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 /* Replace the constant term of "constraint" by "v".
 450  */
 451 __isl_give isl_constraint *isl_constraint_set_constant_val(
 452         __isl_take isl_constraint *constraint, __isl_take isl_val *v)
 453 {
 454         constraint = isl_constraint_cow(constraint);
 455         if (!constraint || !v)
 456                 goto error;
 457         if (!isl_val_is_int(v))
 458                 isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
 459                         "expecting integer value", goto error);
 460         constraint->v = isl_vec_set_element_val(constraint->v, 0, v);
 461         if (!constraint->v)
 462                 constraint = isl_constraint_free(constraint);
 463         return constraint;
 464 error:
 465         isl_val_free(v);
 466         return isl_constraint_free(constraint);
 467 }
 468
 469 __isl_give isl_constraint *isl_constraint_set_constant_si(
 470         __isl_take isl_constraint *constraint, int v)
 471 {
 472         constraint = isl_constraint_cow(constraint);
 473         if (!constraint)
 474                 return NULL;
 475
 476         constraint->v = isl_vec_cow(constraint->v);
 477         if (!constraint->v)
 478                 return isl_constraint_free(constraint);
 479
 480         isl_int_set_si(constraint->v->el[0], v);
 481         return constraint;
 482 }
 483
 484 __isl_give isl_constraint *isl_constraint_set_coefficient(
 485         __isl_take isl_constraint *constraint,
 486         enum isl_dim_type type, int pos, isl_int v)
 487 {
 488         constraint = isl_constraint_cow(constraint);
 489         if (!constraint)
 490                 return NULL;
 491
 492         if (pos >= isl_local_space_dim(constraint->ls, type))
 493                 isl_die(constraint->v->ctx, isl_error_invalid,
 494                         "position out of bounds",
 495                         return isl_constraint_free(constraint));
 496
 497         constraint = isl_constraint_cow(constraint);
 498         if (!constraint)
 499                 return NULL;
 500
 501         constraint->v = isl_vec_cow(constraint->v);
 502         if (!constraint->v)
 503                 return isl_constraint_free(constraint);
 504
 505         pos += isl_local_space_offset(constraint->ls, type);
 506         isl_int_set(constraint->v->el[pos], v);
 507
 508         return constraint;
 509 }
 510
 511 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
 512         __isl_take isl_constraint *constraint,
 513         enum isl_dim_type type, int pos, int v)
 514 {
 515         constraint = isl_constraint_cow(constraint);
 516         if (!constraint)
 517                 return NULL;
 518
 519         if (pos >= isl_local_space_dim(constraint->ls, type))
 520                 isl_die(constraint->v->ctx, isl_error_invalid,
 521                         "position out of bounds",
 522                         return isl_constraint_free(constraint));
 523
 524         constraint = isl_constraint_cow(constraint);
 525         if (!constraint)
 526                 return NULL;
 527
 528         constraint->v = isl_vec_cow(constraint->v);
 529         if (!constraint->v)
 530                 return isl_constraint_free(constraint);
 531
 532         pos += isl_local_space_offset(constraint->ls, type);
 533         isl_int_set_si(constraint->v->el[pos], v);
 534
 535         return constraint;
 536 }
 537
 538 /* Drop any constraint from "bset" that is identical to "constraint".
 539  * In particular, this means that the local spaces of "bset" and
 540  * "constraint" need to be the same.
 541  *
 542  * Since the given constraint may actually be a pointer into the bset,
 543  * we have to be careful not to reorder the constraints as the user
 544  * may be holding on to other constraints from the same bset.
 545  * This should be cleaned up when the internal representation of
 546  * isl_constraint is changed to use isl_aff.
