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 GNU LGPLv2.1 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_dim_private.h>
  16 #include <isl_div_private.h>
  17 #include <isl/seq.h>
  18 #include <isl_aff_private.h>
  19
  20 isl_ctx *isl_constraint_get_ctx(__isl_keep isl_constraint *c)
  21 {
  22         return c ? c->ctx : NULL;
  23 }
  24
  25 static unsigned n(struct isl_constraint *c, enum isl_dim_type type)
  26 {
  27         return isl_basic_map_dim(c->bmap, type);
  28 }
  29
  30 static unsigned offset(struct isl_constraint *c, enum isl_dim_type type)
  31 {
  32         struct isl_dim *dim = c->bmap->dim;
  33         switch (type) {
  34         case isl_dim_param:     return 1;
  35         case isl_dim_in:        return 1 + dim->nparam;
  36         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  37         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
  38         default:                return 0;
  39         }
  40 }
  41
  42 static unsigned basic_map_offset(__isl_keep isl_basic_map *bmap,
  43                                                         enum isl_dim_type type)
  44 {
  45         return type == isl_dim_div ? 1 + isl_dim_total(bmap->dim)
  46                                    : 1 + isl_dim_offset(bmap->dim, type);
  47 }
  48
  49 static unsigned basic_set_offset(struct isl_basic_set *bset,
  50                                                         enum isl_dim_type type)
  51 {
  52         struct isl_dim *dim = bset->dim;
  53         switch (type) {
  54         case isl_dim_param:     return 1;
  55         case isl_dim_in:        return 1 + dim->nparam;
  56         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  57         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
  58         default:                return 0;
  59         }
  60 }
  61
  62 struct isl_constraint *isl_basic_map_constraint(struct isl_basic_map *bmap,
  63         isl_int **line)
  64 {
  65         struct isl_constraint *constraint;
  66
  67         if (!bmap || !line)
  68                 goto error;
  69
  70         constraint = isl_alloc_type(bmap->ctx, struct isl_constraint);
  71         if (!constraint)
  72                 goto error;
  73
  74         constraint->ctx = bmap->ctx;
  75         isl_ctx_ref(constraint->ctx);
  76         constraint->ref = 1;
  77         constraint->bmap = bmap;
  78         constraint->line = line;
  79
  80         return constraint;
  81 error:
  82         isl_basic_map_free(bmap);
  83         return NULL;
  84 }
  85
  86 struct isl_constraint *isl_basic_set_constraint(struct isl_basic_set *bset,
  87         isl_int **line)
  88 {
  89         return isl_basic_map_constraint((struct isl_basic_map *)bset, line);
  90 }
  91
  92 struct isl_constraint *isl_equality_alloc(struct isl_dim *dim)
  93 {
  94         struct isl_basic_map *bmap;
  95
  96         if (!dim)
  97                 return NULL;
  98
  99         bmap = isl_basic_map_alloc_dim(dim, 0, 1, 0);
 100         if (!bmap)
 101                 return NULL;
 102
 103         isl_basic_map_alloc_equality(bmap);
 104         isl_seq_clr(bmap->eq[0], 1 + isl_basic_map_total_dim(bmap));
 105         return isl_basic_map_constraint(bmap, &bmap->eq[0]);
 106 }
 107
 108 struct isl_constraint *isl_inequality_alloc(struct isl_dim *dim)
 109 {
 110         struct isl_basic_map *bmap;
 111
 112         if (!dim)
 113                 return NULL;
 114
 115         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 1);
 116         if (!bmap)
 117                 return NULL;
 118
 119         isl_basic_map_alloc_inequality(bmap);
 120         isl_seq_clr(bmap->ineq[0], 1 + isl_basic_map_total_dim(bmap));
 121         return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
 122 }
 123
 124 struct isl_constraint *isl_constraint_dup(struct isl_constraint *c)
 125 {
 126         struct isl_basic_map *bmap;
 127         int i;
 128         int eq;
 129
 130         if (!c)
 131                 return NULL;
 132
 133         eq = c->line < c->bmap->eq + c->bmap->n_eq;
 134         i = eq ? c->line - c->bmap->eq : c->line - c->bmap->ineq;
 135         bmap = isl_basic_map_copy(c->bmap);
 136         if (!bmap)
 137                 return NULL;
 138         return isl_basic_map_constraint(bmap, eq ? bmap->eq + i : bmap->ineq + i);
 139 }
 140
 141 struct isl_constraint *isl_constraint_cow(struct isl_constraint *c)
 142 {
 143         if (!c)
 144                 return NULL;
 145
 146         if (c->ref == 1)
 147                 return c;
 148         c->ref--;
 149         return isl_constraint_dup(c);
 150 }
 151
 152 struct isl_constraint *isl_constraint_copy(struct isl_constraint *constraint)
 153 {
 154         if (!constraint)
 155                 return NULL;
 156
 157         constraint->ref++;
 158         return constraint;
 159 }
 160
 161 void isl_constraint_free(struct isl_constraint *c)
 162 {
 163         if (!c)
 164                 return;
 165
 166         if (--c->ref > 0)
 167                 return;
 168
 169         isl_basic_map_free(c->bmap);
 170         isl_ctx_deref(c->ctx);
 171         free(c);
 172 }
 173
 174 int isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
 175         int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
 176 {
 177         int i;
 178         struct isl_constraint *c;
 179
 180         if (!bmap)
 181                 return -1;
 182
