isl_map_simplify.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2012      Ecole Normale Superieure
   4  *
   5  * Use of this software is governed by the MIT license
   6  *
   7  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   8  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   9  * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  10  */
  11
  12 #include <strings.h>
  13 #include <isl_ctx_private.h>
  14 #include <isl_map_private.h>
  15 #include "isl_equalities.h"
  16 #include <isl/map.h>
  17 #include <isl/seq.h>
  18 #include "isl_tab.h"
  19 #include <isl_space_private.h>
  20 #include <isl_mat_private.h>
  21
  22 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
  23 {
  24         isl_int *t = bmap->eq[a];
  25         bmap->eq[a] = bmap->eq[b];
  26         bmap->eq[b] = t;
  27 }
  28
  29 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  30 {
  31         if (a != b) {
  32                 isl_int *t = bmap->ineq[a];
  33                 bmap->ineq[a] = bmap->ineq[b];
  34                 bmap->ineq[b] = t;
  35         }
  36 }
  37
  38 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  39 {
  40         isl_seq_cpy(c, c + n, rem);
  41         isl_seq_clr(c + rem, n);
  42 }
  43
  44 /* Drop n dimensions starting at first.
  45  *
  46  * In principle, this frees up some extra variables as the number
  47  * of columns remains constant, but we would have to extend
  48  * the div array too as the number of rows in this array is assumed
  49  * to be equal to extra.
  50  */
  51 struct isl_basic_set *isl_basic_set_drop_dims(
  52                 struct isl_basic_set *bset, unsigned first, unsigned n)
  53 {
  54         int i;
  55
  56         if (!bset)
  57                 goto error;
  58
  59         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  60
  61         if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
  62                 return bset;
  63
  64         bset = isl_basic_set_cow(bset);
  65         if (!bset)
  66                 return NULL;
  67
  68         for (i = 0; i < bset->n_eq; ++i)
  69                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  70                                      (bset->dim->n_out-first-n)+bset->extra);
  71
  72         for (i = 0; i < bset->n_ineq; ++i)
  73                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  74                                      (bset->dim->n_out-first-n)+bset->extra);
  75
  76         for (i = 0; i < bset->n_div; ++i)
  77                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  78                                      (bset->dim->n_out-first-n)+bset->extra);
  79
  80         bset->dim = isl_space_drop_outputs(bset->dim, first, n);
  81         if (!bset->dim)
  82                 goto error;
  83
  84         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  85         bset = isl_basic_set_simplify(bset);
  86         return isl_basic_set_finalize(bset);
  87 error:
  88         isl_basic_set_free(bset);
  89         return NULL;
  90 }
  91
  92 struct isl_set *isl_set_drop_dims(
  93                 struct isl_set *set, unsigned first, unsigned n)
  94 {
  95         int i;
  96
  97         if (!set)
  98                 goto error;
  99
 100         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 101
 102         if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
 103                 return set;
 104         set = isl_set_cow(set);
 105         if (!set)
 106                 goto error;
 107         set->dim = isl_space_drop_outputs(set->dim, first, n);
 108         if (!set->dim)
 109                 goto error;
 110
 111         for (i = 0; i < set->n; ++i) {
 112                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 113                 if (!set->p[i])
 114                         goto error;
 115         }
 116
 117         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 118         return set;
 119 error:
 120         isl_set_free(set);
 121         return NULL;
 122 }
 123
 124 /* Move "n" divs starting at "first" to the end of the list of divs.
 125  */
 126 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 127         unsigned first, unsigned n)
 128 {
 129         isl_int **div;
 130         int i;
 131
 132         if (first + n == bmap->n_div)
 133                 return bmap;
 134
 135         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 136         if (!div)
 137                 goto error;
 138         for (i = 0; i < n; ++i)
 139                 div[i] = bmap->div[first + i];
 140         for (i = 0; i < bmap->n_div - first - n; ++i)
 141                 bmap->div[first + i] = bmap->div[first + n + i];
 142         for (i = 0; i < n; ++i)
 143                 bmap->div[bmap->n_div - n + i] = div[i];
 144         free(div);
 145         return bmap;
 146 error:
 147         isl_basic_map_free(bmap);
 148         return NULL;
 149 }
 150
 151 /* Drop "n" dimensions of type "type" starting at "first".
 152  *
 153  * In principle, this frees up some extra variables as the number
 154  * of columns remains constant, but we would have to extend
 155  * the div array too as the number of rows in this array is assumed
 156  * to be equal to extra.
 157  */
 158 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 159         enum isl_dim_type type, unsigned first, unsigned n)
 160 {
 161         int i;
 162         unsigned dim;
 163         unsigned offset;
 164         unsigned left;
 165
 166         if (!bmap)
 167                 goto error;
 168
 169         dim = isl_basic_map_dim(bmap, type);
 170         isl_assert(bmap->ctx, first + n <= dim, goto error);
 171
 172         if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
 173                 return bmap;
 174
 175         bmap = isl_basic_map_cow(bmap);
 176         if (!bmap)
 177                 return NULL;
 178
 179         offset = isl_basic_map_offset(bmap, type) + first;
 180         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 181         for (i = 0; i < bmap->n_eq; ++i)
 182                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 183
 184         for (i = 0; i < bmap->n_ineq; ++i)
 185                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 186
 187         for (i = 0; i < bmap->n_div; ++i)
 188                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 189
 190         if (type == isl_dim_div) {
 191                 bmap = move_divs_last(bmap, first, n);
 192                 if (!bmap)
 193                         goto error;
 194                 isl_basic_map_free_div(bmap, n);
 195         } else
 196                 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
 197         if (!bmap->dim)
 198                 goto error;
 199
 200         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 201         bmap = isl_basic_map_simplify(bmap);
 202         return isl_basic_map_finalize(bmap);
 203 error:
 204         isl_basic_map_free(bmap);
 205         return NULL;
 206 }
 207
 208 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
 209         enum isl_dim_type type, unsigned first, unsigned n)
 210 {
 211         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
 212                                                         type, first, n);
 213 }
 214
 215 struct isl_basic_map *isl_basic_map_drop_inputs(
 216                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 217 {
 218         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 219 }
 220
 221 struct isl_map *isl_map_drop(struct isl_map *map,
 222         enum isl_dim_type type, unsigned first, unsigned n)
 223 {
 224         int i;
 225
 226         if (!map)
 227                 goto error;
 228
 229         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 230
 231         if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
 232                 return map;
 233         map = isl_map_cow(map);
 234         if (!map)
 235                 goto error;
 236         map->dim = isl_space_drop_dims(map->dim, type, first, n);
 237         if (!map->dim)
 238                 goto error;
 239
 240         for (i = 0; i < map->n; ++i) {
 241                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 242                 if (!map->p[i])
 243                         goto error;
 244         }
 245         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 246
 247         return map;
 248 error:
 249         isl_map_free(map);
 250         return NULL;
 251 }
 252
 253 struct isl_set *isl_set_drop(struct isl_set *set,
 254         enum isl_dim_type type, unsigned first, unsigned n)
 255 {
 256         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
 257 }
 258
 259 struct isl_map *isl_map_drop_inputs(
 260                 struct isl_map *map, unsigned first, unsigned n)
 261 {
 262         return isl_map_drop(map, isl_dim_in, first, n);
 263 }
 264
 265 /*
 266  * We don't cow, as the div is assumed to be redundant.
 267  */
 268 static struct isl_basic_map *isl_basic_map_drop_div(
 269                 struct isl_basic_map *bmap, unsigned div)
 270 {
 271         int i;
 272         unsigned pos;
 273
 274         if (!bmap)
 275                 goto error;
 276
 277         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 278
 279         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 280
 281         for (i = 0; i < bmap->n_eq; ++i)
 282                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 283
 284         for (i = 0; i < bmap->n_ineq; ++i) {
 285                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 286                         isl_basic_map_drop_inequality(bmap, i);
 287                         --i;
 288                         continue;
 289                 }
 290                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 291         }
 292
 293         for (i = 0; i < bmap->n_div; ++i)
 294                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 295
 296         if (div != bmap->n_div - 1) {
 297                 int j;
 298                 isl_int *t = bmap->div[div];
 299
 300                 for (j = div; j < bmap->n_div - 1; ++j)
 301                         bmap->div[j] = bmap->div[j+1];
 302
 303                 bmap->div[bmap->n_div - 1] = t;
 304         }
 305         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 306         isl_basic_map_free_div(bmap, 1);
 307
 308         return bmap;
 309 error:
 310         isl_basic_map_free(bmap);
 311         return NULL;
 312 }
 313
 314 struct isl_basic_map *isl_basic_map_normalize_constraints(
 315         struct isl_basic_map *bmap)
 316 {
 317         int i;
 318         isl_int gcd;
 319         unsigned total = isl_basic_map_total_dim(bmap);
 320
 321         if (!bmap)
 322                 return NULL;
 323
 324         isl_int_init(gcd);
 325         for (i = bmap->n_eq - 1; i >= 0; --i) {
 326                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 327                 if (isl_int_is_zero(gcd)) {
 328                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 329                                 bmap = isl_basic_map_set_to_empty(bmap);
 330                                 break;
 331                         }
 332                         isl_basic_map_drop_equality(bmap, i);
 333                         continue;
 334                 }
 335                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 336                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 337                 if (isl_int_is_one(gcd))
 338                         continue;
 339                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 340                         bmap = isl_basic_map_set_to_empty(bmap);
 341                         break;
 342                 }
 343                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 344         }
 345
 346         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 347                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 348                 if (isl_int_is_zero(gcd)) {
 349                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 350                                 bmap = isl_basic_map_set_to_empty(bmap);
 351                                 break;
 352                         }
 353                         isl_basic_map_drop_inequality(bmap, i);
 354                         continue;
 355                 }
 356                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 357                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 358                 if (isl_int_is_one(gcd))
 359                         continue;
 360                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 361                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 362         }
 363         isl_int_clear(gcd);
 364
 365         return bmap;
 366 }
 367
 368 struct isl_basic_set *isl_basic_set_normalize_constraints(
 369         struct isl_basic_set *bset)
 370 {
 371         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 372                 (struct isl_basic_map *)bset);
 373 }
 374
 375 /* Remove any common factor in numerator and denominator of the div expression,
 376  * not taking into account the constant term.
