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         return isl_basic_map_finalize(bmap);
1943 error:
1944         isl_basic_map_free(bmap1);
1945         isl_basic_map_free(bmap2);
1946         return NULL;
1947 }
1948
1949 struct isl_basic_set *isl_basic_set_apply(
1950                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1951 {
1952         if (!bset || !bmap)
1953                 goto error;
1954
1955         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
1956                     goto error);
1957
1958         return (struct isl_basic_set *)
1959                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1960 error:
1961         isl_basic_set_free(bset);
1962         isl_basic_map_free(bmap);
1963         return NULL;
1964 }
1965
1966 struct isl_basic_map *isl_basic_map_apply_domain(
1967                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1968 {
1969         if (!bmap1 || !bmap2)
1970                 goto error;
1971
1972         isl_assert(ctx,
1973             isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
1974         isl_assert(ctx,
1975             isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
1976             goto error);
1977
1978         bmap1 = isl_basic_map_reverse(bmap1);
1979         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1980         return isl_basic_map_reverse(bmap1);
1981 error:
1982         isl_basic_map_free(bmap1);
1983         isl_basic_map_free(bmap2);
1984         return NULL;
1985 }
1986
1987 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
1988  * A \cap B -> f(A) + f(B)
1989  */
1990 struct isl_basic_map *isl_basic_map_sum(
1991                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1992 {
1993         unsigned n_in, n_out, nparam, total, pos;
1994         struct isl_basic_map *bmap = NULL;
1995         struct isl_dim_map *dim_map1, *dim_map2;
1996         int i;
1997
1998         if (!bmap1 || !bmap2)
1999                 goto error;
2000
2001         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
2002                 goto error);
2003
2004         nparam = isl_basic_map_n_param(bmap1);
2005         n_in = isl_basic_map_n_in(bmap1);
2006         n_out = isl_basic_map_n_out(bmap1);
2007
2008         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
2009         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
2010         dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
2011         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
2012         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
2013         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
2014         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
2015         isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
2016         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
2017         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
2018         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
2019
2020         bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
2021                         bmap1->n_div + bmap2->n_div + 2 * n_out,
2022                         bmap1->n_eq + bmap2->n_eq + n_out,
2023                         bmap1->n_ineq + bmap2->n_ineq);
2024         for (i = 0; i < n_out; ++i) {
2025                 int j = isl_basic_map_alloc_equality(bmap);
2026                 if (j < 0)
2027                         goto error;
2028                 isl_seq_clr(bmap->eq[j], 1+total);
2029                 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
2030                 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
2031                 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
2032         }
2033         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
2034         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
2035         bmap = add_divs(bmap, 2 * n_out);
2036
2037         bmap = isl_basic_map_simplify(bmap);
2038         return isl_basic_map_finalize(bmap);
2039 error:
2040         isl_basic_map_free(bmap);
2041         isl_basic_map_free(bmap1);
2042         isl_basic_map_free(bmap2);
2043         return NULL;
2044 }
2045
2046 /* Given a basic map A -> f(A), construct A -> -f(A).
2047  */
2048 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
2049 {
2050         int i, j;
2051         unsigned off, n;
2052
2053         bmap = isl_basic_map_cow(bmap);
2054         if (!bmap)
2055                 return NULL;
2056
2057         n = isl_basic_map_dim(bmap, isl_dim_out);
2058         off = isl_basic_map_offset(bmap, isl_dim_out);
2059         for (i = 0; i < bmap->n_eq; ++i)
2060                 for (j = 0; j < n; ++j)
2061                         isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
2062         for (i = 0; i < bmap->n_ineq; ++i)
2063                 for (j = 0; j < n; ++j)
2064                         isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
2065         for (i = 0; i < bmap->n_div; ++i)
2066                 for (j = 0; j < n; ++j)
2067                         isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
2068         return isl_basic_map_finalize(bmap);
2069 }
2070
2071 /* Given a basic map A -> f(A) and an integer d, construct a basic map
2072  * A -> floor(f(A)/d).
2073  */
2074 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
2075                 isl_int d)
2076 {
2077         unsigned n_in, n_out, nparam, total, pos;
2078         struct isl_basic_map *result = NULL;
2079         struct isl_dim_map *dim_map;
2080         int i;
2081
2082         if (!bmap)
2083                 return NULL;
2084
2085         nparam = isl_basic_map_n_param(bmap);
2086         n_in = isl_basic_map_n_in(bmap);
2087         n_out = isl_basic_map_n_out(bmap);
2088
2089         total = nparam + n_in + n_out + bmap->n_div + n_out;
2090         dim_map = isl_dim_map_alloc(bmap->ctx, total);
2091         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
2092         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
2093         isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
2094         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
2095
2096         result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
2097                         bmap->n_div + n_out,
2098                         bmap->n_eq, bmap->n_ineq + 2 * n_out);
2099         result = add_constraints_dim_map(result, bmap, dim_map);
2100         result = add_divs(result, n_out);
2101         for (i = 0; i < n_out; ++i) {
2102                 int j;
2103                 j = isl_basic_map_alloc_inequality(result);
2104                 if (j < 0)
2105                         goto error;
2106                 isl_seq_clr(result->ineq[j], 1+total);
2107                 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
2108                 isl_int_set_si(result->ineq[j][1+pos+i], 1);
2109                 j = isl_basic_map_alloc_inequality(result);
2110                 if (j < 0)
2111                         goto error;
2112                 isl_seq_clr(result->ineq[j], 1+total);
2113                 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
2114                 isl_int_set_si(result->ineq[j][1+pos+i], -1);
2115                 isl_int_sub_ui(result->ineq[j][0], d, 1);
2116         }
2117
2118         result = isl_basic_map_simplify(result);
2119         return isl_basic_map_finalize(result);
2120 error:
2121         isl_basic_map_free(result);
2122         return NULL;
2123 }
2124
2125 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
2126 {
2127         int i;
2128         unsigned nparam;
2129         unsigned n_in;
2130
2131         i = isl_basic_map_alloc_equality(bmap);
2132         if (i < 0)
2133                 goto error;
2134         nparam = isl_basic_map_n_param(bmap);
2135         n_in = isl_basic_map_n_in(bmap);
2136         isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
2137         isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
2138         isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
2139         return isl_basic_map_finalize(bmap);
2140 error:
2141         isl_basic_map_free(bmap);
2142         return NULL;
2143 }
2144
2145 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
2146 {
2147         int i;
2148         unsigned nparam;
2149         unsigned n_in;
2150
2151         i = isl_basic_map_alloc_inequality(bmap);
2152         if (i < 0)
2153                 goto error;
2154         nparam = isl_basic_map_n_param(bmap);
2155         n_in = isl_basic_map_n_in(bmap);
2156         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2157         isl_int_set_si(bmap->ineq[i][0], -1);
2158         isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
2159         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
2160         return isl_basic_map_finalize(bmap);
2161 error:
2162         isl_basic_map_free(bmap);
2163         return NULL;
2164 }
2165
2166 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
2167 {
2168         int i;
2169         unsigned nparam;
2170         unsigned n_in;
2171
2172         i = isl_basic_map_alloc_inequality(bmap);
2173         if (i < 0)
2174                 goto error;
2175         nparam = isl_basic_map_n_param(bmap);
2176         n_in = isl_basic_map_n_in(bmap);
2177         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2178         isl_int_set_si(bmap->ineq[i][0], -1);
2179         isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
2180         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
2181         return isl_basic_map_finalize(bmap);
2182 error:
2183         isl_basic_map_free(bmap);
2184         return NULL;
2185 }
2186
2187 struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
2188 {
2189         int i;
2190         struct isl_basic_map *bmap;
2191         bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
2192         if (!bmap)
2193                 return NULL;
2194         for (i = 0; i < n_equal && bmap; ++i)
2195                 bmap = var_equal(bmap, i);
2196         return isl_basic_map_finalize(bmap);
2197 }
2198
2199 struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
2200 {
2201         int i;
2202         struct isl_basic_map *bmap;
2203         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2204         if (!bmap)
2205                 return NULL;
2206         for (i = 0; i < pos && bmap; ++i)
2207                 bmap = var_equal(bmap, i);
2208         if (bmap)
2209                 bmap = var_less(bmap, pos);
2210         return isl_basic_map_finalize(bmap);
2211 }
2212
2213 struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
2214 {
2215         int i;
2216         struct isl_basic_map *bmap;
2217         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2218         if (!bmap)
2219                 return NULL;
2220         for (i = 0; i < pos && bmap; ++i)
2221                 bmap = var_equal(bmap, i);
2222         if (bmap)
2223                 bmap = var_more(bmap, pos);
2224         return isl_basic_map_finalize(bmap);
2225 }
2226
2227 struct isl_basic_map *isl_basic_map_from_basic_set(
2228                 struct isl_basic_set *bset, struct isl_dim *dim)
2229 {
2230         struct isl_basic_map *bmap;
2231
2232         bset = isl_basic_set_cow(bset);
2233         if (!bset || !dim)
2234                 goto error;
2235
2236         isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
2237         isl_dim_free(bset->dim);
2238         bmap = (struct isl_basic_map *) bset;
2239         bmap->dim = dim;
2240         return isl_basic_map_finalize(bmap);
2241 error:
2242         isl_basic_set_free(bset);
2243         isl_dim_free(dim);
2244         return NULL;
2245 }
2246
2247 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2248 {
2249         if (!bmap)
2250                 goto error;
2251         if (bmap->dim->n_in == 0)
2252                 return (struct isl_basic_set *)bmap;
2253         bmap = isl_basic_map_cow(bmap);
2254         if (!bmap)
2255                 goto error;
2256         bmap->dim = isl_dim_cow(bmap->dim);
2257         if (!bmap->dim)
2258                 goto error;
2259         bmap->dim->n_out += bmap->dim->n_in;
2260         bmap->dim->n_in = 0;
2261         bmap = isl_basic_map_finalize(bmap);
2262         return (struct isl_basic_set *)bmap;
2263 error:
2264         isl_basic_map_free(bmap);
2265         return NULL;
2266 }
2267
2268 /* For a div d = floor(f/m), add the constraints
2269  *
2270  *              f - m d >= 0
2271  *              -(f-(n-1)) + m d >= 0
2272  *
2273  * Note that the second constraint is the negation of
2274  *
2275  *              f - m d >= n
2276  */
2277 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2278 {
2279         int i, j;
2280         unsigned total = isl_basic_map_total_dim(bmap);
2281         unsigned div_pos = 1 + total - bmap->n_div + div;
2282
2283         i = isl_basic_map_alloc_inequality(bmap);
2284         if (i < 0)
2285                 return -1;
2286         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2287         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2288
2289         j = isl_basic_map_alloc_inequality(bmap);
2290         if (j < 0)
2291                 return -1;
2292         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2293         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2294         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2295         return j;
2296 }
2297
2298 struct isl_basic_set *isl_basic_map_underlying_set(
2299                 struct isl_basic_map *bmap)
2300 {
2301         if (!bmap)
2302                 goto error;
2303         if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
2304                 return (struct isl_basic_set *)bmap;
2305         bmap = isl_basic_map_cow(bmap);
2306         if (!bmap)
2307                 goto error;
2308         bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
2309         if (!bmap->dim)
