isl_map_simplify.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2012      Ecole Normale Superieure
   4  *
   5  * Use of this software is governed by the GNU LGPLv2.1 license
   6  *
   7  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   8  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   9  * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  10  */
  11
  12 #include <strings.h>
  13 #include <isl_ctx_private.h>
  14 #include <isl_map_private.h>
  15 #include "isl_equalities.h"
  16 #include <isl/map.h>
  17 #include <isl/seq.h>
  18 #include "isl_tab.h"
  19 #include <isl_space_private.h>
  20 #include <isl_mat_private.h>
  21
  22 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  23 {
  24         isl_int *t = bmap->eq[a];
  25         bmap->eq[a] = bmap->eq[b];
  26         bmap->eq[b] = t;
  27 }
  28
  29 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  30 {
  31         if (a != b) {
  32                 isl_int *t = bmap->ineq[a];
  33                 bmap->ineq[a] = bmap->ineq[b];
  34                 bmap->ineq[b] = t;
  35         }
  36 }
  37
  38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  39 {
  40         isl_seq_cpy(c, c + n, rem);
  41         isl_seq_clr(c + rem, n);
  42 }
  43
  44 /* Drop n dimensions starting at first.
  45  *
  46  * In principle, this frees up some extra variables as the number
  47  * of columns remains constant, but we would have to extend
  48  * the div array too as the number of rows in this array is assumed
  49  * to be equal to extra.
  50  */
  51 struct isl_basic_set *isl_basic_set_drop_dims(
  52                 struct isl_basic_set *bset, unsigned first, unsigned n)
  53 {
  54         int i;
  55
  56         if (!bset)
  57                 goto error;
  58
  59         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  60
  61         if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
  62                 return bset;
  63
  64         bset = isl_basic_set_cow(bset);
  65         if (!bset)
  66                 return NULL;
  67
  68         for (i = 0; i < bset->n_eq; ++i)
  69                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  70                                      (bset->dim->n_out-first-n)+bset->extra);
  71
  72         for (i = 0; i < bset->n_ineq; ++i)
  73                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  74                                      (bset->dim->n_out-first-n)+bset->extra);
  75
  76         for (i = 0; i < bset->n_div; ++i)
  77                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  78                                      (bset->dim->n_out-first-n)+bset->extra);
  79
  80         bset->dim = isl_space_drop_outputs(bset->dim, first, n);
  81         if (!bset->dim)
  82                 goto error;
  83
  84         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  85         bset = isl_basic_set_simplify(bset);
  86         return isl_basic_set_finalize(bset);
  87 error:
  88         isl_basic_set_free(bset);
  89         return NULL;
  90 }
  91
  92 struct isl_set *isl_set_drop_dims(
  93                 struct isl_set *set, unsigned first, unsigned n)
  94 {
  95         int i;
  96
  97         if (!set)
  98                 goto error;
  99
 100         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 101
 102         if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
 103                 return set;
 104         set = isl_set_cow(set);
 105         if (!set)
 106                 goto error;
 107         set->dim = isl_space_drop_outputs(set->dim, first, n);
 108         if (!set->dim)
 109                 goto error;
 110
 111         for (i = 0; i < set->n; ++i) {
 112                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 113                 if (!set->p[i])
 114                         goto error;
 115         }
 116
 117         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 118         return set;
 119 error:
 120         isl_set_free(set);
 121         return NULL;
 122 }
 123
 124 /* Move "n" divs starting at "first" to the end of the list of divs.
 125  */
 126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 127         unsigned first, unsigned n)
 128 {
 129         isl_int **div;
 130         int i;
 131
 132         if (first + n == bmap->n_div)
 133                 return bmap;
 134
 135         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 136         if (!div)
 137                 goto error;
 138         for (i = 0; i < n; ++i)
 139                 div[i] = bmap->div[first + i];
 140         for (i = 0; i < bmap->n_div - first - n; ++i)
 141                 bmap->div[first + i] = bmap->div[first + n + i];
 142         for (i = 0; i < n; ++i)
 143                 bmap->div[bmap->n_div - n + i] = div[i];
 144         free(div);
 145         return bmap;
 146 error:
 147         isl_basic_map_free(bmap);
 148         return NULL;
 149 }
 150
 151 /* Drop "n" dimensions of type "type" starting at "first".
 152  *
 153  * In principle, this frees up some extra variables as the number
 154  * of columns remains constant, but we would have to extend
 155  * the div array too as the number of rows in this array is assumed
 156  * to be equal to extra.
 157  */
 158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 159         enum isl_dim_type type, unsigned first, unsigned n)
 160 {
 161         int i;
 162         unsigned dim;
 163         unsigned offset;
 164         unsigned left;
 165
 166         if (!bmap)
 167                 goto error;
 168
 169         dim = isl_basic_map_dim(bmap, type);
 170         isl_assert(bmap->ctx, first + n <= dim, goto error);
 171
 172         if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
 173                 return bmap;
 174
 175         bmap = isl_basic_map_cow(bmap);
 176         if (!bmap)
 177                 return NULL;
 178
 179         offset = isl_basic_map_offset(bmap, type) + first;
 180         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 181         for (i = 0; i < bmap->n_eq; ++i)
 182                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 183
 184         for (i = 0; i < bmap->n_ineq; ++i)
 185                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 186
 187         for (i = 0; i < bmap->n_div; ++i)
 188                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 189
 190         if (type == isl_dim_div) {
 191                 bmap = move_divs_last(bmap, first, n);
 192                 if (!bmap)
 193                         goto error;
 194                 isl_basic_map_free_div(bmap, n);
 195         } else
 196                 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
 197         if (!bmap->dim)
 198                 goto error;
 199
 200         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 201         bmap = isl_basic_map_simplify(bmap);
 202         return isl_basic_map_finalize(bmap);
 203 error:
 204         isl_basic_map_free(bmap);
 205         return NULL;
 206 }
 207
 208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 209         enum isl_dim_type type, unsigned first, unsigned n)
 210 {
 211         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 212                                                         type, first, n);
 213 }
 214
 215 struct isl_basic_map *isl_basic_map_drop_inputs(
 216                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 217 {
 218         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 219 }
 220
 221 struct isl_map *isl_map_drop(struct isl_map *map,
 222         enum isl_dim_type type, unsigned first, unsigned n)
 223 {
 224         int i;
 225
 226         if (!map)
 227                 goto error;
 228
 229         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 230
 231         if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
 232                 return map;
 233         map = isl_map_cow(map);
 234         if (!map)
 235                 goto error;
 236         map->dim = isl_space_drop_dims(map->dim, type, first, n);
 237         if (!map->dim)
 238                 goto error;
 239
 240         for (i = 0; i < map->n; ++i) {
 241                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 242                 if (!map->p[i])
 243                         goto error;
 244         }
 245         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 246
 247         return map;
 248 error:
 249         isl_map_free(map);
 250         return NULL;
 251 }
 252
 253 struct isl_set *isl_set_drop(struct isl_set *set,
 254         enum isl_dim_type type, unsigned first, unsigned n)
 255 {
 256         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 257 }
 258
 259 struct isl_map *isl_map_drop_inputs(
 260                 struct isl_map *map, unsigned first, unsigned n)
 261 {
 262         return isl_map_drop(map, isl_dim_in, first, n);
 263 }
 264
 265 /*
 266  * We don't cow, as the div is assumed to be redundant.
 267  */
 268 static struct isl_basic_map *isl_basic_map_drop_div(
 269                 struct isl_basic_map *bmap, unsigned div)
 270 {
 271         int i;
 272         unsigned pos;
 273
 274         if (!bmap)
 275                 goto error;
 276
 277         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 278
 279         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 280
 281         for (i = 0; i < bmap->n_eq; ++i)
 282                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 283
 284         for (i = 0; i < bmap->n_ineq; ++i) {
 285                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 286                         isl_basic_map_drop_inequality(bmap, i);
 287                         --i;
 288                         continue;
 289                 }
 290                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 291         }
 292
 293         for (i = 0; i < bmap->n_div; ++i)
 294                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 295
 296         if (div != bmap->n_div - 1) {
 297                 int j;
 298                 isl_int *t = bmap->div[div];
 299
 300                 for (j = div; j < bmap->n_div - 1; ++j)
 301                         bmap->div[j] = bmap->div[j+1];
 302
 303                 bmap->div[bmap->n_div - 1] = t;
 304         }
 305         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 306         isl_basic_map_free_div(bmap, 1);
 307
 308         return bmap;
 309 error:
 310         isl_basic_map_free(bmap);
 311         return NULL;
 312 }
 313
 314 struct isl_basic_map *isl_basic_map_normalize_constraints(
 315         struct isl_basic_map *bmap)
 316 {
 317         int i;
 318         isl_int gcd;
 319         unsigned total = isl_basic_map_total_dim(bmap);
 320
 321         if (!bmap)
 322                 return NULL;
 323
 324         isl_int_init(gcd);
 325         for (i = bmap->n_eq - 1; i >= 0; --i) {
 326                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 327                 if (isl_int_is_zero(gcd)) {
 328                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 329                                 bmap = isl_basic_map_set_to_empty(bmap);
 330                                 break;
 331                         }
 332                         isl_basic_map_drop_equality(bmap, i);
 333                         continue;
 334                 }
 335                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 336                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 337                 if (isl_int_is_one(gcd))
 338                         continue;
 339                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 340                         bmap = isl_basic_map_set_to_empty(bmap);
 341                         break;
 342                 }
 343                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 344         }
 345
 346         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 347                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 348                 if (isl_int_is_zero(gcd)) {
 349                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 350                                 bmap = isl_basic_map_set_to_empty(bmap);
 351                                 break;
 352                         }
 353                         isl_basic_map_drop_inequality(bmap, i);
 354                         continue;
 355                 }
 356                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 357                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 358                 if (isl_int_is_one(gcd))
 359                         continue;
 360                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 361                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 362         }
 363         isl_int_clear(gcd);
 364
 365         return bmap;
 366 }
 367
 368 struct isl_basic_set *isl_basic_set_normalize_constraints(
 369         struct isl_basic_set *bset)
 370 {
 371         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 372                 (struct isl_basic_map *)bset);
 373 }
 374
 375 /* Remove any common factor in numerator and denominator of a div expression,
 376  * not taking into account the constant term.