 377  * That is, if the div is of the form
 378  *
 379  *      floor((a + m f(x))/(m d))
 380  *
 381  * then replace it by
 382  *
 383  *      floor((floor(a/m) + f(x))/d)
 384  *
 385  * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
 386  * and can therefore not influence the result of the floor.
 387  */
 388 static void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div)
 389 {
 390         unsigned total = isl_basic_map_total_dim(bmap);
 391         isl_ctx *ctx = bmap->ctx;
 392
 393         if (isl_int_is_zero(bmap->div[div][0]))
 394                 return;
 395         isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
 396         isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]);
 397         if (isl_int_is_one(ctx->normalize_gcd))
 398                 return;
 399         isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1],
 400                         ctx->normalize_gcd);
 401         isl_int_divexact(bmap->div[div][0], bmap->div[div][0],
 402                         ctx->normalize_gcd);
 403         isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
 404                         ctx->normalize_gcd, total);
 405 }
 406
 407 /* Remove any common factor in numerator and denominator of a div expression,
 408  * not taking into account the constant term.
 409  * That is, look for any div of the form
 410  *
 411  *      floor((a + m f(x))/(m d))
 412  *
 413  * and replace it by
 414  *
 415  *      floor((floor(a/m) + f(x))/d)
 416  *
 417  * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
 418  * and can therefore not influence the result of the floor.
 419  */
 420 static __isl_give isl_basic_map *normalize_div_expressions(
 421         __isl_take isl_basic_map *bmap)
 422 {
 423         int i;
 424
 425         if (!bmap)
 426                 return NULL;
 427         if (bmap->n_div == 0)
 428                 return bmap;
 429
 430         for (i = 0; i < bmap->n_div; ++i)
 431                 normalize_div_expression(bmap, i);
 432
 433         return bmap;
 434 }
 435
 436 /* Assumes divs have been ordered if keep_divs is set.
 437  */
 438 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 439         unsigned pos, isl_int *eq, int keep_divs, int *progress)
 440 {
 441         unsigned total;
 442         unsigned space_total;
 443         int k;
 444         int last_div;
 445
 446         total = isl_basic_map_total_dim(bmap);
 447         space_total = isl_space_dim(bmap->dim, isl_dim_all);
 448         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 449         for (k = 0; k < bmap->n_eq; ++k) {
 450                 if (bmap->eq[k] == eq)
 451                         continue;
 452                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 453                         continue;
 454                 if (progress)
 455                         *progress = 1;
 456                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 457                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
 458         }
 459
 460         for (k = 0; k < bmap->n_ineq; ++k) {
 461                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 462                         continue;
 463                 if (progress)
 464                         *progress = 1;
 465                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 466                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
 467                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 468         }
 469
 470         for (k = 0; k < bmap->n_div; ++k) {
 471                 if (isl_int_is_zero(bmap->div[k][0]))
 472                         continue;
 473                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 474                         continue;
 475                 if (progress)
 476                         *progress = 1;
 477                 /* We need to be careful about circular definitions,
 478                  * so for now we just remove the definition of div k
 479                  * if the equality contains any divs.
 480                  * If keep_divs is set, then the divs have been ordered
 481                  * and we can keep the definition as long as the result
 482                  * is still ordered.
 483                  */
 484                 if (last_div == -1 || (keep_divs && last_div < k)) {
 485                         isl_seq_elim(bmap->div[k]+1, eq,
 486                                         1+pos, 1+total, &bmap->div[k][0]);
 487                         normalize_div_expression(bmap, k);
 488                 } else
 489                         isl_seq_clr(bmap->div[k], 1 + total);
 490                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 491         }
 492 }
 493
 494 /* Assumes divs have been ordered if keep_divs is set.
 495  */
 496 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 497         unsigned div, int keep_divs)
 498 {
 499         unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
 500
 501         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 502
 503         isl_basic_map_drop_div(bmap, div);
 504 }
 505
 506 /* Check if elimination of div "div" using equality "eq" would not
 507  * result in a div depending on a later div.
 508  */
 509 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
 510         unsigned div)
 511 {
 512         int k;
 513         int last_div;
 514         unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
 515         unsigned pos = space_total + div;
 516
 517         last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
 518         if (last_div < 0 || last_div <= div)
 519                 return 1;
 520
 521         for (k = 0; k <= last_div; ++k) {
 522                 if (isl_int_is_zero(bmap->div[k][0]))
 523                         return 1;
 524                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
 525                         return 0;
 526         }
 527
 528         return 1;
 529 }
 530
 531 /* Elimininate divs based on equalities
 532  */
 533 static struct isl_basic_map *eliminate_divs_eq(
 534                 struct isl_basic_map *bmap, int *progress)
 535 {
 536         int d;
 537         int i;
 538         int modified = 0;
 539         unsigned off;
 540
 541         bmap = isl_basic_map_order_divs(bmap);
 542
 543         if (!bmap)
 544                 return NULL;
 545
 546         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 547
 548         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 549                 for (i = 0; i < bmap->n_eq; ++i) {
 550                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 551                             !isl_int_is_negone(bmap->eq[i][off + d]))
 552                                 continue;
 553                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
 554                                 continue;
 555                         modified = 1;
 556                         *progress = 1;
 557                         eliminate_div(bmap, bmap->eq[i], d, 1);
 558                         isl_basic_map_drop_equality(bmap, i);
 559                         break;
 560                 }
 561         }
 562         if (modified)
 563                 return eliminate_divs_eq(bmap, progress);
 564         return bmap;
 565 }
 566
 567 /* Elimininate divs based on inequalities
 568  */
 569 static struct isl_basic_map *eliminate_divs_ineq(
 570                 struct isl_basic_map *bmap, int *progress)
 571 {
 572         int d;
 573         int i;
 574         unsigned off;
 575         struct isl_ctx *ctx;
 576
 577         if (!bmap)
 578                 return NULL;
 579
 580         ctx = bmap->ctx;
 581         off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 582
 583         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 584                 for (i = 0; i < bmap->n_eq; ++i)
 585                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 586                                 break;
 587                 if (i < bmap->n_eq)
 588                         continue;
 589                 for (i = 0; i < bmap->n_ineq; ++i)
 590                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 591                                 break;
 592                 if (i < bmap->n_ineq)
 593                         continue;
 594                 *progress = 1;
 595                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 596                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 597                         break;
 598                 bmap = isl_basic_map_drop_div(bmap, d);
 599                 if (!bmap)
 600                         break;
 601         }
 602         return bmap;
 603 }
 604
 605 struct isl_basic_map *isl_basic_map_gauss(
 606         struct isl_basic_map *bmap, int *progress)
 607 {
 608         int k;
 609         int done;
 610         int last_var;
 611         unsigned total_var;
 612         unsigned total;
 613
 614         bmap = isl_basic_map_order_divs(bmap);
 615
 616         if (!bmap)
 617                 return NULL;
 618
 619         total = isl_basic_map_total_dim(bmap);
 620         total_var = total - bmap->n_div;
 621
 622         last_var = total - 1;
 623         for (done = 0; done < bmap->n_eq; ++done) {
 624                 for (; last_var >= 0; --last_var) {
 625                         for (k = done; k < bmap->n_eq; ++k)
 626                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 627                                         break;
 628                         if (k < bmap->n_eq)
 629                                 break;
 630                 }
 631                 if (last_var < 0)
 632                         break;
 633                 if (k != done)
 634                         swap_equality(bmap, k, done);
 635                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 636                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 637
 638                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 639                                                 progress);
 640
 641                 if (last_var >= total_var &&
 642                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 643                         unsigned div = last_var - total_var;
 644                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 645                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 646                         isl_int_set(bmap->div[div][0],
 647                                     bmap->eq[done][1+last_var]);
 648                         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         bmap = isl_basic_map_order_divs(bmap);
 719         if (!bmap || bmap->n_div <= 1)
 720                 return bmap;
 721
 722         total_var = isl_space_dim(bmap->dim, isl_dim_all);
 723         total = total_var + bmap->n_div;
 724
 725         ctx = bmap->ctx;
 726         for (k = bmap->n_div - 1; k >= 0; --k)
 727                 if (!isl_int_is_zero(bmap->div[k][0]))
 728                         break;
 729         if (k <= 0)
 730                 return bmap;
 731
 732         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 733         size = round_up(4 * bmap->n_div / 3 - 1);
 734         bits = ffs(size) - 1;
 735         index = isl_calloc_array(ctx, int, size);
 736         if (!index)
 737                 return bmap;
 738         eq = isl_blk_alloc(ctx, 1+total);
 739         if (isl_blk_is_error(eq))
 740                 goto out;
 741
 742         isl_seq_clr(eq.data, 1+total);
 743         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 744         for (--k; k >= 0; --k) {
 745                 uint32_t hash;
 746
 747                 if (isl_int_is_zero(bmap->div[k][0]))
 748                         continue;
 749
 750                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 751                 for (h = hash; index[h]; h = (h+1) % size)
 752                         if (isl_seq_eq(bmap->div[k],
 753                                        bmap->div[index[h]-1], 2+total))
 754                                 break;
 755                 if (index[h]) {
 756                         *progress = 1;
 757                         l = index[h] - 1;
 758                         elim_for[l] = k + 1;
 759                 }
 760                 index[h] = k+1;
 761         }
 762         for (l = bmap->n_div - 1; l >= 0; --l) {
 763                 if (!elim_for[l])
 764                         continue;
 765                 k = elim_for[l] - 1;
 766                 isl_int_set_si(eq.data[1+total_var+k], -1);
 767                 isl_int_set_si(eq.data[1+total_var+l], 1);
 768                 eliminate_div(bmap, eq.data, l, 1);
 769                 isl_int_set_si(eq.data[1+total_var+k], 0);
 770                 isl_int_set_si(eq.data[1+total_var+l], 0);
 771         }
 772
 773         isl_blk_free(ctx, eq);
 774 out:
 775         free(index);
 776         free(elim_for);
 777         return bmap;
 778 }
 779
 780 static int n_pure_div_eq(struct isl_basic_map *bmap)
 781 {
 782         int i, j;
 783         unsigned total;
 784
 785         total = isl_space_dim(bmap->dim, isl_dim_all);
 786         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 787                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 788                         --j;
 789                 if (j < 0)
 790                         break;
 791                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 792                         return 0;
 793         }
 794         return i;
 795 }
 796
 797 /* Normalize divs that appear in equalities.
