isl_map.c

   1 #include <string.h>
   2 #include <strings.h>
   3 #include "isl_ctx.h"
   4 #include "isl_blk.h"
   5 #include "isl_dim.h"
   6 #include "isl_equalities.h"
   7 #include "isl_list.h"
   8 #include "isl_lp.h"
   9 #include "isl_seq.h"
  10 #include "isl_set.h"
  11 #include "isl_map.h"
  12 #include "isl_map_private.h"
  13 #include "isl_map_piplib.h"
  14 #include "isl_sample.h"
  15 #include "isl_tab.h"
  16 #include "isl_vec.h"
  17
  18 /* Maps dst positions to src positions */
  19 struct isl_dim_map {
  20         unsigned len;
  21         int pos[1];
  22 };
  23
  24 static struct isl_dim_map *isl_dim_map_alloc(struct isl_ctx *ctx, unsigned len)
  25 {
  26         int i;
  27         struct isl_dim_map *dim_map;
  28         dim_map = isl_alloc(ctx, struct isl_dim_map,
  29                                 sizeof(struct isl_dim_map) + len * sizeof(int));
  30         if (!dim_map)
  31                 return NULL;
  32         dim_map->len = 1 + len;
  33         dim_map->pos[0] = 0;
  34         for (i = 0; i < len; ++i)
  35                 dim_map->pos[1 + i] = -1;
  36         return dim_map;
  37 }
  38
  39 static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
  40 {
  41         switch (type) {
  42         case isl_dim_param:     return dim->nparam;
  43         case isl_dim_in:        return dim->n_in;
  44         case isl_dim_out:       return dim->n_out;
  45         case isl_dim_all:       return dim->nparam + dim->n_in + dim->n_out;
  46         }
  47 }
  48
  49 static unsigned pos(struct isl_dim *dim, enum isl_dim_type type)
  50 {
  51         switch (type) {
  52         case isl_dim_param:     return 1;
  53         case isl_dim_in:        return 1 + dim->nparam;
  54         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  55         }
  56 }
  57
  58 static void isl_dim_map_dim(struct isl_dim_map *dim_map, struct isl_dim *dim,
  59                 enum isl_dim_type type, unsigned dst_pos)
  60 {
  61         int i;
  62         unsigned src_pos;
  63
  64         if (!dim_map || !dim)
  65                 return;
  66
  67         src_pos = pos(dim, type);
  68         for (i = 0; i < n(dim, type); ++i)
  69                 dim_map->pos[1 + dst_pos + i] = src_pos + i;
  70 }
  71
  72 static void isl_dim_map_div(struct isl_dim_map *dim_map,
  73                 struct isl_basic_map *bmap, unsigned dst_pos)
  74 {
  75         int i;
  76         unsigned src_pos;
  77
  78         if (!dim_map || !bmap)
  79                 return;
  80
  81         src_pos = 1 + isl_dim_total(bmap->dim);
  82         for (i = 0; i < bmap->n_div; ++i)
  83                 dim_map->pos[1 + dst_pos + i] = src_pos + i;
  84 }
  85
  86 static void isl_dim_map_dump(struct isl_dim_map *dim_map)
  87 {
  88         int i;
  89
  90         for (i = 0; i < dim_map->len; ++i)
  91                 fprintf(stderr, "%d -> %d; ", i, dim_map->pos[i]);
  92         fprintf(stderr, "\n");
  93 }
  94
  95 unsigned isl_basic_map_dim(const struct isl_basic_map *bmap,
  96                                 enum isl_dim_type type)
  97 {
  98         struct isl_dim *dim = bmap->dim;
  99         switch (type) {
 100         case isl_dim_param:
 101         case isl_dim_in:
 102         case isl_dim_out:       return isl_dim_size(bmap->dim, type);
 103         case isl_dim_div:       return bmap->n_div;
 104         case isl_dim_all:       return isl_basic_map_total_dim(bmap);
 105         }
 106 }
 107
 108 unsigned isl_map_dim(const struct isl_map *map, enum isl_dim_type type)
 109 {
 110         return n(map->dim, type);
 111 }
 112
 113 unsigned isl_set_dim(const struct isl_set *set, enum isl_dim_type type)
 114 {
 115         return n(set->dim, type);
 116 }
 117
 118 unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
 119                                         enum isl_dim_type type)
 120 {
 121         struct isl_dim *dim = bmap->dim;
 122         switch (type) {
 123         case isl_dim_param:     return 1;
 124         case isl_dim_in:        return 1 + dim->nparam;
 125         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 126         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 127         }
 128 }
 129
 130 static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
 131 {
 132         return pos(map->dim, type);
 133 }
 134
 135 unsigned isl_basic_set_dim(const struct isl_basic_set *bset,
 136                                 enum isl_dim_type type)
 137 {
 138         return isl_basic_map_dim((const struct isl_basic_map*)bset, type);
 139 }
 140
 141 unsigned isl_basic_set_n_dim(const struct isl_basic_set *bset)
 142 {
 143         return bset->dim->n_out;
 144 }
 145
 146 unsigned isl_basic_set_n_param(const struct isl_basic_set *bset)
 147 {
 148         return bset->dim->nparam;
 149 }
 150
 151 unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
 152 {
 153         return isl_dim_total(bset->dim) + bset->n_div;
 154 }
 155
 156 unsigned isl_set_n_dim(const struct isl_set *set)
 157 {
 158         return set->dim->n_out;
 159 }
 160
 161 unsigned isl_set_n_param(const struct isl_set *set)
 162 {
 163         return set->dim->nparam;
 164 }
 165
 166 unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
 167 {
 168         return bmap->dim->n_in;
 169 }
 170
 171 unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
 172 {
 173         return bmap->dim->n_out;
 174 }
 175
 176 unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
 177 {
 178         return bmap->dim->nparam;
 179 }
 180
 181 unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
 182 {
 183         return bmap->n_div;
 184 }
 185
 186 unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
 187 {
 188         return isl_dim_total(bmap->dim) + bmap->n_div;
 189 }
 190
 191 unsigned isl_map_n_in(const struct isl_map *map)
 192 {
 193         return map->dim->n_in;
 194 }
 195
 196 unsigned isl_map_n_out(const struct isl_map *map)
 197 {
 198         return map->dim->n_out;
 199 }
 200
 201 unsigned isl_map_n_param(const struct isl_map *map)
 202 {
 203         return map->dim->nparam;
 204 }
 205
 206 int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
 207 {
 208         return map->dim->n_in == set->dim->n_out &&
 209                map->dim->nparam == set->dim->nparam;
 210 }
 211
 212 int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
 213                 struct isl_basic_set *bset)
 214 {
 215         return bmap->dim->n_in == bset->dim->n_out &&
 216                bmap->dim->nparam == bset->dim->nparam;
 217 }
 218
 219 int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
 220                 struct isl_basic_set *bset)
 221 {
 222         return bmap->dim->n_out == bset->dim->n_out &&
 223                bmap->dim->nparam == bset->dim->nparam;
 224 }
 225
 226 struct isl_dim *isl_basic_map_get_dim(struct isl_basic_map *bmap)
 227 {
 228         if (!bmap)
 229                 return NULL;
 230         return isl_dim_copy(bmap->dim);
 231 }
 232
 233 struct isl_dim *isl_basic_set_get_dim(struct isl_basic_set *bset)
 234 {
 235         if (!bset)
 236                 return NULL;
 237         return isl_dim_copy(bset->dim);
 238 }
 239
 240 struct isl_dim *isl_map_get_dim(struct isl_map *map)
 241 {
 242         if (!map)
 243                 return NULL;
 244         return isl_dim_copy(map->dim);
 245 }
 246
 247 struct isl_dim *isl_set_get_dim(struct isl_set *set)
 248 {
 249         if (!set)
 250                 return NULL;
 251         return isl_dim_copy(set->dim);
 252 }
 253
 254 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 255                 struct isl_basic_map *bmap, unsigned extra,
 256                 unsigned n_eq, unsigned n_ineq)
 257 {
 258         int i;
 259         size_t row_size = 1 + isl_dim_total(bmap->dim) + extra;
 260
 261         bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
 262         if (isl_blk_is_error(bmap->block)) {
 263                 free(bmap);
 264                 return NULL;
 265         }
 266
 267         bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
 268         if (!bmap->ineq) {
 269                 isl_blk_free(ctx, bmap->block);
 270                 free(bmap);
 271                 return NULL;
 272         }
 273
 274         if (extra == 0) {
 275                 bmap->block2 = isl_blk_empty();
 276                 bmap->div = NULL;
 277         } else {
 278                 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
 279                 if (isl_blk_is_error(bmap->block2)) {
 280                         free(bmap->ineq);
 281                         isl_blk_free(ctx, bmap->block);
 282                         free(bmap);
 283                         return NULL;
 284                 }
 285
 286                 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
 287                 if (!bmap->div) {
 288                         isl_blk_free(ctx, bmap->block2);
 289                         free(bmap->ineq);
 290                         isl_blk_free(ctx, bmap->block);
 291                         free(bmap);
 292                         return NULL;
 293                 }
 294         }
 295
 296         for (i = 0; i < n_ineq + n_eq; ++i)
 297                 bmap->ineq[i] = bmap->block.data + i * row_size;
 298
 299         for (i = 0; i < extra; ++i)
 300                 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
 301
 302         bmap->ctx = ctx;
 303         isl_ctx_ref(ctx);
 304         bmap->ref = 1;
 305         bmap->flags = 0;
 306         bmap->c_size = n_eq + n_ineq;
 307         bmap->eq = bmap->ineq + n_ineq;
 308         bmap->extra = extra;
 309         bmap->n_eq = 0;
 310         bmap->n_ineq = 0;
 311         bmap->n_div = 0;
 312         bmap->sample = NULL;
 313
 314         return bmap;
 315 error:
 316         isl_basic_map_free(bmap);
 317         return NULL;
 318 }
 319
 320 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
 321                 unsigned nparam, unsigned dim, unsigned extra,
 322                 unsigned n_eq, unsigned n_ineq)
 323 {
 324         struct isl_basic_map *bmap;
 325         bmap = isl_basic_map_alloc(ctx, nparam, 0, dim, extra, n_eq, n_ineq);
 326         return (struct isl_basic_set *)bmap;
 327 }
 328
 329 struct isl_basic_set *isl_basic_set_alloc_dim(struct isl_dim *dim,
 330                 unsigned extra, unsigned n_eq, unsigned n_ineq)
 331 {
 332         struct isl_basic_map *bmap;
 333         if (!dim)
 334                 return NULL;
 335         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
 336         bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 337         return (struct isl_basic_set *)bmap;
 338 }
 339
 340 struct isl_basic_map *isl_basic_map_alloc_dim(struct isl_dim *dim,
 341                 unsigned extra, unsigned n_eq, unsigned n_ineq)
 342 {
 343         struct isl_basic_map *bmap;
 344
 345         if (!dim)
 346                 return NULL;
 347         bmap = isl_alloc_type(dim->ctx, struct isl_basic_map);
 348         if (!bmap)
 349                 goto error;
 350         bmap->dim = dim;
 351
 352         return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
 353 error:
 354         isl_dim_free(dim);
 355         return NULL;
 356 }
 357
 358 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
 359                 unsigned nparam, unsigned in, unsigned out, unsigned extra,
 360                 unsigned n_eq, unsigned n_ineq)
 361 {
 362         struct isl_basic_map *bmap;
 363         struct isl_dim *dim;
 364
 365         dim = isl_dim_alloc(ctx, nparam, in, out);
 366         if (!dim)
 367                 return NULL;
 368
 369         bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 370         return bmap;
 371 }
 372
 373 static void dup_constraints(
 374                 struct isl_basic_map *dst, struct isl_basic_map *src)
 375 {
 376         int i;
 377         unsigned total = isl_basic_map_total_dim(src);
 378
 379         for (i = 0; i < src->n_eq; ++i) {
 380                 int j = isl_basic_map_alloc_equality(dst);
 381                 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
 382         }
 383
 384         for (i = 0; i < src->n_ineq; ++i) {
 385                 int j = isl_basic_map_alloc_inequality(dst);
 386                 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
 387         }
 388
 389         for (i = 0; i < src->n_div; ++i) {
 390                 int j = isl_basic_map_alloc_div(dst);
 391                 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
 392         }
 393         ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
 394 }
 395
 396 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 397 {
 398         struct isl_basic_map *dup;
 399
 400         if (!bmap)
 401                 return NULL;
 402         dup = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
 403                         bmap->n_div, bmap->n_eq, bmap->n_ineq);
 404         if (!dup)
 405                 return NULL;
 406         dup_constraints(dup, bmap);
 407         dup->flags = bmap->flags;
 408         dup->sample = isl_vec_copy(bmap->sample);
 409         return dup;
 410 }
 411
 412 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
 413 {
 414         struct isl_basic_map *dup;
 415
 416         dup = isl_basic_map_dup((struct isl_basic_map *)bset);
 417         return (struct isl_basic_set *)dup;
 418 }
 419
 420 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
 421 {
 422         if (!bset)
 423                 return NULL;
 424
 425         if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
 426                 bset->ref++;
 427                 return bset;
 428         }
 429         return isl_basic_set_dup(bset);
 430 }
 431
 432 struct isl_set *isl_set_copy(struct isl_set *set)
 433 {
 434         if (!set)
 435                 return NULL;
 436
 437         set->ref++;
 438         return set;
 439 }
 440
 441 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
 442 {
 443         if (!bmap)
 444                 return NULL;
 445
 446         if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
 447                 bmap->ref++;
 448                 return bmap;
 449         }
 450         return isl_basic_map_dup(bmap);
 451 }
 452
 453 struct isl_map *isl_map_copy(struct isl_map *map)
 454 {
 455         if (!map)
 456                 return NULL;
 457
 458         map->ref++;
 459         return map;
 460 }
 461
 462 void isl_basic_map_free(struct isl_basic_map *bmap)
 463 {
 464         if (!bmap)
 465                 return;
 466
 467         if (--bmap->ref > 0)
 468                 return;
 469
 470         isl_ctx_deref(bmap->ctx);
 471         free(bmap->div);
 472         isl_blk_free(bmap->ctx, bmap->block2);
 473         free(bmap->ineq);
 474         isl_blk_free(bmap->ctx, bmap->block);
 475         isl_vec_free(bmap->sample);
 476         isl_dim_free(bmap->dim);
 477         free(bmap);
 478 }
 479
 480 void isl_basic_set_free(struct isl_basic_set *bset)
 481 {
 482         isl_basic_map_free((struct isl_basic_map *)bset);
 483 }
 484
 485 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
 486 {
 487         return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
 488 }
 489
 490 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
 491 {
 492         struct isl_ctx *ctx;
 493         if (!bmap)
 494                 return -1;
 495         ctx = bmap->ctx;
 496         isl_assert(ctx, room_for_con(bmap, 1), return -1);
 497         isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
 498                         return -1);
 499         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 500         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 501         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 502         ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
 503         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 504         if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
 505                 isl_int *t;
 506                 int j = isl_basic_map_alloc_inequality(bmap);
 507                 if (j < 0)
 508                         return -1;
 509                 t = bmap->ineq[j];
 510                 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
 511                 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
 512                 bmap->eq[-1] = t;
 513                 bmap->n_eq++;
 514                 bmap->n_ineq--;
 515                 bmap->eq--;
 516                 return 0;
 517         }
 518         isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
 519                       bmap->extra - bmap->n_div);
 520         return bmap->n_eq++;
 521 }
 522
 523 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
 524 {
 525         return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
 526 }
 527
 528 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
 529 {
 530         if (!bmap)
 531                 return -1;
 532         isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
 533         bmap->n_eq -= n;
 534         return 0;
 535 }
 536
 537 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
 538 {
 539         return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
 540 }
 541
 542 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 543 {
 544         isl_int *t;
 545         if (!bmap)
 546                 return -1;
 547         isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
 548
 549         if (pos != bmap->n_eq - 1) {
 550                 t = bmap->eq[pos];
 551                 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
 552                 bmap->eq[bmap->n_eq - 1] = t;
 553         }
 554         bmap->n_eq--;
 555         return 0;
 556 }
 557
 558 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
 559 {
 560         return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
 561 }
 562
 563 void isl_basic_map_inequality_to_equality(
 564                 struct isl_basic_map *bmap, unsigned pos)
 565 {
 566         isl_int *t;
 567
 568         t = bmap->ineq[pos];
 569         bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 570         bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
 571         bmap->eq[-1] = t;
 572         bmap->n_eq++;
 573         bmap->n_ineq--;
 574         bmap->eq--;
 575         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 576         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 577         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 578         ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
 579 }
 580
 581 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
 582 {
 583         return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
 584 }
 585
 586 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
 587 {
 588         struct isl_ctx *ctx;
 589         if (!bmap)
 590                 return -1;
 591         ctx = bmap->ctx;
 592         isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
 593         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 594         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 595         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 596         ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
 597         isl_seq_clr(bmap->ineq[bmap->n_ineq] +
 598                       1 + isl_basic_map_total_dim(bmap),
 599                       bmap->extra - bmap->n_div);
 600         return bmap->n_ineq++;
 601 }
 602
 603 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
 604 {
 605         return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
 606 }
 607
 608 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
 609 {
 610         if (!bmap)
 611                 return -1;
 612         isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
 613         bmap->n_ineq -= n;
 614         return 0;
 615 }
 616
 617 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
 618 {
 619         return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
 620 }
 621
 622 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
 623 {
 624         isl_int *t;
 625         if (!bmap)
 626                 return -1;
 627         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
 628
 629         if (pos != bmap->n_ineq - 1) {
 630                 t = bmap->ineq[pos];
 631                 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 632                 bmap->ineq[bmap->n_ineq - 1] = t;
 633                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 634         }
 635         bmap->n_ineq--;
 636         return 0;
 637 }
 638
 639 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
 640 {
 641         return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
 642 }
 643
 644 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
 645 {
 646         if (!bmap)
 647                 return -1;
 648         isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
 649         isl_seq_clr(bmap->div[bmap->n_div] +
 650                       1 + 1 + isl_basic_map_total_dim(bmap),
 651                       bmap->extra - bmap->n_div);
 652         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 653         return bmap->n_div++;
 654 }
 655
 656 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
 657 {
 658         return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
 659 }
 660
 661 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 662 {
 663         if (!bmap)
 664                 return -1;
 665         isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
 666         bmap->n_div -= n;
 667         return 0;
 668 }
 669
 670 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
 671 {
 672         return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
 673 }
 674
 675 /* Copy constraint from src to dst, putting the vars of src at offset
 676  * dim_off in dst and the divs of src at offset div_off in dst.
