
3830                 if (equal < 0)
3831                         return -1;
3832                 if (!equal)
3833                         isl_die(ctx, isl_error_unknown, "bad preimage",
3834                                 return -1);
3835         }
3836
3837         return 0;
3838 }
3839
3840 static int test_preimage(isl_ctx *ctx)
3841 {
3842         if (test_preimage_basic_set(ctx) < 0)
3843                 return -1;
3844         if (test_preimage_union_map(ctx) < 0)
3845                 return -1;
3846
3847         return 0;
3848 }
3849
3850 struct {
3851         const char *ma1;
3852         const char *ma;
3853         const char *res;
3854 } pullback_tests[] = {
3855         { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3856           "{ A[a,b] -> C[b + 2a] }" },
3857         { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3858         { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3859         { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3860           "{ A[a] -> C[(a)/6] }" },
3861         { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3862         { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3863           "{ A[a] -> C[(2a)/3] }" },
3864         { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3865         { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3866           "{ A[i,j] -> C[i + j, i + j] }"},
3867         { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3868         { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3869           "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3870 };
3871
3872 static int test_pullback(isl_ctx *ctx)
3873 {
3874         int i;
3875         isl_multi_aff *ma1, *ma2;
3876         isl_multi_aff *ma;
3877         int equal;
3878
3879         for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
3880                 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
3881                 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
3882                 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
3883                 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
3884                 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3885                 isl_multi_aff_free(ma1);
3886                 isl_multi_aff_free(ma2);
3887                 if (equal < 0)
3888                         return -1;
3889                 if (!equal)
3890                         isl_die(ctx, isl_error_unknown, "bad pullback",
3891                                 return -1);
3892         }
3893
3894         return 0;
3895 }
3896
3897 /* Check that negation is printed correctly.
3898  */
3899 static int test_ast(isl_ctx *ctx)
3900 {
3901         isl_ast_expr *expr, *expr1, *expr2, *expr3;
3902         char *str;
3903         int ok;
3904
3905         expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3906         expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3907         expr = isl_ast_expr_add(expr1, expr2);
3908         expr = isl_ast_expr_neg(expr);
3909         str = isl_ast_expr_to_str(expr);
3910         ok = str ? !strcmp(str, "-(A + B)") : -1;
3911         free(str);
3912         isl_ast_expr_free(expr);
3913
3914         if (ok < 0)
3915                 return -1;
3916         if (!ok)
3917                 isl_die(ctx, isl_error_unknown,
3918                         "isl_ast_expr printed incorrectly", return -1);
3919
3920         expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3921         expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3922         expr = isl_ast_expr_add(expr1, expr2);
3923         expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
3924         expr = isl_ast_expr_sub(expr3, expr);
3925         str = isl_ast_expr_to_str(expr);
3926         ok = str ? !strcmp(str, "C - (A + B)") : -1;
3927         free(str);
3928         isl_ast_expr_free(expr);
3929
3930         if (ok < 0)
3931                 return -1;
3932         if (!ok)
3933                 isl_die(ctx, isl_error_unknown,
3934                         "isl_ast_expr printed incorrectly", return -1);
3935
3936         return 0;
3937 }
3938
3939 /* Internal data structure for before_for and after_for callbacks.
3940  *
3941  * depth is the current depth
3942  * before is the number of times before_for has been called
3943  * after is the number of times after_for has been called
3944  */
3945 struct isl_test_codegen_data {
3946         int depth;
3947         int before;
3948         int after;
3949 };
3950
3951 /* This function is called before each for loop in the AST generated
3952  * from test_ast_gen1.
3953  *
3954  * Increment the number of calls and the depth.
3955  * Check that the space returned by isl_ast_build_get_schedule_space
3956  * matches the target space of the schedule returned by
3957  * isl_ast_build_get_schedule.
3958  * Return an isl_id that is checked by the corresponding call
3959  * to after_for.