2310                 goto error;
2311         bmap->extra -= bmap->n_div;
2312         bmap->n_div = 0;
2313         bmap = isl_basic_map_finalize(bmap);
2314         return (struct isl_basic_set *)bmap;
2315 error:
2316         return NULL;
2317 }
2318
2319 struct isl_basic_map *isl_basic_map_overlying_set(
2320         struct isl_basic_set *bset, struct isl_basic_map *like)
2321 {
2322         struct isl_basic_map *bmap;
2323         struct isl_ctx *ctx;
2324         unsigned total;
2325         int i;
2326
2327         if (!bset || !like)
2328                 goto error;
2329         ctx = bset->ctx;
2330         isl_assert(ctx, bset->n_div == 0, goto error);
2331         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
2332         isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
2333                         goto error);
2334         if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
2335                 isl_basic_map_free(like);
2336                 return (struct isl_basic_map *)bset;
2337         }
2338         bset = isl_basic_set_cow(bset);
2339         if (!bset)
2340                 goto error;
2341         total = bset->dim->n_out + bset->extra;
2342         bmap = (struct isl_basic_map *)bset;
2343         isl_dim_free(bmap->dim);
2344         bmap->dim = isl_dim_copy(like->dim);
2345         if (!bmap->dim)
2346                 goto error;
2347         bmap->n_div = like->n_div;
2348         bmap->extra += like->n_div;
2349         if (bmap->extra) {
2350                 unsigned ltotal;
2351                 ltotal = total - bmap->extra + like->extra;
2352                 if (ltotal > total)
2353                         ltotal = total;
2354                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2355                                         bmap->extra * (1 + 1 + total));
2356                 if (isl_blk_is_error(bmap->block2))
2357                         goto error;
2358                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2359                                                 bmap->extra);
2360                 if (!bmap->div)
2361                         goto error;
2362                 for (i = 0; i < bmap->extra; ++i)
2363                         bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
2364                 for (i = 0; i < like->n_div; ++i) {
2365                         isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
2366                         isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
2367                 }
2368                 bmap = isl_basic_map_extend_constraints(bmap,
2369                                                         0, 2 * like->n_div);
2370                 for (i = 0; i < like->n_div; ++i) {
2371                         if (isl_int_is_zero(bmap->div[i][0]))
2372                                 continue;
2373                         if (add_div_constraints(bmap, i) < 0)
2374                                 goto error;
2375                 }
2376         }
2377         isl_basic_map_free(like);
2378         bmap = isl_basic_map_simplify(bmap);
2379         bmap = isl_basic_map_finalize(bmap);
2380         return bmap;
2381 error:
2382         isl_basic_map_free(like);
2383         isl_basic_set_free(bset);
2384         return NULL;
2385 }
2386
2387 struct isl_basic_set *isl_basic_set_from_underlying_set(
2388         struct isl_basic_set *bset, struct isl_basic_set *like)
2389 {
2390         return (struct isl_basic_set *)
2391                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2392 }
2393
2394 struct isl_set *isl_set_from_underlying_set(
2395         struct isl_set *set, struct isl_basic_set *like)
2396 {
2397         int i;
2398
2399         if (!set || !like)
2400                 goto error;
2401         isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
2402                     goto error);
2403         if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
2404                 isl_basic_set_free(like);
2405                 return set;
2406         }
2407         set = isl_set_cow(set);
2408         if (!set)
2409                 goto error;
2410         for (i = 0; i < set->n; ++i) {
2411                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2412                                                       isl_basic_set_copy(like));
2413                 if (!set->p[i])
2414                         goto error;
2415         }
2416         isl_dim_free(set->dim);
2417         set->dim = isl_dim_copy(like->dim);
2418         if (!set->dim)
2419                 goto error;
2420         isl_basic_set_free(like);
2421         return set;
2422 error:
2423         isl_basic_set_free(like);
2424         isl_set_free(set);
2425         return NULL;
2426 }
2427
2428 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2429 {
2430         int i;
2431
2432         map = isl_map_cow(map);
2433         if (!map)
2434                 return NULL;
2435         map->dim = isl_dim_cow(map->dim);
2436         if (!map->dim)
2437                 goto error;
2438
2439         for (i = 1; i < map->n; ++i)
2440                 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
2441                                 goto error);
2442         for (i = 0; i < map->n; ++i) {
2443                 map->p[i] = (struct isl_basic_map *)
2444                                 isl_basic_map_underlying_set(map->p[i]);
2445                 if (!map->p[i])
2446                         goto error;
2447         }
2448         if (map->n == 0)
2449                 map->dim = isl_dim_underlying(map->dim, 0);
2450         else {
2451                 isl_dim_free(map->dim);
2452                 map->dim = isl_dim_copy(map->p[0]->dim);
2453         }
2454         if (!map->dim)
2455                 goto error;
2456         return (struct isl_set *)map;
2457 error:
2458         isl_map_free(map);
2459         return NULL;
2460 }
2461
2462 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2463 {
2464         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2465 }
2466
2467 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2468 {
2469         struct isl_basic_set *domain;
2470         unsigned n_out;
2471         if (!bmap)
2472                 return NULL;
2473         n_out = isl_basic_map_n_out(bmap);
2474         domain = isl_basic_set_from_basic_map(bmap);
2475         return isl_basic_set_project_out(domain, n_out, 0);
2476 }
2477
2478 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2479 {
2480         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2481 }
2482
2483 struct isl_set *isl_map_range(struct isl_map *map)
2484 {
2485         int i;
2486         struct isl_set *set;
2487
2488         if (!map)
2489                 goto error;
2490         map = isl_map_cow(map);
2491         if (!map)
2492                 goto error;
2493
2494         set = (struct isl_set *) map;
2495         if (set->dim->n_in != 0) {
2496                 set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
2497                 if (!set->dim)
2498                         goto error;
2499         }
2500         for (i = 0; i < map->n; ++i) {
2501                 set->p[i] = isl_basic_map_range(map->p[i]);
2502                 if (!set->p[i])
2503                         goto error;
2504         }
2505         ISL_F_CLR(set, ISL_MAP_DISJOINT);
2506         ISL_F_CLR(set, ISL_SET_NORMALIZED);
2507         return set;
2508 error:
2509         isl_map_free(map);
2510         return NULL;
2511 }
2512
2513 struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
2514 {
2515         int i;
2516         struct isl_map *map = NULL;
2517
2518         set = isl_set_cow(set);
2519         if (!set || !dim)
2520                 goto error;
2521         isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
2522         map = (struct isl_map *)set;
2523         for (i = 0; i < set->n; ++i) {
2524                 map->p[i] = isl_basic_map_from_basic_set(
2525                                 set->p[i], isl_dim_copy(dim));
2526                 if (!map->p[i])
2527                         goto error;
2528         }
2529         isl_dim_free(map->dim);
2530         map->dim = dim;
2531         return map;
2532 error:
2533         isl_dim_free(dim);
2534         isl_set_free(set);
2535         return NULL;
2536 }
2537
2538 struct isl_map *isl_map_from_range(struct isl_set *set)
2539 {
2540         return (struct isl_map *)set;
2541 }
2542
2543 struct isl_set *isl_set_from_map(struct isl_map *map)
2544 {
2545         int i;
2546         struct isl_set *set = NULL;
2547
2548         if (!map)
2549                 return NULL;
2550         map = isl_map_cow(map);
2551         if (!map)
2552                 return NULL;
2553         map->dim = isl_dim_cow(map->dim);
2554         if (!map->dim)
2555                 goto error;
2556         map->dim->n_out += map->dim->n_in;
2557         map->dim->n_in = 0;
2558         set = (struct isl_set *)map;
2559         for (i = 0; i < map->n; ++i) {
2560                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2561                 if (!set->p[i])
2562                         goto error;
2563         }
2564         return set;
2565 error:
2566         isl_map_free(map);
2567         return NULL;
2568 }
2569
2570 struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
2571 {
2572         struct isl_map *map;
2573
2574         if (!dim)
2575                 return NULL;
2576         isl_assert(dim->ctx, n >= 0, return NULL);
2577         map = isl_alloc(dim->ctx, struct isl_map,
2578                         sizeof(struct isl_map) +
2579                         n * sizeof(struct isl_basic_map *));
2580         if (!map)
2581                 goto error;
2582
2583         map->ctx = dim->ctx;
2584         isl_ctx_ref(map->ctx);
2585         map->ref = 1;
2586         map->size = n;
2587         map->n = 0;
2588         map->dim = dim;
2589         map->flags = flags;
2590         return map;
2591 error:
2592         isl_dim_free(dim);
2593         return NULL;
2594 }
2595
2596 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2597                 unsigned nparam, unsigned in, unsigned out, int n,
2598                 unsigned flags)
2599 {
2600         struct isl_map *map;
2601         struct isl_dim *dims;
2602
2603         dims = isl_dim_alloc(ctx, nparam, in, out);
2604         if (!dims)
2605                 return NULL;
2606
2607         map = isl_map_alloc_dim(dims, n, flags);
2608         return map;
2609 }
2610
2611 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2612                 unsigned nparam, unsigned in, unsigned out)
2613 {
2614         struct isl_basic_map *bmap;
2615         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2616         bmap = isl_basic_map_set_to_empty(bmap);
2617         return bmap;
2618 }
2619
2620 struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
2621 {
2622         struct isl_basic_set *bset;
2623         bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
2624         bset = isl_basic_set_set_to_empty(bset);
2625         return bset;
2626 }
2627
2628 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
2629 {
2630         struct isl_basic_map *bmap;
2631         if (!model)
2632                 return NULL;
2633         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2634         bmap = isl_basic_map_set_to_empty(bmap);
2635         return bmap;
2636 }
2637
2638 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
2639 {
2640         struct isl_basic_map *bmap;
2641         if (!model)
2642                 return NULL;
2643         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2644         bmap = isl_basic_map_set_to_empty(bmap);
2645         return bmap;
2646 }
2647
2648 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
2649 {
2650         struct isl_basic_set *bset;
2651         if (!model)
2652                 return NULL;
2653         bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2654         bset = isl_basic_set_set_to_empty(bset);
2655         return bset;
2656 }
2657
2658 struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
2659 {
2660         struct isl_basic_map *bmap;
2661         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
2662         return bmap;
2663 }
2664
2665 struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
2666 {
2667         struct isl_basic_set *bset;
2668         bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
2669         return bset;
2670 }
2671
2672 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
2673 {
2674         if (!model)
2675                 return NULL;
2676         return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
2677 }
2678
2679 struct isl_map *isl_map_empty(struct isl_dim *dim)
2680 {
2681         return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2682 }
2683
2684 struct isl_map *isl_map_empty_like(struct isl_map *model)
2685 {
2686         if (!model)
2687                 return NULL;
2688         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2689 }
2690
2691 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
2692 {
2693         if (!model)
2694                 return NULL;
2695         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2696 }
2697
2698 struct isl_set *isl_set_empty(struct isl_dim *dim)
2699 {
2700         return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2701 }
2702
2703 struct isl_set *isl_set_empty_like(struct isl_set *model)
2704 {
2705         if (!model)
2706                 return NULL;
2707         return isl_set_empty(isl_dim_copy(model->dim));
2708 }
2709
2710 struct isl_map *isl_map_universe(struct isl_dim *dim)
2711 {
2712         struct isl_map *map;
2713         if (!dim)
2714                 return NULL;
2715         map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2716         map = isl_map_add(map, isl_basic_map_universe(dim));
2717         return map;
2718 }
2719
2720 struct isl_set *isl_set_universe(struct isl_dim *dim)