 677  * If both sets are actually map, then dim_off applies to the input
 678  * variables.
 679  */
 680 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
 681                             struct isl_basic_map *src_map, isl_int *src,
 682                             unsigned in_off, unsigned out_off, unsigned div_off)
 683 {
 684         unsigned src_nparam = isl_basic_map_n_param(src_map);
 685         unsigned dst_nparam = isl_basic_map_n_param(dst_map);
 686         unsigned src_in = isl_basic_map_n_in(src_map);
 687         unsigned dst_in = isl_basic_map_n_in(dst_map);
 688         unsigned src_out = isl_basic_map_n_out(src_map);
 689         unsigned dst_out = isl_basic_map_n_out(dst_map);
 690         isl_int_set(dst[0], src[0]);
 691         isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
 692         if (dst_nparam > src_nparam)
 693                 isl_seq_clr(dst+1+src_nparam,
 694                                 dst_nparam - src_nparam);
 695         isl_seq_clr(dst+1+dst_nparam, in_off);
 696         isl_seq_cpy(dst+1+dst_nparam+in_off,
 697                     src+1+src_nparam,
 698                     isl_min(dst_in-in_off, src_in));
 699         if (dst_in-in_off > src_in)
 700                 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
 701                                 dst_in - in_off - src_in);
 702         isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
 703         isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
 704                     src+1+src_nparam+src_in,
 705                     isl_min(dst_out-out_off, src_out));
 706         if (dst_out-out_off > src_out)
 707                 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
 708                                 dst_out - out_off - src_out);
 709         isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
 710         isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
 711                     src+1+src_nparam+src_in+src_out,
 712                     isl_min(dst_map->extra-div_off, src_map->n_div));
 713         if (dst_map->n_div-div_off > src_map->n_div)
 714                 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
 715                                 div_off+src_map->n_div,
 716                                 dst_map->n_div - div_off - src_map->n_div);
 717 }
 718
 719 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
 720                      struct isl_basic_map *src_map, isl_int *src,
 721                      unsigned in_off, unsigned out_off, unsigned div_off)
 722 {
 723         isl_int_set(dst[0], src[0]);
 724         copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
 725 }
 726
 727 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
 728                 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 729 {
 730         int i;
 731         unsigned div_off;
 732
 733         if (!bmap1 || !bmap2)
 734                 goto error;
 735
 736         div_off = bmap1->n_div;
 737
 738         for (i = 0; i < bmap2->n_eq; ++i) {
 739                 int i1 = isl_basic_map_alloc_equality(bmap1);
 740                 if (i1 < 0)
 741                         goto error;
 742                 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
 743                                 i_pos, o_pos, div_off);
 744         }
 745
 746         for (i = 0; i < bmap2->n_ineq; ++i) {
 747                 int i1 = isl_basic_map_alloc_inequality(bmap1);
 748                 if (i1 < 0)
 749                         goto error;
 750                 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
 751                                 i_pos, o_pos, div_off);
 752         }
 753
 754         for (i = 0; i < bmap2->n_div; ++i) {
 755                 int i1 = isl_basic_map_alloc_div(bmap1);
 756                 if (i1 < 0)
 757                         goto error;
 758                 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
 759                          i_pos, o_pos, div_off);
 760         }
 761
 762         isl_basic_map_free(bmap2);
 763
 764         return bmap1;
 765
 766 error:
 767         isl_basic_map_free(bmap1);
 768         isl_basic_map_free(bmap2);
 769         return NULL;
 770 }
 771
 772 static void copy_constraint_dim_map(isl_int *dst, isl_int *src,
 773                                         struct isl_dim_map *dim_map)
 774 {
 775         int i;
 776
 777         for (i = 0; i < dim_map->len; ++i) {
 778                 if (dim_map->pos[i] < 0)
 779                         isl_int_set_si(dst[i], 0);
 780                 else
 781                         isl_int_set(dst[i], src[dim_map->pos[i]]);
 782         }
 783 }
 784
 785 static void copy_div_dim_map(isl_int *dst, isl_int *src,
 786                                         struct isl_dim_map *dim_map)
 787 {
 788         isl_int_set(dst[0], src[0]);
 789         copy_constraint_dim_map(dst+1, src+1, dim_map);
 790 }
 791
 792 static struct isl_basic_map *add_constraints_dim_map(struct isl_basic_map *dst,
 793                 struct isl_basic_map *src, struct isl_dim_map *dim_map)
 794 {
 795         int i;
 796
 797         if (!src || !dst || !dim_map)
 798                 goto error;
 799
 800         for (i = 0; i < src->n_eq; ++i) {
 801                 int i1 = isl_basic_map_alloc_equality(dst);
 802                 if (i1 < 0)
 803                         goto error;
 804                 copy_constraint_dim_map(dst->eq[i1], src->eq[i], dim_map);
 805         }
 806
 807         for (i = 0; i < src->n_ineq; ++i) {
 808                 int i1 = isl_basic_map_alloc_inequality(dst);
 809                 if (i1 < 0)
 810                         goto error;
 811                 copy_constraint_dim_map(dst->ineq[i1], src->ineq[i], dim_map);
 812         }
 813
 814         for (i = 0; i < src->n_div; ++i) {
 815                 int i1 = isl_basic_map_alloc_div(dst);
 816                 if (i1 < 0)
 817                         goto error;
 818                 copy_div_dim_map(dst->div[i1], src->div[i], dim_map);
 819         }
 820
 821         free(dim_map);
 822         isl_basic_map_free(src);
 823
 824         return dst;
 825 error:
 826         free(dim_map);
 827         isl_basic_map_free(src);
 828         isl_basic_map_free(dst);
 829         return NULL;
 830 }
 831
 832 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
 833                 struct isl_basic_set *bset2, unsigned pos)
 834 {
 835         return (struct isl_basic_set *)
 836                 add_constraints((struct isl_basic_map *)bset1,
 837                                 (struct isl_basic_map *)bset2, 0, pos);
 838 }
 839
 840 struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
 841                 struct isl_dim *dim, unsigned extra,
 842                 unsigned n_eq, unsigned n_ineq)
 843 {
 844         struct isl_basic_map *ext;
 845         unsigned flags;
 846         int dims_ok;
 847
 848         if (!dim)
 849                 goto error;
 850
 851         if (!base)
 852                 goto error;
 853
 854         dims_ok = isl_dim_equal(base->dim, dim) &&
 855                   base->extra >= base->n_div + extra;
 856
 857         if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
 858                        room_for_ineq(base, n_ineq)) {
 859                 isl_dim_free(dim);
 860                 return base;
 861         }
 862
 863         isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
 864         isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
 865         isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
 866         extra += base->extra;
 867         n_eq += base->n_eq;
 868         n_ineq += base->n_ineq;
 869
 870         ext = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 871         dim = NULL;
 872         if (!ext)
 873                 goto error;
 874
 875         if (dims_ok)
 876                 ext->sample = isl_vec_copy(base->sample);
 877         flags = base->flags;
 878         ext = add_constraints(ext, base, 0, 0);
 879         if (ext) {
 880                 ext->flags = flags;
 881                 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
 882         }
 883
 884         return ext;
 885
 886 error:
 887         isl_dim_free(dim);
 888         isl_basic_map_free(base);
 889         return NULL;
 890 }
 891
 892 struct isl_basic_set *isl_basic_set_extend_dim(struct isl_basic_set *base,
 893                 struct isl_dim *dim, unsigned extra,
 894                 unsigned n_eq, unsigned n_ineq)
 895 {
 896         return (struct isl_basic_set *)
 897                 isl_basic_map_extend_dim((struct isl_basic_map *)base, dim,
 898                                                         extra, n_eq, n_ineq);
 899 }
 900
 901 struct isl_basic_map *isl_basic_map_extend_constraints(
 902                 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
 903 {
 904         if (!base)
 905                 return NULL;
 906         return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
 907                                         0, n_eq, n_ineq);
 908 }
 909
 910 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
 911                 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
 912                 unsigned n_eq, unsigned n_ineq)
 913 {
 914         struct isl_basic_map *bmap;
 915         struct isl_dim *dim;
 916
 917         if (!base)
 918                 return NULL;
 919         dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
 920         if (!dim)
 921                 return NULL;
 922
 923         bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
 924         return bmap;
 925 }
 926
 927 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 928                 unsigned nparam, unsigned dim, unsigned extra,
 929                 unsigned n_eq, unsigned n_ineq)
 930 {
 931         return (struct isl_basic_set *)
 932                 isl_basic_map_extend((struct isl_basic_map *)base,
 933                                         nparam, 0, dim, extra, n_eq, n_ineq);
 934 }
 935
 936 struct isl_basic_set *isl_basic_set_extend_constraints(
 937                 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
 938 {
 939         return (struct isl_basic_set *)
 940                 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
 941                                                     n_eq, n_ineq);
 942 }
 943
 944 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 945 {
 946         return (struct isl_basic_set *)
 947                 isl_basic_map_cow((struct isl_basic_map *)bset);
 948 }
 949
 950 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 951 {
 952         if (!bmap)
 953                 return NULL;
 954
 955         if (bmap->ref > 1) {
 956                 bmap->ref--;
 957                 bmap = isl_basic_map_dup(bmap);
 958         }
 959         ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
 960         return bmap;
 961 }
 962
 963 struct isl_set *isl_set_cow(struct isl_set *set)
 964 {
 965         if (!set)
 966                 return NULL;
 967
 968         if (set->ref == 1)
 969                 return set;
 970         set->ref--;
 971         return isl_set_dup(set);
 972 }
 973
 974 struct isl_map *isl_map_cow(struct isl_map *map)
 975 {
 976         if (!map)
 977                 return NULL;
 978
 979         if (map->ref == 1)
 980                 return map;
 981         map->ref--;
 982         return isl_map_dup(map);
 983 }
 984
 985 static void swap_vars(struct isl_blk blk, isl_int *a,
 986                         unsigned a_len, unsigned b_len)
 987 {
 988         isl_seq_cpy(blk.data, a+a_len, b_len);
 989         isl_seq_cpy(blk.data+b_len, a, a_len);
 990         isl_seq_cpy(a, blk.data, b_len+a_len);
 991 }
 992
 993 struct isl_basic_set *isl_basic_set_swap_vars(
 994                 struct isl_basic_set *bset, unsigned n)
 995 {
 996         int i;
 997         struct isl_blk blk;
 998         unsigned dim;
 999         unsigned nparam;
1000
1001         if (!bset)
1002                 goto error;
1003
1004         nparam = isl_basic_set_n_param(bset);
1005         dim = isl_basic_set_n_dim(bset);
1006         isl_assert(bset->ctx, n <= dim, goto error);
1007
1008         if (n == dim)
1009                 return bset;
1010
1011         bset = isl_basic_set_cow(bset);
1012         if (!bset)
1013                 return NULL;
1014
1015         blk = isl_blk_alloc(bset->ctx, dim);
1016         if (isl_blk_is_error(blk))
1017                 goto error;
1018
1019         for (i = 0; i < bset->n_eq; ++i)
1020                 swap_vars(blk,
1021                           bset->eq[i]+1+nparam, n, dim - n);
1022
1023         for (i = 0; i < bset->n_ineq; ++i)
1024                 swap_vars(blk,
1025                           bset->ineq[i]+1+nparam, n, dim - n);
1026
1027         for (i = 0; i < bset->n_div; ++i)
1028                 swap_vars(blk,
1029                           bset->div[i]+1+1+nparam, n, dim - n);
1030
1031         isl_blk_free(bset->ctx, blk);
1032
1033         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1034         return bset;
1035
1036 error:
1037         isl_basic_set_free(bset);
1038         return NULL;
1039 }
1040
1041 struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
1042 {
1043         int i;
1044         set = isl_set_cow(set);
1045         if (!set)
1046                 return NULL;
1047
1048         for (i = 0; i < set->n; ++i) {
1049                 set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
1050                 if (!set->p[i]) {
1051                         isl_set_free(set);
1052                         return NULL;
1053                 }
1054         }
1055         ISL_F_CLR(set, ISL_SET_NORMALIZED);
1056         return set;
1057 }
1058
1059 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1060 {
1061         int i = 0;
1062         unsigned total;
1063         if (!bmap)
1064                 goto error;
1065         total = isl_basic_map_total_dim(bmap);
1066         isl_basic_map_free_div(bmap, bmap->n_div);
1067         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1068         if (bmap->n_eq > 0)
1069                 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1070         else {
1071                 isl_basic_map_alloc_equality(bmap);
1072                 if (i < 0)
1073                         goto error;
1074         }
1075         isl_int_set_si(bmap->eq[i][0], 1);
1076         isl_seq_clr(bmap->eq[i]+1, total);
1077         ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1078         return isl_basic_map_finalize(bmap);
1079 error:
1080         isl_basic_map_free(bmap);
1081         return NULL;
1082 }
1083
1084 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1085 {
1086         return (struct isl_basic_set *)
1087                 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1088 }
1089
1090 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1091 {
1092         int i;
1093         unsigned off = isl_dim_total(bmap->dim);
1094         isl_int *t = bmap->div[a];
1095         bmap->div[a] = bmap->div[b];
1096         bmap->div[b] = t;
1097
1098         for (i = 0; i < bmap->n_eq; ++i)
1099                 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1100
1101         for (i = 0; i < bmap->n_ineq; ++i)
1102                 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1103
1104         for (i = 0; i < bmap->n_div; ++i)
1105                 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1106         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1107 }
1108
1109 /* Eliminate the specified n dimensions starting at first from the
1110  * constraints using Fourier-Motzkin, The dimensions themselves
1111  * are not removed.
