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                         if (progress)
1011                                 *progress = 1;
1012                         isl_basic_map_drop_inequality(bmap, l);
1013                         isl_basic_map_inequality_to_equality(bmap, k);
1014                 } else
1015                         bmap = isl_basic_map_set_to_empty(bmap);
1016                 break;
1017         }
1018         isl_int_clear(sum);
1019
1020         free(index);
1021         return bmap;
1022 }
1023
1024
1025 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1026 {
1027         int progress = 1;
1028         if (!bmap)
1029                 return NULL;
1030         while (progress) {
1031                 progress = 0;
1032                 bmap = isl_basic_map_normalize_constraints(bmap);
1033                 bmap = remove_duplicate_divs(bmap, &progress);
1034                 bmap = eliminate_divs_eq(bmap, &progress);
1035                 bmap = eliminate_divs_ineq(bmap, &progress);
1036                 bmap = isl_basic_map_gauss(bmap, &progress);
1037                 /* requires equalities in normal form */
1038                 bmap = normalize_divs(bmap, &progress);
1039                 bmap = remove_duplicate_constraints(bmap, &progress);
1040         }
1041         return bmap;
1042 }
1043
1044 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1045 {
1046         return (struct isl_basic_set *)
1047                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1048 }
1049
1050
1051 /* If the only constraints a div d=floor(f/m)
1052  * appears in are its two defining constraints
1053  *
1054  *      f - m d >=0
1055  *      -(f - (m - 1)) + m d >= 0
1056  *
1057  * then it can safely be removed.
1058  */
1059 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1060 {
1061         int i;
1062         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1063
1064         for (i = 0; i < bmap->n_eq; ++i)
1065                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1066                         return 0;
1067
1068         for (i = 0; i < bmap->n_ineq; ++i) {
1069                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1070                         continue;
1071                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1072                         int neg;
1073                         isl_int_sub(bmap->div[div][1],
1074                                         bmap->div[div][1], bmap->div[div][0]);
1075                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1076                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1077                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1078                         isl_int_add(bmap->div[div][1],
1079                                         bmap->div[div][1], bmap->div[div][0]);
1080                         if (!neg)
1081                                 return 0;
1082                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1083                                                     bmap->n_div-div-1) != -1)
1084                                 return 0;
1085                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1086                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1087                                 return 0;
1088                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1089                                                     bmap->n_div-div-1) != -1)
1090                                 return 0;
1091                 } else
1092                         return 0;
1093         }
1094
1095         for (i = 0; i < bmap->n_div; ++i)
1096                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1097                         return 0;
1098
1099         return 1;
1100 }
1101
1102 /*
1103  * Remove divs that don't occur in any of the constraints or other divs.
1104  * These can arise when dropping some of the variables in a quast
1105  * returned by piplib.
1106  */
1107 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1108 {
1109         int i;
1110
1111         if (!bmap)
1112                 return NULL;
1113
1114         for (i = bmap->n_div-1; i >= 0; --i) {
1115                 if (!div_is_redundant(bmap, i))
1116                         continue;
1117                 bmap = isl_basic_map_drop_div(bmap, i);
1118         }
1119         return bmap;
1120 }
1121
1122 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1123 {
1124         bmap = remove_redundant_divs(bmap);
1125         if (!bmap)
1126                 return NULL;
1127         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1128         return bmap;
1129 }
1130
1131 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1132 {
1133         return (struct isl_basic_set *)
1134                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1135 }
1136
1137 struct isl_set *isl_set_finalize(struct isl_set *set)
1138 {
1139         int i;
1140
1141         if (!set)
1142                 return NULL;
1143         for (i = 0; i < set->n; ++i) {
1144                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1145                 if (!set->p[i])
1146                         goto error;
1147         }
1148         return set;
1149 error:
1150         isl_set_free(set);
1151         return NULL;
1152 }
1153
1154 struct isl_map *isl_map_finalize(struct isl_map *map)
1155 {
1156         int i;
1157
1158         if (!map)
1159                 return NULL;
1160         for (i = 0; i < map->n; ++i) {
1161                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1162                 if (!map->p[i])
1163                         goto error;
1164         }
1165         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1166         return map;
1167 error:
1168         isl_map_free(map);
1169         return NULL;
1170 }
1171
1172
1173 /* Remove definition of any div that is defined in terms of the given variable.
1174  * The div itself is not removed.  Functions such as
1175  * eliminate_divs_ineq depend on the other divs remaining in place.
1176  */
1177 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1178                                                                         int pos)
1179 {
1180         int i;
1181
1182         for (i = 0; i < bmap->n_div; ++i) {
1183                 if (isl_int_is_zero(bmap->div[i][0]))
1184                         continue;
1185                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1186                         continue;
1187                 isl_int_set_si(bmap->div[i][0], 0);
1188         }
1189         return bmap;
1190 }
1191
1192 /* Eliminate the specified variables from the constraints using
1193  * Fourier-Motzkin.  The variables themselves are not removed.