 547  */
 548 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
 549         __isl_take isl_basic_set *bset, __isl_take isl_constraint *constraint)
 550 {
 551         int i;
 552         unsigned n;
 553         isl_int **row;
 554         unsigned total;
 555         isl_local_space *ls1;
 556         int equal;
 557
 558         if (!bset || !constraint)
 559                 goto error;
 560
 561         ls1 = isl_basic_set_get_local_space(bset);
 562         equal = isl_local_space_is_equal(ls1, constraint->ls);
 563         isl_local_space_free(ls1);
 564         if (equal < 0)
 565                 goto error;
 566         if (!equal) {
 567                 isl_constraint_free(constraint);
 568                 return bset;
 569         }
 570
 571         if (isl_constraint_is_equality(constraint)) {
 572                 n = bset->n_eq;
 573                 row = bset->eq;
 574         } else {
 575                 n = bset->n_ineq;
 576                 row = bset->ineq;
 577         }
 578
 579         total = isl_constraint_dim(constraint, isl_dim_all);
 580         for (i = 0; i < n; ++i)
 581                 if (isl_seq_eq(row[i], constraint->v->el, 1 + total))
 582                         isl_seq_clr(row[i], 1 + total);
 583
 584         isl_constraint_free(constraint);
 585         return bset;
 586 error:
 587         isl_constraint_free(constraint);
 588         isl_basic_set_free(bset);
 589         return NULL;
 590 }
 591
 592 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
 593 {
 594         isl_ctx *ctx;
 595
 596         constraint = isl_constraint_cow(constraint);
 597         if (!constraint)
 598                 return NULL;
 599
 600         ctx = isl_constraint_get_ctx(constraint);
 601         if (isl_constraint_is_equality(constraint))
 602                 isl_die(ctx, isl_error_invalid, "cannot negate equality",
 603                         return isl_constraint_free(constraint));
 604         constraint->v = isl_vec_neg(constraint->v);
 605         constraint->v = isl_vec_cow(constraint->v);
 606         if (!constraint->v)
 607                 return isl_constraint_free(constraint);
 608         isl_int_sub_ui(constraint->v->el[0], constraint->v->el[0], 1);
 609         return constraint;
 610 }
 611
 612 int isl_constraint_is_equality(struct isl_constraint *constraint)
 613 {
 614         if (!constraint)
 615                 return -1;
 616         return constraint->eq;
 617 }
 618
 619 int isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
 620 {
 621         int i;
 622         int n_div;
 623
 624         if (!constraint)
 625                 return -1;
 626         if (isl_constraint_is_equality(constraint))
 627                 return 0;
 628         n_div = isl_constraint_dim(constraint, isl_dim_div);
 629         for (i = 0; i < n_div; ++i) {
 630                 if (isl_local_space_is_div_constraint(constraint->ls,
 631                                                         constraint->v->el, i))
 632                         return 1;
 633         }
 634
 635         return 0;
 636 }
 637
 638 /* We manually set ISL_BASIC_SET_FINAL instead of calling
 639  * isl_basic_map_finalize because we want to keep the position
 640  * of the divs and we therefore do not want to throw away redundant divs.
 641  * This is arguably a bit fragile.
 642  */
 643 __isl_give isl_basic_map *isl_basic_map_from_constraint(
 644         __isl_take isl_constraint *constraint)
 645 {
 646         int k;
 647         isl_local_space *ls;
 648         struct isl_basic_map *bmap;
 649         isl_int *c;
 650         unsigned total;
 651
 652         if (!constraint)
 653                 return NULL;
 654
 655         ls = isl_local_space_copy(constraint->ls);
 656         bmap = isl_basic_map_from_local_space(ls);
 657         bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
 658         if (isl_constraint_is_equality(constraint)) {
 659                 k = isl_basic_map_alloc_equality(bmap);
 660                 if (k < 0)
 661                         goto error;
 662                 c = bmap->eq[k];
 663         }
 664         else {
 665                 k = isl_basic_map_alloc_inequality(bmap);
 666                 if (k < 0)
 667                         goto error;
 668                 c = bmap->ineq[k];
 669         }
 670         total = isl_basic_map_total_dim(bmap);
 671         isl_seq_cpy(c, constraint->v->el, 1 + total);
 672         isl_constraint_free(constraint);
 673         if (bmap)
 674                 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
 675         return bmap;
 676 error:
 677         isl_constraint_free(constraint);
 678         isl_basic_map_free(bmap);
 679         return NULL;
 680 }
 681
 682 struct isl_basic_set *isl_basic_set_from_constraint(
 683         struct isl_constraint *constraint)
 684 {
 685         if (!constraint)
 686                 return NULL;
 687
 688         if (isl_constraint_dim(constraint, isl_dim_in) != 0)
 689                 isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
 690                         "not a set constraint",
 691                         return isl_constraint_free(constraint));
 692         return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
 693 }
 694
 695 int isl_basic_map_has_defining_equality(
 696         __isl_keep isl_basic_map *bmap, enum isl_dim_type type, int pos,
 697         __isl_give isl_constraint **c)
 698 {
 699         int i;
 700         unsigned offset;
 701         unsigned total;
 702
 703         if (!bmap)
 704                 return -1;
 705         offset = basic_map_offset(bmap, type);
 706         total = isl_basic_map_total_dim(bmap);
 707         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
 708         for (i = 0; i < bmap->n_eq; ++i)
 709                 if (!isl_int_is_zero(bmap->eq[i][offset + pos]) &&
 710                     isl_seq_first_non_zero(bmap->eq[i]+offset+pos+1,
 711                                            1+total-offset-pos-1) == -1) {
