isl_map_simplify.c

   1 #include "isl_equalities.h"
   2 #include "isl_map.h"
   3 #include "isl_map_private.h"
   4 #include "isl_seq.h"
   5 #include "isl_tab.h"
   6
   7 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
   8 {
   9         isl_int *t = bmap->eq[a];
  10         bmap->eq[a] = bmap->eq[b];
  11         bmap->eq[b] = t;
  12 }
  13
  14 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  15 {
  16         if (a != b) {
  17                 isl_int *t = bmap->ineq[a];
  18                 bmap->ineq[a] = bmap->ineq[b];
  19                 bmap->ineq[b] = t;
  20         }
  21 }
  22
  23 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
  24 {
  25         swap_inequality((struct isl_basic_map *)bset, a, b);
  26 }
  27
  28 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  29 {
  30         isl_seq_cpy(c, c + n, rem);
  31         isl_seq_clr(c + rem, n);
  32 }
  33
  34 /* Drop n dimensions starting at first.
  35  *
  36  * In principle, this frees up some extra variables as the number
  37  * of columns remains constant, but we would have to extend
  38  * the div array too as the number of rows in this array is assumed
  39  * to be equal to extra.
  40  */
  41 struct isl_basic_set *isl_basic_set_drop_dims(
  42                 struct isl_basic_set *bset, unsigned first, unsigned n)
  43 {
  44         int i;
  45
  46         if (!bset)
  47                 goto error;
  48
  49         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  50
  51         if (n == 0)
  52                 return bset;
  53
  54         bset = isl_basic_set_cow(bset);
  55         if (!bset)
  56                 return NULL;
  57
  58         for (i = 0; i < bset->n_eq; ++i)
  59                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  60                                      (bset->dim->n_out-first-n)+bset->extra);
  61
  62         for (i = 0; i < bset->n_ineq; ++i)
  63                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  64                                      (bset->dim->n_out-first-n)+bset->extra);
  65
  66         for (i = 0; i < bset->n_div; ++i)
  67                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  68                                      (bset->dim->n_out-first-n)+bset->extra);
  69
  70         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  71         if (!bset->dim)
  72                 goto error;
  73
  74         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  75         bset = isl_basic_set_simplify(bset);
  76         return isl_basic_set_finalize(bset);
  77 error:
  78         isl_basic_set_free(bset);
  79         return NULL;
  80 }
  81
  82 struct isl_set *isl_set_drop_dims(
  83                 struct isl_set *set, unsigned first, unsigned n)
  84 {
  85         int i;
  86
  87         if (!set)
  88                 goto error;
  89
  90         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  91
  92         if (n == 0)
  93                 return set;
  94         set = isl_set_cow(set);
  95         if (!set)
  96                 goto error;
  97         set->dim = isl_dim_drop_outputs(set->dim, first, n);
  98         if (!set->dim)
  99                 goto error;
 100
 101         for (i = 0; i < set->n; ++i) {
 102                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 103                 if (!set->p[i])
 104                         goto error;
 105         }
 106
 107         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 108         return set;
 109 error:
 110         isl_set_free(set);
 111         return NULL;
 112 }
 113
 114 /* Move "n" divs starting at "first" to the end of the list of divs.
 115  */
 116 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 117         unsigned first, unsigned n)
 118 {
 119         isl_int **div;
 120         int i;
 121
 122         if (first + n == bmap->n_div)
 123                 return bmap;
 124
 125         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 126         if (!div)
 127                 goto error;
 128         for (i = 0; i < n; ++i)
 129                 div[i] = bmap->div[first + i];
 130         for (i = 0; i < bmap->n_div - first - n; ++i)
 131                 bmap->div[first + i] = bmap->div[first + n + i];
 132         for (i = 0; i < n; ++i)
 133                 bmap->div[bmap->n_div - n + i] = div[i];
 134         free(div);
 135         return bmap;
 136 error:
 137         isl_basic_map_free(bmap);
 138         return NULL;
 139 }
 140
 141 /* Drop "n" dimensions of type "type" starting at "first".
 142  *
 143  * In principle, this frees up some extra variables as the number
 144  * of columns remains constant, but we would have to extend
 145  * the div array too as the number of rows in this array is assumed
 146  * to be equal to extra.
 147  */
 148 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 149         enum isl_dim_type type, unsigned first, unsigned n)
 150 {
 151         int i;
 152         unsigned dim;
 153         unsigned offset;
 154         unsigned left;
 155
 156         if (!bmap)
 157                 goto error;
 158
 159         dim = isl_basic_map_dim(bmap, type);
 160         isl_assert(bmap->ctx, first + n <= dim, goto error);
 161
 162         if (n == 0)
 163                 return bmap;
 164
 165         bmap = isl_basic_map_cow(bmap);
 166         if (!bmap)
 167                 return NULL;
 168
 169         offset = isl_basic_map_offset(bmap, type) + first;
 170         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 171         for (i = 0; i < bmap->n_eq; ++i)
 172                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 173
 174         for (i = 0; i < bmap->n_ineq; ++i)
 175                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 176
 177         for (i = 0; i < bmap->n_div; ++i)
 178                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 179
 180         if (type == isl_dim_div) {
 181                 bmap = move_divs_last(bmap, first, n);
 182                 if (!bmap)
 183                         goto error;
 184                 isl_basic_map_free_div(bmap, n);
 185         } else
 186                 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 187         if (!bmap->dim)
 188                 goto error;
 189
 190         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 191         bmap = isl_basic_map_simplify(bmap);
 192         return isl_basic_map_finalize(bmap);
 193 error:
 194         isl_basic_map_free(bmap);
 195         return NULL;
 196 }
 197
 198 struct isl_basic_map *isl_basic_map_drop_inputs(
 199                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 200 {
 201         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 202 }
 203
 204 struct isl_map *isl_map_drop(struct isl_map *map,
 205         enum isl_dim_type type, unsigned first, unsigned n)
 206 {
 207         int i;
 208
 209         if (!map)
 210                 goto error;
 211
 212         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 213
 214         if (n == 0)
 215                 return map;
 216         map = isl_map_cow(map);
 217         if (!map)
 218                 goto error;
 219         map->dim = isl_dim_drop(map->dim, type, first, n);
 220         if (!map->dim)
 221                 goto error;
 222
 223         for (i = 0; i < map->n; ++i) {
 224                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 225                 if (!map->p[i])
 226                         goto error;
 227         }
 228         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 229
 230         return map;
 231 error:
 232         isl_map_free(map);
 233         return NULL;
 234 }
 235
 236 struct isl_map *isl_map_drop_inputs(
 237                 struct isl_map *map, unsigned first, unsigned n)
 238 {
 239         return isl_map_drop(map, isl_dim_in, first, n);
 240 }
 241
 242 /*
 243  * We don't cow, as the div is assumed to be redundant.
 244  */
 245 static struct isl_basic_map *isl_basic_map_drop_div(
 246                 struct isl_basic_map *bmap, unsigned div)
 247 {
 248         int i;
 249         unsigned pos;
 250
 251         if (!bmap)
 252                 goto error;
 253
 254         pos = 1 + isl_dim_total(bmap->dim) + div;
 255
 256         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 257
 258         for (i = 0; i < bmap->n_eq; ++i)
 259                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 260
 261         for (i = 0; i < bmap->n_ineq; ++i) {
 262                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 263                         isl_basic_map_drop_inequality(bmap, i);
 264                         --i;
 265                         continue;
 266                 }
 267                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 268         }
 269
 270         for (i = 0; i < bmap->n_div; ++i)
 271                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 272
 273         if (div != bmap->n_div - 1) {
 274                 int j;
 275                 isl_int *t = bmap->div[div];
 276
 277                 for (j = div; j < bmap->n_div - 1; ++j)
 278                         bmap->div[j] = bmap->div[j+1];
 279
 280                 bmap->div[bmap->n_div - 1] = t;
 281         }
 282         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 283         isl_basic_map_free_div(bmap, 1);
 284
 285         return bmap;
 286 error:
 287         isl_basic_map_free(bmap);
 288         return NULL;
 289 }
 290
 291 struct isl_basic_map *isl_basic_map_normalize_constraints(
 292         struct isl_basic_map *bmap)
 293 {
 294         int i;
 295         isl_int gcd;
 296         unsigned total = isl_basic_map_total_dim(bmap);
 297
 298         isl_int_init(gcd);
 299         for (i = bmap->n_eq - 1; i >= 0; --i) {
 300                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 301                 if (isl_int_is_zero(gcd)) {
 302                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 303                                 bmap = isl_basic_map_set_to_empty(bmap);
 304                                 break;
 305                         }
 306                         isl_basic_map_drop_equality(bmap, i);
 307                         continue;
 308                 }
 309                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 310                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 311                 if (isl_int_is_one(gcd))
 312                         continue;
 313                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 314                         bmap = isl_basic_map_set_to_empty(bmap);
 315                         break;
 316                 }
 317                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 318         }
 319
 320         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 321                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 322                 if (isl_int_is_zero(gcd)) {
 323                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 324                                 bmap = isl_basic_map_set_to_empty(bmap);
 325                                 break;
 326                         }
 327                         isl_basic_map_drop_inequality(bmap, i);
 328                         continue;
 329                 }
 330                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 331                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 332                 if (isl_int_is_one(gcd))
 333                         continue;
 334                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 335                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 336         }
 337         isl_int_clear(gcd);
 338
 339         return bmap;
 340 }
 341
 342 struct isl_basic_set *isl_basic_set_normalize_constraints(
 343         struct isl_basic_set *bset)
 344 {
 345         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 346                 (struct isl_basic_map *)bset);
 347 }
 348
 349 /* Assumes divs have been ordered if keep_divs is set.