 377  * That is, look for any div of the form
 378  *
 379  *      floor((a + m f(x))/(m d))
 380  *
 381  * and replace it by
 382  *
 383  *      floor((floor(a/m) + f(x))/d)
 384  *
 385  * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
 386  * and can therefore not influence the result of the floor.
 387  */
 388 static __isl_give isl_basic_map *normalize_div_expressions(
 389         __isl_take isl_basic_map *bmap)
 390 {
 391         int i;
 392         isl_int gcd;
 393         unsigned total = isl_basic_map_total_dim(bmap);
 394
 395         if (!bmap)
 396                 return NULL;
 397         if (bmap->n_div == 0)
 398                 return bmap;
 399
 400         isl_int_init(gcd);
 401         for (i = 0; i < bmap->n_div; ++i) {
 402                 if (isl_int_is_zero(bmap->div[i][0]))
 403                         continue;
 404                 isl_seq_gcd(bmap->div[i] + 2, total, &gcd);
 405                 isl_int_gcd(gcd, gcd, bmap->div[i][0]);
 406                 if (isl_int_is_one(gcd))
 407                         continue;
 408                 isl_int_fdiv_q(bmap->div[i][1], bmap->div[i][1], gcd);
 409                 isl_int_divexact(bmap->div[i][0], bmap->div[i][0], gcd);
 410                 isl_seq_scale_down(bmap->div[i] + 2, bmap->div[i] + 2, gcd,
 411                                         total);
 412         }
 413         isl_int_clear(gcd);
 414
 415         return bmap;
 416 }
 417
 418 /* Assumes divs have been ordered if keep_divs is set.
 419  */
 420 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 421         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 422 {
 423         unsigned total;
 424         unsigned space_total;
 425         int k;
 426         int last_div;
 427
 428         total = isl_basic_map_total_dim(bmap);
 429         space_total = isl_space_dim(bmap->dim, isl_dim_all);
 430         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 431         for (k = 0; k < bmap->n_eq; ++k) {
 432                 if (bmap->eq[k] == eq)
 433                         continue;
 434                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 435                         continue;
 436                 if (progress)
 437                         *progress = 1;
 438                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 439                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
 440         }
 441
 442         for (k = 0; k < bmap->n_ineq; ++k) {
 443                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 444                         continue;
 445                 if (progress)
 446                         *progress = 1;
 447                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 448                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
 449                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 450         }
 451
 452         for (k = 0; k < bmap->n_div; ++k) {
 453                 if (isl_int_is_zero(bmap->div[k][0]))
 454                         continue;
 455                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 456                         continue;
 457                 if (progress)
 458                         *progress = 1;
 459                 /* We need to be careful about circular definitions,
 460                  * so for now we just remove the definition of div k
 461                  * if the equality contains any divs.
 462                  * If keep_divs is set, then the divs have been ordered
 463                  * and we can keep the definition as long as the result
 464                  * is still ordered.
 465                  */
 466                 if (last_div == -1 || (keep_divs && last_div < k))
 467                         isl_seq_elim(bmap->div[k]+1, eq,
 468                                         1+pos, 1+total, &bmap->div[k][0]);
 469                 else
 470                         isl_seq_clr(bmap->div[k], 1 + total);
 471                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 472         }
 473 }
 474
 475 /* Assumes divs have been ordered if keep_divs is set.
 476  */
 477 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 478         unsigned div, int keep_divs)
 479 {
 480         unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
 481
 482         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 483
 484         isl_basic_map_drop_div(bmap, div);
 485 }
 486
 487 /* Check if elimination of div "div" using equality "eq" would not
 488  * result in a div depending on a later div.
 489  */
 490 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 491         unsigned div)
 492 {
 493         int k;
 494         int last_div;
 495         unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
 496         unsigned pos = space_total + div;
 497
 498         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 499         if (last_div < 0 || last_div <= div)
 500                 return 1;
 501
 502         for (k = 0; k <= last_div; ++k) {
 503                 if (isl_int_is_zero(bmap->div[k][0]))
 504                         return 1;
 505                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 506                         return 0;
 507         }
 508
 509         return 1;
 510 }
 511
 512 /* Elimininate divs based on equalities
 513  */
 514 static struct isl_basic_map *eliminate_divs_eq(
 515                 struct isl_basic_map *bmap, int *progress)
 516 {
 517         int d;
 518         int i;
 519         int modified = 0;
 520         unsigned off;
 521
 522         bmap = isl_basic_map_order_divs(bmap);
 523
 524         if (!bmap)
 525                 return NULL;
 526
 527         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 528
 529         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 530                 for (i = 0; i < bmap->n_eq; ++i) {
 531                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 532                             !isl_int_is_negone(bmap->eq[i][off + d]))
 533                                 continue;
 534                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 535                                 continue;
 536                         modified = 1;
 537                         *progress = 1;
 538                         eliminate_div(bmap, bmap->eq[i], d, 1);
 539                         isl_basic_map_drop_equality(bmap, i);
 540                         break;
 541                 }
 542         }
 543         if (modified)
 544                 return eliminate_divs_eq(bmap, progress);
 545         return bmap;
 546 }
 547
 548 /* Elimininate divs based on inequalities
 549  */
 550 static struct isl_basic_map *eliminate_divs_ineq(
 551                 struct isl_basic_map *bmap, int *progress)
 552 {
 553         int d;
 554         int i;
 555         unsigned off;
 556         struct isl_ctx *ctx;
 557
 558         if (!bmap)
 559                 return NULL;
 560
 561         ctx = bmap->ctx;
 562         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 563
 564         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 565                 for (i = 0; i < bmap->n_eq; ++i)
 566                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 567                                 break;
 568                 if (i < bmap->n_eq)
 569                         continue;
 570                 for (i = 0; i < bmap->n_ineq; ++i)
 571                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 572                                 break;
 573                 if (i < bmap->n_ineq)
 574                         continue;
 575                 *progress = 1;
 576                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 577                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 578                         break;
 579                 bmap = isl_basic_map_drop_div(bmap, d);
 580                 if (!bmap)
 581                         break;
 582         }
 583         return bmap;
 584 }
 585
 586 struct isl_basic_map *isl_basic_map_gauss(
 587         struct isl_basic_map *bmap, int *progress)
 588 {
 589         int k;
 590         int done;
 591         int last_var;
 592         unsigned total_var;
 593         unsigned total;
 594
 595         bmap = isl_basic_map_order_divs(bmap);
 596
 597         if (!bmap)
 598                 return NULL;
 599
 600         total = isl_basic_map_total_dim(bmap);
 601         total_var = total - bmap->n_div;
 602
 603         last_var = total - 1;
 604         for (done = 0; done < bmap->n_eq; ++done) {
 605                 for (; last_var >= 0; --last_var) {
 606                         for (k = done; k < bmap->n_eq; ++k)
 607                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 608                                         break;
 609                         if (k < bmap->n_eq)
 610                                 break;
 611                 }
 612                 if (last_var < 0)
 613                         break;
 614                 if (k != done)
 615                         swap_equality(bmap, k, done);
 616                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 617                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 618
 619                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 620                                                 progress);
 621
 622                 if (last_var >= total_var &&
 623                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 624                         unsigned div = last_var - total_var;
 625                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 626                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 627                         isl_int_set(bmap->div[div][0],
 628                                     bmap->eq[done][1+last_var]);
 629                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 630                 }
 631         }
 632         if (done == bmap->n_eq)
 633                 return bmap;
 634         for (k = done; k < bmap->n_eq; ++k) {
 635                 if (isl_int_is_zero(bmap->eq[k][0]))
 636                         continue;
 637                 return isl_basic_map_set_to_empty(bmap);
 638         }
 639         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 640         return bmap;
 641 }
 642
 643 struct isl_basic_set *isl_basic_set_gauss(
 644         struct isl_basic_set *bset, int *progress)
 645 {
 646         return (struct isl_basic_set*)isl_basic_map_gauss(
 647                         (struct isl_basic_map *)bset, progress);
 648 }
 649
 650
 651 static unsigned int round_up(unsigned int v)
 652 {
 653         int old_v = v;
 654
 655         while (v) {
 656                 old_v = v;
 657                 v ^= v & -v;
 658         }
 659         return old_v << 1;
 660 }
 661
 662 static int hash_index(isl_int ***index, unsigned int size, int bits,
 663                         struct isl_basic_map *bmap, int k)
 664 {
 665         int h;
 666         unsigned total = isl_basic_map_total_dim(bmap);
 667         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 668         for (h = hash; index[h]; h = (h+1) % size)
 669                 if (&bmap->ineq[k] != index[h] &&
 670                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 671                         break;
 672         return h;
 673 }
 674
 675 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 676                           struct isl_basic_set *bset, int k)
 677 {
 678         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 679 }
 680
 681 /* If we can eliminate more than one div, then we need to make
 682  * sure we do it from last div to first div, in order not to
 683  * change the position of the other divs that still need to
 684  * be removed.