2721 {
2722         struct isl_set *set;
2723         if (!dim)
2724                 return NULL;
2725         set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2726         set = isl_set_add(set, isl_basic_set_universe(dim));
2727         return set;
2728 }
2729
2730 struct isl_map *isl_map_dup(struct isl_map *map)
2731 {
2732         int i;
2733         struct isl_map *dup;
2734
2735         if (!map)
2736                 return NULL;
2737         dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
2738         for (i = 0; i < map->n; ++i)
2739                 dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
2740         return dup;
2741 }
2742
2743 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2744 {
2745         if (!bmap || !map)
2746                 goto error;
2747         if (isl_basic_map_fast_is_empty(bmap)) {
2748                 isl_basic_map_free(bmap);
2749                 return map;
2750         }
2751         isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
2752         isl_assert(map->ctx, map->n < map->size, goto error);
2753         map->p[map->n] = bmap;
2754         map->n++;
2755         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2756         return map;
2757 error:
2758         if (map)
2759                 isl_map_free(map);
2760         if (bmap)
2761                 isl_basic_map_free(bmap);
2762         return NULL;
2763 }
2764
2765 void isl_map_free(struct isl_map *map)
2766 {
2767         int i;
2768
2769         if (!map)
2770                 return;
2771
2772         if (--map->ref > 0)
2773                 return;
2774
2775         isl_ctx_deref(map->ctx);
2776         for (i = 0; i < map->n; ++i)
2777                 isl_basic_map_free(map->p[i]);
2778         isl_dim_free(map->dim);
2779         free(map);
2780 }
2781
2782 struct isl_map *isl_map_extend(struct isl_map *base,
2783                 unsigned nparam, unsigned n_in, unsigned n_out)
2784 {
2785         int i;
2786
2787         base = isl_map_cow(base);
2788         if (!base)
2789                 return NULL;
2790
2791         base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
2792         if (!base->dim)
2793                 goto error;
2794         for (i = 0; i < base->n; ++i) {
2795                 base->p[i] = isl_basic_map_extend_dim(base->p[i],
2796                                 isl_dim_copy(base->dim), 0, 0, 0);
2797                 if (!base->p[i])
2798                         goto error;
2799         }
2800         return base;
2801 error:
2802         isl_map_free(base);
2803         return NULL;
2804 }
2805
2806 struct isl_set *isl_set_extend(struct isl_set *base,
2807                 unsigned nparam, unsigned dim)
2808 {
2809         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2810                                                         nparam, 0, dim);
2811 }
2812
2813 static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
2814                 unsigned pos, int value)
2815 {
2816         int j;
2817
2818         bmap = isl_basic_map_cow(bmap);
2819         bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
2820         j = isl_basic_map_alloc_equality(bmap);
2821         if (j < 0)
2822                 goto error;
2823         isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
2824         isl_int_set_si(bmap->eq[j][pos], -1);
2825         isl_int_set_si(bmap->eq[j][0], value);
2826         bmap = isl_basic_map_simplify(bmap);
2827         return isl_basic_map_finalize(bmap);
2828 error:
2829         isl_basic_map_free(bmap);
2830         return NULL;
2831 }
2832
2833 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
2834                 enum isl_dim_type type, unsigned pos, int value)
2835 {
2836         if (!bmap)
2837                 return NULL;
2838         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
2839         return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
2840                                         value);
2841 error:
2842         isl_basic_map_free(bmap);
2843         return NULL;
2844 }
2845
2846 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
2847                 enum isl_dim_type type, unsigned pos, int value)
2848 {
2849         return (struct isl_basic_set *)
2850                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2851                                         type, pos, value);
2852 }
2853
2854 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2855                 unsigned input, int value)
2856 {
2857         return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
2858 }
2859
2860 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2861                 unsigned dim, int value)
2862 {
2863         return (struct isl_basic_set *)
2864                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2865                                         isl_dim_set, dim, value);
2866 }
2867
2868 struct isl_map *isl_map_fix_si(struct isl_map *map,
2869                 enum isl_dim_type type, unsigned pos, int value)
2870 {
2871         int i;
2872
2873         map = isl_map_cow(map);
2874         if (!map)
2875                 return NULL;
2876
2877         isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
2878         for (i = 0; i < map->n; ++i) {
2879                 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
2880                 if (!map->p[i])
2881                         goto error;
2882         }
2883         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2884         return map;
2885 error:
2886         isl_map_free(map);
2887         return NULL;
2888 }
2889
2890 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2891                 unsigned input, int value)
2892 {
2893         return isl_map_fix_si(map, isl_dim_in, input, value);
2894 }
2895
2896 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2897 {
2898         return (struct isl_set *)
2899                 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
2900 }
2901
2902 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
2903         unsigned dim, isl_int value)
2904 {
2905         int j;
2906         unsigned nparam;
2907
2908         bset = isl_basic_set_cow(bset);
2909         bset = isl_basic_set_extend_constraints(bset, 0, 1);
2910         j = isl_basic_set_alloc_inequality(bset);
2911         if (j < 0)
2912                 goto error;
2913         isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
2914         isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
2915         isl_int_neg(bset->ineq[j][0], value);
2916         bset = isl_basic_set_simplify(bset);
2917         return isl_basic_set_finalize(bset);
2918 error:
2919         isl_basic_set_free(bset);
2920         return NULL;
2921 }
2922
2923 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
2924                                         isl_int value)
2925 {
2926         int i;
2927
2928         set = isl_set_cow(set);
2929         if (!set)
2930                 return NULL;
2931
2932         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
2933         for (i = 0; i < set->n; ++i) {
2934                 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
2935                 if (!set->p[i])
2936                         goto error;
2937         }
2938         return set;
2939 error:
2940         isl_set_free(set);
2941         return NULL;
2942 }
2943
2944 struct isl_map *isl_map_reverse(struct isl_map *map)
2945 {
2946         int i;
2947         unsigned t;
2948
2949         map = isl_map_cow(map);
2950         if (!map)
2951                 return NULL;
2952
2953         map->dim = isl_dim_reverse(map->dim);
2954         if (!map->dim)
2955                 goto error;
2956         for (i = 0; i < map->n; ++i) {
2957                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2958                 if (!map->p[i])
2959                         goto error;
2960         }
2961         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2962         return map;
2963 error:
2964         isl_map_free(map);
2965         return NULL;
2966 }
2967
2968 static struct isl_map *isl_basic_map_partial_lexopt(
2969                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2970                 struct isl_set **empty, int max)
2971 {
2972         if (!bmap)
2973                 goto error;
2974         if (bmap->ctx->pip == ISL_PIP_PIP)
2975                 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
2976         else
2977                 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
2978 error:
2979         isl_basic_map_free(bmap);
2980         isl_basic_set_free(dom);
2981         if (empty)
2982                 *empty = NULL;
2983         return NULL;
2984 }
2985
2986 struct isl_map *isl_basic_map_partial_lexmax(
2987                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2988                 struct isl_set **empty)
2989 {
2990         return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
2991 }
2992
2993 struct isl_map *isl_basic_map_partial_lexmin(
2994                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2995                 struct isl_set **empty)
2996 {
2997         return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
2998 }
2999
3000 struct isl_set *isl_basic_set_partial_lexmin(
3001                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3002                 struct isl_set **empty)
3003 {
3004         return (struct isl_set *)
3005                 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
3006                         dom, empty);
3007 }
3008
3009 struct isl_set *isl_basic_set_partial_lexmax(
3010                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3011                 struct isl_set **empty)
3012 {
3013         return (struct isl_set *)
3014                 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
3015                         dom, empty);
3016 }
3017
3018 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
3019 {
3020         struct isl_basic_map *bmap = NULL;
3021         struct isl_basic_set *dom = NULL;
3022         struct isl_map *min;
3023         struct isl_dim *param_dim;
3024
3025         if (!bset)
3026                 goto error;
3027         bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
3028         if (!bmap)
3029                 goto error;
3030         param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3031         dom = isl_basic_set_universe(param_dim);
3032         if (!dom)
3033                 goto error;
3034         min = isl_basic_map_partial_lexmin(bmap, dom, NULL);
3035         return isl_map_range(min);
3036 error:
3037         isl_basic_map_free(bmap);
3038         return NULL;
3039 }
3040
3041 static struct isl_map *isl_map_reset_dim(struct isl_map *map,
3042         struct isl_dim *dim)
3043 {
3044         int i;
3045
3046         if (!map || !dim)
3047                 goto error;
3048
3049         for (i = 0; i < map->n; ++i) {
3050                 isl_dim_free(map->p[i]->dim);
3051                 map->p[i]->dim = isl_dim_copy(dim);
3052         }
3053         isl_dim_free(map->dim);
3054         map->dim = dim;
3055
3056         return map;
3057 error:
3058         isl_map_free(map);
3059         isl_dim_free(dim);
3060         return NULL;
3061 }
3062
3063 static struct isl_set *isl_set_reset_dim(struct isl_set *set,
3064         struct isl_dim *dim)
3065 {
3066         return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
3067 }
3068
3069 /* Apply a preimage specified by "mat" on the parameters of "bset".
3070  * bset is assumed to have only parameters and divs.
3071  */
3072 static struct isl_basic_set *basic_set_parameter_preimage(
3073         struct isl_basic_set *bset, struct isl_mat *mat)
3074 {
3075         unsigned nparam;
3076
3077         if (!bset || !mat)
3078                 goto error;
3079
3080         bset->dim = isl_dim_cow(bset->dim);
3081         if (!bset->dim)
3082                 goto error;
3083
3084         nparam = isl_basic_set_dim(bset, isl_dim_param);
3085
3086         isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
3087
3088         bset->dim->nparam = 0;
3089         bset->dim->n_out = nparam;
3090         bset = isl_basic_set_preimage(bset, mat);
3091         if (bset) {
3092                 bset->dim->nparam = bset->dim->n_out;
3093                 bset->dim->n_out = 0;
3094         }
3095         return bset;
3096 error:
3097         isl_mat_free(mat);
3098         isl_basic_set_free(bset);
3099         return NULL;
3100 }
3101
3102 /* Apply a preimage specified by "mat" on the parameters of "set".
3103  * set is assumed to have only parameters and divs.
3104  */
3105 static struct isl_set *set_parameter_preimage(
3106         struct isl_set *set, struct isl_mat *mat)
3107 {
3108         struct isl_dim *dim = NULL;
3109         unsigned nparam;
3110
3111         if (!set || !mat)
3112                 goto error;
3113
3114         dim = isl_dim_copy(set->dim);
3115         dim = isl_dim_cow(dim);
3116         if (!dim)
3117                 goto error;
3118
3119         nparam = isl_set_dim(set, isl_dim_param);
3120
3121         isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
3122
3123         dim->nparam = 0;
3124         dim->n_out = nparam;
3125         isl_set_reset_dim(set, dim);
3126         set = isl_set_preimage(set, mat);
3127         if (!set)
3128                 goto error2;
3129         dim = isl_dim_copy(set->dim);
3130         dim = isl_dim_cow(dim);
3131         if (!dim)
3132                 goto error2;
3133         dim->nparam = dim->n_out;
3134         dim->n_out = 0;
3135         isl_set_reset_dim(set, dim);
3136         return set;
3137 error:
3138         isl_dim_free(dim);
3139         isl_mat_free(mat);
3140 error2:
3141         isl_set_free(set);
3142         return NULL;
3143 }
3144
3145 /* Intersect the basic set "bset" with the affine space specified by the
3146  * equalities in "eq".