 350  */
 351 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 352         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 353 {
 354         unsigned total;
 355         int k;
 356         int last_div;
 357
 358         total = isl_basic_map_total_dim(bmap);
 359         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 360                                                 bmap->n_div);
 361         for (k = 0; k < bmap->n_eq; ++k) {
 362                 if (bmap->eq[k] == eq)
 363                         continue;
 364                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 365                         continue;
 366                 if (progress)
 367                         *progress = 1;
 368                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 369         }
 370
 371         for (k = 0; k < bmap->n_ineq; ++k) {
 372                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 373                         continue;
 374                 if (progress)
 375                         *progress = 1;
 376                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 377                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 378         }
 379
 380         for (k = 0; k < bmap->n_div; ++k) {
 381                 if (isl_int_is_zero(bmap->div[k][0]))
 382                         continue;
 383                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 384                         continue;
 385                 if (progress)
 386                         *progress = 1;
 387                 /* We need to be careful about circular definitions,
 388                  * so for now we just remove the definition of div k
 389                  * if the equality contains any divs.
 390                  * If keep_divs is set, then the divs have been ordered
 391                  * and we can keep the definition as long as the result
 392                  * is still ordered.
 393                  */
 394                 if (last_div == -1 || (keep_divs && last_div < k))
 395                         isl_seq_elim(bmap->div[k]+1, eq,
 396                                         1+pos, 1+total, &bmap->div[k][0]);
 397                 else
 398                         isl_seq_clr(bmap->div[k], 1 + total);
 399                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 400         }
 401 }
 402
 403 /* Assumes divs have been ordered if keep_divs is set.
 404  */
 405 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 406         unsigned div, int keep_divs)
 407 {
 408         unsigned pos = isl_dim_total(bmap->dim) + div;
 409
 410         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 411
 412         isl_basic_map_drop_div(bmap, div);
 413 }
 414
 415 /* Elimininate divs based on equalities
 416  */
 417 static struct isl_basic_map *eliminate_divs_eq(
 418                 struct isl_basic_map *bmap, int *progress)
 419 {
 420         int d;
 421         int i;
 422         int modified = 0;
 423         unsigned off;
 424
 425         bmap = isl_basic_map_order_divs(bmap);
 426
 427         if (!bmap)
 428                 return NULL;
 429
 430         off = 1 + isl_dim_total(bmap->dim);
 431
 432         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 433                 for (i = 0; i < bmap->n_eq; ++i) {
 434                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 435                             !isl_int_is_negone(bmap->eq[i][off + d]))
 436                                 continue;
 437                         modified = 1;
 438                         *progress = 1;
 439                         eliminate_div(bmap, bmap->eq[i], d, 1);
 440                         isl_basic_map_drop_equality(bmap, i);
 441                         break;
 442                 }
 443         }
 444         if (modified)
 445                 return eliminate_divs_eq(bmap, progress);
 446         return bmap;
 447 }
 448
 449 /* Elimininate divs based on inequalities
 450  */
 451 static struct isl_basic_map *eliminate_divs_ineq(
 452                 struct isl_basic_map *bmap, int *progress)
 453 {
 454         int d;
 455         int i;
 456         unsigned off;
 457         struct isl_ctx *ctx;
 458
 459         if (!bmap)
 460                 return NULL;
 461
 462         ctx = bmap->ctx;
 463         off = 1 + isl_dim_total(bmap->dim);
 464
 465         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 466                 for (i = 0; i < bmap->n_eq; ++i)
 467                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 468                                 break;
 469                 if (i < bmap->n_eq)
 470                         continue;
 471                 for (i = 0; i < bmap->n_ineq; ++i)
 472                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 473                                 break;
 474                 if (i < bmap->n_ineq)
 475                         continue;
 476                 *progress = 1;
 477                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 478                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 479                         break;
 480                 bmap = isl_basic_map_drop_div(bmap, d);
 481                 if (!bmap)
 482                         break;
 483         }
 484         return bmap;
 485 }
 486
 487 struct isl_basic_map *isl_basic_map_gauss(
 488         struct isl_basic_map *bmap, int *progress)
 489 {
 490         int k;
 491         int done;
 492         int last_var;
 493         unsigned total_var;
 494         unsigned total;
 495
 496         bmap = isl_basic_map_order_divs(bmap);
 497
 498         if (!bmap)
 499                 return NULL;
 500
 501         total = isl_basic_map_total_dim(bmap);
 502         total_var = total - bmap->n_div;
 503
 504         last_var = total - 1;
 505         for (done = 0; done < bmap->n_eq; ++done) {
 506                 for (; last_var >= 0; --last_var) {
 507                         for (k = done; k < bmap->n_eq; ++k)
 508                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 509                                         break;
 510                         if (k < bmap->n_eq)
 511                                 break;
 512                 }
 513                 if (last_var < 0)
 514                         break;
 515                 if (k != done)
 516                         swap_equality(bmap, k, done);
 517                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 518                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 519
 520                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 521                                                 progress);
 522
 523                 if (last_var >= total_var &&
 524                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 525                         unsigned div = last_var - total_var;
 526                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 527                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 528                         isl_int_set(bmap->div[div][0],
 529                                     bmap->eq[done][1+last_var]);
 530                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 531                 }
 532         }
 533         if (done == bmap->n_eq)
 534                 return bmap;
 535         for (k = done; k < bmap->n_eq; ++k) {
 536                 if (isl_int_is_zero(bmap->eq[k][0]))
 537                         continue;
 538                 return isl_basic_map_set_to_empty(bmap);
 539         }
 540         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 541         return bmap;
 542 }
 543
 544 struct isl_basic_set *isl_basic_set_gauss(
 545         struct isl_basic_set *bset, int *progress)
 546 {
 547         return (struct isl_basic_set*)isl_basic_map_gauss(
 548                         (struct isl_basic_map *)bset, progress);
 549 }
 550
 551
 552 static unsigned int round_up(unsigned int v)
 553 {
 554         int old_v = v;
 555
 556         while (v) {
 557                 old_v = v;
 558                 v ^= v & -v;
 559         }
 560         return old_v << 1;
 561 }
 562
 563 static int hash_index(isl_int ***index, unsigned int size, int bits,
 564                         struct isl_basic_map *bmap, int k)
 565 {
 566         int h;
 567         unsigned total = isl_basic_map_total_dim(bmap);
 568         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 569         for (h = hash; index[h]; h = (h+1) % size)
 570                 if (&bmap->ineq[k] != index[h] &&
 571                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 572                         break;
 573         return h;
 574 }
 575
 576 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 577                           struct isl_basic_set *bset, int k)
 578 {
 579         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 580 }
 581
 582 /* If we can eliminate more than one div, then we need to make
 583  * sure we do it from last div to first div, in order not to
 584  * change the position of the other divs that still need to
 585  * be removed.
 586  */
 587 static struct isl_basic_map *remove_duplicate_divs(
 588         struct isl_basic_map *bmap, int *progress)
 589 {
 590         unsigned int size;
 591         int *index;
 592         int *elim_for;
 593         int k, l, h;
 594         int bits;
 595         struct isl_blk eq;
 596         unsigned total_var = isl_dim_total(bmap->dim);
 597         unsigned total = total_var + bmap->n_div;
 598         struct isl_ctx *ctx;
 599
 600         if (bmap->n_div <= 1)
 601                 return bmap;
 602
 603         ctx = bmap->ctx;
 604         for (k = bmap->n_div - 1; k >= 0; --k)
 605                 if (!isl_int_is_zero(bmap->div[k][0]))
 606                         break;
 607         if (k <= 0)
 608                 return bmap;
 609
 610         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 611         size = round_up(4 * bmap->n_div / 3 - 1);
 612         bits = ffs(size) - 1;
 613         index = isl_calloc_array(ctx, int, size);
 614         if (!index)
 615                 return bmap;
 616         eq = isl_blk_alloc(ctx, 1+total);
 617         if (isl_blk_is_error(eq))
 618                 goto out;
 619
 620         isl_seq_clr(eq.data, 1+total);
 621         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 622         for (--k; k >= 0; --k) {
 623                 uint32_t hash;
 624
 625                 if (isl_int_is_zero(bmap->div[k][0]))
 626                         continue;
 627
 628                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 629                 for (h = hash; index[h]; h = (h+1) % size)
 630                         if (isl_seq_eq(bmap->div[k],
 631                                        bmap->div[index[h]-1], 2+total))
 632                                 break;
 633                 if (index[h]) {
 634                         *progress = 1;
 635                         l = index[h] - 1;
 636                         elim_for[l] = k + 1;
 637                 }
 638                 index[h] = k+1;
 639         }
 640         for (l = bmap->n_div - 1; l >= 0; --l) {
 641                 if (!elim_for[l])
 642                         continue;
 643                 k = elim_for[l] - 1;
 644                 isl_int_set_si(eq.data[1+total_var+k], -1);
 645                 isl_int_set_si(eq.data[1+total_var+l], 1);
 646                 eliminate_div(bmap, eq.data, l, 0);
 647                 isl_int_set_si(eq.data[1+total_var+k], 0);
 648                 isl_int_set_si(eq.data[1+total_var+l], 0);
 649         }
 650
 651         isl_blk_free(ctx, eq);
 652 out:
 653         free(index);
 654         free(elim_for);
 655         return bmap;
 656 }
 657
 658 static int n_pure_div_eq(struct isl_basic_map *bmap)
 659 {
 660         int i, j;
 661         unsigned total;
 662
 663         total = isl_dim_total(bmap->dim);
 664         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 665                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 666                         --j;
 667                 if (j < 0)
 668                         break;
 669                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 670                         return 0;
 671         }
 672         return i;
 673 }
 674
 675 /* Normalize divs that appear in equalities.