 712                         *c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 713                                                                 &bmap->eq[i]);
 714                         return 1;
 715                 }
 716         return 0;
 717 }
 718
 719 int isl_basic_set_has_defining_equality(
 720         __isl_keep isl_basic_set *bset, enum isl_dim_type type, int pos,
 721         __isl_give isl_constraint **c)
 722 {
 723         return isl_basic_map_has_defining_equality((isl_basic_map *)bset,
 724                                                     type, pos, c);
 725 }
 726
 727 int isl_basic_set_has_defining_inequalities(
 728         struct isl_basic_set *bset, enum isl_dim_type type, int pos,
 729         struct isl_constraint **lower,
 730         struct isl_constraint **upper)
 731 {
 732         int i, j;
 733         unsigned offset;
 734         unsigned total;
 735         isl_int m;
 736         isl_int **lower_line, **upper_line;
 737
 738         if (!bset)
 739                 return -1;
 740         offset = basic_set_offset(bset, type);
 741         total = isl_basic_set_total_dim(bset);
 742         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
 743         isl_int_init(m);
 744         for (i = 0; i < bset->n_ineq; ++i) {
 745                 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
 746                         continue;
 747                 if (isl_int_is_one(bset->ineq[i][offset + pos]))
 748                         continue;
 749                 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
 750                         continue;
 751                 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
 752                                                 1+total-offset-pos-1) != -1)
 753                         continue;
 754                 for (j = i + 1; j < bset->n_ineq; ++j) {
 755                         if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
 756                                             total))
 757                                 continue;
 758                         isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
 759                         if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
 760                                 continue;
 761
 762                         if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
 763                                 lower_line = &bset->ineq[i];
 764                                 upper_line = &bset->ineq[j];
 765                         } else {
 766                                 lower_line = &bset->ineq[j];
 767                                 upper_line = &bset->ineq[i];
 768                         }
 769                         *lower = isl_basic_set_constraint(
 770                                         isl_basic_set_copy(bset), lower_line);
 771                         *upper = isl_basic_set_constraint(
 772                                         isl_basic_set_copy(bset), upper_line);
 773                         isl_int_clear(m);
 774                         return 1;
 775                 }
 776         }
 777         *lower = NULL;
 778         *upper = NULL;
 779         isl_int_clear(m);
 780         return 0;
 781 }
 782
 783 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
 784  * (in "a" and "b"), add a constraint to "bset" that ensures that the
 785  * bound implied by "a" is (strictly) larger than the bound implied by "b".
 786  *
 787  * If both constraints imply lower bounds, then this means that "a" is
 788  * active in the result.
 789  * If both constraints imply upper bounds, then this means that "b" is
 790  * active in the result.
 791  */
 792 static __isl_give isl_basic_set *add_larger_bound_constraint(
 793         __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
 794         unsigned abs_pos, int strict)
 795 {
 796         int k;
 797         isl_int t;
 798         unsigned total;
 799
 800         k = isl_basic_set_alloc_inequality(bset);
 801         if (k < 0)
 802                 goto error;
 803
 804         total = isl_basic_set_dim(bset, isl_dim_all);
 805
 806         isl_int_init(t);
 807         isl_int_neg(t, b[1 + abs_pos]);
 808
 809         isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
 810         isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
 811                 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
 812                 total - abs_pos);
 813
 814         if (strict)
 815                 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
 816
 817         isl_int_clear(t);
 818
 819         return bset;
 820 error:
 821         isl_basic_set_free(bset);
 822         return NULL;
 823 }
 824
 825 /* Add constraints to "context" that ensure that "u" is the smallest
 826  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 827  * the resulting basic set.
 828  */
 829 static __isl_give isl_basic_set *set_smallest_upper_bound(
 830         __isl_keep isl_basic_set *context,
 831         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
 832 {
 833         int j;
 834
 835         context = isl_basic_set_copy(context);
 836         context = isl_basic_set_cow(context);
 837
 838         context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
 839
 840         for (j = 0; j < bset->n_ineq; ++j) {
 841                 if (j == u)
 842                         continue;
 843                 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 844                         continue;
 845                 context = add_larger_bound_constraint(context,
 846                         bset->ineq[j], bset->ineq[u], abs_pos, j > u);
 847         }
 848
 849         context = isl_basic_set_simplify(context);
 850         context = isl_basic_set_finalize(context);
 851
 852         return context;
 853 }
 854
 855 /* Add constraints to "context" that ensure that "u" is the largest
 856  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 857  * the resulting basic set.