 798  *
 799  * In particular, we assume that bmap contains some equalities
 800  * of the form
 801  *
 802  *      a x = m * e_i
 803  *
 804  * and we want to replace the set of e_i by a minimal set and
 805  * such that the new e_i have a canonical representation in terms
 806  * of the vector x.
 807  * If any of the equalities involves more than one divs, then
 808  * we currently simply bail out.
 809  *
 810  * Let us first additionally assume that all equalities involve
 811  * a div.  The equalities then express modulo constraints on the
 812  * remaining variables and we can use "parameter compression"
 813  * to find a minimal set of constraints.  The result is a transformation
 814  *
 815  *      x = T(x') = x_0 + G x'
 816  *
 817  * with G a lower-triangular matrix with all elements below the diagonal
 818  * non-negative and smaller than the diagonal element on the same row.
 819  * We first normalize x_0 by making the same property hold in the affine
 820  * T matrix.
 821  * The rows i of G with a 1 on the diagonal do not impose any modulo
 822  * constraint and simply express x_i = x'_i.
 823  * For each of the remaining rows i, we introduce a div and a corresponding
 824  * equality.  In particular
 825  *
 826  *      g_ii e_j = x_i - g_i(x')
 827  *
 828  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 829  * corresponding div (if g_kk != 1).
 830  *
 831  * If there are any equalities not involving any div, then we
 832  * first apply a variable compression on the variables x:
 833  *
 834  *      x = C x''       x'' = C_2 x
 835  *
 836  * and perform the above parameter compression on A C instead of on A.
 837  * The resulting compression is then of the form
 838  *
 839  *      x'' = T(x') = x_0 + G x'
 840  *
 841  * and in constructing the new divs and the corresponding equalities,
 842  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 843  * by the corresponding row from C_2.
 844  */
 845 static struct isl_basic_map *normalize_divs(
 846         struct isl_basic_map *bmap, int *progress)
 847 {
 848         int i, j, k;
 849         int total;
 850         int div_eq;
 851         struct isl_mat *B;
 852         struct isl_vec *d;
 853         struct isl_mat *T = NULL;
 854         struct isl_mat *C = NULL;
 855         struct isl_mat *C2 = NULL;
 856         isl_int v;
 857         int *pos;
 858         int dropped, needed;
 859
 860         if (!bmap)
 861                 return NULL;
 862
 863         if (bmap->n_div == 0)
 864                 return bmap;
 865
 866         if (bmap->n_eq == 0)
 867                 return bmap;
 868
 869         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 870                 return bmap;
 871
 872         total = isl_space_dim(bmap->dim, isl_dim_all);
 873         div_eq = n_pure_div_eq(bmap);
 874         if (div_eq == 0)
 875                 return bmap;
 876
 877         if (div_eq < bmap->n_eq) {
 878                 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
 879                                         bmap->n_eq - div_eq, 0, 1 + total);
 880                 C = isl_mat_variable_compression(B, &C2);
 881                 if (!C || !C2)
 882                         goto error;
 883                 if (C->n_col == 0) {
 884                         bmap = isl_basic_map_set_to_empty(bmap);
 885                         isl_mat_free(C);
 886                         isl_mat_free(C2);
 887                         goto done;
 888                 }
 889         }
 890
 891         d = isl_vec_alloc(bmap->ctx, div_eq);
 892         if (!d)
 893                 goto error;
 894         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 895                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 896                         --j;
 897                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 898         }
 899         B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 900
 901         if (C) {
 902                 B = isl_mat_product(B, C);
 903                 C = NULL;
 904         }
 905
 906         T = isl_mat_parameter_compression(B, d);
 907         if (!T)
 908                 goto error;
 909         if (T->n_col == 0) {
 910                 bmap = isl_basic_map_set_to_empty(bmap);
 911                 isl_mat_free(C2);
 912                 isl_mat_free(T);
 913                 goto done;
 914         }
 915         isl_int_init(v);
 916         for (i = 0; i < T->n_row - 1; ++i) {
 917                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 918                 if (isl_int_is_zero(v))
 919                         continue;
 920                 isl_mat_col_submul(T, 0, v, 1 + i);
 921         }
 922         isl_int_clear(v);
 923         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 924         if (!pos)
 925                 goto error;
 926         /* We have to be careful because dropping equalities may reorder them */
 927         dropped = 0;
 928         for (j = bmap->n_div - 1; j >= 0; --j) {
 929                 for (i = 0; i < bmap->n_eq; ++i)
 930                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 931                                 break;
 932                 if (i < bmap->n_eq) {
 933                         bmap = isl_basic_map_drop_div(bmap, j);
 934                         isl_basic_map_drop_equality(bmap, i);
 935                         ++dropped;
 936                 }
 937         }
 938         pos[0] = 0;
 939         needed = 0;
 940         for (i = 1; i < T->n_row; ++i) {
 941                 if (isl_int_is_one(T->row[i][i]))
 942                         pos[i] = i;
 943                 else
 944                         needed++;
 945         }
 946         if (needed > dropped) {
 947                 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 948                                 needed, needed, 0);
 949                 if (!bmap)
 950                         goto error;
 951         }
 952         for (i = 1; i < T->n_row; ++i) {
 953                 if (isl_int_is_one(T->row[i][i]))
 954                         continue;
 955                 k = isl_basic_map_alloc_div(bmap);
 956                 pos[i] = 1 + total + k;
 957                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 958                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 959                 if (C2)
 960                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 961                 else
 962                         isl_int_set_si(bmap->div[k][1 + i], 1);
 963                 for (j = 0; j < i; ++j) {
 964                         if (isl_int_is_zero(T->row[i][j]))
 965                                 continue;
 966                         if (pos[j] < T->n_row && C2)
 967                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 968                                                 C2->row[pos[j]], 1 + total);
 969                         else
 970                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 971                                                                 T->row[i][j]);
 972                 }
 973                 j = isl_basic_map_alloc_equality(bmap);
 974                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 975                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 976         }
 977         free(pos);
 978         isl_mat_free(C2);
 979         isl_mat_free(T);
 980
 981         if (progress)
 982                 *progress = 1;
 983 done:
 984         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 985
 986         return bmap;
 987 error:
 988         isl_mat_free(C);
 989         isl_mat_free(C2);
 990         isl_mat_free(T);
 991         return bmap;
 992 }
 993
 994 static struct isl_basic_map *set_div_from_lower_bound(
 995         struct isl_basic_map *bmap, int div, int ineq)
 996 {
 997         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 998
 999         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
1000         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
1001         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
1002         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1003         isl_int_set_si(bmap->div[div][1 + total + div], 0);
1004
1005         return bmap;
1006 }
1007
1008 /* Check whether it is ok to define a div based on an inequality.
1009  * To avoid the introduction of circular definitions of divs, we
1010  * do not allow such a definition if the resulting expression would refer to
1011  * any other undefined divs or if any known div is defined in
1012  * terms of the unknown div.
1013  */
1014 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
1015         int div, int ineq)
1016 {
1017         int j;
1018         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1019
1020         /* Not defined in terms of unknown divs */
1021         for (j = 0; j < bmap->n_div; ++j) {
1022                 if (div == j)
1023                         continue;
1024                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
1025                         continue;
1026                 if (isl_int_is_zero(bmap->div[j][0]))
1027                         return 0;
1028         }
1029
1030         /* No other div defined in terms of this one => avoid loops */
1031         for (j = 0; j < bmap->n_div; ++j) {
1032                 if (div == j)
1033                         continue;
1034                 if (isl_int_is_zero(bmap->div[j][0]))
1035                         continue;
1036                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
1037                         return 0;
1038         }
1039
1040         return 1;
1041 }
1042
1043 /* Given two constraints "k" and "l" that are opposite to each other,
1044  * except for the constant term, check if we can use them
1045  * to obtain an expression for one of the hitherto unknown divs.
1046  * "sum" is the sum of the constant terms of the constraints.
1047  * If this sum is strictly smaller than the coefficient of one
1048  * of the divs, then this pair can be used define the div.
1049  * To avoid the introduction of circular definitions of divs, we
1050  * do not use the pair if the resulting expression would refer to
1051  * any other undefined divs or if any known div is defined in
1052  * terms of the unknown div.
1053  */
1054 static struct isl_basic_map *check_for_div_constraints(
1055         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
1056 {
1057         int i;
1058         unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1059
1060         for (i = 0; i < bmap->n_div; ++i) {
1061                 if (!isl_int_is_zero(bmap->div[i][0]))
1062                         continue;
1063                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1064                         continue;
1065                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1066                         continue;
1067                 if (!ok_to_set_div_from_bound(bmap, i, k))
1068                         break;
1069                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1070                         bmap = set_div_from_lower_bound(bmap, i, k);
1071                 else
1072                         bmap = set_div_from_lower_bound(bmap, i, l);
1073                 if (progress)
1074                         *progress = 1;
1075                 break;
1076         }
1077         return bmap;
1078 }
1079
1080 static struct isl_basic_map *remove_duplicate_constraints(
1081         struct isl_basic_map *bmap, int *progress, int detect_divs)
1082 {
1083         unsigned int size;
1084         isl_int ***index;
1085         int k, l, h;
1086         int bits;
1087         unsigned total = isl_basic_map_total_dim(bmap);
1088         isl_int sum;
1089         isl_ctx *ctx;
1090
1091         if (!bmap || bmap->n_ineq <= 1)
1092                 return bmap;
1093
1094         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1095         bits = ffs(size) - 1;
1096         ctx = isl_basic_map_get_ctx(bmap);
1097         index = isl_calloc_array(ctx, isl_int **, size);
1098         if (!index)
1099                 return bmap;
1100
1101         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1102         for (k = 1; k < bmap->n_ineq; ++k) {
1103                 h = hash_index(index, size, bits, bmap, k);
1104                 if (!index[h]) {
1105                         index[h] = &bmap->ineq[k];
1106                         continue;
1107                 }
1108                 if (progress)
1109                         *progress = 1;
1110                 l = index[h] - &bmap->ineq[0];
1111                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1112                         swap_inequality(bmap, k, l);
1113                 isl_basic_map_drop_inequality(bmap, k);
1114                 --k;
1115         }
1116         isl_int_init(sum);
1117         for (k = 0; k < bmap->n_ineq-1; ++k) {
1118                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1119                 h = hash_index(index, size, bits, bmap, k);
1120                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1121                 if (!index[h])
1122                         continue;
1123                 l = index[h] - &bmap->ineq[0];
1124                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1125                 if (isl_int_is_pos(sum)) {
1126                         if (detect_divs)
1127                                 bmap = check_for_div_constraints(bmap, k, l,
1128                                                                  sum, progress);
1129                         continue;
1130                 }
1131                 if (isl_int_is_zero(sum)) {
1132                         /* We need to break out of the loop after these
1133                          * changes since the contents of the hash
1134                          * will no longer be valid.