3960  */
3961 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
3962         void *user)
3963 {
3964         struct isl_test_codegen_data *data = user;
3965         isl_ctx *ctx;
3966         isl_space *space;
3967         isl_union_map *schedule;
3968         isl_union_set *uset;
3969         isl_set *set;
3970         int empty;
3971         char name[] = "d0";
3972
3973         ctx = isl_ast_build_get_ctx(build);
3974
3975         if (data->before >= 3)
3976                 isl_die(ctx, isl_error_unknown,
3977                         "unexpected number of for nodes", return NULL);
3978         if (data->depth >= 2)
3979                 isl_die(ctx, isl_error_unknown,
3980                         "unexpected depth", return NULL);
3981
3982         snprintf(name, sizeof(name), "d%d", data->depth);
3983         data->before++;
3984         data->depth++;
3985
3986         schedule = isl_ast_build_get_schedule(build);
3987         uset = isl_union_map_range(schedule);
3988         if (!uset)
3989                 return NULL;
3990         if (isl_union_set_n_set(uset) != 1) {
3991                 isl_union_set_free(uset);
3992                 isl_die(ctx, isl_error_unknown,
3993                         "expecting single range space", return NULL);
3994         }
3995
3996         space = isl_ast_build_get_schedule_space(build);
3997         set = isl_union_set_extract_set(uset, space);
3998         isl_union_set_free(uset);
3999         empty = isl_set_is_empty(set);
4000         isl_set_free(set);
4001
4002         if (empty < 0)
4003                 return NULL;
4004         if (empty)
4005                 isl_die(ctx, isl_error_unknown,
4006                         "spaces don't match", return NULL);
4007
4008         return isl_id_alloc(ctx, name, NULL);
4009 }
4010
4011 /* This function is called after each for loop in the AST generated
4012  * from test_ast_gen1.
4013  *
4014  * Increment the number of calls and decrement the depth.
4015  * Check that the annotation attached to the node matches
4016  * the isl_id returned by the corresponding call to before_for.
4017  */
4018 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
4019         __isl_keep isl_ast_build *build, void *user)
4020 {
4021         struct isl_test_codegen_data *data = user;
4022         isl_id *id;
4023         const char *name;
4024         int valid;
4025
4026         data->after++;
4027         data->depth--;
4028
4029         if (data->after > data->before)
4030                 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4031                         "mismatch in number of for nodes",
4032                         return isl_ast_node_free(node));
4033
4034         id = isl_ast_node_get_annotation(node);
4035         if (!id)
4036                 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4037                         "missing annotation", return isl_ast_node_free(node));
4038
4039         name = isl_id_get_name(id);
4040         valid = name && atoi(name + 1) == data->depth;
4041         isl_id_free(id);
4042
4043         if (!valid)
4044                 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4045                         "wrong annotation", return isl_ast_node_free(node));
4046
4047         return node;
4048 }
4049
4050 /* Check that the before_each_for and after_each_for callbacks
4051  * are called for each for loop in the generated code,
4052  * that they are called in the right order and that the isl_id
4053  * returned from the before_each_for callback is attached to
4054  * the isl_ast_node passed to the corresponding after_each_for call.
4055  */
4056 static int test_ast_gen1(isl_ctx *ctx)
4057 {
4058         const char *str;
4059         isl_set *set;
4060         isl_union_map *schedule;
4061         isl_ast_build *build;
4062         isl_ast_node *tree;
4063         struct isl_test_codegen_data data;
4064
4065         str = "[N] -> { : N >= 10 }";
4066         set = isl_set_read_from_str(ctx, str);
4067         str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4068                     "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4069         schedule = isl_union_map_read_from_str(ctx, str);
4070
4071         data.before = 0;
4072         data.after = 0;
4073         data.depth = 0;
4074         build = isl_ast_build_from_context(set);
4075         build = isl_ast_build_set_before_each_for(build,
4076                         &before_for, &data);
4077         build = isl_ast_build_set_after_each_for(build,
4078                         &after_for, &data);
4079         tree = isl_ast_build_ast_from_schedule(build, schedule);
4080         isl_ast_build_free(build);
4081         if (!tree)
4082                 return -1;
4083
4084         isl_ast_node_free(tree);
4085
4086         if (data.before != 3 || data.after != 3)
4087                 isl_die(ctx, isl_error_unknown,
4088                         "unexpected number of for nodes", return -1);
4089
4090         return 0;
4091 }
4092
4093 /* Check that the AST generator handles domains that are integrally disjoint
4094  * but not ratinoally disjoint.