 685  */
 686 static struct isl_basic_map *remove_duplicate_divs(
 687         struct isl_basic_map *bmap, int *progress)
 688 {
 689         unsigned int size;
 690         int *index;
 691         int *elim_for;
 692         int k, l, h;
 693         int bits;
 694         struct isl_blk eq;
 695         unsigned total_var;
 696         unsigned total;
 697         struct isl_ctx *ctx;
 698
 699         if (!bmap || bmap->n_div <= 1)
 700                 return bmap;
 701
 702         total_var = isl_space_dim(bmap->dim, isl_dim_all);
 703         total = total_var + bmap->n_div;
 704
 705         ctx = bmap->ctx;
 706         for (k = bmap->n_div - 1; k >= 0; --k)
 707                 if (!isl_int_is_zero(bmap->div[k][0]))
 708                         break;
 709         if (k <= 0)
 710                 return bmap;
 711
 712         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 713         size = round_up(4 * bmap->n_div / 3 - 1);
 714         bits = ffs(size) - 1;
 715         index = isl_calloc_array(ctx, int, size);
 716         if (!index)
 717                 return bmap;
 718         eq = isl_blk_alloc(ctx, 1+total);
 719         if (isl_blk_is_error(eq))
 720                 goto out;
 721
 722         isl_seq_clr(eq.data, 1+total);
 723         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 724         for (--k; k >= 0; --k) {
 725                 uint32_t hash;
 726
 727                 if (isl_int_is_zero(bmap->div[k][0]))
 728                         continue;
 729
 730                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 731                 for (h = hash; index[h]; h = (h+1) % size)
 732                         if (isl_seq_eq(bmap->div[k],
 733                                        bmap->div[index[h]-1], 2+total))
 734                                 break;
 735                 if (index[h]) {
 736                         *progress = 1;
 737                         l = index[h] - 1;
 738                         elim_for[l] = k + 1;
 739                 }
 740                 index[h] = k+1;
 741         }
 742         for (l = bmap->n_div - 1; l >= 0; --l) {
 743                 if (!elim_for[l])
 744                         continue;
 745                 k = elim_for[l] - 1;
 746                 isl_int_set_si(eq.data[1+total_var+k], -1);
 747                 isl_int_set_si(eq.data[1+total_var+l], 1);
 748                 eliminate_div(bmap, eq.data, l, 0);
 749                 isl_int_set_si(eq.data[1+total_var+k], 0);
 750                 isl_int_set_si(eq.data[1+total_var+l], 0);
 751         }
 752
 753         isl_blk_free(ctx, eq);
 754 out:
 755         free(index);
 756         free(elim_for);
 757         return bmap;
 758 }
 759
 760 static int n_pure_div_eq(struct isl_basic_map *bmap)
 761 {
 762         int i, j;
 763         unsigned total;
 764
 765         total = isl_space_dim(bmap->dim, isl_dim_all);
 766         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 767                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 768                         --j;
 769                 if (j < 0)
 770                         break;
 771                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 772                         return 0;
 773         }
 774         return i;
 775 }
 776
 777 /* Normalize divs that appear in equalities.
 778  *
 779  * In particular, we assume that bmap contains some equalities
 780  * of the form
 781  *
 782  *      a x = m * e_i
 783  *
 784  * and we want to replace the set of e_i by a minimal set and
 785  * such that the new e_i have a canonical representation in terms
 786  * of the vector x.
 787  * If any of the equalities involves more than one divs, then
 788  * we currently simply bail out.
 789  *
 790  * Let us first additionally assume that all equalities involve
 791  * a div.  The equalities then express modulo constraints on the
 792  * remaining variables and we can use "parameter compression"
 793  * to find a minimal set of constraints.  The result is a transformation
 794  *
 795  *      x = T(x') = x_0 + G x'
 796  *
 797  * with G a lower-triangular matrix with all elements below the diagonal
 798  * non-negative and smaller than the diagonal element on the same row.
 799  * We first normalize x_0 by making the same property hold in the affine
 800  * T matrix.
 801  * The rows i of G with a 1 on the diagonal do not impose any modulo
 802  * constraint and simply express x_i = x'_i.
 803  * For each of the remaining rows i, we introduce a div and a corresponding
 804  * equality.  In particular
 805  *
 806  *      g_ii e_j = x_i - g_i(x')
 807  *
 808  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 809  * corresponding div (if g_kk != 1).
 810  *
 811  * If there are any equalities not involving any div, then we
 812  * first apply a variable compression on the variables x:
 813  *
 814  *      x = C x''       x'' = C_2 x
 815  *
 816  * and perform the above parameter compression on A C instead of on A.
 817  * The resulting compression is then of the form
 818  *
 819  *      x'' = T(x') = x_0 + G x'
 820  *
 821  * and in constructing the new divs and the corresponding equalities,
 822  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 823  * by the corresponding row from C_2.
 824  */
 825 static struct isl_basic_map *normalize_divs(
 826         struct isl_basic_map *bmap, int *progress)
 827 {
 828         int i, j, k;
 829         int total;
 830         int div_eq;
 831         struct isl_mat *B;
 832         struct isl_vec *d;
 833         struct isl_mat *T = NULL;
 834         struct isl_mat *C = NULL;
 835         struct isl_mat *C2 = NULL;
 836         isl_int v;
 837         int *pos;
 838         int dropped, needed;
 839
 840         if (!bmap)
 841                 return NULL;
 842
 843         if (bmap->n_div == 0)
 844                 return bmap;
 845
 846         if (bmap->n_eq == 0)
 847                 return bmap;
 848
 849         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 850                 return bmap;
 851
 852         total = isl_space_dim(bmap->dim, isl_dim_all);
 853         div_eq = n_pure_div_eq(bmap);
 854         if (div_eq == 0)
 855                 return bmap;
 856
 857         if (div_eq < bmap->n_eq) {
 858                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 859                                         bmap->n_eq - div_eq, 0, 1 + total);
 860                 C = isl_mat_variable_compression(B, &C2);
 861                 if (!C || !C2)
 862                         goto error;
 863                 if (C->n_col == 0) {
 864                         bmap = isl_basic_map_set_to_empty(bmap);
 865                         isl_mat_free(C);
 866                         isl_mat_free(C2);
 867                         goto done;
 868                 }
 869         }
 870
 871         d = isl_vec_alloc(bmap->ctx, div_eq);
 872         if (!d)
 873                 goto error;
 874         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 875                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 876                         --j;
 877                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 878         }
 879         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 880
 881         if (C) {
 882                 B = isl_mat_product(B, C);
 883                 C = NULL;
 884         }
 885
 886         T = isl_mat_parameter_compression(B, d);
 887         if (!T)
 888                 goto error;
 889         if (T->n_col == 0) {
 890                 bmap = isl_basic_map_set_to_empty(bmap);
 891                 isl_mat_free(C2);
 892                 isl_mat_free(T);
 893                 goto done;
 894         }
 895         isl_int_init(v);
 896         for (i = 0; i < T->n_row - 1; ++i) {
 897                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 898                 if (isl_int_is_zero(v))
 899                         continue;
 900                 isl_mat_col_submul(T, 0, v, 1 + i);
 901         }
 902         isl_int_clear(v);
 903         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 904         if (!pos)
 905                 goto error;
 906         /* We have to be careful because dropping equalities may reorder them */
 907         dropped = 0;
 908         for (j = bmap->n_div - 1; j >= 0; --j) {
 909                 for (i = 0; i < bmap->n_eq; ++i)
 910                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 911                                 break;
 912                 if (i < bmap->n_eq) {
 913                         bmap = isl_basic_map_drop_div(bmap, j);
 914                         isl_basic_map_drop_equality(bmap, i);
 915                         ++dropped;
 916                 }
 917         }
 918         pos[0] = 0;
 919         needed = 0;
 920         for (i = 1; i < T->n_row; ++i) {
 921                 if (isl_int_is_one(T->row[i][i]))
 922                         pos[i] = i;
 923                 else
 924                         needed++;
 925         }
 926         if (needed > dropped) {
 927                 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 928                                 needed, needed, 0);
 929                 if (!bmap)
 930                         goto error;
 931         }
 932         for (i = 1; i < T->n_row; ++i) {
 933                 if (isl_int_is_one(T->row[i][i]))
 934                         continue;
 935                 k = isl_basic_map_alloc_div(bmap);
 936                 pos[i] = 1 + total + k;
 937                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 938                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 939                 if (C2)
 940                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 941                 else
 942                         isl_int_set_si(bmap->div[k][1 + i], 1);
 943                 for (j = 0; j < i; ++j) {
 944                         if (isl_int_is_zero(T->row[i][j]))
 945                                 continue;
 946                         if (pos[j] < T->n_row && C2)
 947                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 948                                                 C2->row[pos[j]], 1 + total);
 949                         else
 950                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 951                                                                 T->row[i][j]);
 952                 }
 953                 j = isl_basic_map_alloc_equality(bmap);
 954                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 955                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 956         }
 957         free(pos);
 958         isl_mat_free(C2);
 959         isl_mat_free(T);
 960
 961         if (progress)
 962                 *progress = 1;
 963 done:
 964         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 965
 966         return bmap;
 967 error:
 968         isl_mat_free(C);
 969         isl_mat_free(C2);
 970         isl_mat_free(T);
 971         return bmap;
 972 }
 973
 974 static struct isl_basic_map *set_div_from_lower_bound(
 975         struct isl_basic_map *bmap, int div, int ineq)
 976 {
 977         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 978
 979         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 980         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
 981         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
 982         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 983         isl_int_set_si(bmap->div[div][1 + total + div], 0);
 984
 985         return bmap;
 986 }
 987
 988 /* Check whether it is ok to define a div based on an inequality.
 989  * To avoid the introduction of circular definitions of divs, we
 990  * do not allow such a definition if the resulting expression would refer to
 991  * any other undefined divs or if any known div is defined in
 992  * terms of the unknown div.
 993  */
 994 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
 995         int div, int ineq)
 996 {
 997         int j;
 998         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 999
1000         /* Not defined in terms of unknown divs */
1001         for (j = 0; j < bmap->n_div; ++j) {
1002                 if (div == j)
1003                         continue;
1004                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1005                         continue;
1006                 if (isl_int_is_zero(bmap->div[j][0]))
1007                         return 0;
1008         }
1009
1010         /* No other div defined in terms of this one => avoid loops */
1011         for (j = 0; j < bmap->n_div; ++j) {
1012                 if (div == j)
1013                         continue;
1014                 if (isl_int_is_zero(bmap->div[j][0]))
1015                         continue;
1016                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1017                         return 0;
1018         }
1019
1020         return 1;
1021 }
1022
1023 /* Given two constraints "k" and "l" that are opposite to each other,
1024  * except for the constant term, check if we can use them
1025  * to obtain an expression for one of the hitherto unknown divs.
1026  * "sum" is the sum of the constant terms of the constraints.
1027  * If this sum is strictly smaller than the coefficient of one
1028  * of the divs, then this pair can be used define the div.
1029  * To avoid the introduction of circular definitions of divs, we
1030  * do not use the pair if the resulting expression would refer to
1031  * any other undefined divs or if any known div is defined in
1032  * terms of the unknown div.
