isl_map_simplify.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2012      Ecole Normale Superieure
   4  *
   5  * Use of this software is governed by the GNU LGPLv2.1 license
   6  *
   7  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   8  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   9  * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  10  */
  11
  12 #include <strings.h>
  13 #include <isl_ctx_private.h>
  14 #include <isl_map_private.h>
  15 #include "isl_equalities.h"
  16 #include <isl/map.h>
  17 #include <isl/seq.h>
  18 #include "isl_tab.h"
  19 #include <isl_space_private.h>
  20 #include <isl_mat_private.h>
  21
  22 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  23 {
  24         isl_int *t = bmap->eq[a];
  25         bmap->eq[a] = bmap->eq[b];
  26         bmap->eq[b] = t;
  27 }
  28
  29 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  30 {
  31         if (a != b) {
  32                 isl_int *t = bmap->ineq[a];
  33                 bmap->ineq[a] = bmap->ineq[b];
  34                 bmap->ineq[b] = t;
  35         }
  36 }
  37
  38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  39 {
  40         isl_seq_cpy(c, c + n, rem);
  41         isl_seq_clr(c + rem, n);
  42 }
  43
  44 /* Drop n dimensions starting at first.
  45  *
  46  * In principle, this frees up some extra variables as the number
  47  * of columns remains constant, but we would have to extend
  48  * the div array too as the number of rows in this array is assumed
  49  * to be equal to extra.
  50  */
  51 struct isl_basic_set *isl_basic_set_drop_dims(
  52                 struct isl_basic_set *bset, unsigned first, unsigned n)
  53 {
  54         int i;
  55
  56         if (!bset)
  57                 goto error;
  58
  59         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  60
  61         if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
  62                 return bset;
  63
  64         bset = isl_basic_set_cow(bset);
  65         if (!bset)
  66                 return NULL;
  67
  68         for (i = 0; i < bset->n_eq; ++i)
  69                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  70                                      (bset->dim->n_out-first-n)+bset->extra);
  71
  72         for (i = 0; i < bset->n_ineq; ++i)
  73                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  74                                      (bset->dim->n_out-first-n)+bset->extra);
  75
  76         for (i = 0; i < bset->n_div; ++i)
  77                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  78                                      (bset->dim->n_out-first-n)+bset->extra);
  79
  80         bset->dim = isl_space_drop_outputs(bset->dim, first, n);
  81         if (!bset->dim)
  82                 goto error;
  83
  84         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  85         bset = isl_basic_set_simplify(bset);
  86         return isl_basic_set_finalize(bset);
  87 error:
  88         isl_basic_set_free(bset);
  89         return NULL;
  90 }
  91
  92 struct isl_set *isl_set_drop_dims(
  93                 struct isl_set *set, unsigned first, unsigned n)
  94 {
  95         int i;
  96
  97         if (!set)
  98                 goto error;
  99
 100         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 101
 102         if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
 103                 return set;
 104         set = isl_set_cow(set);
 105         if (!set)
 106                 goto error;
 107         set->dim = isl_space_drop_outputs(set->dim, first, n);
 108         if (!set->dim)
 109                 goto error;
 110
 111         for (i = 0; i < set->n; ++i) {
 112                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 113                 if (!set->p[i])
 114                         goto error;
 115         }
 116
 117         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 118         return set;
 119 error:
 120         isl_set_free(set);
 121         return NULL;
 122 }
 123
 124 /* Move "n" divs starting at "first" to the end of the list of divs.
 125  */
 126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 127         unsigned first, unsigned n)
 128 {
 129         isl_int **div;
 130         int i;
 131
 132         if (first + n == bmap->n_div)
 133                 return bmap;
 134
 135         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 136         if (!div)
 137                 goto error;
 138         for (i = 0; i < n; ++i)
 139                 div[i] = bmap->div[first + i];
 140         for (i = 0; i < bmap->n_div - first - n; ++i)
 141                 bmap->div[first + i] = bmap->div[first + n + i];
 142         for (i = 0; i < n; ++i)
 143                 bmap->div[bmap->n_div - n + i] = div[i];
 144         free(div);
 145         return bmap;
 146 error:
 147         isl_basic_map_free(bmap);
 148         return NULL;
 149 }
 150
 151 /* Drop "n" dimensions of type "type" starting at "first".
 152  *
 153  * In principle, this frees up some extra variables as the number
 154  * of columns remains constant, but we would have to extend
 155  * the div array too as the number of rows in this array is assumed
 156  * to be equal to extra.
 157  */
 158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 159         enum isl_dim_type type, unsigned first, unsigned n)
 160 {
 161         int i;
 162         unsigned dim;
 163         unsigned offset;
 164         unsigned left;
 165
 166         if (!bmap)
 167                 goto error;
 168
 169         dim = isl_basic_map_dim(bmap, type);
 170         isl_assert(bmap->ctx, first + n <= dim, goto error);
 171
 172         if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
 173                 return bmap;
 174
 175         bmap = isl_basic_map_cow(bmap);
 176         if (!bmap)
 177                 return NULL;
 178
 179         offset = isl_basic_map_offset(bmap, type) + first;
 180         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 181         for (i = 0; i < bmap->n_eq; ++i)
 182                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 183
 184         for (i = 0; i < bmap->n_ineq; ++i)
 185                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 186
 187         for (i = 0; i < bmap->n_div; ++i)
 188                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 189
 190         if (type == isl_dim_div) {
 191                 bmap = move_divs_last(bmap, first, n);
 192                 if (!bmap)
 193                         goto error;
 194                 isl_basic_map_free_div(bmap, n);
 195         } else
 196                 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
 197         if (!bmap->dim)
 198                 goto error;
 199
 200         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 201         bmap = isl_basic_map_simplify(bmap);
 202         return isl_basic_map_finalize(bmap);
 203 error:
 204         isl_basic_map_free(bmap);
 205         return NULL;
 206 }
 207
 208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 209         enum isl_dim_type type, unsigned first, unsigned n)
 210 {
 211         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 212                                                         type, first, n);
 213 }
 214
 215 struct isl_basic_map *isl_basic_map_drop_inputs(
 216                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 217 {
 218         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 219 }
 220
 221 struct isl_map *isl_map_drop(struct isl_map *map,
 222         enum isl_dim_type type, unsigned first, unsigned n)
 223 {
 224         int i;
 225
 226         if (!map)
 227                 goto error;
 228
 229         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 230
 231         if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
 232                 return map;
 233         map = isl_map_cow(map);
 234         if (!map)
 235                 goto error;
 236         map->dim = isl_space_drop_dims(map->dim, type, first, n);
 237         if (!map->dim)
 238                 goto error;
 239
 240         for (i = 0; i < map->n; ++i) {
 241                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 242                 if (!map->p[i])
 243                         goto error;
 244         }
 245         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 246
 247         return map;
 248 error:
 249         isl_map_free(map);
 250         return NULL;
 251 }
 252
 253 struct isl_set *isl_set_drop(struct isl_set *set,
 254         enum isl_dim_type type, unsigned first, unsigned n)
 255 {
 256         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 257 }
 258
 259 struct isl_map *isl_map_drop_inputs(
 260                 struct isl_map *map, unsigned first, unsigned n)
 261 {
 262         return isl_map_drop(map, isl_dim_in, first, n);
 263 }
 264
 265 /*
 266  * We don't cow, as the div is assumed to be redundant.
