isl_constraint.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2010      INRIA Saclay
   4  *
   5  * Use of this software is governed by the MIT license
   6  *
   7  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   8  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   9  * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
  10  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
  11  */
  12
  13 #include <isl_map_private.h>
  14 #include <isl_constraint_private.h>
  15 #include <isl_space_private.h>
  16 #include <isl/seq.h>
  17 #include <isl_aff_private.h>
  18 #include <isl_local_space_private.h>
  19
  20 #undef BASE
  21 #define BASE constraint
  22
  23 #include <isl_list_templ.c>
  24
  25 isl_ctx *isl_constraint_get_ctx(__isl_keep isl_constraint *c)
  26 {
  27         return c ? isl_local_space_get_ctx(c->ls) : NULL;
  28 }
  29
  30 static unsigned n(struct isl_constraint *c, enum isl_dim_type type)
  31 {
  32         return isl_local_space_dim(c->ls, type);
  33 }
  34
  35 static unsigned offset(struct isl_constraint *c, enum isl_dim_type type)
  36 {
  37         return isl_local_space_offset(c->ls, type);
  38 }
  39
  40 static unsigned basic_map_offset(__isl_keep isl_basic_map *bmap,
  41                                                         enum isl_dim_type type)
  42 {
  43         return type == isl_dim_div ? 1 + isl_space_dim(bmap->dim, isl_dim_all)
  44                                    : 1 + isl_space_offset(bmap->dim, type);
  45 }
  46
  47 static unsigned basic_set_offset(struct isl_basic_set *bset,
  48                                                         enum isl_dim_type type)
  49 {
  50         isl_space *dim = bset->dim;
  51         switch (type) {
  52         case isl_dim_param:     return 1;
  53         case isl_dim_in:        return 1 + dim->nparam;
  54         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  55         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
  56         default:                return 0;
  57         }
  58 }
  59
  60 __isl_give isl_constraint *isl_constraint_alloc_vec(int eq,
  61         __isl_take isl_local_space *ls, __isl_take isl_vec *v)
  62 {
  63         isl_constraint *constraint;
  64
  65         if (!ls || !v)
  66                 goto error;
  67
  68         constraint = isl_alloc_type(isl_vec_get_ctx(v), isl_constraint);
  69         if (!constraint)
  70                 goto error;
  71
  72         constraint->ref = 1;
  73         constraint->eq = eq;
  74         constraint->ls = ls;
  75         constraint->v = v;
  76
  77         return constraint;
  78 error:
  79         isl_local_space_free(ls);
  80         isl_vec_free(v);
  81         return NULL;
  82 }
  83
  84 __isl_give isl_constraint *isl_constraint_alloc(int eq,
  85         __isl_take isl_local_space *ls)
  86 {
  87         isl_ctx *ctx;
  88         isl_vec *v;
  89
  90         if (!ls)
  91                 return NULL;
  92
  93         ctx = isl_local_space_get_ctx(ls);
  94         v = isl_vec_alloc(ctx, 1 + isl_local_space_dim(ls, isl_dim_all));
  95         v = isl_vec_clr(v);
  96         return isl_constraint_alloc_vec(eq, ls, v);
  97 }
  98
  99 struct isl_constraint *isl_basic_map_constraint(struct isl_basic_map *bmap,
 100         isl_int **line)
 101 {
 102         int eq;
 103         isl_ctx *ctx;
 104         isl_vec *v;
 105         isl_local_space *ls = NULL;
 106         isl_constraint *constraint;
 107
 108         if (!bmap || !line)
 109                 goto error;
 110
 111         eq = line >= bmap->eq;
 112
 113         ctx = isl_basic_map_get_ctx(bmap);
 114         ls = isl_basic_map_get_local_space(bmap);
 115         v = isl_vec_alloc(ctx, 1 + isl_local_space_dim(ls, isl_dim_all));
 116         if (!v)
 117                 goto error;
 118         isl_seq_cpy(v->el, line[0], v->size);
 119         constraint = isl_constraint_alloc_vec(eq, ls, v);
 120
 121         isl_basic_map_free(bmap);
 122         return constraint;
 123 error:
 124         isl_local_space_free(ls);
 125         isl_basic_map_free(bmap);
 126         return NULL;
 127 }
 128
 129 struct isl_constraint *isl_basic_set_constraint(struct isl_basic_set *bset,
 130         isl_int **line)
 131 {
 132         return isl_basic_map_constraint((struct isl_basic_map *)bset, line);
 133 }
 134
 135 __isl_give isl_constraint *isl_equality_alloc(__isl_take isl_local_space *ls)
 136 {
 137         return isl_constraint_alloc(1, ls);
 138 }
 139
 140 __isl_give isl_constraint *isl_inequality_alloc(__isl_take isl_local_space *ls)
 141 {
 142         return isl_constraint_alloc(0, ls);
 143 }
 144
 145 struct isl_constraint *isl_constraint_dup(struct isl_constraint *c)
 146 {
 147         if (!c)
 148                 return NULL;
 149
 150         return isl_constraint_alloc_vec(c->eq, isl_local_space_copy(c->ls),
 151                                                 isl_vec_copy(c->v));
 152 }
 153
 154 struct isl_constraint *isl_constraint_cow(struct isl_constraint *c)
 155 {
 156         if (!c)
 157                 return NULL;
 158
 159         if (c->ref == 1)
 160                 return c;
 161         c->ref--;
 162         return isl_constraint_dup(c);
 163 }
 164
 165 struct isl_constraint *isl_constraint_copy(struct isl_constraint *constraint)
 166 {
 167         if (!constraint)
 168                 return NULL;
 169
 170         constraint->ref++;
 171         return constraint;
 172 }
 173
 174 void *isl_constraint_free(struct isl_constraint *c)
 175 {
 176         if (!c)
 177                 return NULL;
 178
 179         if (--c->ref > 0)
 180                 return NULL;
 181
 182         isl_local_space_free(c->ls);
 183         isl_vec_free(c->v);
 184         free(c);
 185
 186         return NULL;
 187 }
 188
 189 /* Return the number of constraints in "bset", i.e., the
 190  * number of times isl_basic_set_foreach_constraint will
 191  * call the callback.