 676  *
 677  * In particular, we assume that bmap contains some equalities
 678  * of the form
 679  *
 680  *      a x = m * e_i
 681  *
 682  * and we want to replace the set of e_i by a minimal set and
 683  * such that the new e_i have a canonical representation in terms
 684  * of the vector x.
 685  * If any of the equalities involves more than one divs, then
 686  * we currently simply bail out.
 687  *
 688  * Let us first additionally assume that all equalities involve
 689  * a div.  The equalities then express modulo constraints on the
 690  * remaining variables and we can use "parameter compression"
 691  * to find a minimal set of constraints.  The result is a transformation
 692  *
 693  *      x = T(x') = x_0 + G x'
 694  *
 695  * with G a lower-triangular matrix with all elements below the diagonal
 696  * non-negative and smaller than the diagonal element on the same row.
 697  * We first normalize x_0 by making the same property hold in the affine
 698  * T matrix.
 699  * The rows i of G with a 1 on the diagonal do not impose any modulo
 700  * constraint and simply express x_i = x'_i.
 701  * For each of the remaining rows i, we introduce a div and a corresponding
 702  * equality.  In particular
 703  *
 704  *      g_ii e_j = x_i - g_i(x')
 705  *
 706  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 707  * corresponding div (if g_kk != 1).
 708  *
 709  * If there are any equalities not involving any div, then we
 710  * first apply a variable compression on the variables x:
 711  *
 712  *      x = C x''       x'' = C_2 x
 713  *
 714  * and perform the above parameter compression on A C instead of on A.
 715  * The resulting compression is then of the form
 716  *
 717  *      x'' = T(x') = x_0 + G x'
 718  *
 719  * and in constructing the new divs and the corresponding equalities,
 720  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 721  * by the corresponding row from C_2.
 722  */
 723 static struct isl_basic_map *normalize_divs(
 724         struct isl_basic_map *bmap, int *progress)
 725 {
 726         int i, j, k;
 727         int total;
 728         int div_eq;
 729         struct isl_mat *B;
 730         struct isl_vec *d;
 731         struct isl_mat *T = NULL;
 732         struct isl_mat *C = NULL;
 733         struct isl_mat *C2 = NULL;
 734         isl_int v;
 735         int *pos;
 736         int dropped, needed;
 737
 738         if (!bmap)
 739                 return NULL;
 740
 741         if (bmap->n_div == 0)
 742                 return bmap;
 743
 744         if (bmap->n_eq == 0)
 745                 return bmap;
 746
 747         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 748                 return bmap;
 749
 750         total = isl_dim_total(bmap->dim);
 751         div_eq = n_pure_div_eq(bmap);
 752         if (div_eq == 0)
 753                 return bmap;
 754
 755         if (div_eq < bmap->n_eq) {
 756                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 757                                         bmap->n_eq - div_eq, 0, 1 + total);
 758                 C = isl_mat_variable_compression(B, &C2);
 759                 if (!C || !C2)
 760                         goto error;
 761                 if (C->n_col == 0) {
 762                         bmap = isl_basic_map_set_to_empty(bmap);
 763                         isl_mat_free(C);
 764                         isl_mat_free(C2);
 765                         goto done;
 766                 }
 767         }
 768
 769         d = isl_vec_alloc(bmap->ctx, div_eq);
 770         if (!d)
 771                 goto error;
 772         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 773                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 774                         --j;
 775                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 776         }
 777         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 778
 779         if (C) {
 780                 B = isl_mat_product(B, C);
 781                 C = NULL;
 782         }
 783
 784         T = isl_mat_parameter_compression(B, d);
 785         if (!T)
 786                 goto error;
 787         if (T->n_col == 0) {
 788                 bmap = isl_basic_map_set_to_empty(bmap);
 789                 isl_mat_free(C2);
 790                 isl_mat_free(T);
 791                 goto done;
 792         }
 793         isl_int_init(v);
 794         for (i = 0; i < T->n_row - 1; ++i) {
 795                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 796                 if (isl_int_is_zero(v))
 797                         continue;
 798                 isl_mat_col_submul(T, 0, v, 1 + i);
 799         }
 800         isl_int_clear(v);
 801         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 802         /* We have to be careful because dropping equalities may reorder them */
 803         dropped = 0;
 804         for (j = bmap->n_div - 1; j >= 0; --j) {
 805                 for (i = 0; i < bmap->n_eq; ++i)
 806                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 807                                 break;
 808                 if (i < bmap->n_eq) {
 809                         bmap = isl_basic_map_drop_div(bmap, j);
 810                         isl_basic_map_drop_equality(bmap, i);
 811                         ++dropped;
 812                 }
 813         }
 814         pos[0] = 0;
 815         needed = 0;
 816         for (i = 1; i < T->n_row; ++i) {
 817                 if (isl_int_is_one(T->row[i][i]))
 818                         pos[i] = i;
 819                 else
 820                         needed++;
 821         }
 822         if (needed > dropped) {
 823                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 824                                 needed, needed, 0);
 825                 if (!bmap)
 826                         goto error;
 827         }
 828         for (i = 1; i < T->n_row; ++i) {
 829                 if (isl_int_is_one(T->row[i][i]))
 830                         continue;
 831                 k = isl_basic_map_alloc_div(bmap);
 832                 pos[i] = 1 + total + k;
 833                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 834                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 835                 if (C2)
 836                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 837                 else
 838                         isl_int_set_si(bmap->div[k][1 + i], 1);
 839                 for (j = 0; j < i; ++j) {
 840                         if (isl_int_is_zero(T->row[i][j]))
 841                                 continue;
 842                         if (pos[j] < T->n_row && C2)
 843                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 844                                                 C2->row[pos[j]], 1 + total);
 845                         else
 846                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 847                                                                 T->row[i][j]);
 848                 }
 849                 j = isl_basic_map_alloc_equality(bmap);
 850                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 851                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 852         }
 853         free(pos);
 854         isl_mat_free(C2);
 855         isl_mat_free(T);
 856
 857         if (progress)
 858                 *progress = 1;
 859 done:
 860         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 861
 862         return bmap;
 863 error:
 864         isl_mat_free(C);
 865         isl_mat_free(C2);
 866         isl_mat_free(T);
 867         return bmap;
 868 }
 869
 870 static struct isl_basic_map *set_div_from_lower_bound(
 871         struct isl_basic_map *bmap, int div, int ineq)
 872 {
 873         unsigned total = 1 + isl_dim_total(bmap->dim);
 874
 875         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 876         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 877         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 878         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 879         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 880
 881         return bmap;
 882 }
 883
 884 /* Check whether it is ok to define a div based on an inequality.
 885  * To avoid the introduction of circular definitions of divs, we
 886  * do not allow such a definition if the resulting expression would refer to
 887  * any other undefined divs or if any known div is defined in
 888  * terms of the unknown div.
 889  */
 890 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 891         int div, int ineq)
 892 {
 893         int j;
 894         unsigned total = 1 + isl_dim_total(bmap->dim);
 895
 896         /* Not defined in terms of unknown divs */
 897         for (j = 0; j < bmap->n_div; ++j) {
 898                 if (div == j)
 899                         continue;
 900                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
 901                         continue;
 902                 if (isl_int_is_zero(bmap->div[j][0]))
 903                         return 0;
 904         }
 905
 906         /* No other div defined in terms of this one => avoid loops */
 907         for (j = 0; j < bmap->n_div; ++j) {
 908                 if (div == j)
 909                         continue;
 910                 if (isl_int_is_zero(bmap->div[j][0]))
 911                         continue;
 912                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
 913                         return 0;
 914         }
 915
 916         return 1;
 917 }
 918
 919 /* Given two constraints "k" and "l" that are opposite to each other,
 920  * except for the constant term, check if we can use them
 921  * to obtain an expression for one of the hitherto unknown divs.