 267  */
 268 static struct isl_basic_map *isl_basic_map_drop_div(
 269                 struct isl_basic_map *bmap, unsigned div)
 270 {
 271         int i;
 272         unsigned pos;
 273
 274         if (!bmap)
 275                 goto error;
 276
 277         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 278
 279         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 280
 281         for (i = 0; i < bmap->n_eq; ++i)
 282                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 283
 284         for (i = 0; i < bmap->n_ineq; ++i) {
 285                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 286                         isl_basic_map_drop_inequality(bmap, i);
 287                         --i;
 288                         continue;
 289                 }
 290                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 291         }
 292
 293         for (i = 0; i < bmap->n_div; ++i)
 294                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 295
 296         if (div != bmap->n_div - 1) {
 297                 int j;
 298                 isl_int *t = bmap->div[div];
 299
 300                 for (j = div; j < bmap->n_div - 1; ++j)
 301                         bmap->div[j] = bmap->div[j+1];
 302
 303                 bmap->div[bmap->n_div - 1] = t;
 304         }
 305         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 306         isl_basic_map_free_div(bmap, 1);
 307
 308         return bmap;
 309 error:
 310         isl_basic_map_free(bmap);
 311         return NULL;
 312 }
 313
 314 struct isl_basic_map *isl_basic_map_normalize_constraints(
 315         struct isl_basic_map *bmap)
 316 {
 317         int i;
 318         isl_int gcd;
 319         unsigned total = isl_basic_map_total_dim(bmap);
 320
 321         if (!bmap)
 322                 return NULL;
 323
 324         isl_int_init(gcd);
 325         for (i = bmap->n_eq - 1; i >= 0; --i) {
 326                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 327                 if (isl_int_is_zero(gcd)) {
 328                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 329                                 bmap = isl_basic_map_set_to_empty(bmap);
 330                                 break;
 331                         }
 332                         isl_basic_map_drop_equality(bmap, i);
 333                         continue;
 334                 }
 335                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 336                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 337                 if (isl_int_is_one(gcd))
 338                         continue;
 339                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 340                         bmap = isl_basic_map_set_to_empty(bmap);
 341                         break;
 342                 }
 343                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 344         }
 345
 346         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 347                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 348                 if (isl_int_is_zero(gcd)) {
 349                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 350                                 bmap = isl_basic_map_set_to_empty(bmap);
 351                                 break;
 352                         }
 353                         isl_basic_map_drop_inequality(bmap, i);
 354                         continue;
 355                 }
 356                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 357                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 358                 if (isl_int_is_one(gcd))
 359                         continue;
 360                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 361                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 362         }
 363         isl_int_clear(gcd);
 364
 365         return bmap;
 366 }
 367
 368 struct isl_basic_set *isl_basic_set_normalize_constraints(
 369         struct isl_basic_set *bset)
 370 {
 371         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 372                 (struct isl_basic_map *)bset);
 373 }
 374
 375 /* Remove any common factor in numerator and denominator of 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                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 649                 }
 650         }
 651         if (done == bmap->n_eq)
 652                 return bmap;
 653         for (k = done; k < bmap->n_eq; ++k) {
 654                 if (isl_int_is_zero(bmap->eq[k][0]))
 655                         continue;
 656                 return isl_basic_map_set_to_empty(bmap);
 657         }
 658         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 659         return bmap;
 660 }
 661
 662 struct isl_basic_set *isl_basic_set_gauss(
 663         struct isl_basic_set *bset, int *progress)
 664 {
 665         return (struct isl_basic_set*)isl_basic_map_gauss(
 666                         (struct isl_basic_map *)bset, progress);
 667 }
 668
 669
 670 static unsigned int round_up(unsigned int v)
 671 {
 672         int old_v = v;
 673
 674         while (v) {
 675                 old_v = v;
 676                 v ^= v & -v;
 677         }
 678         return old_v << 1;
 679 }
 680
 681 static int hash_index(isl_int ***index, unsigned int size, int bits,
 682                         struct isl_basic_map *bmap, int k)
 683 {
 684         int h;
 685         unsigned total = isl_basic_map_total_dim(bmap);
 686         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 687         for (h = hash; index[h]; h = (h+1) % size)
 688                 if (&bmap->ineq[k] != index[h] &&
 689                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 690                         break;
 691         return h;
 692 }
 693
 694 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 695                           struct isl_basic_set *bset, int k)
 696 {
 697         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 698 }
 699
 700 /* If we can eliminate more than one div, then we need to make
 701  * sure we do it from last div to first div, in order not to
 702  * change the position of the other divs that still need to
 703  * be removed.
 704  */
 705 static struct isl_basic_map *remove_duplicate_divs(
 706         struct isl_basic_map *bmap, int *progress)
 707 {
 708         unsigned int size;
 709         int *index;
 710         int *elim_for;
 711         int k, l, h;
 712         int bits;
 713         struct isl_blk eq;
 714         unsigned total_var;
 715         unsigned total;
 716         struct isl_ctx *ctx;
 717
 718         if (!bmap || bmap->n_div <= 1)
 719                 return bmap;
 720
 721         total_var = isl_space_dim(bmap->dim, isl_dim_all);
 722         total = total_var + bmap->n_div;
 723
 724         ctx = bmap->ctx;
 725         for (k = bmap->n_div - 1; k >= 0; --k)
 726                 if (!isl_int_is_zero(bmap->div[k][0]))
 727                         break;
 728         if (k <= 0)
 729                 return bmap;
 730
 731         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 732         size = round_up(4 * bmap->n_div / 3 - 1);
 733         bits = ffs(size) - 1;
 734         index = isl_calloc_array(ctx, int, size);
 735         if (!index)
 736                 return bmap;
 737         eq = isl_blk_alloc(ctx, 1+total);
 738         if (isl_blk_is_error(eq))
 739                 goto out;
 740
 741         isl_seq_clr(eq.data, 1+total);
 742         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 743         for (--k; k >= 0; --k) {
 744                 uint32_t hash;
 745
 746                 if (isl_int_is_zero(bmap->div[k][0]))
 747                         continue;
 748
 749                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 750                 for (h = hash; index[h]; h = (h+1) % size)
 751                         if (isl_seq_eq(bmap->div[k],
 752                                        bmap->div[index[h]-1], 2+total))
 753                                 break;
 754                 if (index[h]) {
 755                         *progress = 1;
 756                         l = index[h] - 1;
 757                         elim_for[l] = k + 1;
 758                 }
 759                 index[h] = k+1;
 760         }
 761         for (l = bmap->n_div - 1; l >= 0; --l) {
 762                 if (!elim_for[l])
 763                         continue;
 764                 k = elim_for[l] - 1;
 765                 isl_int_set_si(eq.data[1+total_var+k], -1);
 766                 isl_int_set_si(eq.data[1+total_var+l], 1);
 767                 eliminate_div(bmap, eq.data, l, 0);
 768                 isl_int_set_si(eq.data[1+total_var+k], 0);
 769                 isl_int_set_si(eq.data[1+total_var+l], 0);
 770         }
 771
 772         isl_blk_free(ctx, eq);
 773 out:
 774         free(index);
 775         free(elim_for);
 776         return bmap;
 777 }
 778
 779 static int n_pure_div_eq(struct isl_basic_map *bmap)
 780 {
 781         int i, j;
 782         unsigned total;
 783
 784         total = isl_space_dim(bmap->dim, isl_dim_all);
 785         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 786                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 787                         --j;
 788                 if (j < 0)
 789                         break;
 790                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 791                         return 0;
 792         }
 793         return i;
 794 }
 795
 796 /* Normalize divs that appear in equalities.
 797  *
 798  * In particular, we assume that bmap contains some equalities
 799  * of the form
 800  *
 801  *      a x = m * e_i
 802  *
 803  * and we want to replace the set of e_i by a minimal set and
 804  * such that the new e_i have a canonical representation in terms
 805  * of the vector x.
 806  * If any of the equalities involves more than one divs, then
 807  * we currently simply bail out.
 808  *
 809  * Let us first additionally assume that all equalities involve
 810  * a div.  The equalities then express modulo constraints on the
 811  * remaining variables and we can use "parameter compression"
 812  * to find a minimal set of constraints.  The result is a transformation
 813  *
 814  *      x = T(x') = x_0 + G x'
 815  *
 816  * with G a lower-triangular matrix with all elements below the diagonal
 817  * non-negative and smaller than the diagonal element on the same row.
 818  * We first normalize x_0 by making the same property hold in the affine
 819  * T matrix.
 820  * The rows i of G with a 1 on the diagonal do not impose any modulo
 821  * constraint and simply express x_i = x'_i.
 822  * For each of the remaining rows i, we introduce a div and a corresponding
 823  * equality.  In particular
 824  *
 825  *      g_ii e_j = x_i - g_i(x')
 826  *
 827  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 828  * corresponding div (if g_kk != 1).
 829  *
 830  * If there are any equalities not involving any div, then we
 831  * first apply a variable compression on the variables x:
 832  *
 833  *      x = C x''       x'' = C_2 x
 834  *
 835  * and perform the above parameter compression on A C instead of on A.
 836  * The resulting compression is then of the form
 837  *
 838  *      x'' = T(x') = x_0 + G x'
 839  *
 840  * and in constructing the new divs and the corresponding equalities,
 841  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 842  * by the corresponding row from C_2.