 183         isl_assert(bmap->ctx, ISL_F_ISSET(bmap, ISL_BASIC_MAP_FINAL),
 184                         return -1);
 185
 186         for (i = 0; i < bmap->n_eq; ++i) {
 187                 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 188                                                 &bmap->eq[i]);
 189                 if (!c)
 190                         return -1;
 191                 if (fn(c, user) < 0)
 192                         return -1;
 193         }
 194
 195         for (i = 0; i < bmap->n_ineq; ++i) {
 196                 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 197                                                 &bmap->ineq[i]);
 198                 if (!c)
 199                         return -1;
 200                 if (fn(c, user) < 0)
 201                         return -1;
 202         }
 203
 204         return 0;
 205 }
 206
 207 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
 208         int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
 209 {
 210         return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
 211 }
 212
 213 int isl_constraint_is_equal(struct isl_constraint *constraint1,
 214         struct isl_constraint *constraint2)
 215 {
 216         if (!constraint1 || !constraint2)
 217                 return 0;
 218         return constraint1->bmap == constraint2->bmap &&
 219                constraint1->line == constraint2->line;
 220 }
 221
 222 struct isl_basic_map *isl_basic_map_add_constraint(
 223         struct isl_basic_map *bmap, struct isl_constraint *constraint)
 224 {
 225         if (!bmap || !constraint)
 226                 goto error;
 227
 228         isl_assert(constraint->ctx,
 229                 isl_dim_equal(bmap->dim, constraint->bmap->dim), goto error);
 230
 231         bmap = isl_basic_map_intersect(bmap,
 232                                 isl_basic_map_from_constraint(constraint));
 233         return bmap;
 234 error:
 235         isl_basic_map_free(bmap);
 236         isl_constraint_free(constraint);
 237         return NULL;
 238 }
 239
 240 struct isl_basic_set *isl_basic_set_add_constraint(
 241         struct isl_basic_set *bset, struct isl_constraint *constraint)
 242 {
 243         return (struct isl_basic_set *)
 244                 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
 245                                                 constraint);
 246 }
 247
 248 __isl_give isl_map *isl_map_add_constraint(__isl_take isl_map *map,
 249         __isl_take isl_constraint *constraint)
 250 {
 251         isl_basic_map *bmap;
 252
 253         bmap = isl_basic_map_from_constraint(constraint);
 254         map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
 255
 256         return map;
 257 }
 258
 259 __isl_give isl_set *isl_set_add_constraint(__isl_take isl_set *set,
 260         __isl_take isl_constraint *constraint)
 261 {
 262         return isl_map_add_constraint(set, constraint);
 263 }
 264
 265 struct isl_constraint *isl_constraint_add_div(struct isl_constraint *constraint,
 266         struct isl_div *div, int *pos)
 267 {
 268         if (!constraint || !div)
 269                 goto error;
 270
 271         isl_assert(constraint->ctx,
 272             isl_dim_equal(div->bmap->dim, constraint->bmap->dim), goto error);
 273         isl_assert(constraint->ctx,
 274             constraint->bmap->n_eq + constraint->bmap->n_ineq == 1, goto error);
 275
 276         constraint->bmap = isl_basic_map_cow(constraint->bmap);
 277         constraint->bmap = isl_basic_map_extend_dim(constraint->bmap,
 278                                 isl_dim_copy(constraint->bmap->dim), 1, 0, 0);
 279         if (!constraint->bmap)
 280                 goto error;
 281         constraint->line = &constraint->bmap->ineq[0];
 282         *pos = isl_basic_map_alloc_div(constraint->bmap);
 283         if (*pos < 0)
 284                 goto error;
 285         isl_seq_cpy(constraint->bmap->div[*pos], div->line[0],
 286                         1 + 1 + isl_basic_map_total_dim(constraint->bmap));
 287         isl_div_free(div);
 288         return constraint;
 289 error:
 290         isl_constraint_free(constraint);
 291         isl_div_free(div);
 292         return NULL;
 293 }
 294
 295 __isl_give isl_dim *isl_constraint_get_dim(
 296         __isl_keep isl_constraint *constraint)
 297 {
 298         return constraint ? isl_basic_map_get_dim(constraint->bmap) : NULL;
 299 }
 300
 301 int isl_constraint_dim(struct isl_constraint *constraint,
 302         enum isl_dim_type type)
 303 {
 304         if (!constraint)
 305                 return -1;
 306         return n(constraint, type);
 307 }
 308
 309 int isl_constraint_involves_dims(__isl_keep isl_constraint *constraint,
 310         enum isl_dim_type type, unsigned first, unsigned n)
 311 {
 312         if (!constraint)
 313                 return -1;
 314
 315         if (first + n > isl_basic_set_dim(constraint->bmap, type))
 316                 isl_die(constraint->ctx, isl_error_invalid,
 317                         "index out of bounds", return -1);
 318
 319         first += isl_basic_map_offset(constraint->bmap, type);
 320
 321         if (isl_seq_first_non_zero(constraint->line[0] + first, n) >= 0)
 322                 return 1;
 323
 324         return 0;
 325 }
 326
 327 const char *isl_constraint_get_dim_name(__isl_keep isl_constraint *constraint,
 328         enum isl_dim_type type, unsigned pos)
 329 {
 330         return constraint ?