 858  */
 859 static __isl_give isl_basic_set *set_largest_lower_bound(
 860         __isl_keep isl_basic_set *context,
 861         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
 862 {
 863         int j;
 864
 865         context = isl_basic_set_copy(context);
 866         context = isl_basic_set_cow(context);
 867
 868         context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
 869
 870         for (j = 0; j < bset->n_ineq; ++j) {
 871                 if (j == l)
 872                         continue;
 873                 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
 874                         continue;
 875                 context = add_larger_bound_constraint(context,
 876                         bset->ineq[l], bset->ineq[j], abs_pos, j > l);
 877         }
 878
 879         context = isl_basic_set_simplify(context);
 880         context = isl_basic_set_finalize(context);
 881
 882         return context;
 883 }
 884
 885 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
 886         enum isl_dim_type type, unsigned abs_pos,
 887         __isl_take isl_basic_set *context, int n_upper,
 888         int (*fn)(__isl_take isl_constraint *lower,
 889                   __isl_take isl_constraint *upper,
 890                   __isl_take isl_basic_set *bset, void *user), void *user)
 891 {
 892         isl_basic_set *context_i;
 893         isl_constraint *upper = NULL;
 894         int i;
 895
 896         for (i = 0; i < bset->n_ineq; ++i) {
 897                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 898                         continue;
 899
 900                 context_i = set_smallest_upper_bound(context, bset,
 901                                                         abs_pos, n_upper, i);
 902                 if (isl_basic_set_is_empty(context_i)) {
 903                         isl_basic_set_free(context_i);
 904                         continue;
 905                 }
 906                 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 907                                                 &bset->ineq[i]);
 908                 if (!upper || !context_i)
 909                         goto error;
 910                 if (fn(NULL, upper, context_i, user) < 0)
 911                         break;
 912         }
 913
 914         isl_basic_set_free(context);
 915
 916         if (i < bset->n_ineq)
 917                 return -1;
 918
 919         return 0;
 920 error:
 921         isl_constraint_free(upper);
 922         isl_basic_set_free(context_i);
 923         isl_basic_set_free(context);
 924         return -1;
 925 }
 926
 927 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
 928         enum isl_dim_type type, unsigned abs_pos,
 929         __isl_take isl_basic_set *context, int n_lower,
 930         int (*fn)(__isl_take isl_constraint *lower,
 931                   __isl_take isl_constraint *upper,
 932                   __isl_take isl_basic_set *bset, void *user), void *user)
 933 {
 934         isl_basic_set *context_i;
 935         isl_constraint *lower = NULL;
 936         int i;
 937
 938         for (i = 0; i < bset->n_ineq; ++i) {
 939                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 940                         continue;
 941
 942                 context_i = set_largest_lower_bound(context, bset,
 943                                                         abs_pos, n_lower, i);
 944                 if (isl_basic_set_is_empty(context_i)) {
 945                         isl_basic_set_free(context_i);
 946                         continue;
 947                 }
 948                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 949                                                 &bset->ineq[i]);
 950                 if (!lower || !context_i)
 951                         goto error;
 952                 if (fn(lower, NULL, context_i, user) < 0)
 953                         break;
 954         }
 955
 956         isl_basic_set_free(context);
 957
 958         if (i < bset->n_ineq)
 959                 return -1;
 960
 961         return 0;
 962 error:
 963         isl_constraint_free(lower);
 964         isl_basic_set_free(context_i);
 965         isl_basic_set_free(context);
 966         return -1;
 967 }
 968
 969 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
 970         enum isl_dim_type type, unsigned abs_pos,
 971         __isl_take isl_basic_set *context, int n_lower, int n_upper,
 972         int (*fn)(__isl_take isl_constraint *lower,
 973                   __isl_take isl_constraint *upper,
 974                   __isl_take isl_basic_set *bset, void *user), void *user)
 975 {
 976         isl_basic_set *context_i, *context_j;
 977         isl_constraint *lower = NULL;
 978         isl_constraint *upper = NULL;
 979         int i, j;
 980
 981         for (i = 0; i < bset->n_ineq; ++i) {
 982                 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
 983                         continue;
 984
 985                 context_i = set_largest_lower_bound(context, bset,
 986                                                         abs_pos, n_lower, i);