 192  */
 193 int isl_basic_set_n_constraint(__isl_keep isl_basic_set *bset)
 194 {
 195         if (!bset)
 196                 return -1;
 197
 198         return bset->n_eq + bset->n_ineq;
 199 }
 200
 201 int isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
 202         int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
 203 {
 204         int i;
 205         struct isl_constraint *c;
 206
 207         if (!bmap)
 208                 return -1;
 209
 210         isl_assert(bmap->ctx, ISL_F_ISSET(bmap, ISL_BASIC_MAP_FINAL),
 211                         return -1);
 212
 213         for (i = 0; i < bmap->n_eq; ++i) {
 214                 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 215                                                 &bmap->eq[i]);
 216                 if (!c)
 217                         return -1;
 218                 if (fn(c, user) < 0)
 219                         return -1;
 220         }
 221
 222         for (i = 0; i < bmap->n_ineq; ++i) {
 223                 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 224                                                 &bmap->ineq[i]);
 225                 if (!c)
 226                         return -1;
 227                 if (fn(c, user) < 0)
 228                         return -1;
 229         }
 230
 231         return 0;
 232 }
 233
 234 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
 235         int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
 236 {
 237         return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
 238 }
 239
 240 int isl_constraint_is_equal(struct isl_constraint *constraint1,
 241         struct isl_constraint *constraint2)
 242 {
 243         int equal;
 244
 245         if (!constraint1 || !constraint2)
 246                 return 0;
 247         if (constraint1->eq != constraint2->eq)
 248                 return 0;
 249         equal = isl_local_space_is_equal(constraint1->ls, constraint2->ls);
 250         if (equal < 0 || !equal)
 251                 return equal;
 252         return isl_vec_is_equal(constraint1->v, constraint2->v);
 253 }
 254
 255 struct isl_basic_map *isl_basic_map_add_constraint(
 256         struct isl_basic_map *bmap, struct isl_constraint *constraint)
 257 {
 258         isl_ctx *ctx;
 259         isl_space *dim;
 260         int equal_space;
 261
 262         if (!bmap || !constraint)
 263                 goto error;
 264
 265         ctx = isl_constraint_get_ctx(constraint);
 266         dim = isl_constraint_get_space(constraint);
 267         equal_space = isl_space_is_equal(bmap->dim, dim);
 268         isl_space_free(dim);
 269         isl_assert(ctx, equal_space, goto error);
 270
 271         bmap = isl_basic_map_intersect(bmap,
 272                                 isl_basic_map_from_constraint(constraint));
 273         return bmap;
 274 error:
 275         isl_basic_map_free(bmap);
 276         isl_constraint_free(constraint);
 277         return NULL;
 278 }
 279
 280 struct isl_basic_set *isl_basic_set_add_constraint(
 281         struct isl_basic_set *bset, struct isl_constraint *constraint)
 282 {
 283         return (struct isl_basic_set *)
 284                 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
 285                                                 constraint);
 286 }
 287
 288 __isl_give isl_map *isl_map_add_constraint(__isl_take isl_map *map,
 289         __isl_take isl_constraint *constraint)
 290 {
 291         isl_basic_map *bmap;
 292
 293         bmap = isl_basic_map_from_constraint(constraint);
 294         map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
 295
 296         return map;
 297 }
 298
 299 __isl_give isl_set *isl_set_add_constraint(__isl_take isl_set *set,
 300         __isl_take isl_constraint *constraint)
 301 {
 302         return isl_map_add_constraint(set, constraint);
 303 }
 304
 305 __isl_give isl_space *isl_constraint_get_space(
 306         __isl_keep isl_constraint *constraint)
 307 {
 308         return constraint ? isl_local_space_get_space(constraint->ls) : NULL;
 309 }
 310
 311 __isl_give isl_local_space *isl_constraint_get_local_space(
 312         __isl_keep isl_constraint *constraint)
 313 {
 314         return constraint ? isl_local_space_copy(constraint->ls) : NULL;
 315 }
 316
 317 int isl_constraint_dim(struct isl_constraint *constraint,
 318         enum isl_dim_type type)
 319 {
 320         if (!constraint)
 321                 return -1;
 322         return n(constraint, type);
 323 }
 324
 325 int isl_constraint_involves_dims(__isl_keep isl_constraint *constraint,
 326         enum isl_dim_type type, unsigned first, unsigned n)
 327 {
 328         int i;
 329         isl_ctx *ctx;
 330         int *active = NULL;
 331         int involves = 0;
 332
 333         if (!constraint)
 334                 return -1;
 335         if (n == 0)
 336                 return 0;
 337
 338         ctx = isl_constraint_get_ctx(constraint);
 339         if (first + n > isl_constraint_dim(constraint, type))
 340                 isl_die(ctx, isl_error_invalid,
 341                         "range out of bounds", return -1);
 342
 343         active = isl_local_space_get_active(constraint->ls,
 344                                             constraint->v->el + 1);
 345         if (!active)
 346                 goto error;
 347
 348         first += isl_local_space_offset(constraint->ls, type) - 1;
 349         for (i = 0; i < n; ++i)
 350                 if (active[first + i]) {
 351                         involves = 1;
 352                         break;
 353                 }
 354
 355         free(active);
 356
 357         return involves;
 358 error:
 359         free(active);
 360         return -1;
 361 }
 362
 363 /* Does the given constraint represent a lower bound on the given
 364  * dimension?
