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 MIT 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 the div expression,
 376  * not taking into account the constant term.
 377  * That is, if the div is of the form
 378  *
 379  *      floor((a + m f(x))/(m d))
 380  *
 381  * then 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 void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div)
 389 {
 390         unsigned total = isl_basic_map_total_dim(bmap);
 391         isl_ctx *ctx = bmap->ctx;
 392
 393         if (isl_int_is_zero(bmap->div[div][0]))
 394                 return;
 395         isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
 396         isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]);
 397         if (isl_int_is_one(ctx->normalize_gcd))
 398                 return;
 399         isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1],
 400                         ctx->normalize_gcd);
 401         isl_int_divexact(bmap->div[div][0], bmap->div[div][0],
 402                         ctx->normalize_gcd);
 403         isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
 404                         ctx->normalize_gcd, total);
 405 }
 406
 407 /* Remove any common factor in numerator and denominator of a div expression,
 408  * not taking into account the constant term.
 409  * That is, look for any div of the form
 410  *
 411  *      floor((a + m f(x))/(m d))
 412  *
 413  * and replace it by
 414  *
 415  *      floor((floor(a/m) + f(x))/d)
 416  *
 417  * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
 418  * and can therefore not influence the result of the floor.
 419  */
 420 static __isl_give isl_basic_map *normalize_div_expressions(
 421         __isl_take isl_basic_map *bmap)
 422 {
 423         int i;
 424
 425         if (!bmap)
 426                 return NULL;
 427         if (bmap->n_div == 0)
 428                 return bmap;
 429
 430         for (i = 0; i < bmap->n_div; ++i)
 431                 normalize_div_expression(bmap, i);
 432
 433         return bmap;
 434 }
 435
 436 /* Assumes divs have been ordered if keep_divs is set.
 437  */
 438 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 439         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 440 {
 441         unsigned total;
 442         unsigned space_total;
 443         int k;
 444         int last_div;
 445
 446         total = isl_basic_map_total_dim(bmap);
 447         space_total = isl_space_dim(bmap->dim, isl_dim_all);
 448         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 449         for (k = 0; k < bmap->n_eq; ++k) {
 450                 if (bmap->eq[k] == eq)
 451                         continue;
 452                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 453                         continue;
 454                 if (progress)
 455                         *progress = 1;
 456                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 457                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
 458         }
 459
 460         for (k = 0; k < bmap->n_ineq; ++k) {
 461                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 462                         continue;
 463                 if (progress)
 464                         *progress = 1;
 465                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 466                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
 467                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 468         }
 469
 470         for (k = 0; k < bmap->n_div; ++k) {
 471                 if (isl_int_is_zero(bmap->div[k][0]))
 472                         continue;
 473                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 474                         continue;
 475                 if (progress)
 476                         *progress = 1;
 477                 /* We need to be careful about circular definitions,
 478                  * so for now we just remove the definition of div k
 479                  * if the equality contains any divs.
 480                  * If keep_divs is set, then the divs have been ordered
 481                  * and we can keep the definition as long as the result
 482                  * is still ordered.
 483                  */
 484                 if (last_div == -1 || (keep_divs && last_div < k)) {
 485                         isl_seq_elim(bmap->div[k]+1, eq,
 486                                         1+pos, 1+total, &bmap->div[k][0]);
 487                         normalize_div_expression(bmap, k);
 488                 } else
 489                         isl_seq_clr(bmap->div[k], 1 + total);
 490                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 491         }
 492 }
 493
 494 /* Assumes divs have been ordered if keep_divs is set.
 495  */
 496 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 497         unsigned div, int keep_divs)
 498 {
 499         unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
 500
 501         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 502
 503         isl_basic_map_drop_div(bmap, div);
 504 }
 505
 506 /* Check if elimination of div "div" using equality "eq" would not
 507  * result in a div depending on a later div.
 508  */
 509 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 510         unsigned div)
 511 {
 512         int k;
 513         int last_div;
 514         unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
 515         unsigned pos = space_total + div;
 516
 517         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 518         if (last_div < 0 || last_div <= div)
 519                 return 1;
 520
 521         for (k = 0; k <= last_div; ++k) {
 522                 if (isl_int_is_zero(bmap->div[k][0]))
 523                         return 1;
 524                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 525                         return 0;
 526         }
 527
 528         return 1;
 529 }
 530
 531 /* Elimininate divs based on equalities
 532  */
 533 static struct isl_basic_map *eliminate_divs_eq(
 534                 struct isl_basic_map *bmap, int *progress)
 535 {
 536         int d;
 537         int i;
 538         int modified = 0;
 539         unsigned off;
 540
 541         bmap = isl_basic_map_order_divs(bmap);
 542
 543         if (!bmap)
 544                 return NULL;
 545
 546         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 547
 548         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 549                 for (i = 0; i < bmap->n_eq; ++i) {
 550                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 551                             !isl_int_is_negone(bmap->eq[i][off + d]))
 552                                 continue;
 553                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 554                                 continue;
 555                         modified = 1;
 556                         *progress = 1;
 557                         eliminate_div(bmap, bmap->eq[i], d, 1);
 558                         isl_basic_map_drop_equality(bmap, i);
 559                         break;
 560                 }
 561         }
 562         if (modified)
 563                 return eliminate_divs_eq(bmap, progress);
 564         return bmap;
 565 }
 566
 567 /* Elimininate divs based on inequalities
 568  */
 569 static struct isl_basic_map *eliminate_divs_ineq(
 570                 struct isl_basic_map *bmap, int *progress)
 571 {
 572         int d;
 573         int i;
 574         unsigned off;
 575         struct isl_ctx *ctx;
 576
 577         if (!bmap)
 578                 return NULL;
 579
 580         ctx = bmap->ctx;
 581         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 582
 583         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 584                 for (i = 0; i < bmap->n_eq; ++i)
 585                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 586                                 break;
 587                 if (i < bmap->n_eq)
 588                         continue;
 589                 for (i = 0; i < bmap->n_ineq; ++i)
 590                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 591                                 break;
 592                 if (i < bmap->n_ineq)
 593                         continue;
 594                 *progress = 1;
 595                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 596                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 597                         break;
 598                 bmap = isl_basic_map_drop_div(bmap, d);
 599                 if (!bmap)
 600                         break;
 601         }
 602         return bmap;
 603 }
 604
 605 struct isl_basic_map *isl_basic_map_gauss(
 606         struct isl_basic_map *bmap, int *progress)
 607 {
 608         int k;
 609         int done;
 610         int last_var;
 611         unsigned total_var;
 612         unsigned total;
 613
 614         bmap = isl_basic_map_order_divs(bmap);
 615
 616         if (!bmap)
 617                 return NULL;
 618
 619         total = isl_basic_map_total_dim(bmap);
 620         total_var = total - bmap->n_div;
 621
 622         last_var = total - 1;
 623         for (done = 0; done < bmap->n_eq; ++done) {
 624                 for (; last_var >= 0; --last_var) {
 625                         for (k = done; k < bmap->n_eq; ++k)
 626                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 627                                         break;
 628                         if (k < bmap->n_eq)
 629                                 break;
 630                 }
 631                 if (last_var < 0)
 632                         break;
 633                 if (k != done)
 634                         swap_equality(bmap, k, done);
 635                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 636                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 637
 638                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 639                                                 progress);
 640
 641                 if (last_var >= total_var &&
 642                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 643                         unsigned div = last_var - total_var;
 644                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 645                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 646                         isl_int_set(bmap->div[div][0],
 647                                     bmap->eq[done][1+last_var]);
 648                         if (progress)
 649                                 *progress = 1;
 650                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 651                 }
 652         }
 653         if (done == bmap->n_eq)
 654                 return bmap;
 655         for (k = done; k < bmap->n_eq; ++k) {
 656                 if (isl_int_is_zero(bmap->eq[k][0]))
 657                         continue;
 658                 return isl_basic_map_set_to_empty(bmap);
 659         }
 660         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 661         return bmap;
 662 }
 663
 664 struct isl_basic_set *isl_basic_set_gauss(
 665         struct isl_basic_set *bset, int *progress)
 666 {
 667         return (struct isl_basic_set*)isl_basic_map_gauss(
 668                         (struct isl_basic_map *)bset, progress);
 669 }
 670
 671
 672 static unsigned int round_up(unsigned int v)
 673 {
 674         int old_v = v;
 675
 676         while (v) {
 677                 old_v = v;
 678                 v ^= v & -v;
 679         }
 680         return old_v << 1;
 681 }
 682
 683 static int hash_index(isl_int ***index, unsigned int size, int bits,
 684                         struct isl_basic_map *bmap, int k)
 685 {
 686         int h;
 687         unsigned total = isl_basic_map_total_dim(bmap);
 688         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 689         for (h = hash; index[h]; h = (h+1) % size)
 690                 if (&bmap->ineq[k] != index[h] &&
 691                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 692                         break;
 693         return h;
 694 }
 695
 696 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 697                           struct isl_basic_set *bset, int k)
 698 {
 699         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 700 }
 701
 702 /* If we can eliminate more than one div, then we need to make
 703  * sure we do it from last div to first div, in order not to
 704  * change the position of the other divs that still need to
 705  * be removed.