 331             isl_basic_map_get_dim_name(constraint->bmap, type, pos) : NULL;
 332 }
 333
 334 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
 335 {
 336         if (!constraint)
 337                 return;
 338         isl_int_set(*v, constraint->line[0][0]);
 339 }
 340
 341 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
 342         enum isl_dim_type type, int pos, isl_int *v)
 343 {
 344         if (!constraint)
 345                 return;
 346
 347         isl_assert(constraint->ctx, pos < n(constraint, type), return);
 348         isl_int_set(*v, constraint->line[0][offset(constraint, type) + pos]);
 349 }
 350
 351 struct isl_div *isl_constraint_div(struct isl_constraint *constraint, int pos)
 352 {
 353         if (!constraint)
 354                 return NULL;
 355
 356         isl_assert(constraint->ctx, pos < n(constraint, isl_dim_div),
 357                         return NULL);
 358         isl_assert(constraint->ctx,
 359                 !isl_int_is_zero(constraint->bmap->div[pos][0]), return NULL);
 360         return isl_basic_map_div(isl_basic_map_copy(constraint->bmap), pos);
 361 }
 362
 363 void isl_constraint_set_constant(struct isl_constraint *constraint, isl_int v)
 364 {
 365         if (!constraint)
 366                 return;
 367         isl_int_set(constraint->line[0][0], v);
 368 }
 369
 370 void isl_constraint_set_constant_si(__isl_keep isl_constraint *constraint,
 371         int v)
 372 {
 373         if (!constraint)
 374                 return;
 375         isl_int_set_si(constraint->line[0][0], v);
 376 }
 377
 378 void isl_constraint_set_coefficient(struct isl_constraint *constraint,
 379         enum isl_dim_type type, int pos, isl_int v)
 380 {
 381         if (!constraint)
 382                 return;
 383
 384         isl_assert(constraint->ctx, pos < n(constraint, type), return);
 385         isl_int_set(constraint->line[0][offset(constraint, type) + pos], v);
 386 }
 387
 388 void isl_constraint_set_coefficient_si(__isl_keep isl_constraint *constraint,
 389         enum isl_dim_type type, int pos, int v)
 390 {
 391         if (!constraint)
 392                 return;
 393
 394         isl_assert(constraint->ctx, pos < n(constraint, type), return);
 395         isl_int_set_si(constraint->line[0][offset(constraint, type) + pos], v);
 396 }
 397
 398
 399 /* Check whether the two basic maps have identical divs in the same order.
 400  */
 401 static int equal_divs(__isl_keep isl_basic_map *bmap1,
 402         __isl_keep isl_basic_map *bmap2)
 403 {
 404         int i;
 405         unsigned total;
 406
 407         if (!isl_basic_map_divs_known(bmap1))
 408                 return 0;
 409         if (!isl_basic_map_divs_known(bmap2))
 410                 return 0;
 411         if (bmap1->n_div != bmap2->n_div)
 412                 return 0;
 413
 414         total = isl_basic_map_total_dim(bmap1);
 415         for (i = 0; i < bmap1->n_div; ++i)
 416                 if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
 417                         return 0;
 418
 419         return 1;
 420 }
 421
 422 /* Drop any constraint from "bset" that is identical to "constraint".
 423  * In particular, this means that the local spaces of "bset" and
 424  * "constraint" need to be the same.
 425  *
 426  * Since the given constraint may actually be a pointer into the bset,
 427  * we have to be careful not to reorder the constraints as the user
 428  * may be holding on to other constraints from the same bset.