 365  */
 366 int isl_constraint_is_lower_bound(__isl_keep isl_constraint *constraint,
 367         enum isl_dim_type type, unsigned pos)
 368 {
 369         if (!constraint)
 370                 return -1;
 371
 372         if (pos >= isl_local_space_dim(constraint->ls, type))
 373                 isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
 374                         "position out of bounds", return -1);
 375
 376         pos += isl_local_space_offset(constraint->ls, type);
 377         return isl_int_is_pos(constraint->v->el[pos]);
 378 }
 379
 380 /* Does the given constraint represent an upper bound on the given
 381  * dimension?
 382  */
 383 int isl_constraint_is_upper_bound(__isl_keep isl_constraint *constraint,
 384         enum isl_dim_type type, unsigned pos)
 385 {
 386         if (!constraint)
 387                 return -1;
 388
 389         if (pos >= isl_local_space_dim(constraint->ls, type))
 390                 isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
 391                         "position out of bounds", return -1);
 392
 393         pos += isl_local_space_offset(constraint->ls, type);
 394         return isl_int_is_neg(constraint->v->el[pos]);
 395 }
 396
 397 const char *isl_constraint_get_dim_name(__isl_keep isl_constraint *constraint,
 398         enum isl_dim_type type, unsigned pos)
 399 {
 400         return constraint ?
 401             isl_local_space_get_dim_name(constraint->ls, type, pos) : NULL;
 402 }
 403
 404 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
 405 {
 406         if (!constraint)
 407                 return;
 408         isl_int_set(*v, constraint->v->el[0]);
 409 }
 410
 411 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
 412         enum isl_dim_type type, int pos, isl_int *v)
 413 {
 414         if (!constraint)
 415                 return;
 416
 417         if (pos >= isl_local_space_dim(constraint->ls, type))
 418                 isl_die(constraint->v->ctx, isl_error_invalid,
 419                         "position out of bounds", return);
 420
 421         pos += isl_local_space_offset(constraint->ls, type);
 422         isl_int_set(*v, constraint->v->el[pos]);
 423 }
 424
 425 __isl_give isl_aff *isl_constraint_get_div(__isl_keep isl_constraint *constraint,
 426         int pos)
 427 {
 428         if (!constraint)
 429                 return NULL;
 430
 431         return isl_local_space_get_div(constraint->ls, pos);
 432 }
 433
 434 __isl_give isl_constraint *isl_constraint_set_constant(
 435         __isl_take isl_constraint *constraint, isl_int v)
 436 {
 437         constraint = isl_constraint_cow(constraint);
 438         if (!constraint)
 439                 return NULL;
 440
 441         constraint->v = isl_vec_cow(constraint->v);
 442         if (!constraint->v)
 443                 return isl_constraint_free(constraint);
 444
 445         isl_int_set(constraint->v->el[0], v);
 446         return constraint;
 447 }
 448
 449 __isl_give isl_constraint *isl_constraint_set_constant_si(
 450         __isl_take isl_constraint *constraint, int v)
 451 {
 452         constraint = isl_constraint_cow(constraint);
 453         if (!constraint)
 454                 return NULL;
 455
 456         constraint->v = isl_vec_cow(constraint->v);
 457         if (!constraint->v)
 458                 return isl_constraint_free(constraint);
 459
 460         isl_int_set_si(constraint->v->el[0], v);
 461         return constraint;
 462 }
 463
 464 __isl_give isl_constraint *isl_constraint_set_coefficient(
 465         __isl_take isl_constraint *constraint,
 466         enum isl_dim_type type, int pos, isl_int v)
 467 {
 468         constraint = isl_constraint_cow(constraint);
 469         if (!constraint)
 470                 return NULL;
 471
 472         if (pos >= isl_local_space_dim(constraint->ls, type))
 473                 isl_die(constraint->v->ctx, isl_error_invalid,
 474                         "position out of bounds",
 475                         return isl_constraint_free(constraint));
 476
 477         constraint = isl_constraint_cow(constraint);
 478         if (!constraint)
 479                 return NULL;
 480
 481         constraint->v = isl_vec_cow(constraint->v);
 482         if (!constraint->v)
 483                 return isl_constraint_free(constraint);
 484
 485         pos += isl_local_space_offset(constraint->ls, type);
 486         isl_int_set(constraint->v->el[pos], v);
 487
 488         return constraint;
 489 }
 490
 491 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
 492         __isl_take isl_constraint *constraint,
 493         enum isl_dim_type type, int pos, int v)
 494 {