1112  */
1113 struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
1114         unsigned first, unsigned n)
1115 {
1116         int i;
1117         unsigned nparam;
1118
1119         if (!set)
1120                 return NULL;
1121         if (n == 0)
1122                 return set;
1123
1124         set = isl_set_cow(set);
1125         if (!set)
1126                 return NULL;
1127         isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
1128         nparam = isl_set_n_param(set);
1129
1130         for (i = 0; i < set->n; ++i) {
1131                 set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
1132                                                             nparam + first, n);
1133                 if (!set->p[i])
1134                         goto error;
1135         }
1136         return set;
1137 error:
1138         isl_set_free(set);
1139         return NULL;
1140 }
1141
1142 /* Project out n dimensions starting at first using Fourier-Motzkin */
1143 struct isl_set *isl_set_remove_dims(struct isl_set *set,
1144         unsigned first, unsigned n)
1145 {
1146         set = isl_set_eliminate_dims(set, first, n);
1147         set = isl_set_drop_dims(set, first, n);
1148         return set;
1149 }
1150
1151 struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
1152 {
1153         bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
1154                                                 bset->n_div);
1155         if (!bset)
1156                 return NULL;
1157         bset->n_div = 0;
1158         return bset;
1159 }
1160
1161 struct isl_set *isl_set_remove_divs(struct isl_set *set)
1162 {
1163         int i;
1164
1165         if (!set)
1166                 return NULL;
1167         if (set->n == 0)
1168                 return set;
1169
1170         set = isl_set_cow(set);
1171         if (!set)
1172                 return NULL;
1173
1174         for (i = 0; i < set->n; ++i) {
1175                 set->p[i] = isl_basic_set_remove_divs(set->p[i]);
1176                 if (!set->p[i])
1177                         goto error;
1178         }
1179         return set;
1180 error:
1181         isl_set_free(set);
1182         return NULL;
1183 }
1184
1185 struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
1186         enum isl_dim_type type, unsigned first, unsigned n)
1187 {
1188         if (!bmap)
1189                 return NULL;
1190         isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1191                         goto error);
1192         if (n == 0)
1193                 return bmap;
1194         bmap = isl_basic_map_eliminate_vars(bmap,
1195                         isl_basic_map_offset(bmap, type) - 1 + first, n);
1196         if (!bmap)
1197                 return bmap;
1198         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1199                 return bmap;
1200         bmap = isl_basic_map_drop(bmap, type, first, n);
1201         return bmap;
1202 error:
1203         isl_basic_map_free(bmap);
1204         return NULL;
1205 }
1206
1207 struct isl_map *isl_map_remove(struct isl_map *map,
1208         enum isl_dim_type type, unsigned first, unsigned n)
1209 {
1210         int i;
1211         unsigned nparam;
1212
1213         if (n == 0)
1214                 return map;
1215
1216         map = isl_map_cow(map);
1217         if (!map)
1218                 return NULL;
1219         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
1220
1221         for (i = 0; i < map->n; ++i) {
1222                 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
1223                         isl_basic_map_offset(map->p[i], type) - 1 + first, n);
1224                 if (!map->p[i])
1225                         goto error;
1226         }
1227         map = isl_map_drop(map, type, first, n);
1228         return map;
1229 error:
1230         isl_map_free(map);
1231         return NULL;
1232 }
1233
1234 /* Project out n inputs starting at first using Fourier-Motzkin */
1235 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
1236         unsigned first, unsigned n)
1237 {
1238         return isl_map_remove(map, isl_dim_in, first, n);
1239 }
1240
1241 /* Project out n dimensions starting at first using Fourier-Motzkin */
1242 struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
1243         unsigned first, unsigned n)
1244 {
1245         unsigned nparam = isl_basic_set_n_param(bset);
1246         bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
1247         bset = isl_basic_set_drop_dims(bset, first, n);
1248         return bset;
1249 }
1250
1251 static void dump_term(struct isl_basic_map *bmap,
1252                         isl_int c, int pos, FILE *out)
1253 {
1254         const char *name;
1255         unsigned in = isl_basic_map_n_in(bmap);
1256         unsigned dim = in + isl_basic_map_n_out(bmap);
1257         unsigned nparam = isl_basic_map_n_param(bmap);
1258         if (!pos)
1259                 isl_int_print(out, c, 0);
1260         else {
1261                 if (!isl_int_is_one(c))
1262                         isl_int_print(out, c, 0);
1263                 if (pos < 1 + nparam) {
1264                         name = isl_dim_get_name(bmap->dim,
1265                                                 isl_dim_param, pos - 1);
1266                         if (name)
1267                                 fprintf(out, "%s", name);
1268                         else
1269                                 fprintf(out, "p%d", pos - 1);
1270                 } else if (pos < 1 + nparam + in)
1271                         fprintf(out, "i%d", pos - 1 - nparam);
1272                 else if (pos < 1 + nparam + dim)
1273                         fprintf(out, "o%d", pos - 1 - nparam - in);
1274                 else
1275                         fprintf(out, "e%d", pos - 1 - nparam - dim);
1276         }
1277 }
1278
1279 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
1280                                 int sign, FILE *out)
1281 {
1282         int i;
1283         int first;
1284         unsigned len = 1 + isl_basic_map_total_dim(bmap);
1285         isl_int v;
1286
1287         isl_int_init(v);
1288         for (i = 0, first = 1; i < len; ++i) {
1289                 if (isl_int_sgn(c[i]) * sign <= 0)
1290                         continue;
1291                 if (!first)
1292                         fprintf(out, " + ");
1293                 first = 0;
1294                 isl_int_abs(v, c[i]);
1295                 dump_term(bmap, v, i, out);
1296         }
1297         isl_int_clear(v);
1298         if (first)
1299                 fprintf(out, "0");
1300 }
1301
1302 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
1303                                 const char *op, FILE *out, int indent)
1304 {
1305         int i;
1306
1307         fprintf(out, "%*s", indent, "");
1308
1309         dump_constraint_sign(bmap, c, 1, out);
1310         fprintf(out, " %s ", op);
1311         dump_constraint_sign(bmap, c, -1, out);
1312
1313         fprintf(out, "\n");
1314
1315         for (i = bmap->n_div; i < bmap->extra; ++i) {
1316                 if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
1317                         continue;
1318                 fprintf(out, "%*s", indent, "");
1319                 fprintf(out, "ERROR: unused div coefficient not zero\n");
1320                 abort();
1321         }
1322 }
1323
1324 static void dump_constraints(struct isl_basic_map *bmap,
1325                                 isl_int **c, unsigned n,
1326                                 const char *op, FILE *out, int indent)
1327 {
1328         int i;
1329
1330         for (i = 0; i < n; ++i)
1331                 dump_constraint(bmap, c[i], op, out, indent);
1332 }
1333
1334 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
1335 {
1336         int j;
1337         int first = 1;
1338         unsigned total = isl_basic_map_total_dim(bmap);
1339
1340         for (j = 0; j < 1 + total; ++j) {
1341                 if (isl_int_is_zero(exp[j]))
1342                         continue;
1343                 if (!first && isl_int_is_pos(exp[j]))
1344                         fprintf(out, "+");
1345                 dump_term(bmap, exp[j], j, out);
1346                 first = 0;
1347         }
1348 }
1349
1350 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
1351 {
1352         int i;
1353
1354         dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
1355         dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
1356
1357         for (i = 0; i < bmap->n_div; ++i) {
1358                 fprintf(out, "%*s", indent, "");
1359                 fprintf(out, "e%d = [(", i);
1360                 dump_affine(bmap, bmap->div[i]+1, out);
1361                 fprintf(out, ")/");
1362                 isl_int_print(out, bmap->div[i][0], 0);
1363                 fprintf(out, "]\n");
1364         }
1365 }
1366
1367 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
1368 {
1369         if (!bset) {
1370                 fprintf(out, "null basic set\n");
1371                 return;
1372         }
1373
1374         fprintf(out, "%*s", indent, "");
1375         fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
1376                         bset->ref, bset->dim->nparam, bset->dim->n_out,
1377                         bset->extra, bset->flags);
1378         dump((struct isl_basic_map *)bset, out, indent);
1379 }
1380
1381 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
1382 {
1383         if (!bmap) {
1384                 fprintf(out, "null basic map\n");
1385                 return;
1386         }
1387
1388         fprintf(out, "%*s", indent, "");
1389         fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
1390                         "flags: %x, n_name: %d\n",
1391                 bmap->ref,
1392                 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
1393                 bmap->extra, bmap->flags, bmap->dim->n_name);
1394         dump(bmap, out, indent);
1395 }
1396
1397 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
1398 {
1399         unsigned total;
1400         if (!bmap)
1401                 return -1;
1402         total = isl_basic_map_total_dim(bmap);
1403         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1404         isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
1405         isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
1406         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1407         return 0;
1408 }
1409
1410 struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
1411 {
1412         struct isl_set *set;
1413
1414         if (!dim)
1415                 return NULL;
1416         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
1417         isl_assert(dim->ctx, n >= 0, return NULL);
1418         set = isl_alloc(dim->ctx, struct isl_set,
1419                         sizeof(struct isl_set) +
1420                         n * sizeof(struct isl_basic_set *));
1421         if (!set)
1422                 goto error;
1423
1424         set->ctx = dim->ctx;
1425         isl_ctx_ref(set->ctx);
1426         set->ref = 1;
1427         set->size = n;
1428         set->n = 0;
1429         set->dim = dim;
1430         set->flags = flags;
1431         return set;
1432 error:
1433         isl_dim_free(dim);
1434         return NULL;
1435 }
1436
1437 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
1438                 unsigned nparam, unsigned dim, int n, unsigned flags)
1439 {
1440         struct isl_set *set;
1441         struct isl_dim *dims;
1442
1443         dims = isl_dim_alloc(ctx, nparam, 0, dim);
1444         if (!dims)
1445                 return NULL;
1446
1447         set = isl_set_alloc_dim(dims, n, flags);
1448         return set;
1449 }
1450
1451 /* Make sure "map" has room for at least "n" more basic maps.
1452  */
1453 struct isl_map *isl_map_grow(struct isl_map *map, int n)
1454 {
1455         int i;
1456         struct isl_map *grown = NULL;
1457
1458         if (!map)
1459                 return NULL;
1460         isl_assert(map->ctx, n >= 0, goto error);
1461         if (map->n + n <= map->size)
1462                 return map;
1463         grown = isl_map_alloc_dim(isl_map_get_dim(map), map->n + n, map->flags);
1464         if (!grown)
1465                 goto error;
1466         for (i = 0; i < map->n; ++i) {
1467                 grown->p[i] = isl_basic_map_copy(map->p[i]);
1468                 if (!grown->p[i])
1469                         goto error;
1470                 grown->n++;
1471         }
1472         isl_map_free(map);
1473         return grown;
1474 error:
1475         isl_map_free(grown);
1476         isl_map_free(map);
1477         return NULL;
1478 }
1479
1480 /* Make sure "set" has room for at least "n" more basic sets.
1481  */
1482 struct isl_set *isl_set_grow(struct isl_set *set, int n)
1483 {
1484         return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
1485 }
1486
1487 struct isl_set *isl_set_dup(struct isl_set *set)
1488 {
1489         int i;
1490         struct isl_set *dup;
1491
1492         if (!set)
1493                 return NULL;
1494
1495         dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
1496         if (!dup)
1497                 return NULL;
1498         for (i = 0; i < set->n; ++i)
1499                 dup = isl_set_add(dup, isl_basic_set_copy(set->p[i]));
1500         return dup;
1501 }
1502
1503 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
1504 {
1505         struct isl_set *set;
1506
1507         if (!bset)
1508                 return NULL;
1509
1510         set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
1511         if (!set) {
1512                 isl_basic_set_free(bset);
1513                 return NULL;
1514         }
1515         return isl_set_add(set, bset);
1516 }
1517
1518 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
1519 {
1520         struct isl_map *map;
1521
1522         if (!bmap)
1523                 return NULL;
1524
1525         map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
1526         if (!map) {
1527                 isl_basic_map_free(bmap);
1528                 return NULL;
1529         }
1530         return isl_map_add(map, bmap);
1531 }
1532
1533 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
1534 {
1535         return (struct isl_set *)isl_map_add((struct isl_map *)set,
1536                                                 (struct isl_basic_map *)bset);
1537 }
1538
1539 void isl_set_free(struct isl_set *set)
1540 {
1541         int i;
1542
1543         if (!set)
1544                 return;
1545
1546         if (--set->ref > 0)
1547                 return;
1548
1549         isl_ctx_deref(set->ctx);
1550         for (i = 0; i < set->n; ++i)
1551                 isl_basic_set_free(set->p[i]);
1552         isl_dim_free(set->dim);
1553         free(set);
1554 }
1555
1556 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
1557 {
1558         int i;
1559
1560         if (!set) {
1561                 fprintf(out, "null set\n");
1562                 return;
1563         }
1564
1565         fprintf(out, "%*s", indent, "");
1566         fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
1567                         set->ref, set->n, set->dim->nparam, set->dim->n_out,
1568                         set->flags);
1569         for (i = 0; i < set->n; ++i) {
1570                 fprintf(out, "%*s", indent, "");
1571                 fprintf(out, "basic set %d:\n", i);
1572                 isl_basic_set_dump(set->p[i], out, indent+4);
1573         }
1574 }
1575
1576 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
1577 {
1578         int i;
1579
1580         if (!map) {
1581                 fprintf(out, "null map\n");
1582                 return;
1583         }
1584
1585         fprintf(out, "%*s", indent, "");
1586         fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
1587                      "flags: %x, n_name: %d\n",
1588                         map->ref, map->n, map->dim->nparam, map->dim->n_in,
1589                         map->dim->n_out, map->flags, map->dim->n_name);
1590         for (i = 0; i < map->n; ++i) {
1591                 fprintf(out, "%*s", indent, "");
1592                 fprintf(out, "basic map %d:\n", i);
1593                 isl_basic_map_dump(map->p[i], out, indent+4);
1594         }
1595 }
1596
1597 struct isl_basic_map *isl_basic_map_intersect_domain(
1598                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1599 {
1600         struct isl_basic_map *bmap_domain;
1601         struct isl_dim *dim;
1602
1603         if (!bmap || !bset)
1604                 goto error;
1605
1606         isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
1607                                         bset->dim, isl_dim_param), goto error);
1608
1609         if (isl_dim_size(bset->dim, isl_dim_set) != 0)
1610                 isl_assert(bset->ctx,
1611                     isl_basic_map_compatible_domain(bmap, bset), goto error);
1612
1613         bmap = isl_basic_map_cow(bmap);
1614         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
1615                         bset->n_div, bset->n_eq, bset->n_ineq);
1616         if (!bmap)
1617                 goto error;
1618         dim = isl_dim_reverse(isl_dim_copy(bset->dim));
1619         bmap_domain = isl_basic_map_from_basic_set(bset, dim);
1620         bmap = add_constraints(bmap, bmap_domain, 0, 0);
1621
1622         bmap = isl_basic_map_simplify(bmap);
1623         return isl_basic_map_finalize(bmap);
1624 error:
1625         isl_basic_map_free(bmap);
1626         isl_basic_set_free(bset);
1627         return NULL;
1628 }
1629
1630 struct isl_basic_map *isl_basic_map_intersect_range(
1631                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1632 {
1633         struct isl_basic_map *bmap_range;
1634
1635         if (!bmap || !bset)
1636                 goto error;
1637
1638         isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
1639                                         bset->dim, isl_dim_param), goto error);
1640
1641         if (isl_dim_size(bset->dim, isl_dim_set) != 0)
1642                 isl_assert(bset->ctx,
1643                     isl_basic_map_compatible_range(bmap, bset), goto error);
1644
1645         bmap = isl_basic_map_cow(bmap);
1646         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
1647                         bset->n_div, bset->n_eq, bset->n_ineq);
1648         if (!bmap)
1649                 goto error;
1650         bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
1651         bmap = add_constraints(bmap, bmap_range, 0, 0);
1652
1653         bmap = isl_basic_map_simplify(bmap);
1654         return isl_basic_map_finalize(bmap);
1655 error:
1656         isl_basic_map_free(bmap);
1657         isl_basic_set_free(bset);
1658         return NULL;
1659 }
1660
1661 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
1662 {
1663         int i;
1664         unsigned total;
1665         isl_int s;
1666
1667         total = 1 + isl_basic_map_total_dim(bmap);
1668         if (total != vec->size)
1669                 return -1;
1670
1671         isl_int_init(s);
1672
1673         for (i = 0; i < bmap->n_eq; ++i) {
1674                 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
1675                 if (!isl_int_is_zero(s)) {
1676                         isl_int_clear(s);
1677                         return 0;
1678                 }
1679         }
1680
1681         for (i = 0; i < bmap->n_ineq; ++i) {
1682                 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
1683                 if (isl_int_is_neg(s)) {
1684                         isl_int_clear(s);
1685                         return 0;
1686                 }
1687         }
1688
1689         isl_int_clear(s);
1690
1691         return 1;
1692 }
1693
1694 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
1695 {
1696         return basic_map_contains((struct isl_basic_map *)bset, vec);
1697 }
1698
1699 struct isl_basic_map *isl_basic_map_intersect(
1700                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1701 {
1702         struct isl_vec *sample = NULL;
1703
1704         if (!bmap1 || !bmap2)
1705                 goto error;
1706
1707         isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
1708                                      bmap2->dim, isl_dim_param), goto error);
1709         if (isl_dim_total(bmap1->dim) ==
1710                                 isl_dim_size(bmap1->dim, isl_dim_param) &&
1711             isl_dim_total(bmap2->dim) !=
1712                                 isl_dim_size(bmap2->dim, isl_dim_param))
1713                 return isl_basic_map_intersect(bmap2, bmap1);
1714
1715         if (isl_dim_total(bmap2->dim) !=
1716                                         isl_dim_size(bmap2->dim, isl_dim_param))
1717                 isl_assert(bmap1->ctx,
1718                             isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
1719
1720         if (bmap1->sample &&
1721             basic_map_contains(bmap1, bmap1->sample) > 0 &&
1722             basic_map_contains(bmap2, bmap1->sample) > 0)
1723                 sample = isl_vec_copy(bmap1->sample);
1724         else if (bmap2->sample &&
1725             basic_map_contains(bmap1, bmap2->sample) > 0 &&
1726             basic_map_contains(bmap2, bmap2->sample) > 0)
1727                 sample = isl_vec_copy(bmap2->sample);
1728
1729         bmap1 = isl_basic_map_cow(bmap1);
1730         bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
1731                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
1732         if (!bmap1)
1733                 goto error;
1734         bmap1 = add_constraints(bmap1, bmap2, 0, 0);
1735
1736         if (sample) {
1737                 isl_vec_free(bmap1->sample);
1738                 bmap1->sample = sample;
1739         }
1740
1741         bmap1 = isl_basic_map_simplify(bmap1);
1742         return isl_basic_map_finalize(bmap1);
1743 error:
1744         if (sample)
1745                 isl_vec_free(sample);
1746         isl_basic_map_free(bmap1);
1747         isl_basic_map_free(bmap2);
1748         return NULL;
1749 }
1750
1751 struct isl_basic_set *isl_basic_set_intersect(
1752                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1753 {
1754         return (struct isl_basic_set *)
1755                 isl_basic_map_intersect(
1756                         (struct isl_basic_map *)bset1,
1757                         (struct isl_basic_map *)bset2);
1758 }
1759
1760 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
1761 {
1762         unsigned flags = 0;
1763         struct isl_map *result;
1764         int i, j;
1765
1766         if (!map1 || !map2)
1767                 goto error;
1768
1769         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
1770                                          map2->dim, isl_dim_param), goto error);
1771         if (isl_dim_total(map1->dim) ==
1772                                 isl_dim_size(map1->dim, isl_dim_param) &&
1773             isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
1774                 return isl_map_intersect(map2, map1);
1775
1776         if (isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
1777                 isl_assert(map1->ctx,
1778                             isl_dim_equal(map1->dim, map2->dim), goto error);
1779
1780         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
1781             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
1782                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
1783
1784         result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
1785                                 map1->n * map2->n, flags);
1786         if (!result)
1787                 goto error;
1788         for (i = 0; i < map1->n; ++i)
1789                 for (j = 0; j < map2->n; ++j) {
1790                         struct isl_basic_map *part;
1791                         part = isl_basic_map_intersect(
1792                                     isl_basic_map_copy(map1->p[i]),
1793                                     isl_basic_map_copy(map2->p[j]));
1794                         if (isl_basic_map_is_empty(part))
1795                                 isl_basic_map_free(part);
1796                         else
1797                                 result = isl_map_add(result, part);
1798                         if (!result)
1799                                 goto error;
1800                 }
1801         isl_map_free(map1);
1802         isl_map_free(map2);
1803         return result;
1804 error:
1805         isl_map_free(map1);
1806         isl_map_free(map2);
1807         return NULL;
1808 }
1809
1810 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
1811 {
1812         return (struct isl_set *)
1813                 isl_map_intersect((struct isl_map *)set1,
1814                                   (struct isl_map *)set2);
1815 }
1816
1817 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
1818 {
1819         struct isl_dim *dim;
1820         struct isl_basic_set *bset;
1821         unsigned in;
1822
1823         if (!bmap)
1824                 return NULL;
1825         bmap = isl_basic_map_cow(bmap);
1826         if (!bmap)
1827                 return NULL;
1828         dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
1829         in = isl_basic_map_n_in(bmap);
1830         bset = isl_basic_set_from_basic_map(bmap);
1831         bset = isl_basic_set_swap_vars(bset, in);
1832         return isl_basic_map_from_basic_set(bset, dim);
1833 }
1834
1835 /* Turn final n dimensions into existentially quantified variables.