1033  */
1034 static struct isl_basic_map *check_for_div_constraints(
1035         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
1036 {
1037         int i;
1038         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1039
1040         for (i = 0; i < bmap->n_div; ++i) {
1041                 if (!isl_int_is_zero(bmap->div[i][0]))
1042                         continue;
1043                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1044                         continue;
1045                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1046                         continue;
1047                 if (!ok_to_set_div_from_bound(bmap, i, k))
1048                         break;
1049                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1050                         bmap = set_div_from_lower_bound(bmap, i, k);
1051                 else
1052                         bmap = set_div_from_lower_bound(bmap, i, l);
1053                 if (progress)
1054                         *progress = 1;
1055                 break;
1056         }
1057         return bmap;
1058 }
1059
1060 static struct isl_basic_map *remove_duplicate_constraints(
1061         struct isl_basic_map *bmap, int *progress, int detect_divs)
1062 {
1063         unsigned int size;
1064         isl_int ***index;
1065         int k, l, h;
1066         int bits;
1067         unsigned total = isl_basic_map_total_dim(bmap);
1068         isl_int sum;
1069         isl_ctx *ctx;
1070
1071         if (!bmap || bmap->n_ineq <= 1)
1072                 return bmap;
1073
1074         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1075         bits = ffs(size) - 1;
1076         ctx = isl_basic_map_get_ctx(bmap);
1077         index = isl_calloc_array(ctx, isl_int **, size);
1078         if (!index)
1079                 return bmap;
1080
1081         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1082         for (k = 1; k < bmap->n_ineq; ++k) {
1083                 h = hash_index(index, size, bits, bmap, k);
1084                 if (!index[h]) {
1085                         index[h] = &bmap->ineq[k];
1086                         continue;
1087                 }
1088                 if (progress)
1089                         *progress = 1;
1090                 l = index[h] - &bmap->ineq[0];
1091                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1092                         swap_inequality(bmap, k, l);
1093                 isl_basic_map_drop_inequality(bmap, k);
1094                 --k;
1095         }
1096         isl_int_init(sum);
1097         for (k = 0; k < bmap->n_ineq-1; ++k) {
1098                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1099                 h = hash_index(index, size, bits, bmap, k);
1100                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1101                 if (!index[h])
1102                         continue;
1103                 l = index[h] - &bmap->ineq[0];
1104                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1105                 if (isl_int_is_pos(sum)) {
1106                         if (detect_divs)
1107                                 bmap = check_for_div_constraints(bmap, k, l,
1108                                                                  sum, progress);
1109                         continue;
1110                 }
1111                 if (isl_int_is_zero(sum)) {
1112                         /* We need to break out of the loop after these
1113                          * changes since the contents of the hash
1114                          * will no longer be valid.
1115                          * Plus, we probably we want to regauss first.
1116                          */
1117                         if (progress)
1118                                 *progress = 1;
1119                         isl_basic_map_drop_inequality(bmap, l);
1120                         isl_basic_map_inequality_to_equality(bmap, k);
1121                 } else
1122                         bmap = isl_basic_map_set_to_empty(bmap);
1123                 break;
1124         }
1125         isl_int_clear(sum);
1126
1127         free(index);
1128         return bmap;
1129 }
1130
1131
1132 /* Eliminate knowns divs from constraints where they appear with
1133  * a (positive or negative) unit coefficient.
1134  *
1135  * That is, replace
1136  *
1137  *      floor(e/m) + f >= 0
1138  *
1139  * by
1140  *
1141  *      e + m f >= 0
1142  *
1143  * and
1144  *
1145  *      -floor(e/m) + f >= 0
1146  *
1147  * by
1148  *
1149  *      -e + m f + m - 1 >= 0
1150  *
1151  * The first conversion is valid because floor(e/m) >= -f is equivalent
1152  * to e/m >= -f because -f is an integral expression.
1153  * The second conversion follows from the fact that
1154  *
1155  *      -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1156  *
1157  *
1158  * We skip integral divs, i.e., those with denominator 1, as we would
1159  * risk eliminating the div from the div constraints.  We do not need
1160  * to handle those divs here anyway since the div constraints will turn
1161  * out to form an equality and this equality can then be use to eliminate
1162  * the div from all constraints.
1163  */
1164 static __isl_give isl_basic_map *eliminate_unit_divs(
1165         __isl_take isl_basic_map *bmap, int *progress)
1166 {
1167         int i, j;
1168         isl_ctx *ctx;
1169         unsigned total;
1170
1171         if (!bmap)
1172                 return NULL;
1173
1174         ctx = isl_basic_map_get_ctx(bmap);
1175         total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1176
1177         for (i = 0; i < bmap->n_div; ++i) {
1178                 if (isl_int_is_zero(bmap->div[i][0]))
1179                         continue;
1180                 if (isl_int_is_one(bmap->div[i][0]))
1181                         continue;
1182                 for (j = 0; j < bmap->n_ineq; ++j) {
1183                         int s;
1184
1185                         if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
1186                             !isl_int_is_negone(bmap->ineq[j][total + i]))
1187                                 continue;
1188
1189                         *progress = 1;
1190
1191                         s = isl_int_sgn(bmap->ineq[j][total + i]);
1192                         isl_int_set_si(bmap->ineq[j][total + i], 0);
1193                         if (s < 0)
1194                                 isl_seq_combine(bmap->ineq[j],
1195                                         ctx->negone, bmap->div[i] + 1,
1196                                         bmap->div[i][0], bmap->ineq[j],
1197                                         total + bmap->n_div);
1198                         else
1199                                 isl_seq_combine(bmap->ineq[j],
1200                                         ctx->one, bmap->div[i] + 1,
1201                                         bmap->div[i][0], bmap->ineq[j],
1202                                         total + bmap->n_div);
1203                         if (s < 0) {
1204                                 isl_int_add(bmap->ineq[j][0],
1205                                         bmap->ineq[j][0], bmap->div[i][0]);
1206                                 isl_int_sub_ui(bmap->ineq[j][0],
1207                                         bmap->ineq[j][0], 1);
1208                         }
1209                 }
1210         }
1211
1212         return bmap;
1213 }
1214
1215 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1216 {
1217         int progress = 1;
1218         if (!bmap)
1219                 return NULL;
1220         while (progress) {
1221                 progress = 0;
1222                 bmap = isl_basic_map_normalize_constraints(bmap);
1223                 bmap = normalize_div_expressions(bmap);
1224                 bmap = remove_duplicate_divs(bmap, &progress);
1225                 bmap = eliminate_unit_divs(bmap, &progress);
1226                 bmap = eliminate_divs_eq(bmap, &progress);
1227                 bmap = eliminate_divs_ineq(bmap, &progress);
1228                 bmap = isl_basic_map_gauss(bmap, &progress);
1229                 /* requires equalities in normal form */
1230                 bmap = normalize_divs(bmap, &progress);
1231                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1232         }
1233         return bmap;
1234 }
1235
1236 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1237 {
1238         return (struct isl_basic_set *)
1239                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1240 }
1241
1242
1243 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1244         isl_int *constraint, unsigned div)
1245 {
1246         unsigned pos;
1247
1248         if (!bmap)
1249                 return -1;
1250
1251         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1252
1253         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1254                 int neg;
1255                 isl_int_sub(bmap->div[div][1],
1256                                 bmap->div[div][1], bmap->div[div][0]);
1257                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1258                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1259                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1260                 isl_int_add(bmap->div[div][1],
1261                                 bmap->div[div][1], bmap->div[div][0]);
1262                 if (!neg)
1263                         return 0;
1264                 if (isl_seq_first_non_zero(constraint+pos+1,
1265                                             bmap->n_div-div-1) != -1)
1266                         return 0;
1267         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1268                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1269                         return 0;
1270                 if (isl_seq_first_non_zero(constraint+pos+1,
1271                                             bmap->n_div-div-1) != -1)
1272                         return 0;
1273         } else
1274                 return 0;
1275
1276         return 1;
1277 }
1278
1279 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1280         isl_int *constraint, unsigned div)
1281 {
1282         return isl_basic_map_is_div_constraint(bset, constraint, div);
1283 }
1284
1285
1286 /* If the only constraints a div d=floor(f/m)
1287  * appears in are its two defining constraints
1288  *
1289  *      f - m d >=0
1290  *      -(f - (m - 1)) + m d >= 0
1291  *
1292  * then it can safely be removed.
1293  */
1294 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1295 {
1296         int i;
1297         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1298
1299         for (i = 0; i < bmap->n_eq; ++i)
1300                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1301                         return 0;
1302
1303         for (i = 0; i < bmap->n_ineq; ++i) {
1304                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1305                         continue;
1306                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1307                         return 0;
1308         }
1309
1310         for (i = 0; i < bmap->n_div; ++i)
1311                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1312                         return 0;
1313
1314         return 1;
1315 }
1316
1317 /*
1318  * Remove divs that don't occur in any of the constraints or other divs.
1319  * These can arise when dropping some of the variables in a quast
1320  * returned by piplib.
1321  */
1322 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1323 {
1324         int i;
1325
1326         if (!bmap)
1327                 return NULL;
1328
1329         for (i = bmap->n_div-1; i >= 0; --i) {
1330                 if (!div_is_redundant(bmap, i))
1331                         continue;
1332                 bmap = isl_basic_map_drop_div(bmap, i);
1333         }
1334         return bmap;
1335 }
1336
1337 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1338 {
1339         bmap = remove_redundant_divs(bmap);
1340         if (!bmap)
1341                 return NULL;
1342         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1343         return bmap;
1344 }
1345
1346 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1347 {
1348         return (struct isl_basic_set *)
1349                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1350 }
1351
1352 struct isl_set *isl_set_finalize(struct isl_set *set)
1353 {
1354         int i;
1355
1356         if (!set)
1357                 return NULL;
1358         for (i = 0; i < set->n; ++i) {
1359                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1360                 if (!set->p[i])
1361                         goto error;
1362         }
1363         return set;
1364 error:
1365         isl_set_free(set);
1366         return NULL;
1367 }
1368
1369 struct isl_map *isl_map_finalize(struct isl_map *map)
1370 {
1371         int i;
1372
1373         if (!map)
1374                 return NULL;
1375         for (i = 0; i < map->n; ++i) {
1376                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1377                 if (!map->p[i])
1378                         goto error;
1379         }
1380         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1381         return map;
1382 error:
1383         isl_map_free(map);
1384         return NULL;
1385 }
1386
1387
1388 /* Remove definition of any div that is defined in terms of the given variable.
1389  * The div itself is not removed.  Functions such as
1390  * eliminate_divs_ineq depend on the other divs remaining in place.