 922  * "sum" is the sum of the constant terms of the constraints.
 923  * If this sum is strictly smaller than the coefficient of one
 924  * of the divs, then this pair can be used define the div.
 925  * To avoid the introduction of circular definitions of divs, we
 926  * do not use the pair if the resulting expression would refer to
 927  * any other undefined divs or if any known div is defined in
 928  * terms of the unknown div.
 929  */
 930 static struct isl_basic_map *check_for_div_constraints(
 931         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
 932 {
 933         int i;
 934         unsigned total = 1 + isl_dim_total(bmap->dim);
 935
 936         for (i = 0; i < bmap->n_div; ++i) {
 937                 if (!isl_int_is_zero(bmap->div[i][0]))
 938                         continue;
 939                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
 940                         continue;
 941                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
 942                         continue;
 943                 if (!ok_to_set_div_from_bound(bmap, i, k))
 944                         break;
 945                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
 946                         bmap = set_div_from_lower_bound(bmap, i, k);
 947                 else
 948                         bmap = set_div_from_lower_bound(bmap, i, l);
 949                 if (progress)
 950                         *progress = 1;
 951                 break;
 952         }
 953         return bmap;
 954 }
 955
 956 static struct isl_basic_map *remove_duplicate_constraints(
 957         struct isl_basic_map *bmap, int *progress)
 958 {
 959         unsigned int size;
 960         isl_int ***index;
 961         int k, l, h;
 962         int bits;
 963         unsigned total = isl_basic_map_total_dim(bmap);
 964         isl_int sum;
 965
 966         if (bmap->n_ineq <= 1)
 967                 return bmap;
 968
 969         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 970         bits = ffs(size) - 1;
 971         index = isl_calloc_array(ctx, isl_int **, size);
 972         if (!index)
 973                 return bmap;
 974
 975         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 976         for (k = 1; k < bmap->n_ineq; ++k) {
 977                 h = hash_index(index, size, bits, bmap, k);
 978                 if (!index[h]) {
 979                         index[h] = &bmap->ineq[k];
 980                         continue;
 981                 }
 982                 if (progress)
 983                         *progress = 1;
 984                 l = index[h] - &bmap->ineq[0];
 985                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 986                         swap_inequality(bmap, k, l);
 987                 isl_basic_map_drop_inequality(bmap, k);
 988                 --k;
 989         }
 990         isl_int_init(sum);
 991         for (k = 0; k < bmap->n_ineq-1; ++k) {
 992                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 993                 h = hash_index(index, size, bits, bmap, k);
 994                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 995                 if (!index[h])
 996                         continue;
 997                 l = index[h] - &bmap->ineq[0];
 998                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 999                 if (isl_int_is_pos(sum)) {
1000                         bmap = check_for_div_constraints(bmap, k, l, sum,
1001                                                          progress);
1002                         continue;
1003                 }
1004                 if (isl_int_is_zero(sum)) {
1005                         /* We need to break out of the loop after these
1006                          * changes since the contents of the hash
1007                          * will no longer be valid.
1008                          * Plus, we probably we want to regauss first.
1009                          */
1010                         isl_basic_map_drop_inequality(bmap, l);
1011                         isl_basic_map_inequality_to_equality(bmap, k);
1012                 } else
1013                         bmap = isl_basic_map_set_to_empty(bmap);
1014                 break;
1015         }
1016         isl_int_clear(sum);
1017
1018         free(index);
1019         return bmap;
1020 }
1021
1022
1023 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1024 {
1025         int progress = 1;
1026         if (!bmap)
1027                 return NULL;
1028         while (progress) {
1029                 progress = 0;
1030                 bmap = isl_basic_map_normalize_constraints(bmap);
1031                 bmap = remove_duplicate_divs(bmap, &progress);
1032                 bmap = eliminate_divs_eq(bmap, &progress);
1033                 bmap = eliminate_divs_ineq(bmap, &progress);
1034                 bmap = isl_basic_map_gauss(bmap, &progress);
1035                 /* requires equalities in normal form */
1036                 bmap = normalize_divs(bmap, &progress);
1037                 bmap = remove_duplicate_constraints(bmap, &progress);
1038         }
1039         return bmap;
1040 }
1041
1042 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1043 {
1044         return (struct isl_basic_set *)
1045                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1046 }
1047
1048
1049 /* If the only constraints a div d=floor(f/m)
1050  * appears in are its two defining constraints
1051  *
1052  *      f - m d >=0
1053  *      -(f - (m - 1)) + m d >= 0
1054  *
1055  * then it can safely be removed.
1056  */
1057 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1058 {
1059         int i;
1060         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1061
1062         for (i = 0; i < bmap->n_eq; ++i)
1063                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1064                         return 0;
1065
1066         for (i = 0; i < bmap->n_ineq; ++i) {
1067                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1068                         continue;
1069                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1070                         int neg;
1071                         isl_int_sub(bmap->div[div][1],
1072                                         bmap->div[div][1], bmap->div[div][0]);
1073                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1074                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1075                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1076                         isl_int_add(bmap->div[div][1],
1077                                         bmap->div[div][1], bmap->div[div][0]);
1078                         if (!neg)
1079                                 return 0;
1080                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1081                                                     bmap->n_div-div-1) != -1)
1082                                 return 0;
1083                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1084                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1085                                 return 0;
1086                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1087                                                     bmap->n_div-div-1) != -1)
1088                                 return 0;
1089                 } else
1090                         return 0;
1091         }
1092
1093         for (i = 0; i < bmap->n_div; ++i)
1094                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1095                         return 0;
1096
1097         return 1;
1098 }
1099
1100 /*
1101  * Remove divs that don't occur in any of the constraints or other divs.
1102  * These can arise when dropping some of the variables in a quast
1103  * returned by piplib.
1104  */
1105 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1106 {
1107         int i;
1108
1109         if (!bmap)
1110                 return NULL;
1111
1112         for (i = bmap->n_div-1; i >= 0; --i) {
1113                 if (!div_is_redundant(bmap, i))
1114                         continue;
1115                 bmap = isl_basic_map_drop_div(bmap, i);
1116         }
1117         return bmap;
1118 }
1119
1120 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1121 {
1122         bmap = remove_redundant_divs(bmap);
1123         if (!bmap)
1124                 return NULL;
1125         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1126         return bmap;
1127 }
1128
1129 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1130 {
1131         return (struct isl_basic_set *)
1132                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1133 }
1134
1135 struct isl_set *isl_set_finalize(struct isl_set *set)
1136 {
1137         int i;
1138
1139         if (!set)
1140                 return NULL;
1141         for (i = 0; i < set->n; ++i) {
1142                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1143                 if (!set->p[i])
1144                         goto error;
1145         }
1146         return set;
1147 error:
1148         isl_set_free(set);
1149         return NULL;
1150 }
1151
1152 struct isl_map *isl_map_finalize(struct isl_map *map)
1153 {
1154         int i;
1155
1156         if (!map)
1157                 return NULL;
1158         for (i = 0; i < map->n; ++i) {
1159                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1160                 if (!map->p[i])
1161                         goto error;
1162         }
1163         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1164         return map;
1165 error:
1166         isl_map_free(map);
1167         return NULL;
1168 }
1169
1170
1171 /* Remove definition of any div that is defined in terms of the given variable.
1172  * The div itself is not removed.  Functions such as
1173  * eliminate_divs_ineq depend on the other divs remaining in place.
1174  */
1175 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1176                                                                         int pos)
1177 {
1178         int i;
1179
1180         for (i = 0; i < bmap->n_div; ++i) {
1181                 if (isl_int_is_zero(bmap->div[i][0]))
1182                         continue;
1183                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1184                         continue;
1185                 isl_int_set_si(bmap->div[i][0], 0);
1186         }
1187         return bmap;
1188 }
1189
1190 /* Eliminate the specified variables from the constraints using
1191  * Fourier-Motzkin.  The variables themselves are not removed.