1836  */
1837 struct isl_basic_set *isl_basic_set_project_out(
1838                 struct isl_basic_set *bset, unsigned n, unsigned flags)
1839 {
1840         int i;
1841         size_t row_size;
1842         isl_int **new_div;
1843         isl_int *old;
1844
1845         if (!bset)
1846                 return NULL;
1847
1848         isl_assert(bset->ctx, n <= isl_basic_set_n_dim(bset), goto error);
1849
1850         if (n == 0)
1851                 return bset;
1852
1853         bset = isl_basic_set_cow(bset);
1854
1855         row_size = 1 + isl_dim_total(bset->dim) + bset->extra;
1856         old = bset->block2.data;
1857         bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
1858                                         (bset->extra + n) * (1 + row_size));
1859         if (!bset->block2.data)
1860                 goto error;
1861         new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
1862         if (!new_div)
1863                 goto error;
1864         for (i = 0; i < n; ++i) {
1865                 new_div[i] = bset->block2.data +
1866                                 (bset->extra + i) * (1 + row_size);
1867                 isl_seq_clr(new_div[i], 1 + row_size);
1868         }
1869         for (i = 0; i < bset->extra; ++i)
1870                 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
1871         free(bset->div);
1872         bset->div = new_div;
1873         bset->n_div += n;
1874         bset->extra += n;
1875         bset->dim = isl_dim_drop_outputs(bset->dim,
1876                                             isl_basic_set_n_dim(bset) - n, n);
1877         if (!bset->dim)
1878                 goto error;
1879         bset = isl_basic_set_simplify(bset);
1880         bset = isl_basic_set_drop_redundant_divs(bset);
1881         return isl_basic_set_finalize(bset);
1882 error:
1883         isl_basic_set_free(bset);
1884         return NULL;
1885 }
1886
1887 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
1888 {
1889         int i, j;
1890
1891         for (i = 0; i < n; ++i) {
1892                 j = isl_basic_map_alloc_div(bmap);
1893                 if (j < 0)
1894                         goto error;
1895                 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
1896         }
1897         return bmap;
1898 error:
1899         isl_basic_map_free(bmap);
1900         return NULL;
1901 }
1902
1903 struct isl_basic_map *isl_basic_map_apply_range(
1904                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1905 {
1906         struct isl_dim *dim_result = NULL;
1907         struct isl_basic_map *bmap;
1908         unsigned n_in, n_out, n, nparam, total, pos;
1909         struct isl_dim_map *dim_map1, *dim_map2;
1910
1911         if (!bmap1 || !bmap2)
1912                 goto error;
1913
1914         dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
1915                                   isl_dim_copy(bmap2->dim));
1916
1917         n_in = isl_basic_map_n_in(bmap1);
1918         n_out = isl_basic_map_n_out(bmap2);
1919         n = isl_basic_map_n_out(bmap1);
1920         nparam = isl_basic_map_n_param(bmap1);
1921
1922         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
1923         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
1924         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
1925         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
1926         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
1927         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
1928         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
1929         isl_dim_map_div(dim_map1, bmap1, pos += n_out);
1930         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
1931         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
1932         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
1933
1934         bmap = isl_basic_map_alloc_dim(dim_result,
1935                         bmap1->n_div + bmap2->n_div + n,
1936                         bmap1->n_eq + bmap2->n_eq,
1937                         bmap1->n_ineq + bmap2->n_ineq);
1938         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
1939         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
1940         bmap = add_divs(bmap, n);
1941         bmap = isl_basic_map_simplify(bmap);
1942         bmap = isl_basic_map_drop_redundant_divs(bmap);
1943         return isl_basic_map_finalize(bmap);
1944 error:
1945         isl_basic_map_free(bmap1);
1946         isl_basic_map_free(bmap2);
1947         return NULL;
1948 }
1949
1950 struct isl_basic_set *isl_basic_set_apply(
1951                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1952 {
1953         if (!bset || !bmap)
1954                 goto error;
1955
1956         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
1957                     goto error);
1958
1959         return (struct isl_basic_set *)
1960                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1961 error:
1962         isl_basic_set_free(bset);
1963         isl_basic_map_free(bmap);
1964         return NULL;
1965 }
1966
1967 struct isl_basic_map *isl_basic_map_apply_domain(
1968                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1969 {
1970         if (!bmap1 || !bmap2)
1971                 goto error;
1972
1973         isl_assert(ctx,
1974             isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
1975         isl_assert(ctx,
1976             isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
1977             goto error);
1978
1979         bmap1 = isl_basic_map_reverse(bmap1);
1980         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1981         return isl_basic_map_reverse(bmap1);
1982 error:
1983         isl_basic_map_free(bmap1);
1984         isl_basic_map_free(bmap2);
1985         return NULL;
1986 }
1987
1988 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
1989  * A \cap B -> f(A) + f(B)
1990  */
1991 struct isl_basic_map *isl_basic_map_sum(
1992                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1993 {
1994         unsigned n_in, n_out, nparam, total, pos;
1995         struct isl_basic_map *bmap = NULL;
1996         struct isl_dim_map *dim_map1, *dim_map2;
1997         int i;
1998
1999         if (!bmap1 || !bmap2)
2000                 goto error;
2001
2002         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
2003                 goto error);
2004
2005         nparam = isl_basic_map_n_param(bmap1);
2006         n_in = isl_basic_map_n_in(bmap1);
2007         n_out = isl_basic_map_n_out(bmap1);
2008
2009         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
2010         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
2011         dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
2012         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
2013         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
2014         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
2015         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
2016         isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
2017         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
2018         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
2019         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
2020
2021         bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
2022                         bmap1->n_div + bmap2->n_div + 2 * n_out,
2023                         bmap1->n_eq + bmap2->n_eq + n_out,
2024                         bmap1->n_ineq + bmap2->n_ineq);
2025         for (i = 0; i < n_out; ++i) {
2026                 int j = isl_basic_map_alloc_equality(bmap);
2027                 if (j < 0)
2028                         goto error;
2029                 isl_seq_clr(bmap->eq[j], 1+total);
2030                 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
2031                 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
2032                 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
2033         }
2034         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
2035         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
2036         bmap = add_divs(bmap, 2 * n_out);
2037
2038         bmap = isl_basic_map_simplify(bmap);
2039         return isl_basic_map_finalize(bmap);
2040 error:
2041         isl_basic_map_free(bmap);
2042         isl_basic_map_free(bmap1);
2043         isl_basic_map_free(bmap2);
2044         return NULL;
2045 }
2046
2047 /* Given a basic map A -> f(A), construct A -> -f(A).
2048  */
2049 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
2050 {
2051         int i, j;
2052         unsigned off, n;
2053
2054         bmap = isl_basic_map_cow(bmap);
2055         if (!bmap)
2056                 return NULL;
2057
2058         n = isl_basic_map_dim(bmap, isl_dim_out);
2059         off = isl_basic_map_offset(bmap, isl_dim_out);
2060         for (i = 0; i < bmap->n_eq; ++i)
2061                 for (j = 0; j < n; ++j)
2062                         isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
2063         for (i = 0; i < bmap->n_ineq; ++i)
2064                 for (j = 0; j < n; ++j)
2065                         isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
2066         for (i = 0; i < bmap->n_div; ++i)
2067                 for (j = 0; j < n; ++j)
2068                         isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
2069         return isl_basic_map_finalize(bmap);
2070 }
2071
2072 /* Given a basic map A -> f(A) and an integer d, construct a basic map
2073  * A -> floor(f(A)/d).
2074  */
2075 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
2076                 isl_int d)
2077 {
2078         unsigned n_in, n_out, nparam, total, pos;
2079         struct isl_basic_map *result = NULL;
2080         struct isl_dim_map *dim_map;
2081         int i;
2082
2083         if (!bmap)
2084                 return NULL;
2085
2086         nparam = isl_basic_map_n_param(bmap);
2087         n_in = isl_basic_map_n_in(bmap);
2088         n_out = isl_basic_map_n_out(bmap);
2089
2090         total = nparam + n_in + n_out + bmap->n_div + n_out;
2091         dim_map = isl_dim_map_alloc(bmap->ctx, total);
2092         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
2093         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
2094         isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
2095         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
2096
2097         result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
2098                         bmap->n_div + n_out,
2099                         bmap->n_eq, bmap->n_ineq + 2 * n_out);
2100         result = add_constraints_dim_map(result, bmap, dim_map);
2101         result = add_divs(result, n_out);
2102         for (i = 0; i < n_out; ++i) {
2103                 int j;
2104                 j = isl_basic_map_alloc_inequality(result);
2105                 if (j < 0)
2106                         goto error;
2107                 isl_seq_clr(result->ineq[j], 1+total);
2108                 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
2109                 isl_int_set_si(result->ineq[j][1+pos+i], 1);
2110                 j = isl_basic_map_alloc_inequality(result);
2111                 if (j < 0)
2112                         goto error;
2113                 isl_seq_clr(result->ineq[j], 1+total);
2114                 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
2115                 isl_int_set_si(result->ineq[j][1+pos+i], -1);
2116                 isl_int_sub_ui(result->ineq[j][0], d, 1);
2117         }
2118
2119         result = isl_basic_map_simplify(result);
2120         return isl_basic_map_finalize(result);
2121 error:
2122         isl_basic_map_free(result);
2123         return NULL;
2124 }
2125
2126 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
2127 {
2128         int i;
2129         unsigned nparam;
2130         unsigned n_in;
2131
2132         i = isl_basic_map_alloc_equality(bmap);
2133         if (i < 0)
2134                 goto error;
2135         nparam = isl_basic_map_n_param(bmap);
2136         n_in = isl_basic_map_n_in(bmap);
2137         isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
2138         isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
2139         isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
2140         return isl_basic_map_finalize(bmap);
2141 error:
2142         isl_basic_map_free(bmap);
2143         return NULL;
2144 }
2145
2146 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
2147 {
2148         int i;
2149         unsigned nparam;
2150         unsigned n_in;
2151
2152         i = isl_basic_map_alloc_inequality(bmap);
2153         if (i < 0)
2154                 goto error;
2155         nparam = isl_basic_map_n_param(bmap);
2156         n_in = isl_basic_map_n_in(bmap);
2157         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2158         isl_int_set_si(bmap->ineq[i][0], -1);
2159         isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
2160         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
2161         return isl_basic_map_finalize(bmap);
2162 error:
2163         isl_basic_map_free(bmap);
2164         return NULL;
2165 }
2166
2167 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
2168 {
2169         int i;
2170         unsigned nparam;
2171         unsigned n_in;
2172
2173         i = isl_basic_map_alloc_inequality(bmap);
2174         if (i < 0)
2175                 goto error;
2176         nparam = isl_basic_map_n_param(bmap);
2177         n_in = isl_basic_map_n_in(bmap);
2178         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2179         isl_int_set_si(bmap->ineq[i][0], -1);
2180         isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
2181         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
2182         return isl_basic_map_finalize(bmap);
2183 error:
2184         isl_basic_map_free(bmap);
2185         return NULL;
2186 }
2187
2188 struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
2189 {
2190         int i;
2191         struct isl_basic_map *bmap;
2192         bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
2193         if (!bmap)
2194                 return NULL;
2195         for (i = 0; i < n_equal && bmap; ++i)
2196                 bmap = var_equal(bmap, i);
2197         return isl_basic_map_finalize(bmap);
2198 }
2199
2200 struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
2201 {
2202         int i;
2203         struct isl_basic_map *bmap;
2204         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2205         if (!bmap)
2206                 return NULL;
2207         for (i = 0; i < pos && bmap; ++i)
2208                 bmap = var_equal(bmap, i);
2209         if (bmap)
2210                 bmap = var_less(bmap, pos);
2211         return isl_basic_map_finalize(bmap);
2212 }
2213
2214 struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
2215 {
2216         int i;
2217         struct isl_basic_map *bmap;
2218         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2219         if (!bmap)
2220                 return NULL;
2221         for (i = 0; i < pos && bmap; ++i)
2222                 bmap = var_equal(bmap, i);
2223         if (bmap)
2224                 bmap = var_more(bmap, pos);
2225         return isl_basic_map_finalize(bmap);
2226 }
2227
2228 struct isl_basic_map *isl_basic_map_from_basic_set(
2229                 struct isl_basic_set *bset, struct isl_dim *dim)
2230 {
2231         struct isl_basic_map *bmap;
2232
2233         bset = isl_basic_set_cow(bset);
2234         if (!bset || !dim)
2235                 goto error;
2236
2237         isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
2238         isl_dim_free(bset->dim);
2239         bmap = (struct isl_basic_map *) bset;
2240         bmap->dim = dim;
2241         return isl_basic_map_finalize(bmap);
2242 error:
2243         isl_basic_set_free(bset);
2244         isl_dim_free(dim);
2245         return NULL;
2246 }
2247
2248 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2249 {
2250         if (!bmap)
2251                 goto error;
2252         if (bmap->dim->n_in == 0)
2253                 return (struct isl_basic_set *)bmap;
2254         bmap = isl_basic_map_cow(bmap);
2255         if (!bmap)
2256                 goto error;
2257         bmap->dim = isl_dim_cow(bmap->dim);
2258         if (!bmap->dim)
2259                 goto error;
2260         bmap->dim->n_out += bmap->dim->n_in;
2261         bmap->dim->n_in = 0;
2262         bmap = isl_basic_map_finalize(bmap);
2263         return (struct isl_basic_set *)bmap;
2264 error:
2265         isl_basic_map_free(bmap);
2266         return NULL;
2267 }
2268
2269 /* For a div d = floor(f/m), add the constraints
2270  *
2271  *              f - m d >= 0
2272  *              -(f-(n-1)) + m d >= 0
2273  *
2274  * Note that the second constraint is the negation of
2275  *
2276  *              f - m d >= n
2277  */
2278 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2279 {
2280         int i, j;
2281         unsigned total = isl_basic_map_total_dim(bmap);
2282         unsigned div_pos = 1 + total - bmap->n_div + div;
2283
2284         i = isl_basic_map_alloc_inequality(bmap);
2285         if (i < 0)
2286                 return -1;
2287         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2288         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2289
2290         j = isl_basic_map_alloc_inequality(bmap);
2291         if (j < 0)
2292                 return -1;
2293         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2294         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2295         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2296         return j;
2297 }
2298
2299 struct isl_basic_set *isl_basic_map_underlying_set(
2300                 struct isl_basic_map *bmap)
2301 {
2302         if (!bmap)
2303                 goto error;
2304         if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
2305                 return (struct isl_basic_set *)bmap;
2306         bmap = isl_basic_map_cow(bmap);
2307         if (!bmap)
2308                 goto error;
2309         bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
2310         if (!bmap->dim)
2311                 goto error;
2312         bmap->extra -= bmap->n_div;
2313         bmap->n_div = 0;
2314         bmap = isl_basic_map_finalize(bmap);
2315         return (struct isl_basic_set *)bmap;
2316 error:
2317         return NULL;
2318 }
2319
2320 struct isl_basic_map *isl_basic_map_overlying_set(
2321         struct isl_basic_set *bset, struct isl_basic_map *like)
2322 {
2323         struct isl_basic_map *bmap;
2324         struct isl_ctx *ctx;
2325         unsigned total;
2326         int i;
2327
2328         if (!bset || !like)
2329                 goto error;
2330         ctx = bset->ctx;
2331         isl_assert(ctx, bset->n_div == 0, goto error);
2332         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
2333         isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
2334                         goto error);
2335         if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
2336                 isl_basic_map_free(like);
2337                 return (struct isl_basic_map *)bset;
2338         }
2339         bset = isl_basic_set_cow(bset);
2340         if (!bset)
2341                 goto error;
2342         total = bset->dim->n_out + bset->extra;
2343         bmap = (struct isl_basic_map *)bset;
2344         isl_dim_free(bmap->dim);
2345         bmap->dim = isl_dim_copy(like->dim);
2346         if (!bmap->dim)
2347                 goto error;
2348         bmap->n_div = like->n_div;
2349         bmap->extra += like->n_div;
2350         if (bmap->extra) {
2351                 unsigned ltotal;
2352                 ltotal = total - bmap->extra + like->extra;
2353                 if (ltotal > total)
2354                         ltotal = total;
2355                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2356                                         bmap->extra * (1 + 1 + total));
2357                 if (isl_blk_is_error(bmap->block2))
2358                         goto error;
2359                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2360                                                 bmap->extra);
2361                 if (!bmap->div)
2362                         goto error;
2363                 for (i = 0; i < bmap->extra; ++i)
2364                         bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
2365                 for (i = 0; i < like->n_div; ++i) {
2366                         isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
2367                         isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
2368                 }
2369                 bmap = isl_basic_map_extend_constraints(bmap,
2370                                                         0, 2 * like->n_div);
2371                 for (i = 0; i < like->n_div; ++i) {
2372                         if (isl_int_is_zero(bmap->div[i][0]))
2373                                 continue;
2374                         if (add_div_constraints(bmap, i) < 0)
2375                                 goto error;
2376                 }
2377         }
2378         isl_basic_map_free(like);
2379         bmap = isl_basic_map_simplify(bmap);
2380         bmap = isl_basic_map_finalize(bmap);
2381         return bmap;
2382 error:
2383         isl_basic_map_free(like);
2384         isl_basic_set_free(bset);
2385         return NULL;
2386 }
2387
2388 struct isl_basic_set *isl_basic_set_from_underlying_set(
2389         struct isl_basic_set *bset, struct isl_basic_set *like)
2390 {
2391         return (struct isl_basic_set *)
2392                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2393 }
2394
2395 struct isl_set *isl_set_from_underlying_set(
2396         struct isl_set *set, struct isl_basic_set *like)
2397 {
2398         int i;
2399
2400         if (!set || !like)
2401                 goto error;
2402         isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
2403                     goto error);
2404         if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
2405                 isl_basic_set_free(like);
2406                 return set;
2407         }
2408         set = isl_set_cow(set);
2409         if (!set)
2410                 goto error;
2411         for (i = 0; i < set->n; ++i) {
2412                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2413                                                       isl_basic_set_copy(like));
2414                 if (!set->p[i])
2415                         goto error;
2416         }
2417         isl_dim_free(set->dim);
2418         set->dim = isl_dim_copy(like->dim);
2419         if (!set->dim)
2420                 goto error;
2421         isl_basic_set_free(like);
2422         return set;
2423 error:
2424         isl_basic_set_free(like);
2425         isl_set_free(set);
2426         return NULL;
2427 }
2428
2429 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2430 {
2431         int i;
2432
2433         map = isl_map_cow(map);
2434         if (!map)
2435                 return NULL;
2436         map->dim = isl_dim_cow(map->dim);
2437         if (!map->dim)
2438                 goto error;
2439
2440         for (i = 1; i < map->n; ++i)
2441                 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
2442                                 goto error);
2443         for (i = 0; i < map->n; ++i) {
2444                 map->p[i] = (struct isl_basic_map *)
2445                                 isl_basic_map_underlying_set(map->p[i]);