1391  */
1392 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1393                                                                         int pos)
1394 {
1395         int i;
1396
1397         for (i = 0; i < bmap->n_div; ++i) {
1398                 if (isl_int_is_zero(bmap->div[i][0]))
1399                         continue;
1400                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1401                         continue;
1402                 isl_int_set_si(bmap->div[i][0], 0);
1403         }
1404         return bmap;
1405 }
1406
1407 /* Eliminate the specified variables from the constraints using
1408  * Fourier-Motzkin.  The variables themselves are not removed.
1409  */
1410 struct isl_basic_map *isl_basic_map_eliminate_vars(
1411         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1412 {
1413         int d;
1414         int i, j, k;
1415         unsigned total;
1416         int need_gauss = 0;
1417
1418         if (n == 0)
1419                 return bmap;
1420         if (!bmap)
1421                 return NULL;
1422         total = isl_basic_map_total_dim(bmap);
1423
1424         bmap = isl_basic_map_cow(bmap);
1425         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1426                 bmap = remove_dependent_vars(bmap, d);
1427
1428         for (d = pos + n - 1;
1429              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1430                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1431         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1432                 int n_lower, n_upper;
1433                 if (!bmap)
1434                         return NULL;
1435                 for (i = 0; i < bmap->n_eq; ++i) {
1436                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1437                                 continue;
1438                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1439                         isl_basic_map_drop_equality(bmap, i);
1440                         need_gauss = 1;
1441                         break;
1442                 }
1443                 if (i < bmap->n_eq)
1444                         continue;
1445                 n_lower = 0;
1446                 n_upper = 0;
1447                 for (i = 0; i < bmap->n_ineq; ++i) {
1448                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1449                                 n_lower++;
1450                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1451                                 n_upper++;
1452                 }
1453                 bmap = isl_basic_map_extend_constraints(bmap,
1454                                 0, n_lower * n_upper);
1455                 if (!bmap)
1456                         goto error;
1457                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1458                         int last;
1459                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1460                                 continue;
1461                         last = -1;
1462                         for (j = 0; j < i; ++j) {
1463                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1464                                         continue;
1465                                 last = j;
1466                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1467                                     isl_int_sgn(bmap->ineq[j][1+d]))
1468                                         continue;
1469                                 k = isl_basic_map_alloc_inequality(bmap);
1470                                 if (k < 0)
1471                                         goto error;
1472                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1473                                                 1+total);
1474                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1475                                                 1+d, 1+total, NULL);
1476                         }
1477                         isl_basic_map_drop_inequality(bmap, i);
1478                         i = last + 1;
1479                 }
1480                 if (n_lower > 0 && n_upper > 0) {
1481                         bmap = isl_basic_map_normalize_constraints(bmap);
1482                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1483                         bmap = isl_basic_map_gauss(bmap, NULL);
1484                         bmap = isl_basic_map_remove_redundancies(bmap);
1485                         need_gauss = 0;
1486                         if (!bmap)
1487                                 goto error;
1488                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1489                                 break;
1490                 }
1491         }
1492         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1493         if (need_gauss)
1494                 bmap = isl_basic_map_gauss(bmap, NULL);
1495         return bmap;
1496 error:
1497         isl_basic_map_free(bmap);
1498         return NULL;
1499 }
1500
1501 struct isl_basic_set *isl_basic_set_eliminate_vars(
1502         struct isl_basic_set *bset, unsigned pos, unsigned n)
1503 {
1504         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1505                         (struct isl_basic_map *)bset, pos, n);
1506 }
1507
1508 /* Eliminate the specified n dimensions starting at first from the
1509  * constraints, without removing the dimensions from the space.
1510  * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1511  * Otherwise, they are projected out and the original space is restored.
1512  */
1513 __isl_give isl_basic_map *isl_basic_map_eliminate(
1514         __isl_take isl_basic_map *bmap,
1515         enum isl_dim_type type, unsigned first, unsigned n)
1516 {
1517         isl_space *space;
1518
1519         if (!bmap)
1520                 return NULL;
1521         if (n == 0)
1522                 return bmap;
1523
1524         if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1525                 isl_die(bmap->ctx, isl_error_invalid,
1526                         "index out of bounds", goto error);
1527
1528         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1529                 first += isl_basic_map_offset(bmap, type) - 1;
1530                 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1531                 return isl_basic_map_finalize(bmap);
1532         }
1533
1534         space = isl_basic_map_get_space(bmap);
1535         bmap = isl_basic_map_project_out(bmap, type, first, n);
1536         bmap = isl_basic_map_insert_dims(bmap, type, first, n);
1537         bmap = isl_basic_map_reset_space(bmap, space);
1538         return bmap;
1539 error:
1540         isl_basic_map_free(bmap);
1541         return NULL;
1542 }
1543
1544 /* Don't assume equalities are in order, because align_divs
1545  * may have changed the order of the divs.
1546  */
1547 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1548 {
1549         int d, i;
1550         unsigned total;
1551
1552         total = isl_space_dim(bmap->dim, isl_dim_all);
1553         for (d = 0; d < total; ++d)
1554                 elim[d] = -1;
1555         for (i = 0; i < bmap->n_eq; ++i) {
1556                 for (d = total - 1; d >= 0; --d) {
1557                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1558                                 continue;
1559                         elim[d] = i;
1560                         break;
1561                 }
1562         }
1563 }
1564
1565 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1566 {
1567         compute_elimination_index((struct isl_basic_map *)bset, elim);
1568 }
1569
1570 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1571         struct isl_basic_map *bmap, int *elim)
1572 {
1573         int d;
1574         int copied = 0;
1575         unsigned total;
1576
1577         total = isl_space_dim(bmap->dim, isl_dim_all);
1578         for (d = total - 1; d >= 0; --d) {
1579                 if (isl_int_is_zero(src[1+d]))
1580                         continue;
1581                 if (elim[d] == -1)
1582                         continue;
1583                 if (!copied) {
1584                         isl_seq_cpy(dst, src, 1 + total);
1585                         copied = 1;
1586                 }
1587                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1588         }
1589         return copied;
1590 }
1591
1592 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1593         struct isl_basic_set *bset, int *elim)
1594 {
1595         return reduced_using_equalities(dst, src,
1596                                         (struct isl_basic_map *)bset, elim);
1597 }
1598
1599 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1600         struct isl_basic_set *bset, struct isl_basic_set *context)
1601 {
1602         int i;
1603         int *elim;
1604
1605         if (!bset || !context)
1606                 goto error;
1607
1608         if (context->n_eq == 0) {
1609                 isl_basic_set_free(context);
1610                 return bset;
1611         }
1612
1613         bset = isl_basic_set_cow(bset);
1614         if (!bset)
1615                 goto error;
1616
1617         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1618         if (!elim)
1619                 goto error;
1620         set_compute_elimination_index(context, elim);
1621         for (i = 0; i < bset->n_eq; ++i)
1622                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1623                                                         context, elim);
1624         for (i = 0; i < bset->n_ineq; ++i)
1625                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1626                                                         context, elim);
1627         isl_basic_set_free(context);
1628         free(elim);
1629         bset = isl_basic_set_simplify(bset);
1630         bset = isl_basic_set_finalize(bset);
1631         return bset;
1632 error:
1633         isl_basic_set_free(bset);
1634         isl_basic_set_free(context);
1635         return NULL;
1636 }
1637
1638 static struct isl_basic_set *remove_shifted_constraints(
1639         struct isl_basic_set *bset, struct isl_basic_set *context)
1640 {
1641         unsigned int size;
1642         isl_int ***index;
1643         int bits;
1644         int k, h, l;
1645         isl_ctx *ctx;
1646
1647         if (!bset)
1648                 return NULL;
1649
1650         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1651         bits = ffs(size) - 1;
1652         ctx = isl_basic_set_get_ctx(bset);
1653         index = isl_calloc_array(ctx, isl_int **, size);
1654         if (!index)
1655                 return bset;
1656
1657         for (k = 0; k < context->n_ineq; ++k) {
1658                 h = set_hash_index(index, size, bits, context, k);
1659                 index[h] = &context->ineq[k];
1660         }
1661         for (k = 0; k < bset->n_ineq; ++k) {
1662                 h = set_hash_index(index, size, bits, bset, k);
1663                 if (!index[h])
1664                         continue;
1665                 l = index[h] - &context->ineq[0];
1666                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1667                         continue;
1668                 bset = isl_basic_set_cow(bset);
1669                 if (!bset)
1670                         goto error;
1671                 isl_basic_set_drop_inequality(bset, k);
1672                 --k;
1673         }
1674         free(index);
1675         return bset;
1676 error:
1677         free(index);
1678         return bset;
1679 }
1680
1681 /* Remove all information from bset that is redundant in the context
1682  * of context.  Both bset and context are assumed to be full-dimensional.
1683  *
1684  * We first * remove the inequalities from "bset"
1685  * that are obviously redundant with respect to some inequality in "context".
1686  *
1687  * If there are any inequalities left, we construct a tableau for
1688  * the context and then add the inequalities of "bset".
1689  * Before adding these inequalities, we freeze all constraints such that
1690  * they won't be considered redundant in terms of the constraints of "bset".
1691  * Then we detect all redundant constraints (among the
1692  * constraints that weren't frozen), first by checking for redundancy in the
1693  * the tableau and then by checking if replacing a constraint by its negation
1694  * would lead to an empty set.  This last step is fairly expensive
1695  * and could be optimized by more reuse of the tableau.
1696  * Finally, we update bset according to the results.