4095  */
4096 static int test_ast_gen2(isl_ctx *ctx)
4097 {
4098         const char *str;
4099         isl_set *set;
4100         isl_union_map *schedule;
4101         isl_union_map *options;
4102         isl_ast_build *build;
4103         isl_ast_node *tree;
4104
4105         str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4106         schedule = isl_union_map_read_from_str(ctx, str);
4107         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4108         build = isl_ast_build_from_context(set);
4109
4110         str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4111         options = isl_union_map_read_from_str(ctx, str);
4112         build = isl_ast_build_set_options(build, options);
4113         tree = isl_ast_build_ast_from_schedule(build, schedule);
4114         isl_ast_build_free(build);
4115         if (!tree)
4116                 return -1;
4117         isl_ast_node_free(tree);
4118
4119         return 0;
4120 }
4121
4122 /* Increment *user on each call.
4123  */
4124 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
4125         __isl_keep isl_ast_build *build, void *user)
4126 {
4127         int *n = user;
4128
4129         (*n)++;
4130
4131         return node;
4132 }
4133
4134 /* Test that unrolling tries to minimize the number of instances.
4135  * In particular, for the schedule given below, make sure it generates
4136  * 3 nodes (rather than 101).
4137  */
4138 static int test_ast_gen3(isl_ctx *ctx)
4139 {
4140         const char *str;
4141         isl_set *set;
4142         isl_union_map *schedule;
4143         isl_union_map *options;
4144         isl_ast_build *build;
4145         isl_ast_node *tree;
4146         int n_domain = 0;
4147
4148         str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4149         schedule = isl_union_map_read_from_str(ctx, str);
4150         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4151
4152         str = "{ [i] -> unroll[0] }";
4153         options = isl_union_map_read_from_str(ctx, str);
4154
4155         build = isl_ast_build_from_context(set);
4156         build = isl_ast_build_set_options(build, options);
4157         build = isl_ast_build_set_at_each_domain(build,
4158                         &count_domains, &n_domain);
4159         tree = isl_ast_build_ast_from_schedule(build, schedule);
4160         isl_ast_build_free(build);
4161         if (!tree)
4162                 return -1;
4163
4164         isl_ast_node_free(tree);
4165
4166         if (n_domain != 3)
4167                 isl_die(ctx, isl_error_unknown,
4168                         "unexpected number of for nodes", return -1);
4169
4170         return 0;
4171 }
4172
4173 /* Check that if the ast_build_exploit_nested_bounds options is set,
4174  * we do not get an outer if node in the generated AST,
4175  * while we do get such an outer if node if the options is not set.