1135                          * Plus, we probably we want to regauss first.
1136                          */
1137                         if (progress)
1138                                 *progress = 1;
1139                         isl_basic_map_drop_inequality(bmap, l);
1140                         isl_basic_map_inequality_to_equality(bmap, k);
1141                 } else
1142                         bmap = isl_basic_map_set_to_empty(bmap);
1143                 break;
1144         }
1145         isl_int_clear(sum);
1146
1147         free(index);
1148         return bmap;
1149 }
1150
1151
1152 /* Eliminate knowns divs from constraints where they appear with
1153  * a (positive or negative) unit coefficient.
1154  *
1155  * That is, replace
1156  *
1157  *      floor(e/m) + f >= 0
1158  *
1159  * by
1160  *
1161  *      e + m f >= 0
1162  *
1163  * and
1164  *
1165  *      -floor(e/m) + f >= 0
1166  *
1167  * by
1168  *
1169  *      -e + m f + m - 1 >= 0
1170  *
1171  * The first conversion is valid because floor(e/m) >= -f is equivalent
1172  * to e/m >= -f because -f is an integral expression.
1173  * The second conversion follows from the fact that
1174  *
1175  *      -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
1176  *
1177  *
1178  * We skip integral divs, i.e., those with denominator 1, as we would
1179  * risk eliminating the div from the div constraints.  We do not need
1180  * to handle those divs here anyway since the div constraints will turn
1181  * out to form an equality and this equality can then be use to eliminate
1182  * the div from all constraints.
1183  */
1184 static __isl_give isl_basic_map *eliminate_unit_divs(
1185         __isl_take isl_basic_map *bmap, int *progress)
1186 {
1187         int i, j;
1188         isl_ctx *ctx;
1189         unsigned total;
1190
1191         if (!bmap)
1192                 return NULL;
1193
1194         ctx = isl_basic_map_get_ctx(bmap);
1195         total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
1196
1197         for (i = 0; i < bmap->n_div; ++i) {
1198                 if (isl_int_is_zero(bmap->div[i][0]))
1199                         continue;
1200                 if (isl_int_is_one(bmap->div[i][0]))
1201                         continue;
1202                 for (j = 0; j < bmap->n_ineq; ++j) {
1203                         int s;
1204
1205                         if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
1206                             !isl_int_is_negone(bmap->ineq[j][total + i]))
1207                                 continue;
1208
1209                         *progress = 1;
1210
1211                         s = isl_int_sgn(bmap->ineq[j][total + i]);
1212                         isl_int_set_si(bmap->ineq[j][total + i], 0);
1213                         if (s < 0)
1214                                 isl_seq_combine(bmap->ineq[j],
1215                                         ctx->negone, bmap->div[i] + 1,
1216                                         bmap->div[i][0], bmap->ineq[j],
1217                                         total + bmap->n_div);
1218                         else
1219                                 isl_seq_combine(bmap->ineq[j],
1220                                         ctx->one, bmap->div[i] + 1,
1221                                         bmap->div[i][0], bmap->ineq[j],
1222                                         total + bmap->n_div);
1223                         if (s < 0) {
1224                                 isl_int_add(bmap->ineq[j][0],
1225                                         bmap->ineq[j][0], bmap->div[i][0]);
1226                                 isl_int_sub_ui(bmap->ineq[j][0],
1227                                         bmap->ineq[j][0], 1);
1228                         }
1229                 }
1230         }
1231
1232         return bmap;
1233 }
1234
1235 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1236 {
1237         int progress = 1;
1238         if (!bmap)
1239                 return NULL;
1240         while (progress) {
1241                 progress = 0;
1242                 bmap = isl_basic_map_normalize_constraints(bmap);
1243                 bmap = normalize_div_expressions(bmap);
1244                 bmap = remove_duplicate_divs(bmap, &progress);
1245                 bmap = eliminate_unit_divs(bmap, &progress);
1246                 bmap = eliminate_divs_eq(bmap, &progress);
1247                 bmap = eliminate_divs_ineq(bmap, &progress);
1248                 bmap = isl_basic_map_gauss(bmap, &progress);
1249                 /* requires equalities in normal form */
1250                 bmap = normalize_divs(bmap, &progress);
1251                 bmap = remove_duplicate_constraints(bmap, &progress, 1);
1252         }
1253         return bmap;
1254 }
1255
1256 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1257 {
1258         return (struct isl_basic_set *)
1259                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1260 }
1261
1262
1263 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1264         isl_int *constraint, unsigned div)
1265 {
1266         unsigned pos;
1267
1268         if (!bmap)
1269                 return -1;
1270
1271         pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1272
1273         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1274                 int neg;
1275                 isl_int_sub(bmap->div[div][1],
1276                                 bmap->div[div][1], bmap->div[div][0]);
1277                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1278                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1279                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1280                 isl_int_add(bmap->div[div][1],
1281                                 bmap->div[div][1], bmap->div[div][0]);
1282                 if (!neg)
1283                         return 0;
1284                 if (isl_seq_first_non_zero(constraint+pos+1,
1285                                             bmap->n_div-div-1) != -1)
1286                         return 0;
1287         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1288                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1289                         return 0;
1290                 if (isl_seq_first_non_zero(constraint+pos+1,
1291                                             bmap->n_div-div-1) != -1)
1292                         return 0;
1293         } else
1294                 return 0;
1295
1296         return 1;
1297 }
1298
1299 int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
1300         isl_int *constraint, unsigned div)
1301 {
1302         return isl_basic_map_is_div_constraint(bset, constraint, div);
1303 }
1304
1305
1306 /* If the only constraints a div d=floor(f/m)
1307  * appears in are its two defining constraints
1308  *
1309  *      f - m d >=0
1310  *      -(f - (m - 1)) + m d >= 0
1311  *
1312  * then it can safely be removed.
1313  */
1314 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1315 {
1316         int i;
1317         unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
1318
1319         for (i = 0; i < bmap->n_eq; ++i)
1320                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1321                         return 0;
1322
1323         for (i = 0; i < bmap->n_ineq; ++i) {
1324                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1325                         continue;
1326                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1327                         return 0;
1328         }
1329
1330         for (i = 0; i < bmap->n_div; ++i)
1331                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1332                         return 0;
1333
1334         return 1;
1335 }
1336
1337 /*
1338  * Remove divs that don't occur in any of the constraints or other divs.
1339  * These can arise when dropping some of the variables in a quast
1340  * returned by piplib.
1341  */
1342 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1343 {
1344         int i;
1345
1346         if (!bmap)
1347                 return NULL;
1348
1349         for (i = bmap->n_div-1; i >= 0; --i) {
1350                 if (!div_is_redundant(bmap, i))
1351                         continue;
1352                 bmap = isl_basic_map_drop_div(bmap, i);
1353         }
1354         return bmap;
1355 }
1356
1357 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1358 {
1359         bmap = remove_redundant_divs(bmap);
1360         if (!bmap)
1361                 return NULL;
1362         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1363         return bmap;
1364 }
1365
1366 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1367 {
1368         return (struct isl_basic_set *)
1369                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1370 }
1371
1372 struct isl_set *isl_set_finalize(struct isl_set *set)
1373 {
1374         int i;
1375
1376         if (!set)
1377                 return NULL;
1378         for (i = 0; i < set->n; ++i) {
1379                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1380                 if (!set->p[i])
1381                         goto error;
1382         }
1383         return set;
1384 error:
1385         isl_set_free(set);
1386         return NULL;
1387 }
1388
1389 struct isl_map *isl_map_finalize(struct isl_map *map)
1390 {
1391         int i;
1392
1393         if (!map)
1394                 return NULL;
1395         for (i = 0; i < map->n; ++i) {
1396                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1397                 if (!map->p[i])
1398                         goto error;
1399         }
1400         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1401         return map;
1402 error:
1403         isl_map_free(map);
1404         return NULL;
1405 }
1406
1407
1408 /* Remove definition of any div that is defined in terms of the given variable.
1409  * The div itself is not removed.  Functions such as
1410  * eliminate_divs_ineq depend on the other divs remaining in place.
1411  */
1412 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1413                                                                         int pos)
1414 {
1415         int i;
1416
1417         for (i = 0; i < bmap->n_div; ++i) {
1418                 if (isl_int_is_zero(bmap->div[i][0]))
1419                         continue;
1420                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1421                         continue;
1422                 isl_int_set_si(bmap->div[i][0], 0);
1423         }
1424         return bmap;
1425 }
1426
1427 /* Eliminate the specified variables from the constraints using
1428  * Fourier-Motzkin.  The variables themselves are not removed.