1194  */
1195 struct isl_basic_map *isl_basic_map_eliminate_vars(
1196         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1197 {
1198         int d;
1199         int i, j, k;
1200         unsigned total;
1201
1202         if (n == 0)
1203                 return bmap;
1204         if (!bmap)
1205                 return NULL;
1206         total = isl_basic_map_total_dim(bmap);
1207
1208         bmap = isl_basic_map_cow(bmap);
1209         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1210                 bmap = remove_dependent_vars(bmap, d);
1211
1212         for (d = pos + n - 1;
1213              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1214                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1215         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1216                 int n_lower, n_upper;
1217                 if (!bmap)
1218                         return NULL;
1219                 for (i = 0; i < bmap->n_eq; ++i) {
1220                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1221                                 continue;
1222                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1223                         isl_basic_map_drop_equality(bmap, i);
1224                         break;
1225                 }
1226                 if (i < bmap->n_eq)
1227                         continue;
1228                 n_lower = 0;
1229                 n_upper = 0;
1230                 for (i = 0; i < bmap->n_ineq; ++i) {
1231                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1232                                 n_lower++;
1233                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1234                                 n_upper++;
1235                 }
1236                 bmap = isl_basic_map_extend_constraints(bmap,
1237                                 0, n_lower * n_upper);
1238                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1239                         int last;
1240                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1241                                 continue;
1242                         last = -1;
1243                         for (j = 0; j < i; ++j) {
1244                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1245                                         continue;
1246                                 last = j;
1247                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1248                                     isl_int_sgn(bmap->ineq[j][1+d]))
1249                                         continue;
1250                                 k = isl_basic_map_alloc_inequality(bmap);
1251                                 if (k < 0)
1252                                         goto error;
1253                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1254                                                 1+total);
1255                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1256                                                 1+d, 1+total, NULL);
1257                         }
1258                         isl_basic_map_drop_inequality(bmap, i);
1259                         i = last + 1;
1260                 }
1261                 if (n_lower > 0 && n_upper > 0) {
1262                         bmap = isl_basic_map_normalize_constraints(bmap);
1263                         bmap = remove_duplicate_constraints(bmap, NULL);
1264                         bmap = isl_basic_map_gauss(bmap, NULL);
1265                         bmap = isl_basic_map_convex_hull(bmap);
1266                         if (!bmap)
1267                                 goto error;
1268                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1269                                 break;
1270                 }
1271         }
1272         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1273         return bmap;
1274 error:
1275         isl_basic_map_free(bmap);
1276         return NULL;
1277 }
1278
1279 struct isl_basic_set *isl_basic_set_eliminate_vars(
1280         struct isl_basic_set *bset, unsigned pos, unsigned n)
1281 {
1282         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1283                         (struct isl_basic_map *)bset, pos, n);
1284 }
1285
1286 /* Don't assume equalities are in order, because align_divs
1287  * may have changed the order of the divs.
1288  */
1289 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1290 {
1291         int d, i;
1292         unsigned total;
1293
1294         total = isl_dim_total(bmap->dim);
1295         for (d = 0; d < total; ++d)
1296                 elim[d] = -1;
1297         for (i = 0; i < bmap->n_eq; ++i) {
1298                 for (d = total - 1; d >= 0; --d) {
1299                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1300                                 continue;
1301                         elim[d] = i;
1302                         break;
1303                 }
1304         }
1305 }
1306
1307 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1308 {
1309         compute_elimination_index((struct isl_basic_map *)bset, elim);
1310 }
1311
1312 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1313         struct isl_basic_map *bmap, int *elim)
1314 {
1315         int d;
1316         int copied = 0;
1317         unsigned total;
1318
1319         total = isl_dim_total(bmap->dim);
1320         for (d = total - 1; d >= 0; --d) {
1321                 if (isl_int_is_zero(src[1+d]))
1322                         continue;
1323                 if (elim[d] == -1)
1324                         continue;
1325                 if (!copied) {
1326                         isl_seq_cpy(dst, src, 1 + total);
1327                         copied = 1;
1328                 }
1329                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1330         }
1331         return copied;
1332 }
1333
1334 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1335         struct isl_basic_set *bset, int *elim)
1336 {
1337         return reduced_using_equalities(dst, src,
1338                                         (struct isl_basic_map *)bset, elim);
1339 }
1340
1341 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1342         struct isl_basic_set *bset, struct isl_basic_set *context)
1343 {
1344         int i;
1345         int *elim;
1346
1347         if (!bset || !context)
1348                 goto error;
1349
1350         bset = isl_basic_set_cow(bset);
1351         if (!bset)
1352                 goto error;
1353
1354         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1355         if (!elim)
1356                 goto error;
1357         set_compute_elimination_index(context, elim);
1358         for (i = 0; i < bset->n_eq; ++i)
1359                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1360                                                         context, elim);
1361         for (i = 0; i < bset->n_ineq; ++i)
1362                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1363                                                         context, elim);
1364         isl_basic_set_free(context);
1365         free(elim);
1366         bset = isl_basic_set_simplify(bset);
1367         bset = isl_basic_set_finalize(bset);
1368         return bset;
1369 error:
1370         isl_basic_set_free(bset);
1371         isl_basic_set_free(context);
1372         return NULL;
1373 }
1374
1375 static struct isl_basic_set *remove_shifted_constraints(
1376         struct isl_basic_set *bset, struct isl_basic_set *context)
1377 {
1378         unsigned int size;
1379         isl_int ***index;
1380         int bits;
1381         int k, h, l;
1382
1383         if (!bset)
1384                 return NULL;
1385
1386         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1387         bits = ffs(size) - 1;
1388         index = isl_calloc_array(ctx, isl_int **, size);
1389         if (!index)
1390                 return bset;
1391
1392         for (k = 0; k < context->n_ineq; ++k) {
1393                 h = set_hash_index(index, size, bits, context, k);
1394                 index[h] = &context->ineq[k];
1395         }
1396         for (k = 0; k < bset->n_ineq; ++k) {
1397                 h = set_hash_index(index, size, bits, bset, k);
1398                 if (!index[h])
1399                         continue;
1400                 l = index[h] - &context->ineq[0];
1401                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1402                         continue;
1403                 bset = isl_basic_set_cow(bset);
1404                 if (!bset)
1405                         goto error;
1406                 isl_basic_set_drop_inequality(bset, k);
1407                 --k;
1408         }
1409         free(index);
1410         return bset;
1411 error:
1412         free(index);
1413         return bset;
1414 }
1415
1416 /* Tighten (decrease) the constant terms of the inequalities based
1417  * on the equalities, without removing any integer points.