4176  */
4177 static int test_ast_gen4(isl_ctx *ctx)
4178 {
4179         const char *str;
4180         isl_set *set;
4181         isl_union_map *schedule;
4182         isl_ast_build *build;
4183         isl_ast_node *tree;
4184         enum isl_ast_node_type type;
4185         int enb;
4186
4187         enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
4188         str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4189
4190         isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
4191
4192         schedule = isl_union_map_read_from_str(ctx, str);
4193         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4194         build = isl_ast_build_from_context(set);
4195         tree = isl_ast_build_ast_from_schedule(build, schedule);
4196         isl_ast_build_free(build);
4197         if (!tree)
4198                 return -1;
4199
4200         type = isl_ast_node_get_type(tree);
4201         isl_ast_node_free(tree);
4202
4203         if (type == isl_ast_node_if)
4204                 isl_die(ctx, isl_error_unknown,
4205                         "not expecting if node", return -1);
4206
4207         isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
4208
4209         schedule = isl_union_map_read_from_str(ctx, str);
4210         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4211         build = isl_ast_build_from_context(set);
4212         tree = isl_ast_build_ast_from_schedule(build, schedule);
4213         isl_ast_build_free(build);
4214         if (!tree)
4215                 return -1;
4216
4217         type = isl_ast_node_get_type(tree);
4218         isl_ast_node_free(tree);
4219
4220         if (type != isl_ast_node_if)
4221                 isl_die(ctx, isl_error_unknown,
4222                         "expecting if node", return -1);
4223
4224         isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
4225
4226         return 0;
4227 }
4228
4229 /* This function is called for each leaf in the AST generated
4230  * from test_ast_gen5.
4231  *
4232  * We finalize the AST generation by extending the outer schedule
4233  * with a zero-dimensional schedule.  If this results in any for loops,
4234  * then this means that we did not pass along enough information
4235  * about the outer schedule to the inner AST generation.
4236  */
4237 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
4238         void *user)
4239 {
4240         isl_union_map *schedule, *extra;
4241         isl_ast_node *tree;
4242
4243         schedule = isl_ast_build_get_schedule(build);
4244         extra = isl_union_map_copy(schedule);
4245         extra = isl_union_map_from_domain(isl_union_map_domain(extra));
4246         schedule = isl_union_map_range_product(schedule, extra);
4247         tree = isl_ast_build_ast_from_schedule(build, schedule);
4248         isl_ast_build_free(build);
4249
4250         if (!tree)
4251                 return NULL;
4252
4253         if (isl_ast_node_get_type(tree) == isl_ast_node_for)
4254                 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
4255                         "code should not contain any for loop",
4256                         return isl_ast_node_free(tree));
4257
4258         return tree;
4259 }
4260
4261 /* Check that we do not lose any information when going back and
4262  * forth between internal and external schedule.
4263  *
4264  * In particular, we create an AST where we unroll the only
4265  * non-constant dimension in the schedule.  We therefore do
4266  * not expect any for loops in the AST.  However, older versions
4267  * of isl would not pass along enough information about the outer
4268  * schedule when performing an inner code generation from a create_leaf
4269  * callback, resulting in the inner code generation producing a for loop.
4270  */
4271 static int test_ast_gen5(isl_ctx *ctx)
4272 {
4273         const char *str;
4274         isl_set *set;
4275         isl_union_map *schedule, *options;
4276         isl_ast_build *build;
4277         isl_ast_node *tree;
4278
4279         str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4280         schedule = isl_union_map_read_from_str(ctx, str);
4281
4282         str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4283                                 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4284         options = isl_union_map_read_from_str(ctx, str);
4285
4286         set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4287         build = isl_ast_build_from_context(set);
4288         build = isl_ast_build_set_options(build, options);
4289         build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
4290         tree = isl_ast_build_ast_from_schedule(build, schedule);
4291         isl_ast_build_free(build);
4292         isl_ast_node_free(tree);
4293         if (!tree)
4294                 return -1;
4295
4296         return 0;
4297 }
4298
4299 static int test_ast_gen(isl_ctx *ctx)
4300 {
4301         if (test_ast_gen1(ctx) < 0)
4302                 return -1;
4303         if (test_ast_gen2(ctx) < 0)
4304                 return -1;
4305         if (test_ast_gen3(ctx) < 0)
4306                 return -1;
4307         if (test_ast_gen4(ctx) < 0)
4308                 return -1;
4309         if (test_ast_gen5(ctx) < 0)
4310                 return -1;
4311         return 0;
4312 }
4313
4314 /* Check if dropping output dimensions from an isl_pw_multi_aff
4315  * works properly.