 843  */
 844 static struct isl_basic_map *normalize_divs(
 845         struct isl_basic_map *bmap, int *progress)
 846 {
 847         int i, j, k;
 848         int total;
 849         int div_eq;
 850         struct isl_mat *B;
 851         struct isl_vec *d;
 852         struct isl_mat *T = NULL;
 853         struct isl_mat *C = NULL;
 854         struct isl_mat *C2 = NULL;
 855         isl_int v;
 856         int *pos;
 857         int dropped, needed;
 858
 859         if (!bmap)
 860                 return NULL;
 861
 862         if (bmap->n_div == 0)
 863                 return bmap;
 864
 865         if (bmap->n_eq == 0)
 866                 return bmap;
 867
 868         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 869                 return bmap;
 870
 871         total = isl_space_dim(bmap->dim, isl_dim_all);
 872         div_eq = n_pure_div_eq(bmap);
 873         if (div_eq == 0)
 874                 return bmap;
 875
 876         if (div_eq < bmap->n_eq) {
 877                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 878                                         bmap->n_eq - div_eq, 0, 1 + total);
 879                 C = isl_mat_variable_compression(B, &C2);
 880                 if (!C || !C2)
 881                         goto error;
 882                 if (C->n_col == 0) {
 883                         bmap = isl_basic_map_set_to_empty(bmap);
 884                         isl_mat_free(C);
 885                         isl_mat_free(C2);
 886                         goto done;
 887                 }
 888         }
 889
 890         d = isl_vec_alloc(bmap->ctx, div_eq);
 891         if (!d)
 892                 goto error;
 893         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 894                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 895                         --j;
 896                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 897         }
 898         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 899
 900         if (C) {
 901                 B = isl_mat_product(B, C);
 902                 C = NULL;
 903         }
 904
 905         T = isl_mat_parameter_compression(B, d);
 906         if (!T)
 907                 goto error;
 908         if (T->n_col == 0) {
 909                 bmap = isl_basic_map_set_to_empty(bmap);
 910                 isl_mat_free(C2);
 911                 isl_mat_free(T);
 912                 goto done;
 913         }
 914         isl_int_init(v);
 915         for (i = 0; i < T->n_row - 1; ++i) {
 916                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 917                 if (isl_int_is_zero(v))
 918                         continue;
 919                 isl_mat_col_submul(T, 0, v, 1 + i);
 920         }
 921         isl_int_clear(v);
 922         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 923         if (!pos)
 924                 goto error;
 925         /* We have to be careful because dropping equalities may reorder them */
 926         dropped = 0;
 927         for (j = bmap->n_div - 1; j >= 0; --j) {
 928                 for (i = 0; i < bmap->n_eq; ++i)
 929                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 930                                 break;
 931                 if (i < bmap->n_eq) {
 932                         bmap = isl_basic_map_drop_div(bmap, j);
 933                         isl_basic_map_drop_equality(bmap, i);
 934                         ++dropped;
 935                 }
 936         }
 937         pos[0] = 0;
 938         needed = 0;
 939         for (i = 1; i < T->n_row; ++i) {
 940                 if (isl_int_is_one(T->row[i][i]))
 941                         pos[i] = i;
 942                 else
 943                         needed++;
 944         }
 945         if (needed > dropped) {
 946                 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 947                                 needed, needed, 0);
 948                 if (!bmap)
 949                         goto error;
 950         }
 951         for (i = 1; i < T->n_row; ++i) {
 952                 if (isl_int_is_one(T->row[i][i]))
 953                         continue;
 954                 k = isl_basic_map_alloc_div(bmap);
 955                 pos[i] = 1 + total + k;
 956                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 957                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 958                 if (C2)
 959                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 960                 else
 961                         isl_int_set_si(bmap->div[k][1 + i], 1);
 962                 for (j = 0; j < i; ++j) {
 963                         if (isl_int_is_zero(T->row[i][j]))
 964                                 continue;
 965                         if (pos[j] < T->n_row && C2)
 966                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 967                                                 C2->row[pos[j]], 1 + total);
 968                         else
 969                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 970                                                                 T->row[i][j]);
 971                 }
 972                 j = isl_basic_map_alloc_equality(bmap);
 973                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 974                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 975         }
 976         free(pos);
 977         isl_mat_free(C2);
 978         isl_mat_free(T);
 979
 980         if (progress)
 981                 *progress = 1;
 982 done:
 983         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 984
 985         return bmap;
 986 error:
 987         isl_mat_free(C);
 988         isl_mat_free(C2);
 989         isl_mat_free(T);
 990         return bmap;
 991 }
 992
 993 static struct isl_basic_map *set_div_from_lower_bound(
 994         struct isl_basic_map *bmap, int div, int ineq)
 995 {
 996         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 997
 998         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
 999         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
1000         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
1001         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1002         isl_int_set_si(bmap->div[div][1 + total + div], 0);
1003
1004         return bmap;
1005 }
1006
1007 /* Check whether it is ok to define a div based on an inequality.
1008  * To avoid the introduction of circular definitions of divs, we
1009  * do not allow such a definition if the resulting expression would refer to
1010  * any other undefined divs or if any known div is defined in
1011  * terms of the unknown div.
1012  */
1013 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
1014         int div, int ineq)
1015 {
1016         int j;
1017         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1018
1019         /* Not defined in terms of unknown divs */
1020         for (j = 0; j < bmap->n_div; ++j) {
1021                 if (div == j)
1022                         continue;
1023                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1024                         continue;
1025                 if (isl_int_is_zero(bmap->div[j][0]))
1026                         return 0;
1027         }
1028
1029         /* No other div defined in terms of this one => avoid loops */
1030         for (j = 0; j < bmap->n_div; ++j) {
1031                 if (div == j)
1032                         continue;
1033                 if (isl_int_is_zero(bmap->div[j][0]))
1034                         continue;
1035                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1036                         return 0;
1037         }
1038
1039         return 1;
1040 }
1041
1042 /* Given two constraints "k" and "l" that are opposite to each other,
1043  * except for the constant term, check if we can use them
1044  * to obtain an expression for one of the hitherto unknown divs.
1045  * "sum" is the sum of the constant terms of the constraints.
1046  * If this sum is strictly smaller than the coefficient of one
1047  * of the divs, then this pair can be used define the div.
1048  * To avoid the introduction of circular definitions of divs, we
1049  * do not use the pair if the resulting expression would refer to
1050  * any other undefined divs or if any known div is defined in
1051  * terms of the unknown div.
1052  */
1053 static struct isl_basic_map *check_for_div_constraints(
1054         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
1055 {
1056         int i;
1057         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1058
1059         for (i = 0; i < bmap->n_div; ++i) {
1060                 if (!isl_int_is_zero(bmap->div[i][0]))
1061                         continue;
1062                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1063                         continue;
1064                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1065                         continue;
1066                 if (!ok_to_set_div_from_bound(bmap, i, k))
1067                         break;
1068                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1069                         bmap = set_div_from_lower_bound(bmap, i, k);
1070                 else
1071                         bmap = set_div_from_lower_bound(bmap, i, l);
1072                 if (progress)
1073                         *progress = 1;
1074                 break;
1075         }
1076         return bmap;
1077 }
1078
1079 static struct isl_basic_map *remove_duplicate_constraints(
1080         struct isl_basic_map *bmap, int *progress, int detect_divs)
1081 {
1082         unsigned int size;
1083         isl_int ***index;
1084         int k, l, h;
1085         int bits;
1086         unsigned total = isl_basic_map_total_dim(bmap);
1087         isl_int sum;
1088         isl_ctx *ctx;
1089
1090         if (!bmap || bmap->n_ineq <= 1)
1091                 return bmap;
1092
1093         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1094         bits = ffs(size) - 1;
1095         ctx = isl_basic_map_get_ctx(bmap);
1096         index = isl_calloc_array(ctx, isl_int **, size);
1097         if (!index)
1098                 return bmap;
1099
1100         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1101         for (k = 1; k < bmap->n_ineq; ++k) {
1102                 h = hash_index(index, size, bits, bmap, k);
1103                 if (!index[h]) {
1104                         index[h] = &bmap->ineq[k];
1105                         continue;
1106                 }
1107                 if (progress)
1108                         *progress = 1;
1109                 l = index[h] - &bmap->ineq[0];
1110                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1111                         swap_inequality(bmap, k, l);
1112                 isl_basic_map_drop_inequality(bmap, k);
1113                 --k;
1114         }
1115         isl_int_init(sum);
1116         for (k = 0; k < bmap->n_ineq-1; ++k) {
1117                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1118                 h = hash_index(index, size, bits, bmap, k);
1119                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1120                 if (!index[h])
1121                         continue;
1122                 l = index[h] - &bmap->ineq[0];
1123                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1124                 if (isl_int_is_pos(sum)) {
1125                         if (detect_divs)
1126                                 bmap = check_for_div_constraints(bmap, k, l,
1127                                                                  sum, progress);
1128                         continue;
1129                 }
1130                 if (isl_int_is_zero(sum)) {
1131                         /* We need to break out of the loop after these
1132                          * changes since the contents of the hash
1133                          * will no longer be valid.
1134                          * Plus, we probably we want to regauss first.
1135                          */
1136                         if (progress)
1137                                 *progress = 1;
1138                         isl_basic_map_drop_inequality(bmap, l);
1139                         isl_basic_map_inequality_to_equality(bmap, k);
1140                 } else
1141                         bmap = isl_basic_map_set_to_empty(bmap);
1142                 break;
1143         }
1144         isl_int_clear(sum);
1145
1146         free(index);
1147         return bmap;
1148 }
1149
1150
1151 /* Eliminate knowns divs from constraints where they appear with
1152  * a (positive or negative) unit coefficient.
1153  *
1154  * That is, replace
1155  *
1156  *      floor(e/m) + f >= 0
1157  *
1158  * by
1159  *
1160  *      e + m f >= 0
1161  *
1162  * and
1163  *
1164  *      -floor(e/m) + f >= 0
1165  *
1166  * by
1167  *
1168  *      -e + m f + m - 1 >= 0
1169  *
1170  * The first conversion is valid because floor(e/m) >= -f is equivalent
1171  * to e/m >= -f because -f is an integral expression.
1172  * The second conversion follows from the fact that
1173  *
1174  *      -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1175  *
1176  *
1177  * We skip integral divs, i.e., those with denominator 1, as we would
1178  * risk eliminating the div from the div constraints.  We do not need
1179  * to handle those divs here anyway since the div constraints will turn
1180  * out to form an equality and this equality can then be use to eliminate
1181  * the div from all constraints.