 429  * This should be cleaned up when the internal representation of
 430  * isl_constraint is changed to use isl_aff.
 431  */
 432 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
 433         __isl_take isl_basic_set *bset, __isl_take isl_constraint *constraint)
 434 {
 435         int i;
 436         unsigned n;
 437         isl_int **row;
 438         unsigned total;
 439
 440         if (!bset || !constraint)
 441                 goto error;
 442
 443         if (!isl_dim_equal(bset->dim, constraint->bmap->dim))
 444                 isl_die(bset->ctx, isl_error_invalid,
 445                         "spaces don't match", goto error);
 446
 447         if (bset != constraint->bmap && !equal_divs(bset, constraint->bmap)) {
 448                 isl_constraint_free(constraint);
 449                 return bset;
 450         }
 451
 452         if (isl_constraint_is_equality(constraint)) {
 453                 n = bset->n_eq;
 454                 row = bset->eq;
 455         } else {
 456                 n = bset->n_ineq;
 457                 row = bset->ineq;
 458         }
 459
 460         total = isl_basic_map_total_dim(constraint->bmap);
 461         for (i = 0; i < n; ++i)
 462                 if (isl_seq_eq(row[i], constraint->line[0], 1 + total))
 463                         isl_seq_clr(row[i], 1 + total);
 464
 465         isl_constraint_free(constraint);
 466         return bset;
 467 error:
 468         isl_constraint_free(constraint);
 469         isl_basic_set_free(bset);
 470         return NULL;
 471 }
 472
 473 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
 474 {
 475         unsigned total;
 476
 477         if (!constraint)
 478                 return NULL;
 479
 480         isl_assert(constraint->ctx, !isl_constraint_is_equality(constraint),
 481                         goto error);
 482         isl_assert(constraint->ctx, constraint->bmap->ref == 1, goto error);
 483         total = isl_basic_map_total_dim(constraint->bmap);
 484         isl_seq_neg(constraint->line[0], constraint->line[0], 1 + total);
 485         isl_int_sub_ui(constraint->line[0][0], constraint->line[0][0], 1);
 486         ISL_F_CLR(constraint->bmap, ISL_BASIC_MAP_NORMALIZED);
 487         return constraint;
 488 error:
 489         isl_constraint_free(constraint);
 490         return NULL;
 491 }
 492
 493 int isl_constraint_is_equality(struct isl_constraint *constraint)
 494 {
 495         if (!constraint)
 496                 return -1;
 497         return constraint->line >= constraint->bmap->eq;
 498 }
 499
 500 int isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
 501 {
 502         int i;
 503
 504         if (!constraint)
 505                 return -1;
 506         if (isl_constraint_is_equality(constraint))
 507                 return 0;
 508         for (i = 0; i < constraint->bmap->n_div; ++i) {
 509                 if (isl_int_is_zero(constraint->bmap->div[i][0]))
 510                         continue;
 511                 if (isl_basic_map_is_div_constraint(constraint->bmap,
 512                                         constraint->line[0], i))
 513                         return 1;
 514         }
 515
 516         return 0;
 517 }
 518
 519 /* We manually set ISL_BASIC_SET_FINAL instead of calling
 520  * isl_basic_map_finalize because we want to keep the position
 521  * of the divs and we therefore do not want to throw away redundant divs.
 522  * This is arguably a bit fragile.
 523  */
 524 __isl_give isl_basic_map *isl_basic_map_from_constraint(
 525         __isl_take isl_constraint *constraint)
 526 {
 527         int k;
 528         struct isl_basic_map *bmap;
 529         isl_int *c;
 530         unsigned total;
 531
 532         if (!constraint)
 533                 return NULL;
 534
 535         if (constraint->bmap->n_eq == 1 && constraint->bmap->n_ineq == 0) {
 536                 bmap = isl_basic_map_copy(constraint->bmap);
 537                 isl_constraint_free(constraint);
 538                 return bmap;
 539         }
 540
 541         bmap = isl_basic_map_universe_like(constraint->bmap);
 542         bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
 543         bmap = isl_basic_map_cow(bmap);
 544         bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
 545         if (isl_constraint_is_equality(constraint)) {
 546                 k = isl_basic_map_alloc_equality(bmap);
 547                 if (k < 0)
 548                         goto error;
 549                 c = bmap->eq[k];
 550         }
 551         else {
 552                 k = isl_basic_map_alloc_inequality(bmap);
 553                 if (k < 0)
 554                         goto error;
 555                 c = bmap->ineq[k];
 556         }
 557         total = isl_basic_map_total_dim(bmap);
 558         isl_seq_cpy(c, constraint->line[0], 1 + total);
 559         isl_constraint_free(constraint);
 560         if (bmap)
 561                 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
 562         return bmap;
 563 error:
 564         isl_constraint_free(constraint);
 565         isl_basic_map_free(bmap);
 566         return NULL;
 567 }
 568
 569 struct isl_basic_set *isl_basic_set_from_constraint(
 570         struct isl_constraint *constraint)
 571 {
 572         if (!constraint)
 573                 return NULL;
 574
 575         isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
 576         return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
 577 error:
 578         isl_constraint_free(constraint);
 579         return NULL;
 580 }
 581
 582 int isl_basic_map_has_defining_equality(