 706  */
 707 static struct isl_basic_map *remove_duplicate_divs(
 708         struct isl_basic_map *bmap, int *progress)
 709 {
 710         unsigned int size;
 711         int *index;
 712         int *elim_for;
 713         int k, l, h;
 714         int bits;
 715         struct isl_blk eq;
 716         unsigned total_var;
 717         unsigned total;
 718         struct isl_ctx *ctx;
 719
 720         bmap = isl_basic_map_order_divs(bmap);
 721         if (!bmap || bmap->n_div <= 1)
 722                 return bmap;
 723
 724         total_var = isl_space_dim(bmap->dim, isl_dim_all);
 725         total = total_var + bmap->n_div;
 726
 727         ctx = bmap->ctx;
 728         for (k = bmap->n_div - 1; k >= 0; --k)
 729                 if (!isl_int_is_zero(bmap->div[k][0]))
 730                         break;
 731         if (k <= 0)
 732                 return bmap;
 733
 734         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 735         size = round_up(4 * bmap->n_div / 3 - 1);
 736         bits = ffs(size) - 1;
 737         index = isl_calloc_array(ctx, int, size);
 738         if (!index)
 739                 return bmap;
 740         eq = isl_blk_alloc(ctx, 1+total);
 741         if (isl_blk_is_error(eq))
 742                 goto out;
 743
 744         isl_seq_clr(eq.data, 1+total);
 745         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 746         for (--k; k >= 0; --k) {
 747                 uint32_t hash;
 748
 749                 if (isl_int_is_zero(bmap->div[k][0]))
 750                         continue;
 751
 752                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 753                 for (h = hash; index[h]; h = (h+1) % size)
 754                         if (isl_seq_eq(bmap->div[k],
 755                                        bmap->div[index[h]-1], 2+total))
 756                                 break;
 757                 if (index[h]) {
 758                         *progress = 1;
 759                         l = index[h] - 1;
 760                         elim_for[l] = k + 1;
 761                 }
 762                 index[h] = k+1;
 763         }
 764         for (l = bmap->n_div - 1; l >= 0; --l) {
 765                 if (!elim_for[l])
 766                         continue;
 767                 k = elim_for[l] - 1;
 768                 isl_int_set_si(eq.data[1+total_var+k], -1);
 769                 isl_int_set_si(eq.data[1+total_var+l], 1);
 770                 eliminate_div(bmap, eq.data, l, 1);
 771                 isl_int_set_si(eq.data[1+total_var+k], 0);
 772                 isl_int_set_si(eq.data[1+total_var+l], 0);
 773         }
 774
 775         isl_blk_free(ctx, eq);
 776 out:
 777         free(index);
 778         free(elim_for);
 779         return bmap;
 780 }
 781
 782 static int n_pure_div_eq(struct isl_basic_map *bmap)
 783 {
 784         int i, j;
 785         unsigned total;
 786
 787         total = isl_space_dim(bmap->dim, isl_dim_all);
 788         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 789                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 790                         --j;
 791                 if (j < 0)
 792                         break;
 793                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 794                         return 0;
 795         }
 796         return i;
 797 }
 798
 799 /* Normalize divs that appear in equalities.
 800  *
 801  * In particular, we assume that bmap contains some equalities
 802  * of the form
 803  *
 804  *      a x = m * e_i
 805  *
 806  * and we want to replace the set of e_i by a minimal set and
 807  * such that the new e_i have a canonical representation in terms
 808  * of the vector x.
 809  * If any of the equalities involves more than one divs, then
 810  * we currently simply bail out.
 811  *
 812  * Let us first additionally assume that all equalities involve
 813  * a div.  The equalities then express modulo constraints on the
 814  * remaining variables and we can use "parameter compression"
 815  * to find a minimal set of constraints.  The result is a transformation
 816  *
 817  *      x = T(x') = x_0 + G x'
 818  *
 819  * with G a lower-triangular matrix with all elements below the diagonal
 820  * non-negative and smaller than the diagonal element on the same row.
 821  * We first normalize x_0 by making the same property hold in the affine
 822  * T matrix.
 823  * The rows i of G with a 1 on the diagonal do not impose any modulo
 824  * constraint and simply express x_i = x'_i.
 825  * For each of the remaining rows i, we introduce a div and a corresponding
 826  * equality.  In particular
 827  *
 828  *      g_ii e_j = x_i - g_i(x')
 829  *
 830  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 831  * corresponding div (if g_kk != 1).
 832  *
 833  * If there are any equalities not involving any div, then we
 834  * first apply a variable compression on the variables x:
 835  *
 836  *      x = C x''       x'' = C_2 x
 837  *
 838  * and perform the above parameter compression on A C instead of on A.
 839  * The resulting compression is then of the form
 840  *
 841  *      x'' = T(x') = x_0 + G x'
 842  *
 843  * and in constructing the new divs and the corresponding equalities,
 844  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 845  * by the corresponding row from C_2.
 846  */
 847 static struct isl_basic_map *normalize_divs(
 848         struct isl_basic_map *bmap, int *progress)
 849 {
 850         int i, j, k;
 851         int total;
 852         int div_eq;
 853         struct isl_mat *B;
 854         struct isl_vec *d;
 855         struct isl_mat *T = NULL;
 856         struct isl_mat *C = NULL;
 857         struct isl_mat *C2 = NULL;
 858         isl_int v;
 859         int *pos;
 860         int dropped, needed;
 861
 862         if (!bmap)
 863                 return NULL;
 864
 865         if (bmap->n_div == 0)
 866                 return bmap;
 867
 868         if (bmap->n_eq == 0)
 869                 return bmap;
 870
 871         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 872                 return bmap;
 873
 874         total = isl_space_dim(bmap->dim, isl_dim_all);
 875         div_eq = n_pure_div_eq(bmap);
 876         if (div_eq == 0)
 877                 return bmap;
 878
 879         if (div_eq < bmap->n_eq) {
 880                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 881                                         bmap->n_eq - div_eq, 0, 1 + total);
 882                 C = isl_mat_variable_compression(B, &C2);
 883                 if (!C || !C2)
 884                         goto error;
 885                 if (C->n_col == 0) {
 886                         bmap = isl_basic_map_set_to_empty(bmap);
 887                         isl_mat_free(C);
 888                         isl_mat_free(C2);
 889                         goto done;
 890                 }
 891         }
 892
 893         d = isl_vec_alloc(bmap->ctx, div_eq);
 894         if (!d)
 895                 goto error;
 896         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 897                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 898                         --j;
 899                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 900         }
 901         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 902
 903         if (C) {
 904                 B = isl_mat_product(B, C);
 905                 C = NULL;
 906         }
 907
 908         T = isl_mat_parameter_compression(B, d);
 909         if (!T)
 910                 goto error;
 911         if (T->n_col == 0) {
 912                 bmap = isl_basic_map_set_to_empty(bmap);
 913                 isl_mat_free(C2);
 914                 isl_mat_free(T);
 915                 goto done;
 916         }
 917         isl_int_init(v);
 918         for (i = 0; i < T->n_row - 1; ++i) {
 919                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 920                 if (isl_int_is_zero(v))
 921                         continue;
 922                 isl_mat_col_submul(T, 0, v, 1 + i);
 923         }
 924         isl_int_clear(v);
 925         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 926         if (!pos)
 927                 goto error;
 928         /* We have to be careful because dropping equalities may reorder them */
 929         dropped = 0;
 930         for (j = bmap->n_div - 1; j >= 0; --j) {
 931                 for (i = 0; i < bmap->n_eq; ++i)
 932                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 933                                 break;
 934                 if (i < bmap->n_eq) {
 935                         bmap = isl_basic_map_drop_div(bmap, j);
 936                         isl_basic_map_drop_equality(bmap, i);
 937                         ++dropped;
 938                 }
 939         }
 940         pos[0] = 0;
 941         needed = 0;
 942         for (i = 1; i < T->n_row; ++i) {
 943                 if (isl_int_is_one(T->row[i][i]))
 944                         pos[i] = i;
 945                 else
 946                         needed++;
 947         }
 948         if (needed > dropped) {
 949                 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 950                                 needed, needed, 0);
 951                 if (!bmap)
 952                         goto error;
 953         }
 954         for (i = 1; i < T->n_row; ++i) {
 955                 if (isl_int_is_one(T->row[i][i]))
 956                         continue;
 957                 k = isl_basic_map_alloc_div(bmap);
 958                 pos[i] = 1 + total + k;
 959                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 960                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 961                 if (C2)
 962                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 963                 else
 964                         isl_int_set_si(bmap->div[k][1 + i], 1);
 965                 for (j = 0; j < i; ++j) {
 966                         if (isl_int_is_zero(T->row[i][j]))
 967                                 continue;
 968                         if (pos[j] < T->n_row && C2)
 969                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 970                                                 C2->row[pos[j]], 1 + total);
 971                         else
 972                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 973                                                                 T->row[i][j]);
 974                 }
 975                 j = isl_basic_map_alloc_equality(bmap);
 976                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 977                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 978         }
 979         free(pos);
 980         isl_mat_free(C2);
 981         isl_mat_free(T);
 982
 983         if (progress)
 984                 *progress = 1;
 985 done:
 986         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 987
 988         return bmap;
 989 error:
 990         isl_mat_free(C);
 991         isl_mat_free(C2);
 992         isl_mat_free(T);
 993         return bmap;
 994 }
 995
 996 static struct isl_basic_map *set_div_from_lower_bound(
 997         struct isl_basic_map *bmap, int div, int ineq)
 998 {
 999         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1000
1001         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
1002         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
1003         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
1004         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1005         isl_int_set_si(bmap->div[div][1 + total + div], 0);
1006
1007         return bmap;
1008 }
1009
1010 /* Check whether it is ok to define a div based on an inequality.
1011  * To avoid the introduction of circular definitions of divs, we
1012  * do not allow such a definition if the resulting expression would refer to
1013  * any other undefined divs or if any known div is defined in
1014  * terms of the unknown div.
1015  */
1016 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
1017         int div, int ineq)
1018 {
1019         int j;
1020         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1021
1022         /* Not defined in terms of unknown divs */
1023         for (j = 0; j < bmap->n_div; ++j) {
1024                 if (div == j)
1025                         continue;
1026                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1027                         continue;
1028                 if (isl_int_is_zero(bmap->div[j][0]))
1029                         return 0;
1030         }
1031
1032         /* No other div defined in terms of this one => avoid loops */
1033         for (j = 0; j < bmap->n_div; ++j) {
1034                 if (div == j)
1035                         continue;
1036                 if (isl_int_is_zero(bmap->div[j][0]))
1037                         continue;
1038                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1039                         return 0;
1040         }
1041
1042         return 1;
1043 }
1044
1045 /* Given two constraints "k" and "l" that are opposite to each other,
1046  * except for the constant term, check if we can use them
1047  * to obtain an expression for one of the hitherto unknown divs.
1048  * "sum" is the sum of the constant terms of the constraints.
1049  * If this sum is strictly smaller than the coefficient of one
1050  * of the divs, then this pair can be used define the div.
1051  * To avoid the introduction of circular definitions of divs, we
1052  * do not use the pair if the resulting expression would refer to
1053  * any other undefined divs or if any known div is defined in
1054  * terms of the unknown div.