3147  */
3148 static struct isl_basic_set *basic_set_append_equalities(
3149         struct isl_basic_set *bset, struct isl_mat *eq)
3150 {
3151         int i, k;
3152         unsigned len;
3153
3154         if (!bset || !eq)
3155                 goto error;
3156
3157         bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
3158                                         eq->n_row, 0);
3159         if (!bset)
3160                 goto error;
3161
3162         len = 1 + isl_dim_total(bset->dim) + bset->extra;
3163         for (i = 0; i < eq->n_row; ++i) {
3164                 k = isl_basic_set_alloc_equality(bset);
3165                 if (k < 0)
3166                         goto error;
3167                 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
3168                 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
3169         }
3170         isl_mat_free(eq);
3171
3172         return bset;
3173 error:
3174         isl_mat_free(eq);
3175         isl_basic_set_free(bset);
3176         return NULL;
3177 }
3178
3179 /* Intersect the set "set" with the affine space specified by the
3180  * equalities in "eq".
3181  */
3182 static struct isl_set *set_append_equalities(struct isl_set *set,
3183         struct isl_mat *eq)
3184 {
3185         int i;
3186
3187         if (!set || !eq)
3188                 goto error;
3189
3190         for (i = 0; i < set->n; ++i) {
3191                 set->p[i] = basic_set_append_equalities(set->p[i],
3192                                         isl_mat_copy(eq));
3193                 if (!set->p[i])
3194                         goto error;
3195         }
3196         isl_mat_free(eq);
3197         return set;
3198 error:
3199         isl_mat_free(eq);
3200         isl_set_free(set);
3201         return NULL;
3202 }
3203
3204 /* Project the given basic set onto its parameter domain, possibly introducing
3205  * new, explicit, existential variables in the constraints.
3206  * The input has parameters and (possibly implicit) existential variables.
3207  * The output has the same parameters, but only
3208  * explicit existentially quantified variables.
3209  *
3210  * The actual projection is performed by pip, but pip doesn't seem
3211  * to like equalities very much, so we first remove the equalities
3212  * among the parameters by performing a variable compression on
3213  * the parameters.  Afterward, an inverse transformation is performed
3214  * and the equalities among the parameters are inserted back in.
3215  */
3216 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
3217 {
3218         int i, j;
3219         struct isl_mat *eq;
3220         struct isl_mat *T, *T2;
3221         struct isl_set *set;
3222         unsigned nparam, n_div;
3223
3224         bset = isl_basic_set_cow(bset);
3225         if (!bset)
3226                 return NULL;
3227
3228         if (bset->n_eq == 0)
3229                 return isl_basic_set_lexmin(bset);
3230
3231         isl_basic_set_gauss(bset, NULL);
3232
3233         nparam = isl_basic_set_dim(bset, isl_dim_param);
3234         n_div = isl_basic_set_dim(bset, isl_dim_div);
3235
3236         for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
3237                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
3238                         ++i;
3239         }
3240         if (i == bset->n_eq)
3241                 return isl_basic_set_lexmin(bset);
3242
3243         eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
3244                 0, 1 + nparam);
3245         eq = isl_mat_cow(eq);
3246         T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
3247         bset = basic_set_parameter_preimage(bset, T);
3248
3249         set = isl_basic_set_lexmin(bset);
3250         set = set_parameter_preimage(set, T2);
3251         set = set_append_equalities(set, eq);
3252         return set;
3253 }
3254
3255 /* Compute an explicit representation for all the existentially
3256  * quantified variables.
3257  * The input and output dimensions are first turned into parameters.
3258  * compute_divs then returns a map with the same parameters and
3259  * no input or output dimensions and the dimension specification
3260  * is reset to that of the input.
3261  */
3262 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
3263 {
3264         struct isl_basic_set *bset;
3265         struct isl_set *set;
3266         struct isl_map *map;
3267         struct isl_dim *dim, *orig_dim = NULL;
3268         unsigned         nparam;
3269         unsigned         n_in;
3270         unsigned         n_out;
3271
3272         bmap = isl_basic_map_cow(bmap);
3273         if (!bmap)
3274                 return NULL;
3275
3276         nparam = isl_basic_map_dim(bmap, isl_dim_param);
3277         n_in = isl_basic_map_dim(bmap, isl_dim_in);
3278         n_out = isl_basic_map_dim(bmap, isl_dim_out);
3279         dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
3280         if (!dim)
3281                 goto error;
3282
3283         orig_dim = bmap->dim;
3284         bmap->dim = dim;
3285         bset = (struct isl_basic_set *)bmap;
3286
3287         set = parameter_compute_divs(bset);
3288         map = (struct isl_map *)set;
3289         map = isl_map_reset_dim(map, orig_dim);
3290
3291         return map;
3292 error:
3293         isl_basic_map_free(bmap);
3294         return NULL;
3295 }
3296
3297 /* If bmap contains any unknown divs, then compute explicit
3298  * expressions for them.  However, this computation may be
3299  * quite expensive, so first try to remove divs that aren't
3300  * strictly needed.
3301  */
3302 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
3303 {
3304         int i;
3305         unsigned off;
3306
3307         if (!bmap)
3308                 return NULL;
3309         off = isl_dim_total(bmap->dim);
3310         for (i = 0; i < bmap->n_div; ++i) {
3311                 if (isl_int_is_zero(bmap->div[i][0]))
3312                         break;
3313                 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
3314                                 goto error);
3315         }
3316         if (i == bmap->n_div)
3317                 return isl_map_from_basic_map(bmap);
3318         bmap = isl_basic_map_drop_redundant_divs(bmap);
3319         if (!bmap)
3320                 goto error;
3321         for (i = 0; i < bmap->n_div; ++i)
3322                 if (isl_int_is_zero(bmap->div[i][0]))
3323                         break;
3324         if (i == bmap->n_div)
3325                 return isl_map_from_basic_map(bmap);
3326         struct isl_map *map = compute_divs(bmap);
3327         return map;
3328 error:
3329         isl_basic_map_free(bmap);
3330         return NULL;
3331 }
3332
3333 struct isl_map *isl_map_compute_divs(struct isl_map *map)
3334 {
3335         int i;
3336         struct isl_map *res;
3337
3338         if (!map)
3339                 return NULL;
3340         if (map->n == 0)
3341                 return map;
3342         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
3343         for (i = 1 ; i < map->n; ++i) {
3344                 struct isl_map *r2;
3345                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
3346                 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
3347                         res = isl_map_union_disjoint(res, r2);
3348                 else
3349                         res = isl_map_union(res, r2);
3350         }
3351         isl_map_free(map);
3352
3353         return res;
3354 }
3355
3356 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
3357 {
3358         return (struct isl_set *)
3359                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
3360 }
3361
3362 struct isl_set *isl_set_compute_divs(struct isl_set *set)
3363 {
3364         return (struct isl_set *)
3365                 isl_map_compute_divs((struct isl_map *)set);
3366 }
3367
3368 struct isl_set *isl_map_domain(struct isl_map *map)
3369 {
3370         int i;
3371         struct isl_set *set;
3372
3373         if (!map)
3374                 goto error;
3375
3376         map = isl_map_cow(map);
3377         if (!map)
3378                 return NULL;
3379
3380         set = (struct isl_set *)map;
3381         set->dim = isl_dim_domain(set->dim);
3382         if (!set->dim)
3383                 goto error;
3384         for (i = 0; i < map->n; ++i) {
3385                 set->p[i] = isl_basic_map_domain(map->p[i]);
3386                 if (!set->p[i])
3387                         goto error;
3388         }
3389         ISL_F_CLR(set, ISL_MAP_DISJOINT);
3390         ISL_F_CLR(set, ISL_SET_NORMALIZED);
3391         return set;
3392 error:
3393         isl_map_free(map);
3394         return NULL;
3395 }
3396
3397 struct isl_map *isl_map_union_disjoint(
3398                         struct isl_map *map1, struct isl_map *map2)
3399 {
3400         int i;
3401         unsigned flags = 0;
3402         struct isl_map *map = NULL;
3403
3404         if (!map1 || !map2)
3405                 goto error;
3406
3407         if (map1->n == 0) {
3408                 isl_map_free(map1);
3409                 return map2;
3410         }
3411         if (map2->n == 0) {
3412                 isl_map_free(map2);
3413                 return map1;
3414         }
3415
3416         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
3417
3418         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
3419             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
3420                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3421
3422         map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
3423                                 map1->n + map2->n, flags);
3424         if (!map)
3425                 goto error;
3426         for (i = 0; i < map1->n; ++i) {
3427                 map = isl_map_add(map,
3428                                   isl_basic_map_copy(map1->p[i]));
3429                 if (!map)
3430                         goto error;
3431         }
3432         for (i = 0; i < map2->n; ++i) {
3433                 map = isl_map_add(map,
3434                                   isl_basic_map_copy(map2->p[i]));
3435                 if (!map)
3436                         goto error;
3437         }
3438         isl_map_free(map1);
3439         isl_map_free(map2);
3440         return map;
3441 error:
3442         isl_map_free(map);
3443         isl_map_free(map1);
3444         isl_map_free(map2);
3445         return NULL;
3446 }
3447
3448 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
3449 {
3450         map1 = isl_map_union_disjoint(map1, map2);
3451         if (!map1)
3452                 return NULL;
3453         if (map1->n > 1)
3454                 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
3455         return map1;
3456 }
3457
3458 struct isl_set *isl_set_union_disjoint(
3459                         struct isl_set *set1, struct isl_set *set2)
3460 {
3461         return (struct isl_set *)
3462                 isl_map_union_disjoint(
3463                         (struct isl_map *)set1, (struct isl_map *)set2);
3464 }
3465
3466 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
3467 {
3468         return (struct isl_set *)
3469                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
3470 }
3471
3472 struct isl_map *isl_map_intersect_range(
3473                 struct isl_map *map, struct isl_set *set)
3474 {
3475         unsigned flags = 0;
3476         struct isl_map *result;
3477         int i, j;
3478
3479         if (!map || !set)
3480                 goto error;
3481
3482         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
3483             ISL_F_ISSET(set, ISL_MAP_DISJOINT))
3484                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3485
3486         result = isl_map_alloc_dim(isl_dim_copy(map->dim),
3487                                         map->n * set->n, flags);
3488         if (!result)
3489                 goto error;
3490         for (i = 0; i < map->n; ++i)
3491                 for (j = 0; j < set->n; ++j) {
3492                         result = isl_map_add(result,
3493                             isl_basic_map_intersect_range(
3494                                 isl_basic_map_copy(map->p[i]),
3495                                 isl_basic_set_copy(set->p[j])));
3496                         if (!result)
3497                                 goto error;
3498                 }
3499         isl_map_free(map);
3500         isl_set_free(set);
3501         return result;
3502 error:
3503         isl_map_free(map);
3504         isl_set_free(set);
3505         return NULL;
3506 }
3507
3508 struct isl_map *isl_map_intersect_domain(
3509                 struct isl_map *map, struct isl_set *set)
3510 {
3511         return isl_map_reverse(
3512                 isl_map_intersect_range(isl_map_reverse(map), set));
3513 }
3514
3515 struct isl_map *isl_map_apply_domain(
3516                 struct isl_map *map1, struct isl_map *map2)
3517 {
3518         if (!map1 || !map2)
3519                 goto error;
3520         map1 = isl_map_reverse(map1);
3521         map1 = isl_map_apply_range(map1, map2);
3522         return isl_map_reverse(map1);
3523 error:
3524         isl_map_free(map1);
3525         isl_map_free(map2);
3526         return NULL;
3527 }
3528
3529 struct isl_map *isl_map_apply_range(
3530                 struct isl_map *map1, struct isl_map *map2)
3531 {
3532         struct isl_dim *dim_result;
3533         struct isl_map *result;
3534         int i, j;
3535         unsigned nparam;
3536         unsigned n_in;
3537         unsigned n_out;
3538
3539         if (!map1 || !map2)
3540                 goto error;
3541
3542         dim_result = isl_dim_join(isl_dim_copy(map1->dim),
3543                                   isl_dim_copy(map2->dim));
3544
3545         result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
3546         if (!result)
3547                 goto error;
3548         for (i = 0; i < map1->n; ++i)
3549                 for (j = 0; j < map2->n; ++j) {
3550                         result = isl_map_add(result,
3551                             isl_basic_map_apply_range(
3552                                 isl_basic_map_copy(map1->p[i]),
3553                                 isl_basic_map_copy(map2->p[j])));
3554                         if (!result)
3555                                 goto error;
3556                 }
3557         isl_map_free(map1);