1182  */
1183 static __isl_give isl_basic_map *eliminate_unit_divs(
1184         __isl_take isl_basic_map *bmap, int *progress)
1185 {
1186         int i, j;
1187         isl_ctx *ctx;
1188         unsigned total;
1189
1190         if (!bmap)
1191                 return NULL;
1192
1193         ctx = isl_basic_map_get_ctx(bmap);
1194         total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1195
1196         for (i = 0; i < bmap->n_div; ++i) {
1197                 if (isl_int_is_zero(bmap->div[i][0]))
1198                         continue;
1199                 if (isl_int_is_one(bmap->div[i][0]))
1200                         continue;
1201                 for (j = 0; j < bmap->n_ineq; ++j) {
1202                         int s;
1203
1204                         if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
1205                             !isl_int_is_negone(bmap->ineq[j][total + i]))
1206                                 continue;
1207
1208                         *progress = 1;
1209
1210                         s = isl_int_sgn(bmap->ineq[j][total + i]);
1211                         isl_int_set_si(bmap->ineq[j][total + i], 0);
1212                         if (s < 0)
1213                                 isl_seq_combine(bmap->ineq[j],
1214                                         ctx->negone, bmap->div[i] + 1,
1215                                         bmap->div[i][0], bmap->ineq[j],
1216                                         total + bmap->n_div);
1217                         else
1218                                 isl_seq_combine(bmap->ineq[j],
1219                                         ctx->one, bmap->div[i] + 1,
1220                                         bmap->div[i][0], bmap->ineq[j],
1221                                         total + bmap->n_div);
1222                         if (s < 0) {
1223                                 isl_int_add(bmap->ineq[j][0],
1224                                         bmap->ineq[j][0], bmap->div[i][0]);
1225                                 isl_int_sub_ui(bmap->ineq[j][0],
1226                                         bmap->ineq[j][0], 1);
1227                         }
1228                 }
1229         }
1230
1231         return bmap;
1232 }
1233
1234 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1235 {
1236         int progress = 1;
1237         if (!bmap)
1238                 return NULL;
1239         while (progress) {
1240                 progress = 0;
1241                 bmap = isl_basic_map_normalize_constraints(bmap);
1242                 bmap = normalize_div_expressions(bmap);
1243                 bmap = remove_duplicate_divs(bmap, &progress);
1244                 bmap = eliminate_unit_divs(bmap, &progress);
1245                 bmap = eliminate_divs_eq(bmap, &progress);
1246                 bmap = eliminate_divs_ineq(bmap, &progress);
1247                 bmap = isl_basic_map_gauss(bmap, &progress);
1248                 /* requires equalities in normal form */
1249                 bmap = normalize_divs(bmap, &progress);
1250                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1251         }
1252         return bmap;
1253 }
1254
1255 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1256 {
1257         return (struct isl_basic_set *)
1258                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1259 }
1260
1261
1262 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1263         isl_int *constraint, unsigned div)
1264 {
1265         unsigned pos;
1266
1267         if (!bmap)
1268                 return -1;
1269
1270         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1271
1272         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1273                 int neg;
1274                 isl_int_sub(bmap->div[div][1],
1275                                 bmap->div[div][1], bmap->div[div][0]);
1276                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1277                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1278                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1279                 isl_int_add(bmap->div[div][1],
1280                                 bmap->div[div][1], bmap->div[div][0]);
1281                 if (!neg)
1282                         return 0;
1283                 if (isl_seq_first_non_zero(constraint+pos+1,
1284                                             bmap->n_div-div-1) != -1)
1285                         return 0;
1286         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1287                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1288                         return 0;
1289                 if (isl_seq_first_non_zero(constraint+pos+1,
1290                                             bmap->n_div-div-1) != -1)
1291                         return 0;
1292         } else
1293                 return 0;
1294
1295         return 1;
1296 }
1297
1298 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1299         isl_int *constraint, unsigned div)
1300 {
1301         return isl_basic_map_is_div_constraint(bset, constraint, div);
1302 }
1303
1304
1305 /* If the only constraints a div d=floor(f/m)
1306  * appears in are its two defining constraints
1307  *
1308  *      f - m d >=0
1309  *      -(f - (m - 1)) + m d >= 0
1310  *
1311  * then it can safely be removed.
1312  */
1313 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1314 {
1315         int i;
1316         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1317
1318         for (i = 0; i < bmap->n_eq; ++i)
1319                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1320                         return 0;
1321
1322         for (i = 0; i < bmap->n_ineq; ++i) {
1323                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1324                         continue;
1325                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1326                         return 0;
1327         }
1328
1329         for (i = 0; i < bmap->n_div; ++i)
1330                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1331                         return 0;
1332
1333         return 1;
1334 }
1335
1336 /*
1337  * Remove divs that don't occur in any of the constraints or other divs.
1338  * These can arise when dropping some of the variables in a quast
1339  * returned by piplib.
1340  */
1341 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1342 {
1343         int i;
1344
1345         if (!bmap)
1346                 return NULL;
1347
1348         for (i = bmap->n_div-1; i >= 0; --i) {
1349                 if (!div_is_redundant(bmap, i))
1350                         continue;
1351                 bmap = isl_basic_map_drop_div(bmap, i);
1352         }
1353         return bmap;
1354 }
1355
1356 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1357 {
1358         bmap = remove_redundant_divs(bmap);
1359         if (!bmap)
1360                 return NULL;
1361         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1362         return bmap;
1363 }
1364
1365 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1366 {
1367         return (struct isl_basic_set *)
1368                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1369 }
1370
1371 struct isl_set *isl_set_finalize(struct isl_set *set)
1372 {
1373         int i;
1374
1375         if (!set)
1376                 return NULL;
1377         for (i = 0; i < set->n; ++i) {
1378                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1379                 if (!set->p[i])
1380                         goto error;
1381         }
1382         return set;
1383 error:
1384         isl_set_free(set);
1385         return NULL;
1386 }
1387
1388 struct isl_map *isl_map_finalize(struct isl_map *map)
1389 {
1390         int i;
1391
1392         if (!map)
1393                 return NULL;
1394         for (i = 0; i < map->n; ++i) {
1395                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1396                 if (!map->p[i])
1397                         goto error;
1398         }
1399         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1400         return map;
1401 error:
1402         isl_map_free(map);
1403         return NULL;
1404 }
1405
1406
1407 /* Remove definition of any div that is defined in terms of the given variable.
1408  * The div itself is not removed.  Functions such as
1409  * eliminate_divs_ineq depend on the other divs remaining in place.
1410  */
1411 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1412                                                                         int pos)
1413 {
1414         int i;
1415
1416         for (i = 0; i < bmap->n_div; ++i) {
1417                 if (isl_int_is_zero(bmap->div[i][0]))
1418                         continue;
1419                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1420                         continue;
1421                 isl_int_set_si(bmap->div[i][0], 0);
1422         }
1423         return bmap;
1424 }
1425
1426 /* Eliminate the specified variables from the constraints using
1427  * Fourier-Motzkin.  The variables themselves are not removed.
1428  */
1429 struct isl_basic_map *isl_basic_map_eliminate_vars(
1430         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1431 {
1432         int d;
1433         int i, j, k;
1434         unsigned total;
1435         int need_gauss = 0;
1436
1437         if (n == 0)
1438                 return bmap;
1439         if (!bmap)
1440                 return NULL;
1441         total = isl_basic_map_total_dim(bmap);
1442
1443         bmap = isl_basic_map_cow(bmap);
1444         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1445                 bmap = remove_dependent_vars(bmap, d);
1446
1447         for (d = pos + n - 1;
1448              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1449                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1450         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1451                 int n_lower, n_upper;
1452                 if (!bmap)
1453                         return NULL;
1454                 for (i = 0; i < bmap->n_eq; ++i) {
1455                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1456                                 continue;
1457                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1458                         isl_basic_map_drop_equality(bmap, i);
1459                         need_gauss = 1;
1460                         break;
1461                 }
1462                 if (i < bmap->n_eq)
1463                         continue;
1464                 n_lower = 0;
1465                 n_upper = 0;
1466                 for (i = 0; i < bmap->n_ineq; ++i) {
1467                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1468                                 n_lower++;
1469                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1470                                 n_upper++;
1471                 }
1472                 bmap = isl_basic_map_extend_constraints(bmap,
1473                                 0, n_lower * n_upper);
1474                 if (!bmap)
1475                         goto error;
1476                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1477                         int last;
1478                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1479                                 continue;
1480                         last = -1;
1481                         for (j = 0; j < i; ++j) {
1482                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1483                                         continue;
1484                                 last = j;
1485                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1486                                     isl_int_sgn(bmap->ineq[j][1+d]))
1487                                         continue;
1488                                 k = isl_basic_map_alloc_inequality(bmap);
1489                                 if (k < 0)
1490                                         goto error;
1491                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1492                                                 1+total);
1493                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1494                                                 1+d, 1+total, NULL);
1495                         }
1496                         isl_basic_map_drop_inequality(bmap, i);
1497                         i = last + 1;
1498                 }
1499                 if (n_lower > 0 && n_upper > 0) {
1500                         bmap = isl_basic_map_normalize_constraints(bmap);
1501                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1502                         bmap = isl_basic_map_gauss(bmap, NULL);
1503                         bmap = isl_basic_map_remove_redundancies(bmap);
1504                         need_gauss = 0;
1505                         if (!bmap)
1506                                 goto error;
1507                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1508                                 break;
1509                 }
1510         }
1511         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1512         if (need_gauss)
1513                 bmap = isl_basic_map_gauss(bmap, NULL);
1514         return bmap;
1515 error:
1516         isl_basic_map_free(bmap);
1517         return NULL;
1518 }
1519
1520 struct isl_basic_set *isl_basic_set_eliminate_vars(
1521         struct isl_basic_set *bset, unsigned pos, unsigned n)
1522 {
1523         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1524                         (struct isl_basic_map *)bset, pos, n);
1525 }
1526
1527 /* Eliminate the specified n dimensions starting at first from the
1528  * constraints, without removing the dimensions from the space.
1529  * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1530  * Otherwise, they are projected out and the original space is restored.