1429  */
1430 struct isl_basic_map *isl_basic_map_eliminate_vars(
1431         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1432 {
1433         int d;
1434         int i, j, k;
1435         unsigned total;
1436         int need_gauss = 0;
1437
1438         if (n == 0)
1439                 return bmap;
1440         if (!bmap)
1441                 return NULL;
1442         total = isl_basic_map_total_dim(bmap);
1443
1444         bmap = isl_basic_map_cow(bmap);
1445         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1446                 bmap = remove_dependent_vars(bmap, d);
1447
1448         for (d = pos + n - 1;
1449              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1450                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1451         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1452                 int n_lower, n_upper;
1453                 if (!bmap)
1454                         return NULL;
1455                 for (i = 0; i < bmap->n_eq; ++i) {
1456                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1457                                 continue;
1458                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1459                         isl_basic_map_drop_equality(bmap, i);
1460                         need_gauss = 1;
1461                         break;
1462                 }
1463                 if (i < bmap->n_eq)
1464                         continue;
1465                 n_lower = 0;
1466                 n_upper = 0;
1467                 for (i = 0; i < bmap->n_ineq; ++i) {
1468                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1469                                 n_lower++;
1470                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1471                                 n_upper++;
1472                 }
1473                 bmap = isl_basic_map_extend_constraints(bmap,
1474                                 0, n_lower * n_upper);
1475                 if (!bmap)
1476                         goto error;
1477                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1478                         int last;
1479                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1480                                 continue;
1481                         last = -1;
1482                         for (j = 0; j < i; ++j) {
1483                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1484                                         continue;
1485                                 last = j;
1486                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1487                                     isl_int_sgn(bmap->ineq[j][1+d]))
1488                                         continue;
1489                                 k = isl_basic_map_alloc_inequality(bmap);
1490                                 if (k < 0)
1491                                         goto error;
1492                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1493                                                 1+total);
1494                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1495                                                 1+d, 1+total, NULL);
1496                         }
1497                         isl_basic_map_drop_inequality(bmap, i);
1498                         i = last + 1;
1499                 }
1500                 if (n_lower > 0 && n_upper > 0) {
1501                         bmap = isl_basic_map_normalize_constraints(bmap);
1502                         bmap = remove_duplicate_constraints(bmap, NULL, 0);
1503                         bmap = isl_basic_map_gauss(bmap, NULL);
1504                         bmap = isl_basic_map_remove_redundancies(bmap);
1505                         need_gauss = 0;
1506                         if (!bmap)
1507                                 goto error;
1508                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1509                                 break;
1510                 }
1511         }
1512         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1513         if (need_gauss)
1514                 bmap = isl_basic_map_gauss(bmap, NULL);
1515         return bmap;
1516 error:
1517         isl_basic_map_free(bmap);
1518         return NULL;
1519 }
1520
1521 struct isl_basic_set *isl_basic_set_eliminate_vars(
1522         struct isl_basic_set *bset, unsigned pos, unsigned n)
1523 {
1524         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1525                         (struct isl_basic_map *)bset, pos, n);
1526 }
1527
1528 /* Eliminate the specified n dimensions starting at first from the
1529  * constraints, without removing the dimensions from the space.
1530  * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1531  * Otherwise, they are projected out and the original space is restored.
1532  */
1533 __isl_give isl_basic_map *isl_basic_map_eliminate(
1534         __isl_take isl_basic_map *bmap,
1535         enum isl_dim_type type, unsigned first, unsigned n)
1536 {
1537         isl_space *space;
1538
1539         if (!bmap)
1540                 return NULL;
1541         if (n == 0)
1542                 return bmap;
1543
1544         if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
1545                 isl_die(bmap->ctx, isl_error_invalid,
1546                         "index out of bounds", goto error);
1547
1548         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
1549                 first += isl_basic_map_offset(bmap, type) - 1;
1550                 bmap = isl_basic_map_eliminate_vars(bmap, first, n);
1551                 return isl_basic_map_finalize(bmap);
1552         }
1553
1554         space = isl_basic_map_get_space(bmap);
1555         bmap = isl_basic_map_project_out(bmap, type, first, n);
1556         bmap = isl_basic_map_insert_dims(bmap, type, first, n);
1557         bmap = isl_basic_map_reset_space(bmap, space);
1558         return bmap;
1559 error:
1560         isl_basic_map_free(bmap);
1561         return NULL;
1562 }
1563
1564 __isl_give isl_basic_set *isl_basic_set_eliminate(
1565         __isl_take isl_basic_set *bset,
1566         enum isl_dim_type type, unsigned first, unsigned n)
1567 {
1568         return isl_basic_map_eliminate(bset, type, first, n);
1569 }
1570
1571 /* Don't assume equalities are in order, because align_divs
1572  * may have changed the order of the divs.
1573  */
1574 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1575 {
1576         int d, i;
1577         unsigned total;
1578
1579         total = isl_space_dim(bmap->dim, isl_dim_all);
1580         for (d = 0; d < total; ++d)
1581                 elim[d] = -1;
1582         for (i = 0; i < bmap->n_eq; ++i) {
1583                 for (d = total - 1; d >= 0; --d) {
1584                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1585                                 continue;
1586                         elim[d] = i;
1587                         break;
1588                 }
1589         }
1590 }
1591
1592 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1593 {
1594         compute_elimination_index((struct isl_basic_map *)bset, elim);
1595 }
1596
1597 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1598         struct isl_basic_map *bmap, int *elim)
1599 {
1600         int d;
1601         int copied = 0;
1602         unsigned total;
1603
1604         total = isl_space_dim(bmap->dim, isl_dim_all);
1605         for (d = total - 1; d >= 0; --d) {
1606                 if (isl_int_is_zero(src[1+d]))
1607                         continue;
1608                 if (elim[d] == -1)
1609                         continue;
1610                 if (!copied) {
1611                         isl_seq_cpy(dst, src, 1 + total);
1612                         copied = 1;
1613                 }
1614                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1615         }
1616         return copied;
1617 }
1618
1619 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1620         struct isl_basic_set *bset, int *elim)
1621 {
1622         return reduced_using_equalities(dst, src,
1623                                         (struct isl_basic_map *)bset, elim);
1624 }
1625
1626 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1627         struct isl_basic_set *bset, struct isl_basic_set *context)
1628 {
1629         int i;
1630         int *elim;
1631
1632         if (!bset || !context)
1633                 goto error;
1634
1635         if (context->n_eq == 0) {
1636                 isl_basic_set_free(context);
1637                 return bset;
1638         }
1639
1640         bset = isl_basic_set_cow(bset);
1641         if (!bset)
1642                 goto error;
1643
1644         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1645         if (!elim)
1646                 goto error;
1647         set_compute_elimination_index(context, elim);
1648         for (i = 0; i < bset->n_eq; ++i)
1649                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1650                                                         context, elim);
1651         for (i = 0; i < bset->n_ineq; ++i)
1652                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1653                                                         context, elim);
1654         isl_basic_set_free(context);
1655         free(elim);
1656         bset = isl_basic_set_simplify(bset);
1657         bset = isl_basic_set_finalize(bset);
1658         return bset;
1659 error:
1660         isl_basic_set_free(bset);
1661         isl_basic_set_free(context);
1662         return NULL;
1663 }
1664
1665 static struct isl_basic_set *remove_shifted_constraints(
1666         struct isl_basic_set *bset, struct isl_basic_set *context)
1667 {
1668         unsigned int size;
1669         isl_int ***index;
1670         int bits;
1671         int k, h, l;
1672         isl_ctx *ctx;
1673
1674         if (!bset)
1675                 return NULL;
1676
1677         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1678         bits = ffs(size) - 1;
1679         ctx = isl_basic_set_get_ctx(bset);
1680         index = isl_calloc_array(ctx, isl_int **, size);
1681         if (!index)
1682                 return bset;
1683
1684         for (k = 0; k < context->n_ineq; ++k) {
1685                 h = set_hash_index(index, size, bits, context, k);
1686                 index[h] = &context->ineq[k];
1687         }
1688         for (k = 0; k < bset->n_ineq; ++k) {
1689                 h = set_hash_index(index, size, bits, bset, k);
1690                 if (!index[h])
1691                         continue;
1692                 l = index[h] - &context->ineq[0];
1693                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1694                         continue;
1695                 bset = isl_basic_set_cow(bset);
1696                 if (!bset)
1697                         goto error;
1698                 isl_basic_set_drop_inequality(bset, k);
1699                 --k;
1700         }
1701         free(index);
1702         return bset;
1703 error:
1704         free(index);
1705         return bset;
1706 }
1707
1708 /* Remove all information from bset that is redundant in the context
1709  * of context.  Both bset and context are assumed to be full-dimensional.
1710  *
1711  * We first * remove the inequalities from "bset"
1712  * that are obviously redundant with respect to some inequality in "context".
1713  *
1714  * If there are any inequalities left, we construct a tableau for
1715  * the context and then add the inequalities of "bset".
1716  * Before adding these inequalities, we freeze all constraints such that
1717  * they won't be considered redundant in terms of the constraints of "bset".
1718  * Then we detect all redundant constraints (among the
1719  * constraints that weren't frozen), first by checking for redundancy in the
1720  * the tableau and then by checking if replacing a constraint by its negation
1721  * would lead to an empty set.  This last step is fairly expensive
1722  * and could be optimized by more reuse of the tableau.
1723  * Finally, we update bset according to the results.
1724  */
1725 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1726         __isl_take isl_basic_set *context)
1727 {
1728         int i, k;
1729         isl_basic_set *combined = NULL;
1730         struct isl_tab *tab = NULL;
1731         unsigned context_ineq;
1732         unsigned total;
1733
1734         if (!bset || !context)
1735                 goto error;
1736
1737         if (isl_basic_set_is_universe(bset)) {
1738                 isl_basic_set_free(context);
1739                 return bset;
1740         }
1741
1742         if (isl_basic_set_is_universe(context)) {
1743                 isl_basic_set_free(context);
1744                 return bset;
1745         }
1746
1747         bset = remove_shifted_constraints(bset, context);
1748         if (!bset)
1749                 goto error;
1750         if (bset->n_ineq == 0)
1751                 goto done;
1752
1753         context_ineq = context->n_ineq;
1754         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1755         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1756         tab = isl_tab_from_basic_set(combined, 0);
1757         for (i = 0; i < context_ineq; ++i)
1758                 if (isl_tab_freeze_constraint(tab, i) < 0)
1759                         goto error;
1760         tab = isl_tab_extend(tab, bset->n_ineq);
1761         for (i = 0; i < bset->n_ineq; ++i)
1762                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1763                         goto error;
1764         bset = isl_basic_set_add_constraints(combined, bset, 0);
1765         combined = NULL;
1766         if (!bset)
1767                 goto error;
1768         if (isl_tab_detect_redundant(tab) < 0)
1769                 goto error;
1770         total = isl_basic_set_total_dim(bset);
1771         for (i = context_ineq; i < bset->n_ineq; ++i) {
1772                 int is_empty;
1773                 if (tab->con[i].is_redundant)
1774                         continue;
1775                 tab->con[i].is_redundant = 1;
1776                 combined = isl_basic_set_dup(bset);
1777                 combined = isl_basic_set_update_from_tab(combined, tab);
1778                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1779                 k = isl_basic_set_alloc_inequality(combined);
1780                 if (k < 0)
1781                         goto error;
1782                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1783                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1784                 is_empty = isl_basic_set_is_empty(combined);
1785                 if (is_empty < 0)
1786                         goto error;
1787                 isl_basic_set_free(combined);
1788                 combined = NULL;
1789                 if (!is_empty)
1790                         tab->con[i].is_redundant = 0;
1791         }
1792         for (i = 0; i < context_ineq; ++i)
1793                 tab->con[i].is_redundant = 1;
1794         bset = isl_basic_set_update_from_tab(bset, tab);
1795         if (bset) {
1796                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1797                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1798         }
1799
1800         isl_tab_free(tab);
1801 done:
1802         bset = isl_basic_set_simplify(bset);
1803         bset = isl_basic_set_finalize(bset);
1804         isl_basic_set_free(context);
1805         return bset;
1806 error:
1807         isl_tab_free(tab);
1808         isl_basic_set_free(combined);
1809         isl_basic_set_free(context);
1810         isl_basic_set_free(bset);
1811         return NULL;
1812 }
1813
1814 /* Remove all information from bset that is redundant in the context
1815  * of context.  In particular, equalities that are linear combinations
1816  * of those in context are removed.  Then the inequalities that are
1817  * redundant in the context of the equalities and inequalities of
1818  * context are removed.