3558         isl_map_free(map2);
3559         if (result && result->n <= 1)
3560                 ISL_F_SET(result, ISL_MAP_DISJOINT);
3561         return result;
3562 error:
3563         isl_map_free(map1);
3564         isl_map_free(map2);
3565         return NULL;
3566 }
3567
3568 /*
3569  * returns range - domain
3570  */
3571 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3572 {
3573         struct isl_basic_set *bset;
3574         unsigned dim;
3575         unsigned nparam;
3576         int i;
3577
3578         if (!bmap)
3579                 goto error;
3580         dim = isl_basic_map_n_in(bmap);
3581         nparam = isl_basic_map_n_param(bmap);
3582         isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
3583         bset = isl_basic_set_from_basic_map(bmap);
3584         bset = isl_basic_set_cow(bset);
3585         bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
3586         bset = isl_basic_set_swap_vars(bset, 2*dim);
3587         for (i = 0; i < dim; ++i) {
3588                 int j = isl_basic_map_alloc_equality(
3589                                             (struct isl_basic_map *)bset);
3590                 if (j < 0)
3591                         goto error;
3592                 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
3593                 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
3594                 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
3595                 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
3596         }
3597         return isl_basic_set_project_out(bset, 2*dim, 0);
3598 error:
3599         isl_basic_map_free(bmap);
3600         return NULL;
3601 }
3602
3603 /*
3604  * returns range - domain
3605  */
3606 struct isl_set *isl_map_deltas(struct isl_map *map)
3607 {
3608         int i;
3609         struct isl_set *result;
3610
3611         if (!map)
3612                 return NULL;
3613
3614         isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
3615         result = isl_set_alloc(map->ctx, isl_map_n_param(map),
3616                                         isl_map_n_in(map), map->n, map->flags);
3617         if (!result)
3618                 goto error;
3619         for (i = 0; i < map->n; ++i)
3620                 result = isl_set_add(result,
3621                           isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3622         isl_map_free(map);
3623         return result;
3624 error:
3625         isl_map_free(map);
3626         return NULL;
3627 }
3628
3629 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
3630 {
3631         struct isl_basic_map *bmap;
3632         unsigned nparam;
3633         unsigned dim;
3634         int i;
3635
3636         if (!dims)
3637                 return NULL;
3638
3639         nparam = dims->nparam;
3640         dim = dims->n_out;
3641         bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
3642         if (!bmap)
3643                 goto error;
3644
3645         for (i = 0; i < dim; ++i) {
3646                 int j = isl_basic_map_alloc_equality(bmap);
3647                 if (j < 0)
3648                         goto error;
3649                 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3650                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3651                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3652         }
3653         return isl_basic_map_finalize(bmap);
3654 error:
3655         isl_basic_map_free(bmap);
3656         return NULL;
3657 }
3658
3659 struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
3660 {
3661         struct isl_dim *dim = isl_dim_map(set_dim);
3662         if (!dim)
3663                 return NULL;
3664         return basic_map_identity(dim);
3665 }
3666
3667 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
3668 {
3669         if (!model || !model->dim)
3670                 return NULL;
3671         isl_assert(model->ctx,
3672                         model->dim->n_in == model->dim->n_out, return NULL);
3673         return basic_map_identity(isl_dim_copy(model->dim));
3674 }
3675
3676 static struct isl_map *map_identity(struct isl_dim *dim)
3677 {
3678         struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
3679         return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
3680 }
3681
3682 struct isl_map *isl_map_identity(struct isl_dim *set_dim)
3683 {
3684         struct isl_dim *dim = isl_dim_map(set_dim);
3685         if (!dim)
3686                 return NULL;
3687         return map_identity(dim);
3688 }
3689
3690 struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
3691 {
3692         if (!model || !model->dim)
3693                 return NULL;
3694         isl_assert(model->ctx,
3695                         model->dim->n_in == model->dim->n_out, return NULL);
3696         return map_identity(isl_dim_copy(model->dim));
3697 }
3698
3699 /* Construct a basic set with all set dimensions having only non-negative
3700  * values.
3701  */
3702 struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
3703 {
3704         int i;
3705         unsigned nparam;
3706         unsigned dim;
3707         struct isl_basic_set *bset;
3708
3709         if (!dims)
3710                 return NULL;
3711         nparam = dims->nparam;
3712         dim = dims->n_out;
3713         bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
3714         if (!bset)
3715                 return NULL;
3716         for (i = 0; i < dim; ++i) {
3717                 int k = isl_basic_set_alloc_inequality(bset);
3718                 if (k < 0)
3719                         goto error;
3720                 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
3721                 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
3722         }
3723         return bset;
3724 error:
3725         isl_basic_set_free(bset);
3726         return NULL;
3727 }
3728
3729 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3730 {
3731         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3732 }
3733
3734 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3735 {
3736         return isl_map_is_subset(
3737                         (struct isl_map *)set1, (struct isl_map *)set2);
3738 }
3739
3740 int isl_basic_map_is_subset(
3741                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3742 {
3743         int is_subset;
3744         struct isl_map *map1;
3745         struct isl_map *map2;
3746
3747         if (!bmap1 || !bmap2)
3748                 return -1;
3749
3750         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3751         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3752
3753         is_subset = isl_map_is_subset(map1, map2);
3754
3755         isl_map_free(map1);
3756         isl_map_free(map2);
3757
3758         return is_subset;
3759 }
3760
3761 int isl_basic_map_is_equal(
3762                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3763 {
3764         int is_subset;
3765
3766         if (!bmap1 || !bmap2)
3767                 return -1;
3768         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3769         if (is_subset != 1)
3770                 return is_subset;
3771         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3772         return is_subset;
3773 }
3774
3775 int isl_basic_set_is_equal(
3776                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3777 {
3778         return isl_basic_map_is_equal(
3779                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3780 }
3781
3782 int isl_map_is_empty(struct isl_map *map)
3783 {
3784         int i;
3785         int is_empty;
3786
3787         if (!map)
3788                 return -1;
3789         for (i = 0; i < map->n; ++i) {
3790                 is_empty = isl_basic_map_is_empty(map->p[i]);
3791                 if (is_empty < 0)
3792                         return -1;
3793                 if (!is_empty)
3794                         return 0;
3795         }
3796         return 1;
3797 }
3798
3799 int isl_map_fast_is_empty(struct isl_map *map)
3800 {
3801         return map->n == 0;
3802 }
3803
3804 int isl_set_is_empty(struct isl_set *set)
3805 {
3806         return isl_map_is_empty((struct isl_map *)set);
3807 }
3808
3809 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3810 {
3811         int i;
3812         int is_subset = 0;
3813         struct isl_map *diff;
3814
3815         if (!map1 || !map2)
3816                 return -1;
3817
3818         if (isl_map_is_empty(map1))
3819                 return 1;
3820
3821         if (isl_map_is_empty(map2))
3822                 return 0;
3823
3824         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3825         if (!diff)
3826                 return -1;
3827
3828         is_subset = isl_map_is_empty(diff);
3829         isl_map_free(diff);
3830
3831         return is_subset;
3832 }
3833
3834 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3835 {
3836         int is_subset;
3837
3838         if (!map1 || !map2)
3839                 return -1;
3840         is_subset = isl_map_is_subset(map1, map2);
3841         if (is_subset != 1)
3842                 return is_subset;
3843         is_subset = isl_map_is_subset(map2, map1);
3844         return is_subset;
3845 }
3846
3847 int isl_basic_map_is_strict_subset(
3848                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3849 {
3850         int is_subset;
3851
3852         if (!bmap1 || !bmap2)
3853                 return -1;
3854         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3855         if (is_subset != 1)
3856                 return is_subset;
3857         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3858         if (is_subset == -1)
3859                 return is_subset;
3860         return !is_subset;
3861 }
3862
3863 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3864 {
3865         if (!bmap)
3866                 return -1;
3867         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3868 }
3869
3870 int isl_basic_set_is_universe(struct isl_basic_set *bset)
3871 {
3872         if (!bset)
3873                 return -1;
3874         return bset->n_eq == 0 && bset->n_ineq == 0;
3875 }
3876
3877 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3878 {
3879         struct isl_basic_set *bset = NULL;
3880         struct isl_vec *sample = NULL;
3881         int empty;
3882         unsigned total;
3883
3884         if (!bmap)
3885                 return -1;
3886
3887         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3888                 return 1;
3889
3890         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
3891                 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
3892                 copy = isl_basic_map_convex_hull(copy);
3893                 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
3894                 isl_basic_map_free(copy);
3895                 return empty;
3896         }
3897
3898         total = 1 + isl_basic_map_total_dim(bmap);
3899         if (bmap->sample && bmap->sample->size == total) {
3900                 int contains = basic_map_contains(bmap, bmap->sample);
3901                 if (contains < 0)
3902                         return -1;
3903                 if (contains)
3904                         return 0;
3905         }
3906         isl_vec_free(bmap->sample);
3907         bmap->sample = NULL;
3908         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3909         if (!bset)
3910                 return -1;
3911         sample = isl_basic_set_sample(bset);
3912         if (!sample)
3913                 return -1;
3914         empty = sample->size == 0;
3915         isl_vec_free(bmap->sample);
3916         bmap->sample = sample;
3917         if (empty)
3918                 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
3919
3920         return empty;
3921 }
3922
3923 int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
3924 {
3925         if (!bmap)
3926                 return -1;
3927         return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
3928 }
3929
3930 int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
3931 {
3932         if (!bset)
3933                 return -1;
3934         return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
3935 }
3936
3937 int isl_basic_set_is_empty(struct isl_basic_set *bset)
3938 {
3939         return isl_basic_map_is_empty((struct isl_basic_map *)bset);
3940 }
3941
3942 struct isl_map *isl_basic_map_union(
3943         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3944 {
3945         struct isl_map *map;
3946         if (!bmap1 || !bmap2)
3947                 return NULL;
3948
3949         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
3950
3951         map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
3952         if (!map)
3953                 goto error;
3954         map = isl_map_add(map, bmap1);
3955         map = isl_map_add(map, bmap2);
3956         return map;
3957 error:
3958         isl_basic_map_free(bmap1);
3959         isl_basic_map_free(bmap2);
3960         return NULL;
3961 }
3962
3963 struct isl_set *isl_basic_set_union(
3964                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3965 {
3966         return (struct isl_set *)isl_basic_map_union(
3967                                             (struct isl_basic_map *)bset1,
3968                                             (struct isl_basic_map *)bset2);
3969 }
3970
3971 /* Order divs such that any div only depends on previous divs */
3972 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3973 {
3974         int i;
3975         unsigned off = isl_dim_total(bmap->dim);
3976
3977         for (i = 0; i < bmap->n_div; ++i) {
3978                 int pos;
3979                 if (isl_int_is_zero(bmap->div[i][0]))
3980                         continue;
3981                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3982                                                             bmap->n_div-i);
3983                 if (pos == -1)
3984                         continue;
3985                 isl_basic_map_swap_div(bmap, i, i + pos);
3986                 --i;
3987         }
3988         return bmap;
3989 }
3990
3991 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
3992 {
3993         return (struct isl_basic_set *)order_divs((struct isl_basic_map *)bset);
3994 }
3995
3996 /* Look for a div in dst that corresponds to the div "div" in src.