1055  */
1056 static struct isl_basic_map *check_for_div_constraints(
1057         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
1058 {
1059         int i;
1060         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1061
1062         for (i = 0; i < bmap->n_div; ++i) {
1063                 if (!isl_int_is_zero(bmap->div[i][0]))
1064                         continue;
1065                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1066                         continue;
1067                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1068                         continue;
1069                 if (!ok_to_set_div_from_bound(bmap, i, k))
1070                         break;
1071                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1072                         bmap = set_div_from_lower_bound(bmap, i, k);
1073                 else
1074                         bmap = set_div_from_lower_bound(bmap, i, l);
1075                 if (progress)
1076                         *progress = 1;
1077                 break;
1078         }
1079         return bmap;
1080 }
1081
1082 static struct isl_basic_map *remove_duplicate_constraints(
1083         struct isl_basic_map *bmap, int *progress, int detect_divs)
1084 {
1085         unsigned int size;
1086         isl_int ***index;
1087         int k, l, h;
1088         int bits;
1089         unsigned total = isl_basic_map_total_dim(bmap);
1090         isl_int sum;
1091         isl_ctx *ctx;
1092
1093         if (!bmap || bmap->n_ineq <= 1)
1094                 return bmap;
1095
1096         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1097         bits = ffs(size) - 1;
1098         ctx = isl_basic_map_get_ctx(bmap);
1099         index = isl_calloc_array(ctx, isl_int **, size);
1100         if (!index)
1101                 return bmap;
1102
1103         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1104         for (k = 1; k < bmap->n_ineq; ++k) {
1105                 h = hash_index(index, size, bits, bmap, k);
1106                 if (!index[h]) {
1107                         index[h] = &bmap->ineq[k];
1108                         continue;
1109                 }
1110                 if (progress)
1111                         *progress = 1;
1112                 l = index[h] - &bmap->ineq[0];
1113                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1114                         swap_inequality(bmap, k, l);
1115                 isl_basic_map_drop_inequality(bmap, k);
1116                 --k;
1117         }
1118         isl_int_init(sum);
1119         for (k = 0; k < bmap->n_ineq-1; ++k) {
1120                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1121                 h = hash_index(index, size, bits, bmap, k);
1122                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1123                 if (!index[h])
1124                         continue;
1125                 l = index[h] - &bmap->ineq[0];
1126                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1127                 if (isl_int_is_pos(sum)) {
1128                         if (detect_divs)
1129                                 bmap = check_for_div_constraints(bmap, k, l,
1130                                                                  sum, progress);
1131                         continue;
1132                 }
1133                 if (isl_int_is_zero(sum)) {
1134                         /* We need to break out of the loop after these
1135                          * changes since the contents of the hash
1136                          * will no longer be valid.
1137                          * Plus, we probably we want to regauss first.
1138                          */
1139                         if (progress)
1140                                 *progress = 1;
1141                         isl_basic_map_drop_inequality(bmap, l);
1142                         isl_basic_map_inequality_to_equality(bmap, k);
1143                 } else
1144                         bmap = isl_basic_map_set_to_empty(bmap);
1145                 break;
1146         }
1147         isl_int_clear(sum);
1148
1149         free(index);
1150         return bmap;
1151 }
1152
1153
1154 /* Eliminate knowns divs from constraints where they appear with
1155  * a (positive or negative) unit coefficient.
1156  *
1157  * That is, replace
1158  *
1159  *      floor(e/m) + f >= 0
1160  *
1161  * by
1162  *
1163  *      e + m f >= 0
1164  *
1165  * and
1166  *
1167  *      -floor(e/m) + f >= 0
1168  *
1169  * by
1170  *
1171  *      -e + m f + m - 1 >= 0
1172  *
1173  * The first conversion is valid because floor(e/m) >= -f is equivalent
1174  * to e/m >= -f because -f is an integral expression.
1175  * The second conversion follows from the fact that
1176  *
1177  *      -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1178  *
1179  *
1180  * We skip integral divs, i.e., those with denominator 1, as we would
1181  * risk eliminating the div from the div constraints.  We do not need
1182  * to handle those divs here anyway since the div constraints will turn
1183  * out to form an equality and this equality can then be use to eliminate
1184  * the div from all constraints.
1185  */
1186 static __isl_give isl_basic_map *eliminate_unit_divs(
1187         __isl_take isl_basic_map *bmap, int *progress)
1188 {
1189         int i, j;
1190         isl_ctx *ctx;
1191         unsigned total;
1192
1193         if (!bmap)
1194                 return NULL;
1195
1196         ctx = isl_basic_map_get_ctx(bmap);
1197         total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1198
1199         for (i = 0; i < bmap->n_div; ++i) {
1200                 if (isl_int_is_zero(bmap->div[i][0]))
1201                         continue;
1202                 if (isl_int_is_one(bmap->div[i][0]))
1203                         continue;
1204                 for (j = 0; j < bmap->n_ineq; ++j) {
1205                         int s;
1206
1207                         if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
1208                             !isl_int_is_negone(bmap->ineq[j][total + i]))
1209                                 continue;
1210
1211                         *progress = 1;
1212
1213                         s = isl_int_sgn(bmap->ineq[j][total + i]);
1214                         isl_int_set_si(bmap->ineq[j][total + i], 0);
1215                         if (s < 0)
1216                                 isl_seq_combine(bmap->ineq[j],
1217                                         ctx->negone, bmap->div[i] + 1,
1218                                         bmap->div[i][0], bmap->ineq[j],
1219                                         total + bmap->n_div);
1220                         else
1221                                 isl_seq_combine(bmap->ineq[j],
1222                                         ctx->one, bmap->div[i] + 1,
1223                                         bmap->div[i][0], bmap->ineq[j],
1224                                         total + bmap->n_div);
1225                         if (s < 0) {
1226                                 isl_int_add(bmap->ineq[j][0],
1227                                         bmap->ineq[j][0], bmap->div[i][0]);
1228                                 isl_int_sub_ui(bmap->ineq[j][0],
1229                                         bmap->ineq[j][0], 1);
1230                         }
1231                 }
1232         }
1233
1234         return bmap;
1235 }
1236
1237 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1238 {
1239         int progress = 1;
1240         if (!bmap)
1241                 return NULL;
1242         while (progress) {
1243                 progress = 0;
1244                 bmap = isl_basic_map_normalize_constraints(bmap);
1245                 bmap = normalize_div_expressions(bmap);
1246                 bmap = remove_duplicate_divs(bmap, &progress);
1247                 bmap = eliminate_unit_divs(bmap, &progress);
1248                 bmap = eliminate_divs_eq(bmap, &progress);
1249                 bmap = eliminate_divs_ineq(bmap, &progress);
1250                 bmap = isl_basic_map_gauss(bmap, &progress);
1251                 /* requires equalities in normal form */
1252                 bmap = normalize_divs(bmap, &progress);
1253                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1254         }
1255         return bmap;
1256 }
1257
1258 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1259 {
1260         return (struct isl_basic_set *)
1261                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1262 }
1263
1264
1265 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1266         isl_int *constraint, unsigned div)
1267 {
1268         unsigned pos;
1269
1270         if (!bmap)
1271                 return -1;
1272
1273         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1274
1275         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1276                 int neg;
1277                 isl_int_sub(bmap->div[div][1],
1278                                 bmap->div[div][1], bmap->div[div][0]);
1279                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1280                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1281                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1282                 isl_int_add(bmap->div[div][1],
1283                                 bmap->div[div][1], bmap->div[div][0]);
1284                 if (!neg)
1285                         return 0;
1286                 if (isl_seq_first_non_zero(constraint+pos+1,
1287                                             bmap->n_div-div-1) != -1)
1288                         return 0;
1289         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1290                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1291                         return 0;
1292                 if (isl_seq_first_non_zero(constraint+pos+1,
1293                                             bmap->n_div-div-1) != -1)
1294                         return 0;
1295         } else
1296                 return 0;
1297
1298         return 1;
1299 }
1300
1301 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1302         isl_int *constraint, unsigned div)
1303 {
1304         return isl_basic_map_is_div_constraint(bset, constraint, div);
1305 }
1306
1307
1308 /* If the only constraints a div d=floor(f/m)
1309  * appears in are its two defining constraints
1310  *
1311  *      f - m d >=0
1312  *      -(f - (m - 1)) + m d >= 0
1313  *
1314  * then it can safely be removed.
1315  */
1316 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1317 {
1318         int i;
1319         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1320
1321         for (i = 0; i < bmap->n_eq; ++i)
1322                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1323                         return 0;
1324
1325         for (i = 0; i < bmap->n_ineq; ++i) {
1326                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1327                         continue;
1328                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1329                         return 0;
1330         }
1331
1332         for (i = 0; i < bmap->n_div; ++i)
1333                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1334                         return 0;
1335
1336         return 1;
1337 }
1338
1339 /*
1340  * Remove divs that don't occur in any of the constraints or other divs.
1341  * These can arise when dropping some of the variables in a quast
1342  * returned by piplib.
1343  */
1344 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1345 {
1346         int i;
1347
1348         if (!bmap)
1349                 return NULL;
1350
1351         for (i = bmap->n_div-1; i >= 0; --i) {
1352                 if (!div_is_redundant(bmap, i))
1353                         continue;
1354                 bmap = isl_basic_map_drop_div(bmap, i);
1355         }
1356         return bmap;
1357 }
1358
1359 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1360 {
1361         bmap = remove_redundant_divs(bmap);
1362         if (!bmap)
1363                 return NULL;
1364         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1365         return bmap;
1366 }
1367
1368 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1369 {
1370         return (struct isl_basic_set *)
1371                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1372 }
1373
1374 struct isl_set *isl_set_finalize(struct isl_set *set)
1375 {
1376         int i;
1377
1378         if (!set)
1379                 return NULL;
1380         for (i = 0; i < set->n; ++i) {
1381                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1382                 if (!set->p[i])
1383                         goto error;
1384         }
1385         return set;
1386 error:
1387         isl_set_free(set);
1388         return NULL;
1389 }
1390
1391 struct isl_map *isl_map_finalize(struct isl_map *map)
1392 {
1393         int i;
1394
1395         if (!map)
1396                 return NULL;
1397         for (i = 0; i < map->n; ++i) {
1398                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1399                 if (!map->p[i])
1400                         goto error;
1401         }
1402         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1403         return map;
1404 error:
1405         isl_map_free(map);
1406         return NULL;
1407 }
1408
1409
1410 /* Remove definition of any div that is defined in terms of the given variable.
1411  * The div itself is not removed.  Functions such as
1412  * eliminate_divs_ineq depend on the other divs remaining in place.
1413  */
1414 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1415                                                                         int pos)
1416 {
1417         int i;
1418
1419         for (i = 0; i < bmap->n_div; ++i) {
1420                 if (isl_int_is_zero(bmap->div[i][0]))
1421                         continue;
1422                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1423                         continue;
1424                 isl_int_set_si(bmap->div[i][0], 0);
1425         }
1426         return bmap;
1427 }
1428
1429 /* Eliminate the specified variables from the constraints using
1430  * Fourier-Motzkin.  The variables themselves are not removed.