1192  */
1193 struct isl_basic_map *isl_basic_map_eliminate_vars(
1194         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1195 {
1196         int d;
1197         int i, j, k;
1198         unsigned total;
1199
1200         if (n == 0)
1201                 return bmap;
1202         if (!bmap)
1203                 return NULL;
1204         total = isl_basic_map_total_dim(bmap);
1205
1206         bmap = isl_basic_map_cow(bmap);
1207         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1208                 bmap = remove_dependent_vars(bmap, d);
1209
1210         for (d = pos + n - 1;
1211              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1212                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1213         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1214                 int n_lower, n_upper;
1215                 if (!bmap)
1216                         return NULL;
1217                 for (i = 0; i < bmap->n_eq; ++i) {
1218                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1219                                 continue;
1220                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1221                         isl_basic_map_drop_equality(bmap, i);
1222                         break;
1223                 }
1224                 if (i < bmap->n_eq)
1225                         continue;
1226                 n_lower = 0;
1227                 n_upper = 0;
1228                 for (i = 0; i < bmap->n_ineq; ++i) {
1229                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1230                                 n_lower++;
1231                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1232                                 n_upper++;
1233                 }
1234                 bmap = isl_basic_map_extend_constraints(bmap,
1235                                 0, n_lower * n_upper);
1236                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1237                         int last;
1238                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1239                                 continue;
1240                         last = -1;
1241                         for (j = 0; j < i; ++j) {
1242                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1243                                         continue;
1244                                 last = j;
1245                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1246                                     isl_int_sgn(bmap->ineq[j][1+d]))
1247                                         continue;
1248                                 k = isl_basic_map_alloc_inequality(bmap);
1249                                 if (k < 0)
1250                                         goto error;
1251                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1252                                                 1+total);
1253                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1254                                                 1+d, 1+total, NULL);
1255                         }
1256                         isl_basic_map_drop_inequality(bmap, i);
1257                         i = last + 1;
1258                 }
1259                 if (n_lower > 0 && n_upper > 0) {
1260                         bmap = isl_basic_map_normalize_constraints(bmap);
1261                         bmap = remove_duplicate_constraints(bmap, NULL);
1262                         bmap = isl_basic_map_gauss(bmap, NULL);
1263                         bmap = isl_basic_map_convex_hull(bmap);
1264                         if (!bmap)
1265                                 goto error;
1266                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1267                                 break;
1268                 }
1269         }
1270         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1271         return bmap;
1272 error:
1273         isl_basic_map_free(bmap);
1274         return NULL;
1275 }
1276
1277 struct isl_basic_set *isl_basic_set_eliminate_vars(
1278         struct isl_basic_set *bset, unsigned pos, unsigned n)
1279 {
1280         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1281                         (struct isl_basic_map *)bset, pos, n);
1282 }
1283
1284 /* Don't assume equalities are in order, because align_divs
1285  * may have changed the order of the divs.
1286  */
1287 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1288 {
1289         int d, i;
1290         unsigned total;
1291
1292         total = isl_dim_total(bmap->dim);
1293         for (d = 0; d < total; ++d)
1294                 elim[d] = -1;
1295         for (i = 0; i < bmap->n_eq; ++i) {
1296                 for (d = total - 1; d >= 0; --d) {
1297                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1298                                 continue;
1299                         elim[d] = i;
1300                         break;
1301                 }
1302         }
1303 }
1304
1305 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1306 {
1307         compute_elimination_index((struct isl_basic_map *)bset, elim);
1308 }
1309
1310 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1311         struct isl_basic_map *bmap, int *elim)
1312 {
1313         int d;
1314         int copied = 0;
1315         unsigned total;
1316
1317         total = isl_dim_total(bmap->dim);
1318         for (d = total - 1; d >= 0; --d) {
1319                 if (isl_int_is_zero(src[1+d]))
1320                         continue;
1321                 if (elim[d] == -1)
1322                         continue;
1323                 if (!copied) {
1324                         isl_seq_cpy(dst, src, 1 + total);
1325                         copied = 1;
1326                 }
1327                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1328         }
1329         return copied;
1330 }
1331
1332 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1333         struct isl_basic_set *bset, int *elim)
1334 {
1335         return reduced_using_equalities(dst, src,
1336                                         (struct isl_basic_map *)bset, elim);
1337 }
1338
1339 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1340         struct isl_basic_set *bset, struct isl_basic_set *context)
1341 {
1342         int i;
1343         int *elim;
1344
1345         if (!bset || !context)
1346                 goto error;
1347
1348         bset = isl_basic_set_cow(bset);
1349         if (!bset)
1350                 goto error;
1351
1352         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1353         if (!elim)
1354                 goto error;
1355         set_compute_elimination_index(context, elim);
1356         for (i = 0; i < bset->n_eq; ++i)
1357                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1358                                                         context, elim);
1359         for (i = 0; i < bset->n_ineq; ++i)
1360                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1361                                                         context, elim);
1362         isl_basic_set_free(context);
1363         free(elim);
1364         bset = isl_basic_set_simplify(bset);
1365         bset = isl_basic_set_finalize(bset);
1366         return bset;
1367 error:
1368         isl_basic_set_free(bset);
1369         isl_basic_set_free(context);
1370         return NULL;
1371 }
1372
1373 static struct isl_basic_set *remove_shifted_constraints(
1374         struct isl_basic_set *bset, struct isl_basic_set *context)
1375 {
1376         unsigned int size;
1377         isl_int ***index;
1378         int bits;
1379         int k, h, l;
1380
1381         if (!bset)
1382                 return NULL;
1383
1384         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1385         bits = ffs(size) - 1;
1386         index = isl_calloc_array(ctx, isl_int **, size);
1387         if (!index)
1388                 return bset;
1389
1390         for (k = 0; k < context->n_ineq; ++k) {
1391                 h = set_hash_index(index, size, bits, context, k);
1392                 index[h] = &context->ineq[k];
1393         }
1394         for (k = 0; k < bset->n_ineq; ++k) {
1395                 h = set_hash_index(index, size, bits, bset, k);
1396                 if (!index[h])
1397                         continue;
1398                 l = index[h] - &context->ineq[0];
1399                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1400                         continue;
1401                 bset = isl_basic_set_cow(bset);
1402                 if (!bset)
1403                         goto error;
1404                 isl_basic_set_drop_inequality(bset, k);
1405                 --k;
1406         }
1407         free(index);
1408         return bset;
1409 error:
1410         free(index);
1411         return bset;
1412 }
1413
1414 /* Tighten (decrease) the constant terms of the inequalities based
1415  * on the equalities, without removing any integer points.
1416  * For example, if there is an equality
1417  *
1418  *              i = 3 * j
1419  *
1420  * and an inequality
1421  *
1422  *              i >= 1
1423  *
1424  * then we want to replace the inequality by
1425  *
1426  *              i >= 3
1427  *
1428  * We do this by computing a variable compression and translating
1429  * the constraints to the compressed space.
1430  * If any constraint has coefficients (except the contant term)
1431  * with a common factor "f", then we can replace the constant term "c"
1432  * by
1433  *
1434  *              f * floor(c/f)
1435  *
1436  * That is, we add
1437  *
1438  *              f * floor(c/f) - c = -fract(c/f)
1439  *
1440  * and we can add the same value to the original constraint.
1441  *
1442  * In the example, the compressed space only contains "j",
1443  * and the inequality translates to
1444  *
1445  *              3 * j - 1 >= 0
1446  *
1447  * We add -fract(-1/3) = -2 to the original constraint to obtain
1448  *
1449  *              i - 3 >= 0
1450  */
1451 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1452         struct isl_basic_set *bset)
1453 {
1454         int i;
1455         unsigned total;
1456         struct isl_mat *B, *C;
1457         isl_int gcd;
1458
1459         if (!bset)
1460                 return NULL;
1461
1462         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1463                 return bset;
1464
1465         if (!bset->n_ineq)
1466                 return bset;
1467
1468         bset = isl_basic_set_cow(bset);
1469         if (!bset)
1470                 return NULL;
1471
1472         total = isl_basic_set_total_dim(bset);
1473         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1474         C = isl_mat_variable_compression(B, NULL);
1475         if (!C)
1476                 return bset;
1477         if (C->n_col == 0) {
1478                 isl_mat_free(C);
1479                 return isl_basic_set_set_to_empty(bset);
1480         }
1481         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1482                                                 0, bset->n_ineq, 0, 1 + total);
1483         C = isl_mat_product(B, C);
1484         if (!C)
1485                 return bset;
1486
1487         isl_int_init(gcd);
1488         for (i = 0; i < bset->n_ineq; ++i) {
1489                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1490                 if (isl_int_is_one(gcd))
1491                         continue;
1492                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1493                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1494         }
1495         isl_int_clear(gcd);
1496
1497         isl_mat_free(C);
1498
1499         return bset;
1500 }
1501
1502 /* Remove all information from bset that is redundant in the context
1503  * of context.  In particular, equalities that are linear combinations
1504  * of those in context are removed.  Then the inequalities that are
1505  * redundant in the context of the equalities and inequalities of
1506  * context are removed.
1507  *
1508  * We first simplify the constraints of "bset" in the context of the
1509  * equalities of "context".
1510  * Then we simplify the inequalities of the context in the context
1511  * of the equalities of bset and remove the inequalities from "bset"
1512  * that are obviously redundant with respect to some inequality in "context".
1513  *
1514  * If there are any inequalities left, we construct a tableau for
1515  * the context and then add the inequalities of "bset".
1516  * Before adding these equalities, we freeze all constraints such that
1517  * they won't be considered redundant in terms of the constraints of "bset".
1518  * Then we detect all equalities and redundant constraints (among the
1519  * constraints that weren't frozen) and update bset according to the results.
1520  * We have to be careful here because we don't want any of the context
1521  * constraints to remain and because we haven't added the equalities of "bset"
1522  * to the tableau so we temporarily have to pretend that there were no
1523  * equalities.