1418  * For example, if there is an equality
1419  *
1420  *              i = 3 * j
1421  *
1422  * and an inequality
1423  *
1424  *              i >= 1
1425  *
1426  * then we want to replace the inequality by
1427  *
1428  *              i >= 3
1429  *
1430  * We do this by computing a variable compression and translating
1431  * the constraints to the compressed space.
1432  * If any constraint has coefficients (except the contant term)
1433  * with a common factor "f", then we can replace the constant term "c"
1434  * by
1435  *
1436  *              f * floor(c/f)
1437  *
1438  * That is, we add
1439  *
1440  *              f * floor(c/f) - c = -fract(c/f)
1441  *
1442  * and we can add the same value to the original constraint.
1443  *
1444  * In the example, the compressed space only contains "j",
1445  * and the inequality translates to
1446  *
1447  *              3 * j - 1 >= 0
1448  *
1449  * We add -fract(-1/3) = -2 to the original constraint to obtain
1450  *
1451  *              i - 3 >= 0
1452  */
1453 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1454         struct isl_basic_set *bset)
1455 {
1456         int i;
1457         unsigned total;
1458         struct isl_mat *B, *C;
1459         isl_int gcd;
1460
1461         if (!bset)
1462                 return NULL;
1463
1464         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1465                 return bset;
1466
1467         if (!bset->n_ineq)
1468                 return bset;
1469
1470         bset = isl_basic_set_cow(bset);
1471         if (!bset)
1472                 return NULL;
1473
1474         total = isl_basic_set_total_dim(bset);
1475         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1476         C = isl_mat_variable_compression(B, NULL);
1477         if (!C)
1478                 return bset;
1479         if (C->n_col == 0) {
1480                 isl_mat_free(C);
1481                 return isl_basic_set_set_to_empty(bset);
1482         }
1483         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1484                                                 0, bset->n_ineq, 0, 1 + total);
1485         C = isl_mat_product(B, C);
1486         if (!C)
1487                 return bset;
1488
1489         isl_int_init(gcd);
1490         for (i = 0; i < bset->n_ineq; ++i) {
1491                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1492                 if (isl_int_is_one(gcd))
1493                         continue;
1494                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1495                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1496         }
1497         isl_int_clear(gcd);
1498
1499         isl_mat_free(C);
1500
1501         return bset;
1502 }
1503
1504 /* Remove all information from bset that is redundant in the context
1505  * of context.  In particular, equalities that are linear combinations
1506  * of those in context are removed.  Then the inequalities that are
1507  * redundant in the context of the equalities and inequalities of
1508  * context are removed.
1509  *
1510  * We first simplify the constraints of "bset" in the context of the
1511  * equalities of "context".
1512  * Then we simplify the inequalities of the context in the context
1513  * of the equalities of bset and remove the inequalities from "bset"
1514  * that are obviously redundant with respect to some inequality in "context".
1515  *
1516  * If there are any inequalities left, we construct a tableau for
1517  * the context and then add the inequalities of "bset".
1518  * Before adding these equalities, we freeze all constraints such that
1519  * they won't be considered redundant in terms of the constraints of "bset".
1520  * Then we detect all equalities and redundant constraints (among the
1521  * constraints that weren't frozen) and update bset according to the results.
1522  * We have to be careful here because we don't want any of the context
1523  * constraints to remain and because we haven't added the equalities of "bset"
1524  * to the tableau so we temporarily have to pretend that there were no
1525  * equalities.