 987                 if (isl_basic_set_is_empty(context_i)) {
 988                         isl_basic_set_free(context_i);
 989                         continue;
 990                 }
 991
 992                 for (j = 0; j < bset->n_ineq; ++j) {
 993                         if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 994                                 continue;
 995
 996                         context_j = set_smallest_upper_bound(context_i, bset,
 997                                                             abs_pos, n_upper, j);
 998                         context_j = isl_basic_set_extend_constraints(context_j,
 999                                                                         0, 1);
1000                         context_j = add_larger_bound_constraint(context_j,
1001                                 bset->ineq[i], bset->ineq[j], abs_pos, 0);
1002                         context_j = isl_basic_set_simplify(context_j);
1003                         context_j = isl_basic_set_finalize(context_j);
1004                         if (isl_basic_set_is_empty(context_j)) {
1005                                 isl_basic_set_free(context_j);
1006                                 continue;
1007                         }
1008                         lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
1009                                                         &bset->ineq[i]);
1010                         upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
1011                                                         &bset->ineq[j]);
1012                         if (!lower || !upper || !context_j)
1013                                 goto error;
1014                         if (fn(lower, upper, context_j, user) < 0)
1015                                 break;
1016                 }
1017
1018                 isl_basic_set_free(context_i);
1019
1020                 if (j < bset->n_ineq)
1021                         break;
1022         }
1023
1024         isl_basic_set_free(context);
1025
1026         if (i < bset->n_ineq)
1027                 return -1;
1028
1029         return 0;
1030 error:
1031         isl_constraint_free(lower);
1032         isl_constraint_free(upper);
1033         isl_basic_set_free(context_i);
1034         isl_basic_set_free(context_j);
1035         isl_basic_set_free(context);
1036         return -1;
1037 }
1038
1039 /* For each pair of lower and upper bounds on the variable "pos"
1040  * of type "type", call "fn" with these lower and upper bounds and the
1041  * set of constraints on the remaining variables where these bounds
1042  * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
1043  *
1044  * If the designated variable is equal to an affine combination of the
1045  * other variables then fn is called with both lower and upper
1046  * set to the corresponding equality.
1047  *
1048  * If there is no lower (or upper) bound, then NULL is passed
1049  * as the corresponding bound.
1050  *
1051  * We first check if the variable is involved in any equality.
1052  * If not, we count the number of lower and upper bounds and
1053  * act accordingly.
1054  */
1055 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
1056         enum isl_dim_type type, unsigned pos,
1057         int (*fn)(__isl_take isl_constraint *lower,
1058                   __isl_take isl_constraint *upper,
1059                   __isl_take isl_basic_set *bset, void *user), void *user)
1060 {
1061         int i;
1062         isl_constraint *lower = NULL;
1063         isl_constraint *upper = NULL;
1064         isl_basic_set *context = NULL;
1065         unsigned abs_pos;
1066         int n_lower, n_upper;
1067
1068         if (!bset)
1069                 return -1;
1070         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
1071         isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
1072                 return -1);
1073
1074         abs_pos = pos;
1075         if (type == isl_dim_set)
1076                 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
1077
1078         for (i = 0; i < bset->n_eq; ++i) {
1079                 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
1080                         continue;
1081
1082                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
1083                                                 &bset->eq[i]);
1084                 upper = isl_constraint_copy(lower);
1085                 context = isl_basic_set_remove_dims(isl_basic_set_copy(bset),
1086                                         type, pos, 1);
1087                 if (!lower || !upper || !context)
1088                         goto error;
1089                 return fn(lower, upper, context, user);
1090         }
1091
1092         n_lower = 0;
1093         n_upper = 0;
1094         for (i = 0; i < bset->n_ineq; ++i) {
1095                 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
1096                         n_lower++;
1097                 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
1098                         n_upper++;
1099         }
1100
1101         context = isl_basic_set_copy(bset);