1819  *
1820  * We first compute the integer affine hull of the intersection,
1821  * compute the gist inside this affine hull and then add back
1822  * those equalities that are not implied by the context.
1823  *
1824  * If two constraints are mutually redundant, then uset_gist_full
1825  * will remove the second of those constraints.  We therefore first
1826  * sort the constraints so that constraints not involving existentially
1827  * quantified variables are given precedence over those that do.
1828  * We have to perform this sorting before the variable compression,
1829  * because that may effect the order of the variables.
1830  */
1831 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1832         __isl_take isl_basic_set *context)
1833 {
1834         isl_mat *eq;
1835         isl_mat *T, *T2;
1836         isl_basic_set *aff;
1837         isl_basic_set *aff_context;
1838         unsigned total;
1839
1840         if (!bset || !context)
1841                 goto error;
1842
1843         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1844         if (isl_basic_set_plain_is_empty(bset)) {
1845                 isl_basic_set_free(context);
1846                 return bset;
1847         }
1848         bset = isl_basic_set_sort_constraints(bset);
1849         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1850         if (!aff)
1851                 goto error;
1852         if (isl_basic_set_plain_is_empty(aff)) {
1853                 isl_basic_set_free(aff);
1854                 isl_basic_set_free(context);
1855                 return bset;
1856         }
1857         if (aff->n_eq == 0) {
1858                 isl_basic_set_free(aff);
1859                 return uset_gist_full(bset, context);
1860         }
1861         total = isl_basic_set_total_dim(bset);
1862         eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1863         eq = isl_mat_cow(eq);
1864         T = isl_mat_variable_compression(eq, &T2);
1865         if (T && T->n_col == 0) {
1866                 isl_mat_free(T);
1867                 isl_mat_free(T2);
1868                 isl_basic_set_free(context);
1869                 isl_basic_set_free(aff);
1870                 return isl_basic_set_set_to_empty(bset);
1871         }
1872
1873         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1874
1875         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1876         context = isl_basic_set_preimage(context, T);
1877
1878         bset = uset_gist_full(bset, context);
1879         bset = isl_basic_set_preimage(bset, T2);
1880         bset = isl_basic_set_intersect(bset, aff);
1881         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1882
1883         if (bset) {
1884                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1885                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1886         }
1887
1888         return bset;
1889 error:
1890         isl_basic_set_free(bset);
1891         isl_basic_set_free(context);
1892         return NULL;
1893 }
1894
1895 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1896  * We simply add the equalities in context to bmap and then do a regular
1897  * div normalizations.  Better results can be obtained by normalizing
1898  * only the divs in bmap than do not also appear in context.
1899  * We need to be careful to reduce the divs using the equalities
1900  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1901  * spurious constraints.
1902  */
1903 static struct isl_basic_map *normalize_divs_in_context(
1904         struct isl_basic_map *bmap, struct isl_basic_map *context)
1905 {
1906         int i;
1907         unsigned total_context;
1908         int div_eq;
1909
1910         div_eq = n_pure_div_eq(bmap);
1911         if (div_eq == 0)
1912                 return bmap;
1913
1914         if (context->n_div > 0)
1915                 bmap = isl_basic_map_align_divs(bmap, context);
1916
1917         total_context = isl_basic_map_total_dim(context);
1918         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1919         for (i = 0; i < context->n_eq; ++i) {
1920                 int k;
1921                 k = isl_basic_map_alloc_equality(bmap);
1922                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1923                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1924                                 isl_basic_map_total_dim(bmap) - total_context);
1925         }
1926         bmap = isl_basic_map_gauss(bmap, NULL);
1927         bmap = normalize_divs(bmap, NULL);
1928         bmap = isl_basic_map_gauss(bmap, NULL);
1929         return bmap;
1930 }
1931
1932 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1933         struct isl_basic_map *context)
1934 {
1935         struct isl_basic_set *bset;
1936
1937         if (!bmap || !context)
1938                 goto error;
1939
1940         if (isl_basic_map_is_universe(bmap)) {
1941                 isl_basic_map_free(context);
1942                 return bmap;
1943         }
1944         if (isl_basic_map_plain_is_empty(context)) {
1945                 isl_basic_map_free(bmap);
1946                 return context;
1947         }
1948         if (isl_basic_map_plain_is_empty(bmap)) {
1949                 isl_basic_map_free(context);
1950                 return bmap;
1951         }
1952
1953         bmap = isl_basic_map_remove_redundancies(bmap);
1954         context = isl_basic_map_remove_redundancies(context);
1955
1956         if (context->n_eq)
1957                 bmap = normalize_divs_in_context(bmap, context);
1958
1959         context = isl_basic_map_align_divs(context, bmap);
1960         bmap = isl_basic_map_align_divs(bmap, context);
1961
1962         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1963                          isl_basic_map_underlying_set(context));
1964
1965         return isl_basic_map_overlying_set(bset, bmap);
1966 error:
1967         isl_basic_map_free(bmap);
1968         isl_basic_map_free(context);
1969         return NULL;
1970 }
1971
1972 /*
1973  * Assumes context has no implicit divs.
1974  */
1975 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1976         __isl_take isl_basic_map *context)
1977 {
1978         int i;
1979
1980         if (!map || !context)
1981                 goto error;;
1982
1983         if (isl_basic_map_plain_is_empty(context)) {
1984                 isl_map_free(map);
1985                 return isl_map_from_basic_map(context);
1986         }
1987
1988         context = isl_basic_map_remove_redundancies(context);
1989         map = isl_map_cow(map);
1990         if (!map || !context)
1991                 goto error;;
1992         isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
1993         map = isl_map_compute_divs(map);
1994         for (i = 0; i < map->n; ++i)
1995                 context = isl_basic_map_align_divs(context, map->p[i]);
1996         for (i = map->n - 1; i >= 0; --i) {
1997                 map->p[i] = isl_basic_map_gist(map->p[i],
1998                                                 isl_basic_map_copy(context));
1999                 if (!map->p[i])
2000                         goto error;
2001                 if (isl_basic_map_plain_is_empty(map->p[i])) {
2002                         isl_basic_map_free(map->p[i]);
2003                         if (i != map->n - 1)
2004                                 map->p[i] = map->p[map->n - 1];
2005                         map->n--;
2006                 }
2007         }
2008         isl_basic_map_free(context);
2009         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2010         return map;
2011 error:
2012         isl_map_free(map);
2013         isl_basic_map_free(context);
2014         return NULL;
2015 }
2016
2017 static __isl_give isl_map *map_gist(__isl_take isl_map *map,
2018         __isl_take isl_map *context)
2019 {
2020         context = isl_map_compute_divs(context);
2021         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
2022 }
2023
2024 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2025         __isl_take isl_map *context)
2026 {
2027         return isl_map_align_params_map_map_and(map, context, &map_gist);
2028 }
2029
2030 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
2031                                                 struct isl_basic_set *context)
2032 {
2033         return (struct isl_basic_set *)isl_basic_map_gist(
2034                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
2035 }
2036
2037 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
2038         __isl_take isl_basic_set *context)
2039 {
2040         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
2041                                         (struct isl_basic_map *)context);
2042 }
2043
2044 __isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
2045         __isl_take isl_basic_set *context)
2046 {
2047         isl_space *space = isl_set_get_space(set);
2048         isl_basic_set *dom_context = isl_basic_set_universe(space);
2049         dom_context = isl_basic_set_intersect_params(dom_context, context);
2050         return isl_set_gist_basic_set(set, dom_context);
2051 }
2052
2053 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2054         __isl_take isl_set *context)
2055 {
2056         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
2057                                         (struct isl_map *)context);
2058 }
2059
2060 __isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
2061         __isl_take isl_set *context)
2062 {
2063         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2064         map_context = isl_map_intersect_domain(map_context, context);
2065         return isl_map_gist(map, map_context);
2066 }
2067
2068 __isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
2069         __isl_take isl_set *context)
2070 {
2071         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2072         map_context = isl_map_intersect_range(map_context, context);
2073         return isl_map_gist(map, map_context);
2074 }
2075
2076 __isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
2077         __isl_take isl_set *context)
2078 {
2079         isl_map *map_context = isl_map_universe(isl_map_get_space(map));
2080         map_context = isl_map_intersect_params(map_context, context);
2081         return isl_map_gist(map, map_context);
2082 }
2083
2084 __isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
2085         __isl_take isl_set *context)
2086 {
2087         return isl_map_gist_params(set, context);
2088 }
2089
2090 /* Quick check to see if two basic maps are disjoint.
2091  * In particular, we reduce the equalities and inequalities of
2092  * one basic map in the context of the equalities of the other
2093  * basic map and check if we get a contradiction.