1431  */
1432 struct isl_basic_map *isl_basic_map_eliminate_vars(
1433         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1434 {
1435         int d;
1436         int i, j, k;
1437         unsigned total;
1438         int need_gauss = 0;
1439
1440         if (n == 0)
1441                 return bmap;
1442         if (!bmap)
1443                 return NULL;
1444         total = isl_basic_map_total_dim(bmap);
1445
1446         bmap = isl_basic_map_cow(bmap);
1447         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1448                 bmap = remove_dependent_vars(bmap, d);
1449
1450         for (d = pos + n - 1;
1451              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1452                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1453         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1454                 int n_lower, n_upper;
1455                 if (!bmap)
1456                         return NULL;
1457                 for (i = 0; i < bmap->n_eq; ++i) {
1458                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1459                                 continue;
1460                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1461                         isl_basic_map_drop_equality(bmap, i);
1462                         need_gauss = 1;
1463                         break;
1464                 }
1465                 if (i < bmap->n_eq)
1466                         continue;
1467                 n_lower = 0;
1468                 n_upper = 0;
1469                 for (i = 0; i < bmap->n_ineq; ++i) {
1470                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1471                                 n_lower++;
1472                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1473                                 n_upper++;
1474                 }
1475                 bmap = isl_basic_map_extend_constraints(bmap,
1476                                 0, n_lower * n_upper);
1477                 if (!bmap)
1478                         goto error;
1479                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1480                         int last;
1481                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1482                                 continue;
1483                         last = -1;
1484                         for (j = 0; j < i; ++j) {
1485                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1486                                         continue;
1487                                 last = j;
1488                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1489                                     isl_int_sgn(bmap->ineq[j][1+d]))
1490                                         continue;
1491                                 k = isl_basic_map_alloc_inequality(bmap);
1492                                 if (k < 0)
1493                                         goto error;
1494                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1495                                                 1+total);
1496                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1497                                                 1+d, 1+total, NULL);
1498                         }
1499                         isl_basic_map_drop_inequality(bmap, i);
1500                         i = last + 1;
1501                 }
1502                 if (n_lower > 0 && n_upper > 0) {
1503                         bmap = isl_basic_map_normalize_constraints(bmap);
1504                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1505                         bmap = isl_basic_map_gauss(bmap, NULL);
1506                         bmap = isl_basic_map_remove_redundancies(bmap);
1507                         need_gauss = 0;
1508                         if (!bmap)
1509                                 goto error;
1510                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1511                                 break;
1512                 }
1513         }
1514         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1515         if (need_gauss)
1516                 bmap = isl_basic_map_gauss(bmap, NULL);
1517         return bmap;
1518 error:
1519         isl_basic_map_free(bmap);
1520         return NULL;
1521 }
1522
1523 struct isl_basic_set *isl_basic_set_eliminate_vars(
1524         struct isl_basic_set *bset, unsigned pos, unsigned n)
1525 {
1526         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1527                         (struct isl_basic_map *)bset, pos, n);
1528 }
1529
1530 /* Eliminate the specified n dimensions starting at first from the
1531  * constraints, without removing the dimensions from the space.
1532  * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1533  * Otherwise, they are projected out and the original space is restored.
1534  */
1535 __isl_give isl_basic_map *isl_basic_map_eliminate(
1536         __isl_take isl_basic_map *bmap,
1537         enum isl_dim_type type, unsigned first, unsigned n)
1538 {
1539         isl_space *space;
1540
1541         if (!bmap)
1542                 return NULL;
1543         if (n == 0)
1544                 return bmap;
1545
1546         if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1547                 isl_die(bmap->ctx, isl_error_invalid,
1548                         "index out of bounds", goto error);
1549
1550         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1551                 first += isl_basic_map_offset(bmap, type) - 1;
1552                 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1553                 return isl_basic_map_finalize(bmap);
1554         }
1555
1556         space = isl_basic_map_get_space(bmap);
1557         bmap = isl_basic_map_project_out(bmap, type, first, n);
1558         bmap = isl_basic_map_insert_dims(bmap, type, first, n);
1559         bmap = isl_basic_map_reset_space(bmap, space);
1560         return bmap;
1561 error:
1562         isl_basic_map_free(bmap);
1563         return NULL;
1564 }
1565
1566 __isl_give isl_basic_set *isl_basic_set_eliminate(
1567         __isl_take isl_basic_set *bset,
1568         enum isl_dim_type type, unsigned first, unsigned n)
1569 {
1570         return isl_basic_map_eliminate(bset, type, first, n);
1571 }
1572
1573 /* Don't assume equalities are in order, because align_divs
1574  * may have changed the order of the divs.
1575  */
1576 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1577 {
1578         int d, i;
1579         unsigned total;
1580
1581         total = isl_space_dim(bmap->dim, isl_dim_all);
1582         for (d = 0; d < total; ++d)
1583                 elim[d] = -1;
1584         for (i = 0; i < bmap->n_eq; ++i) {
1585                 for (d = total - 1; d >= 0; --d) {
1586                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1587                                 continue;
1588                         elim[d] = i;
1589                         break;
1590                 }
1591         }
1592 }
1593
1594 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1595 {
1596         compute_elimination_index((struct isl_basic_map *)bset, elim);
1597 }
1598
1599 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1600         struct isl_basic_map *bmap, int *elim)
1601 {
1602         int d;
1603         int copied = 0;
1604         unsigned total;
1605
1606         total = isl_space_dim(bmap->dim, isl_dim_all);
1607         for (d = total - 1; d >= 0; --d) {
1608                 if (isl_int_is_zero(src[1+d]))
1609                         continue;
1610                 if (elim[d] == -1)
1611                         continue;
1612                 if (!copied) {
1613                         isl_seq_cpy(dst, src, 1 + total);
1614                         copied = 1;
1615                 }
1616                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1617         }
1618         return copied;
1619 }
1620
1621 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1622         struct isl_basic_set *bset, int *elim)
1623 {
1624         return reduced_using_equalities(dst, src,
1625                                         (struct isl_basic_map *)bset, elim);
1626 }
1627
1628 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1629         struct isl_basic_set *bset, struct isl_basic_set *context)
1630 {
1631         int i;
1632         int *elim;
1633
1634         if (!bset || !context)
1635                 goto error;
1636
1637         if (context->n_eq == 0) {
1638                 isl_basic_set_free(context);
1639                 return bset;
1640         }
1641
1642         bset = isl_basic_set_cow(bset);
1643         if (!bset)
1644                 goto error;
1645
1646         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1647         if (!elim)
1648                 goto error;
1649         set_compute_elimination_index(context, elim);
1650         for (i = 0; i < bset->n_eq; ++i)
1651                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1652                                                         context, elim);
1653         for (i = 0; i < bset->n_ineq; ++i)
1654                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1655                                                         context, elim);
1656         isl_basic_set_free(context);
1657         free(elim);
1658         bset = isl_basic_set_simplify(bset);
1659         bset = isl_basic_set_finalize(bset);
1660         return bset;
1661 error:
1662         isl_basic_set_free(bset);
1663         isl_basic_set_free(context);
1664         return NULL;
1665 }
1666
1667 static struct isl_basic_set *remove_shifted_constraints(
1668         struct isl_basic_set *bset, struct isl_basic_set *context)
1669 {
1670         unsigned int size;
1671         isl_int ***index;
1672         int bits;
1673         int k, h, l;
1674         isl_ctx *ctx;
1675
1676         if (!bset)
1677                 return NULL;
1678
1679         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1680         bits = ffs(size) - 1;
1681         ctx = isl_basic_set_get_ctx(bset);
1682         index = isl_calloc_array(ctx, isl_int **, size);
1683         if (!index)
1684                 return bset;
1685
1686         for (k = 0; k < context->n_ineq; ++k) {
1687                 h = set_hash_index(index, size, bits, context, k);
1688                 index[h] = &context->ineq[k];
1689         }
1690         for (k = 0; k < bset->n_ineq; ++k) {
1691                 h = set_hash_index(index, size, bits, bset, k);
1692                 if (!index[h])
1693                         continue;
1694                 l = index[h] - &context->ineq[0];
1695                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1696                         continue;
1697                 bset = isl_basic_set_cow(bset);
1698                 if (!bset)
1699                         goto error;
1700                 isl_basic_set_drop_inequality(bset, k);
1701                 --k;
1702         }
1703         free(index);
1704         return bset;
1705 error:
1706         free(index);
1707         return bset;
1708 }
1709
1710 /* Does the (linear part of a) constraint "c" involve any of the "len"
1711  * "relevant" dimensions?
1712  */
1713 static int is_related(isl_int *c, int len, int *relevant)
1714 {
1715         int i;
1716
1717         for (i = 0; i < len; ++i) {
1718                 if (!relevant[i])
1719                         continue;
1720                 if (!isl_int_is_zero(c[i]))
1721                         return 1;
1722         }
1723
1724         return 0;
1725 }
1726
1727 /* Drop constraints from "bset" that do not involve any of
1728  * the dimensions marked "relevant".
1729  */
1730 static __isl_give isl_basic_set *drop_unrelated_constraints(
1731         __isl_take isl_basic_set *bset, int *relevant)
1732 {
1733         int i, dim;
1734
1735         dim = isl_basic_set_dim(bset, isl_dim_set);
1736         for (i = 0; i < dim; ++i)
1737                 if (!relevant[i])
1738                         break;
1739         if (i >= dim)
1740                 return bset;
1741
1742         for (i = bset->n_eq - 1; i >= 0; --i)
1743                 if (!is_related(bset->eq[i] + 1, dim, relevant))
1744                         isl_basic_set_drop_equality(bset, i);
1745
1746         for (i = bset->n_ineq - 1; i >= 0; --i)
1747                 if (!is_related(bset->ineq[i] + 1, dim, relevant))
1748                         isl_basic_set_drop_inequality(bset, i);
1749
1750         return bset;
1751 }
1752
1753 /* Update the groups in "group" based on the (linear part of a) constraint "c".
1754  *
1755  * In particular, for any variable involved in the constraint,
1756  * find the actual group id from before and replace the group
1757  * of the corresponding variable by the minimal group of all
1758  * the variables involved in the constraint considered so far
1759  * (if this minimum is smaller) or replace the minimum by this group
1760  * (if the minimum is larger).
1761  *
1762  * At the end, all the variables in "c" will (indirectly) point
1763  * to the minimal of the groups that they referred to originally.