3997  * The divs before "div" in src and dst are assumed to be the same.
3998  *
3999  * Returns -1 if no corresponding div was found and the position
4000  * of the corresponding div in dst otherwise.
4001  */
4002 static int find_div(struct isl_basic_map *dst,
4003                         struct isl_basic_map *src, unsigned div)
4004 {
4005         int i;
4006
4007         unsigned total = isl_dim_total(src->dim);
4008
4009         isl_assert(dst->ctx, div <= dst->n_div, return -1);
4010         for (i = div; i < dst->n_div; ++i)
4011                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
4012                     isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
4013                                                 dst->n_div - div) == -1)
4014                         return i;
4015         return -1;
4016 }
4017
4018 struct isl_basic_map *isl_basic_map_align_divs(
4019                 struct isl_basic_map *dst, struct isl_basic_map *src)
4020 {
4021         int i;
4022         unsigned total = isl_dim_total(src->dim);
4023
4024         if (!dst || !src)
4025                 goto error;
4026
4027         if (src->n_div == 0)
4028                 return dst;
4029
4030         for (i = 0; i < src->n_div; ++i)
4031                 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
4032
4033         src = order_divs(src);
4034         dst = isl_basic_map_cow(dst);
4035         dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
4036                         src->n_div, 0, 2 * src->n_div);
4037         if (!dst)
4038                 return NULL;
4039         for (i = 0; i < src->n_div; ++i) {
4040                 int j = find_div(dst, src, i);
4041                 if (j < 0) {
4042                         j = isl_basic_map_alloc_div(dst);
4043                         if (j < 0)
4044                                 goto error;
4045                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
4046                         isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
4047                         if (add_div_constraints(dst, j) < 0)
4048                                 goto error;
4049                 }
4050                 if (j != i)
4051                         isl_basic_map_swap_div(dst, i, j);
4052         }
4053         return dst;
4054 error:
4055         isl_basic_map_free(dst);
4056         return NULL;
4057 }
4058
4059 struct isl_basic_set *isl_basic_set_align_divs(
4060                 struct isl_basic_set *dst, struct isl_basic_set *src)
4061 {
4062         return (struct isl_basic_set *)isl_basic_map_align_divs(
4063                 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
4064 }
4065
4066 struct isl_map *isl_map_align_divs(struct isl_map *map)
4067 {
4068         int i;
4069
4070         map = isl_map_compute_divs(map);
4071         map = isl_map_cow(map);
4072         if (!map)
4073                 return NULL;
4074
4075         for (i = 1; i < map->n; ++i)
4076                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
4077         for (i = 1; i < map->n; ++i)
4078                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
4079
4080         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4081         return map;
4082 }
4083
4084 struct isl_set *isl_set_align_divs(struct isl_set *set)
4085 {
4086         return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
4087 }
4088
4089 static struct isl_map *add_cut_constraint(struct isl_map *dst,
4090                 struct isl_basic_map *src, isl_int *c,
4091                 unsigned len, int oppose)
4092 {
4093         struct isl_basic_map *copy = NULL;
4094         int is_empty;
4095         int k;
4096         unsigned total;
4097
4098         copy = isl_basic_map_copy(src);
4099         copy = isl_basic_map_cow(copy);
4100         if (!copy)
4101                 goto error;
4102         copy = isl_basic_map_extend_constraints(copy, 0, 1);
4103         k = isl_basic_map_alloc_inequality(copy);
4104         if (k < 0)
4105                 goto error;
4106         if (oppose)
4107                 isl_seq_neg(copy->ineq[k], c, len);
4108         else
4109                 isl_seq_cpy(copy->ineq[k], c, len);
4110         total = 1 + isl_basic_map_total_dim(copy);
4111         isl_seq_clr(copy->ineq[k]+len, total - len);
4112         isl_inequality_negate(copy, k);
4113         copy = isl_basic_map_simplify(copy);
4114         copy = isl_basic_map_finalize(copy);
4115         is_empty = isl_basic_map_is_empty(copy);
4116         if (is_empty < 0)
4117                 goto error;
4118         if (!is_empty)
4119                 dst = isl_map_add(dst, copy);
4120         else
4121                 isl_basic_map_free(copy);
4122         return dst;
4123 error:
4124         isl_basic_map_free(copy);
4125         isl_map_free(dst);
4126         return NULL;
4127 }
4128
4129 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
4130 {
4131         int i, j, k;
4132         unsigned flags = 0;
4133         struct isl_map *rest = NULL;
4134         unsigned max;
4135         unsigned total = isl_basic_map_total_dim(bmap);
4136
4137         assert(bmap);
4138
4139         if (!map)
4140                 goto error;
4141
4142         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
4143                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4144
4145         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
4146         rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
4147         if (!rest)
4148                 goto error;
4149
4150         for (i = 0; i < map->n; ++i) {
4151                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
4152                 if (!map->p[i])
4153                         goto error;
4154         }
4155
4156         for (j = 0; j < map->n; ++j)
4157                 map->p[j] = isl_basic_map_cow(map->p[j]);
4158
4159         for (i = 0; i < bmap->n_eq; ++i) {
4160                 for (j = 0; j < map->n; ++j) {
4161                         rest = add_cut_constraint(rest,
4162                                 map->p[j], bmap->eq[i], 1+total, 0);
4163                         if (!rest)
4164                                 goto error;
4165
4166                         rest = add_cut_constraint(rest,
4167                                 map->p[j], bmap->eq[i], 1+total, 1);
4168                         if (!rest)
4169                                 goto error;
4170
4171                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4172                                 1, 0);
4173                         if (!map->p[j])
4174                                 goto error;
4175                         k = isl_basic_map_alloc_equality(map->p[j]);
4176                         if (k < 0)
4177                                 goto error;
4178                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
4179                         isl_seq_clr(map->p[j]->eq[k]+1+total,
4180                                         map->p[j]->n_div - bmap->n_div);
4181                 }
4182         }
4183
4184         for (i = 0; i < bmap->n_ineq; ++i) {
4185                 for (j = 0; j < map->n; ++j) {
4186                         rest = add_cut_constraint(rest,
4187                                 map->p[j], bmap->ineq[i], 1+total, 0);
4188                         if (!rest)
4189                                 goto error;
4190
4191                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4192                                 0, 1);
4193                         if (!map->p[j])
4194                                 goto error;
4195                         k = isl_basic_map_alloc_inequality(map->p[j]);
4196                         if (k < 0)
4197                                 goto error;
4198                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
4199                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
4200                                         map->p[j]->n_div - bmap->n_div);
4201                 }
4202         }
4203
4204         isl_map_free(map);
4205         return rest;
4206 error:
4207         isl_map_free(map);
4208         isl_map_free(rest);
4209         return NULL;
4210 }
4211
4212 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
4213 {
4214         int i;
4215         if (!map1 || !map2)
4216                 goto error;
4217
4218         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
4219
4220         if (isl_map_is_empty(map2)) {
4221                 isl_map_free(map2);
4222                 return map1;
4223         }
4224
4225         map1 = isl_map_compute_divs(map1);
4226         map2 = isl_map_compute_divs(map2);
4227         if (!map1 || !map2)
4228                 goto error;
4229
4230         for (i = 0; map1 && i < map2->n; ++i)
4231                 map1 = subtract(map1, map2->p[i]);
4232
4233         isl_map_free(map2);
4234         return map1;
4235 error:
4236         isl_map_free(map1);
4237         isl_map_free(map2);
4238         return NULL;
4239 }
4240
4241 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
4242 {
4243         return (struct isl_set *)
4244                 isl_map_subtract(
4245                         (struct isl_map *)set1, (struct isl_map *)set2);
4246 }
4247
4248 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
4249 {
4250         if (!set || !map)
4251                 goto error;
4252         isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
4253         map = isl_map_intersect_domain(map, set);
4254         set = isl_map_range(map);
4255         return set;
4256 error:
4257         isl_set_free(set);
4258         isl_map_free(map);
4259         return NULL;
4260 }
4261
4262 /* There is no need to cow as removing empty parts doesn't change
4263  * the meaning of the set.
4264  */
4265 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
4266 {
4267         int i;
4268
4269         if (!map)
4270                 return NULL;
4271
4272         for (i = map->n-1; i >= 0; --i) {
4273                 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
4274                         continue;
4275                 isl_basic_map_free(map->p[i]);
4276                 if (i != map->n-1) {
4277                         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4278                         map->p[i] = map->p[map->n-1];
4279                 }
4280                 map->n--;
4281         }
4282
4283         return map;
4284 }
4285
4286 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
4287 {
4288         return (struct isl_set *)
4289                 isl_map_remove_empty_parts((struct isl_map *)set);
4290 }
4291
4292 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
4293 {
4294         struct isl_basic_map *bmap;
4295         if (!map || map->n == 0)
4296                 return NULL;
4297         bmap = map->p[map->n-1];
4298         isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
4299         return isl_basic_map_copy(bmap);
4300 }
4301
4302 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
4303 {
4304         (struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
4305 }
4306
4307 struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
4308                                                 struct isl_basic_map *bmap)
4309 {
4310         int i;
4311
4312         if (!map || !bmap)
4313                 goto error;
4314         for (i = map->n-1; i >= 0; --i) {
4315                 if (map->p[i] != bmap)
4316                         continue;
4317                 map = isl_map_cow(map);
4318                 if (!map)
4319                         goto error;
4320                 isl_basic_map_free(map->p[i]);
4321                 if (i != map->n-1) {
4322                         ISL_F_CLR(map, ISL_SET_NORMALIZED);
4323                         map->p[i] = map->p[map->n-1];
4324                 }
4325                 map->n--;
4326                 return map;
4327         }
4328         isl_basic_map_free(bmap);
4329         return map;
4330 error:
4331         isl_map_free(map);
4332         isl_basic_map_free(bmap);
4333         return NULL;
4334 }
4335
4336 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
4337                                                 struct isl_basic_set *bset)
4338 {
4339         (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
4340                                                 (struct isl_basic_map *)bset);
4341 }
4342
4343 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
4344  * for any common value of the parameters and dimensions preceding dim
4345  * in both basic sets, the values of dimension pos in bset1 are
4346  * smaller or larger than those in bset2.