2446                 if (!map->p[i])
2447                         goto error;
2448         }
2449         if (map->n == 0)
2450                 map->dim = isl_dim_underlying(map->dim, 0);
2451         else {
2452                 isl_dim_free(map->dim);
2453                 map->dim = isl_dim_copy(map->p[0]->dim);
2454         }
2455         if (!map->dim)
2456                 goto error;
2457         return (struct isl_set *)map;
2458 error:
2459         isl_map_free(map);
2460         return NULL;
2461 }
2462
2463 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2464 {
2465         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2466 }
2467
2468 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2469 {
2470         struct isl_basic_set *domain;
2471         unsigned n_out;
2472         if (!bmap)
2473                 return NULL;
2474         n_out = isl_basic_map_n_out(bmap);
2475         domain = isl_basic_set_from_basic_map(bmap);
2476         return isl_basic_set_project_out(domain, n_out, 0);
2477 }
2478
2479 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2480 {
2481         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2482 }
2483
2484 struct isl_set *isl_map_range(struct isl_map *map)
2485 {
2486         int i;
2487         struct isl_set *set;
2488
2489         if (!map)
2490                 goto error;
2491         map = isl_map_cow(map);
2492         if (!map)
2493                 goto error;
2494
2495         set = (struct isl_set *) map;
2496         if (set->dim->n_in != 0) {
2497                 set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
2498                 if (!set->dim)
2499                         goto error;
2500         }
2501         for (i = 0; i < map->n; ++i) {
2502                 set->p[i] = isl_basic_map_range(map->p[i]);
2503                 if (!set->p[i])
2504                         goto error;
2505         }
2506         ISL_F_CLR(set, ISL_MAP_DISJOINT);
2507         ISL_F_CLR(set, ISL_SET_NORMALIZED);
2508         return set;
2509 error:
2510         isl_map_free(map);
2511         return NULL;
2512 }
2513
2514 struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
2515 {
2516         int i;
2517         struct isl_map *map = NULL;
2518
2519         set = isl_set_cow(set);
2520         if (!set || !dim)
2521                 goto error;
2522         isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
2523         map = (struct isl_map *)set;
2524         for (i = 0; i < set->n; ++i) {
2525                 map->p[i] = isl_basic_map_from_basic_set(
2526                                 set->p[i], isl_dim_copy(dim));
2527                 if (!map->p[i])
2528                         goto error;
2529         }
2530         isl_dim_free(map->dim);
2531         map->dim = dim;
2532         return map;
2533 error:
2534         isl_dim_free(dim);
2535         isl_set_free(set);
2536         return NULL;
2537 }
2538
2539 struct isl_map *isl_map_from_range(struct isl_set *set)
2540 {
2541         return (struct isl_map *)set;
2542 }
2543
2544 struct isl_set *isl_set_from_map(struct isl_map *map)
2545 {
2546         int i;
2547         struct isl_set *set = NULL;
2548
2549         if (!map)
2550                 return NULL;
2551         map = isl_map_cow(map);
2552         if (!map)
2553                 return NULL;
2554         map->dim = isl_dim_cow(map->dim);
2555         if (!map->dim)
2556                 goto error;
2557         map->dim->n_out += map->dim->n_in;
2558         map->dim->n_in = 0;
2559         set = (struct isl_set *)map;
2560         for (i = 0; i < map->n; ++i) {
2561                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2562                 if (!set->p[i])
2563                         goto error;
2564         }
2565         return set;
2566 error:
2567         isl_map_free(map);
2568         return NULL;
2569 }
2570
2571 struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
2572 {
2573         struct isl_map *map;
2574
2575         if (!dim)
2576                 return NULL;
2577         isl_assert(dim->ctx, n >= 0, return NULL);
2578         map = isl_alloc(dim->ctx, struct isl_map,
2579                         sizeof(struct isl_map) +
2580                         n * sizeof(struct isl_basic_map *));
2581         if (!map)
2582                 goto error;
2583
2584         map->ctx = dim->ctx;
2585         isl_ctx_ref(map->ctx);
2586         map->ref = 1;
2587         map->size = n;
2588         map->n = 0;
2589         map->dim = dim;
2590         map->flags = flags;
2591         return map;
2592 error:
2593         isl_dim_free(dim);
2594         return NULL;
2595 }
2596
2597 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2598                 unsigned nparam, unsigned in, unsigned out, int n,
2599                 unsigned flags)
2600 {
2601         struct isl_map *map;
2602         struct isl_dim *dims;
2603
2604         dims = isl_dim_alloc(ctx, nparam, in, out);
2605         if (!dims)
2606                 return NULL;
2607
2608         map = isl_map_alloc_dim(dims, n, flags);
2609         return map;
2610 }
2611
2612 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2613                 unsigned nparam, unsigned in, unsigned out)
2614 {
2615         struct isl_basic_map *bmap;
2616         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2617         bmap = isl_basic_map_set_to_empty(bmap);
2618         return bmap;
2619 }
2620
2621 struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
2622 {
2623         struct isl_basic_set *bset;
2624         bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
2625         bset = isl_basic_set_set_to_empty(bset);
2626         return bset;
2627 }
2628
2629 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
2630 {
2631         struct isl_basic_map *bmap;
2632         if (!model)
2633                 return NULL;
2634         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2635         bmap = isl_basic_map_set_to_empty(bmap);
2636         return bmap;
2637 }
2638
2639 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
2640 {
2641         struct isl_basic_map *bmap;
2642         if (!model)
2643                 return NULL;
2644         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2645         bmap = isl_basic_map_set_to_empty(bmap);
2646         return bmap;
2647 }
2648
2649 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
2650 {
2651         struct isl_basic_set *bset;
2652         if (!model)
2653                 return NULL;
2654         bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2655         bset = isl_basic_set_set_to_empty(bset);
2656         return bset;
2657 }
2658
2659 struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
2660 {
2661         struct isl_basic_map *bmap;
2662         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
2663         return bmap;
2664 }
2665
2666 struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
2667 {
2668         struct isl_basic_set *bset;
2669         bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
2670         return bset;
2671 }
2672
2673 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
2674 {
2675         if (!model)
2676                 return NULL;
2677         return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
2678 }
2679
2680 struct isl_map *isl_map_empty(struct isl_dim *dim)
2681 {
2682         return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2683 }
2684
2685 struct isl_map *isl_map_empty_like(struct isl_map *model)
2686 {
2687         if (!model)
2688                 return NULL;
2689         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2690 }
2691
2692 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
2693 {
2694         if (!model)
2695                 return NULL;
2696         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2697 }
2698
2699 struct isl_set *isl_set_empty(struct isl_dim *dim)
2700 {
2701         return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2702 }
2703
2704 struct isl_set *isl_set_empty_like(struct isl_set *model)
2705 {
2706         if (!model)
2707                 return NULL;
2708         return isl_set_empty(isl_dim_copy(model->dim));
2709 }
2710
2711 struct isl_map *isl_map_universe(struct isl_dim *dim)
2712 {
2713         struct isl_map *map;
2714         if (!dim)
2715                 return NULL;
2716         map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2717         map = isl_map_add(map, isl_basic_map_universe(dim));
2718         return map;
2719 }
2720
2721 struct isl_set *isl_set_universe(struct isl_dim *dim)
2722 {
2723         struct isl_set *set;
2724         if (!dim)
2725                 return NULL;
2726         set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2727         set = isl_set_add(set, isl_basic_set_universe(dim));
2728         return set;
2729 }
2730
2731 struct isl_map *isl_map_dup(struct isl_map *map)
2732 {
2733         int i;
2734         struct isl_map *dup;
2735
2736         if (!map)
2737                 return NULL;
2738         dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
2739         for (i = 0; i < map->n; ++i)
2740                 dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
2741         return dup;
2742 }
2743
2744 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2745 {
2746         if (!bmap || !map)
2747                 goto error;
2748         if (isl_basic_map_fast_is_empty(bmap)) {
2749                 isl_basic_map_free(bmap);
2750                 return map;
2751         }
2752         isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
2753         isl_assert(map->ctx, map->n < map->size, goto error);
2754         map->p[map->n] = bmap;
2755         map->n++;
2756         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2757         return map;
2758 error:
2759         if (map)
2760                 isl_map_free(map);
2761         if (bmap)
2762                 isl_basic_map_free(bmap);
2763         return NULL;
2764 }
2765
2766 void isl_map_free(struct isl_map *map)
2767 {
2768         int i;
2769
2770         if (!map)
2771                 return;
2772
2773         if (--map->ref > 0)
2774                 return;
2775
2776         isl_ctx_deref(map->ctx);
2777         for (i = 0; i < map->n; ++i)
2778                 isl_basic_map_free(map->p[i]);
2779         isl_dim_free(map->dim);
2780         free(map);
2781 }
2782
2783 struct isl_map *isl_map_extend(struct isl_map *base,
2784                 unsigned nparam, unsigned n_in, unsigned n_out)
2785 {
2786         int i;
2787
2788         base = isl_map_cow(base);
2789         if (!base)
2790                 return NULL;
2791
2792         base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
2793         if (!base->dim)
2794                 goto error;
2795         for (i = 0; i < base->n; ++i) {
2796                 base->p[i] = isl_basic_map_extend_dim(base->p[i],
2797                                 isl_dim_copy(base->dim), 0, 0, 0);
2798                 if (!base->p[i])
2799                         goto error;
2800         }
2801         return base;
2802 error:
2803         isl_map_free(base);
2804         return NULL;
2805 }
2806
2807 struct isl_set *isl_set_extend(struct isl_set *base,
2808                 unsigned nparam, unsigned dim)
2809 {
2810         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2811                                                         nparam, 0, dim);
2812 }
2813
2814 static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
2815                 unsigned pos, int value)
2816 {
2817         int j;
2818
2819         bmap = isl_basic_map_cow(bmap);
2820         bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
2821         j = isl_basic_map_alloc_equality(bmap);
2822         if (j < 0)
2823                 goto error;
2824         isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
2825         isl_int_set_si(bmap->eq[j][pos], -1);
2826         isl_int_set_si(bmap->eq[j][0], value);
2827         bmap = isl_basic_map_simplify(bmap);
2828         return isl_basic_map_finalize(bmap);
2829 error:
2830         isl_basic_map_free(bmap);
2831         return NULL;
2832 }
2833
2834 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
2835                 enum isl_dim_type type, unsigned pos, int value)
2836 {
2837         if (!bmap)
2838                 return NULL;
2839         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
2840         return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
2841                                         value);
2842 error:
2843         isl_basic_map_free(bmap);
2844         return NULL;
2845 }
2846
2847 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
2848                 enum isl_dim_type type, unsigned pos, int value)
2849 {
2850         return (struct isl_basic_set *)
2851                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2852                                         type, pos, value);
2853 }
2854
2855 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2856                 unsigned input, int value)
2857 {
2858         return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
2859 }
2860
2861 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2862                 unsigned dim, int value)
2863 {
2864         return (struct isl_basic_set *)
2865                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2866                                         isl_dim_set, dim, value);
2867 }
2868
2869 struct isl_map *isl_map_fix_si(struct isl_map *map,
2870                 enum isl_dim_type type, unsigned pos, int value)
2871 {
2872         int i;
2873
2874         map = isl_map_cow(map);
2875         if (!map)
2876                 return NULL;
2877
2878         isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
2879         for (i = 0; i < map->n; ++i) {
2880                 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
2881                 if (!map->p[i])
2882                         goto error;
2883         }
2884         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2885         return map;
2886 error:
2887         isl_map_free(map);
2888         return NULL;
2889 }
2890
2891 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2892                 unsigned input, int value)
2893 {
2894         return isl_map_fix_si(map, isl_dim_in, input, value);
2895 }
2896
2897 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2898 {
2899         return (struct isl_set *)
2900                 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
2901 }
2902
2903 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
2904         unsigned dim, isl_int value)
2905 {
2906         int j;
2907         unsigned nparam;
2908
2909         bset = isl_basic_set_cow(bset);
2910         bset = isl_basic_set_extend_constraints(bset, 0, 1);
2911         j = isl_basic_set_alloc_inequality(bset);
2912         if (j < 0)
2913                 goto error;
2914         isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
2915         isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
2916         isl_int_neg(bset->ineq[j][0], value);
2917         bset = isl_basic_set_simplify(bset);
2918         return isl_basic_set_finalize(bset);
2919 error:
2920         isl_basic_set_free(bset);
2921         return NULL;
2922 }
2923
2924 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
2925                                         isl_int value)
2926 {
2927         int i;
2928
2929         set = isl_set_cow(set);
2930         if (!set)
2931                 return NULL;
2932
2933         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
2934         for (i = 0; i < set->n; ++i) {
2935                 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
2936                 if (!set->p[i])
2937                         goto error;
2938         }
2939         return set;
2940 error:
2941         isl_set_free(set);
2942         return NULL;
2943 }
2944
2945 struct isl_map *isl_map_reverse(struct isl_map *map)
2946 {
2947         int i;
2948         unsigned t;
2949
2950         map = isl_map_cow(map);
2951         if (!map)
2952                 return NULL;
2953
2954         map->dim = isl_dim_reverse(map->dim);
2955         if (!map->dim)
2956                 goto error;
2957         for (i = 0; i < map->n; ++i) {
2958                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2959                 if (!map->p[i])
2960                         goto error;
2961         }
2962         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2963         return map;
2964 error:
2965         isl_map_free(map);
2966         return NULL;
2967 }
2968
2969 static struct isl_map *isl_basic_map_partial_lexopt(
2970                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2971                 struct isl_set **empty, int max)
2972 {
2973         if (!bmap)
2974                 goto error;
2975         if (bmap->ctx->pip == ISL_PIP_PIP)
2976                 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
2977         else
2978                 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
2979 error:
2980         isl_basic_map_free(bmap);
2981         isl_basic_set_free(dom);
2982         if (empty)
2983                 *empty = NULL;
2984         return NULL;
2985 }
2986
2987 struct isl_map *isl_basic_map_partial_lexmax(
2988                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2989                 struct isl_set **empty)
2990 {
2991         return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
2992 }
2993
2994 struct isl_map *isl_basic_map_partial_lexmin(
2995                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2996                 struct isl_set **empty)
2997 {
2998         return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
2999 }
3000
3001 struct isl_set *isl_basic_set_partial_lexmin(
3002                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3003                 struct isl_set **empty)
3004 {
3005         return (struct isl_set *)
3006                 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
3007                         dom, empty);
3008 }
3009
3010 struct isl_set *isl_basic_set_partial_lexmax(
3011                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3012                 struct isl_set **empty)
3013 {
3014         return (struct isl_set *)
3015                 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
3016                         dom, empty);
3017 }
3018
3019 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
3020 {
3021         struct isl_basic_map *bmap = NULL;
3022         struct isl_basic_set *dom = NULL;
3023         struct isl_map *min;
3024         struct isl_dim *param_dim;
3025
3026         if (!bset)
3027                 goto error;
3028         bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
3029         if (!bmap)
3030                 goto error;
3031         param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3032         dom = isl_basic_set_universe(param_dim);
3033         if (!dom)
3034                 goto error;
3035         min = isl_basic_map_partial_lexmin(bmap, dom, NULL);
3036         return isl_map_range(min);
3037 error:
3038         isl_basic_map_free(bmap);
3039         return NULL;
3040 }
3041
3042 static struct isl_map *isl_map_reset_dim(struct isl_map *map,
3043         struct isl_dim *dim)
3044 {
3045         int i;
3046
3047         if (!map || !dim)
3048                 goto error;
3049
3050         for (i = 0; i < map->n; ++i) {
3051                 isl_dim_free(map->p[i]->dim);
3052                 map->p[i]->dim = isl_dim_copy(dim);
3053         }
3054         isl_dim_free(map->dim);
3055         map->dim = dim;
3056
3057         return map;
3058 error:
3059         isl_map_free(map);
3060         isl_dim_free(dim);
3061         return NULL;
3062 }
3063
3064 static struct isl_set *isl_set_reset_dim(struct isl_set *set,
3065         struct isl_dim *dim)
3066 {
3067         return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
3068 }
3069
3070 /* Apply a preimage specified by "mat" on the parameters of "bset".
3071  * bset is assumed to have only parameters and divs.
3072  */
3073 static struct isl_basic_set *basic_set_parameter_preimage(
3074         struct isl_basic_set *bset, struct isl_mat *mat)
3075 {
3076         unsigned nparam;
3077
3078         if (!bset || !mat)
3079                 goto error;
3080
3081         bset->dim = isl_dim_cow(bset->dim);
3082         if (!bset->dim)
3083                 goto error;
3084
3085         nparam = isl_basic_set_dim(bset, isl_dim_param);
3086
3087         isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
3088
3089         bset->dim->nparam = 0;
3090         bset->dim->n_out = nparam;
3091         bset = isl_basic_set_preimage(bset, mat);
3092         if (bset) {
3093                 bset->dim->nparam = bset->dim->n_out;
3094                 bset->dim->n_out = 0;
3095         }
3096         return bset;
3097 error:
3098         isl_mat_free(mat);
3099         isl_basic_set_free(bset);
3100         return NULL;
3101 }
3102
3103 /* Apply a preimage specified by "mat" on the parameters of "set".
3104  * set is assumed to have only parameters and divs.
3105  */
3106 static struct isl_set *set_parameter_preimage(
3107         struct isl_set *set, struct isl_mat *mat)
3108 {
3109         struct isl_dim *dim = NULL;
3110         unsigned nparam;
3111
3112         if (!set || !mat)
3113                 goto error;
3114
3115         dim = isl_dim_copy(set->dim);
3116         dim = isl_dim_cow(dim);
3117         if (!dim)
3118                 goto error;
3119
3120         nparam = isl_set_dim(set, isl_dim_param);
3121
3122         isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
3123
3124         dim->nparam = 0;
3125         dim->n_out = nparam;
3126         isl_set_reset_dim(set, dim);
3127         set = isl_set_preimage(set, mat);
3128         if (!set)
3129                 goto error2;
3130         dim = isl_dim_copy(set->dim);
3131         dim = isl_dim_cow(dim);
3132         if (!dim)
3133                 goto error2;
3134         dim->nparam = dim->n_out;
3135         dim->n_out = 0;
3136         isl_set_reset_dim(set, dim);
3137         return set;
3138 error:
3139         isl_dim_free(dim);
3140         isl_mat_free(mat);
3141 error2:
3142         isl_set_free(set);
3143         return NULL;
3144 }
3145
3146 /* Intersect the basic set "bset" with the affine space specified by the
3147  * equalities in "eq".
3148  */
3149 static struct isl_basic_set *basic_set_append_equalities(
3150         struct isl_basic_set *bset, struct isl_mat *eq)
3151 {
3152         int i, k;
3153         unsigned len;
3154
3155         if (!bset || !eq)
3156                 goto error;
3157
3158         bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
3159                                         eq->n_row, 0);
3160         if (!bset)
3161                 goto error;
3162
3163         len = 1 + isl_dim_total(bset->dim) + bset->extra;
3164         for (i = 0; i < eq->n_row; ++i) {
3165                 k = isl_basic_set_alloc_equality(bset);
3166                 if (k < 0)
3167                         goto error;
3168                 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
3169                 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
3170         }
3171         isl_mat_free(eq);
3172
3173         return bset;
3174 error:
3175         isl_mat_free(eq);
3176         isl_basic_set_free(bset);
3177         return NULL;
3178 }
3179
3180 /* Intersect the set "set" with the affine space specified by the
3181  * equalities in "eq".