 495         constraint = isl_constraint_cow(constraint);
 496         if (!constraint)
 497                 return NULL;
 498
 499         if (pos >= isl_local_space_dim(constraint->ls, type))
 500                 isl_die(constraint->v->ctx, isl_error_invalid,
 501                         "position out of bounds",
 502                         return isl_constraint_free(constraint));
 503
 504         constraint = isl_constraint_cow(constraint);
 505         if (!constraint)
 506                 return NULL;
 507
 508         constraint->v = isl_vec_cow(constraint->v);
 509         if (!constraint->v)
 510                 return isl_constraint_free(constraint);
 511
 512         pos += isl_local_space_offset(constraint->ls, type);
 513         isl_int_set_si(constraint->v->el[pos], v);
 514
 515         return constraint;
 516 }
 517
 518 /* Drop any constraint from "bset" that is identical to "constraint".
 519  * In particular, this means that the local spaces of "bset" and
 520  * "constraint" need to be the same.
 521  *
 522  * Since the given constraint may actually be a pointer into the bset,
 523  * we have to be careful not to reorder the constraints as the user
 524  * may be holding on to other constraints from the same bset.
 525  * This should be cleaned up when the internal representation of
 526  * isl_constraint is changed to use isl_aff.
 527  */
 528 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
 529         __isl_take isl_basic_set *bset, __isl_take isl_constraint *constraint)
 530 {
 531         int i;
 532         unsigned n;
 533         isl_int **row;
 534         unsigned total;
 535         isl_local_space *ls1;
 536         int equal;
 537
 538         if (!bset || !constraint)
 539                 goto error;
 540
 541         ls1 = isl_basic_set_get_local_space(bset);
 542         equal = isl_local_space_is_equal(ls1, constraint->ls);
 543         isl_local_space_free(ls1);
 544         if (equal < 0)
 545                 goto error;
 546         if (!equal) {
 547                 isl_constraint_free(constraint);
 548                 return bset;
 549         }
 550
 551         if (isl_constraint_is_equality(constraint)) {
 552                 n = bset->n_eq;
 553                 row = bset->eq;
 554         } else {
 555                 n = bset->n_ineq;
 556                 row = bset->ineq;
 557         }
 558
 559         total = isl_constraint_dim(constraint, isl_dim_all);
 560         for (i = 0; i < n; ++i)
 561                 if (isl_seq_eq(row[i], constraint->v->el, 1 + total))
 562                         isl_seq_clr(row[i], 1 + total);
 563
 564         isl_constraint_free(constraint);
 565         return bset;
 566 error:
 567         isl_constraint_free(constraint);
 568         isl_basic_set_free(bset);
 569         return NULL;
 570 }
 571
 572 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
 573 {
 574         isl_ctx *ctx;
 575
 576         constraint = isl_constraint_cow(constraint);
 577         if (!constraint)
 578                 return NULL;
 579
 580         ctx = isl_constraint_get_ctx(constraint);
 581         if (isl_constraint_is_equality(constraint))
 582                 isl_die(ctx, isl_error_invalid, "cannot negate equality",
 583                         return isl_constraint_free(constraint));
 584         constraint->v = isl_vec_neg(constraint->v);
 585         constraint->v = isl_vec_cow(constraint->v);
 586         if (!constraint->v)
 587                 return isl_constraint_free(constraint);
 588         isl_int_sub_ui(constraint->v->el[0], constraint->v->el[0], 1);
 589         return constraint;
 590 }
 591
 592 int isl_constraint_is_equality(struct isl_constraint *constraint)
 593 {
 594         if (!constraint)
 595                 return -1;
 596         return constraint->eq;
 597 }
 598
 599 int isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
 600 {
 601         int i;
 602         int n_div;
 603
 604         if (!constraint)
 605                 return -1;
 606         if (isl_constraint_is_equality(constraint))
 607                 return 0;
 608         n_div = isl_constraint_dim(constraint, isl_dim_div);
 609         for (i = 0; i < n_div; ++i) {
 610                 if (isl_local_space_is_div_constraint(constraint->ls,
 611                                                         constraint->v->el, i))
 612                         return 1;
 613         }
 614
 615         return 0;
 616 }
 617
 618 /* We manually set ISL_BASIC_SET_FINAL instead of calling
 619  * isl_basic_map_finalize because we want to keep the position
 620  * of the divs and we therefore do not want to throw away redundant divs.