2094  */
2095 int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
2096         __isl_keep isl_basic_map *bmap2)
2097 {
2098         struct isl_vec *v = NULL;
2099         int *elim = NULL;
2100         unsigned total;
2101         int i;
2102
2103         if (!bmap1 || !bmap2)
2104                 return -1;
2105         isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
2106                         return -1);
2107         if (bmap1->n_div || bmap2->n_div)
2108                 return 0;
2109         if (!bmap1->n_eq && !bmap2->n_eq)
2110                 return 0;
2111
2112         total = isl_space_dim(bmap1->dim, isl_dim_all);
2113         if (total == 0)
2114                 return 0;
2115         v = isl_vec_alloc(bmap1->ctx, 1 + total);
2116         if (!v)
2117                 goto error;
2118         elim = isl_alloc_array(bmap1->ctx, int, total);
2119         if (!elim)
2120                 goto error;
2121         compute_elimination_index(bmap1, elim);
2122         for (i = 0; i < bmap2->n_eq; ++i) {
2123                 int reduced;
2124                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
2125                                                         bmap1, elim);
2126                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
2127                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2128                         goto disjoint;
2129         }
2130         for (i = 0; i < bmap2->n_ineq; ++i) {
2131                 int reduced;
2132                 reduced = reduced_using_equalities(v->block.data,
2133                                                 bmap2->ineq[i], bmap1, elim);
2134                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2135                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2136                         goto disjoint;
2137         }
2138         compute_elimination_index(bmap2, elim);
2139         for (i = 0; i < bmap1->n_ineq; ++i) {
2140                 int reduced;
2141                 reduced = reduced_using_equalities(v->block.data,
2142                                                 bmap1->ineq[i], bmap2, elim);
2143                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
2144                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
2145                         goto disjoint;
2146         }
2147         isl_vec_free(v);
2148         free(elim);
2149         return 0;
2150 disjoint:
2151         isl_vec_free(v);
2152         free(elim);
2153         return 1;
2154 error:
2155         isl_vec_free(v);
2156         free(elim);
2157         return -1;
2158 }
2159
2160 int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
2161         __isl_keep isl_basic_set *bset2)
2162 {
2163         return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
2164                                               (struct isl_basic_map *)bset2);
2165 }
2166
2167 int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
2168         __isl_keep isl_map *map2)
2169 {
2170         int i, j;
2171
2172         if (!map1 || !map2)
2173                 return -1;
2174
2175         if (isl_map_plain_is_equal(map1, map2))
2176                 return 0;
2177
2178         for (i = 0; i < map1->n; ++i) {
2179                 for (j = 0; j < map2->n; ++j) {
2180                         int d = isl_basic_map_plain_is_disjoint(map1->p[i],
2181                                                                map2->p[j]);
2182                         if (d != 1)
2183                                 return d;
2184                 }
2185         }
2186         return 1;
2187 }
2188
2189 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2190         __isl_keep isl_set *set2)
2191 {
2192         return isl_map_plain_is_disjoint((struct isl_map *)set1,
2193                                         (struct isl_map *)set2);
2194 }
2195
2196 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
2197 {
2198         return isl_set_plain_is_disjoint(set1, set2);
2199 }
2200
2201 /* Check if we can combine a given div with lower bound l and upper
2202  * bound u with some other div and if so return that other div.
2203  * Otherwise return -1.
2204  *
2205  * We first check that
2206  *      - the bounds are opposites of each other (except for the constant
2207  *        term)
2208  *      - the bounds do not reference any other div
2209  *      - no div is defined in terms of this div
2210  *
2211  * Let m be the size of the range allowed on the div by the bounds.
2212  * That is, the bounds are of the form
2213  *
2214  *      e <= a <= e + m - 1
2215  *
2216  * with e some expression in the other variables.
2217  * We look for another div b such that no third div is defined in terms
2218  * of this second div b and such that in any constraint that contains
2219  * a (except for the given lower and upper bound), also contains b
2220  * with a coefficient that is m times that of b.
2221  * That is, all constraints (execpt for the lower and upper bound)
2222  * are of the form
2223  *
2224  *      e + f (a + m b) >= 0
2225  *
2226  * If so, we return b so that "a + m b" can be replaced by
2227  * a single div "c = a + m b".
2228  */
2229 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2230         unsigned div, unsigned l, unsigned u)
2231 {
2232         int i, j;
2233         unsigned dim;
2234         int coalesce = -1;
2235
2236         if (bmap->n_div <= 1)
2237                 return -1;
2238         dim = isl_space_dim(bmap->dim, isl_dim_all);
2239         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2240                 return -1;
2241         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2242                                    bmap->n_div - div - 1) != -1)
2243                 return -1;
2244         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2245                             dim + bmap->n_div))
2246                 return -1;
2247
2248         for (i = 0; i < bmap->n_div; ++i) {
2249                 if (isl_int_is_zero(bmap->div[i][0]))
2250                         continue;
2251                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2252                         return -1;
2253         }
2254
2255         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2256         if (isl_int_is_neg(bmap->ineq[l][0])) {
2257                 isl_int_sub(bmap->ineq[l][0],
2258                             bmap->ineq[l][0], bmap->ineq[u][0]);
2259                 bmap = isl_basic_map_copy(bmap);
2260                 bmap = isl_basic_map_set_to_empty(bmap);
2261                 isl_basic_map_free(bmap);
2262                 return -1;
2263         }
2264         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2265         for (i = 0; i < bmap->n_div; ++i) {
2266                 if (i == div)
2267                         continue;
2268                 if (!pairs[i])
2269                         continue;
2270                 for (j = 0; j < bmap->n_div; ++j) {
2271                         if (isl_int_is_zero(bmap->div[j][0]))
2272                                 continue;
2273                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2274                                 break;
2275                 }
2276                 if (j < bmap->n_div)
2277                         continue;
2278                 for (j = 0; j < bmap->n_ineq; ++j) {
2279                         int valid;
2280                         if (j == l || j == u)
2281                                 continue;
2282                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2283                                 continue;
2284                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2285                                 break;
2286                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2287                                     bmap->ineq[j][1 + dim + div],
2288                                     bmap->ineq[l][0]);
2289                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2290                                            bmap->ineq[j][1 + dim + i]);
2291                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2292                                          bmap->ineq[j][1 + dim + div],
2293                                          bmap->ineq[l][0]);
2294                         if (!valid)
2295                                 break;
2296                 }
2297                 if (j < bmap->n_ineq)
2298                         continue;
2299                 coalesce = i;
2300                 break;
2301         }
2302         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2303         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2304         return coalesce;
2305 }
2306
2307 /* Given a lower and an upper bound on div i, construct an inequality
2308  * that when nonnegative ensures that this pair of bounds always allows
2309  * for an integer value of the given div.
2310  * The lower bound is inequality l, while the upper bound is inequality u.
2311  * The constructed inequality is stored in ineq.
2312  * g, fl, fu are temporary scalars.
2313  *
2314  * Let the upper bound be
2315  *
2316  *      -n_u a + e_u >= 0
2317  *
2318  * and the lower bound
2319  *
2320  *      n_l a + e_l >= 0
2321  *
2322  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2323  * We have
2324  *
2325  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2326  *
2327  * Since all variables are integer valued, this is equivalent to
2328  *
2329  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2330  *
2331  * If this interval is at least f_u f_l g, then it contains at least
2332  * one integer value for a.
2333  * That is, the test constraint is
2334  *
2335  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2336  */
2337 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2338         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2339 {
2340         unsigned dim;
2341         dim = isl_space_dim(bmap->dim, isl_dim_all);
2342
2343         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2344         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2345         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2346         isl_int_neg(fu, fu);
2347         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2348                         1 + dim + bmap->n_div);
2349         isl_int_add(ineq[0], ineq[0], fl);
2350         isl_int_add(ineq[0], ineq[0], fu);
2351         isl_int_sub_ui(ineq[0], ineq[0], 1);
2352         isl_int_mul(g, g, fl);
2353         isl_int_mul(g, g, fu);
2354         isl_int_sub(ineq[0], ineq[0], g);
2355 }
2356
2357 /* Remove more kinds of divs that are not strictly needed.
2358  * In particular, if all pairs of lower and upper bounds on a div
2359  * are such that they allow at least one integer value of the div,
2360  * the we can eliminate the div using Fourier-Motzkin without
2361  * introducing any spurious solutions.
2362  */
2363 static struct isl_basic_map *drop_more_redundant_divs(
2364         struct isl_basic_map *bmap, int *pairs, int n)
2365 {
2366         struct isl_tab *tab = NULL;
2367         struct isl_vec *vec = NULL;
2368         unsigned dim;
2369         int remove = -1;
2370         isl_int g, fl, fu;
2371
2372         isl_int_init(g);
2373         isl_int_init(fl);
2374         isl_int_init(fu);
2375
2376         if (!bmap)
2377                 goto error;
2378
2379         dim = isl_space_dim(bmap->dim, isl_dim_all);
2380         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2381         if (!vec)
2382                 goto error;
2383
2384         tab = isl_tab_from_basic_map(bmap, 0);
2385
2386         while (n > 0) {
2387                 int i, l, u;
2388                 int best = -1;
2389                 enum isl_lp_result res;
2390
2391                 for (i = 0; i < bmap->n_div; ++i) {
2392                         if (!pairs[i])
2393                                 continue;
2394                         if (best >= 0 && pairs[best] <= pairs[i])
2395                                 continue;
2396                         best = i;
2397                 }
2398
2399                 i = best;
2400                 for (l = 0; l < bmap->n_ineq; ++l) {
2401                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2402                                 continue;
2403                         for (u = 0; u < bmap->n_ineq; ++u) {
2404                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2405                                         continue;
2406                                 construct_test_ineq(bmap, i, l, u,
2407                                                     vec->el, g, fl, fu);
2408                                 res = isl_tab_min(tab, vec->el,
2409                                                   bmap->ctx->one, &g, NULL, 0);
2410                                 if (res == isl_lp_error)
2411                                         goto error;
2412                                 if (res == isl_lp_empty) {
2413                                         bmap = isl_basic_map_set_to_empty(bmap);
2414                                         break;
2415                                 }
2416                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2417                                         break;
2418                         }
2419                         if (u < bmap->n_ineq)
2420                                 break;
2421                 }
2422                 if (l == bmap->n_ineq) {
2423                         remove = i;
2424                         break;
2425                 }
2426                 pairs[i] = 0;
2427                 --n;
2428         }
2429
2430         isl_tab_free(tab);
2431         isl_vec_free(vec);
2432
2433         isl_int_clear(g);
2434         isl_int_clear(fl);
2435         isl_int_clear(fu);
2436
2437         free(pairs);
2438
2439         if (remove < 0)
2440                 return bmap;
2441
2442         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2443         return isl_basic_map_drop_redundant_divs(bmap);
2444 error:
2445         free(pairs);
2446         isl_basic_map_free(bmap);
2447         isl_tab_free(tab);
2448         isl_vec_free(vec);
2449         isl_int_clear(g);
2450         isl_int_clear(fl);
2451         isl_int_clear(fu);
2452         return NULL;
2453 }
2454
2455 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2456  * and the upper bound u, div1 always occurs together with div2 in the form
2457  * (div1 + m div2), where m is the constant range on the variable div1
2458  * allowed by l and u, replace the pair div1 and div2 by a single
2459  * div that is equal to div1 + m div2.