1764  */
1765 static void update_groups(int dim, int *group, isl_int *c)
1766 {
1767         int j;
1768         int min = dim;
1769
1770         for (j = 0; j < dim; ++j) {
1771                 if (isl_int_is_zero(c[j]))
1772                         continue;
1773                 while (group[j] >= 0 && group[group[j]] != group[j])
1774                         group[j] = group[group[j]];
1775                 if (group[j] == min)
1776                         continue;
1777                 if (group[j] < min) {
1778                         if (min >= 0 && min < dim)
1779                                 group[min] = group[j];
1780                         min = group[j];
1781                 } else
1782                         group[group[j]] = min;
1783         }
1784 }
1785
1786 /* Drop constraints from "context" that are irrelevant for computing
1787  * the gist of "bset".
1788  *
1789  * In particular, drop constraints in variables that are not related
1790  * to any of the variables involved in the constraints of "bset"
1791  * in the sense that there is no sequence of constraints that connects them.
1792  *
1793  * We construct groups of variables that collect variables that
1794  * (indirectly) appear in some common constraint of "context".
1795  * Each group is identified by the first variable in the group,
1796  * except for the special group of variables that appear in "bset"
1797  * (or are related to those variables), which is identified by -1.
1798  * If group[i] is equal to i (or -1), then the group of i is i (or -1),
1799  * otherwise the group of i is the group of group[i].
1800  *
1801  * We first initialize the -1 group with the variables that appear in "bset".
1802  * Then we initialize groups for the remaining variables.
1803  * Then we iterate over the constraints of "context" and update the
1804  * group of the variables in the constraint by the smallest group.
1805  * Finally, we resolve indirect references to groups by running over
1806  * the variables.
1807  *
1808  * After computing the groups, we drop constraints that do not involve
1809  * any variables in the -1 group.
1810  */
1811 static __isl_give isl_basic_set *drop_irrelevant_constraints(
1812         __isl_take isl_basic_set *context, __isl_keep isl_basic_set *bset)
1813 {
1814         isl_ctx *ctx;
1815         int *group;
1816         int dim;
1817         int i, j;
1818         int last;
1819
1820         if (!context || !bset)
1821                 return isl_basic_set_free(context);
1822
1823         dim = isl_basic_set_dim(bset, isl_dim_set);
1824         ctx = isl_basic_set_get_ctx(bset);
1825         group = isl_calloc_array(ctx, int, dim);
1826
1827         if (!group)
1828                 goto error;
1829
1830         for (i = 0; i < dim; ++i) {
1831                 for (j = 0; j < bset->n_eq; ++j)
1832                         if (!isl_int_is_zero(bset->eq[j][1 + i]))
1833                                 break;
1834                 if (j < bset->n_eq) {
1835                         group[i] = -1;
1836                         continue;
1837                 }
1838                 for (j = 0; j < bset->n_ineq; ++j)
1839                         if (!isl_int_is_zero(bset->ineq[j][1 + i]))
1840                                 break;
1841                 if (j < bset->n_ineq)
1842                         group[i] = -1;
1843         }
1844
1845         last = -1;
1846         for (i = 0; i < dim; ++i)
1847                 if (group[i] >= 0)
1848                         last = group[i] = i;
1849         if (last < 0) {
1850                 free(group);
1851                 return context;
1852         }
1853
1854         for (i = 0; i < context->n_eq; ++i)
1855                 update_groups(dim, group, context->eq[i] + 1);
1856         for (i = 0; i < context->n_ineq; ++i)
1857                 update_groups(dim, group, context->ineq[i] + 1);
1858
1859         for (i = 0; i < dim; ++i)
1860                 if (group[i] >= 0)
1861                         group[i] = group[group[i]];
1862
1863         for (i = 0; i < dim; ++i)
1864                 group[i] = group[i] == -1;
1865
1866         context = drop_unrelated_constraints(context, group);
1867
1868         free(group);
1869         return context;
1870 error:
1871         free(group);
1872         return isl_basic_set_free(context);
1873 }
1874
1875 /* Remove all information from bset that is redundant in the context
1876  * of context.  Both bset and context are assumed to be full-dimensional.
1877  *
1878  * We first remove the inequalities from "bset"
1879  * that are obviously redundant with respect to some inequality in "context".
1880  * Then we remove those constraints from "context" that have become
1881  * irrelevant for computing the gist of "bset".
1882  * Note that this removal of constraints cannot be replaced by
1883  * a factorization because factors in "bset" may still be connected
1884  * to each other through constraints in "context".
1885  *
1886  * If there are any inequalities left, we construct a tableau for
1887  * the context and then add the inequalities of "bset".
1888  * Before adding these inequalities, we freeze all constraints such that
1889  * they won't be considered redundant in terms of the constraints of "bset".
1890  * Then we detect all redundant constraints (among the
1891  * constraints that weren't frozen), first by checking for redundancy in the
1892  * the tableau and then by checking if replacing a constraint by its negation
1893  * would lead to an empty set.  This last step is fairly expensive
1894  * and could be optimized by more reuse of the tableau.
1895  * Finally, we update bset according to the results.
1896  */
1897 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1898         __isl_take isl_basic_set *context)
1899 {
1900         int i, k;
1901         isl_basic_set *combined = NULL;
1902         struct isl_tab *tab = NULL;
1903         unsigned context_ineq;
1904         unsigned total;
1905
1906         if (!bset || !context)
1907                 goto error;
1908
1909         if (isl_basic_set_is_universe(bset)) {
1910                 isl_basic_set_free(context);
1911                 return bset;
1912         }
1913
1914         if (isl_basic_set_is_universe(context)) {
1915                 isl_basic_set_free(context);
1916                 return bset;
1917         }
1918
1919         bset = remove_shifted_constraints(bset, context);
1920         if (!bset)
1921                 goto error;
1922         if (bset->n_ineq == 0)
1923                 goto done;
1924
1925         context = drop_irrelevant_constraints(context, bset);
1926         if (!context)
1927                 goto error;
1928         if (isl_basic_set_is_universe(context)) {
1929                 isl_basic_set_free(context);
1930                 return bset;
1931         }
1932
1933         context_ineq = context->n_ineq;
1934         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1935         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1936         tab = isl_tab_from_basic_set(combined, 0);
1937         for (i = 0; i < context_ineq; ++i)
1938                 if (isl_tab_freeze_constraint(tab, i) < 0)
1939                         goto error;
1940         tab = isl_tab_extend(tab, bset->n_ineq);
1941         for (i = 0; i < bset->n_ineq; ++i)
1942                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1943                         goto error;
1944         bset = isl_basic_set_add_constraints(combined, bset, 0);
1945         combined = NULL;
1946         if (!bset)
1947                 goto error;
1948         if (isl_tab_detect_redundant(tab) < 0)
1949                 goto error;
1950         total = isl_basic_set_total_dim(bset);
1951         for (i = context_ineq; i < bset->n_ineq; ++i) {
1952                 int is_empty;
1953                 if (tab->con[i].is_redundant)
1954                         continue;
1955                 tab->con[i].is_redundant = 1;
1956                 combined = isl_basic_set_dup(bset);
1957                 combined = isl_basic_set_update_from_tab(combined, tab);
1958                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1959                 k = isl_basic_set_alloc_inequality(combined);
1960                 if (k < 0)
1961                         goto error;
1962                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1963                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1964                 is_empty = isl_basic_set_is_empty(combined);
1965                 if (is_empty < 0)
1966                         goto error;
1967                 isl_basic_set_free(combined);
1968                 combined = NULL;
1969                 if (!is_empty)
1970                         tab->con[i].is_redundant = 0;
1971         }
1972         for (i = 0; i < context_ineq; ++i)
1973                 tab->con[i].is_redundant = 1;
1974         bset = isl_basic_set_update_from_tab(bset, tab);
1975         if (bset) {
1976                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1977                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1978         }
1979
1980         isl_tab_free(tab);
1981 done:
1982         bset = isl_basic_set_simplify(bset);
1983         bset = isl_basic_set_finalize(bset);
1984         isl_basic_set_free(context);
1985         return bset;
1986 error:
1987         isl_tab_free(tab);
1988         isl_basic_set_free(combined);
1989         isl_basic_set_free(context);
1990         isl_basic_set_free(bset);
1991         return NULL;
1992 }
1993
1994 /* Remove all information from bset that is redundant in the context
1995  * of context.  In particular, equalities that are linear combinations
1996  * of those in context are removed.  Then the inequalities that are
1997  * redundant in the context of the equalities and inequalities of
1998  * context are removed.
1999  *
2000  * First of all, we drop those constraints from "context"
2001  * that are irrelevant for computing the gist of "bset".
2002  * Alternatively, we could factorize the intersection of "context" and "bset".
2003  *
2004  * We first compute the integer affine hull of the intersection,
2005  * compute the gist inside this affine hull and then add back
2006  * those equalities that are not implied by the context.
2007  *
2008  * If two constraints are mutually redundant, then uset_gist_full
2009  * will remove the second of those constraints.  We therefore first
2010  * sort the constraints so that constraints not involving existentially
2011  * quantified variables are given precedence over those that do.
2012  * We have to perform this sorting before the variable compression,
2013  * because that may effect the order of the variables.
2014  */
2015 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
2016         __isl_take isl_basic_set *context)
2017 {
2018         isl_mat *eq;
2019         isl_mat *T, *T2;
2020         isl_basic_set *aff;
2021         isl_basic_set *aff_context;
2022         unsigned total;
2023
2024         if (!bset || !context)
2025                 goto error;
2026
2027         context = drop_irrelevant_constraints(context, bset);
2028
2029         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
2030         if (isl_basic_set_plain_is_empty(bset)) {
2031                 isl_basic_set_free(context);
2032                 return bset;
2033         }
2034         bset = isl_basic_set_sort_constraints(bset);
2035         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
2036         if (!aff)
2037                 goto error;
2038         if (isl_basic_set_plain_is_empty(aff)) {
2039                 isl_basic_set_free(aff);
2040                 isl_basic_set_free(context);
2041                 return bset;
2042         }
2043         if (aff->n_eq == 0) {
2044                 isl_basic_set_free(aff);
2045                 return uset_gist_full(bset, context);
2046         }
2047         total = isl_basic_set_total_dim(bset);
2048         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
2049         eq = isl_mat_cow(eq);
2050         T = isl_mat_variable_compression(eq, &T2);
2051         if (T && T->n_col == 0) {
2052                 isl_mat_free(T);
2053                 isl_mat_free(T2);
2054                 isl_basic_set_free(context);
2055                 isl_basic_set_free(aff);
2056                 return isl_basic_set_set_to_empty(bset);
2057         }
2058
2059         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
2060
2061         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
2062         context = isl_basic_set_preimage(context, T);
2063
2064         bset = uset_gist_full(bset, context);
2065         bset = isl_basic_set_preimage(bset, T2);
2066         bset = isl_basic_set_intersect(bset, aff);
2067         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
2068
2069         if (bset) {
2070                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
2071                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
2072         }
2073
2074         return bset;
2075 error:
2076         isl_basic_set_free(bset);
2077         isl_basic_set_free(context);
2078         return NULL;
2079 }
2080
2081 /* Normalize the divs in "bmap" in the context of the equalities in "context".