4316  */
4317 static int test_pw_multi_aff(isl_ctx *ctx)
4318 {
4319         const char *str;
4320         isl_pw_multi_aff *pma1, *pma2;
4321         int equal;
4322
4323         str = "{ [i,j] -> [i+j, 4i-j] }";
4324         pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4325         str = "{ [i,j] -> [4i-j] }";
4326         pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4327
4328         pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
4329
4330         equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
4331
4332         isl_pw_multi_aff_free(pma1);
4333         isl_pw_multi_aff_free(pma2);
4334         if (equal < 0)
4335                 return -1;
4336         if (!equal)
4337                 isl_die(ctx, isl_error_unknown,
4338                         "expressions not equal", return -1);
4339
4340         return 0;
4341 }
4342
4343 /* Check that we can properly parse multi piecewise affine expressions
4344  * where the piecewise affine expressions have different domains.
4345  */
4346 static int test_multi_pw_aff(isl_ctx *ctx)
4347 {
4348         const char *str;
4349         isl_set *dom, *dom2;
4350         isl_multi_pw_aff *mpa1, *mpa2;
4351         isl_pw_aff *pa;
4352         int equal;
4353         int equal_domain;
4354
4355         mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
4356         dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
4357         mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
4358         mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
4359         mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
4360         str = "{ [i] -> [(i : i > 0), 2i] }";
4361         mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
4362
4363         equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
4364
4365         pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
4366         dom = isl_pw_aff_domain(pa);
4367         pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
4368         dom2 = isl_pw_aff_domain(pa);
4369         equal_domain = isl_set_is_equal(dom, dom2);
4370
4371         isl_set_free(dom);
4372         isl_set_free(dom2);
4373         isl_multi_pw_aff_free(mpa1);
4374         isl_multi_pw_aff_free(mpa2);
4375
4376         if (equal < 0)
4377                 return -1;
4378         if (!equal)
4379                 isl_die(ctx, isl_error_unknown,
4380                         "expressions not equal", return -1);
4381
4382         if (equal_domain < 0)
4383                 return -1;
4384         if (equal_domain)
4385                 isl_die(ctx, isl_error_unknown,
4386                         "domains unexpectedly equal", return -1);
4387
4388         return 0;
4389 }
4390
4391 /* This is a regression test for a bug where isl_basic_map_simplify
4392  * would end up in an infinite loop.  In particular, we construct
4393  * an empty basic set that is not obviously empty.
4394  * isl_basic_set_is_empty marks the basic set as empty.
4395  * After projecting out i3, the variable can be dropped completely,
4396  * but isl_basic_map_simplify refrains from doing so if the basic set
4397  * is empty and would end up in an infinite loop if it didn't test
4398  * explicitly for empty basic maps in the outer loop.
4399  */
4400 static int test_simplify(isl_ctx *ctx)
4401 {
4402         const char *str;
4403         isl_basic_set *bset;
4404         int empty;
4405
4406         str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4407                 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4408                 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4409                 "i3 >= i2 }";
4410         bset = isl_basic_set_read_from_str(ctx, str);
4411         empty = isl_basic_set_is_empty(bset);
4412         bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
4413         isl_basic_set_free(bset);
4414         if (!bset)
4415                 return -1;
4416         if (!empty)
4417                 isl_die(ctx, isl_error_unknown,
4418                         "basic set should be empty", return -1);
4419
4420         return 0;
4421 }
4422
4423 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4424  * with gbr context would fail to disable the use of the shifted tableau
4425  * when transferring equalities for the input to the context, resulting
4426  * in invalid sample values.