 621  * This is arguably a bit fragile.
 622  */
 623 __isl_give isl_basic_map *isl_basic_map_from_constraint(
 624         __isl_take isl_constraint *constraint)
 625 {
 626         int k;
 627         isl_local_space *ls;
 628         struct isl_basic_map *bmap;
 629         isl_int *c;
 630         unsigned total;
 631
 632         if (!constraint)
 633                 return NULL;
 634
 635         ls = isl_local_space_copy(constraint->ls);
 636         bmap = isl_basic_map_from_local_space(ls);
 637         bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
 638         if (isl_constraint_is_equality(constraint)) {
 639                 k = isl_basic_map_alloc_equality(bmap);
 640                 if (k < 0)
 641                         goto error;
 642                 c = bmap->eq[k];
 643         }
 644         else {
 645                 k = isl_basic_map_alloc_inequality(bmap);
 646                 if (k < 0)
 647                         goto error;
 648                 c = bmap->ineq[k];
 649         }
 650         total = isl_basic_map_total_dim(bmap);
 651         isl_seq_cpy(c, constraint->v->el, 1 + total);
 652         isl_constraint_free(constraint);
 653         if (bmap)
 654                 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
 655         return bmap;
 656 error:
 657         isl_constraint_free(constraint);
 658         isl_basic_map_free(bmap);
 659         return NULL;
 660 }
 661
 662 struct isl_basic_set *isl_basic_set_from_constraint(
 663         struct isl_constraint *constraint)
 664 {
 665         if (!constraint)
 666                 return NULL;
 667
 668         if (isl_constraint_dim(constraint, isl_dim_in) != 0)
 669                 isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
 670                         "not a set constraint",
 671                         return isl_constraint_free(constraint));
 672         return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
 673 }
 674
 675 int isl_basic_map_has_defining_equality(
 676         __isl_keep isl_basic_map *bmap, enum isl_dim_type type, int pos,
 677         __isl_give isl_constraint **c)
 678 {
 679         int i;
 680         unsigned offset;
 681         unsigned total;
 682
 683         if (!bmap)
 684                 return -1;
 685         offset = basic_map_offset(bmap, type);
 686         total = isl_basic_map_total_dim(bmap);
 687         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
 688         for (i = 0; i < bmap->n_eq; ++i)
 689                 if (!isl_int_is_zero(bmap->eq[i][offset + pos]) &&
 690                     isl_seq_first_non_zero(bmap->eq[i]+offset+pos+1,
 691                                            1+total-offset-pos-1) == -1) {
 692                         *c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 693                                                                 &bmap->eq[i]);
 694                         return 1;
 695                 }
 696         return 0;
 697 }
 698
 699 int isl_basic_set_has_defining_equality(
 700         __isl_keep isl_basic_set *bset, enum isl_dim_type type, int pos,
 701         __isl_give isl_constraint **c)
 702 {
 703         return isl_basic_map_has_defining_equality((isl_basic_map *)bset,
 704                                                     type, pos, c);
 705 }
 706
 707 int isl_basic_set_has_defining_inequalities(
 708         struct isl_basic_set *bset, enum isl_dim_type type, int pos,
 709         struct isl_constraint **lower,
 710         struct isl_constraint **upper)
 711 {
 712         int i, j;
 713         unsigned offset;
 714         unsigned total;
 715         isl_int m;
 716         isl_int **lower_line, **upper_line;
 717
 718         if (!bset)
 719                 return -1;
 720         offset = basic_set_offset(bset, type);
 721         total = isl_basic_set_total_dim(bset);
 722         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
 723         isl_int_init(m);
 724         for (i = 0; i < bset->n_ineq; ++i) {
 725                 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
 726                         continue;
 727                 if (isl_int_is_one(bset->ineq[i][offset + pos]))
 728                         continue;
 729                 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
 730                         continue;
 731                 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
 732                                                 1+total-offset-pos-1) != -1)
 733                         continue;
 734                 for (j = i + 1; j < bset->n_ineq; ++j) {
 735                         if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
 736                                             total))
 737                                 continue;
 738                         isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
 739                         if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
 740                                 continue;
 741
 742                         if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
 743                                 lower_line = &bset->ineq[i];
 744                                 upper_line = &bset->ineq[j];
 745                         } else {
 746                                 lower_line = &bset->ineq[j];
 747                                 upper_line = &bset->ineq[i];
 748                         }
 749                         *lower = isl_basic_set_constraint(
 750                                         isl_basic_set_copy(bset), lower_line);
 751                         *upper = isl_basic_set_constraint(
 752                                         isl_basic_set_copy(bset), upper_line);
 753                         isl_int_clear(m);
 754                         return 1;
 755                 }
 756         }
 757         *lower = NULL;
 758         *upper = NULL;
 759         isl_int_clear(m);
 760         return 0;
 761 }
 762
 763 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
 764  * (in "a" and "b"), add a constraint to "bset" that ensures that the
 765  * bound implied by "a" is (strictly) larger than the bound implied by "b".