1524  */
1525 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1526         struct isl_basic_set *context)
1527 {
1528         int i;
1529         struct isl_tab *tab;
1530         unsigned context_ineq;
1531         struct isl_basic_set *combined = NULL;
1532
1533         if (!context || !bset)
1534                 goto error;
1535
1536         if (context->n_eq > 0)
1537                 bset = isl_basic_set_reduce_using_equalities(bset,
1538                                         isl_basic_set_copy(context));
1539         if (!bset)
1540                 goto error;
1541         if (isl_basic_set_fast_is_empty(bset))
1542                 goto done;
1543         if (!bset->n_ineq)
1544                 goto done;
1545
1546         if (bset->n_eq > 0) {
1547                 struct isl_basic_set *affine_hull;
1548                 affine_hull = isl_basic_set_copy(bset);
1549                 affine_hull = isl_basic_set_cow(affine_hull);
1550                 if (!affine_hull)
1551                         goto error;
1552                 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1553                 context = isl_basic_set_intersect(context, affine_hull);
1554                 context = isl_basic_set_gauss(context, NULL);
1555                 context = normalize_constraints_in_compressed_space(context);
1556         }
1557         if (!context)
1558                 goto error;
1559         if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1560                 isl_basic_set_free(bset);
1561                 return context;
1562         }
1563         if (!context->n_ineq)
1564                 goto done;
1565         bset = remove_shifted_constraints(bset, context);
1566         if (!bset->n_ineq)
1567                 goto done;
1568         isl_basic_set_free_equality(context, context->n_eq);
1569         context_ineq = context->n_ineq;
1570         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1571         combined = isl_basic_set_extend_constraints(combined,
1572                                                     bset->n_eq, bset->n_ineq);
1573         tab = isl_tab_from_basic_set(combined);
1574         if (!tab)
1575                 goto error;
1576         for (i = 0; i < context_ineq; ++i)
1577                 tab->con[i].frozen = 1;
1578         tab = isl_tab_extend(tab, bset->n_ineq);
1579         if (!tab)
1580                 goto error;
1581         for (i = 0; i < bset->n_ineq; ++i)
1582                 tab = isl_tab_add_ineq(tab, bset->ineq[i]);
1583         bset = isl_basic_set_add_constraints(combined, bset, 0);
1584         tab = isl_tab_detect_implicit_equalities(tab);
1585         tab = isl_tab_detect_redundant(tab);
1586         if (!tab)
1587                 goto error2;
1588         for (i = 0; i < context_ineq; ++i) {
1589                 tab->con[i].is_zero = 0;
1590                 tab->con[i].is_redundant = 1;
1591         }
1592         bset = isl_basic_set_update_from_tab(bset, tab);
1593         isl_tab_free(tab);
1594         ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1595         ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1596 done:
1597         bset = isl_basic_set_simplify(bset);
1598         bset = isl_basic_set_finalize(bset);
1599         isl_basic_set_free(context);
1600         return bset;
1601 error:
1602         isl_basic_set_free(combined);
1603 error2:
1604         isl_basic_set_free(bset);
1605         isl_basic_set_free(context);
1606         return NULL;
1607 }
1608
1609 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1610  * We simply add the equalities in context to bmap and then do a regular
1611  * div normalizations.  Better results can be obtained by normalizing
1612  * only the divs in bmap than do not also appear in context.
1613  * We need to be careful to reduce the divs using the equalities
1614  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1615  * spurious constraints.
1616  */
1617 static struct isl_basic_map *normalize_divs_in_context(
1618         struct isl_basic_map *bmap, struct isl_basic_map *context)
1619 {
1620         int i;
1621         unsigned total_context;
1622         int div_eq;
1623
1624         div_eq = n_pure_div_eq(bmap);
1625         if (div_eq == 0)
1626                 return bmap;
1627
1628         if (context->n_div > 0)
1629                 bmap = isl_basic_map_align_divs(bmap, context);
1630
1631         total_context = isl_basic_map_total_dim(context);
1632         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1633         for (i = 0; i < context->n_eq; ++i) {
1634                 int k;
1635                 k = isl_basic_map_alloc_equality(bmap);
1636                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1637                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1638                                 isl_basic_map_total_dim(bmap) - total_context);
1639         }
1640         bmap = isl_basic_map_gauss(bmap, NULL);
1641         bmap = normalize_divs(bmap, NULL);
1642         bmap = isl_basic_map_gauss(bmap, NULL);
1643         return bmap;
1644 }
1645
1646 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1647         struct isl_basic_map *context)
1648 {
1649         struct isl_basic_set *bset;
1650
1651         if (!bmap || !context)
1652                 goto error;
1653
1654         if (isl_basic_map_is_universe(context)) {
1655                 isl_basic_map_free(context);
1656                 return bmap;
1657         }
1658         if (isl_basic_map_is_universe(bmap)) {
1659                 isl_basic_map_free(context);
1660                 return bmap;
1661         }
1662         if (isl_basic_map_fast_is_empty(context)) {
1663                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1664                 isl_basic_map_free(context);
1665                 isl_basic_map_free(bmap);
1666                 return isl_basic_map_universe(dim);
1667         }
1668         if (isl_basic_map_fast_is_empty(bmap)) {
1669                 isl_basic_map_free(context);
1670                 return bmap;
1671         }
1672
1673         bmap = isl_basic_map_convex_hull(bmap);
1674         context = isl_basic_map_convex_hull(context);
1675
1676         if (context->n_eq)
1677                 bmap = normalize_divs_in_context(bmap, context);
1678
1679         context = isl_basic_map_align_divs(context, bmap);
1680         bmap = isl_basic_map_align_divs(bmap, context);
1681
1682         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1683                          isl_basic_map_underlying_set(context));
1684
1685         return isl_basic_map_overlying_set(bset, bmap);
1686 error:
1687         isl_basic_map_free(bmap);
1688         isl_basic_map_free(context);
1689         return NULL;
1690 }
1691
1692 /*
1693  * Assumes context has no implicit divs.
1694  */
1695 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1696 {
1697         int i;
1698
1699         if (!map || !context)
1700                 goto error;;
1701
1702         if (isl_basic_map_is_universe(context)) {
1703                 isl_basic_map_free(context);
1704                 return map;
1705         }
1706         if (isl_basic_map_fast_is_empty(context)) {
1707                 struct isl_dim *dim = isl_dim_copy(map->dim);
1708                 isl_basic_map_free(context);
1709                 isl_map_free(map);
1710                 return isl_map_universe(dim);
1711         }
1712
1713         context = isl_basic_map_convex_hull(context);
1714         map = isl_map_cow(map);
1715         if (!map || !context)
1716                 goto error;;
1717         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1718         map = isl_map_compute_divs(map);
1719         for (i = 0; i < map->n; ++i)
1720                 context = isl_basic_map_align_divs(context, map->p[i]);
1721         for (i = 0; i < map->n; ++i) {
1722                 map->p[i] = isl_basic_map_gist(map->p[i],
1723                                                 isl_basic_map_copy(context));
1724                 if (!map->p[i])
1725                         goto error;
1726         }
1727         isl_basic_map_free(context);
1728         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1729         return map;
1730 error:
1731         isl_map_free(map);
1732         isl_basic_map_free(context);
1733         return NULL;
1734 }
1735
1736 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1737                                                 struct isl_basic_set *context)
1738 {
1739         return (struct isl_basic_set *)isl_basic_map_gist(
1740                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1741 }
1742
1743 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1744 {
1745         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1746                                         (struct isl_basic_map *)context);
1747 }
1748
1749 /* Quick check to see if two basic maps are disjoint.
1750  * In particular, we reduce the equalities and inequalities of
1751  * one basic map in the context of the equalities of the other
1752  * basic map and check if we get a contradiction.
1753  */
1754 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1755         struct isl_basic_map *bmap2)
1756 {
1757         struct isl_vec *v = NULL;
1758         int *elim = NULL;
1759         unsigned total;
1760         int i;
1761
1762         if (!bmap1 || !bmap2)
1763                 return -1;
1764         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1765                         return -1);
1766         if (bmap1->n_div || bmap2->n_div)
1767                 return 0;
1768         if (!bmap1->n_eq && !bmap2->n_eq)
1769                 return 0;
1770
1771         total = isl_dim_total(bmap1->dim);
1772         if (total == 0)
1773                 return 0;
1774         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1775         if (!v)
1776                 goto error;
1777         elim = isl_alloc_array(bmap1->ctx, int, total);
1778         if (!elim)
1779                 goto error;
1780         compute_elimination_index(bmap1, elim);
1781         for (i = 0; i < bmap2->n_eq; ++i) {
1782                 int reduced;
1783                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1784                                                         bmap1, elim);
1785                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1786                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1787                         goto disjoint;
1788         }
1789         for (i = 0; i < bmap2->n_ineq; ++i) {
1790                 int reduced;
1791                 reduced = reduced_using_equalities(v->block.data,
1792                                                 bmap2->ineq[i], bmap1, elim);
1793                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1794                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1795                         goto disjoint;
1796         }
1797         compute_elimination_index(bmap2, elim);
1798         for (i = 0; i < bmap1->n_ineq; ++i) {
1799                 int reduced;
1800                 reduced = reduced_using_equalities(v->block.data,
1801                                                 bmap1->ineq[i], bmap2, elim);
1802                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1803                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1804                         goto disjoint;
1805         }
1806         isl_vec_free(v);
1807         free(elim);
1808         return 0;
1809 disjoint:
1810         isl_vec_free(v);
1811         free(elim);
1812         return 1;
1813 error:
1814         isl_vec_free(v);
1815         free(elim);
1816         return -1;
1817 }
1818
1819 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1820         struct isl_basic_set *bset2)
1821 {
1822         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1823                                               (struct isl_basic_map *)bset2);
1824 }
1825
1826 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1827 {
1828         int i, j;
1829
1830         if (!map1 || !map2)
1831                 return -1;
1832
1833         if (isl_map_fast_is_equal(map1, map2))
1834                 return 0;
1835
1836         for (i = 0; i < map1->n; ++i) {
1837                 for (j = 0; j < map2->n; ++j) {
1838                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1839                                                                map2->p[j]);
1840                         if (d != 1)
1841                                 return d;
1842                 }
1843         }
1844         return 1;
1845 }
1846
1847 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1848 {
1849         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1850                                         (struct isl_map *)set2);
1851 }
1852
1853 /* Check if we can combine a given div with lower bound l and upper
1854  * bound u with some other div and if so return that other div.