1531  */
1532 __isl_give isl_basic_map *isl_basic_map_eliminate(
1533         __isl_take isl_basic_map *bmap,
1534         enum isl_dim_type type, unsigned first, unsigned n)
1535 {
1536         isl_space *space;
1537
1538         if (!bmap)
1539                 return NULL;
1540         if (n == 0)
1541                 return bmap;
1542
1543         if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1544                 isl_die(bmap->ctx, isl_error_invalid,
1545                         "index out of bounds", goto error);
1546
1547         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1548                 first += isl_basic_map_offset(bmap, type) - 1;
1549                 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1550                 return isl_basic_map_finalize(bmap);
1551         }
1552
1553         space = isl_basic_map_get_space(bmap);
1554         bmap = isl_basic_map_project_out(bmap, type, first, n);
1555         bmap = isl_basic_map_insert_dims(bmap, type, first, n);
1556         bmap = isl_basic_map_reset_space(bmap, space);
1557         return bmap;
1558 error:
1559         isl_basic_map_free(bmap);
1560         return NULL;
1561 }
1562
1563 __isl_give isl_basic_set *isl_basic_set_eliminate(
1564         __isl_take isl_basic_set *bset,
1565         enum isl_dim_type type, unsigned first, unsigned n)
1566 {
1567         return isl_basic_map_eliminate(bset, type, first, n);
1568 }
1569
1570 /* Don't assume equalities are in order, because align_divs
1571  * may have changed the order of the divs.
1572  */
1573 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1574 {
1575         int d, i;
1576         unsigned total;
1577
1578         total = isl_space_dim(bmap->dim, isl_dim_all);
1579         for (d = 0; d < total; ++d)
1580                 elim[d] = -1;
1581         for (i = 0; i < bmap->n_eq; ++i) {
1582                 for (d = total - 1; d >= 0; --d) {
1583                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1584                                 continue;
1585                         elim[d] = i;
1586                         break;
1587                 }
1588         }
1589 }
1590
1591 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1592 {
1593         compute_elimination_index((struct isl_basic_map *)bset, elim);
1594 }
1595
1596 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1597         struct isl_basic_map *bmap, int *elim)
1598 {
1599         int d;
1600         int copied = 0;
1601         unsigned total;
1602
1603         total = isl_space_dim(bmap->dim, isl_dim_all);
1604         for (d = total - 1; d >= 0; --d) {
1605                 if (isl_int_is_zero(src[1+d]))
1606                         continue;
1607                 if (elim[d] == -1)
1608                         continue;
1609                 if (!copied) {
1610                         isl_seq_cpy(dst, src, 1 + total);
1611                         copied = 1;
1612                 }
1613                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1614         }
1615         return copied;
1616 }
1617
1618 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1619         struct isl_basic_set *bset, int *elim)
1620 {
1621         return reduced_using_equalities(dst, src,
1622                                         (struct isl_basic_map *)bset, elim);
1623 }
1624
1625 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1626         struct isl_basic_set *bset, struct isl_basic_set *context)
1627 {
1628         int i;
1629         int *elim;
1630
1631         if (!bset || !context)
1632                 goto error;
1633
1634         if (context->n_eq == 0) {
1635                 isl_basic_set_free(context);
1636                 return bset;
1637         }
1638
1639         bset = isl_basic_set_cow(bset);
1640         if (!bset)
1641                 goto error;
1642
1643         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1644         if (!elim)
1645                 goto error;
1646         set_compute_elimination_index(context, elim);
1647         for (i = 0; i < bset->n_eq; ++i)
1648                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1649                                                         context, elim);
1650         for (i = 0; i < bset->n_ineq; ++i)
1651                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1652                                                         context, elim);
1653         isl_basic_set_free(context);
1654         free(elim);
1655         bset = isl_basic_set_simplify(bset);
1656         bset = isl_basic_set_finalize(bset);
1657         return bset;
1658 error:
1659         isl_basic_set_free(bset);
1660         isl_basic_set_free(context);
1661         return NULL;
1662 }
1663
1664 static struct isl_basic_set *remove_shifted_constraints(
1665         struct isl_basic_set *bset, struct isl_basic_set *context)
1666 {
1667         unsigned int size;
1668         isl_int ***index;
1669         int bits;
1670         int k, h, l;
1671         isl_ctx *ctx;
1672
1673         if (!bset)
1674                 return NULL;
1675
1676         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1677         bits = ffs(size) - 1;
1678         ctx = isl_basic_set_get_ctx(bset);
1679         index = isl_calloc_array(ctx, isl_int **, size);
1680         if (!index)
1681                 return bset;
1682
1683         for (k = 0; k < context->n_ineq; ++k) {
1684                 h = set_hash_index(index, size, bits, context, k);
1685                 index[h] = &context->ineq[k];
1686         }
1687         for (k = 0; k < bset->n_ineq; ++k) {
1688                 h = set_hash_index(index, size, bits, bset, k);
1689                 if (!index[h])
1690                         continue;
1691                 l = index[h] - &context->ineq[0];
1692                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1693                         continue;
1694                 bset = isl_basic_set_cow(bset);
1695                 if (!bset)
1696                         goto error;
1697                 isl_basic_set_drop_inequality(bset, k);
1698                 --k;
1699         }
1700         free(index);
1701         return bset;
1702 error:
1703         free(index);
1704         return bset;
1705 }
1706
1707 /* Remove all information from bset that is redundant in the context
1708  * of context.  Both bset and context are assumed to be full-dimensional.
1709  *
1710  * We first * remove the inequalities from "bset"
1711  * that are obviously redundant with respect to some inequality in "context".
1712  *
1713  * If there are any inequalities left, we construct a tableau for
1714  * the context and then add the inequalities of "bset".
1715  * Before adding these inequalities, we freeze all constraints such that
1716  * they won't be considered redundant in terms of the constraints of "bset".
1717  * Then we detect all redundant constraints (among the
1718  * constraints that weren't frozen), first by checking for redundancy in the
1719  * the tableau and then by checking if replacing a constraint by its negation
1720  * would lead to an empty set.  This last step is fairly expensive
1721  * and could be optimized by more reuse of the tableau.
1722  * Finally, we update bset according to the results.
1723  */
1724 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1725         __isl_take isl_basic_set *context)
1726 {
1727         int i, k;
1728         isl_basic_set *combined = NULL;
1729         struct isl_tab *tab = NULL;
1730         unsigned context_ineq;
1731         unsigned total;
1732
1733         if (!bset || !context)
1734                 goto error;
1735
1736         if (isl_basic_set_is_universe(bset)) {
1737                 isl_basic_set_free(context);
1738                 return bset;
1739         }
1740
1741         if (isl_basic_set_is_universe(context)) {
1742                 isl_basic_set_free(context);
1743                 return bset;
1744         }
1745
1746         bset = remove_shifted_constraints(bset, context);
1747         if (!bset)
1748                 goto error;
1749         if (bset->n_ineq == 0)
1750                 goto done;
1751
1752         context_ineq = context->n_ineq;
1753         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1754         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1755         tab = isl_tab_from_basic_set(combined, 0);
1756         for (i = 0; i < context_ineq; ++i)
1757                 if (isl_tab_freeze_constraint(tab, i) < 0)
1758                         goto error;
1759         tab = isl_tab_extend(tab, bset->n_ineq);
1760         for (i = 0; i < bset->n_ineq; ++i)
1761                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1762                         goto error;
1763         bset = isl_basic_set_add_constraints(combined, bset, 0);
1764         combined = NULL;
1765         if (!bset)
1766                 goto error;
1767         if (isl_tab_detect_redundant(tab) < 0)
1768                 goto error;
1769         total = isl_basic_set_total_dim(bset);
1770         for (i = context_ineq; i < bset->n_ineq; ++i) {
1771                 int is_empty;
1772                 if (tab->con[i].is_redundant)
1773                         continue;
1774                 tab->con[i].is_redundant = 1;
1775                 combined = isl_basic_set_dup(bset);
1776                 combined = isl_basic_set_update_from_tab(combined, tab);
1777                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1778                 k = isl_basic_set_alloc_inequality(combined);
1779                 if (k < 0)
1780                         goto error;
1781                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1782                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1783                 is_empty = isl_basic_set_is_empty(combined);
1784                 if (is_empty < 0)
1785                         goto error;
1786                 isl_basic_set_free(combined);
1787                 combined = NULL;
1788                 if (!is_empty)
1789                         tab->con[i].is_redundant = 0;
1790         }
1791         for (i = 0; i < context_ineq; ++i)
1792                 tab->con[i].is_redundant = 1;
1793         bset = isl_basic_set_update_from_tab(bset, tab);
1794         if (bset) {
1795                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1796                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1797         }
1798
1799         isl_tab_free(tab);
1800 done:
1801         bset = isl_basic_set_simplify(bset);
1802         bset = isl_basic_set_finalize(bset);
1803         isl_basic_set_free(context);
1804         return bset;
1805 error:
1806         isl_tab_free(tab);
1807         isl_basic_set_free(combined);
1808         isl_basic_set_free(context);
1809         isl_basic_set_free(bset);
1810         return NULL;
1811 }
1812
1813 /* Remove all information from bset that is redundant in the context
1814  * of context.  In particular, equalities that are linear combinations
1815  * of those in context are removed.  Then the inequalities that are
1816  * redundant in the context of the equalities and inequalities of
1817  * context are removed.
1818  *
1819  * We first compute the integer affine hull of the intersection,
1820  * compute the gist inside this affine hull and then add back
1821  * those equalities that are not implied by the context.