 583         __isl_keep isl_basic_map *bmap, enum isl_dim_type type, int pos,
 584         __isl_give isl_constraint **c)
 585 {
 586         int i;
 587         unsigned offset;
 588         unsigned total;
 589
 590         if (!bmap)
 591                 return -1;
 592         offset = basic_map_offset(bmap, type);
 593         total = isl_basic_map_total_dim(bmap);
 594         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
 595         for (i = 0; i < bmap->n_eq; ++i)
 596                 if (!isl_int_is_zero(bmap->eq[i][offset + pos]) &&
 597                     isl_seq_first_non_zero(bmap->eq[i]+offset+pos+1,
 598                                            1+total-offset-pos-1) == -1) {
 599                         *c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
 600                                                                 &bmap->eq[i]);
 601                         return 1;
 602                 }
 603         return 0;
 604 }
 605
 606 int isl_basic_set_has_defining_equality(
 607         __isl_keep isl_basic_set *bset, enum isl_dim_type type, int pos,
 608         __isl_give isl_constraint **c)
 609 {
 610         return isl_basic_map_has_defining_equality((isl_basic_map *)bset,
 611                                                     type, pos, c);
 612 }
 613
 614 int isl_basic_set_has_defining_inequalities(
 615         struct isl_basic_set *bset, enum isl_dim_type type, int pos,
 616         struct isl_constraint **lower,
 617         struct isl_constraint **upper)
 618 {
 619         int i, j;
 620         unsigned offset;
 621         unsigned total;
 622         isl_int m;
 623         isl_int **lower_line, **upper_line;
 624
 625         if (!bset)
 626                 return -1;
 627         offset = basic_set_offset(bset, type);
 628         total = isl_basic_set_total_dim(bset);
 629         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
 630         isl_int_init(m);
 631         for (i = 0; i < bset->n_ineq; ++i) {
 632                 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
 633                         continue;
 634                 if (isl_int_is_one(bset->ineq[i][offset + pos]))
 635                         continue;
 636                 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
 637                         continue;
 638                 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
 639                                                 1+total-offset-pos-1) != -1)
 640                         continue;
 641                 for (j = i + 1; j < bset->n_ineq; ++j) {
 642                         if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
 643                                             total))
 644                                 continue;
 645                         isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
 646                         if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
 647                                 continue;
 648
 649                         if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
 650                                 lower_line = &bset->ineq[i];
 651                                 upper_line = &bset->ineq[j];
 652                         } else {
 653                                 lower_line = &bset->ineq[j];
 654                                 upper_line = &bset->ineq[i];
 655                         }
 656                         *lower = isl_basic_set_constraint(
 657                                         isl_basic_set_copy(bset), lower_line);
 658                         *upper = isl_basic_set_constraint(
 659                                         isl_basic_set_copy(bset), upper_line);
 660                         isl_int_clear(m);
 661                         return 1;
 662                 }
 663         }
 664         *lower = NULL;
 665         *upper = NULL;
 666         isl_int_clear(m);
 667         return 0;
 668 }
 669
 670 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
 671  * (in "a" and "b"), add a constraint to "bset" that ensures that the
 672  * bound implied by "a" is (strictly) larger than the bound implied by "b".
 673  *
 674  * If both constraints imply lower bounds, then this means that "a" is
 675  * active in the result.
 676  * If both constraints imply upper bounds, then this means that "b" is
 677  * active in the result.
 678  */
 679 static __isl_give isl_basic_set *add_larger_bound_constraint(
 680         __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
 681         unsigned abs_pos, int strict)
 682 {
 683         int k;
 684         isl_int t;
 685         unsigned total;
 686
 687         k = isl_basic_set_alloc_inequality(bset);
 688         if (k < 0)
 689                 goto error;
 690
 691         total = isl_basic_set_dim(bset, isl_dim_all);
 692
 693         isl_int_init(t);
 694         isl_int_neg(t, b[1 + abs_pos]);
 695
 696         isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
 697         isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
 698                 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
 699                 total - abs_pos);
 700
 701         if (strict)
 702                 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
 703
 704         isl_int_clear(t);
 705
 706         return bset;
 707 error:
 708         isl_basic_set_free(bset);
 709         return NULL;
 710 }
 711
 712 /* Add constraints to "context" that ensure that "u" is the smallest
 713  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 714  * the resulting basic set.