1697  */
1698 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1699         __isl_take isl_basic_set *context)
1700 {
1701         int i, k;
1702         isl_basic_set *combined = NULL;
1703         struct isl_tab *tab = NULL;
1704         unsigned context_ineq;
1705         unsigned total;
1706
1707         if (!bset || !context)
1708                 goto error;
1709
1710         if (isl_basic_set_is_universe(bset)) {
1711                 isl_basic_set_free(context);
1712                 return bset;
1713         }
1714
1715         if (isl_basic_set_is_universe(context)) {
1716                 isl_basic_set_free(context);
1717                 return bset;
1718         }
1719
1720         bset = remove_shifted_constraints(bset, context);
1721         if (!bset)
1722                 goto error;
1723         if (bset->n_ineq == 0)
1724                 goto done;
1725
1726         context_ineq = context->n_ineq;
1727         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1728         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1729         tab = isl_tab_from_basic_set(combined, 0);
1730         for (i = 0; i < context_ineq; ++i)
1731                 if (isl_tab_freeze_constraint(tab, i) < 0)
1732                         goto error;
1733         tab = isl_tab_extend(tab, bset->n_ineq);
1734         for (i = 0; i < bset->n_ineq; ++i)
1735                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1736                         goto error;
1737         bset = isl_basic_set_add_constraints(combined, bset, 0);
1738         combined = NULL;
1739         if (!bset)
1740                 goto error;
1741         if (isl_tab_detect_redundant(tab) < 0)
1742                 goto error;
1743         total = isl_basic_set_total_dim(bset);
1744         for (i = context_ineq; i < bset->n_ineq; ++i) {
1745                 int is_empty;
1746                 if (tab->con[i].is_redundant)
1747                         continue;
1748                 tab->con[i].is_redundant = 1;
1749                 combined = isl_basic_set_dup(bset);
1750                 combined = isl_basic_set_update_from_tab(combined, tab);
1751                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1752                 k = isl_basic_set_alloc_inequality(combined);
1753                 if (k < 0)
1754                         goto error;
1755                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1756                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1757                 is_empty = isl_basic_set_is_empty(combined);
1758                 if (is_empty < 0)
1759                         goto error;
1760                 isl_basic_set_free(combined);
1761                 combined = NULL;
1762                 if (!is_empty)
1763                         tab->con[i].is_redundant = 0;
1764         }
1765         for (i = 0; i < context_ineq; ++i)
1766                 tab->con[i].is_redundant = 1;
1767         bset = isl_basic_set_update_from_tab(bset, tab);
1768         if (bset) {
1769                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1770                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1771         }
1772
1773         isl_tab_free(tab);
1774 done:
1775         bset = isl_basic_set_simplify(bset);
1776         bset = isl_basic_set_finalize(bset);
1777         isl_basic_set_free(context);
1778         return bset;
1779 error:
1780         isl_tab_free(tab);
1781         isl_basic_set_free(combined);
1782         isl_basic_set_free(context);
1783         isl_basic_set_free(bset);
1784         return NULL;
1785 }
1786
1787 /* Remove all information from bset that is redundant in the context
1788  * of context.  In particular, equalities that are linear combinations
1789  * of those in context are removed.  Then the inequalities that are
1790  * redundant in the context of the equalities and inequalities of
1791  * context are removed.
1792  *
1793  * We first compute the integer affine hull of the intersection,
1794  * compute the gist inside this affine hull and then add back
1795  * those equalities that are not implied by the context.
1796  *
1797  * If two constraints are mutually redundant, then uset_gist_full
1798  * will remove the second of those constraints.  We therefore first
1799  * sort the constraints so that constraints not involving existentially
1800  * quantified variables are given precedence over those that do.
1801  * We have to perform this sorting before the variable compression,
1802  * because that may effect the order of the variables.
1803  */
1804 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1805         __isl_take isl_basic_set *context)
1806 {
1807         isl_mat *eq;
1808         isl_mat *T, *T2;
1809         isl_basic_set *aff;
1810         isl_basic_set *aff_context;
1811         unsigned total;
1812
1813         if (!bset || !context)
1814                 goto error;
1815
1816         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1817         if (isl_basic_set_plain_is_empty(bset)) {
1818                 isl_basic_set_free(context);
1819                 return bset;
1820         }
1821         bset = isl_basic_set_sort_constraints(bset);
1822         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1823         if (!aff)
1824                 goto error;
1825         if (isl_basic_set_plain_is_empty(aff)) {
1826                 isl_basic_set_free(aff);
1827                 isl_basic_set_free(context);
1828                 return bset;
1829         }
1830         if (aff->n_eq == 0) {
1831                 isl_basic_set_free(aff);
1832                 return uset_gist_full(bset, context);
1833         }
1834         total = isl_basic_set_total_dim(bset);
1835         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1836         eq = isl_mat_cow(eq);
1837         T = isl_mat_variable_compression(eq, &T2);
1838         if (T && T->n_col == 0) {
1839                 isl_mat_free(T);
1840                 isl_mat_free(T2);
1841                 isl_basic_set_free(context);
1842                 isl_basic_set_free(aff);
1843                 return isl_basic_set_set_to_empty(bset);
1844         }
1845
1846         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1847
1848         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1849         context = isl_basic_set_preimage(context, T);
1850
1851         bset = uset_gist_full(bset, context);
1852         bset = isl_basic_set_preimage(bset, T2);
1853         bset = isl_basic_set_intersect(bset, aff);
1854         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1855
1856         if (bset) {
1857                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1858                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1859         }
1860
1861         return bset;
1862 error:
1863         isl_basic_set_free(bset);
1864         isl_basic_set_free(context);
1865         return NULL;
1866 }
1867
1868 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1869  * We simply add the equalities in context to bmap and then do a regular
1870  * div normalizations.  Better results can be obtained by normalizing
1871  * only the divs in bmap than do not also appear in context.
1872  * We need to be careful to reduce the divs using the equalities
1873  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1874  * spurious constraints.
1875  */
1876 static struct isl_basic_map *normalize_divs_in_context(
1877         struct isl_basic_map *bmap, struct isl_basic_map *context)
1878 {
1879         int i;
1880         unsigned total_context;
1881         int div_eq;
1882
1883         div_eq = n_pure_div_eq(bmap);
1884         if (div_eq == 0)
1885                 return bmap;
1886
1887         if (context->n_div > 0)
1888                 bmap = isl_basic_map_align_divs(bmap, context);
1889
1890         total_context = isl_basic_map_total_dim(context);
1891         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1892         for (i = 0; i < context->n_eq; ++i) {
1893                 int k;
1894                 k = isl_basic_map_alloc_equality(bmap);
1895                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1896                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1897                                 isl_basic_map_total_dim(bmap) - total_context);
1898         }
1899         bmap = isl_basic_map_gauss(bmap, NULL);
1900         bmap = normalize_divs(bmap, NULL);
1901         bmap = isl_basic_map_gauss(bmap, NULL);
1902         return bmap;
1903 }
1904
1905 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1906         struct isl_basic_map *context)
1907 {
1908         struct isl_basic_set *bset;
1909
1910         if (!bmap || !context)
1911                 goto error;
1912
1913         if (isl_basic_map_is_universe(bmap)) {
1914                 isl_basic_map_free(context);
1915                 return bmap;
1916         }
1917         if (isl_basic_map_plain_is_empty(context)) {
1918                 isl_basic_map_free(bmap);
1919                 return context;
1920         }
1921         if (isl_basic_map_plain_is_empty(bmap)) {
1922                 isl_basic_map_free(context);
1923                 return bmap;
1924         }
1925
1926         bmap = isl_basic_map_remove_redundancies(bmap);
1927         context = isl_basic_map_remove_redundancies(context);
1928
1929         if (context->n_eq)
1930                 bmap = normalize_divs_in_context(bmap, context);
1931
1932         context = isl_basic_map_align_divs(context, bmap);
1933         bmap = isl_basic_map_align_divs(bmap, context);
1934
1935         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1936                          isl_basic_map_underlying_set(context));
1937
1938         return isl_basic_map_overlying_set(bset, bmap);
1939 error:
1940         isl_basic_map_free(bmap);
1941         isl_basic_map_free(context);
1942         return NULL;
1943 }
1944
1945 /*
1946  * Assumes context has no implicit divs.
1947  */
1948 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1949         __isl_take isl_basic_map *context)
1950 {
1951         int i;
1952
1953         if (!map || !context)
1954                 goto error;;
1955
1956         if (isl_basic_map_plain_is_empty(context)) {
1957                 isl_map_free(map);
1958                 return isl_map_from_basic_map(context);
1959         }
1960
1961         context = isl_basic_map_remove_redundancies(context);
1962         map = isl_map_cow(map);
1963         if (!map || !context)
1964                 goto error;;
1965         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1966         map = isl_map_compute_divs(map);
1967         for (i = 0; i < map->n; ++i)
1968                 context = isl_basic_map_align_divs(context, map->p[i]);
1969         for (i = map->n - 1; i >= 0; --i) {
1970                 map->p[i] = isl_basic_map_gist(map->p[i],
1971                                                 isl_basic_map_copy(context));
1972                 if (!map->p[i])
1973                         goto error;
1974                 if (isl_basic_map_plain_is_empty(map->p[i])) {
1975                         isl_basic_map_free(map->p[i]);
1976                         if (i != map->n - 1)
1977                                 map->p[i] = map->p[map->n - 1];
1978                         map->n--;
1979                 }
1980         }
1981         isl_basic_map_free(context);
1982         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1983         return map;
1984 error:
1985         isl_map_free(map);
1986         isl_basic_map_free(context);
1987         return NULL;
1988 }
1989
1990 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
1991         __isl_take isl_map *context)
1992 {
1993         context = isl_map_compute_divs(context);
1994         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1995 }
1996
1997 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1998         __isl_take isl_map *context)
1999 {
2000         return isl_map_align_params_map_map_and(map, context, &map_gist);
2001 }
2002
2003 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
2004                                                 struct isl_basic_set *context)
2005 {
2006         return (struct isl_basic_set *)isl_basic_map_gist(
2007                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
2008 }
2009
2010 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
2011         __isl_take isl_basic_set *context)
2012 {
2013         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
2014                                         (struct isl_basic_map *)context);
2015 }
2016
2017 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
2018         __isl_take isl_basic_set *context)
2019 {
2020         isl_space *space = isl_set_get_space(set);
2021         isl_basic_set *dom_context = isl_basic_set_universe(space);
2022         dom_context = isl_basic_set_intersect_params(dom_context, context);
2023         return isl_set_gist_basic_set(set, dom_context);
2024 }
2025
2026 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2027         __isl_take isl_set *context)
2028 {
2029         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
2030                                         (struct isl_map *)context);
2031 }
2032
2033 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
2034         __isl_take isl_set *context)
2035 {
2036         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2037         map_context = isl_map_intersect_domain(map_context, context);
2038         return isl_map_gist(map, map_context);
2039 }
2040
2041 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
2042         __isl_take isl_set *context)
2043 {
2044         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2045         map_context = isl_map_intersect_range(map_context, context);
2046         return isl_map_gist(map, map_context);
2047 }
2048
2049 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
2050         __isl_take isl_set *context)
2051 {
2052         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2053         map_context = isl_map_intersect_params(map_context, context);
2054         return isl_map_gist(map, map_context);
2055 }
2056
2057 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
2058         __isl_take isl_set *context)
2059 {
2060         return isl_map_gist_params(set, context);
2061 }
2062
2063 /* Quick check to see if two basic maps are disjoint.