1822  *
1823  * If two constraints are mutually redundant, then uset_gist_full
1824  * will remove the second of those constraints.  We therefore first
1825  * sort the constraints so that constraints not involving existentially
1826  * quantified variables are given precedence over those that do.
1827  * We have to perform this sorting before the variable compression,
1828  * because that may effect the order of the variables.
1829  */
1830 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1831         __isl_take isl_basic_set *context)
1832 {
1833         isl_mat *eq;
1834         isl_mat *T, *T2;
1835         isl_basic_set *aff;
1836         isl_basic_set *aff_context;
1837         unsigned total;
1838
1839         if (!bset || !context)
1840                 goto error;
1841
1842         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1843         if (isl_basic_set_plain_is_empty(bset)) {
1844                 isl_basic_set_free(context);
1845                 return bset;
1846         }
1847         bset = isl_basic_set_sort_constraints(bset);
1848         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1849         if (!aff)
1850                 goto error;
1851         if (isl_basic_set_plain_is_empty(aff)) {
1852                 isl_basic_set_free(aff);
1853                 isl_basic_set_free(context);
1854                 return bset;
1855         }
1856         if (aff->n_eq == 0) {
1857                 isl_basic_set_free(aff);
1858                 return uset_gist_full(bset, context);
1859         }
1860         total = isl_basic_set_total_dim(bset);
1861         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1862         eq = isl_mat_cow(eq);
1863         T = isl_mat_variable_compression(eq, &T2);
1864         if (T && T->n_col == 0) {
1865                 isl_mat_free(T);
1866                 isl_mat_free(T2);
1867                 isl_basic_set_free(context);
1868                 isl_basic_set_free(aff);
1869                 return isl_basic_set_set_to_empty(bset);
1870         }
1871
1872         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1873
1874         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1875         context = isl_basic_set_preimage(context, T);
1876
1877         bset = uset_gist_full(bset, context);
1878         bset = isl_basic_set_preimage(bset, T2);
1879         bset = isl_basic_set_intersect(bset, aff);
1880         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1881
1882         if (bset) {
1883                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1884                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1885         }
1886
1887         return bset;
1888 error:
1889         isl_basic_set_free(bset);
1890         isl_basic_set_free(context);
1891         return NULL;
1892 }
1893
1894 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1895  * We simply add the equalities in context to bmap and then do a regular
1896  * div normalizations.  Better results can be obtained by normalizing
1897  * only the divs in bmap than do not also appear in context.
1898  * We need to be careful to reduce the divs using the equalities
1899  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1900  * spurious constraints.
1901  */
1902 static struct isl_basic_map *normalize_divs_in_context(
1903         struct isl_basic_map *bmap, struct isl_basic_map *context)
1904 {
1905         int i;
1906         unsigned total_context;
1907         int div_eq;
1908
1909         div_eq = n_pure_div_eq(bmap);
1910         if (div_eq == 0)
1911                 return bmap;
1912
1913         if (context->n_div > 0)
1914                 bmap = isl_basic_map_align_divs(bmap, context);
1915
1916         total_context = isl_basic_map_total_dim(context);
1917         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1918         for (i = 0; i < context->n_eq; ++i) {
1919                 int k;
1920                 k = isl_basic_map_alloc_equality(bmap);
1921                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1922                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1923                                 isl_basic_map_total_dim(bmap) - total_context);
1924         }
1925         bmap = isl_basic_map_gauss(bmap, NULL);
1926         bmap = normalize_divs(bmap, NULL);
1927         bmap = isl_basic_map_gauss(bmap, NULL);
1928         return bmap;
1929 }
1930
1931 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1932         struct isl_basic_map *context)
1933 {
1934         struct isl_basic_set *bset;
1935
1936         if (!bmap || !context)
1937                 goto error;
1938
1939         if (isl_basic_map_is_universe(bmap)) {
1940                 isl_basic_map_free(context);
1941                 return bmap;
1942         }
1943         if (isl_basic_map_plain_is_empty(context)) {
1944                 isl_basic_map_free(bmap);
1945                 return context;
1946         }
1947         if (isl_basic_map_plain_is_empty(bmap)) {
1948                 isl_basic_map_free(context);
1949                 return bmap;
1950         }
1951
1952         bmap = isl_basic_map_remove_redundancies(bmap);
1953         context = isl_basic_map_remove_redundancies(context);
1954
1955         if (context->n_eq)
1956                 bmap = normalize_divs_in_context(bmap, context);
1957
1958         context = isl_basic_map_align_divs(context, bmap);
1959         bmap = isl_basic_map_align_divs(bmap, context);
1960
1961         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1962                          isl_basic_map_underlying_set(context));
1963
1964         return isl_basic_map_overlying_set(bset, bmap);
1965 error:
1966         isl_basic_map_free(bmap);
1967         isl_basic_map_free(context);
1968         return NULL;
1969 }
1970
1971 /*
1972  * Assumes context has no implicit divs.
1973  */
1974 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1975         __isl_take isl_basic_map *context)
1976 {
1977         int i;
1978
1979         if (!map || !context)
1980                 goto error;;
1981
1982         if (isl_basic_map_plain_is_empty(context)) {
1983                 isl_map_free(map);
1984                 return isl_map_from_basic_map(context);
1985         }
1986
1987         context = isl_basic_map_remove_redundancies(context);
1988         map = isl_map_cow(map);
1989         if (!map || !context)
1990                 goto error;;
1991         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1992         map = isl_map_compute_divs(map);
1993         for (i = 0; i < map->n; ++i)
1994                 context = isl_basic_map_align_divs(context, map->p[i]);
1995         for (i = map->n - 1; i >= 0; --i) {
1996                 map->p[i] = isl_basic_map_gist(map->p[i],
1997                                                 isl_basic_map_copy(context));
1998                 if (!map->p[i])
1999                         goto error;
2000                 if (isl_basic_map_plain_is_empty(map->p[i])) {
2001                         isl_basic_map_free(map->p[i]);
2002                         if (i != map->n - 1)
2003                                 map->p[i] = map->p[map->n - 1];
2004                         map->n--;
2005                 }
2006         }
2007         isl_basic_map_free(context);
2008         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2009         return map;
2010 error:
2011         isl_map_free(map);
2012         isl_basic_map_free(context);
2013         return NULL;
2014 }
2015
2016 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
2017         __isl_take isl_map *context)
2018 {
2019         context = isl_map_compute_divs(context);
2020         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
2021 }
2022
2023 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2024         __isl_take isl_map *context)
2025 {
2026         return isl_map_align_params_map_map_and(map, context, &map_gist);
2027 }
2028
2029 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
2030                                                 struct isl_basic_set *context)
2031 {
2032         return (struct isl_basic_set *)isl_basic_map_gist(
2033                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
2034 }
2035
2036 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
2037         __isl_take isl_basic_set *context)
2038 {
2039         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
2040                                         (struct isl_basic_map *)context);
2041 }
2042
2043 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
2044         __isl_take isl_basic_set *context)
2045 {
2046         isl_space *space = isl_set_get_space(set);
2047         isl_basic_set *dom_context = isl_basic_set_universe(space);
2048         dom_context = isl_basic_set_intersect_params(dom_context, context);
2049         return isl_set_gist_basic_set(set, dom_context);
2050 }
2051
2052 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2053         __isl_take isl_set *context)
2054 {
2055         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
2056                                         (struct isl_map *)context);
2057 }
2058
2059 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
2060         __isl_take isl_set *context)
2061 {
2062         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2063         map_context = isl_map_intersect_domain(map_context, context);
2064         return isl_map_gist(map, map_context);
2065 }
2066
2067 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
2068         __isl_take isl_set *context)
2069 {
2070         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2071         map_context = isl_map_intersect_range(map_context, context);
2072         return isl_map_gist(map, map_context);
2073 }
2074
2075 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
2076         __isl_take isl_set *context)
2077 {
2078         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2079         map_context = isl_map_intersect_params(map_context, context);
2080         return isl_map_gist(map, map_context);
2081 }
2082
2083 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
2084         __isl_take isl_set *context)
2085 {
2086         return isl_map_gist_params(set, context);
2087 }
2088
2089 /* Quick check to see if two basic maps are disjoint.
2090  * In particular, we reduce the equalities and inequalities of
2091  * one basic map in the context of the equalities of the other
2092  * basic map and check if we get a contradiction.