2082  * We simply add the equalities in context to bmap and then do a regular
2083  * div normalizations.  Better results can be obtained by normalizing
2084  * only the divs in bmap than do not also appear in context.
2085  * We need to be careful to reduce the divs using the equalities
2086  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
2087  * spurious constraints.
2088  */
2089 static struct isl_basic_map *normalize_divs_in_context(
2090         struct isl_basic_map *bmap, struct isl_basic_map *context)
2091 {
2092         int i;
2093         unsigned total_context;
2094         int div_eq;
2095
2096         div_eq = n_pure_div_eq(bmap);
2097         if (div_eq == 0)
2098                 return bmap;
2099
2100         if (context->n_div > 0)
2101                 bmap = isl_basic_map_align_divs(bmap, context);
2102
2103         total_context = isl_basic_map_total_dim(context);
2104         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
2105         for (i = 0; i < context->n_eq; ++i) {
2106                 int k;
2107                 k = isl_basic_map_alloc_equality(bmap);
2108                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
2109                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
2110                                 isl_basic_map_total_dim(bmap) - total_context);
2111         }
2112         bmap = isl_basic_map_gauss(bmap, NULL);
2113         bmap = normalize_divs(bmap, NULL);
2114         bmap = isl_basic_map_gauss(bmap, NULL);
2115         return bmap;
2116 }
2117
2118 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
2119         struct isl_basic_map *context)
2120 {
2121         struct isl_basic_set *bset;
2122
2123         if (!bmap || !context)
2124                 goto error;
2125
2126         if (isl_basic_map_is_universe(bmap)) {
2127                 isl_basic_map_free(context);
2128                 return bmap;
2129         }
2130         if (isl_basic_map_plain_is_empty(context)) {
2131                 isl_basic_map_free(bmap);
2132                 return context;
2133         }
2134         if (isl_basic_map_plain_is_empty(bmap)) {
2135                 isl_basic_map_free(context);
2136                 return bmap;
2137         }
2138
2139         bmap = isl_basic_map_remove_redundancies(bmap);
2140         context = isl_basic_map_remove_redundancies(context);
2141
2142         if (context->n_eq)
2143                 bmap = normalize_divs_in_context(bmap, context);
2144
2145         context = isl_basic_map_align_divs(context, bmap);
2146         bmap = isl_basic_map_align_divs(bmap, context);
2147
2148         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
2149                          isl_basic_map_underlying_set(context));
2150
2151         return isl_basic_map_overlying_set(bset, bmap);
2152 error:
2153         isl_basic_map_free(bmap);
2154         isl_basic_map_free(context);
2155         return NULL;
2156 }
2157
2158 /*
2159  * Assumes context has no implicit divs.
2160  */
2161 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
2162         __isl_take isl_basic_map *context)
2163 {
2164         int i;
2165
2166         if (!map || !context)
2167                 goto error;;
2168
2169         if (isl_basic_map_plain_is_empty(context)) {
2170                 isl_map_free(map);
2171                 return isl_map_from_basic_map(context);
2172         }
2173
2174         context = isl_basic_map_remove_redundancies(context);
2175         map = isl_map_cow(map);
2176         if (!map || !context)
2177                 goto error;;
2178         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
2179         map = isl_map_compute_divs(map);
2180         for (i = 0; i < map->n; ++i)
2181                 context = isl_basic_map_align_divs(context, map->p[i]);
2182         for (i = map->n - 1; i >= 0; --i) {
2183                 map->p[i] = isl_basic_map_gist(map->p[i],
2184                                                 isl_basic_map_copy(context));
2185                 if (!map->p[i])
2186                         goto error;
2187                 if (isl_basic_map_plain_is_empty(map->p[i])) {
2188                         isl_basic_map_free(map->p[i]);
2189                         if (i != map->n - 1)
2190                                 map->p[i] = map->p[map->n - 1];
2191                         map->n--;
2192                 }
2193         }
2194         isl_basic_map_free(context);
2195         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2196         return map;
2197 error:
2198         isl_map_free(map);
2199         isl_basic_map_free(context);
2200         return NULL;
2201 }
2202
2203 /* Return a map that has the same intersection with "context" as "map"
2204  * and that as "simple" as possible.
2205  *
2206  * If "map" is already the universe, then we cannot make it any simpler.
2207  * Similarly, if "context" is the universe, then we cannot exploit it
2208  * to simplify "map"
2209  * If "map" and "context" are identical to each other, then we can
2210  * return the corresponding universe.
2211  *
2212  * If none of these cases apply, we have to work a bit harder.
2213  */
2214 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
2215         __isl_take isl_map *context)
2216 {
2217         int equal;
2218         int is_universe;
2219
2220         is_universe = isl_map_plain_is_universe(map);
2221         if (is_universe >= 0 && !is_universe)
2222                 is_universe = isl_map_plain_is_universe(context);
2223         if (is_universe < 0)
2224                 goto error;
2225         if (is_universe) {
2226                 isl_map_free(context);
2227                 return map;
2228         }
2229
2230         equal = isl_map_plain_is_equal(map, context);
2231         if (equal < 0)
2232                 goto error;
2233         if (equal) {
2234                 isl_map *res = isl_map_universe(isl_map_get_space(map));
2235                 isl_map_free(map);
2236                 isl_map_free(context);
2237                 return res;
2238         }
2239
2240         context = isl_map_compute_divs(context);
2241         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
2242 error:
2243         isl_map_free(map);
2244         isl_map_free(context);
2245         return NULL;
2246 }
2247
2248 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2249         __isl_take isl_map *context)
2250 {
2251         return isl_map_align_params_map_map_and(map, context, &map_gist);
2252 }
2253
2254 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
2255                                                 struct isl_basic_set *context)
2256 {
2257         return (struct isl_basic_set *)isl_basic_map_gist(
2258                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
2259 }
2260
2261 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
2262         __isl_take isl_basic_set *context)
2263 {
2264         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
2265                                         (struct isl_basic_map *)context);
2266 }
2267
2268 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
2269         __isl_take isl_basic_set *context)
2270 {
2271         isl_space *space = isl_set_get_space(set);
2272         isl_basic_set *dom_context = isl_basic_set_universe(space);
2273         dom_context = isl_basic_set_intersect_params(dom_context, context);
2274         return isl_set_gist_basic_set(set, dom_context);
2275 }
2276
2277 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2278         __isl_take isl_set *context)
2279 {
2280         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
2281                                         (struct isl_map *)context);
2282 }
2283
2284 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
2285         __isl_take isl_set *context)
2286 {
2287         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2288         map_context = isl_map_intersect_domain(map_context, context);
2289         return isl_map_gist(map, map_context);
2290 }
2291
2292 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
2293         __isl_take isl_set *context)
2294 {
2295         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2296         map_context = isl_map_intersect_range(map_context, context);
2297         return isl_map_gist(map, map_context);
2298 }
2299
2300 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
2301         __isl_take isl_set *context)
2302 {
2303         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2304         map_context = isl_map_intersect_params(map_context, context);
2305         return isl_map_gist(map, map_context);
2306 }
2307
2308 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
2309         __isl_take isl_set *context)
2310 {
2311         return isl_map_gist_params(set, context);
2312 }
2313
2314 /* Quick check to see if two basic maps are disjoint.
2315  * In particular, we reduce the equalities and inequalities of
2316  * one basic map in the context of the equalities of the other
2317  * basic map and check if we get a contradiction.
2318  */
2319 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
2320         __isl_keep isl_basic_map *bmap2)
2321 {
2322         struct isl_vec *v = NULL;
2323         int *elim = NULL;
2324         unsigned total;
2325         int i;
2326
2327         if (!bmap1 || !bmap2)
2328                 return -1;
2329         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
2330                         return -1);
2331         if (bmap1->n_div || bmap2->n_div)
2332                 return 0;
2333         if (!bmap1->n_eq && !bmap2->n_eq)
2334                 return 0;
2335
2336         total = isl_space_dim(bmap1->dim, isl_dim_all);
2337         if (total == 0)
2338                 return 0;
2339         v = isl_vec_alloc(bmap1->ctx, 1 + total);
2340         if (!v)
2341                 goto error;
2342         elim = isl_alloc_array(bmap1->ctx, int, total);
2343         if (!elim)
2344                 goto error;
2345         compute_elimination_index(bmap1, elim);
2346         for (i = 0; i < bmap2->n_eq; ++i) {
2347                 int reduced;
2348                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
2349                                                         bmap1, elim);
2350                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
2351                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2352                         goto disjoint;
2353         }
2354         for (i = 0; i < bmap2->n_ineq; ++i) {
2355                 int reduced;
2356                 reduced = reduced_using_equalities(v->block.data,
2357                                                 bmap2->ineq[i], bmap1, elim);
2358                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2359                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2360                         goto disjoint;
2361         }
2362         compute_elimination_index(bmap2, elim);
2363         for (i = 0; i < bmap1->n_ineq; ++i) {
2364                 int reduced;
2365                 reduced = reduced_using_equalities(v->block.data,
2366                                                 bmap1->ineq[i], bmap2, elim);
2367                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2368                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2369                         goto disjoint;
2370         }
2371         isl_vec_free(v);
2372         free(elim);
2373         return 0;
2374 disjoint:
2375         isl_vec_free(v);
2376         free(elim);
2377         return 1;
2378 error:
2379         isl_vec_free(v);
2380         free(elim);
2381         return -1;
2382 }
2383
2384 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2385         __isl_keep isl_basic_set *bset2)
2386 {
2387         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2388                                               (struct isl_basic_map *)bset2);
2389 }
2390
2391 /* Are "map1" and "map2" obviously disjoint?
2392  *
2393  * If one of them is empty or if they live in different spaces (ignoring
2394  * parameters), then they are clearly disjoint.
2395  *
2396  * If they have different parameters, then we skip any further tests.
