isl_local_space.c

   1 /*
   2  * Copyright 2011      INRIA Saclay
   3  * Copyright 2012      Ecole Normale Superieure
   4  *
   5  * Use of this software is governed by the MIT license
   6  *
   7  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   8  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   9  * 91893 Orsay, France
  10  * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
  11  */
  12
  13 #include <isl_ctx_private.h>
  14 #include <isl_map_private.h>
  15 #include <isl_local_space_private.h>
  16 #include <isl_space_private.h>
  17 #include <isl_mat_private.h>
  18 #include <isl_aff_private.h>
  19 #include <isl/seq.h>
  20
  21 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
  22 {
  23         return ls ? ls->dim->ctx : NULL;
  24 }
  25
  26 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
  27         __isl_take isl_mat *div)
  28 {
  29         isl_ctx *ctx;
  30         isl_local_space *ls = NULL;
  31
  32         if (!dim || !div)
  33                 goto error;
  34
  35         ctx = isl_space_get_ctx(dim);
  36         ls = isl_calloc_type(ctx, struct isl_local_space);
  37         if (!ls)
  38                 goto error;
  39
  40         ls->ref = 1;
  41         ls->dim = dim;
  42         ls->div = div;
  43
  44         return ls;
  45 error:
  46         isl_mat_free(div);
  47         isl_space_free(dim);
  48         isl_local_space_free(ls);
  49         return NULL;
  50 }
  51
  52 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
  53         unsigned n_div)
  54 {
  55         isl_ctx *ctx;
  56         isl_mat *div;
  57         unsigned total;
  58
  59         if (!dim)
  60                 return NULL;
  61
  62         total = isl_space_dim(dim, isl_dim_all);
  63
  64         ctx = isl_space_get_ctx(dim);
  65         div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
  66         return isl_local_space_alloc_div(dim, div);
  67 }
  68
  69 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
  70 {
  71         return isl_local_space_alloc(dim, 0);
  72 }
  73
  74 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
  75 {
  76         if (!ls)
  77                 return NULL;
  78
  79         ls->ref++;
  80         return ls;
  81 }
  82
  83 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
  84 {
  85         if (!ls)
  86                 return NULL;
  87
  88         return isl_local_space_alloc_div(isl_space_copy(ls->dim),
  89                                          isl_mat_copy(ls->div));
  90
  91 }
  92
  93 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
  94 {
  95         if (!ls)
  96                 return NULL;
  97
  98         if (ls->ref == 1)
  99                 return ls;
 100         ls->ref--;
 101         return isl_local_space_dup(ls);
 102 }
 103
 104 void *isl_local_space_free(__isl_take isl_local_space *ls)
 105 {
 106         if (!ls)
 107                 return NULL;
 108
 109         if (--ls->ref > 0)
 110                 return NULL;
 111
 112         isl_space_free(ls->dim);
 113         isl_mat_free(ls->div);
 114
 115         free(ls);
 116
 117         return NULL;
 118 }
 119
 120 /* Is the local space that of a set?
 121  */
 122 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
 123 {
 124         return ls ? isl_space_is_set(ls->dim) : -1;
 125 }
 126
 127 /* Return true if the two local spaces are identical, with identical
 128  * expressions for the integer divisions.