3182  */
3183 static struct isl_set *set_append_equalities(struct isl_set *set,
3184         struct isl_mat *eq)
3185 {
3186         int i;
3187
3188         if (!set || !eq)
3189                 goto error;
3190
3191         for (i = 0; i < set->n; ++i) {
3192                 set->p[i] = basic_set_append_equalities(set->p[i],
3193                                         isl_mat_copy(eq));
3194                 if (!set->p[i])
3195                         goto error;
3196         }
3197         isl_mat_free(eq);
3198         return set;
3199 error:
3200         isl_mat_free(eq);
3201         isl_set_free(set);
3202         return NULL;
3203 }
3204
3205 /* Project the given basic set onto its parameter domain, possibly introducing
3206  * new, explicit, existential variables in the constraints.
3207  * The input has parameters and (possibly implicit) existential variables.
3208  * The output has the same parameters, but only
3209  * explicit existentially quantified variables.
3210  *
3211  * The actual projection is performed by pip, but pip doesn't seem
3212  * to like equalities very much, so we first remove the equalities
3213  * among the parameters by performing a variable compression on
3214  * the parameters.  Afterward, an inverse transformation is performed
3215  * and the equalities among the parameters are inserted back in.
3216  */
3217 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
3218 {
3219         int i, j;
3220         struct isl_mat *eq;
3221         struct isl_mat *T, *T2;
3222         struct isl_set *set;
3223         unsigned nparam, n_div;
3224
3225         bset = isl_basic_set_cow(bset);
3226         if (!bset)
3227                 return NULL;
3228
3229         if (bset->n_eq == 0)
3230                 return isl_basic_set_lexmin(bset);
3231
3232         isl_basic_set_gauss(bset, NULL);
3233
3234         nparam = isl_basic_set_dim(bset, isl_dim_param);
3235         n_div = isl_basic_set_dim(bset, isl_dim_div);
3236
3237         for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
3238                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
3239                         ++i;
3240         }
3241         if (i == bset->n_eq)
3242                 return isl_basic_set_lexmin(bset);
3243
3244         eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
3245                 0, 1 + nparam);
3246         eq = isl_mat_cow(eq);
3247         T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
3248         bset = basic_set_parameter_preimage(bset, T);
3249
3250         set = isl_basic_set_lexmin(bset);
3251         set = set_parameter_preimage(set, T2);
3252         set = set_append_equalities(set, eq);
3253         return set;
3254 }
3255
3256 /* Compute an explicit representation for all the existentially
3257  * quantified variables.
3258  * The input and output dimensions are first turned into parameters.
3259  * compute_divs then returns a map with the same parameters and
3260  * no input or output dimensions and the dimension specification
3261  * is reset to that of the input.
3262  */
3263 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
3264 {
3265         struct isl_basic_set *bset;
3266         struct isl_set *set;
3267         struct isl_map *map;
3268         struct isl_dim *dim, *orig_dim = NULL;
3269         unsigned         nparam;
3270         unsigned         n_in;
3271         unsigned         n_out;
3272
3273         bmap = isl_basic_map_cow(bmap);
3274         if (!bmap)
3275                 return NULL;
3276
3277         nparam = isl_basic_map_dim(bmap, isl_dim_param);
3278         n_in = isl_basic_map_dim(bmap, isl_dim_in);
3279         n_out = isl_basic_map_dim(bmap, isl_dim_out);
3280         dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
3281         if (!dim)
3282                 goto error;
3283
3284         orig_dim = bmap->dim;
3285         bmap->dim = dim;
3286         bset = (struct isl_basic_set *)bmap;
3287
3288         set = parameter_compute_divs(bset);
3289         map = (struct isl_map *)set;
3290         map = isl_map_reset_dim(map, orig_dim);
3291
3292         return map;
3293 error:
3294         isl_basic_map_free(bmap);
3295         return NULL;
3296 }
3297
3298 /* If bmap contains any unknown divs, then compute explicit
3299  * expressions for them.  However, this computation may be
3300  * quite expensive, so first try to remove divs that aren't
3301  * strictly needed.
3302  */
3303 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
3304 {
3305         int i;
3306         unsigned off;
3307
3308         if (!bmap)
3309                 return NULL;
3310         off = isl_dim_total(bmap->dim);
3311         for (i = 0; i < bmap->n_div; ++i) {
3312                 if (isl_int_is_zero(bmap->div[i][0]))
3313                         break;
3314                 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
3315                                 goto error);
3316         }
3317         if (i == bmap->n_div)
3318                 return isl_map_from_basic_map(bmap);
3319         bmap = isl_basic_map_drop_redundant_divs(bmap);
3320         if (!bmap)
3321                 goto error;
3322         for (i = 0; i < bmap->n_div; ++i)
3323                 if (isl_int_is_zero(bmap->div[i][0]))
3324                         break;
3325         if (i == bmap->n_div)
3326                 return isl_map_from_basic_map(bmap);
3327         struct isl_map *map = compute_divs(bmap);
3328         return map;
3329 error:
3330         isl_basic_map_free(bmap);
3331         return NULL;
3332 }
3333
3334 struct isl_map *isl_map_compute_divs(struct isl_map *map)
3335 {
3336         int i;
3337         struct isl_map *res;
3338
3339         if (!map)
3340                 return NULL;
3341         if (map->n == 0)
3342                 return map;
3343         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
3344         for (i = 1 ; i < map->n; ++i) {
3345                 struct isl_map *r2;
3346                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
3347                 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
3348                         res = isl_map_union_disjoint(res, r2);
3349                 else
3350                         res = isl_map_union(res, r2);
3351         }
3352         isl_map_free(map);
3353
3354         return res;
3355 }
3356
3357 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
3358 {
3359         return (struct isl_set *)
3360                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
3361 }
3362
3363 struct isl_set *isl_set_compute_divs(struct isl_set *set)
3364 {
3365         return (struct isl_set *)
3366                 isl_map_compute_divs((struct isl_map *)set);
3367 }
3368
3369 struct isl_set *isl_map_domain(struct isl_map *map)
3370 {
3371         int i;
3372         struct isl_set *set;
3373
3374         if (!map)
3375                 goto error;
3376
3377         map = isl_map_cow(map);
3378         if (!map)
3379                 return NULL;
3380
3381         set = (struct isl_set *)map;
3382         set->dim = isl_dim_domain(set->dim);
3383         if (!set->dim)
3384                 goto error;
3385         for (i = 0; i < map->n; ++i) {
3386                 set->p[i] = isl_basic_map_domain(map->p[i]);
3387                 if (!set->p[i])
3388                         goto error;
3389         }
3390         ISL_F_CLR(set, ISL_MAP_DISJOINT);
3391         ISL_F_CLR(set, ISL_SET_NORMALIZED);
3392         return set;
3393 error:
3394         isl_map_free(map);
3395         return NULL;
3396 }
3397
3398 struct isl_map *isl_map_union_disjoint(
3399                         struct isl_map *map1, struct isl_map *map2)
3400 {
3401         int i;
3402         unsigned flags = 0;
3403         struct isl_map *map = NULL;
3404
3405         if (!map1 || !map2)
3406                 goto error;
3407
3408         if (map1->n == 0) {
3409                 isl_map_free(map1);
3410                 return map2;
3411         }
3412         if (map2->n == 0) {
3413                 isl_map_free(map2);
3414                 return map1;
3415         }
3416
3417         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
3418
3419         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
3420             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
3421                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3422
3423         map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
3424                                 map1->n + map2->n, flags);
3425         if (!map)
3426                 goto error;
3427         for (i = 0; i < map1->n; ++i) {
3428                 map = isl_map_add(map,
3429                                   isl_basic_map_copy(map1->p[i]));
3430                 if (!map)
3431                         goto error;
3432         }
3433         for (i = 0; i < map2->n; ++i) {
3434                 map = isl_map_add(map,
3435                                   isl_basic_map_copy(map2->p[i]));
3436                 if (!map)
3437                         goto error;
3438         }
3439         isl_map_free(map1);
3440         isl_map_free(map2);
3441         return map;
3442 error:
3443         isl_map_free(map);
3444         isl_map_free(map1);
3445         isl_map_free(map2);
3446         return NULL;
3447 }
3448
3449 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
3450 {
3451         map1 = isl_map_union_disjoint(map1, map2);
3452         if (!map1)
3453                 return NULL;
3454         if (map1->n > 1)
3455                 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
3456         return map1;
3457 }
3458
3459 struct isl_set *isl_set_union_disjoint(
3460                         struct isl_set *set1, struct isl_set *set2)
3461 {
3462         return (struct isl_set *)
3463                 isl_map_union_disjoint(
3464                         (struct isl_map *)set1, (struct isl_map *)set2);
3465 }
3466
3467 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
3468 {
3469         return (struct isl_set *)
3470                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
3471 }
3472
3473 struct isl_map *isl_map_intersect_range(
3474                 struct isl_map *map, struct isl_set *set)
3475 {
3476         unsigned flags = 0;
3477         struct isl_map *result;
3478         int i, j;
3479
3480         if (!map || !set)
3481                 goto error;
3482
3483         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
3484             ISL_F_ISSET(set, ISL_MAP_DISJOINT))
3485                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3486
3487         result = isl_map_alloc_dim(isl_dim_copy(map->dim),
3488                                         map->n * set->n, flags);
3489         if (!result)
3490                 goto error;
3491         for (i = 0; i < map->n; ++i)
3492                 for (j = 0; j < set->n; ++j) {
3493                         result = isl_map_add(result,
3494                             isl_basic_map_intersect_range(
3495                                 isl_basic_map_copy(map->p[i]),
3496                                 isl_basic_set_copy(set->p[j])));
3497                         if (!result)
3498                                 goto error;
3499                 }
3500         isl_map_free(map);
3501         isl_set_free(set);
3502         return result;
3503 error:
3504         isl_map_free(map);
3505         isl_set_free(set);
3506         return NULL;
3507 }
3508
3509 struct isl_map *isl_map_intersect_domain(
3510                 struct isl_map *map, struct isl_set *set)
3511 {
3512         return isl_map_reverse(
3513                 isl_map_intersect_range(isl_map_reverse(map), set));
3514 }
3515
3516 struct isl_map *isl_map_apply_domain(
3517                 struct isl_map *map1, struct isl_map *map2)
3518 {
3519         if (!map1 || !map2)
3520                 goto error;
3521         map1 = isl_map_reverse(map1);
3522         map1 = isl_map_apply_range(map1, map2);
3523         return isl_map_reverse(map1);
3524 error:
3525         isl_map_free(map1);
3526         isl_map_free(map2);
3527         return NULL;
3528 }
3529
3530 struct isl_map *isl_map_apply_range(
3531                 struct isl_map *map1, struct isl_map *map2)
3532 {
3533         struct isl_dim *dim_result;
3534         struct isl_map *result;
3535         int i, j;
3536         unsigned nparam;
3537         unsigned n_in;
3538         unsigned n_out;
3539
3540         if (!map1 || !map2)
3541                 goto error;
3542
3543         dim_result = isl_dim_join(isl_dim_copy(map1->dim),
3544                                   isl_dim_copy(map2->dim));
3545
3546         result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
3547         if (!result)
3548                 goto error;
3549         for (i = 0; i < map1->n; ++i)
3550                 for (j = 0; j < map2->n; ++j) {
3551                         result = isl_map_add(result,
3552                             isl_basic_map_apply_range(
3553                                 isl_basic_map_copy(map1->p[i]),
3554                                 isl_basic_map_copy(map2->p[j])));
3555                         if (!result)
3556                                 goto error;
3557                 }
3558         isl_map_free(map1);
3559         isl_map_free(map2);
3560         if (result && result->n <= 1)
3561                 ISL_F_SET(result, ISL_MAP_DISJOINT);
3562         return result;
3563 error:
3564         isl_map_free(map1);
3565         isl_map_free(map2);
3566         return NULL;
3567 }
3568
3569 /*
3570  * returns range - domain
3571  */
3572 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3573 {
3574         struct isl_basic_set *bset;
3575         unsigned dim;
3576         unsigned nparam;
3577         int i;
3578
3579         if (!bmap)
3580                 goto error;
3581         dim = isl_basic_map_n_in(bmap);
3582         nparam = isl_basic_map_n_param(bmap);
3583         isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
3584         bset = isl_basic_set_from_basic_map(bmap);
3585         bset = isl_basic_set_cow(bset);
3586         bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
3587         bset = isl_basic_set_swap_vars(bset, 2*dim);
3588         for (i = 0; i < dim; ++i) {
3589                 int j = isl_basic_map_alloc_equality(
3590                                             (struct isl_basic_map *)bset);
3591                 if (j < 0)
3592                         goto error;
3593                 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
3594                 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
3595                 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
3596                 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
3597         }
3598         return isl_basic_set_project_out(bset, 2*dim, 0);
3599 error:
3600         isl_basic_map_free(bmap);
3601         return NULL;
3602 }
3603
3604 /*
3605  * returns range - domain
3606  */
3607 struct isl_set *isl_map_deltas(struct isl_map *map)
3608 {
3609         int i;
3610         struct isl_set *result;
3611
3612         if (!map)
3613                 return NULL;
3614
3615         isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
3616         result = isl_set_alloc(map->ctx, isl_map_n_param(map),
3617                                         isl_map_n_in(map), map->n, map->flags);
3618         if (!result)
3619                 goto error;
3620         for (i = 0; i < map->n; ++i)
3621                 result = isl_set_add(result,
3622                           isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3623         isl_map_free(map);
3624         return result;
3625 error:
3626         isl_map_free(map);
3627         return NULL;
3628 }
3629
3630 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
3631 {
3632         struct isl_basic_map *bmap;
3633         unsigned nparam;
3634         unsigned dim;
3635         int i;
3636
3637         if (!dims)
3638                 return NULL;
3639
3640         nparam = dims->nparam;
3641         dim = dims->n_out;
3642         bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
3643         if (!bmap)
3644                 goto error;
3645
3646         for (i = 0; i < dim; ++i) {
3647                 int j = isl_basic_map_alloc_equality(bmap);
3648                 if (j < 0)
3649                         goto error;
3650                 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3651                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3652                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3653         }
3654         return isl_basic_map_finalize(bmap);
3655 error:
3656         isl_basic_map_free(bmap);
3657         return NULL;
3658 }
3659
3660 struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
3661 {
3662         struct isl_dim *dim = isl_dim_map(set_dim);
3663         if (!dim)
3664                 return NULL;
3665         return basic_map_identity(dim);
3666 }
3667
3668 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
3669 {
3670         if (!model || !model->dim)
3671                 return NULL;
3672         isl_assert(model->ctx,
3673                         model->dim->n_in == model->dim->n_out, return NULL);
3674         return basic_map_identity(isl_dim_copy(model->dim));
3675 }
3676
3677 static struct isl_map *map_identity(struct isl_dim *dim)
3678 {
3679         struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
3680         return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
3681 }
3682
3683 struct isl_map *isl_map_identity(struct isl_dim *set_dim)
3684 {
3685         struct isl_dim *dim = isl_dim_map(set_dim);
3686         if (!dim)
3687                 return NULL;
3688         return map_identity(dim);
3689 }
3690
3691 struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
3692 {
3693         if (!model || !model->dim)
3694                 return NULL;
3695         isl_assert(model->ctx,
3696                         model->dim->n_in == model->dim->n_out, return NULL);
3697         return map_identity(isl_dim_copy(model->dim));
3698 }
3699
3700 /* Construct a basic set with all set dimensions having only non-negative
3701  * values.