2093  */
2094 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
2095         __isl_keep isl_basic_map *bmap2)
2096 {
2097         struct isl_vec *v = NULL;
2098         int *elim = NULL;
2099         unsigned total;
2100         int i;
2101
2102         if (!bmap1 || !bmap2)
2103                 return -1;
2104         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
2105                         return -1);
2106         if (bmap1->n_div || bmap2->n_div)
2107                 return 0;
2108         if (!bmap1->n_eq && !bmap2->n_eq)
2109                 return 0;
2110
2111         total = isl_space_dim(bmap1->dim, isl_dim_all);
2112         if (total == 0)
2113                 return 0;
2114         v = isl_vec_alloc(bmap1->ctx, 1 + total);
2115         if (!v)
2116                 goto error;
2117         elim = isl_alloc_array(bmap1->ctx, int, total);
2118         if (!elim)
2119                 goto error;
2120         compute_elimination_index(bmap1, elim);
2121         for (i = 0; i < bmap2->n_eq; ++i) {
2122                 int reduced;
2123                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
2124                                                         bmap1, elim);
2125                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
2126                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2127                         goto disjoint;
2128         }
2129         for (i = 0; i < bmap2->n_ineq; ++i) {
2130                 int reduced;
2131                 reduced = reduced_using_equalities(v->block.data,
2132                                                 bmap2->ineq[i], bmap1, elim);
2133                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2134                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2135                         goto disjoint;
2136         }
2137         compute_elimination_index(bmap2, elim);
2138         for (i = 0; i < bmap1->n_ineq; ++i) {
2139                 int reduced;
2140                 reduced = reduced_using_equalities(v->block.data,
2141                                                 bmap1->ineq[i], bmap2, elim);
2142                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2143                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2144                         goto disjoint;
2145         }
2146         isl_vec_free(v);
2147         free(elim);
2148         return 0;
2149 disjoint:
2150         isl_vec_free(v);
2151         free(elim);
2152         return 1;
2153 error:
2154         isl_vec_free(v);
2155         free(elim);
2156         return -1;
2157 }
2158
2159 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2160         __isl_keep isl_basic_set *bset2)
2161 {
2162         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2163                                               (struct isl_basic_map *)bset2);
2164 }
2165
2166 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2167         __isl_keep isl_map *map2)
2168 {
2169         int i, j;
2170
2171         if (!map1 || !map2)
2172                 return -1;
2173
2174         if (isl_map_plain_is_equal(map1, map2))
2175                 return 0;
2176
2177         for (i = 0; i < map1->n; ++i) {
2178                 for (j = 0; j < map2->n; ++j) {
2179                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2180                                                                map2->p[j]);
2181                         if (d != 1)
2182                                 return d;
2183                 }
2184         }
2185         return 1;
2186 }
2187
2188 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2189         __isl_keep isl_set *set2)
2190 {
2191         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2192                                         (struct isl_map *)set2);
2193 }
2194
2195 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2196 {
2197         return isl_set_plain_is_disjoint(set1, set2);
2198 }
2199
2200 /* Check if we can combine a given div with lower bound l and upper
2201  * bound u with some other div and if so return that other div.
2202  * Otherwise return -1.
2203  *
2204  * We first check that
2205  *      - the bounds are opposites of each other (except for the constant
2206  *        term)
2207  *      - the bounds do not reference any other div
2208  *      - no div is defined in terms of this div
2209  *
2210  * Let m be the size of the range allowed on the div by the bounds.
2211  * That is, the bounds are of the form
2212  *
2213  *      e <= a <= e + m - 1
2214  *
2215  * with e some expression in the other variables.
2216  * We look for another div b such that no third div is defined in terms
2217  * of this second div b and such that in any constraint that contains
2218  * a (except for the given lower and upper bound), also contains b
2219  * with a coefficient that is m times that of b.
2220  * That is, all constraints (execpt for the lower and upper bound)
2221  * are of the form
2222  *
2223  *      e + f (a + m b) >= 0
2224  *
2225  * If so, we return b so that "a + m b" can be replaced by
2226  * a single div "c = a + m b".
2227  */
2228 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2229         unsigned div, unsigned l, unsigned u)
2230 {
2231         int i, j;
2232         unsigned dim;
2233         int coalesce = -1;
2234
2235         if (bmap->n_div <= 1)
2236                 return -1;
2237         dim = isl_space_dim(bmap->dim, isl_dim_all);
2238         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2239                 return -1;
2240         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2241                                    bmap->n_div - div - 1) != -1)
2242                 return -1;
2243         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2244                             dim + bmap->n_div))
2245                 return -1;
2246
2247         for (i = 0; i < bmap->n_div; ++i) {
2248                 if (isl_int_is_zero(bmap->div[i][0]))
2249                         continue;
2250                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2251                         return -1;
2252         }
2253
2254         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2255         if (isl_int_is_neg(bmap->ineq[l][0])) {
2256                 isl_int_sub(bmap->ineq[l][0],
2257                             bmap->ineq[l][0], bmap->ineq[u][0]);
2258                 bmap = isl_basic_map_copy(bmap);
2259                 bmap = isl_basic_map_set_to_empty(bmap);
2260                 isl_basic_map_free(bmap);
2261                 return -1;
2262         }
2263         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2264         for (i = 0; i < bmap->n_div; ++i) {
2265                 if (i == div)
2266                         continue;
2267                 if (!pairs[i])
2268                         continue;
2269                 for (j = 0; j < bmap->n_div; ++j) {
2270                         if (isl_int_is_zero(bmap->div[j][0]))
2271                                 continue;
2272                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2273                                 break;
2274                 }
2275                 if (j < bmap->n_div)
2276                         continue;
2277                 for (j = 0; j < bmap->n_ineq; ++j) {
2278                         int valid;
2279                         if (j == l || j == u)
2280                                 continue;
2281                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2282                                 continue;
2283                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2284                                 break;
2285                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2286                                     bmap->ineq[j][1 + dim + div],
2287                                     bmap->ineq[l][0]);
2288                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2289                                            bmap->ineq[j][1 + dim + i]);
2290                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2291                                          bmap->ineq[j][1 + dim + div],
2292                                          bmap->ineq[l][0]);
2293                         if (!valid)
2294                                 break;
2295                 }
2296                 if (j < bmap->n_ineq)
2297                         continue;
2298                 coalesce = i;
2299                 break;
2300         }
2301         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2302         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2303         return coalesce;
2304 }
2305
2306 /* Given a lower and an upper bound on div i, construct an inequality
2307  * that when nonnegative ensures that this pair of bounds always allows
2308  * for an integer value of the given div.
2309  * The lower bound is inequality l, while the upper bound is inequality u.
2310  * The constructed inequality is stored in ineq.
2311  * g, fl, fu are temporary scalars.
2312  *
2313  * Let the upper bound be
2314  *
2315  *      -n_u a + e_u >= 0
2316  *
2317  * and the lower bound
2318  *
2319  *      n_l a + e_l >= 0
2320  *
2321  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2322  * We have
2323  *
2324  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2325  *
2326  * Since all variables are integer valued, this is equivalent to
2327  *
2328  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2329  *
2330  * If this interval is at least f_u f_l g, then it contains at least
2331  * one integer value for a.
2332  * That is, the test constraint is
2333  *
2334  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2335  */
2336 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2337         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2338 {
2339         unsigned dim;
2340         dim = isl_space_dim(bmap->dim, isl_dim_all);
2341
2342         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2343         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2344         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2345         isl_int_neg(fu, fu);
2346         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2347                         1 + dim + bmap->n_div);
2348         isl_int_add(ineq[0], ineq[0], fl);
2349         isl_int_add(ineq[0], ineq[0], fu);
2350         isl_int_sub_ui(ineq[0], ineq[0], 1);
2351         isl_int_mul(g, g, fl);
2352         isl_int_mul(g, g, fu);
2353         isl_int_sub(ineq[0], ineq[0], g);
2354 }
2355
2356 /* Remove more kinds of divs that are not strictly needed.
2357  * In particular, if all pairs of lower and upper bounds on a div
2358  * are such that they allow at least one integer value of the div,
2359  * the we can eliminate the div using Fourier-Motzkin without
2360  * introducing any spurious solutions.
2361  */
2362 static struct isl_basic_map *drop_more_redundant_divs(
2363         struct isl_basic_map *bmap, int *pairs, int n)
2364 {
2365         struct isl_tab *tab = NULL;
2366         struct isl_vec *vec = NULL;
2367         unsigned dim;
2368         int remove = -1;
2369         isl_int g, fl, fu;
2370
2371         isl_int_init(g);
2372         isl_int_init(fl);
2373         isl_int_init(fu);
2374
2375         if (!bmap)
2376                 goto error;
2377
2378         dim = isl_space_dim(bmap->dim, isl_dim_all);
2379         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2380         if (!vec)
2381                 goto error;
2382
2383         tab = isl_tab_from_basic_map(bmap, 0);
2384
2385         while (n > 0) {
2386                 int i, l, u;
2387                 int best = -1;
2388                 enum isl_lp_result res;
2389
2390                 for (i = 0; i < bmap->n_div; ++i) {
2391                         if (!pairs[i])
2392                                 continue;
2393                         if (best >= 0 && pairs[best] <= pairs[i])
2394                                 continue;
2395                         best = i;
2396                 }
2397
2398                 i = best;
2399                 for (l = 0; l < bmap->n_ineq; ++l) {
2400                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2401                                 continue;
2402                         for (u = 0; u < bmap->n_ineq; ++u) {
2403                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2404                                         continue;
2405                                 construct_test_ineq(bmap, i, l, u,
2406                                                     vec->el, g, fl, fu);
2407                                 res = isl_tab_min(tab, vec->el,
2408                                                   bmap->ctx->one, &g, NULL, 0);
2409                                 if (res == isl_lp_error)
2410                                         goto error;
2411                                 if (res == isl_lp_empty) {
2412                                         bmap = isl_basic_map_set_to_empty(bmap);
2413                                         break;
2414                                 }
2415                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2416                                         break;
2417                         }
2418                         if (u < bmap->n_ineq)
2419                                 break;
2420                 }
2421                 if (l == bmap->n_ineq) {
2422                         remove = i;
2423                         break;
2424                 }
2425                 pairs[i] = 0;
2426                 --n;
2427         }
2428
2429         isl_tab_free(tab);
2430         isl_vec_free(vec);
2431
2432         isl_int_clear(g);
2433         isl_int_clear(fl);
2434         isl_int_clear(fu);
2435
2436         free(pairs);
2437
2438         if (remove < 0)
2439                 return bmap;
2440
2441         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2442         return isl_basic_map_drop_redundant_divs(bmap);
2443 error:
2444         free(pairs);
2445         isl_basic_map_free(bmap);
2446         isl_tab_free(tab);
2447         isl_vec_free(vec);
2448         isl_int_clear(g);
2449         isl_int_clear(fl);
2450         isl_int_clear(fu);
2451         return NULL;
2452 }
2453
2454 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2455  * and the upper bound u, div1 always occurs together with div2 in the form
2456  * (div1 + m div2), where m is the constant range on the variable div1
2457  * allowed by l and u, replace the pair div1 and div2 by a single
2458  * div that is equal to div1 + m div2.