 129  */
 130 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 131         __isl_keep isl_local_space *ls2)
 132 {
 133         int equal;
 134
 135         if (!ls1 || !ls2)
 136                 return -1;
 137
 138         equal = isl_space_is_equal(ls1->dim, ls2->dim);
 139         if (equal < 0 || !equal)
 140                 return equal;
 141
 142         if (!isl_local_space_divs_known(ls1))
 143                 return 0;
 144         if (!isl_local_space_divs_known(ls2))
 145                 return 0;
 146
 147         return isl_mat_is_equal(ls1->div, ls2->div);
 148 }
 149
 150 int isl_local_space_dim(__isl_keep isl_local_space *ls,
 151         enum isl_dim_type type)
 152 {
 153         if (!ls)
 154                 return 0;
 155         if (type == isl_dim_div)
 156                 return ls->div->n_row;
 157         if (type == isl_dim_all)
 158                 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
 159         return isl_space_dim(ls->dim, type);
 160 }
 161
 162 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 163         enum isl_dim_type type)
 164 {
 165         isl_space *dim;
 166
 167         if (!ls)
 168                 return 0;
 169
 170         dim = ls->dim;
 171         switch (type) {
 172         case isl_dim_cst:       return 0;
 173         case isl_dim_param:     return 1;
 174         case isl_dim_in:        return 1 + dim->nparam;
 175         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 176         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 177         default:                return 0;
 178         }
 179 }
 180
 181 /* Does the given dimension have a name?
 182  */
 183 int isl_local_space_has_dim_name(__isl_keep isl_local_space *ls,
 184         enum isl_dim_type type, unsigned pos)
 185 {
 186         return ls ? isl_space_has_dim_name(ls->dim, type, pos) : -1;
 187 }
 188
 189 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 190         enum isl_dim_type type, unsigned pos)
 191 {
 192         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 193 }
 194
 195 int isl_local_space_has_dim_id(__isl_keep isl_local_space *ls,
 196         enum isl_dim_type type, unsigned pos)
 197 {
 198         return ls ? isl_space_has_dim_id(ls->dim, type, pos) : -1;
 199 }
 200
 201 __isl_give isl_id *isl_local_space_get_dim_id(__isl_keep isl_local_space *ls,
 202         enum isl_dim_type type, unsigned pos)
 203 {
 204         return ls ? isl_space_get_dim_id(ls->dim, type, pos) : NULL;
 205 }
 206
 207 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 208         int pos)
 209 {
 210         isl_aff *aff;
 211
 212         if (!ls)
 213                 return NULL;
 214
 215         if (pos < 0 || pos >= ls->div->n_row)
 216                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 217                         "index out of bounds", return NULL);
 218
 219         if (isl_int_is_zero(ls->div->row[pos][0]))
 220                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 221                         "expression of div unknown", return NULL);
 222         if (!isl_local_space_is_set(ls))
 223                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 224                         "cannot represent divs of map spaces", return NULL);
 225
 226         aff = isl_aff_alloc(isl_local_space_copy(ls));
 227         if (!aff)
 228                 return NULL;
 229         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 230         return aff;
 231 }
 232
 233 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 234 {
 235         if (!ls)
 236                 return NULL;
 237
 238         return isl_space_copy(ls->dim);
 239 }
 240
 241 __isl_give isl_local_space *isl_local_space_set_dim_name(
 242         __isl_take isl_local_space *ls,
 243         enum isl_dim_type type, unsigned pos, const char *s)
 244 {
 245         ls = isl_local_space_cow(ls);
 246         if (!ls)
 247                 return NULL;
 248         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 249         if (!ls->dim)
 250                 return isl_local_space_free(ls);
 251
 252         return ls;
 253 }
 254
 255 __isl_give isl_local_space *isl_local_space_set_dim_id(
 256         __isl_take isl_local_space *ls,
 257         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 258 {
 259         ls = isl_local_space_cow(ls);
 260         if (!ls)
 261                 return isl_id_free(id);
 262         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 263         if (!ls->dim)
 264                 return isl_local_space_free(ls);
 265
 266         return ls;
 267 }
 268
 269 __isl_give isl_local_space *isl_local_space_reset_space(
 270         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 271 {
 272         ls = isl_local_space_cow(ls);
 273         if (!ls || !dim)
 274                 goto error;
 275
 276         isl_space_free(ls->dim);
 277         ls->dim = dim;
 278
 279         return ls;
 280 error:
 281         isl_local_space_free(ls);
 282         isl_space_free(dim);
 283         return NULL;
 284 }
 285
 286 /* Reorder the columns of the given div definitions according to the
 287  * given reordering.
 288  * The order of the divs themselves is assumed not to change.