3702  */
3703 struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
3704 {
3705         int i;
3706         unsigned nparam;
3707         unsigned dim;
3708         struct isl_basic_set *bset;
3709
3710         if (!dims)
3711                 return NULL;
3712         nparam = dims->nparam;
3713         dim = dims->n_out;
3714         bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
3715         if (!bset)
3716                 return NULL;
3717         for (i = 0; i < dim; ++i) {
3718                 int k = isl_basic_set_alloc_inequality(bset);
3719                 if (k < 0)
3720                         goto error;
3721                 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
3722                 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
3723         }
3724         return bset;
3725 error:
3726         isl_basic_set_free(bset);
3727         return NULL;
3728 }
3729
3730 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3731 {
3732         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3733 }
3734
3735 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3736 {
3737         return isl_map_is_subset(
3738                         (struct isl_map *)set1, (struct isl_map *)set2);
3739 }
3740
3741 int isl_basic_map_is_subset(
3742                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3743 {
3744         int is_subset;
3745         struct isl_map *map1;
3746         struct isl_map *map2;
3747
3748         if (!bmap1 || !bmap2)
3749                 return -1;
3750
3751         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3752         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3753
3754         is_subset = isl_map_is_subset(map1, map2);
3755
3756         isl_map_free(map1);
3757         isl_map_free(map2);
3758
3759         return is_subset;
3760 }
3761
3762 int isl_basic_map_is_equal(
3763                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3764 {
3765         int is_subset;
3766
3767         if (!bmap1 || !bmap2)
3768                 return -1;
3769         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3770         if (is_subset != 1)
3771                 return is_subset;
3772         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3773         return is_subset;
3774 }
3775
3776 int isl_basic_set_is_equal(
3777                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3778 {
3779         return isl_basic_map_is_equal(
3780                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3781 }
3782
3783 int isl_map_is_empty(struct isl_map *map)
3784 {
3785         int i;
3786         int is_empty;
3787
3788         if (!map)
3789                 return -1;
3790         for (i = 0; i < map->n; ++i) {
3791                 is_empty = isl_basic_map_is_empty(map->p[i]);
3792                 if (is_empty < 0)
3793                         return -1;
3794                 if (!is_empty)
3795                         return 0;
3796         }
3797         return 1;
3798 }
3799
3800 int isl_map_fast_is_empty(struct isl_map *map)
3801 {
3802         return map->n == 0;
3803 }
3804
3805 int isl_set_is_empty(struct isl_set *set)
3806 {
3807         return isl_map_is_empty((struct isl_map *)set);
3808 }
3809
3810 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3811 {
3812         int i;
3813         int is_subset = 0;
3814         struct isl_map *diff;
3815
3816         if (!map1 || !map2)
3817                 return -1;
3818
3819         if (isl_map_is_empty(map1))
3820                 return 1;
3821
3822         if (isl_map_is_empty(map2))
3823                 return 0;
3824
3825         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3826         if (!diff)
3827                 return -1;
3828
3829         is_subset = isl_map_is_empty(diff);
3830         isl_map_free(diff);
3831
3832         return is_subset;
3833 }
3834
3835 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3836 {
3837         int is_subset;
3838
3839         if (!map1 || !map2)
3840                 return -1;
3841         is_subset = isl_map_is_subset(map1, map2);
3842         if (is_subset != 1)
3843                 return is_subset;
3844         is_subset = isl_map_is_subset(map2, map1);
3845         return is_subset;
3846 }
3847
3848 int isl_basic_map_is_strict_subset(
3849                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3850 {
3851         int is_subset;
3852
3853         if (!bmap1 || !bmap2)
3854                 return -1;
3855         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3856         if (is_subset != 1)
3857                 return is_subset;
3858         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3859         if (is_subset == -1)
3860                 return is_subset;
3861         return !is_subset;
3862 }
3863
3864 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3865 {
3866         if (!bmap)
3867                 return -1;
3868         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3869 }
3870
3871 int isl_basic_set_is_universe(struct isl_basic_set *bset)
3872 {
3873         if (!bset)
3874                 return -1;
3875         return bset->n_eq == 0 && bset->n_ineq == 0;
3876 }
3877
3878 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3879 {
3880         struct isl_basic_set *bset = NULL;
3881         struct isl_vec *sample = NULL;
3882         int empty;
3883         unsigned total;
3884
3885         if (!bmap)
3886                 return -1;
3887
3888         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3889                 return 1;
3890
3891         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
3892                 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
3893                 copy = isl_basic_map_convex_hull(copy);
3894                 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
3895                 isl_basic_map_free(copy);
3896                 return empty;
3897         }
3898
3899         total = 1 + isl_basic_map_total_dim(bmap);
3900         if (bmap->sample && bmap->sample->size == total) {
3901                 int contains = basic_map_contains(bmap, bmap->sample);
3902                 if (contains < 0)
3903                         return -1;
3904                 if (contains)
3905                         return 0;
3906         }
3907         isl_vec_free(bmap->sample);
3908         bmap->sample = NULL;
3909         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3910         if (!bset)
3911                 return -1;
3912         sample = isl_basic_set_sample(bset);
3913         if (!sample)
3914                 return -1;
3915         empty = sample->size == 0;
3916         isl_vec_free(bmap->sample);
3917         bmap->sample = sample;
3918         if (empty)
3919                 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
3920
3921         return empty;
3922 }
3923
3924 int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
3925 {
3926         if (!bmap)
3927                 return -1;
3928         return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
3929 }
3930
3931 int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
3932 {
3933         if (!bset)
3934                 return -1;
3935         return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
3936 }
3937
3938 int isl_basic_set_is_empty(struct isl_basic_set *bset)
3939 {
3940         return isl_basic_map_is_empty((struct isl_basic_map *)bset);
3941 }
3942
3943 struct isl_map *isl_basic_map_union(
3944         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3945 {
3946         struct isl_map *map;
3947         if (!bmap1 || !bmap2)
3948                 return NULL;
3949
3950         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
3951
3952         map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
3953         if (!map)
3954                 goto error;
3955         map = isl_map_add(map, bmap1);
3956         map = isl_map_add(map, bmap2);
3957         return map;
3958 error:
3959         isl_basic_map_free(bmap1);
3960         isl_basic_map_free(bmap2);
3961         return NULL;
3962 }
3963
3964 struct isl_set *isl_basic_set_union(
3965                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3966 {
3967         return (struct isl_set *)isl_basic_map_union(
3968                                             (struct isl_basic_map *)bset1,
3969                                             (struct isl_basic_map *)bset2);
3970 }
3971
3972 /* Order divs such that any div only depends on previous divs */
3973 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3974 {
3975         int i;
3976         unsigned off = isl_dim_total(bmap->dim);
3977
3978         for (i = 0; i < bmap->n_div; ++i) {
3979                 int pos;
3980                 if (isl_int_is_zero(bmap->div[i][0]))
3981                         continue;
3982                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3983                                                             bmap->n_div-i);
3984                 if (pos == -1)
3985                         continue;
3986                 isl_basic_map_swap_div(bmap, i, i + pos);
3987                 --i;
3988         }
3989         return bmap;
3990 }
3991
3992 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
3993 {
3994         return (struct isl_basic_set *)order_divs((struct isl_basic_map *)bset);
3995 }
3996
3997 /* Look for a div in dst that corresponds to the div "div" in src.
3998  * The divs before "div" in src and dst are assumed to be the same.
3999  *
4000  * Returns -1 if no corresponding div was found and the position
4001  * of the corresponding div in dst otherwise.
4002  */
4003 static int find_div(struct isl_basic_map *dst,
4004                         struct isl_basic_map *src, unsigned div)
4005 {
4006         int i;
4007
4008         unsigned total = isl_dim_total(src->dim);
4009
4010         isl_assert(dst->ctx, div <= dst->n_div, return -1);
4011         for (i = div; i < dst->n_div; ++i)
4012                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
4013                     isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
4014                                                 dst->n_div - div) == -1)
4015                         return i;
4016         return -1;
4017 }
4018
4019 struct isl_basic_map *isl_basic_map_align_divs(
4020                 struct isl_basic_map *dst, struct isl_basic_map *src)
4021 {
4022         int i;
4023         unsigned total = isl_dim_total(src->dim);
4024
4025         if (!dst || !src)
4026                 goto error;
4027
4028         if (src->n_div == 0)
4029                 return dst;
4030
4031         for (i = 0; i < src->n_div; ++i)
4032                 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
4033
4034         src = order_divs(src);
4035         dst = isl_basic_map_cow(dst);
4036         dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
4037                         src->n_div, 0, 2 * src->n_div);
4038         if (!dst)
4039                 return NULL;
4040         for (i = 0; i < src->n_div; ++i) {
4041                 int j = find_div(dst, src, i);
4042                 if (j < 0) {
4043                         j = isl_basic_map_alloc_div(dst);
4044                         if (j < 0)
4045                                 goto error;
4046                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
4047                         isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
4048                         if (add_div_constraints(dst, j) < 0)
4049                                 goto error;
4050                 }
4051                 if (j != i)
4052                         isl_basic_map_swap_div(dst, i, j);
4053         }
4054         return dst;
4055 error:
4056         isl_basic_map_free(dst);
4057         return NULL;
4058 }
4059
4060 struct isl_basic_set *isl_basic_set_align_divs(
4061                 struct isl_basic_set *dst, struct isl_basic_set *src)
4062 {
4063         return (struct isl_basic_set *)isl_basic_map_align_divs(
4064                 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
4065 }
4066
4067 struct isl_map *isl_map_align_divs(struct isl_map *map)
4068 {
4069         int i;
4070
4071         map = isl_map_compute_divs(map);
4072         map = isl_map_cow(map);
4073         if (!map)
4074                 return NULL;
4075
4076         for (i = 1; i < map->n; ++i)
4077                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
4078         for (i = 1; i < map->n; ++i)
4079                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
4080
4081         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4082         return map;
4083 }
4084
4085 struct isl_set *isl_set_align_divs(struct isl_set *set)
4086 {
4087         return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
4088 }
4089
4090 static struct isl_map *add_cut_constraint(struct isl_map *dst,
4091                 struct isl_basic_map *src, isl_int *c,
4092                 unsigned len, int oppose)
4093 {
4094         struct isl_basic_map *copy = NULL;
4095         int is_empty;
4096         int k;
4097         unsigned total;
4098
4099         copy = isl_basic_map_copy(src);
4100         copy = isl_basic_map_cow(copy);
4101         if (!copy)
4102                 goto error;
4103         copy = isl_basic_map_extend_constraints(copy, 0, 1);
4104         k = isl_basic_map_alloc_inequality(copy);
4105         if (k < 0)
4106                 goto error;
4107         if (oppose)
4108                 isl_seq_neg(copy->ineq[k], c, len);
4109         else
4110                 isl_seq_cpy(copy->ineq[k], c, len);
4111         total = 1 + isl_basic_map_total_dim(copy);
4112         isl_seq_clr(copy->ineq[k]+len, total - len);
4113         isl_inequality_negate(copy, k);
4114         copy = isl_basic_map_simplify(copy);
4115         copy = isl_basic_map_finalize(copy);
4116         is_empty = isl_basic_map_is_empty(copy);
4117         if (is_empty < 0)
4118                 goto error;
4119         if (!is_empty)
4120                 dst = isl_map_add(dst, copy);
4121         else
4122                 isl_basic_map_free(copy);
4123         return dst;
4124 error:
4125         isl_basic_map_free(copy);
4126         isl_map_free(dst);
4127         return NULL;
4128 }
4129
4130 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
4131 {
4132         int i, j, k;
4133         unsigned flags = 0;
4134         struct isl_map *rest = NULL;
4135         unsigned max;
4136         unsigned total = isl_basic_map_total_dim(bmap);
4137
4138         assert(bmap);
4139
4140         if (!map)
4141                 goto error;
4142
4143         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
4144                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4145
4146         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
4147         rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
4148         if (!rest)
4149                 goto error;
4150
4151         for (i = 0; i < map->n; ++i) {
4152                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
4153                 if (!map->p[i])
4154                         goto error;
4155         }
4156
4157         for (j = 0; j < map->n; ++j)
4158                 map->p[j] = isl_basic_map_cow(map->p[j]);
4159
4160         for (i = 0; i < bmap->n_eq; ++i) {
4161                 for (j = 0; j < map->n; ++j) {
4162                         rest = add_cut_constraint(rest,
4163                                 map->p[j], bmap->eq[i], 1+total, 0);
4164                         if (!rest)
4165                                 goto error;
4166
4167                         rest = add_cut_constraint(rest,
4168                                 map->p[j], bmap->eq[i], 1+total, 1);
4169                         if (!rest)
4170                                 goto error;
4171
4172                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4173                                 1, 0);
4174                         if (!map->p[j])
4175                                 goto error;
4176                         k = isl_basic_map_alloc_equality(map->p[j]);
4177                         if (k < 0)
4178                                 goto error;
4179                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
4180                         isl_seq_clr(map->p[j]->eq[k]+1+total,
4181                                         map->p[j]->n_div - bmap->n_div);
4182                 }
4183         }
4184
4185         for (i = 0; i < bmap->n_ineq; ++i) {
4186                 for (j = 0; j < map->n; ++j) {
4187                         rest = add_cut_constraint(rest,
4188                                 map->p[j], bmap->ineq[i], 1+total, 0);
4189                         if (!rest)
4190                                 goto error;
4191
4192                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4193                                 0, 1);
4194                         if (!map->p[j])
4195                                 goto error;
4196                         k = isl_basic_map_alloc_inequality(map->p[j]);
4197                         if (k < 0)
4198                                 goto error;
4199                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
4200                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
4201                                         map->p[j]->n_div - bmap->n_div);
4202                 }
4203         }
4204
4205         isl_map_free(map);
4206         return rest;
4207 error:
4208         isl_map_free(map);
4209         isl_map_free(rest);
4210         return NULL;
4211 }
4212
4213 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
4214 {
4215         int i;
4216         if (!map1 || !map2)
4217                 goto error;
4218
4219         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
4220
4221         if (isl_map_is_empty(map2)) {
4222                 isl_map_free(map2);
4223                 return map1;
4224         }
4225
4226         map1 = isl_map_compute_divs(map1);
4227         map2 = isl_map_compute_divs(map2);
4228         if (!map1 || !map2)
4229                 goto error;
4230
4231         for (i = 0; map1 && i < map2->n; ++i)
4232                 map1 = subtract(map1, map2->p[i]);
4233
4234         isl_map_free(map2);
4235         return map1;
4236 error:
4237         isl_map_free(map1);
4238         isl_map_free(map2);
4239         return NULL;
4240 }
4241
4242 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
4243 {
4244         return (struct isl_set *)
4245                 isl_map_subtract(
4246                         (struct isl_map *)set1, (struct isl_map *)set2);
4247 }
4248
4249 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
4250 {
4251         if (!set || !map)
4252                 goto error;
4253         isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
4254         map = isl_map_intersect_domain(map, set);
4255         set = isl_map_range(map);
4256         return set;
4257 error:
4258         isl_set_free(set);
4259         isl_map_free(map);
4260         return NULL;
4261 }
4262
4263 /* There is no need to cow as removing empty parts doesn't change
4264  * the meaning of the set.
4265  */
4266 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
4267 {
4268         int i;
4269
4270         if (!map)
4271                 return NULL;
4272
4273         for (i = map->n-1; i >= 0; --i) {
4274                 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
4275                         continue;
4276                 isl_basic_map_free(map->p[i]);
4277                 if (i != map->n-1) {
4278                         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4279                         map->p[i] = map->p[map->n-1];
4280                 }
4281                 map->n--;
4282         }
4283
4284         return map;
4285 }
4286
4287 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
4288 {
4289         return (struct isl_set *)
4290                 isl_map_remove_empty_parts((struct isl_map *)set);
4291 }
4292
4293 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
4294 {
4295         struct isl_basic_map *bmap;
4296         if (!map || map->n == 0)
4297                 return NULL;
4298         bmap = map->p[map->n-1];
4299         isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
4300         return isl_basic_map_copy(bmap);
4301 }
4302
4303 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
4304 {
4305         (struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
4306 }
4307
4308 struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
4309                                                 struct isl_basic_map *bmap)
4310 {
4311         int i;
4312
4313         if (!map || !bmap)
4314                 goto error;
4315         for (i = map->n-1; i >= 0; --i) {
4316                 if (map->p[i] != bmap)
4317                         continue;
4318                 map = isl_map_cow(map);
4319                 if (!map)
4320                         goto error;
4321                 isl_basic_map_free(map->p[i]);
4322                 if (i != map->n-1) {
4323                         ISL_F_CLR(map, ISL_SET_NORMALIZED);
4324                         map->p[i] = map->p[map->n-1];
4325                 }
4326                 map->n--;
4327                 return map;
4328         }
4329         isl_basic_map_free(bmap);
4330         return map;
4331 error:
4332         isl_map_free(map);
4333         isl_basic_map_free(bmap);
4334         return NULL;
4335 }
4336
4337 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
4338                                                 struct isl_basic_set *bset)
4339 {
4340         (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
4341                                                 (struct isl_basic_map *)bset);
4342 }
4343
4344 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
4345  * for any common value of the parameters and dimensions preceding dim
4346  * in both basic sets, the values of dimension pos in bset1 are
4347  * smaller or larger than those in bset2.
4348  *
4349  * Returns
4350  *       1 if bset1 follows bset2
4351  *      -1 if bset1 precedes bset2
4352  *       0 if bset1 and bset2 are incomparable
4353  *      -2 if some error occurred.
4354  */
4355 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
4356         struct isl_basic_set *bset2, int pos)
4357 {
4358         struct isl_dim *dims;
4359         struct isl_basic_map *bmap1 = NULL;
4360         struct isl_basic_map *bmap2 = NULL;
4361         struct isl_ctx *ctx;
4362         struct isl_vec *obj;
4363         unsigned total;
4364         unsigned nparam;
4365         unsigned dim1, dim2;
4366         isl_int num, den;
4367         enum isl_lp_result res;
4368         int cmp;
4369
4370         if (!bset1 || !bset2)
4371                 return -2;
4372
4373         nparam = isl_basic_set_n_param(bset1);
4374         dim1 = isl_basic_set_n_dim(bset1);
4375         dim2 = isl_basic_set_n_dim(bset2);
4376         dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
4377         bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
4378         dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
4379         bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
4380         if (!bmap1 || !bmap2)
4381                 goto error;
4382         bmap1 = isl_basic_map_cow(bmap1);
4383         bmap1 = isl_basic_map_extend(bmap1, nparam,
4384                         pos, (dim1 - pos) + (dim2 - pos),
4385                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
4386         bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
4387         if (!bmap1)
4388                 goto error;
4389         total = isl_basic_map_total_dim(bmap1);
4390         ctx = bmap1->ctx;
4391         obj = isl_vec_alloc(ctx, 1 + total);
4392         isl_seq_clr(obj->block.data, 1 + total);
4393         isl_int_set_si(obj->block.data[1+nparam+pos], 1);
4394         isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
4395         if (!obj)
4396                 goto error;
4397         isl_int_init(num);
4398         isl_int_init(den);
4399         res = isl_basic_map_solve_lp(bmap1, 0, obj->block.data, ctx->one,
4400                                         &num, &den, NULL);
4401         if (res == isl_lp_empty)
4402                 cmp = 0;
4403         else if (res == isl_lp_ok && isl_int_is_pos(num))
4404                 cmp = 1;
4405         else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
4406                   res == isl_lp_unbounded)
4407                 cmp = -1;
4408         else
4409                 cmp = -2;
4410         isl_int_clear(num);
4411         isl_int_clear(den);
4412         isl_basic_map_free(bmap1);
4413         isl_vec_free(obj);
4414         return cmp;
4415 error:
4416         isl_basic_map_free(bmap1);
4417         isl_basic_map_free(bmap2);
4418         return -2;
4419 }
4420
4421 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
4422         unsigned pos, isl_int *val)
4423 {
4424         int i;
4425         int d;
4426         unsigned total;
4427
4428         if (!bmap)
4429                 return -1;
4430         total = isl_basic_map_total_dim(bmap);
4431         for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
4432                 for (; d+1 > pos; --d)
4433                         if (!isl_int_is_zero(bmap->eq[i][1+d]))
4434                                 break;
4435                 if (d != pos)
4436                         continue;
4437                 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
4438                         return 0;
4439                 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
4440                         return 0;
4441                 if (!isl_int_is_one(bmap->eq[i][1+d]))
4442                         return 0;
4443                 if (val)
4444                         isl_int_neg(*val, bmap->eq[i][0]);
4445                 return 1;
4446         }
4447         return 0;
4448 }
4449
4450 static int isl_map_fast_has_fixed_var(struct isl_map *map,
4451         unsigned pos, isl_int *val)
4452 {
4453         int i;
4454         isl_int v;
4455         isl_int tmp;
4456         int fixed;
4457
4458         if (!map)
4459                 return -1;
4460         if (map->n == 0)
4461                 return 0;
4462         if (map->n == 1)
4463                 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
4464         isl_int_init(v);
4465         isl_int_init(tmp);
4466         fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
4467         for (i = 1; fixed == 1 && i < map->n; ++i) {
4468                 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
4469                 if (fixed == 1 && isl_int_ne(tmp, v))
4470                         fixed = 0;
4471         }
4472         if (val)
4473                 isl_int_set(*val, v);
4474         isl_int_clear(tmp);
4475         isl_int_clear(v);
4476         return fixed;
4477 }
4478
4479 static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
4480         unsigned pos, isl_int *val)
4481 {
4482         return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
4483                                                 pos, val);
4484 }
4485
4486 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
4487         isl_int *val)
4488 {
4489         return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
4490 }
4491
4492 int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
4493         enum isl_dim_type type, unsigned pos, isl_int *val)
4494 {
4495         if (pos >= isl_basic_map_dim(bmap, type))
4496                 return -1;
4497         return isl_basic_map_fast_has_fixed_var(bmap,
4498                 isl_basic_map_offset(bmap, type) - 1 + pos, val);
4499 }
4500
4501 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4502  * then return this fixed value in *val.