1526  */
1527 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1528         struct isl_basic_set *context)
1529 {
1530         int i;
1531         struct isl_tab *tab;
1532         unsigned context_ineq;
1533         struct isl_basic_set *combined = NULL;
1534
1535         if (!context || !bset)
1536                 goto error;
1537
1538         if (context->n_eq > 0)
1539                 bset = isl_basic_set_reduce_using_equalities(bset,
1540                                         isl_basic_set_copy(context));
1541         if (!bset)
1542                 goto error;
1543         if (isl_basic_set_fast_is_empty(bset))
1544                 goto done;
1545         if (!bset->n_ineq)
1546                 goto done;
1547
1548         if (bset->n_eq > 0) {
1549                 struct isl_basic_set *affine_hull;
1550                 affine_hull = isl_basic_set_copy(bset);
1551                 affine_hull = isl_basic_set_cow(affine_hull);
1552                 if (!affine_hull)
1553                         goto error;
1554                 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1555                 context = isl_basic_set_intersect(context, affine_hull);
1556                 context = isl_basic_set_gauss(context, NULL);
1557                 context = normalize_constraints_in_compressed_space(context);
1558         }
1559         if (!context)
1560                 goto error;
1561         if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1562                 isl_basic_set_free(bset);
1563                 return context;
1564         }
1565         if (!context->n_ineq)
1566                 goto done;
1567         bset = remove_shifted_constraints(bset, context);
1568         if (!bset->n_ineq)
1569                 goto done;
1570         isl_basic_set_free_equality(context, context->n_eq);
1571         context_ineq = context->n_ineq;
1572         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1573         combined = isl_basic_set_extend_constraints(combined,
1574                                                     bset->n_eq, bset->n_ineq);
1575         tab = isl_tab_from_basic_set(combined);
1576         if (!tab)
1577                 goto error;
1578         for (i = 0; i < context_ineq; ++i)
1579                 tab->con[i].frozen = 1;
1580         tab = isl_tab_extend(tab, bset->n_ineq);
1581         if (!tab)
1582                 goto error;
1583         for (i = 0; i < bset->n_ineq; ++i)
1584                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1585                         goto error;
1586         bset = isl_basic_set_add_constraints(combined, bset, 0);
1587         tab = isl_tab_detect_implicit_equalities(tab);
1588         tab = isl_tab_detect_redundant(tab);
1589         if (!tab)
1590                 goto error2;
1591         for (i = 0; i < context_ineq; ++i) {
1592                 tab->con[i].is_zero = 0;
1593                 tab->con[i].is_redundant = 1;
1594         }
1595         bset = isl_basic_set_update_from_tab(bset, tab);
1596         isl_tab_free(tab);
1597         ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1598         ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1599 done:
1600         bset = isl_basic_set_simplify(bset);
1601         bset = isl_basic_set_finalize(bset);
1602         isl_basic_set_free(context);
1603         return bset;
1604 error:
1605         isl_basic_set_free(combined);
1606 error2:
1607         isl_basic_set_free(bset);
1608         isl_basic_set_free(context);
1609         return NULL;
1610 }
1611
1612 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1613  * We simply add the equalities in context to bmap and then do a regular
1614  * div normalizations.  Better results can be obtained by normalizing
1615  * only the divs in bmap than do not also appear in context.
1616  * We need to be careful to reduce the divs using the equalities
1617  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1618  * spurious constraints.
1619  */
1620 static struct isl_basic_map *normalize_divs_in_context(
1621         struct isl_basic_map *bmap, struct isl_basic_map *context)
1622 {
1623         int i;
1624         unsigned total_context;
1625         int div_eq;
1626
1627         div_eq = n_pure_div_eq(bmap);
1628         if (div_eq == 0)
1629                 return bmap;
1630
1631         if (context->n_div > 0)
1632                 bmap = isl_basic_map_align_divs(bmap, context);
1633
1634         total_context = isl_basic_map_total_dim(context);
1635         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1636         for (i = 0; i < context->n_eq; ++i) {
1637                 int k;
1638                 k = isl_basic_map_alloc_equality(bmap);
1639                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1640                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1641                                 isl_basic_map_total_dim(bmap) - total_context);
1642         }
1643         bmap = isl_basic_map_gauss(bmap, NULL);
1644         bmap = normalize_divs(bmap, NULL);
1645         bmap = isl_basic_map_gauss(bmap, NULL);
1646         return bmap;
1647 }
1648
1649 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1650         struct isl_basic_map *context)
1651 {
1652         struct isl_basic_set *bset;
1653
1654         if (!bmap || !context)
1655                 goto error;
1656
1657         if (isl_basic_map_is_universe(context)) {
1658                 isl_basic_map_free(context);
1659                 return bmap;
1660         }
1661         if (isl_basic_map_is_universe(bmap)) {
1662                 isl_basic_map_free(context);
1663                 return bmap;
1664         }
1665         if (isl_basic_map_fast_is_empty(context)) {
1666                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1667                 isl_basic_map_free(context);
1668                 isl_basic_map_free(bmap);
1669                 return isl_basic_map_universe(dim);
1670         }
1671         if (isl_basic_map_fast_is_empty(bmap)) {
1672                 isl_basic_map_free(context);
1673                 return bmap;
1674         }
1675
1676         bmap = isl_basic_map_convex_hull(bmap);
1677         context = isl_basic_map_convex_hull(context);
1678
1679         if (context->n_eq)
1680                 bmap = normalize_divs_in_context(bmap, context);
1681
1682         context = isl_basic_map_align_divs(context, bmap);
1683         bmap = isl_basic_map_align_divs(bmap, context);
1684
1685         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1686                          isl_basic_map_underlying_set(context));
1687
1688         return isl_basic_map_overlying_set(bset, bmap);
1689 error:
1690         isl_basic_map_free(bmap);
1691         isl_basic_map_free(context);
1692         return NULL;
1693 }
1694
1695 /*
1696  * Assumes context has no implicit divs.