 289  */
 290 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 291         __isl_take isl_reordering *r)
 292 {
 293         int i, j;
 294         isl_mat *mat;
 295         int extra;
 296
 297         if (!div || !r)
 298                 goto error;
 299
 300         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 301         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 302         if (!mat)
 303                 goto error;
 304
 305         for (i = 0; i < div->n_row; ++i) {
 306                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 307                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 308                 for (j = 0; j < r->len; ++j)
 309                         isl_int_set(mat->row[i][2 + r->pos[j]],
 310                                     div->row[i][2 + j]);
 311         }
 312
 313         isl_reordering_free(r);
 314         isl_mat_free(div);
 315         return mat;
 316 error:
 317         isl_reordering_free(r);
 318         isl_mat_free(div);
 319         return NULL;
 320 }
 321
 322 /* Reorder the dimensions of "ls" according to the given reordering.
 323  * The reordering r is assumed to have been extended with the local
 324  * variables, leaving them in the same order.
 325  */
 326 __isl_give isl_local_space *isl_local_space_realign(
 327         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 328 {
 329         ls = isl_local_space_cow(ls);
 330         if (!ls || !r)
 331                 goto error;
 332
 333         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 334         if (!ls->div)
 335                 goto error;
 336
 337         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 338
 339         isl_reordering_free(r);
 340         return ls;
 341 error:
 342         isl_local_space_free(ls);
 343         isl_reordering_free(r);
 344         return NULL;
 345 }
 346
 347 __isl_give isl_local_space *isl_local_space_add_div(
 348         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 349 {
 350         ls = isl_local_space_cow(ls);
 351         if (!ls || !div)
 352                 goto error;
 353
 354         if (ls->div->n_col != div->size)
 355                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 356                         "incompatible dimensions", goto error);
 357
 358         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 359         ls->div = isl_mat_add_rows(ls->div, 1);
 360         if (!ls->div)
 361                 goto error;
 362
 363         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 364         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 365
 366         isl_vec_free(div);
 367         return ls;
 368 error:
 369         isl_local_space_free(ls);
 370         isl_vec_free(div);
 371         return NULL;
 372 }
 373
 374 __isl_give isl_local_space *isl_local_space_replace_divs(
 375         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 376 {
 377         ls = isl_local_space_cow(ls);
 378
 379         if (!ls || !div)
 380                 goto error;
 381
 382         isl_mat_free(ls->div);
 383         ls->div = div;
 384         return ls;
 385 error:
 386         isl_mat_free(div);
 387         isl_local_space_free(ls);
 388         return NULL;
 389 }
 390
 391 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 392  * defined by "exp".
 393  */
 394 static void expand_row(__isl_keep isl_mat *dst, int d,
 395         __isl_keep isl_mat *src, int s, int *exp)
 396 {
 397         int i;
 398         unsigned c = src->n_col - src->n_row;
 399
 400         isl_seq_cpy(dst->row[d], src->row[s], c);
 401         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 402
 403         for (i = 0; i < s; ++i)
 404                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 405 }
 406
 407 /* Compare (known) divs.
 408  * Return non-zero if at least one of the two divs is unknown.
 409  * In particular, if both divs are unknown, we respect their
 410  * current order.  Otherwise, we sort the known div after the unknown
 411  * div only if the known div depends on the unknown div.
 412  */
 413 static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
 414         unsigned n_row, unsigned n_col)
 415 {
 416         int li, lj;
 417         int unknown_i, unknown_j;
 418
 419         unknown_i = isl_int_is_zero(row_i[0]);
 420         unknown_j = isl_int_is_zero(row_j[0]);
 421
 422         if (unknown_i && unknown_j)
 423                 return i - j;
 424
 425         if (unknown_i)
 426                 li = n_col - n_row + i;
 427         else
 428                 li = isl_seq_last_non_zero(row_i, n_col);
 429         if (unknown_j)
 430                 lj = n_col - n_row + j;
 431         else
 432                 lj = isl_seq_last_non_zero(row_j, n_col);
 433
 434         if (li != lj)
 435                 return li - lj;
 436
 437         return isl_seq_cmp(row_i, row_j, n_col);
 438 }
 439
 440 /* Call cmp_row for divs in a matrix.