 766  *
 767  * If both constraints imply lower bounds, then this means that "a" is
 768  * active in the result.
 769  * If both constraints imply upper bounds, then this means that "b" is
 770  * active in the result.
 771  */
 772 static __isl_give isl_basic_set *add_larger_bound_constraint(
 773         __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
 774         unsigned abs_pos, int strict)
 775 {
 776         int k;
 777         isl_int t;
 778         unsigned total;
 779
 780         k = isl_basic_set_alloc_inequality(bset);
 781         if (k < 0)
 782                 goto error;
 783
 784         total = isl_basic_set_dim(bset, isl_dim_all);
 785
 786         isl_int_init(t);
 787         isl_int_neg(t, b[1 + abs_pos]);
 788
 789         isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
 790         isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
 791                 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
 792                 total - abs_pos);
 793
 794         if (strict)
 795                 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
 796
 797         isl_int_clear(t);
 798
 799         return bset;
 800 error:
 801         isl_basic_set_free(bset);
 802         return NULL;
 803 }
 804
 805 /* Add constraints to "context" that ensure that "u" is the smallest
 806  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 807  * the resulting basic set.
 808  */
 809 static __isl_give isl_basic_set *set_smallest_upper_bound(
 810         __isl_keep isl_basic_set *context,
 811         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
 812 {
 813         int j;
 814
 815         context = isl_basic_set_copy(context);
 816         context = isl_basic_set_cow(context);
 817
 818         context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
 819
 820         for (j = 0; j < bset->n_ineq; ++j) {
 821                 if (j == u)
 822                         continue;
 823                 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 824                         continue;
 825                 context = add_larger_bound_constraint(context,
 826                         bset->ineq[j], bset->ineq[u], abs_pos, j > u);
 827         }
 828
 829         context = isl_basic_set_simplify(context);
 830         context = isl_basic_set_finalize(context);
 831
 832         return context;
 833 }
 834
 835 /* Add constraints to "context" that ensure that "u" is the largest
 836  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 837  * the resulting basic set.
 838  */
 839 static __isl_give isl_basic_set *set_largest_lower_bound(
 840         __isl_keep isl_basic_set *context,
 841         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
 842 {
 843         int j;
 844
 845         context = isl_basic_set_copy(context);
 846         context = isl_basic_set_cow(context);
 847
 848         context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
 849
 850         for (j = 0; j < bset->n_ineq; ++j) {
 851                 if (j == l)
 852                         continue;
 853                 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
 854                         continue;
 855                 context = add_larger_bound_constraint(context,
 856                         bset->ineq[l], bset->ineq[j], abs_pos, j > l);
 857         }
 858
 859         context = isl_basic_set_simplify(context);
 860         context = isl_basic_set_finalize(context);
 861
 862         return context;
 863 }
 864
 865 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
 866         enum isl_dim_type type, unsigned abs_pos,
 867         __isl_take isl_basic_set *context, int n_upper,
 868         int (*fn)(__isl_take isl_constraint *lower,
 869                   __isl_take isl_constraint *upper,
 870                   __isl_take isl_basic_set *bset, void *user), void *user)
 871 {
 872         isl_basic_set *context_i;
 873         isl_constraint *upper = NULL;
 874         int i;
 875
 876         for (i = 0; i < bset->n_ineq; ++i) {
 877                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 878                         continue;
 879
 880                 context_i = set_smallest_upper_bound(context, bset,
 881                                                         abs_pos, n_upper, i);
 882                 if (isl_basic_set_is_empty(context_i)) {
 883                         isl_basic_set_free(context_i);
 884                         continue;
 885                 }
 886                 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 887                                                 &bset->ineq[i]);
 888                 if (!upper || !context_i)
 889                         goto error;
 890                 if (fn(NULL, upper, context_i, user) < 0)
 891                         break;
 892         }
 893
 894         isl_basic_set_free(context);
 895
 896         if (i < bset->n_ineq)
 897                 return -1;
 898
 899         return 0;
 900 error:
 901         isl_constraint_free(upper);
 902         isl_basic_set_free(context_i);
 903         isl_basic_set_free(context);
 904         return -1;
 905 }
 906
 907 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
 908         enum isl_dim_type type, unsigned abs_pos,
 909         __isl_take isl_basic_set *context, int n_lower,
 910         int (*fn)(__isl_take isl_constraint *lower,