2064  * In particular, we reduce the equalities and inequalities of
2065  * one basic map in the context of the equalities of the other
2066  * basic map and check if we get a contradiction.
2067  */
2068 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
2069         __isl_keep isl_basic_map *bmap2)
2070 {
2071         struct isl_vec *v = NULL;
2072         int *elim = NULL;
2073         unsigned total;
2074         int i;
2075
2076         if (!bmap1 || !bmap2)
2077                 return -1;
2078         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
2079                         return -1);
2080         if (bmap1->n_div || bmap2->n_div)
2081                 return 0;
2082         if (!bmap1->n_eq && !bmap2->n_eq)
2083                 return 0;
2084
2085         total = isl_space_dim(bmap1->dim, isl_dim_all);
2086         if (total == 0)
2087                 return 0;
2088         v = isl_vec_alloc(bmap1->ctx, 1 + total);
2089         if (!v)
2090                 goto error;
2091         elim = isl_alloc_array(bmap1->ctx, int, total);
2092         if (!elim)
2093                 goto error;
2094         compute_elimination_index(bmap1, elim);
2095         for (i = 0; i < bmap2->n_eq; ++i) {
2096                 int reduced;
2097                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
2098                                                         bmap1, elim);
2099                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
2100                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2101                         goto disjoint;
2102         }
2103         for (i = 0; i < bmap2->n_ineq; ++i) {
2104                 int reduced;
2105                 reduced = reduced_using_equalities(v->block.data,
2106                                                 bmap2->ineq[i], bmap1, elim);
2107                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2108                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2109                         goto disjoint;
2110         }
2111         compute_elimination_index(bmap2, elim);
2112         for (i = 0; i < bmap1->n_ineq; ++i) {
2113                 int reduced;
2114                 reduced = reduced_using_equalities(v->block.data,
2115                                                 bmap1->ineq[i], bmap2, elim);
2116                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2117                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2118                         goto disjoint;
2119         }
2120         isl_vec_free(v);
2121         free(elim);
2122         return 0;
2123 disjoint:
2124         isl_vec_free(v);
2125         free(elim);
2126         return 1;
2127 error:
2128         isl_vec_free(v);
2129         free(elim);
2130         return -1;
2131 }
2132
2133 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2134         __isl_keep isl_basic_set *bset2)
2135 {
2136         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2137                                               (struct isl_basic_map *)bset2);
2138 }
2139
2140 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2141         __isl_keep isl_map *map2)
2142 {
2143         int i, j;
2144
2145         if (!map1 || !map2)
2146                 return -1;
2147
2148         if (isl_map_plain_is_equal(map1, map2))
2149                 return 0;
2150
2151         for (i = 0; i < map1->n; ++i) {
2152                 for (j = 0; j < map2->n; ++j) {
2153                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2154                                                                map2->p[j]);
2155                         if (d != 1)
2156                                 return d;
2157                 }
2158         }
2159         return 1;
2160 }
2161
2162 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2163         __isl_keep isl_set *set2)
2164 {
2165         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2166                                         (struct isl_map *)set2);
2167 }
2168
2169 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2170 {
2171         return isl_set_plain_is_disjoint(set1, set2);
2172 }
2173
2174 /* Check if we can combine a given div with lower bound l and upper
2175  * bound u with some other div and if so return that other div.
2176  * Otherwise return -1.
2177  *
2178  * We first check that
2179  *      - the bounds are opposites of each other (except for the constant
2180  *        term)
2181  *      - the bounds do not reference any other div
2182  *      - no div is defined in terms of this div
2183  *
2184  * Let m be the size of the range allowed on the div by the bounds.
2185  * That is, the bounds are of the form
2186  *
2187  *      e <= a <= e + m - 1
2188  *
2189  * with e some expression in the other variables.
2190  * We look for another div b such that no third div is defined in terms
2191  * of this second div b and such that in any constraint that contains
2192  * a (except for the given lower and upper bound), also contains b
2193  * with a coefficient that is m times that of b.
2194  * That is, all constraints (execpt for the lower and upper bound)
2195  * are of the form
2196  *
2197  *      e + f (a + m b) >= 0
2198  *
2199  * If so, we return b so that "a + m b" can be replaced by
2200  * a single div "c = a + m b".
2201  */
2202 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2203         unsigned div, unsigned l, unsigned u)
2204 {
2205         int i, j;
2206         unsigned dim;
2207         int coalesce = -1;
2208
2209         if (bmap->n_div <= 1)
2210                 return -1;
2211         dim = isl_space_dim(bmap->dim, isl_dim_all);
2212         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2213                 return -1;
2214         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2215                                    bmap->n_div - div - 1) != -1)
2216                 return -1;
2217         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2218                             dim + bmap->n_div))
2219                 return -1;
2220
2221         for (i = 0; i < bmap->n_div; ++i) {
2222                 if (isl_int_is_zero(bmap->div[i][0]))
2223                         continue;
2224                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2225                         return -1;
2226         }
2227
2228         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2229         if (isl_int_is_neg(bmap->ineq[l][0])) {
2230                 isl_int_sub(bmap->ineq[l][0],
2231                             bmap->ineq[l][0], bmap->ineq[u][0]);
2232                 bmap = isl_basic_map_copy(bmap);
2233                 bmap = isl_basic_map_set_to_empty(bmap);
2234                 isl_basic_map_free(bmap);
2235                 return -1;
2236         }
2237         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2238         for (i = 0; i < bmap->n_div; ++i) {
2239                 if (i == div)
2240                         continue;
2241                 if (!pairs[i])
2242                         continue;
2243                 for (j = 0; j < bmap->n_div; ++j) {
2244                         if (isl_int_is_zero(bmap->div[j][0]))
2245                                 continue;
2246                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2247                                 break;
2248                 }
2249                 if (j < bmap->n_div)
2250                         continue;
2251                 for (j = 0; j < bmap->n_ineq; ++j) {
2252                         int valid;
2253                         if (j == l || j == u)
2254                                 continue;
2255                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2256                                 continue;
2257                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2258                                 break;
2259                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2260                                     bmap->ineq[j][1 + dim + div],
2261                                     bmap->ineq[l][0]);
2262                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2263                                            bmap->ineq[j][1 + dim + i]);
2264                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2265                                          bmap->ineq[j][1 + dim + div],
2266                                          bmap->ineq[l][0]);
2267                         if (!valid)
2268                                 break;
2269                 }
2270                 if (j < bmap->n_ineq)
2271                         continue;
2272                 coalesce = i;
2273                 break;
2274         }
2275         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2276         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2277         return coalesce;
2278 }
2279
2280 /* Given a lower and an upper bound on div i, construct an inequality
2281  * that when nonnegative ensures that this pair of bounds always allows
2282  * for an integer value of the given div.
2283  * The lower bound is inequality l, while the upper bound is inequality u.
2284  * The constructed inequality is stored in ineq.
2285  * g, fl, fu are temporary scalars.
2286  *
2287  * Let the upper bound be
2288  *
2289  *      -n_u a + e_u >= 0
2290  *
2291  * and the lower bound
2292  *
2293  *      n_l a + e_l >= 0
2294  *
2295  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2296  * We have
2297  *
2298  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2299  *
2300  * Since all variables are integer valued, this is equivalent to
2301  *
2302  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2303  *
2304  * If this interval is at least f_u f_l g, then it contains at least
2305  * one integer value for a.
2306  * That is, the test constraint is
2307  *
2308  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2309  */
2310 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2311         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2312 {
2313         unsigned dim;
2314         dim = isl_space_dim(bmap->dim, isl_dim_all);
2315
2316         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2317         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2318         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2319         isl_int_neg(fu, fu);
2320         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2321                         1 + dim + bmap->n_div);
2322         isl_int_add(ineq[0], ineq[0], fl);
2323         isl_int_add(ineq[0], ineq[0], fu);
2324         isl_int_sub_ui(ineq[0], ineq[0], 1);
2325         isl_int_mul(g, g, fl);
2326         isl_int_mul(g, g, fu);
2327         isl_int_sub(ineq[0], ineq[0], g);
2328 }
2329
2330 /* Remove more kinds of divs that are not strictly needed.
2331  * In particular, if all pairs of lower and upper bounds on a div
2332  * are such that they allow at least one integer value of the div,
2333  * the we can eliminate the div using Fourier-Motzkin without
2334  * introducing any spurious solutions.