4347  *
4348  * Returns
4349  *       1 if bset1 follows bset2
4350  *      -1 if bset1 precedes bset2
4351  *       0 if bset1 and bset2 are incomparable
4352  *      -2 if some error occurred.
4353  */
4354 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
4355         struct isl_basic_set *bset2, int pos)
4356 {
4357         struct isl_dim *dims;
4358         struct isl_basic_map *bmap1 = NULL;
4359         struct isl_basic_map *bmap2 = NULL;
4360         struct isl_ctx *ctx;
4361         struct isl_vec *obj;
4362         unsigned total;
4363         unsigned nparam;
4364         unsigned dim1, dim2;
4365         isl_int num, den;
4366         enum isl_lp_result res;
4367         int cmp;
4368
4369         if (!bset1 || !bset2)
4370                 return -2;
4371
4372         nparam = isl_basic_set_n_param(bset1);
4373         dim1 = isl_basic_set_n_dim(bset1);
4374         dim2 = isl_basic_set_n_dim(bset2);
4375         dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
4376         bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
4377         dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
4378         bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
4379         if (!bmap1 || !bmap2)
4380                 goto error;
4381         bmap1 = isl_basic_map_cow(bmap1);
4382         bmap1 = isl_basic_map_extend(bmap1, nparam,
4383                         pos, (dim1 - pos) + (dim2 - pos),
4384                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
4385         bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
4386         if (!bmap1)
4387                 goto error;
4388         total = isl_basic_map_total_dim(bmap1);
4389         ctx = bmap1->ctx;
4390         obj = isl_vec_alloc(ctx, 1 + total);
4391         isl_seq_clr(obj->block.data, 1 + total);
4392         isl_int_set_si(obj->block.data[1+nparam+pos], 1);
4393         isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
4394         if (!obj)
4395                 goto error;
4396         isl_int_init(num);
4397         isl_int_init(den);
4398         res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
4399         if (res == isl_lp_empty)
4400                 cmp = 0;
4401         else if (res == isl_lp_ok && isl_int_is_pos(num))
4402                 cmp = 1;
4403         else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
4404                   res == isl_lp_unbounded)
4405                 cmp = -1;
4406         else
4407                 cmp = -2;
4408         isl_int_clear(num);
4409         isl_int_clear(den);
4410         isl_basic_map_free(bmap1);
4411         isl_vec_free(obj);
4412         return cmp;
4413 error:
4414         isl_basic_map_free(bmap1);
4415         isl_basic_map_free(bmap2);
4416         return -2;
4417 }
4418
4419 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
4420         unsigned pos, isl_int *val)
4421 {
4422         int i;
4423         int d;
4424         unsigned total;
4425
4426         if (!bmap)
4427                 return -1;
4428         total = isl_basic_map_total_dim(bmap);
4429         for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
4430                 for (; d+1 > pos; --d)
4431                         if (!isl_int_is_zero(bmap->eq[i][1+d]))
4432                                 break;
4433                 if (d != pos)
4434                         continue;
4435                 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
4436                         return 0;
4437                 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
4438                         return 0;
4439                 if (!isl_int_is_one(bmap->eq[i][1+d]))
4440                         return 0;
4441                 if (val)
4442                         isl_int_neg(*val, bmap->eq[i][0]);
4443                 return 1;
4444         }
4445         return 0;
4446 }
4447
4448 static int isl_map_fast_has_fixed_var(struct isl_map *map,
4449         unsigned pos, isl_int *val)
4450 {
4451         int i;
4452         isl_int v;
4453         isl_int tmp;
4454         int fixed;
4455
4456         if (!map)
4457                 return -1;
4458         if (map->n == 0)
4459                 return 0;
4460         if (map->n == 1)
4461                 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
4462         isl_int_init(v);
4463         isl_int_init(tmp);
4464         fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
4465         for (i = 1; fixed == 1 && i < map->n; ++i) {
4466                 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
4467                 if (fixed == 1 && isl_int_ne(tmp, v))
4468                         fixed = 0;
4469         }
4470         if (val)
4471                 isl_int_set(*val, v);
4472         isl_int_clear(tmp);
4473         isl_int_clear(v);
4474         return fixed;
4475 }
4476
4477 static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
4478         unsigned pos, isl_int *val)
4479 {
4480         return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
4481                                                 pos, val);
4482 }
4483
4484 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
4485         isl_int *val)
4486 {
4487         return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
4488 }
4489
4490 int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
4491         enum isl_dim_type type, unsigned pos, isl_int *val)
4492 {
4493         if (pos >= isl_basic_map_dim(bmap, type))
4494                 return -1;
4495         return isl_basic_map_fast_has_fixed_var(bmap,
4496                 isl_basic_map_offset(bmap, type) - 1 + pos, val);
4497 }
4498
4499 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4500  * then return this fixed value in *val.
4501  */
4502 int isl_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
4503         isl_int *val)
4504 {
4505         return isl_basic_set_fast_has_fixed_var(bset,
4506                                         isl_basic_set_n_param(bset) + dim, val);
4507 }
4508
4509 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4510  * then return this fixed value in *val.
4511  */
4512 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
4513 {
4514         return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
4515 }
4516
4517 /* Check if input variable in has fixed value and if so and if val is not NULL,
4518  * then return this fixed value in *val.
4519  */
4520 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
4521 {
4522         return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
4523 }
4524
4525 /* Check if dimension dim has an (obvious) fixed lower bound and if so
4526  * and if val is not NULL, then return this lower bound in *val.
4527  */
4528 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
4529         unsigned dim, isl_int *val)
4530 {
4531         int i, i_eq = -1, i_ineq = -1;
4532         isl_int *c;
4533         unsigned total;
4534         unsigned nparam;
4535
4536         if (!bset)
4537                 return -1;
4538         total = isl_basic_set_total_dim(bset);
4539         nparam = isl_basic_set_n_param(bset);
4540         for (i = 0; i < bset->n_eq; ++i) {
4541                 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
4542                         continue;
4543                 if (i_eq != -1)
4544                         return 0;
4545                 i_eq = i;
4546         }
4547         for (i = 0; i < bset->n_ineq; ++i) {
4548                 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
4549                         continue;
4550                 if (i_eq != -1 || i_ineq != -1)
4551                         return 0;
4552                 i_ineq = i;
4553         }
4554         if (i_eq == -1 && i_ineq == -1)
4555                 return 0;
4556         c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4557         /* The coefficient should always be one due to normalization. */
4558         if (!isl_int_is_one(c[1+nparam+dim]))
4559                 return 0;
4560         if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
4561                 return 0;
4562         if (isl_seq_first_non_zero(c+1+nparam+dim+1,
4563                                         total - nparam - dim - 1) != -1)
4564                 return 0;
4565         if (val)
4566                 isl_int_neg(*val, c[0]);
4567         return 1;
4568 }
4569
4570 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4571         unsigned dim, isl_int *val)
4572 {
4573         int i;
4574         isl_int v;
4575         isl_int tmp;
4576         int fixed;
4577
4578         if (!set)
4579                 return -1;
4580         if (set->n == 0)
4581                 return 0;
4582         if (set->n == 1)
4583                 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4584                                                                 dim, val);
4585         isl_int_init(v);
4586         isl_int_init(tmp);
4587         fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4588                                                                 dim, &v);
4589         for (i = 1; fixed == 1 && i < set->n; ++i) {
4590                 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4591                                                                 dim, &tmp);
4592                 if (fixed == 1 && isl_int_ne(tmp, v))
4593                         fixed = 0;
4594         }
4595         if (val)
4596                 isl_int_set(*val, v);
4597         isl_int_clear(tmp);
4598         isl_int_clear(v);
4599         return fixed;
4600 }
4601
4602 struct constraint {
4603         unsigned        size;
4604         isl_int         *c;
4605 };
4606
4607 static int qsort_constraint_cmp(const void *p1, const void *p2)
4608 {
4609         const struct constraint *c1 = (const struct constraint *)p1;
4610         const struct constraint *c2 = (const struct constraint *)p2;
4611         unsigned size = isl_min(c1->size, c2->size);
4612         return isl_seq_cmp(c1->c, c2->c, size);
4613 }
4614
4615 static struct isl_basic_map *isl_basic_map_sort_constraints(
4616         struct isl_basic_map *bmap)
4617 {
4618         int i;
4619         struct constraint *c;
4620         unsigned total;
4621
4622         if (!bmap)
4623                 return NULL;
4624         total = isl_basic_map_total_dim(bmap);
4625         c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
4626         if (!c)
4627                 goto error;
4628         for (i = 0; i < bmap->n_ineq; ++i) {
4629                 c[i].size = total;
4630                 c[i].c = bmap->ineq[i];
4631         }
4632         qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
4633         for (i = 0; i < bmap->n_ineq; ++i)
4634                 bmap->ineq[i] = c[i].c;
4635         free(c);
4636         return bmap;
4637 error:
4638         isl_basic_map_free(bmap);
4639         return NULL;
4640 }
4641
4642 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
4643 {
4644         if (!bmap)
4645                 return NULL;
4646         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
4647                 return bmap;
4648         bmap = isl_basic_map_convex_hull(bmap);
4649         bmap = isl_basic_map_sort_constraints(bmap);
4650         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
4651         return bmap;
4652 }
4653
4654 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
4655 {
4656         return (struct isl_basic_set *)isl_basic_map_normalize(
4657                                                 (struct isl_basic_map *)bset);
4658 }
4659
4660 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
4661         const struct isl_basic_map *bmap2)
4662 {
4663         int i, cmp;
4664         unsigned total;
4665
4666         if (bmap1 == bmap2)
4667                 return 0;
4668         if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
4669                 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
4670         if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
4671                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4672         if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
4673                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4674         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
4675             ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4676                 return 0;
4677         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
4678                 return 1;
4679         if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4680                 return -1;
4681         if (bmap1->n_eq != bmap2->n_eq)
4682                 return bmap1->n_eq - bmap2->n_eq;
4683         if (bmap1->n_ineq != bmap2->n_ineq)
4684                 return bmap1->n_ineq - bmap2->n_ineq;
4685         if (bmap1->n_div != bmap2->n_div)
4686                 return bmap1->n_div - bmap2->n_div;
4687         total = isl_basic_map_total_dim(bmap1);
4688         for (i = 0; i < bmap1->n_eq; ++i) {
4689                 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
4690                 if (cmp)
4691                         return cmp;
4692         }
4693         for (i = 0; i < bmap1->n_ineq; ++i) {
4694                 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
4695                 if (cmp)
4696                         return cmp;
4697         }
4698         for (i = 0; i < bmap1->n_div; ++i) {
4699                 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
4700                 if (cmp)
4701                         return cmp;
4702         }
4703         return 0;
4704 }
4705
4706 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
4707         struct isl_basic_map *bmap2)
4708 {
4709         return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
4710 }
4711
4712 static int qsort_bmap_cmp(const void *p1, const void *p2)
4713 {
4714         const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
4715         const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
4716
4717         return isl_basic_map_fast_cmp(bmap1, bmap2);
4718 }
4719
4720 /* We normalize in place, but if anything goes wrong we need
4721  * to return NULL, so we need to make sure we don't change the
4722  * meaning of any possible other copies of map.