 715  */
 716 static __isl_give isl_basic_set *set_smallest_upper_bound(
 717         __isl_keep isl_basic_set *context,
 718         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
 719 {
 720         int j;
 721
 722         context = isl_basic_set_copy(context);
 723         context = isl_basic_set_cow(context);
 724
 725         context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
 726
 727         for (j = 0; j < bset->n_ineq; ++j) {
 728                 if (j == u)
 729                         continue;
 730                 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 731                         continue;
 732                 context = add_larger_bound_constraint(context,
 733                         bset->ineq[j], bset->ineq[u], abs_pos, j > u);
 734         }
 735
 736         context = isl_basic_set_simplify(context);
 737         context = isl_basic_set_finalize(context);
 738
 739         return context;
 740 }
 741
 742 /* Add constraints to "context" that ensure that "u" is the largest
 743  * (and therefore active) upper bound on "abs_pos" in "bset" and return
 744  * the resulting basic set.
 745  */
 746 static __isl_give isl_basic_set *set_largest_lower_bound(
 747         __isl_keep isl_basic_set *context,
 748         __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
 749 {
 750         int j;
 751
 752         context = isl_basic_set_copy(context);
 753         context = isl_basic_set_cow(context);
 754
 755         context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
 756
 757         for (j = 0; j < bset->n_ineq; ++j) {
 758                 if (j == l)
 759                         continue;
 760                 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
 761                         continue;
 762                 context = add_larger_bound_constraint(context,
 763                         bset->ineq[l], bset->ineq[j], abs_pos, j > l);
 764         }
 765
 766         context = isl_basic_set_simplify(context);
 767         context = isl_basic_set_finalize(context);
 768
 769         return context;
 770 }
 771
 772 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
 773         enum isl_dim_type type, unsigned abs_pos,
 774         __isl_take isl_basic_set *context, int n_upper,
 775         int (*fn)(__isl_take isl_constraint *lower,
 776                   __isl_take isl_constraint *upper,
 777                   __isl_take isl_basic_set *bset, void *user), void *user)
 778 {
 779         isl_basic_set *context_i;
 780         isl_constraint *upper = NULL;
 781         int i;
 782
 783         for (i = 0; i < bset->n_ineq; ++i) {
 784                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 785                         continue;
 786
 787                 context_i = set_smallest_upper_bound(context, bset,
 788                                                         abs_pos, n_upper, i);
 789                 if (isl_basic_set_is_empty(context_i)) {
 790                         isl_basic_set_free(context_i);
 791                         continue;
 792                 }
 793                 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 794                                                 &bset->ineq[i]);
 795                 if (!upper || !context_i)
 796                         goto error;
 797                 if (fn(NULL, upper, context_i, user) < 0)
 798                         break;
 799         }
 800
 801         isl_basic_set_free(context);
 802
 803         if (i < bset->n_ineq)
 804                 return -1;
 805
 806         return 0;
 807 error:
 808         isl_constraint_free(upper);
 809         isl_basic_set_free(context_i);
 810         isl_basic_set_free(context);
 811         return -1;
 812 }
 813
 814 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
 815         enum isl_dim_type type, unsigned abs_pos,
 816         __isl_take isl_basic_set *context, int n_lower,
 817         int (*fn)(__isl_take isl_constraint *lower,
 818                   __isl_take isl_constraint *upper,
 819                   __isl_take isl_basic_set *bset, void *user), void *user)
 820 {
 821         isl_basic_set *context_i;
 822         isl_constraint *lower = NULL;
 823         int i;
 824
 825         for (i = 0; i < bset->n_ineq; ++i) {
 826                 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
 827                         continue;
 828
 829                 context_i = set_largest_lower_bound(context, bset,
 830                                                         abs_pos, n_lower, i);
 831                 if (isl_basic_set_is_empty(context_i)) {
 832                         isl_basic_set_free(context_i);
 833                         continue;
 834                 }
 835                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 836                                                 &bset->ineq[i]);
 837                 if (!lower || !context_i)
 838                         goto error;
 839                 if (fn(lower, NULL, context_i, user) < 0)
 840                         break;
 841         }
 842
 843         isl_basic_set_free(context);
 844
 845         if (i < bset->n_ineq)
 846                 return -1;
 847
 848         return 0;
 849 error:
 850         isl_constraint_free(lower);
 851         isl_basic_set_free(context_i);
 852         isl_basic_set_free(context);
 853         return -1;
 854 }
 855
 856 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
 857         enum isl_dim_type type, unsigned abs_pos,