2335  */
2336 static struct isl_basic_map *drop_more_redundant_divs(
2337         struct isl_basic_map *bmap, int *pairs, int n)
2338 {
2339         struct isl_tab *tab = NULL;
2340         struct isl_vec *vec = NULL;
2341         unsigned dim;
2342         int remove = -1;
2343         isl_int g, fl, fu;
2344
2345         isl_int_init(g);
2346         isl_int_init(fl);
2347         isl_int_init(fu);
2348
2349         if (!bmap)
2350                 goto error;
2351
2352         dim = isl_space_dim(bmap->dim, isl_dim_all);
2353         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2354         if (!vec)
2355                 goto error;
2356
2357         tab = isl_tab_from_basic_map(bmap, 0);
2358
2359         while (n > 0) {
2360                 int i, l, u;
2361                 int best = -1;
2362                 enum isl_lp_result res;
2363
2364                 for (i = 0; i < bmap->n_div; ++i) {
2365                         if (!pairs[i])
2366                                 continue;
2367                         if (best >= 0 && pairs[best] <= pairs[i])
2368                                 continue;
2369                         best = i;
2370                 }
2371
2372                 i = best;
2373                 for (l = 0; l < bmap->n_ineq; ++l) {
2374                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2375                                 continue;
2376                         for (u = 0; u < bmap->n_ineq; ++u) {
2377                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2378                                         continue;
2379                                 construct_test_ineq(bmap, i, l, u,
2380                                                     vec->el, g, fl, fu);
2381                                 res = isl_tab_min(tab, vec->el,
2382                                                   bmap->ctx->one, &g, NULL, 0);
2383                                 if (res == isl_lp_error)
2384                                         goto error;
2385                                 if (res == isl_lp_empty) {
2386                                         bmap = isl_basic_map_set_to_empty(bmap);
2387                                         break;
2388                                 }
2389                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2390                                         break;
2391                         }
2392                         if (u < bmap->n_ineq)
2393                                 break;
2394                 }
2395                 if (l == bmap->n_ineq) {
2396                         remove = i;
2397                         break;
2398                 }
2399                 pairs[i] = 0;
2400                 --n;
2401         }
2402
2403         isl_tab_free(tab);
2404         isl_vec_free(vec);
2405
2406         isl_int_clear(g);
2407         isl_int_clear(fl);
2408         isl_int_clear(fu);
2409
2410         free(pairs);
2411
2412         if (remove < 0)
2413                 return bmap;
2414
2415         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2416         return isl_basic_map_drop_redundant_divs(bmap);
2417 error:
2418         free(pairs);
2419         isl_basic_map_free(bmap);
2420         isl_tab_free(tab);
2421         isl_vec_free(vec);
2422         isl_int_clear(g);
2423         isl_int_clear(fl);
2424         isl_int_clear(fu);
2425         return NULL;
2426 }
2427
2428 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2429  * and the upper bound u, div1 always occurs together with div2 in the form
2430  * (div1 + m div2), where m is the constant range on the variable div1
2431  * allowed by l and u, replace the pair div1 and div2 by a single
2432  * div that is equal to div1 + m div2.
2433  *
2434  * The new div will appear in the location that contains div2.
2435  * We need to modify all constraints that contain
2436  * div2 = (div - div1) / m
2437  * (If a constraint does not contain div2, it will also not contain div1.)
2438  * If the constraint also contains div1, then we know they appear
2439  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2440  * i.e., the coefficient of div is f.
2441  *
2442  * Otherwise, we first need to introduce div1 into the constraint.
2443  * Let the l be
2444  *
2445  *      div1 + f >=0
2446  *
2447  * and u
2448  *
2449  *      -div1 + f' >= 0
2450  *
2451  * A lower bound on div2
2452  *
2453  *      n div2 + t >= 0
2454  *
2455  * can be replaced by
2456  *
2457  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2458  *
2459  * with g = gcd(m,n).
2460  * An upper bound
2461  *
2462  *      -n div2 + t >= 0
2463  *
2464  * can be replaced by
2465  *
2466  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2467  *
2468  * These constraint are those that we would obtain from eliminating
2469  * div1 using Fourier-Motzkin.
2470  *
2471  * After all constraints have been modified, we drop the lower and upper
2472  * bound and then drop div1.
2473  */
2474 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2475         unsigned div1, unsigned div2, unsigned l, unsigned u)
2476 {
2477         isl_int a;
2478         isl_int b;
2479         isl_int m;
2480         unsigned dim, total;
2481         int i;
2482
2483         dim = isl_space_dim(bmap->dim, isl_dim_all);
2484         total = 1 + dim + bmap->n_div;
2485
2486         isl_int_init(a);
2487         isl_int_init(b);
2488         isl_int_init(m);
2489         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2490         isl_int_add_ui(m, m, 1);
2491
2492         for (i = 0; i < bmap->n_ineq; ++i) {
2493                 if (i == l || i == u)
2494                         continue;
2495                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2496                         continue;
2497                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2498                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2499                         isl_int_divexact(a, m, b);
2500                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2501                         if (isl_int_is_pos(b)) {
2502                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2503                                                 b, bmap->ineq[l], total);
2504                         } else {
2505                                 isl_int_neg(b, b);
2506                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2507                                                 b, bmap->ineq[u], total);
2508                         }
2509                 }
2510                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2511                             bmap->ineq[i][1 + dim + div1]);
2512                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2513         }
2514
2515         isl_int_clear(a);
2516         isl_int_clear(b);
2517         isl_int_clear(m);
2518         if (l > u) {
2519                 isl_basic_map_drop_inequality(bmap, l);
2520                 isl_basic_map_drop_inequality(bmap, u);
2521         } else {
2522                 isl_basic_map_drop_inequality(bmap, u);
2523                 isl_basic_map_drop_inequality(bmap, l);
2524         }
2525         bmap = isl_basic_map_drop_div(bmap, div1);
2526         return bmap;
2527 }
2528
2529 /* First check if we can coalesce any pair of divs and
2530  * then continue with dropping more redundant divs.
2531  *
2532  * We loop over all pairs of lower and upper bounds on a div
2533  * with coefficient 1 and -1, respectively, check if there
2534  * is any other div "c" with which we can coalesce the div
2535  * and if so, perform the coalescing.
2536  */
2537 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2538         struct isl_basic_map *bmap, int *pairs, int n)
2539 {
2540         int i, l, u;
2541         unsigned dim;
2542
2543         dim = isl_space_dim(bmap->dim, isl_dim_all);
2544
2545         for (i = 0; i < bmap->n_div; ++i) {
2546                 if (!pairs[i])
2547                         continue;
2548                 for (l = 0; l < bmap->n_ineq; ++l) {
2549                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2550                                 continue;
2551                         for (u = 0; u < bmap->n_ineq; ++u) {
2552                                 int c;
2553
2554                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2555                                         continue;
2556                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2557                                 if (c < 0)
2558                                         continue;
2559                                 free(pairs);
2560                                 bmap = coalesce_divs(bmap, i, c, l, u);
2561                                 return isl_basic_map_drop_redundant_divs(bmap);
2562                         }
2563                 }
2564         }
2565
2566         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2567                 return bmap;
2568
2569         return drop_more_redundant_divs(bmap, pairs, n);
2570 }
2571
2572 /* Remove divs that are not strictly needed.
2573  * In particular, if a div only occurs positively (or negatively)
2574  * in constraints, then it can simply be dropped.
2575  * Also, if a div occurs only occurs in two constraints and if moreover
2576  * those two constraints are opposite to each other, except for the constant
2577  * term and if the sum of the constant terms is such that for any value
2578  * of the other values, there is always at least one integer value of the
2579  * div, i.e., if one plus this sum is greater than or equal to
2580  * the (absolute value) of the coefficent of the div in the constraints,
2581  * then we can also simply drop the div.
2582  *
2583  * If any divs are left after these simple checks then we move on
2584  * to more complicated cases in drop_more_redundant_divs.
2585  */
2586 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2587         struct isl_basic_map *bmap)
2588 {
2589         int i, j;
2590         unsigned off;
2591         int *pairs = NULL;
2592         int n = 0;
2593
2594         if (!bmap)
2595                 goto error;
2596
2597         off = isl_space_dim(bmap->dim, isl_dim_all);
2598         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2599         if (!pairs)
2600                 goto error;
2601
2602         for (i = 0; i < bmap->n_div; ++i) {
2603                 int pos, neg;
2604                 int last_pos, last_neg;
2605                 int redundant;
2606                 int defined;
2607
2608                 defined = !isl_int_is_zero(bmap->div[i][0]);
2609                 for (j = 0; j < bmap->n_eq; ++j)
2610                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2611                                 break;
2612                 if (j < bmap->n_eq)
2613                         continue;
2614                 ++n;
2615                 pos = neg = 0;
2616                 for (j = 0; j < bmap->n_ineq; ++j) {
2617                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2618                                 last_pos = j;
2619                                 ++pos;
2620                         }
2621                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2622                                 last_neg = j;
2623                                 ++neg;
2624                         }
2625                 }
2626                 pairs[i] = pos * neg;
2627                 if (pairs[i] == 0) {
2628                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2629                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2630                                         isl_basic_map_drop_inequality(bmap, j);
2631                         bmap = isl_basic_map_drop_div(bmap, i);
2632                         free(pairs);
2633                         return isl_basic_map_drop_redundant_divs(bmap);
2634                 }
2635                 if (pairs[i] != 1)
2636                         continue;
2637                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2638                                     bmap->ineq[last_neg] + 1,
2639                                     off + bmap->n_div))
2640                         continue;
2641
2642                 isl_int_add(bmap->ineq[last_pos][0],
2643                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2644                 isl_int_add_ui(bmap->ineq[last_pos][0],
2645                                bmap->ineq[last_pos][0], 1);
2646                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2647                                 bmap->ineq[last_pos][1+off+i]);
2648                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2649                                bmap->ineq[last_pos][0], 1);
2650                 isl_int_sub(bmap->ineq[last_pos][0],
2651                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2652                 if (!redundant) {
2653                         if (defined ||
2654                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2655                                 pairs[i] = 0;
2656                                 --n;
2657                                 continue;
2658                         }
2659                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2660                         bmap = isl_basic_map_simplify(bmap);
2661                         free(pairs);
2662                         return isl_basic_map_drop_redundant_divs(bmap);
2663                 }
2664                 if (last_pos > last_neg) {
2665                         isl_basic_map_drop_inequality(bmap, last_pos);
2666                         isl_basic_map_drop_inequality(bmap, last_neg);
2667                 } else {
2668                         isl_basic_map_drop_inequality(bmap, last_neg);
2669                         isl_basic_map_drop_inequality(bmap, last_pos);
2670                 }
2671                 bmap = isl_basic_map_drop_div(bmap, i);
2672                 free(pairs);
2673                 return isl_basic_map_drop_redundant_divs(bmap);
2674         }
2675
2676         if (n > 0)
2677                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2678
2679         free(pairs);
2680         return bmap;
2681 error:
2682         free(pairs);
2683         isl_basic_map_free(bmap);
2684         return NULL;
2685 }
2686
2687 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2688         struct isl_basic_set *bset)
2689 {
2690         return (struct isl_basic_set *)
2691             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2692 }
2693
2694 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2695 {
2696         int i;
2697
2698         if (!map)
2699                 return NULL;
2700         for (i = 0; i < map->n; ++i) {
2701                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2702                 if (!map->p[i])
2703                         goto error;
2704         }
2705         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2706         return map;
2707 error:
2708         isl_map_free(map);
2709         return NULL;
2710 }
2711
2712 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2713 {
2714         return (struct isl_set *)
2715             isl_map_drop_redundant_divs((struct isl_map *)set);
2716 }