1697  */
1698 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1699 {
1700         int i;
1701
1702         if (!map || !context)
1703                 goto error;;
1704
1705         if (isl_basic_map_is_universe(context)) {
1706                 isl_basic_map_free(context);
1707                 return map;
1708         }
1709         if (isl_basic_map_fast_is_empty(context)) {
1710                 struct isl_dim *dim = isl_dim_copy(map->dim);
1711                 isl_basic_map_free(context);
1712                 isl_map_free(map);
1713                 return isl_map_universe(dim);
1714         }
1715
1716         context = isl_basic_map_convex_hull(context);
1717         map = isl_map_cow(map);
1718         if (!map || !context)
1719                 goto error;;
1720         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1721         map = isl_map_compute_divs(map);
1722         for (i = 0; i < map->n; ++i)
1723                 context = isl_basic_map_align_divs(context, map->p[i]);
1724         for (i = 0; i < map->n; ++i) {
1725                 map->p[i] = isl_basic_map_gist(map->p[i],
1726                                                 isl_basic_map_copy(context));
1727                 if (!map->p[i])
1728                         goto error;
1729         }
1730         isl_basic_map_free(context);
1731         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1732         return map;
1733 error:
1734         isl_map_free(map);
1735         isl_basic_map_free(context);
1736         return NULL;
1737 }
1738
1739 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1740                                                 struct isl_basic_set *context)
1741 {
1742         return (struct isl_basic_set *)isl_basic_map_gist(
1743                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1744 }
1745
1746 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1747 {
1748         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1749                                         (struct isl_basic_map *)context);
1750 }
1751
1752 /* Quick check to see if two basic maps are disjoint.
1753  * In particular, we reduce the equalities and inequalities of
1754  * one basic map in the context of the equalities of the other
1755  * basic map and check if we get a contradiction.
1756  */
1757 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1758         struct isl_basic_map *bmap2)
1759 {
1760         struct isl_vec *v = NULL;
1761         int *elim = NULL;
1762         unsigned total;
1763         int i;
1764
1765         if (!bmap1 || !bmap2)
1766                 return -1;
1767         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1768                         return -1);
1769         if (bmap1->n_div || bmap2->n_div)
1770                 return 0;
1771         if (!bmap1->n_eq && !bmap2->n_eq)
1772                 return 0;
1773
1774         total = isl_dim_total(bmap1->dim);
1775         if (total == 0)
1776                 return 0;
1777         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1778         if (!v)
1779                 goto error;
1780         elim = isl_alloc_array(bmap1->ctx, int, total);
1781         if (!elim)
1782                 goto error;
1783         compute_elimination_index(bmap1, elim);
1784         for (i = 0; i < bmap2->n_eq; ++i) {
1785                 int reduced;
1786                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1787                                                         bmap1, elim);
1788                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1789                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1790                         goto disjoint;
1791         }
1792         for (i = 0; i < bmap2->n_ineq; ++i) {
1793                 int reduced;
1794                 reduced = reduced_using_equalities(v->block.data,
1795                                                 bmap2->ineq[i], bmap1, elim);
1796                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1797                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1798                         goto disjoint;
1799         }
1800         compute_elimination_index(bmap2, elim);
1801         for (i = 0; i < bmap1->n_ineq; ++i) {
1802                 int reduced;
1803                 reduced = reduced_using_equalities(v->block.data,
1804                                                 bmap1->ineq[i], bmap2, elim);
1805                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1806                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1807                         goto disjoint;
1808         }
1809         isl_vec_free(v);
1810         free(elim);
1811         return 0;
1812 disjoint:
1813         isl_vec_free(v);
1814         free(elim);
1815         return 1;
1816 error:
1817         isl_vec_free(v);
1818         free(elim);
1819         return -1;
1820 }
1821
1822 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1823         struct isl_basic_set *bset2)
1824 {
1825         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1826                                               (struct isl_basic_map *)bset2);
1827 }
1828
1829 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1830 {
1831         int i, j;
1832
1833         if (!map1 || !map2)
1834                 return -1;
1835
1836         if (isl_map_fast_is_equal(map1, map2))
1837                 return 0;
1838
1839         for (i = 0; i < map1->n; ++i) {
1840                 for (j = 0; j < map2->n; ++j) {
1841                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1842                                                                map2->p[j]);
1843                         if (d != 1)
1844                                 return d;
1845                 }
1846         }
1847         return 1;
1848 }
1849
1850 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1851 {
1852         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1853                                         (struct isl_map *)set2);
1854 }
1855
1856 /* Check if we can combine a given div with lower bound l and upper
1857  * bound u with some other div and if so return that other div.
1858  * Otherwise return -1.
1859  *
1860  * We first check that
1861  *      - the bounds are opposites of each other (except for the constant
1862  *        term)
1863  *      - the bounds do not reference any other div
1864  *      - no div is defined in terms of this div
1865  *
1866  * Let m be the size of the range allowed on the div by the bounds.
1867  * That is, the bounds are of the form
1868  *
1869  *      e <= a <= e + m - 1
1870  *
1871  * with e some expression in the other variables.
1872  * We look for another div b such that no third div is defined in terms
1873  * of this second div b and such that in any constraint that contains
1874  * a (except for the given lower and upper bound), also contains b
1875  * with a coefficient that is m times that of b.
1876  * That is, all constraints (execpt for the lower and upper bound)
1877  * are of the form
1878  *
1879  *      e + f (a + m b) >= 0
1880  *
1881  * If so, we return b so that "a + m b" can be replaced by
1882  * a single div "c = a + m b".