1855  * Otherwise return -1.
1856  *
1857  * We first check that
1858  *      - the bounds are opposites of each other (except for the constant
1859  *        term)
1860  *      - the bounds do not reference any other div
1861  *      - no div is defined in terms of this div
1862  *
1863  * Let m be the size of the range allowed on the div by the bounds.
1864  * That is, the bounds are of the form
1865  *
1866  *      e <= a <= e + m - 1
1867  *
1868  * with e some expression in the other variables.
1869  * We look for another div b such that no third div is defined in terms
1870  * of this second div b and such that in any constraint that contains
1871  * a (except for the given lower and upper bound), also contains b
1872  * with a coefficient that is m times that of b.
1873  * That is, all constraints (execpt for the lower and upper bound)
1874  * are of the form
1875  *
1876  *      e + f (a + m b) >= 0
1877  *
1878  * If so, we return b so that "a + m b" can be replaced by
1879  * a single div "c = a + m b".
1880  */
1881 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1882         unsigned div, unsigned l, unsigned u)
1883 {
1884         int i, j;
1885         unsigned dim;
1886         int coalesce = -1;
1887
1888         if (bmap->n_div <= 1)
1889                 return -1;
1890         dim = isl_dim_total(bmap->dim);
1891         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1892                 return -1;
1893         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1894                                    bmap->n_div - div - 1) != -1)
1895                 return -1;
1896         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1897                             dim + bmap->n_div))
1898                 return -1;
1899
1900         for (i = 0; i < bmap->n_div; ++i) {
1901                 if (isl_int_is_zero(bmap->div[i][0]))
1902                         continue;
1903                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1904                         return -1;
1905         }
1906
1907         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1908         if (isl_int_is_neg(bmap->ineq[l][0])) {
1909                 isl_int_sub(bmap->ineq[l][0],
1910                             bmap->ineq[l][0], bmap->ineq[u][0]);
1911                 bmap = isl_basic_map_copy(bmap);
1912                 bmap = isl_basic_map_set_to_empty(bmap);
1913                 isl_basic_map_free(bmap);
1914                 return -1;
1915         }
1916         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1917         for (i = 0; i < bmap->n_div; ++i) {
1918                 if (i == div)
1919                         continue;
1920                 if (!pairs[i])
1921                         continue;
1922                 for (j = 0; j < bmap->n_div; ++j) {
1923                         if (isl_int_is_zero(bmap->div[j][0]))
1924                                 continue;
1925                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1926                                 break;
1927                 }
1928                 if (j < bmap->n_div)
1929                         continue;
1930                 for (j = 0; j < bmap->n_ineq; ++j) {
1931                         int valid;
1932                         if (j == l || j == u)
1933                                 continue;
1934                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1935                                 continue;
1936                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1937                                 break;
1938                         isl_int_mul(bmap->ineq[j][1 + dim + div],
1939                                     bmap->ineq[j][1 + dim + div],
1940                                     bmap->ineq[l][0]);
1941                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1942                                            bmap->ineq[j][1 + dim + i]);
1943                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
1944                                          bmap->ineq[j][1 + dim + div],
1945                                          bmap->ineq[l][0]);
1946                         if (!valid)
1947                                 break;
1948                 }
1949                 if (j < bmap->n_ineq)
1950                         continue;
1951                 coalesce = i;
1952                 break;
1953         }
1954         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1955         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1956         return coalesce;
1957 }
1958
1959 /* Given a lower and an upper bound on div i, construct an inequality
1960  * that when nonnegative ensures that this pair of bounds always allows
1961  * for an integer value of the given div.
1962  * The lower bound is inequality l, while the upper bound is inequality u.
1963  * The constructed inequality is stored in ineq.
1964  * g, fl, fu are temporary scalars.
1965  *
1966  * Let the upper bound be
1967  *
1968  *      -n_u a + e_u >= 0
1969  *
1970  * and the lower bound
1971  *
1972  *      n_l a + e_l >= 0
1973  *
1974  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1975  * We have
1976  *
1977  *      - f_u e_l <= f_u f_l g a <= f_l e_u
1978  *
1979  * Since all variables are integer valued, this is equivalent to
1980  *
1981  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1982  *
1983  * If this interval is at least f_u f_l g, then it contains at least
1984  * one integer value for a.
1985  * That is, the test constraint is
1986  *
1987  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1988  */
1989 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
1990         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
1991 {
1992         unsigned dim;
1993         dim = isl_dim_total(bmap->dim);
1994
1995         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
1996         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
1997         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
1998         isl_int_neg(fu, fu);
1999         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2000                         1 + dim + bmap->n_div);
2001         isl_int_add(ineq[0], ineq[0], fl);
2002         isl_int_add(ineq[0], ineq[0], fu);
2003         isl_int_sub_ui(ineq[0], ineq[0], 1);
2004         isl_int_mul(g, g, fl);
2005         isl_int_mul(g, g, fu);
2006         isl_int_sub(ineq[0], ineq[0], g);
2007 }
2008
2009 /* Remove more kinds of divs that are not strictly needed.
2010  * In particular, if all pairs of lower and upper bounds on a div
2011  * are such that they allow at least one integer value of the div,
2012  * the we can eliminate the div using Fourier-Motzkin without
2013  * introducing any spurious solutions.
2014  */
2015 static struct isl_basic_map *drop_more_redundant_divs(
2016         struct isl_basic_map *bmap, int *pairs, int n)
2017 {
2018         struct isl_tab *tab = NULL;
2019         struct isl_vec *vec = NULL;
2020         unsigned dim;
2021         int remove = -1;
2022         isl_int g, fl, fu;
2023
2024         isl_int_init(g);
2025         isl_int_init(fl);
2026         isl_int_init(fu);
2027
2028         if (!bmap)
2029                 goto error;
2030
2031         dim = isl_dim_total(bmap->dim);
2032         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2033         if (!vec)
2034                 goto error;
2035
2036         tab = isl_tab_from_basic_map(bmap);
2037
2038         while (n > 0) {
2039                 int i, l, u;
2040                 int best = -1;
2041                 enum isl_lp_result res;
2042
2043                 for (i = 0; i < bmap->n_div; ++i) {
2044                         if (!pairs[i])
2045                                 continue;
2046                         if (best >= 0 && pairs[best] <= pairs[i])
2047                                 continue;
2048                         best = i;
2049                 }
2050
2051                 i = best;
2052                 for (l = 0; l < bmap->n_ineq; ++l) {
2053                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2054                                 continue;
2055                         for (u = 0; u < bmap->n_ineq; ++u) {
2056                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2057                                         continue;
2058                                 construct_test_ineq(bmap, i, l, u,
2059                                                     vec->el, g, fl, fu);
2060                                 res = isl_tab_min(tab, vec->el,
2061                                                   bmap->ctx->one, &g, NULL, 0);
2062                                 if (res == isl_lp_error)
2063                                         goto error;
2064                                 if (res == isl_lp_empty) {
2065                                         bmap = isl_basic_map_set_to_empty(bmap);
2066                                         break;
2067                                 }
2068                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2069                                         break;
2070                         }
2071                         if (u < bmap->n_ineq)
2072                                 break;
2073                 }
2074                 if (l == bmap->n_ineq) {
2075                         remove = i;
2076                         break;
2077                 }
2078                 pairs[i] = 0;
2079                 --n;
2080         }
2081
2082         isl_tab_free(tab);
2083         isl_vec_free(vec);
2084
2085         isl_int_clear(g);
2086         isl_int_clear(fl);
2087         isl_int_clear(fu);
2088
2089         free(pairs);
2090
2091         if (remove < 0)
2092                 return bmap;
2093
2094         bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2095         return isl_basic_map_drop_redundant_divs(bmap);
2096 error:
2097         free(pairs);
2098         isl_basic_map_free(bmap);
2099         isl_tab_free(tab);
2100         isl_vec_free(vec);
2101         isl_int_clear(g);
2102         isl_int_clear(fl);
2103         isl_int_clear(fu);
2104         return NULL;
2105 }
2106
2107 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2108  * and the upper bound u, div1 always occurs together with div2 in the form
2109  * (div1 + m div2), where m is the constant range on the variable div1
2110  * allowed by l and u, replace the pair div1 and div2 by a single
2111  * div that is equal to div1 + m div2.