4723  */
4724 struct isl_map *isl_map_normalize(struct isl_map *map)
4725 {
4726         int i, j;
4727         struct isl_basic_map *bmap;
4728
4729         if (!map)
4730                 return NULL;
4731         if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
4732                 return map;
4733         for (i = 0; i < map->n; ++i) {
4734                 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
4735                 if (!bmap)
4736                         goto error;
4737                 isl_basic_map_free(map->p[i]);
4738                 map->p[i] = bmap;
4739         }
4740         qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
4741         ISL_F_SET(map, ISL_MAP_NORMALIZED);
4742         map = isl_map_remove_empty_parts(map);
4743         if (!map)
4744                 return NULL;
4745         for (i = map->n - 1; i >= 1; --i) {
4746                 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
4747                         continue;
4748                 isl_basic_map_free(map->p[i-1]);
4749                 for (j = i; j < map->n; ++j)
4750                         map->p[j-1] = map->p[j];
4751                 map->n--;
4752         }
4753         return map;
4754 error:
4755         isl_map_free(map);
4756         return NULL;
4757
4758 }
4759
4760 struct isl_set *isl_set_normalize(struct isl_set *set)
4761 {
4762         return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
4763 }
4764
4765 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
4766 {
4767         int i;
4768         int equal;
4769
4770         if (!map1 || !map2)
4771                 return -1;
4772
4773         if (map1 == map2)
4774                 return 1;
4775         if (!isl_dim_equal(map1->dim, map2->dim))
4776                 return 0;
4777
4778         map1 = isl_map_copy(map1);
4779         map2 = isl_map_copy(map2);
4780         map1 = isl_map_normalize(map1);
4781         map2 = isl_map_normalize(map2);
4782         if (!map1 || !map2)
4783                 goto error;
4784         equal = map1->n == map2->n;
4785         for (i = 0; equal && i < map1->n; ++i) {
4786                 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
4787                 if (equal < 0)
4788                         goto error;
4789         }
4790         isl_map_free(map1);
4791         isl_map_free(map2);
4792         return equal;
4793 error:
4794         isl_map_free(map1);
4795         isl_map_free(map2);
4796         return -1;
4797 }
4798
4799 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
4800 {
4801         return isl_map_fast_is_equal((struct isl_map *)set1,
4802                                                 (struct isl_map *)set2);
4803 }
4804
4805 /* Return an interval that ranges from min to max (inclusive)
4806  */
4807 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
4808         isl_int min, isl_int max)
4809 {
4810         int k;
4811         struct isl_basic_set *bset = NULL;
4812
4813         bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
4814         if (!bset)
4815                 goto error;
4816
4817         k = isl_basic_set_alloc_inequality(bset);
4818         if (k < 0)
4819                 goto error;
4820         isl_int_set_si(bset->ineq[k][1], 1);
4821         isl_int_neg(bset->ineq[k][0], min);
4822
4823         k = isl_basic_set_alloc_inequality(bset);
4824         if (k < 0)
4825                 goto error;
4826         isl_int_set_si(bset->ineq[k][1], -1);
4827         isl_int_set(bset->ineq[k][0], max);
4828
4829         return bset;
4830 error:
4831         isl_basic_set_free(bset);
4832         return NULL;
4833 }
4834
4835 /* Return the Cartesian product of the basic sets in list (in the given order).
4836  */
4837 struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
4838 {
4839         int i;
4840         unsigned dim;
4841         unsigned nparam;
4842         unsigned extra;
4843         unsigned n_eq;
4844         unsigned n_ineq;
4845         struct isl_basic_set *product = NULL;
4846
4847         if (!list)
4848                 goto error;
4849         isl_assert(list->ctx, list->n > 0, goto error);
4850         isl_assert(list->ctx, list->p[0], goto error);
4851         nparam = isl_basic_set_n_param(list->p[0]);
4852         dim = isl_basic_set_n_dim(list->p[0]);
4853         extra = list->p[0]->n_div;
4854         n_eq = list->p[0]->n_eq;
4855         n_ineq = list->p[0]->n_ineq;
4856         for (i = 1; i < list->n; ++i) {
4857                 isl_assert(list->ctx, list->p[i], goto error);
4858                 isl_assert(list->ctx,
4859                     nparam == isl_basic_set_n_param(list->p[i]), goto error);
4860                 dim += isl_basic_set_n_dim(list->p[i]);
4861                 extra += list->p[i]->n_div;
4862                 n_eq += list->p[i]->n_eq;
4863                 n_ineq += list->p[i]->n_ineq;
4864         }
4865         product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
4866                                         n_eq, n_ineq);
4867         if (!product)
4868                 goto error;
4869         dim = 0;
4870         for (i = 0; i < list->n; ++i) {
4871                 isl_basic_set_add_constraints(product,
4872                                         isl_basic_set_copy(list->p[i]), dim);
4873                 dim += isl_basic_set_n_dim(list->p[i]);
4874         }
4875         isl_basic_set_list_free(list);
4876         return product;
4877 error:
4878         isl_basic_set_free(product);
4879         isl_basic_set_list_free(list);
4880         return NULL;
4881 }
4882
4883 struct isl_basic_map *isl_basic_map_product(
4884                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4885 {
4886         struct isl_dim *dim_result = NULL;
4887         struct isl_basic_map *bmap;
4888         unsigned in1, in2, out1, out2, nparam, total, pos;
4889         struct isl_dim_map *dim_map1, *dim_map2;
4890
4891         if (!bmap1 || !bmap2)
4892                 goto error;
4893
4894         isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
4895                                      bmap2->dim, isl_dim_param), goto error);
4896         dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
4897                                                    isl_dim_copy(bmap2->dim));
4898
4899         in1 = isl_basic_map_n_in(bmap1);
4900         in2 = isl_basic_map_n_in(bmap2);
4901         out1 = isl_basic_map_n_out(bmap1);
4902         out2 = isl_basic_map_n_out(bmap2);
4903         nparam = isl_basic_map_n_param(bmap1);
4904
4905         total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
4906         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
4907         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
4908         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
4909         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
4910         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
4911         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
4912         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
4913         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
4914         isl_dim_map_div(dim_map1, bmap1, pos += out2);
4915         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
4916
4917         bmap = isl_basic_map_alloc_dim(dim_result,
4918                         bmap1->n_div + bmap2->n_div,
4919                         bmap1->n_eq + bmap2->n_eq,
4920                         bmap1->n_ineq + bmap2->n_ineq);
4921         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
4922         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
4923         bmap = isl_basic_map_simplify(bmap);
4924         return isl_basic_map_finalize(bmap);
4925 error:
4926         isl_basic_map_free(bmap1);
4927         isl_basic_map_free(bmap2);
4928         return NULL;
4929 }
4930
4931 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
4932  */
4933 struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
4934 {
4935         unsigned flags = 0;
4936         struct isl_map *result;
4937         int i, j;
4938
4939         if (!map1 || !map2)
4940                 goto error;
4941
4942         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
4943                                          map2->dim, isl_dim_param), goto error);
4944
4945         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
4946             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
4947                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4948
4949         result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
4950                                                    isl_dim_copy(map2->dim)),
4951                                 map1->n * map2->n, flags);
4952         if (!result)
4953                 goto error;
4954         for (i = 0; i < map1->n; ++i)
4955                 for (j = 0; j < map2->n; ++j) {
4956                         struct isl_basic_map *part;
4957                         part = isl_basic_map_product(
4958                                     isl_basic_map_copy(map1->p[i]),
4959                                     isl_basic_map_copy(map2->p[j]));
4960                         if (isl_basic_map_is_empty(part))
4961                                 isl_basic_map_free(part);
4962                         else
4963                                 result = isl_map_add(result, part);
4964                         if (!result)
4965                                 goto error;
4966                 }
4967         isl_map_free(map1);
4968         isl_map_free(map2);
4969         return result;
4970 error:
4971         isl_map_free(map1);
4972         isl_map_free(map2);
4973         return NULL;
4974 }
4975
4976 /* Given two set A and B, construct its Cartesian product A x B.
4977  */
4978 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
4979 {
4980         return (struct isl_set *)isl_map_product((struct isl_map *)set1,
4981                                                  (struct isl_map *)set2);
4982 }
4983
4984 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
4985 {
4986         int i;
4987         uint32_t hash;
4988         unsigned total;
4989
4990         if (!bset)
4991                 return 0;
4992         bset = isl_basic_set_copy(bset);
4993         bset = isl_basic_set_normalize(bset);
4994         if (!bset)
4995                 return 0;
4996         total = isl_basic_set_total_dim(bset);
4997         isl_hash_byte(hash, bset->n_eq & 0xFF);
4998         for (i = 0; i < bset->n_eq; ++i) {
4999                 uint32_t c_hash;
5000                 c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
5001                 isl_hash_hash(hash, c_hash);
5002         }
5003         isl_hash_byte(hash, bset->n_ineq & 0xFF);
5004         for (i = 0; i < bset->n_ineq; ++i) {
5005                 uint32_t c_hash;
5006                 c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
5007                 isl_hash_hash(hash, c_hash);
5008         }
5009         isl_hash_byte(hash, bset->n_div & 0xFF);
5010         for (i = 0; i < bset->n_div; ++i) {
5011                 uint32_t c_hash;
5012                 if (isl_int_is_zero(bset->div[i][0]))
5013                         continue;
5014                 isl_hash_byte(hash, i & 0xFF);
5015                 c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
5016                 isl_hash_hash(hash, c_hash);
5017         }
5018         isl_basic_set_free(bset);
5019         return hash;
5020 }
5021
5022 uint32_t isl_set_get_hash(struct isl_set *set)
5023 {
5024         int i;
5025         uint32_t hash;
5026
5027         if (!set)
5028                 return 0;
5029         set = isl_set_copy(set);
5030         set = isl_set_normalize(set);
5031         if (!set)
5032                 return 0;
5033
5034         hash = isl_hash_init();
5035         for (i = 0; i < set->n; ++i) {
5036                 uint32_t bset_hash;
5037                 bset_hash = isl_basic_set_get_hash(set->p[i]);
5038                 isl_hash_hash(hash, bset_hash);
5039         }
5040
5041         isl_set_free(set);
5042
5043         return hash;
5044 }
5045
5046 /* Check if the value for dimension dim is completely determined
5047  * by the values of the other parameters and variables.
5048  * That is, check if dimension dim is involved in an equality.
5049  */
5050 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
5051 {
5052         int i;
5053         unsigned nparam;
5054
5055         if (!bset)
5056                 return -1;
5057         nparam = isl_basic_set_n_param(bset);
5058         for (i = 0; i < bset->n_eq; ++i)
5059                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
5060                         return 1;
5061         return 0;
5062 }
5063
5064 /* Check if the value for dimension dim is completely determined
5065  * by the values of the other parameters and variables.
5066  * That is, check if dimension dim is involved in an equality
5067  * for each of the subsets.
5068  */
5069 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
5070 {
5071         int i;
5072
5073         if (!set)
5074                 return -1;
5075         for (i = 0; i < set->n; ++i) {
5076                 int unique;
5077                 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
5078                 if (unique != 1)
5079                         return unique;
5080         }
5081         return 1;
5082 }