 911                   __isl_take isl_constraint *upper,
 912                   __isl_take isl_basic_set *bset, void *user), void *user)
 913 {
 914         isl_basic_set *context_i;
 915         isl_constraint *lower = NULL;
 916         int i;
 917
 918         for (i = 0; i < bset->n_ineq; ++i) {
 919                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 920                         continue;
 921
 922                 context_i = set_largest_lower_bound(context, bset,
 923                                                         abs_pos, n_lower, i);
 924                 if (isl_basic_set_is_empty(context_i)) {
 925                         isl_basic_set_free(context_i);
 926                         continue;
 927                 }
 928                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 929                                                 &bset->ineq[i]);
 930                 if (!lower || !context_i)
 931                         goto error;
 932                 if (fn(lower, NULL, context_i, user) < 0)
 933                         break;
 934         }
 935
 936         isl_basic_set_free(context);
 937
 938         if (i < bset->n_ineq)
 939                 return -1;
 940
 941         return 0;
 942 error:
 943         isl_constraint_free(lower);
 944         isl_basic_set_free(context_i);
 945         isl_basic_set_free(context);
 946         return -1;
 947 }
 948
 949 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
 950         enum isl_dim_type type, unsigned abs_pos,
 951         __isl_take isl_basic_set *context, int n_lower, int n_upper,
 952         int (*fn)(__isl_take isl_constraint *lower,
 953                   __isl_take isl_constraint *upper,
 954                   __isl_take isl_basic_set *bset, void *user), void *user)
 955 {
 956         isl_basic_set *context_i, *context_j;
 957         isl_constraint *lower = NULL;
 958         isl_constraint *upper = NULL;
 959         int i, j;
 960
 961         for (i = 0; i < bset->n_ineq; ++i) {
 962                 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
 963                         continue;
 964
 965                 context_i = set_largest_lower_bound(context, bset,
 966                                                         abs_pos, n_lower, i);
 967                 if (isl_basic_set_is_empty(context_i)) {
 968                         isl_basic_set_free(context_i);
 969                         continue;
 970                 }
 971
 972                 for (j = 0; j < bset->n_ineq; ++j) {
 973                         if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 974                                 continue;
 975
 976                         context_j = set_smallest_upper_bound(context_i, bset,
 977                                                             abs_pos, n_upper, j);
 978                         context_j = isl_basic_set_extend_constraints(context_j,
 979                                                                         0, 1);
 980                         context_j = add_larger_bound_constraint(context_j,
 981                                 bset->ineq[i], bset->ineq[j], abs_pos, 0);
 982                         context_j = isl_basic_set_simplify(context_j);
 983                         context_j = isl_basic_set_finalize(context_j);
 984                         if (isl_basic_set_is_empty(context_j)) {
 985                                 isl_basic_set_free(context_j);
 986                                 continue;
 987                         }
 988                         lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 989                                                         &bset->ineq[i]);
 990                         upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 991                                                         &bset->ineq[j]);
 992                         if (!lower || !upper || !context_j)
 993                                 goto error;
 994                         if (fn(lower, upper, context_j, user) < 0)
 995                                 break;
 996                 }
 997
 998                 isl_basic_set_free(context_i);
 999
1000                 if (j < bset->n_ineq)
1001                         break;
1002         }
1003
1004         isl_basic_set_free(context);
1005
1006         if (i < bset->n_ineq)
1007                 return -1;
1008
1009         return 0;
1010 error:
1011         isl_constraint_free(lower);
1012         isl_constraint_free(upper);
1013         isl_basic_set_free(context_i);
1014         isl_basic_set_free(context_j);
1015         isl_basic_set_free(context);
1016         return -1;
1017 }
1018
1019 /* For each pair of lower and upper bounds on the variable "pos"
1020  * of type "type", call "fn" with these lower and upper bounds and the
1021  * set of constraints on the remaining variables where these bounds
1022  * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
1023  *
1024  * If the designated variable is equal to an affine combination of the
1025  * other variables then fn is called with both lower and upper
1026  * set to the corresponding equality.
1027  *
1028  * If there is no lower (or upper) bound, then NULL is passed
1029  * as the corresponding bound.
1030  *
1031  * We first check if the variable is involved in any equality.
1032  * If not, we count the number of lower and upper bounds and
1033  * act accordingly.