4427  */
4428 static int test_partial_lexmin(isl_ctx *ctx)
4429 {
4430         const char *str;
4431         isl_basic_set *bset;
4432         isl_basic_map *bmap;
4433         isl_map *map;
4434
4435         str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
4436         bmap = isl_basic_map_read_from_str(ctx, str);
4437         str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
4438         bset = isl_basic_set_read_from_str(ctx, str);
4439         map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
4440         isl_map_free(map);
4441
4442         if (!map)
4443                 return -1;
4444
4445         return 0;
4446 }
4447
4448 /* Check that the variable compression performed on the existentially
4449  * quantified variables inside isl_basic_set_compute_divs is not confused
4450  * by the implicit equalities among the parameters.
4451  */
4452 static int test_compute_divs(isl_ctx *ctx)
4453 {
4454         const char *str;
4455         isl_basic_set *bset;
4456         isl_set *set;
4457
4458         str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4459                 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4460                 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4461                 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4462         bset = isl_basic_set_read_from_str(ctx, str);
4463         set = isl_basic_set_compute_divs(bset);
4464         isl_set_free(set);
4465         if (!set)
4466                 return -1;
4467
4468         return 0;
4469 }
4470
4471 struct {
4472         const char *name;
4473         int (*fn)(isl_ctx *ctx);
4474 } tests [] = {
4475         { "val", &test_val },
4476         { "compute divs", &test_compute_divs },
4477         { "partial lexmin", &test_partial_lexmin },
4478         { "simplify", &test_simplify },
4479         { "curry", &test_curry },
4480         { "piecewise multi affine expressions", &test_pw_multi_aff },
4481         { "multi piecewise affine expressions", &test_multi_pw_aff },
4482         { "conversion", &test_conversion },
4483         { "list", &test_list },
4484         { "align parameters", &test_align_parameters },
4485         { "preimage", &test_preimage },
4486         { "pullback", &test_pullback },
4487         { "AST", &test_ast },
4488         { "AST generation", &test_ast_gen },
4489         { "eliminate", &test_eliminate },
4490         { "residue class", &test_residue_class },
4491         { "div", &test_div },
4492         { "slice", &test_slice },
4493         { "fixed power", &test_fixed_power },
4494         { "sample", &test_sample },
4495         { "output", &test_output },
4496         { "vertices", &test_vertices },
4497         { "fixed", &test_fixed },
4498         { "equal", &test_equal },
4499         { "product", &test_product },
4500         { "dim_max", &test_dim_max },
4501         { "affine", &test_aff },
4502         { "injective", &test_injective },
4503         { "schedule", &test_schedule },
4504         { "union_pw", &test_union_pw },
4505         { "parse", &test_parse },
4506         { "single-valued", &test_sv },
4507         { "affine hull", &test_affine_hull },
4508         { "coalesce", &test_coalesce },
4509         { "factorize", &test_factorize },
4510         { "subset", &test_subset },
4511         { "subtract", &test_subtract },
4512         { "lexmin", &test_lexmin },
4513         { "gist", &test_gist },
4514         { "piecewise quasi-polynomials", &test_pwqp },
4515 };
4516
4517 int main()
4518 {
4519         int i;
4520         struct isl_ctx *ctx;
4521
4522         srcdir = getenv("srcdir");
4523         assert(srcdir);
4524
4525         ctx = isl_ctx_alloc();
4526         for (i = 0; i < ARRAY_SIZE(tests); ++i) {
4527                 printf("%s\n", tests[i].name);
4528                 if (tests[i].fn(ctx) < 0)
4529                         goto error;
4530         }
4531         test_lift(ctx);
4532         test_bound(ctx);
4533         test_union(ctx);
4534         test_split_periods(ctx);
4535         test_lex(ctx);
4536         test_bijective(ctx);
4537         test_dep(ctx);
4538         test_read(ctx);
4539         test_bounded(ctx);
4540         test_construction(ctx);
4541         test_dim(ctx);
4542         test_application(ctx);
4543         test_convex_hull(ctx);
4544         test_closure(ctx);
4545         isl_ctx_free(ctx);
4546         return 0;
4547 error:
4548         isl_ctx_free(ctx);
4549         return -1;
4550 }