1102         context = isl_basic_set_cow(context);
1103         if (!context)
1104                 goto error;
1105         for (i = context->n_ineq - 1; i >= 0; --i)
1106                 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
1107                         isl_basic_set_drop_inequality(context, i);
1108
1109         context = isl_basic_set_drop(context, type, pos, 1);
1110         if (!n_lower && !n_upper)
1111                 return fn(NULL, NULL, context, user);
1112         if (!n_lower)
1113                 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
1114                                                 fn, user);
1115         if (!n_upper)
1116                 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
1117                                                 fn, user);
1118         return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
1119                                         fn, user);
1120 error:
1121         isl_constraint_free(lower);
1122         isl_constraint_free(upper);
1123         isl_basic_set_free(context);
1124         return -1;
1125 }
1126
1127 __isl_give isl_aff *isl_constraint_get_bound(
1128         __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
1129 {
1130         isl_aff *aff;
1131         isl_ctx *ctx;
1132
1133         if (!constraint)
1134                 return NULL;
1135         ctx = isl_constraint_get_ctx(constraint);
1136         if (pos >= isl_constraint_dim(constraint, type))
1137                 isl_die(ctx, isl_error_invalid,
1138                         "index out of bounds", return NULL);
1139         if (isl_constraint_dim(constraint, isl_dim_in) != 0)
1140                 isl_die(ctx, isl_error_invalid,
1141                         "not a set constraint", return NULL);
1142
1143         pos += offset(constraint, type);
1144         if (isl_int_is_zero(constraint->v->el[pos]))
1145                 isl_die(ctx, isl_error_invalid,
1146                         "constraint does not define a bound on given dimension",
1147                         return NULL);
1148
1149         aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
1150         if (!aff)
1151                 return NULL;
1152
1153         if (isl_int_is_neg(constraint->v->el[pos]))
1154                 isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
1155         else
1156                 isl_seq_neg(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
1157         isl_int_set_si(aff->v->el[1 + pos], 0);
1158         isl_int_abs(aff->v->el[0], constraint->v->el[pos]);
1159
1160         return aff;
1161 }
1162
1163 /* For an inequality constraint
1164  *
1165  *      f >= 0
1166  *
1167  * or an equality constraint
1168  *
1169  *      f = 0
1170  *
1171  * return the affine expression f.
1172  */
1173 __isl_give isl_aff *isl_constraint_get_aff(
1174         __isl_keep isl_constraint *constraint)
1175 {
1176         isl_aff *aff;
1177
1178         if (!constraint)
1179                 return NULL;
1180
1181         aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
1182         if (!aff)
1183                 return NULL;
1184
1185         isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
1186         isl_int_set_si(aff->v->el[0], 1);
1187
1188         return aff;
1189 }
1190
1191 /* Construct an equality constraint equating the given affine expression
1192  * to zero.
1193  */
1194 __isl_give isl_constraint *isl_equality_from_aff(__isl_take isl_aff *aff)
1195 {
1196         int k;
1197         isl_local_space *ls;
1198         isl_basic_set *bset;
1199
1200         if (!aff)
1201                 return NULL;
1202
1203         ls = isl_aff_get_domain_local_space(aff);
1204         bset = isl_basic_set_from_local_space(ls);
1205         bset = isl_basic_set_extend_constraints(bset, 1, 0);
1206         k = isl_basic_set_alloc_equality(bset);
1207         if (k < 0)
1208                 goto error;
1209
1210         isl_seq_cpy(bset->eq[k], aff->v->el + 1, aff->v->size - 1);
1211         isl_aff_free(aff);
1212
1213         return isl_basic_set_constraint(bset, &bset->eq[k]);
1214 error:
1215         isl_aff_free(aff);
1216         isl_basic_set_free(bset);
1217         return NULL;
1218 }
1219
1220 /* Construct an inequality constraint enforcing the given affine expression
1221  * to be non-negative.
1222  */
1223 __isl_give isl_constraint *isl_inequality_from_aff(__isl_take isl_aff *aff)
1224 {
1225         int k;
1226         isl_local_space *ls;
1227         isl_basic_set *bset;
1228
1229         if (!aff)
1230                 return NULL;
1231
1232         ls = isl_aff_get_domain_local_space(aff);
1233         bset = isl_basic_set_from_local_space(ls);
1234         bset = isl_basic_set_extend_constraints(bset, 0, 1);
1235         k = isl_basic_set_alloc_inequality(bset);
1236         if (k < 0)
1237                 goto error;
1238
1239         isl_seq_cpy(bset->ineq[k], aff->v->el + 1, aff->v->size - 1);
1240         isl_aff_free(aff);
1241
1242         return isl_basic_set_constraint(bset, &bset->ineq[k]);
1243 error:
1244         isl_aff_free(aff);
1245         isl_basic_set_free(bset);
1246         return NULL;
1247 }