 858         __isl_take isl_basic_set *context, int n_lower, int n_upper,
 859         int (*fn)(__isl_take isl_constraint *lower,
 860                   __isl_take isl_constraint *upper,
 861                   __isl_take isl_basic_set *bset, void *user), void *user)
 862 {
 863         isl_basic_set *context_i, *context_j;
 864         isl_constraint *lower = NULL;
 865         isl_constraint *upper = NULL;
 866         int i, j;
 867
 868         for (i = 0; i < bset->n_ineq; ++i) {
 869                 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
 870                         continue;
 871
 872                 context_i = set_largest_lower_bound(context, bset,
 873                                                         abs_pos, n_lower, i);
 874                 if (isl_basic_set_is_empty(context_i)) {
 875                         isl_basic_set_free(context_i);
 876                         continue;
 877                 }
 878
 879                 for (j = 0; j < bset->n_ineq; ++j) {
 880                         if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
 881                                 continue;
 882
 883                         context_j = set_smallest_upper_bound(context_i, bset,
 884                                                             abs_pos, n_upper, j);
 885                         context_j = isl_basic_set_extend_constraints(context_j,
 886                                                                         0, 1);
 887                         context_j = add_larger_bound_constraint(context_j,
 888                                 bset->ineq[i], bset->ineq[j], abs_pos, 0);
 889                         context_j = isl_basic_set_simplify(context_j);
 890                         context_j = isl_basic_set_finalize(context_j);
 891                         if (isl_basic_set_is_empty(context_j)) {
 892                                 isl_basic_set_free(context_j);
 893                                 continue;
 894                         }
 895                         lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 896                                                         &bset->ineq[i]);
 897                         upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
 898                                                         &bset->ineq[j]);
 899                         if (!lower || !upper || !context_j)
 900                                 goto error;
 901                         if (fn(lower, upper, context_j, user) < 0)
 902                                 break;
 903                 }
 904
 905                 isl_basic_set_free(context_i);
 906
 907                 if (j < bset->n_ineq)
 908                         break;
 909         }
 910
 911         isl_basic_set_free(context);
 912
 913         if (i < bset->n_ineq)
 914                 return -1;
 915
 916         return 0;
 917 error:
 918         isl_constraint_free(lower);
 919         isl_constraint_free(upper);
 920         isl_basic_set_free(context_i);
 921         isl_basic_set_free(context_j);
 922         isl_basic_set_free(context);
 923         return -1;
 924 }
 925
 926 /* For each pair of lower and upper bounds on the variable "pos"
 927  * of type "type", call "fn" with these lower and upper bounds and the
 928  * set of constraints on the remaining variables where these bounds
 929  * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
 930  *
 931  * If the designated variable is equal to an affine combination of the
 932  * other variables then fn is called with both lower and upper
 933  * set to the corresponding equality.
 934  *
 935  * If there is no lower (or upper) bound, then NULL is passed
 936  * as the corresponding bound.
 937  *
 938  * We first check if the variable is involved in any equality.
 939  * If not, we count the number of lower and upper bounds and
 940  * act accordingly.
 941  */
 942 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
 943         enum isl_dim_type type, unsigned pos,
 944         int (*fn)(__isl_take isl_constraint *lower,
 945                   __isl_take isl_constraint *upper,
 946                   __isl_take isl_basic_set *bset, void *user), void *user)
 947 {
 948         int i;
 949         isl_constraint *lower = NULL;
 950         isl_constraint *upper = NULL;
 951         isl_basic_set *context = NULL;
 952         unsigned abs_pos;
 953         int n_lower, n_upper;
 954
 955         if (!bset)
 956                 return -1;
 957         isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
 958         isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
 959                 return -1);
 960
 961         abs_pos = pos;
 962         if (type == isl_dim_set)
 963                 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
 964
 965         for (i = 0; i < bset->n_eq; ++i) {
 966                 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
 967                         continue;
 968
 969                 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
 970                                                 &bset->eq[i]);
 971                 upper = isl_constraint_copy(lower);
 972                 context = isl_basic_set_remove_dims(isl_basic_set_copy(bset),
 973                                         type, pos, 1);
 974                 if (!lower || !upper || !context)
 975                         goto error;
 976                 return fn(lower, upper, context, user);
 977         }
 978
 979         n_lower = 0;
 980         n_upper = 0;
 981         for (i = 0; i < bset->n_ineq; ++i) {