1034  */
1035 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
1036         enum isl_dim_type type, unsigned pos,
1037         int (*fn)(__isl_take isl_constraint *lower,
1038                   __isl_take isl_constraint *upper,
1039                   __isl_take isl_basic_set *bset, void *user), void *user)
1040 {
1041         int i;
1042         isl_constraint *lower = NULL;
1043         isl_constraint *upper = NULL;
1044         isl_basic_set *context = NULL;
1045         unsigned abs_pos;
1046         int n_lower, n_upper;
1047
1048         if (!bset)
1049                 return -1;
1050         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
1051         isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
1052                 return -1);
1053
1054         abs_pos = pos;
1055         if (type == isl_dim_set)
1056                 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
1057
1058         for (i = 0; i < bset->n_eq; ++i) {
1059                 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
1060                         continue;
1061
1062                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
1063                                                 &bset->eq[i]);
1064                 upper = isl_constraint_copy(lower);
1065                 context = isl_basic_set_remove_dims(isl_basic_set_copy(bset),
1066                                         type, pos, 1);
1067                 if (!lower || !upper || !context)
1068                         goto error;
1069                 return fn(lower, upper, context, user);
1070         }
1071
1072         n_lower = 0;
1073         n_upper = 0;
1074         for (i = 0; i < bset->n_ineq; ++i) {
1075                 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
1076                         n_lower++;
1077                 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
1078                         n_upper++;
1079         }
1080
1081         context = isl_basic_set_copy(bset);
1082         context = isl_basic_set_cow(context);
1083         if (!context)
1084                 goto error;
1085         for (i = context->n_ineq - 1; i >= 0; --i)
1086                 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
1087                         isl_basic_set_drop_inequality(context, i);
1088
1089         context = isl_basic_set_drop(context, type, pos, 1);
1090         if (!n_lower && !n_upper)
1091                 return fn(NULL, NULL, context, user);
1092         if (!n_lower)
1093                 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
1094                                                 fn, user);
1095         if (!n_upper)
1096                 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
1097                                                 fn, user);
1098         return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
1099                                         fn, user);
1100 error:
1101         isl_constraint_free(lower);
1102         isl_constraint_free(upper);
1103         isl_basic_set_free(context);
1104         return -1;
1105 }
1106
1107 __isl_give isl_aff *isl_constraint_get_bound(
1108         __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
1109 {
1110         isl_aff *aff;
1111         isl_ctx *ctx;
1112
1113         if (!constraint)
1114                 return NULL;
1115         ctx = isl_constraint_get_ctx(constraint);
1116         if (pos >= isl_constraint_dim(constraint, type))
1117                 isl_die(ctx, isl_error_invalid,
1118                         "index out of bounds", return NULL);
1119         if (isl_constraint_dim(constraint, isl_dim_in) != 0)
1120                 isl_die(ctx, isl_error_invalid,
1121                         "not a set constraint", return NULL);
1122
1123         pos += offset(constraint, type);
1124         if (isl_int_is_zero(constraint->v->el[pos]))
1125                 isl_die(ctx, isl_error_invalid,
1126                         "constraint does not define a bound on given dimension",
1127                         return NULL);
1128
1129         aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
1130         if (!aff)
1131                 return NULL;
1132
1133         if (isl_int_is_neg(constraint->v->el[pos]))
1134                 isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
1135         else
1136                 isl_seq_neg(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
1137         isl_int_set_si(aff->v->el[1 + pos], 0);
1138         isl_int_abs(aff->v->el[0], constraint->v->el[pos]);
1139
1140         return aff;
1141 }
1142
1143 /* For an inequality constraint
1144  *
1145  *      f >= 0
1146  *
1147  * or an equality constraint
1148  *
1149  *      f = 0
1150  *
1151  * return the affine expression f.
1152  */
1153 __isl_give isl_aff *isl_constraint_get_aff(
1154         __isl_keep isl_constraint *constraint)
1155 {
1156         isl_aff *aff;
1157
1158         if (!constraint)
1159                 return NULL;
1160
1161         aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
1162         if (!aff)
1163                 return NULL;
1164
1165         isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
1166         isl_int_set_si(aff->v->el[0], 1);
1167
1168         return aff;
1169 }
1170
1171 /* Construct an equality constraint equating the given affine expression
1172  * to zero.
1173  */
1174 __isl_give isl_constraint *isl_equality_from_aff(__isl_take isl_aff *aff)
1175 {
1176         int k;
1177         isl_local_space *ls;
1178         isl_basic_set *bset;
1179
1180         if (!aff)
1181                 return NULL;
1182
1183         ls = isl_aff_get_domain_local_space(aff);
1184         bset = isl_basic_set_from_local_space(ls);
1185         bset = isl_basic_set_extend_constraints(bset, 1, 0);
1186         k = isl_basic_set_alloc_equality(bset);
1187         if (k < 0)
1188                 goto error;
1189
1190         isl_seq_cpy(bset->eq[k], aff->v->el + 1, aff->v->size - 1);
1191         isl_aff_free(aff);
1192
1193         return isl_basic_set_constraint(bset, &bset->eq[k]);
1194 error:
1195         isl_aff_free(aff);
1196         isl_basic_set_free(bset);
1197         return NULL;
1198 }
1199
1200 /* Construct an inequality constraint enforcing the given affine expression
1201  * to be non-negative.
1202  */
1203 __isl_give isl_constraint *isl_inequality_from_aff(__isl_take isl_aff *aff)
1204 {
1205         int k;
1206         isl_local_space *ls;
1207         isl_basic_set *bset;
1208
1209         if (!aff)
1210                 return NULL;
1211
1212         ls = isl_aff_get_domain_local_space(aff);
1213         bset = isl_basic_set_from_local_space(ls);
1214         bset = isl_basic_set_extend_constraints(bset, 0, 1);
1215         k = isl_basic_set_alloc_inequality(bset);
1216         if (k < 0)
1217                 goto error;
1218
1219         isl_seq_cpy(bset->ineq[k], aff->v->el + 1, aff->v->size - 1);
1220         isl_aff_free(aff);
1221
1222         return isl_basic_set_constraint(bset, &bset->ineq[k]);
1223 error:
1224         isl_aff_free(aff);
1225         isl_basic_set_free(bset);
1226         return NULL;
1227 }