2112  *
2113  * The new div will appear in the location that contains div2.
2114  * We need to modify all constraints that contain
2115  * div2 = (div - div1) / m
2116  * (If a constraint does not contain div2, it will also not contain div1.)
2117  * If the constraint also contains div1, then we know they appear
2118  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2119  * i.e., the coefficient of div is f.
2120  *
2121  * Otherwise, we first need to introduce div1 into the constraint.
2122  * Let the l be
2123  *
2124  *      div1 + f >=0
2125  *
2126  * and u
2127  *
2128  *      -div1 + f' >= 0
2129  *
2130  * A lower bound on div2
2131  *
2132  *      n div2 + t >= 0
2133  *
2134  * can be replaced by
2135  *
2136  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2137  *
2138  * with g = gcd(m,n).
2139  * An upper bound
2140  *
2141  *      -n div2 + t >= 0
2142  *
2143  * can be replaced by
2144  *
2145  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2146  *
2147  * These constraint are those that we would obtain from eliminating
2148  * div1 using Fourier-Motzkin.
2149  *
2150  * After all constraints have been modified, we drop the lower and upper
2151  * bound and then drop div1.
2152  */
2153 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2154         unsigned div1, unsigned div2, unsigned l, unsigned u)
2155 {
2156         isl_int a;
2157         isl_int b;
2158         isl_int m;
2159         unsigned dim, total;
2160         int i;
2161
2162         dim = isl_dim_total(bmap->dim);
2163         total = 1 + dim + bmap->n_div;
2164
2165         isl_int_init(a);
2166         isl_int_init(b);
2167         isl_int_init(m);
2168         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2169         isl_int_add_ui(m, m, 1);
2170
2171         for (i = 0; i < bmap->n_ineq; ++i) {
2172                 if (i == l || i == u)
2173                         continue;
2174                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2175                         continue;
2176                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2177                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2178                         isl_int_divexact(a, m, b);
2179                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2180                         if (isl_int_is_pos(b)) {
2181                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2182                                                 b, bmap->ineq[l], total);
2183                         } else {
2184                                 isl_int_neg(b, b);
2185                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2186                                                 b, bmap->ineq[u], total);
2187                         }
2188                 }
2189                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2190                             bmap->ineq[i][1 + dim + div1]);
2191                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2192         }
2193
2194         isl_int_clear(a);
2195         isl_int_clear(b);
2196         isl_int_clear(m);
2197         if (l > u) {
2198                 isl_basic_map_drop_inequality(bmap, l);
2199                 isl_basic_map_drop_inequality(bmap, u);
2200         } else {
2201                 isl_basic_map_drop_inequality(bmap, u);
2202                 isl_basic_map_drop_inequality(bmap, l);
2203         }
2204         bmap = isl_basic_map_drop_div(bmap, div1);
2205         return bmap;
2206 }
2207
2208 /* First check if we can coalesce any pair of divs and
2209  * then continue with dropping more redundant divs.
2210  *
2211  * We loop over all pairs of lower and upper bounds on a div
2212  * with coefficient 1 and -1, respectively, check if there
2213  * is any other div "c" with which we can coalesce the div
2214  * and if so, perform the coalescing.
2215  */
2216 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2217         struct isl_basic_map *bmap, int *pairs, int n)
2218 {
2219         int i, l, u;
2220         unsigned dim;
2221
2222         dim = isl_dim_total(bmap->dim);
2223
2224         for (i = 0; i < bmap->n_div; ++i) {
2225                 if (!pairs[i])
2226                         continue;
2227                 for (l = 0; l < bmap->n_ineq; ++l) {
2228                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2229                                 continue;
2230                         for (u = 0; u < bmap->n_ineq; ++u) {
2231                                 int c;
2232
2233                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2234                                         continue;
2235                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2236                                 if (c < 0)
2237                                         continue;
2238                                 free(pairs);
2239                                 bmap = coalesce_divs(bmap, i, c, l, u);
2240                                 return isl_basic_map_drop_redundant_divs(bmap);
2241                         }
2242                 }
2243         }
2244
2245         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2246                 return bmap;
2247
2248         return drop_more_redundant_divs(bmap, pairs, n);
2249 }
2250
2251 /* Remove divs that are not strictly needed.
2252  * In particular, if a div only occurs positively (or negatively)
2253  * in constraints, then it can simply be dropped.
2254  * Also, if a div occurs only occurs in two constraints and if moreover
2255  * those two constraints are opposite to each other, except for the constant
2256  * term and if the sum of the constant terms is such that for any value
2257  * of the other values, there is always at least one integer value of the
2258  * div, i.e., if one plus this sum is greater than or equal to
2259  * the (absolute value) of the coefficent of the div in the constraints,
2260  * then we can also simply drop the div.
2261  *
2262  * If any divs are left after these simple checks then we move on
2263  * to more complicated cases in drop_more_redundant_divs.
2264  */
2265 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2266         struct isl_basic_map *bmap)
2267 {
2268         int i, j;
2269         unsigned off;
2270         int *pairs = NULL;
2271         int n = 0;
2272
2273         if (!bmap)
2274                 goto error;
2275
2276         off = isl_dim_total(bmap->dim);
2277         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2278         if (!pairs)
2279                 goto error;
2280
2281         for (i = 0; i < bmap->n_div; ++i) {
2282                 int pos, neg;
2283                 int last_pos, last_neg;
2284                 int redundant;
2285                 int defined;
2286
2287                 defined = !isl_int_is_zero(bmap->div[i][0]);
2288                 for (j = 0; j < bmap->n_eq; ++j)
2289                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2290                                 break;
2291                 if (j < bmap->n_eq)
2292                         continue;
2293                 ++n;
2294                 pos = neg = 0;
2295                 for (j = 0; j < bmap->n_ineq; ++j) {
2296                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2297                                 last_pos = j;
2298                                 ++pos;
2299                         }
2300                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2301                                 last_neg = j;
2302                                 ++neg;
2303                         }
2304                 }
2305                 pairs[i] = pos * neg;
2306                 if (pairs[i] == 0) {
2307                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2308                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2309                                         isl_basic_map_drop_inequality(bmap, j);
2310                         bmap = isl_basic_map_drop_div(bmap, i);
2311                         free(pairs);
2312                         return isl_basic_map_drop_redundant_divs(bmap);
2313                 }
2314                 if (pairs[i] != 1)
2315                         continue;
2316                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2317                                     bmap->ineq[last_neg] + 1,
2318                                     off + bmap->n_div))
2319                         continue;
2320
2321                 isl_int_add(bmap->ineq[last_pos][0],
2322                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2323                 isl_int_add_ui(bmap->ineq[last_pos][0],
2324                                bmap->ineq[last_pos][0], 1);
2325                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2326                                 bmap->ineq[last_pos][1+off+i]);
2327                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2328                                bmap->ineq[last_pos][0], 1);
2329                 isl_int_sub(bmap->ineq[last_pos][0],
2330                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2331                 if (!redundant) {
2332                         if (defined ||
2333                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2334                                 pairs[i] = 0;
2335                                 --n;
2336                                 continue;
2337                         }
2338                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2339                         bmap = isl_basic_map_simplify(bmap);
2340                         free(pairs);
2341                         return isl_basic_map_drop_redundant_divs(bmap);
2342                 }
2343                 if (last_pos > last_neg) {
2344                         isl_basic_map_drop_inequality(bmap, last_pos);
2345                         isl_basic_map_drop_inequality(bmap, last_neg);
2346                 } else {
2347                         isl_basic_map_drop_inequality(bmap, last_neg);
2348                         isl_basic_map_drop_inequality(bmap, last_pos);
2349                 }
2350                 bmap = isl_basic_map_drop_div(bmap, i);
2351                 free(pairs);
2352                 return isl_basic_map_drop_redundant_divs(bmap);
2353         }
2354
2355         if (n > 0)
2356                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2357
2358         free(pairs);
2359         return bmap;
2360 error:
2361         free(pairs);
2362         isl_basic_map_free(bmap);
2363         return NULL;
2364 }
2365
2366 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2367         struct isl_basic_set *bset)
2368 {
2369         return (struct isl_basic_set *)
2370             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2371 }
2372
2373 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2374 {
2375         int i;
2376
2377         if (!map)
2378                 return NULL;
2379         for (i = 0; i < map->n; ++i) {
2380                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2381                 if (!map->p[i])
2382                         goto error;
2383         }
2384         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2385         return map;
2386 error:
2387         isl_map_free(map);
2388         return NULL;
2389 }
2390
2391 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2392 {
2393         return (struct isl_set *)
2394             isl_map_drop_redundant_divs((struct isl_map *)set);
2395 }