1883  */
1884 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1885         unsigned div, unsigned l, unsigned u)
1886 {
1887         int i, j;
1888         unsigned dim;
1889         int coalesce = -1;
1890
1891         if (bmap->n_div <= 1)
1892                 return -1;
1893         dim = isl_dim_total(bmap->dim);
1894         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1895                 return -1;
1896         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1897                                    bmap->n_div - div - 1) != -1)
1898                 return -1;
1899         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1900                             dim + bmap->n_div))
1901                 return -1;
1902
1903         for (i = 0; i < bmap->n_div; ++i) {
1904                 if (isl_int_is_zero(bmap->div[i][0]))
1905                         continue;
1906                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1907                         return -1;
1908         }
1909
1910         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1911         if (isl_int_is_neg(bmap->ineq[l][0])) {
1912                 isl_int_sub(bmap->ineq[l][0],
1913                             bmap->ineq[l][0], bmap->ineq[u][0]);
1914                 bmap = isl_basic_map_copy(bmap);
1915                 bmap = isl_basic_map_set_to_empty(bmap);
1916                 isl_basic_map_free(bmap);
1917                 return -1;
1918         }
1919         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1920         for (i = 0; i < bmap->n_div; ++i) {
1921                 if (i == div)
1922                         continue;
1923                 if (!pairs[i])
1924                         continue;
1925                 for (j = 0; j < bmap->n_div; ++j) {
1926                         if (isl_int_is_zero(bmap->div[j][0]))
1927                                 continue;
1928                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1929                                 break;
1930                 }
1931                 if (j < bmap->n_div)
1932                         continue;
1933                 for (j = 0; j < bmap->n_ineq; ++j) {
1934                         int valid;
1935                         if (j == l || j == u)
1936                                 continue;
1937                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1938                                 continue;
1939                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1940                                 break;
1941                         isl_int_mul(bmap->ineq[j][1 + dim + div],
1942                                     bmap->ineq[j][1 + dim + div],
1943                                     bmap->ineq[l][0]);
1944                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1945                                            bmap->ineq[j][1 + dim + i]);
1946                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
1947                                          bmap->ineq[j][1 + dim + div],
1948                                          bmap->ineq[l][0]);
1949                         if (!valid)
1950                                 break;
1951                 }
1952                 if (j < bmap->n_ineq)
1953                         continue;
1954                 coalesce = i;
1955                 break;
1956         }
1957         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1958         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1959         return coalesce;
1960 }
1961
1962 /* Given a lower and an upper bound on div i, construct an inequality
1963  * that when nonnegative ensures that this pair of bounds always allows
1964  * for an integer value of the given div.
1965  * The lower bound is inequality l, while the upper bound is inequality u.
1966  * The constructed inequality is stored in ineq.
1967  * g, fl, fu are temporary scalars.
1968  *
1969  * Let the upper bound be
1970  *
1971  *      -n_u a + e_u >= 0
1972  *
1973  * and the lower bound
1974  *
1975  *      n_l a + e_l >= 0
1976  *
1977  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
1978  * We have
1979  *
1980  *      - f_u e_l <= f_u f_l g a <= f_l e_u
1981  *
1982  * Since all variables are integer valued, this is equivalent to
1983  *
1984  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
1985  *
1986  * If this interval is at least f_u f_l g, then it contains at least
1987  * one integer value for a.
1988  * That is, the test constraint is
1989  *
1990  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
1991  */
1992 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
1993         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
1994 {
1995         unsigned dim;
1996         dim = isl_dim_total(bmap->dim);
1997
1998         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
1999         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2000         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2001         isl_int_neg(fu, fu);
2002         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2003                         1 + dim + bmap->n_div);
2004         isl_int_add(ineq[0], ineq[0], fl);
2005         isl_int_add(ineq[0], ineq[0], fu);
2006         isl_int_sub_ui(ineq[0], ineq[0], 1);
2007         isl_int_mul(g, g, fl);
2008         isl_int_mul(g, g, fu);
2009         isl_int_sub(ineq[0], ineq[0], g);
2010 }
2011
2012 /* Remove more kinds of divs that are not strictly needed.
2013  * In particular, if all pairs of lower and upper bounds on a div
2014  * are such that they allow at least one integer value of the div,
2015  * the we can eliminate the div using Fourier-Motzkin without
2016  * introducing any spurious solutions.