2460  *
2461  * The new div will appear in the location that contains div2.
2462  * We need to modify all constraints that contain
2463  * div2 = (div - div1) / m
2464  * (If a constraint does not contain div2, it will also not contain div1.)
2465  * If the constraint also contains div1, then we know they appear
2466  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2467  * i.e., the coefficient of div is f.
2468  *
2469  * Otherwise, we first need to introduce div1 into the constraint.
2470  * Let the l be
2471  *
2472  *      div1 + f >=0
2473  *
2474  * and u
2475  *
2476  *      -div1 + f' >= 0
2477  *
2478  * A lower bound on div2
2479  *
2480  *      n div2 + t >= 0
2481  *
2482  * can be replaced by
2483  *
2484  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2485  *
2486  * with g = gcd(m,n).
2487  * An upper bound
2488  *
2489  *      -n div2 + t >= 0
2490  *
2491  * can be replaced by
2492  *
2493  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2494  *
2495  * These constraint are those that we would obtain from eliminating
2496  * div1 using Fourier-Motzkin.
2497  *
2498  * After all constraints have been modified, we drop the lower and upper
2499  * bound and then drop div1.
2500  */
2501 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2502         unsigned div1, unsigned div2, unsigned l, unsigned u)
2503 {
2504         isl_int a;
2505         isl_int b;
2506         isl_int m;
2507         unsigned dim, total;
2508         int i;
2509
2510         dim = isl_space_dim(bmap->dim, isl_dim_all);
2511         total = 1 + dim + bmap->n_div;
2512
2513         isl_int_init(a);
2514         isl_int_init(b);
2515         isl_int_init(m);
2516         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2517         isl_int_add_ui(m, m, 1);
2518
2519         for (i = 0; i < bmap->n_ineq; ++i) {
2520                 if (i == l || i == u)
2521                         continue;
2522                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2523                         continue;
2524                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2525                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2526                         isl_int_divexact(a, m, b);
2527                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2528                         if (isl_int_is_pos(b)) {
2529                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2530                                                 b, bmap->ineq[l], total);
2531                         } else {
2532                                 isl_int_neg(b, b);
2533                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2534                                                 b, bmap->ineq[u], total);
2535                         }
2536                 }
2537                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2538                             bmap->ineq[i][1 + dim + div1]);
2539                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2540         }
2541
2542         isl_int_clear(a);
2543         isl_int_clear(b);
2544         isl_int_clear(m);
2545         if (l > u) {
2546                 isl_basic_map_drop_inequality(bmap, l);
2547                 isl_basic_map_drop_inequality(bmap, u);
2548         } else {
2549                 isl_basic_map_drop_inequality(bmap, u);
2550                 isl_basic_map_drop_inequality(bmap, l);
2551         }
2552         bmap = isl_basic_map_drop_div(bmap, div1);
2553         return bmap;
2554 }
2555
2556 /* First check if we can coalesce any pair of divs and
2557  * then continue with dropping more redundant divs.
2558  *
2559  * We loop over all pairs of lower and upper bounds on a div
2560  * with coefficient 1 and -1, respectively, check if there
2561  * is any other div "c" with which we can coalesce the div
2562  * and if so, perform the coalescing.
2563  */
2564 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2565         struct isl_basic_map *bmap, int *pairs, int n)
2566 {
2567         int i, l, u;
2568         unsigned dim;
2569
2570         dim = isl_space_dim(bmap->dim, isl_dim_all);
2571
2572         for (i = 0; i < bmap->n_div; ++i) {
2573                 if (!pairs[i])
2574                         continue;
2575                 for (l = 0; l < bmap->n_ineq; ++l) {
2576                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2577                                 continue;
2578                         for (u = 0; u < bmap->n_ineq; ++u) {
2579                                 int c;
2580
2581                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2582                                         continue;
2583                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2584                                 if (c < 0)
2585                                         continue;
2586                                 free(pairs);
2587                                 bmap = coalesce_divs(bmap, i, c, l, u);
2588                                 return isl_basic_map_drop_redundant_divs(bmap);
2589                         }
2590                 }
2591         }
2592
2593         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2594                 return bmap;
2595
2596         return drop_more_redundant_divs(bmap, pairs, n);
2597 }
2598
2599 /* Remove divs that are not strictly needed.
2600  * In particular, if a div only occurs positively (or negatively)
2601  * in constraints, then it can simply be dropped.
2602  * Also, if a div occurs in only two constraints and if moreover
2603  * those two constraints are opposite to each other, except for the constant
2604  * term and if the sum of the constant terms is such that for any value
2605  * of the other values, there is always at least one integer value of the
2606  * div, i.e., if one plus this sum is greater than or equal to
2607  * the (absolute value) of the coefficent of the div in the constraints,
2608  * then we can also simply drop the div.
2609  *
2610  * We skip divs that appear in equalities or in the definition of other divs.
2611  * Divs that appear in the definition of other divs usually occur in at least
2612  * 4 constraints, but the constraints may have been simplified.
2613  *
2614  * If any divs are left after these simple checks then we move on
2615  * to more complicated cases in drop_more_redundant_divs.
2616  */
2617 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2618         struct isl_basic_map *bmap)
2619 {
2620         int i, j;
2621         unsigned off;
2622         int *pairs = NULL;
2623         int n = 0;
2624
2625         if (!bmap)
2626                 goto error;
2627
2628         off = isl_space_dim(bmap->dim, isl_dim_all);
2629         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2630         if (!pairs)
2631                 goto error;
2632
2633         for (i = 0; i < bmap->n_div; ++i) {
2634                 int pos, neg;
2635                 int last_pos, last_neg;
2636                 int redundant;
2637                 int defined;
2638
2639                 defined = !isl_int_is_zero(bmap->div[i][0]);
2640                 for (j = i; j < bmap->n_div; ++j)
2641                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i]))
2642                                 break;
2643                 if (j < bmap->n_div)
2644                         continue;
2645                 for (j = 0; j < bmap->n_eq; ++j)
2646                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2647                                 break;
2648                 if (j < bmap->n_eq)
2649                         continue;
2650                 ++n;
2651                 pos = neg = 0;
2652                 for (j = 0; j < bmap->n_ineq; ++j) {
2653                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2654                                 last_pos = j;
2655                                 ++pos;
2656                         }
2657                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2658                                 last_neg = j;
2659                                 ++neg;
2660                         }
2661                 }
2662                 pairs[i] = pos * neg;
2663                 if (pairs[i] == 0) {
2664                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2665                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2666                                         isl_basic_map_drop_inequality(bmap, j);
2667                         bmap = isl_basic_map_drop_div(bmap, i);
2668                         free(pairs);
2669                         return isl_basic_map_drop_redundant_divs(bmap);
2670                 }
2671                 if (pairs[i] != 1)
2672                         continue;
2673                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2674                                     bmap->ineq[last_neg] + 1,
2675                                     off + bmap->n_div))
2676                         continue;
2677
2678                 isl_int_add(bmap->ineq[last_pos][0],
2679                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2680                 isl_int_add_ui(bmap->ineq[last_pos][0],
2681                                bmap->ineq[last_pos][0], 1);
2682                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2683                                 bmap->ineq[last_pos][1+off+i]);
2684                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2685                                bmap->ineq[last_pos][0], 1);
2686                 isl_int_sub(bmap->ineq[last_pos][0],
2687                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2688                 if (!redundant) {
2689                         if (defined ||
2690                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2691                                 pairs[i] = 0;
2692                                 --n;
2693                                 continue;
2694                         }
2695                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2696                         bmap = isl_basic_map_simplify(bmap);
2697                         free(pairs);
2698                         return isl_basic_map_drop_redundant_divs(bmap);
2699                 }
2700                 if (last_pos > last_neg) {
2701                         isl_basic_map_drop_inequality(bmap, last_pos);
2702                         isl_basic_map_drop_inequality(bmap, last_neg);
2703                 } else {
2704                         isl_basic_map_drop_inequality(bmap, last_neg);
2705                         isl_basic_map_drop_inequality(bmap, last_pos);
2706                 }
2707                 bmap = isl_basic_map_drop_div(bmap, i);
2708                 free(pairs);
2709                 return isl_basic_map_drop_redundant_divs(bmap);
2710         }
2711
2712         if (n > 0)
2713                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2714
2715         free(pairs);
2716         return bmap;
2717 error:
2718         free(pairs);
2719         isl_basic_map_free(bmap);
2720         return NULL;
2721 }
2722
2723 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2724         struct isl_basic_set *bset)
2725 {
2726         return (struct isl_basic_set *)
2727             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2728 }
2729
2730 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2731 {
2732         int i;
2733
2734         if (!map)
2735                 return NULL;
2736         for (i = 0; i < map->n; ++i) {
2737                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2738                 if (!map->p[i])
2739                         goto error;
2740         }
2741         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2742         return map;
2743 error:
2744         isl_map_free(map);
2745         return NULL;
2746 }
2747
2748 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2749 {
2750         return (struct isl_set *)
2751             isl_map_drop_redundant_divs((struct isl_map *)set);
2752 }