2397  *
2398  * If they are obviously equal, but not obviously empty, then we will
2399  * not be able to detect if they are disjoint.
2400  *
2401  * Otherwise we check if each basic map in "map1" is obviously disjoint
2402  * from each basic map in "map2".
2403  */
2404 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2405         __isl_keep isl_map *map2)
2406 {
2407         int i, j;
2408         int disjoint;
2409         int intersect;
2410         int match;
2411
2412         if (!map1 || !map2)
2413                 return -1;
2414
2415         disjoint = isl_map_plain_is_empty(map1);
2416         if (disjoint < 0 || disjoint)
2417                 return disjoint;
2418
2419         disjoint = isl_map_plain_is_empty(map2);
2420         if (disjoint < 0 || disjoint)
2421                 return disjoint;
2422
2423         match = isl_space_tuple_match(map1->dim, isl_dim_in,
2424                                 map2->dim, isl_dim_in);
2425         if (match < 0 || !match)
2426                 return match < 0 ? -1 : 1;
2427
2428         match = isl_space_tuple_match(map1->dim, isl_dim_out,
2429                                 map2->dim, isl_dim_out);
2430         if (match < 0 || !match)
2431                 return match < 0 ? -1 : 1;
2432
2433         match = isl_space_match(map1->dim, isl_dim_param,
2434                                 map2->dim, isl_dim_param);
2435         if (match < 0 || !match)
2436                 return match < 0 ? -1 : 0;
2437
2438         intersect = isl_map_plain_is_equal(map1, map2);
2439         if (intersect < 0 || intersect)
2440                 return intersect < 0 ? -1 : 0;
2441
2442         for (i = 0; i < map1->n; ++i) {
2443                 for (j = 0; j < map2->n; ++j) {
2444                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2445                                                                map2->p[j]);
2446                         if (d != 1)
2447                                 return d;
2448                 }
2449         }
2450         return 1;
2451 }
2452
2453 /* Are "map1" and "map2" disjoint?
2454  *
2455  * They are disjoint if they are "obviously disjoint" or if one of them
2456  * is empty.  Otherwise, they are not disjoint if one of them is universal.
2457  * If none of these cases apply, we compute the intersection and see if
2458  * the result is empty.
2459  */
2460 int isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
2461 {
2462         int disjoint;
2463         int intersect;
2464         isl_map *test;
2465
2466         disjoint = isl_map_plain_is_disjoint(map1, map2);
2467         if (disjoint < 0 || disjoint)
2468                 return disjoint;
2469
2470         disjoint = isl_map_is_empty(map1);
2471         if (disjoint < 0 || disjoint)
2472                 return disjoint;
2473
2474         disjoint = isl_map_is_empty(map2);
2475         if (disjoint < 0 || disjoint)
2476                 return disjoint;
2477
2478         intersect = isl_map_plain_is_universe(map1);
2479         if (intersect < 0 || intersect)
2480                 return intersect < 0 ? -1 : 0;
2481
2482         intersect = isl_map_plain_is_universe(map2);
2483         if (intersect < 0 || intersect)
2484                 return intersect < 0 ? -1 : 0;
2485
2486         test = isl_map_intersect(isl_map_copy(map1), isl_map_copy(map2));
2487         disjoint = isl_map_is_empty(test);
2488         isl_map_free(test);
2489
2490         return disjoint;
2491 }
2492
2493 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2494         __isl_keep isl_set *set2)
2495 {
2496         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2497                                         (struct isl_map *)set2);
2498 }
2499
2500 /* Are "set1" and "set2" disjoint?
2501  */
2502 int isl_set_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2503 {
2504         return isl_map_is_disjoint(set1, set2);
2505 }
2506
2507 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2508 {
2509         return isl_set_plain_is_disjoint(set1, set2);
2510 }
2511
2512 /* Check if we can combine a given div with lower bound l and upper
2513  * bound u with some other div and if so return that other div.
2514  * Otherwise return -1.
2515  *
2516  * We first check that
2517  *      - the bounds are opposites of each other (except for the constant
2518  *        term)
2519  *      - the bounds do not reference any other div
2520  *      - no div is defined in terms of this div
2521  *
2522  * Let m be the size of the range allowed on the div by the bounds.
2523  * That is, the bounds are of the form
2524  *
2525  *      e <= a <= e + m - 1
2526  *
2527  * with e some expression in the other variables.
2528  * We look for another div b such that no third div is defined in terms
2529  * of this second div b and such that in any constraint that contains
2530  * a (except for the given lower and upper bound), also contains b
2531  * with a coefficient that is m times that of b.
2532  * That is, all constraints (execpt for the lower and upper bound)
2533  * are of the form
2534  *
2535  *      e + f (a + m b) >= 0
2536  *
2537  * If so, we return b so that "a + m b" can be replaced by
2538  * a single div "c = a + m b".
2539  */
2540 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2541         unsigned div, unsigned l, unsigned u)
2542 {
2543         int i, j;
2544         unsigned dim;
2545         int coalesce = -1;
2546
2547         if (bmap->n_div <= 1)
2548                 return -1;
2549         dim = isl_space_dim(bmap->dim, isl_dim_all);
2550         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2551                 return -1;
2552         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2553                                    bmap->n_div - div - 1) != -1)
2554                 return -1;
2555         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2556                             dim + bmap->n_div))
2557                 return -1;
2558
2559         for (i = 0; i < bmap->n_div; ++i) {
2560                 if (isl_int_is_zero(bmap->div[i][0]))
2561                         continue;
2562                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2563                         return -1;
2564         }
2565
2566         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2567         if (isl_int_is_neg(bmap->ineq[l][0])) {
2568                 isl_int_sub(bmap->ineq[l][0],
2569                             bmap->ineq[l][0], bmap->ineq[u][0]);
2570                 bmap = isl_basic_map_copy(bmap);
2571                 bmap = isl_basic_map_set_to_empty(bmap);
2572                 isl_basic_map_free(bmap);
2573                 return -1;
2574         }
2575         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2576         for (i = 0; i < bmap->n_div; ++i) {
2577                 if (i == div)
2578                         continue;
2579                 if (!pairs[i])
2580                         continue;
2581                 for (j = 0; j < bmap->n_div; ++j) {
2582                         if (isl_int_is_zero(bmap->div[j][0]))
2583                                 continue;
2584                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2585                                 break;
2586                 }
2587                 if (j < bmap->n_div)
2588                         continue;
2589                 for (j = 0; j < bmap->n_ineq; ++j) {
2590                         int valid;
2591                         if (j == l || j == u)
2592                                 continue;
2593                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2594                                 continue;
2595                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2596                                 break;
2597                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2598                                     bmap->ineq[j][1 + dim + div],
2599                                     bmap->ineq[l][0]);
2600                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2601                                            bmap->ineq[j][1 + dim + i]);
2602                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2603                                          bmap->ineq[j][1 + dim + div],
2604                                          bmap->ineq[l][0]);
2605                         if (!valid)
2606                                 break;
2607                 }
2608                 if (j < bmap->n_ineq)
2609                         continue;
2610                 coalesce = i;
2611                 break;
2612         }
2613         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2614         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2615         return coalesce;
2616 }
2617
2618 /* Given a lower and an upper bound on div i, construct an inequality
2619  * that when nonnegative ensures that this pair of bounds always allows
2620  * for an integer value of the given div.
2621  * The lower bound is inequality l, while the upper bound is inequality u.
2622  * The constructed inequality is stored in ineq.
2623  * g, fl, fu are temporary scalars.
2624  *
2625  * Let the upper bound be
2626  *
2627  *      -n_u a + e_u >= 0
2628  *
2629  * and the lower bound
2630  *
2631  *      n_l a + e_l >= 0
2632  *
2633  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2634  * We have
2635  *
2636  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2637  *
2638  * Since all variables are integer valued, this is equivalent to
2639  *
2640  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2641  *
2642  * If this interval is at least f_u f_l g, then it contains at least
2643  * one integer value for a.
2644  * That is, the test constraint is
2645  *
2646  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2647  */
2648 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2649         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2650 {
2651         unsigned dim;
2652         dim = isl_space_dim(bmap->dim, isl_dim_all);
2653
2654         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2655         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2656         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2657         isl_int_neg(fu, fu);
2658         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2659                         1 + dim + bmap->n_div);
2660         isl_int_add(ineq[0], ineq[0], fl);
2661         isl_int_add(ineq[0], ineq[0], fu);
2662         isl_int_sub_ui(ineq[0], ineq[0], 1);
2663         isl_int_mul(g, g, fl);
2664         isl_int_mul(g, g, fu);
2665         isl_int_sub(ineq[0], ineq[0], g);
2666 }
2667
2668 /* Remove more kinds of divs that are not strictly needed.
2669  * In particular, if all pairs of lower and upper bounds on a div
2670  * are such that they allow at least one integer value of the div,
2671  * the we can eliminate the div using Fourier-Motzkin without
2672  * introducing any spurious solutions.
2673  */
2674 static struct isl_basic_map *drop_more_redundant_divs(
2675         struct isl_basic_map *bmap, int *pairs, int n)
2676 {
2677         struct isl_tab *tab = NULL;
2678         struct isl_vec *vec = NULL;
2679         unsigned dim;
2680         int remove = -1;
2681         isl_int g, fl, fu;
2682
2683         isl_int_init(g);
2684         isl_int_init(fl);
2685         isl_int_init(fu);
2686
2687         if (!bmap)
2688                 goto error;
2689
2690         dim = isl_space_dim(bmap->dim, isl_dim_all);
2691         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2692         if (!vec)
2693                 goto error;
2694
2695         tab = isl_tab_from_basic_map(bmap, 0);
2696
2697         while (n > 0) {
2698                 int i, l, u;
2699                 int best = -1;
2700                 enum isl_lp_result res;
2701
2702                 for (i = 0; i < bmap->n_div; ++i) {
2703                         if (!pairs[i])
2704                                 continue;
2705                         if (best >= 0 && pairs[best] <= pairs[i])
2706                                 continue;
2707                         best = i;
2708                 }
2709
2710                 i = best;
2711                 for (l = 0; l < bmap->n_ineq; ++l) {
2712                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2713                                 continue;
2714                         for (u = 0; u < bmap->n_ineq; ++u) {
2715                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2716                                         continue;
2717                                 construct_test_ineq(bmap, i, l, u,
2718                                                     vec->el, g, fl, fu);
2719                                 res = isl_tab_min(tab, vec->el,
2720                                                   bmap->ctx->one, &g, NULL, 0);
2721                                 if (res == isl_lp_error)
2722                                         goto error;
2723                                 if (res == isl_lp_empty) {
2724                                         bmap = isl_basic_map_set_to_empty(bmap);
2725                                         break;
2726                                 }
2727                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2728                                         break;
2729                         }
2730                         if (u < bmap->n_ineq)
2731                                 break;
2732                 }
2733                 if (l == bmap->n_ineq) {
2734                         remove = i;
2735                         break;
2736                 }
2737                 pairs[i] = 0;
2738                 --n;
2739         }
2740
2741         isl_tab_free(tab);
2742         isl_vec_free(vec);
2743
2744         isl_int_clear(g);
2745         isl_int_clear(fl);
2746         isl_int_clear(fu);
2747
2748         free(pairs);
2749
2750         if (remove < 0)
2751                 return bmap;
2752
2753         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2754         return isl_basic_map_drop_redundant_divs(bmap);
2755 error:
2756         free(pairs);
2757         isl_basic_map_free(bmap);
2758         isl_tab_free(tab);
2759         isl_vec_free(vec);
2760         isl_int_clear(g);
2761         isl_int_clear(fl);
2762         isl_int_clear(fu);
2763         return NULL;
2764 }
2765
2766 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2767  * and the upper bound u, div1 always occurs together with div2 in the form
2768  * (div1 + m div2), where m is the constant range on the variable div1
2769  * allowed by l and u, replace the pair div1 and div2 by a single
2770  * div that is equal to div1 + m div2.