2017  */
2018 static struct isl_basic_map *drop_more_redundant_divs(
2019         struct isl_basic_map *bmap, int *pairs, int n)
2020 {
2021         struct isl_tab *tab = NULL;
2022         struct isl_vec *vec = NULL;
2023         unsigned dim;
2024         int remove = -1;
2025         isl_int g, fl, fu;
2026
2027         isl_int_init(g);
2028         isl_int_init(fl);
2029         isl_int_init(fu);
2030
2031         if (!bmap)
2032                 goto error;
2033
2034         dim = isl_dim_total(bmap->dim);
2035         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2036         if (!vec)
2037                 goto error;
2038
2039         tab = isl_tab_from_basic_map(bmap);
2040
2041         while (n > 0) {
2042                 int i, l, u;
2043                 int best = -1;
2044                 enum isl_lp_result res;
2045
2046                 for (i = 0; i < bmap->n_div; ++i) {
2047                         if (!pairs[i])
2048                                 continue;
2049                         if (best >= 0 && pairs[best] <= pairs[i])
2050                                 continue;
2051                         best = i;
2052                 }
2053
2054                 i = best;
2055                 for (l = 0; l < bmap->n_ineq; ++l) {
2056                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2057                                 continue;
2058                         for (u = 0; u < bmap->n_ineq; ++u) {
2059                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2060                                         continue;
2061                                 construct_test_ineq(bmap, i, l, u,
2062                                                     vec->el, g, fl, fu);
2063                                 res = isl_tab_min(tab, vec->el,
2064                                                   bmap->ctx->one, &g, NULL, 0);
2065                                 if (res == isl_lp_error)
2066                                         goto error;
2067                                 if (res == isl_lp_empty) {
2068                                         bmap = isl_basic_map_set_to_empty(bmap);
2069                                         break;
2070                                 }
2071                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2072                                         break;
2073                         }
2074                         if (u < bmap->n_ineq)
2075                                 break;
2076                 }
2077                 if (l == bmap->n_ineq) {
2078                         remove = i;
2079                         break;
2080                 }
2081                 pairs[i] = 0;
2082                 --n;
2083         }
2084
2085         isl_tab_free(tab);
2086         isl_vec_free(vec);
2087
2088         isl_int_clear(g);
2089         isl_int_clear(fl);
2090         isl_int_clear(fu);
2091
2092         free(pairs);
2093
2094         if (remove < 0)
2095                 return bmap;
2096
2097         bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2098         return isl_basic_map_drop_redundant_divs(bmap);
2099 error:
2100         free(pairs);
2101         isl_basic_map_free(bmap);
2102         isl_tab_free(tab);
2103         isl_vec_free(vec);
2104         isl_int_clear(g);
2105         isl_int_clear(fl);
2106         isl_int_clear(fu);
2107         return NULL;
2108 }
2109
2110 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2111  * and the upper bound u, div1 always occurs together with div2 in the form
2112  * (div1 + m div2), where m is the constant range on the variable div1
2113  * allowed by l and u, replace the pair div1 and div2 by a single
2114  * div that is equal to div1 + m div2.
2115  *
2116  * The new div will appear in the location that contains div2.
2117  * We need to modify all constraints that contain
2118  * div2 = (div - div1) / m
2119  * (If a constraint does not contain div2, it will also not contain div1.)
2120  * If the constraint also contains div1, then we know they appear
2121  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2122  * i.e., the coefficient of div is f.
2123  *
2124  * Otherwise, we first need to introduce div1 into the constraint.
2125  * Let the l be
2126  *
2127  *      div1 + f >=0
2128  *
2129  * and u
2130  *
2131  *      -div1 + f' >= 0
2132  *
2133  * A lower bound on div2
2134  *
2135  *      n div2 + t >= 0
2136  *
2137  * can be replaced by
2138  *
2139  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2140  *
2141  * with g = gcd(m,n).
2142  * An upper bound
2143  *
2144  *      -n div2 + t >= 0
2145  *
2146  * can be replaced by
2147  *
2148  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2149  *
2150  * These constraint are those that we would obtain from eliminating
2151  * div1 using Fourier-Motzkin.
2152  *
2153  * After all constraints have been modified, we drop the lower and upper
2154  * bound and then drop div1.
2155  */
2156 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2157         unsigned div1, unsigned div2, unsigned l, unsigned u)
2158 {
2159         isl_int a;
2160         isl_int b;
2161         isl_int m;
2162         unsigned dim, total;
2163         int i;
2164
2165         dim = isl_dim_total(bmap->dim);
2166         total = 1 + dim + bmap->n_div;
2167
2168         isl_int_init(a);
2169         isl_int_init(b);
2170         isl_int_init(m);
2171         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2172         isl_int_add_ui(m, m, 1);
2173
2174         for (i = 0; i < bmap->n_ineq; ++i) {
2175                 if (i == l || i == u)
2176                         continue;
2177                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2178                         continue;
2179                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2180                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2181                         isl_int_divexact(a, m, b);
2182                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2183                         if (isl_int_is_pos(b)) {
2184                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2185                                                 b, bmap->ineq[l], total);
2186                         } else {
2187                                 isl_int_neg(b, b);
2188                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2189                                                 b, bmap->ineq[u], total);
2190                         }
2191                 }
2192                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2193                             bmap->ineq[i][1 + dim + div1]);
2194                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2195         }
2196
2197         isl_int_clear(a);
2198         isl_int_clear(b);
2199         isl_int_clear(m);
2200         if (l > u) {
2201                 isl_basic_map_drop_inequality(bmap, l);
2202                 isl_basic_map_drop_inequality(bmap, u);
2203         } else {
2204                 isl_basic_map_drop_inequality(bmap, u);
2205                 isl_basic_map_drop_inequality(bmap, l);
2206         }
2207         bmap = isl_basic_map_drop_div(bmap, div1);
2208         return bmap;
2209 }
2210
2211 /* First check if we can coalesce any pair of divs and
2212  * then continue with dropping more redundant divs.
2213  *
2214  * We loop over all pairs of lower and upper bounds on a div
2215  * with coefficient 1 and -1, respectively, check if there
2216  * is any other div "c" with which we can coalesce the div
2217  * and if so, perform the coalescing.