4503  */
4504 int isl_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
4505         isl_int *val)
4506 {
4507         return isl_basic_set_fast_has_fixed_var(bset,
4508                                         isl_basic_set_n_param(bset) + dim, val);
4509 }
4510
4511 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4512  * then return this fixed value in *val.
4513  */
4514 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
4515 {
4516         return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
4517 }
4518
4519 /* Check if input variable in has fixed value and if so and if val is not NULL,
4520  * then return this fixed value in *val.
4521  */
4522 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
4523 {
4524         return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
4525 }
4526
4527 /* Check if dimension dim has an (obvious) fixed lower bound and if so
4528  * and if val is not NULL, then return this lower bound in *val.
4529  */
4530 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
4531         unsigned dim, isl_int *val)
4532 {
4533         int i, i_eq = -1, i_ineq = -1;
4534         isl_int *c;
4535         unsigned total;
4536         unsigned nparam;
4537
4538         if (!bset)
4539                 return -1;
4540         total = isl_basic_set_total_dim(bset);
4541         nparam = isl_basic_set_n_param(bset);
4542         for (i = 0; i < bset->n_eq; ++i) {
4543                 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
4544                         continue;
4545                 if (i_eq != -1)
4546                         return 0;
4547                 i_eq = i;
4548         }
4549         for (i = 0; i < bset->n_ineq; ++i) {
4550                 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
4551                         continue;
4552                 if (i_eq != -1 || i_ineq != -1)
4553                         return 0;
4554                 i_ineq = i;
4555         }
4556         if (i_eq == -1 && i_ineq == -1)
4557                 return 0;
4558         c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4559         /* The coefficient should always be one due to normalization. */
4560         if (!isl_int_is_one(c[1+nparam+dim]))
4561                 return 0;
4562         if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
4563                 return 0;
4564         if (isl_seq_first_non_zero(c+1+nparam+dim+1,
4565                                         total - nparam - dim - 1) != -1)
4566                 return 0;
4567         if (val)
4568                 isl_int_neg(*val, c[0]);
4569         return 1;
4570 }
4571
4572 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4573         unsigned dim, isl_int *val)
4574 {
4575         int i;
4576         isl_int v;
4577         isl_int tmp;
4578         int fixed;
4579
4580         if (!set)
4581                 return -1;
4582         if (set->n == 0)
4583                 return 0;
4584         if (set->n == 1)
4585                 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4586                                                                 dim, val);
4587         isl_int_init(v);
4588         isl_int_init(tmp);
4589         fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4590                                                                 dim, &v);
4591         for (i = 1; fixed == 1 && i < set->n; ++i) {
4592                 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4593                                                                 dim, &tmp);
4594                 if (fixed == 1 && isl_int_ne(tmp, v))
4595                         fixed = 0;
4596         }
4597         if (val)
4598                 isl_int_set(*val, v);
4599         isl_int_clear(tmp);
4600         isl_int_clear(v);
4601         return fixed;
4602 }
4603
4604 struct constraint {
4605         unsigned        size;
4606         isl_int         *c;
4607 };
4608
4609 static int qsort_constraint_cmp(const void *p1, const void *p2)
4610 {
4611         const struct constraint *c1 = (const struct constraint *)p1;
4612         const struct constraint *c2 = (const struct constraint *)p2;
4613         unsigned size = isl_min(c1->size, c2->size);
4614         return isl_seq_cmp(c1->c, c2->c, size);
4615 }
4616
4617 static struct isl_basic_map *isl_basic_map_sort_constraints(
4618         struct isl_basic_map *bmap)
4619 {
4620         int i;
4621         struct constraint *c;
4622         unsigned total;
4623
4624         if (!bmap)
4625                 return NULL;
4626         total = isl_basic_map_total_dim(bmap);
4627         c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
4628         if (!c)
4629                 goto error;
4630         for (i = 0; i < bmap->n_ineq; ++i) {
4631                 c[i].size = total;
4632                 c[i].c = bmap->ineq[i];
4633         }
4634         qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
4635         for (i = 0; i < bmap->n_ineq; ++i)
4636                 bmap->ineq[i] = c[i].c;
4637         free(c);
4638         return bmap;
4639 error:
4640         isl_basic_map_free(bmap);
4641         return NULL;
4642 }
4643
4644 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
4645 {
4646         if (!bmap)
4647                 return NULL;
4648         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
4649                 return bmap;
4650         bmap = isl_basic_map_convex_hull(bmap);
4651         bmap = isl_basic_map_sort_constraints(bmap);
4652         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
4653         return bmap;
4654 }
4655
4656 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
4657 {
4658         return (struct isl_basic_set *)isl_basic_map_normalize(
4659                                                 (struct isl_basic_map *)bset);
4660 }
4661
4662 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
4663         const struct isl_basic_map *bmap2)
4664 {
4665         int i, cmp;
4666         unsigned total;
4667
4668         if (bmap1 == bmap2)
4669                 return 0;
4670         if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
4671                 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
4672         if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
4673                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4674         if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
4675                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4676         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
4677             ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4678                 return 0;
4679         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
4680                 return 1;
4681         if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4682                 return -1;
4683         if (bmap1->n_eq != bmap2->n_eq)
4684                 return bmap1->n_eq - bmap2->n_eq;
4685         if (bmap1->n_ineq != bmap2->n_ineq)
4686                 return bmap1->n_ineq - bmap2->n_ineq;
4687         if (bmap1->n_div != bmap2->n_div)
4688                 return bmap1->n_div - bmap2->n_div;
4689         total = isl_basic_map_total_dim(bmap1);
4690         for (i = 0; i < bmap1->n_eq; ++i) {
4691                 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
4692                 if (cmp)
4693                         return cmp;
4694         }
4695         for (i = 0; i < bmap1->n_ineq; ++i) {
4696                 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
4697                 if (cmp)
4698                         return cmp;
4699         }
4700         for (i = 0; i < bmap1->n_div; ++i) {
4701                 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
4702                 if (cmp)
4703                         return cmp;
4704         }
4705         return 0;
4706 }
4707
4708 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
4709         struct isl_basic_map *bmap2)
4710 {
4711         return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
4712 }
4713
4714 static int qsort_bmap_cmp(const void *p1, const void *p2)
4715 {
4716         const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
4717         const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
4718
4719         return isl_basic_map_fast_cmp(bmap1, bmap2);
4720 }
4721
4722 /* We normalize in place, but if anything goes wrong we need
4723  * to return NULL, so we need to make sure we don't change the
4724  * meaning of any possible other copies of map.
4725  */
4726 struct isl_map *isl_map_normalize(struct isl_map *map)
4727 {
4728         int i, j;
4729         struct isl_basic_map *bmap;
4730
4731         if (!map)
4732                 return NULL;
4733         if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
4734                 return map;
4735         for (i = 0; i < map->n; ++i) {
4736                 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
4737                 if (!bmap)
4738                         goto error;
4739                 isl_basic_map_free(map->p[i]);
4740                 map->p[i] = bmap;
4741         }
4742         qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
4743         ISL_F_SET(map, ISL_MAP_NORMALIZED);
4744         map = isl_map_remove_empty_parts(map);
4745         if (!map)
4746                 return NULL;
4747         for (i = map->n - 1; i >= 1; --i) {
4748                 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
4749                         continue;
4750                 isl_basic_map_free(map->p[i-1]);
4751                 for (j = i; j < map->n; ++j)
4752                         map->p[j-1] = map->p[j];
4753                 map->n--;
4754         }
4755         return map;
4756 error:
4757         isl_map_free(map);
4758         return NULL;
4759
4760 }
4761
4762 struct isl_set *isl_set_normalize(struct isl_set *set)
4763 {
4764         return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
4765 }
4766
4767 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
4768 {
4769         int i;
4770         int equal;
4771
4772         if (!map1 || !map2)
4773                 return -1;
4774
4775         if (map1 == map2)
4776                 return 1;
4777         if (!isl_dim_equal(map1->dim, map2->dim))
4778                 return 0;
4779
4780         map1 = isl_map_copy(map1);
4781         map2 = isl_map_copy(map2);
4782         map1 = isl_map_normalize(map1);
4783         map2 = isl_map_normalize(map2);
4784         if (!map1 || !map2)
4785                 goto error;
4786         equal = map1->n == map2->n;
4787         for (i = 0; equal && i < map1->n; ++i) {
4788                 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
4789                 if (equal < 0)
4790                         goto error;
4791         }
4792         isl_map_free(map1);
4793         isl_map_free(map2);
4794         return equal;
4795 error:
4796         isl_map_free(map1);
4797         isl_map_free(map2);
4798         return -1;
4799 }
4800
4801 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
4802 {
4803         return isl_map_fast_is_equal((struct isl_map *)set1,
4804                                                 (struct isl_map *)set2);
4805 }
4806
4807 /* Return an interval that ranges from min to max (inclusive)
4808  */
4809 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
4810         isl_int min, isl_int max)
4811 {
4812         int k;
4813         struct isl_basic_set *bset = NULL;
4814
4815         bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
4816         if (!bset)
4817                 goto error;
4818
4819         k = isl_basic_set_alloc_inequality(bset);
4820         if (k < 0)
4821                 goto error;
4822         isl_int_set_si(bset->ineq[k][1], 1);
4823         isl_int_neg(bset->ineq[k][0], min);
4824
4825         k = isl_basic_set_alloc_inequality(bset);
4826         if (k < 0)
4827                 goto error;
4828         isl_int_set_si(bset->ineq[k][1], -1);
4829         isl_int_set(bset->ineq[k][0], max);
4830
4831         return bset;
4832 error:
4833         isl_basic_set_free(bset);
4834         return NULL;
4835 }
4836
4837 /* Return the Cartesian product of the basic sets in list (in the given order).
4838  */
4839 struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
4840 {
4841         int i;
4842         unsigned dim;
4843         unsigned nparam;
4844         unsigned extra;
4845         unsigned n_eq;
4846         unsigned n_ineq;
4847         struct isl_basic_set *product = NULL;
4848
4849         if (!list)
4850                 goto error;
4851         isl_assert(list->ctx, list->n > 0, goto error);
4852         isl_assert(list->ctx, list->p[0], goto error);
4853         nparam = isl_basic_set_n_param(list->p[0]);
4854         dim = isl_basic_set_n_dim(list->p[0]);
4855         extra = list->p[0]->n_div;
4856         n_eq = list->p[0]->n_eq;
4857         n_ineq = list->p[0]->n_ineq;
4858         for (i = 1; i < list->n; ++i) {
4859                 isl_assert(list->ctx, list->p[i], goto error);
4860                 isl_assert(list->ctx,
4861                     nparam == isl_basic_set_n_param(list->p[i]), goto error);
4862                 dim += isl_basic_set_n_dim(list->p[i]);
4863                 extra += list->p[i]->n_div;
4864                 n_eq += list->p[i]->n_eq;
4865                 n_ineq += list->p[i]->n_ineq;
4866         }
4867         product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
4868                                         n_eq, n_ineq);
4869         if (!product)
4870                 goto error;
4871         dim = 0;
4872         for (i = 0; i < list->n; ++i) {
4873                 isl_basic_set_add_constraints(product,
4874                                         isl_basic_set_copy(list->p[i]), dim);
4875                 dim += isl_basic_set_n_dim(list->p[i]);
4876         }
4877         isl_basic_set_list_free(list);
4878         return product;
4879 error:
4880         isl_basic_set_free(product);
4881         isl_basic_set_list_free(list);
4882         return NULL;
4883 }
4884
4885 struct isl_basic_map *isl_basic_map_product(
4886                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4887 {
4888         struct isl_dim *dim_result = NULL;
4889         struct isl_basic_map *bmap;
4890         unsigned in1, in2, out1, out2, nparam, total, pos;
4891         struct isl_dim_map *dim_map1, *dim_map2;
4892
4893         if (!bmap1 || !bmap2)
4894                 goto error;
4895
4896         isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
4897                                      bmap2->dim, isl_dim_param), goto error);
4898         dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
4899                                                    isl_dim_copy(bmap2->dim));
4900
4901         in1 = isl_basic_map_n_in(bmap1);
4902         in2 = isl_basic_map_n_in(bmap2);
4903         out1 = isl_basic_map_n_out(bmap1);
4904         out2 = isl_basic_map_n_out(bmap2);
4905         nparam = isl_basic_map_n_param(bmap1);
4906
4907         total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
4908         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
4909         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
4910         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
4911         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
4912         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
4913         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
4914         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
4915         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
4916         isl_dim_map_div(dim_map1, bmap1, pos += out2);
4917         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
4918
4919         bmap = isl_basic_map_alloc_dim(dim_result,
4920                         bmap1->n_div + bmap2->n_div,
4921                         bmap1->n_eq + bmap2->n_eq,
4922                         bmap1->n_ineq + bmap2->n_ineq);
4923         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
4924         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
4925         bmap = isl_basic_map_simplify(bmap);
4926         return isl_basic_map_finalize(bmap);
4927 error:
4928         isl_basic_map_free(bmap1);
4929         isl_basic_map_free(bmap2);
4930         return NULL;
4931 }
4932
4933 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
4934  */
4935 struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
4936 {
4937         unsigned flags = 0;
4938         struct isl_map *result;
4939         int i, j;
4940
4941         if (!map1 || !map2)
4942                 goto error;
4943
4944         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
4945                                          map2->dim, isl_dim_param), goto error);
4946
4947         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
4948             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
4949                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4950
4951         result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
4952                                                    isl_dim_copy(map2->dim)),
4953                                 map1->n * map2->n, flags);
4954         if (!result)
4955                 goto error;
4956         for (i = 0; i < map1->n; ++i)
4957                 for (j = 0; j < map2->n; ++j) {
4958                         struct isl_basic_map *part;
4959                         part = isl_basic_map_product(
4960                                     isl_basic_map_copy(map1->p[i]),
4961                                     isl_basic_map_copy(map2->p[j]));
4962                         if (isl_basic_map_is_empty(part))
4963                                 isl_basic_map_free(part);
4964                         else
4965                                 result = isl_map_add(result, part);
4966                         if (!result)
4967                                 goto error;
4968                 }
4969         isl_map_free(map1);
4970         isl_map_free(map2);
4971         return result;
4972 error:
4973         isl_map_free(map1);
4974         isl_map_free(map2);
4975         return NULL;
4976 }
4977
4978 /* Given two set A and B, construct its Cartesian product A x B.
4979  */
4980 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
4981 {
4982         return (struct isl_set *)isl_map_product((struct isl_map *)set1,
4983                                                  (struct isl_map *)set2);
4984 }
4985
4986 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
4987 {
4988         int i;
4989         uint32_t hash;
4990         unsigned total;
4991
4992         if (!bset)
4993                 return 0;
4994         bset = isl_basic_set_copy(bset);
4995         bset = isl_basic_set_normalize(bset);
4996         if (!bset)
4997                 return 0;
4998         total = isl_basic_set_total_dim(bset);
4999         isl_hash_byte(hash, bset->n_eq & 0xFF);
5000         for (i = 0; i < bset->n_eq; ++i) {
5001                 uint32_t c_hash;
5002                 c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
5003                 isl_hash_hash(hash, c_hash);
5004         }
5005         isl_hash_byte(hash, bset->n_ineq & 0xFF);
5006         for (i = 0; i < bset->n_ineq; ++i) {
5007                 uint32_t c_hash;
5008                 c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
5009                 isl_hash_hash(hash, c_hash);
5010         }
5011         isl_hash_byte(hash, bset->n_div & 0xFF);
5012         for (i = 0; i < bset->n_div; ++i) {
5013                 uint32_t c_hash;
5014                 if (isl_int_is_zero(bset->div[i][0]))
5015                         continue;
5016                 isl_hash_byte(hash, i & 0xFF);
5017                 c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
5018                 isl_hash_hash(hash, c_hash);
5019         }
5020         isl_basic_set_free(bset);
5021         return hash;
5022 }
5023
5024 uint32_t isl_set_get_hash(struct isl_set *set)
5025 {
5026         int i;
5027         uint32_t hash;
5028
5029         if (!set)
5030                 return 0;
5031         set = isl_set_copy(set);
5032         set = isl_set_normalize(set);
5033         if (!set)
5034                 return 0;
5035
5036         hash = isl_hash_init();
5037         for (i = 0; i < set->n; ++i) {
5038                 uint32_t bset_hash;
5039                 bset_hash = isl_basic_set_get_hash(set->p[i]);
5040                 isl_hash_hash(hash, bset_hash);
5041         }
5042
5043         isl_set_free(set);
5044
5045         return hash;
5046 }
5047
5048 /* Check if the value for dimension dim is completely determined
5049  * by the values of the other parameters and variables.
5050  * That is, check if dimension dim is involved in an equality.
5051  */
5052 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
5053 {
5054         int i;
5055         unsigned nparam;
5056
5057         if (!bset)
5058                 return -1;
5059         nparam = isl_basic_set_n_param(bset);
5060         for (i = 0; i < bset->n_eq; ++i)
5061                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
5062                         return 1;
5063         return 0;
5064 }
5065
5066 /* Check if the value for dimension dim is completely determined
5067  * by the values of the other parameters and variables.
5068  * That is, check if dimension dim is involved in an equality
5069  * for each of the subsets.
5070  */
5071 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
5072 {
5073         int i;
5074
5075         if (!set)
5076                 return -1;
5077         for (i = 0; i < set->n; ++i) {
5078                 int unique;
5079                 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
5080                 if (unique != 1)
5081                         return unique;
5082         }
5083         return 1;
5084 }