2771  *
2772  * The new div will appear in the location that contains div2.
2773  * We need to modify all constraints that contain
2774  * div2 = (div - div1) / m
2775  * (If a constraint does not contain div2, it will also not contain div1.)
2776  * If the constraint also contains div1, then we know they appear
2777  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2778  * i.e., the coefficient of div is f.
2779  *
2780  * Otherwise, we first need to introduce div1 into the constraint.
2781  * Let the l be
2782  *
2783  *      div1 + f >=0
2784  *
2785  * and u
2786  *
2787  *      -div1 + f' >= 0
2788  *
2789  * A lower bound on div2
2790  *
2791  *      n div2 + t >= 0
2792  *
2793  * can be replaced by
2794  *
2795  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2796  *
2797  * with g = gcd(m,n).
2798  * An upper bound
2799  *
2800  *      -n div2 + t >= 0
2801  *
2802  * can be replaced by
2803  *
2804  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2805  *
2806  * These constraint are those that we would obtain from eliminating
2807  * div1 using Fourier-Motzkin.
2808  *
2809  * After all constraints have been modified, we drop the lower and upper
2810  * bound and then drop div1.
2811  */
2812 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2813         unsigned div1, unsigned div2, unsigned l, unsigned u)
2814 {
2815         isl_int a;
2816         isl_int b;
2817         isl_int m;
2818         unsigned dim, total;
2819         int i;
2820
2821         dim = isl_space_dim(bmap->dim, isl_dim_all);
2822         total = 1 + dim + bmap->n_div;
2823
2824         isl_int_init(a);
2825         isl_int_init(b);
2826         isl_int_init(m);
2827         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2828         isl_int_add_ui(m, m, 1);
2829
2830         for (i = 0; i < bmap->n_ineq; ++i) {
2831                 if (i == l || i == u)
2832                         continue;
2833                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2834                         continue;
2835                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2836                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2837                         isl_int_divexact(a, m, b);
2838                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2839                         if (isl_int_is_pos(b)) {
2840                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2841                                                 b, bmap->ineq[l], total);
2842                         } else {
2843                                 isl_int_neg(b, b);
2844                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2845                                                 b, bmap->ineq[u], total);
2846                         }
2847                 }
2848                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2849                             bmap->ineq[i][1 + dim + div1]);
2850                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2851         }
2852
2853         isl_int_clear(a);
2854         isl_int_clear(b);
2855         isl_int_clear(m);
2856         if (l > u) {
2857                 isl_basic_map_drop_inequality(bmap, l);
2858                 isl_basic_map_drop_inequality(bmap, u);
2859         } else {
2860                 isl_basic_map_drop_inequality(bmap, u);
2861                 isl_basic_map_drop_inequality(bmap, l);
2862         }
2863         bmap = isl_basic_map_drop_div(bmap, div1);
2864         return bmap;
2865 }
2866
2867 /* First check if we can coalesce any pair of divs and
2868  * then continue with dropping more redundant divs.
2869  *
2870  * We loop over all pairs of lower and upper bounds on a div
2871  * with coefficient 1 and -1, respectively, check if there
2872  * is any other div "c" with which we can coalesce the div
2873  * and if so, perform the coalescing.
2874  */
2875 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2876         struct isl_basic_map *bmap, int *pairs, int n)
2877 {
2878         int i, l, u;
2879         unsigned dim;
2880
2881         dim = isl_space_dim(bmap->dim, isl_dim_all);
2882
2883         for (i = 0; i < bmap->n_div; ++i) {
2884                 if (!pairs[i])
2885                         continue;
2886                 for (l = 0; l < bmap->n_ineq; ++l) {
2887                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2888                                 continue;
2889                         for (u = 0; u < bmap->n_ineq; ++u) {
2890                                 int c;
2891
2892                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2893                                         continue;
2894                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2895                                 if (c < 0)
2896                                         continue;
2897                                 free(pairs);
2898                                 bmap = coalesce_divs(bmap, i, c, l, u);
2899                                 return isl_basic_map_drop_redundant_divs(bmap);
2900                         }
2901                 }
2902         }
2903
2904         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2905                 return bmap;
2906
2907         return drop_more_redundant_divs(bmap, pairs, n);
2908 }
2909
2910 /* Remove divs that are not strictly needed.
2911  * In particular, if a div only occurs positively (or negatively)
2912  * in constraints, then it can simply be dropped.
2913  * Also, if a div occurs in only two constraints and if moreover
2914  * those two constraints are opposite to each other, except for the constant
2915  * term and if the sum of the constant terms is such that for any value
2916  * of the other values, there is always at least one integer value of the
2917  * div, i.e., if one plus this sum is greater than or equal to
2918  * the (absolute value) of the coefficent of the div in the constraints,
2919  * then we can also simply drop the div.
2920  *
2921  * We skip divs that appear in equalities or in the definition of other divs.
2922  * Divs that appear in the definition of other divs usually occur in at least
2923  * 4 constraints, but the constraints may have been simplified.
2924  *
2925  * If any divs are left after these simple checks then we move on
2926  * to more complicated cases in drop_more_redundant_divs.
2927  */
2928 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2929         struct isl_basic_map *bmap)
2930 {
2931         int i, j;
2932         unsigned off;
2933         int *pairs = NULL;
2934         int n = 0;
2935
2936         if (!bmap)
2937                 goto error;
2938
2939         off = isl_space_dim(bmap->dim, isl_dim_all);
2940         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2941         if (!pairs)
2942                 goto error;
2943
2944         for (i = 0; i < bmap->n_div; ++i) {
2945                 int pos, neg;
2946                 int last_pos, last_neg;
2947                 int redundant;
2948                 int defined;
2949
2950                 defined = !isl_int_is_zero(bmap->div[i][0]);
2951                 for (j = i; j < bmap->n_div; ++j)
2952                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i]))
2953                                 break;
2954                 if (j < bmap->n_div)
2955                         continue;
2956                 for (j = 0; j < bmap->n_eq; ++j)
2957                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2958                                 break;
2959                 if (j < bmap->n_eq)
2960                         continue;
2961                 ++n;
2962                 pos = neg = 0;
2963                 for (j = 0; j < bmap->n_ineq; ++j) {
2964                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2965                                 last_pos = j;
2966                                 ++pos;
2967                         }
2968                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2969                                 last_neg = j;
2970                                 ++neg;
2971                         }
2972                 }
2973                 pairs[i] = pos * neg;
2974                 if (pairs[i] == 0) {
2975                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2976                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2977                                         isl_basic_map_drop_inequality(bmap, j);
2978                         bmap = isl_basic_map_drop_div(bmap, i);
2979                         free(pairs);
2980                         return isl_basic_map_drop_redundant_divs(bmap);
2981                 }
2982                 if (pairs[i] != 1)
2983                         continue;
2984                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2985                                     bmap->ineq[last_neg] + 1,
2986                                     off + bmap->n_div))
2987                         continue;
2988
2989                 isl_int_add(bmap->ineq[last_pos][0],
2990                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2991                 isl_int_add_ui(bmap->ineq[last_pos][0],
2992                                bmap->ineq[last_pos][0], 1);
2993                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2994                                 bmap->ineq[last_pos][1+off+i]);
2995                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2996                                bmap->ineq[last_pos][0], 1);
2997                 isl_int_sub(bmap->ineq[last_pos][0],
2998                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2999                 if (!redundant) {
3000                         if (defined ||
3001                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
3002                                 pairs[i] = 0;
3003                                 --n;
3004                                 continue;
3005                         }
3006                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
3007                         bmap = isl_basic_map_simplify(bmap);
3008                         free(pairs);
3009                         return isl_basic_map_drop_redundant_divs(bmap);
3010                 }
3011                 if (last_pos > last_neg) {
3012                         isl_basic_map_drop_inequality(bmap, last_pos);
3013                         isl_basic_map_drop_inequality(bmap, last_neg);
3014                 } else {
3015                         isl_basic_map_drop_inequality(bmap, last_neg);
3016                         isl_basic_map_drop_inequality(bmap, last_pos);
3017                 }
3018                 bmap = isl_basic_map_drop_div(bmap, i);
3019                 free(pairs);
3020                 return isl_basic_map_drop_redundant_divs(bmap);
3021         }
3022
3023         if (n > 0)
3024                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
3025
3026         free(pairs);
3027         return bmap;
3028 error:
3029         free(pairs);
3030         isl_basic_map_free(bmap);
3031         return NULL;
3032 }
3033
3034 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
3035         struct isl_basic_set *bset)
3036 {
3037         return (struct isl_basic_set *)
3038             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
3039 }
3040
3041 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
3042 {
3043         int i;
3044
3045         if (!map)
3046                 return NULL;
3047         for (i = 0; i < map->n; ++i) {
3048                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
3049                 if (!map->p[i])
3050                         goto error;
3051         }
3052         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3053         return map;
3054 error:
3055         isl_map_free(map);
3056         return NULL;
3057 }
3058
3059 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
3060 {
3061         return (struct isl_set *)
3062             isl_map_drop_redundant_divs((struct isl_map *)set);
3063 }