2218  */
2219 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2220         struct isl_basic_map *bmap, int *pairs, int n)
2221 {
2222         int i, l, u;
2223         unsigned dim;
2224
2225         dim = isl_dim_total(bmap->dim);
2226
2227         for (i = 0; i < bmap->n_div; ++i) {
2228                 if (!pairs[i])
2229                         continue;
2230                 for (l = 0; l < bmap->n_ineq; ++l) {
2231                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2232                                 continue;
2233                         for (u = 0; u < bmap->n_ineq; ++u) {
2234                                 int c;
2235
2236                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2237                                         continue;
2238                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2239                                 if (c < 0)
2240                                         continue;
2241                                 free(pairs);
2242                                 bmap = coalesce_divs(bmap, i, c, l, u);
2243                                 return isl_basic_map_drop_redundant_divs(bmap);
2244                         }
2245                 }
2246         }
2247
2248         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2249                 return bmap;
2250
2251         return drop_more_redundant_divs(bmap, pairs, n);
2252 }
2253
2254 /* Remove divs that are not strictly needed.
2255  * In particular, if a div only occurs positively (or negatively)
2256  * in constraints, then it can simply be dropped.
2257  * Also, if a div occurs only occurs in two constraints and if moreover
2258  * those two constraints are opposite to each other, except for the constant
2259  * term and if the sum of the constant terms is such that for any value
2260  * of the other values, there is always at least one integer value of the
2261  * div, i.e., if one plus this sum is greater than or equal to
2262  * the (absolute value) of the coefficent of the div in the constraints,
2263  * then we can also simply drop the div.
2264  *
2265  * If any divs are left after these simple checks then we move on
2266  * to more complicated cases in drop_more_redundant_divs.
2267  */
2268 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2269         struct isl_basic_map *bmap)
2270 {
2271         int i, j;
2272         unsigned off;
2273         int *pairs = NULL;
2274         int n = 0;
2275
2276         if (!bmap)
2277                 goto error;
2278
2279         off = isl_dim_total(bmap->dim);
2280         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2281         if (!pairs)
2282                 goto error;
2283
2284         for (i = 0; i < bmap->n_div; ++i) {
2285                 int pos, neg;
2286                 int last_pos, last_neg;
2287                 int redundant;
2288                 int defined;
2289
2290                 defined = !isl_int_is_zero(bmap->div[i][0]);
2291                 for (j = 0; j < bmap->n_eq; ++j)
2292                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2293                                 break;
2294                 if (j < bmap->n_eq)
2295                         continue;
2296                 ++n;
2297                 pos = neg = 0;
2298                 for (j = 0; j < bmap->n_ineq; ++j) {
2299                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2300                                 last_pos = j;
2301                                 ++pos;
2302                         }
2303                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2304                                 last_neg = j;
2305                                 ++neg;
2306                         }
2307                 }
2308                 pairs[i] = pos * neg;
2309                 if (pairs[i] == 0) {
2310                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2311                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2312                                         isl_basic_map_drop_inequality(bmap, j);
2313                         bmap = isl_basic_map_drop_div(bmap, i);
2314                         free(pairs);
2315                         return isl_basic_map_drop_redundant_divs(bmap);
2316                 }
2317                 if (pairs[i] != 1)
2318                         continue;
2319                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2320                                     bmap->ineq[last_neg] + 1,
2321                                     off + bmap->n_div))
2322                         continue;
2323
2324                 isl_int_add(bmap->ineq[last_pos][0],
2325                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2326                 isl_int_add_ui(bmap->ineq[last_pos][0],
2327                                bmap->ineq[last_pos][0], 1);
2328                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2329                                 bmap->ineq[last_pos][1+off+i]);
2330                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2331                                bmap->ineq[last_pos][0], 1);
2332                 isl_int_sub(bmap->ineq[last_pos][0],
2333                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2334                 if (!redundant) {
2335                         if (defined ||
2336                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2337                                 pairs[i] = 0;
2338                                 --n;
2339                                 continue;
2340                         }
2341                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2342                         bmap = isl_basic_map_simplify(bmap);
2343                         free(pairs);
2344                         return isl_basic_map_drop_redundant_divs(bmap);
2345                 }
2346                 if (last_pos > last_neg) {
2347                         isl_basic_map_drop_inequality(bmap, last_pos);
2348                         isl_basic_map_drop_inequality(bmap, last_neg);
2349                 } else {
2350                         isl_basic_map_drop_inequality(bmap, last_neg);
2351                         isl_basic_map_drop_inequality(bmap, last_pos);
2352                 }
2353                 bmap = isl_basic_map_drop_div(bmap, i);
2354                 free(pairs);
2355                 return isl_basic_map_drop_redundant_divs(bmap);
2356         }
2357
2358         if (n > 0)
2359                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2360
2361         free(pairs);
2362         return bmap;
2363 error:
2364         free(pairs);
2365         isl_basic_map_free(bmap);
2366         return NULL;
2367 }
2368
2369 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2370         struct isl_basic_set *bset)
2371 {
2372         return (struct isl_basic_set *)
2373             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2374 }
2375
2376 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2377 {
2378         int i;
2379
2380         if (!map)
2381                 return NULL;
2382         for (i = 0; i < map->n; ++i) {
2383                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2384                 if (!map->p[i])
2385                         goto error;
2386         }
2387         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2388         return map;
2389 error:
2390         isl_map_free(map);
2391         return NULL;
2392 }
2393
2394 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2395 {
2396         return (struct isl_set *)
2397             isl_map_drop_redundant_divs((struct isl_map *)set);
2398 }