2459  *
2460  * The new div will appear in the location that contains div2.
2461  * We need to modify all constraints that contain
2462  * div2 = (div - div1) / m
2463  * (If a constraint does not contain div2, it will also not contain div1.)
2464  * If the constraint also contains div1, then we know they appear
2465  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2466  * i.e., the coefficient of div is f.
2467  *
2468  * Otherwise, we first need to introduce div1 into the constraint.
2469  * Let the l be
2470  *
2471  *      div1 + f >=0
2472  *
2473  * and u
2474  *
2475  *      -div1 + f' >= 0
2476  *
2477  * A lower bound on div2
2478  *
2479  *      n div2 + t >= 0
2480  *
2481  * can be replaced by
2482  *
2483  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2484  *
2485  * with g = gcd(m,n).
2486  * An upper bound
2487  *
2488  *      -n div2 + t >= 0
2489  *
2490  * can be replaced by
2491  *
2492  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2493  *
2494  * These constraint are those that we would obtain from eliminating
2495  * div1 using Fourier-Motzkin.
2496  *
2497  * After all constraints have been modified, we drop the lower and upper
2498  * bound and then drop div1.
2499  */
2500 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2501         unsigned div1, unsigned div2, unsigned l, unsigned u)
2502 {
2503         isl_int a;
2504         isl_int b;
2505         isl_int m;
2506         unsigned dim, total;
2507         int i;
2508
2509         dim = isl_space_dim(bmap->dim, isl_dim_all);
2510         total = 1 + dim + bmap->n_div;
2511
2512         isl_int_init(a);
2513         isl_int_init(b);
2514         isl_int_init(m);
2515         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2516         isl_int_add_ui(m, m, 1);
2517
2518         for (i = 0; i < bmap->n_ineq; ++i) {
2519                 if (i == l || i == u)
2520                         continue;
2521                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2522                         continue;
2523                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2524                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2525                         isl_int_divexact(a, m, b);
2526                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2527                         if (isl_int_is_pos(b)) {
2528                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2529                                                 b, bmap->ineq[l], total);
2530                         } else {
2531                                 isl_int_neg(b, b);
2532                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2533                                                 b, bmap->ineq[u], total);
2534                         }
2535                 }
2536                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2537                             bmap->ineq[i][1 + dim + div1]);
2538                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2539         }
2540
2541         isl_int_clear(a);
2542         isl_int_clear(b);
2543         isl_int_clear(m);
2544         if (l > u) {
2545                 isl_basic_map_drop_inequality(bmap, l);
2546                 isl_basic_map_drop_inequality(bmap, u);
2547         } else {
2548                 isl_basic_map_drop_inequality(bmap, u);
2549                 isl_basic_map_drop_inequality(bmap, l);
2550         }
2551         bmap = isl_basic_map_drop_div(bmap, div1);
2552         return bmap;
2553 }
2554
2555 /* First check if we can coalesce any pair of divs and
2556  * then continue with dropping more redundant divs.
2557  *
2558  * We loop over all pairs of lower and upper bounds on a div
2559  * with coefficient 1 and -1, respectively, check if there
2560  * is any other div "c" with which we can coalesce the div
2561  * and if so, perform the coalescing.
2562  */
2563 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2564         struct isl_basic_map *bmap, int *pairs, int n)
2565 {
2566         int i, l, u;
2567         unsigned dim;
2568
2569         dim = isl_space_dim(bmap->dim, isl_dim_all);
2570
2571         for (i = 0; i < bmap->n_div; ++i) {
2572                 if (!pairs[i])
2573                         continue;
2574                 for (l = 0; l < bmap->n_ineq; ++l) {
2575                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2576                                 continue;
2577                         for (u = 0; u < bmap->n_ineq; ++u) {
2578                                 int c;
2579
2580                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2581                                         continue;
2582                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2583                                 if (c < 0)
2584                                         continue;
2585                                 free(pairs);
2586                                 bmap = coalesce_divs(bmap, i, c, l, u);
2587                                 return isl_basic_map_drop_redundant_divs(bmap);
2588                         }
2589                 }
2590         }
2591
2592         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2593                 return bmap;
2594
2595         return drop_more_redundant_divs(bmap, pairs, n);
2596 }
2597
2598 /* Remove divs that are not strictly needed.
2599  * In particular, if a div only occurs positively (or negatively)
2600  * in constraints, then it can simply be dropped.
2601  * Also, if a div occurs only occurs in two constraints and if moreover
2602  * those two constraints are opposite to each other, except for the constant
2603  * term and if the sum of the constant terms is such that for any value
2604  * of the other values, there is always at least one integer value of the
2605  * div, i.e., if one plus this sum is greater than or equal to
2606  * the (absolute value) of the coefficent of the div in the constraints,
2607  * then we can also simply drop the div.
2608  *
2609  * If any divs are left after these simple checks then we move on
2610  * to more complicated cases in drop_more_redundant_divs.
2611  */
2612 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2613         struct isl_basic_map *bmap)
2614 {
2615         int i, j;
2616         unsigned off;
2617         int *pairs = NULL;
2618         int n = 0;
2619
2620         if (!bmap)
2621                 goto error;
2622
2623         off = isl_space_dim(bmap->dim, isl_dim_all);
2624         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2625         if (!pairs)
2626                 goto error;
2627
2628         for (i = 0; i < bmap->n_div; ++i) {
2629                 int pos, neg;
2630                 int last_pos, last_neg;
2631                 int redundant;
2632                 int defined;
2633
2634                 defined = !isl_int_is_zero(bmap->div[i][0]);
2635                 for (j = 0; j < bmap->n_eq; ++j)
2636                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2637                                 break;
2638                 if (j < bmap->n_eq)
2639                         continue;
2640                 ++n;
2641                 pos = neg = 0;
2642                 for (j = 0; j < bmap->n_ineq; ++j) {
2643                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2644                                 last_pos = j;
2645                                 ++pos;
2646                         }
2647                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2648                                 last_neg = j;
2649                                 ++neg;
2650                         }
2651                 }
2652                 pairs[i] = pos * neg;
2653                 if (pairs[i] == 0) {
2654                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2655                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2656                                         isl_basic_map_drop_inequality(bmap, j);
2657                         bmap = isl_basic_map_drop_div(bmap, i);
2658                         free(pairs);
2659                         return isl_basic_map_drop_redundant_divs(bmap);
2660                 }
2661                 if (pairs[i] != 1)
2662                         continue;
2663                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2664                                     bmap->ineq[last_neg] + 1,
2665                                     off + bmap->n_div))
2666                         continue;
2667
2668                 isl_int_add(bmap->ineq[last_pos][0],
2669                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2670                 isl_int_add_ui(bmap->ineq[last_pos][0],
2671                                bmap->ineq[last_pos][0], 1);
2672                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2673                                 bmap->ineq[last_pos][1+off+i]);
2674                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2675                                bmap->ineq[last_pos][0], 1);
2676                 isl_int_sub(bmap->ineq[last_pos][0],
2677                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2678                 if (!redundant) {
2679                         if (defined ||
2680                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2681                                 pairs[i] = 0;
2682                                 --n;
2683                                 continue;
2684                         }
2685                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2686                         bmap = isl_basic_map_simplify(bmap);
2687                         free(pairs);
2688                         return isl_basic_map_drop_redundant_divs(bmap);
2689                 }
2690                 if (last_pos > last_neg) {
2691                         isl_basic_map_drop_inequality(bmap, last_pos);
2692                         isl_basic_map_drop_inequality(bmap, last_neg);
2693                 } else {
2694                         isl_basic_map_drop_inequality(bmap, last_neg);
2695                         isl_basic_map_drop_inequality(bmap, last_pos);
2696                 }
2697                 bmap = isl_basic_map_drop_div(bmap, i);
2698                 free(pairs);
2699                 return isl_basic_map_drop_redundant_divs(bmap);
2700         }
2701
2702         if (n > 0)
2703                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2704
2705         free(pairs);
2706         return bmap;
2707 error:
2708         free(pairs);
2709         isl_basic_map_free(bmap);
2710         return NULL;
2711 }
2712
2713 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2714         struct isl_basic_set *bset)
2715 {
2716         return (struct isl_basic_set *)
2717             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2718 }
2719
2720 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2721 {
2722         int i;
2723
2724         if (!map)
2725                 return NULL;
2726         for (i = 0; i < map->n; ++i) {
2727                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2728                 if (!map->p[i])
2729                         goto error;
2730         }
2731         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2732         return map;
2733 error:
2734         isl_map_free(map);
2735         return NULL;
2736 }
2737
2738 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2739 {
2740         return (struct isl_set *)
2741             isl_map_drop_redundant_divs((struct isl_map *)set);
2742 }