 982                 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
 983                         n_lower++;
 984                 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
 985                         n_upper++;
 986         }
 987
 988         context = isl_basic_set_copy(bset);
 989         context = isl_basic_set_cow(context);
 990         if (!context)
 991                 goto error;
 992         for (i = context->n_ineq - 1; i >= 0; --i)
 993                 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
 994                         isl_basic_set_drop_inequality(context, i);
 995
 996         context = isl_basic_set_drop(context, type, pos, 1);
 997         if (!n_lower && !n_upper)
 998                 return fn(NULL, NULL, context, user);
 999         if (!n_lower)
1000                 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
1001                                                 fn, user);
1002         if (!n_upper)
1003                 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
1004                                                 fn, user);
1005         return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
1006                                         fn, user);
1007 error:
1008         isl_constraint_free(lower);
1009         isl_constraint_free(upper);
1010         isl_basic_set_free(context);
1011         return -1;
1012 }
1013
1014 __isl_give isl_aff *isl_constraint_get_bound(
1015         __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
1016 {
1017         isl_aff *aff;
1018         isl_local_space *ls;
1019
1020         if (!constraint)
1021                 return NULL;
1022         if (pos >= isl_basic_set_dim(constraint->bmap, type))
1023                 isl_die(constraint->ctx, isl_error_invalid,
1024                         "index out of bounds", return NULL);
1025         if (!isl_basic_map_may_be_set(constraint->bmap))
1026                 isl_die(constraint->ctx, isl_error_invalid,
1027                         "not a set constraint", return NULL);
1028
1029         pos += offset(constraint, type);
1030         if (isl_int_is_zero(constraint->line[0][pos]))
1031                 isl_die(constraint->ctx, isl_error_invalid,
1032                         "constraint does not define a bound on given dimension",
1033                         return NULL);
1034
1035         ls = isl_basic_set_get_local_space(constraint->bmap);
1036         aff = isl_aff_alloc(ls);
1037         if (!aff)
1038                 return NULL;
1039
1040         if (isl_int_is_neg(constraint->line[0][pos]))
1041                 isl_seq_cpy(aff->v->el + 1, constraint->line[0],
1042                             aff->v->size - 1);
1043         else
1044                 isl_seq_neg(aff->v->el + 1, constraint->line[0],
1045                             aff->v->size - 1);
1046         isl_int_set_si(aff->v->el[1 + pos], 0);
1047         isl_int_abs(aff->v->el[0], constraint->line[0][pos]);
1048
1049         return aff;
1050 }
1051
1052 /* For an inequality constraint
1053  *
1054  *      f >= 0
1055  *
1056  * or an equality constraint
1057  *
1058  *      f = 0
1059  *
1060  * return the affine expression f.
1061  */
1062 __isl_give isl_aff *isl_constraint_get_aff(
1063         __isl_keep isl_constraint *constraint)
1064 {
1065         isl_aff *aff;
1066         isl_local_space *ls;
1067
1068         if (!constraint)
1069                 return NULL;
1070
1071         ls = isl_basic_set_get_local_space(constraint->bmap);
1072         aff = isl_aff_alloc(ls);
1073         if (!aff)
1074                 return NULL;
1075
1076         isl_seq_cpy(aff->v->el + 1, constraint->line[0], aff->v->size - 1);
1077         isl_int_set_si(aff->v->el[0], 1);
1078
1079         return aff;
1080 }
1081
1082 /* Construct an equality constraint equating the given affine expression
1083  * to zero.
1084  */
1085 __isl_give isl_constraint *isl_equality_from_aff(__isl_take isl_aff *aff)
1086 {
1087         int k;
1088         isl_basic_set *bset;
1089
1090         if (!aff)
1091                 return NULL;
1092
1093         bset = isl_basic_set_from_local_space(isl_aff_get_local_space(aff));
1094         bset = isl_basic_set_extend_constraints(bset, 1, 0);
1095         k = isl_basic_set_alloc_equality(bset);
1096         if (k < 0)
1097                 goto error;
1098
1099         isl_seq_cpy(bset->eq[k], aff->v->el + 1, aff->v->size - 1);
1100         isl_aff_free(aff);
1101
1102         return isl_basic_set_constraint(bset, &bset->eq[k]);
1103 error:
1104         isl_aff_free(aff);
1105         isl_basic_set_free(bset);
1106         return NULL;
1107 }
1108
1109 /* Construct an inequality constraint enforcing the given affine expression
1110  * to be non-negative.
1111  */
1112 __isl_give isl_constraint *isl_inequality_from_aff(__isl_take isl_aff *aff)
1113 {
1114         int k;
1115         isl_basic_set *bset;
1116
1117         if (!aff)
1118                 return NULL;
1119
1120         bset = isl_basic_set_from_local_space(isl_aff_get_local_space(aff));
1121         bset = isl_basic_set_extend_constraints(bset, 0, 1);
1122         k = isl_basic_set_alloc_inequality(bset);
1123         if (k < 0)
1124                 goto error;
1125
1126         isl_seq_cpy(bset->ineq[k], aff->v->el + 1, aff->v->size - 1);
1127         isl_aff_free(aff);
1128
1129         return isl_basic_set_constraint(bset, &bset->ineq[k]);
1130 error:
1131         isl_aff_free(aff);
1132         isl_basic_set_free(bset);
1133         return NULL;
1134 }