 441  */
 442 int isl_mat_cmp_div(__isl_keep isl_mat *div, int i, int j)
 443 {
 444         return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
 445 }
 446
 447 /* Call cmp_row for divs in a basic map.
 448  */
 449 static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
 450         unsigned total)
 451 {
 452         return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
 453 }
 454
 455 /* Sort the divs in "bmap".
 456  *
 457  * We first make sure divs are placed after divs on which they depend.
 458  * Then we perform a simple insertion sort based on the same ordering
 459  * that is used in isl_merge_divs.
 460  */
 461 __isl_give isl_basic_map *isl_basic_map_sort_divs(
 462         __isl_take isl_basic_map *bmap)
 463 {
 464         int i, j;
 465         unsigned total;
 466
 467         bmap = isl_basic_map_order_divs(bmap);
 468         if (!bmap)
 469                 return NULL;
 470         if (bmap->n_div <= 1)
 471                 return bmap;
 472
 473         total = 2 + isl_basic_map_total_dim(bmap);
 474         for (i = 1; i < bmap->n_div; ++i) {
 475                 for (j = i - 1; j >= 0; --j) {
 476                         if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
 477                                 break;
 478                         isl_basic_map_swap_div(bmap, j, j + 1);
 479                 }
 480         }
 481
 482         return bmap;
 483 }
 484
 485 /* Sort the divs in the basic maps of "map".
 486  */
 487 __isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
 488 {
 489         return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
 490 }
 491
 492 /* Combine the two lists of divs into a single list.
 493  * For each row i in div1, exp1[i] is set to the position of the corresponding
 494  * row in the result.  Similarly for div2 and exp2.
 495  * This function guarantees
 496  *      exp1[i] >= i
 497  *      exp1[i+1] > exp1[i]
 498  * For optimal merging, the two input list should have been sorted.
 499  */
 500 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 501         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 502 {
 503         int i, j, k;
 504         isl_mat *div = NULL;
 505         unsigned d;
 506
 507         if (!div1 || !div2)
 508                 return NULL;
 509
 510         d = div1->n_col - div1->n_row;
 511         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 512                                 d + div1->n_row + div2->n_row);
 513         if (!div)
 514                 return NULL;
 515
 516         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 517                 int cmp;
 518
 519                 expand_row(div, k, div1, i, exp1);
 520                 expand_row(div, k + 1, div2, j, exp2);
 521
 522                 cmp = isl_mat_cmp_div(div, k, k + 1);
 523                 if (cmp == 0) {
 524                         exp1[i++] = k;
 525                         exp2[j++] = k;
 526                 } else if (cmp < 0) {
 527                         exp1[i++] = k;
 528                 } else {
 529                         exp2[j++] = k;
 530                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 531                 }
 532         }
 533         for (; i < div1->n_row; ++i, ++k) {
 534                 expand_row(div, k, div1, i, exp1);
 535                 exp1[i] = k;
 536         }
 537         for (; j < div2->n_row; ++j, ++k) {
 538                 expand_row(div, k, div2, j, exp2);
 539                 exp2[j] = k;
 540         }
 541
 542         div->n_row = k;
 543         div->n_col = d + k;
 544
 545         return div;
 546 }
 547
 548 /* Swap divs "a" and "b" in "ls".
 549  */
 550 __isl_give isl_local_space *isl_local_space_swap_div(
 551         __isl_take isl_local_space *ls, int a, int b)
 552 {
 553         int offset;
 554
 555         ls = isl_local_space_cow(ls);
 556         if (!ls)
 557                 return NULL;
 558         if (a < 0 || a >= ls->div->n_row || b < 0 || b >= ls->div->n_row)
 559                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 560                         "index out of bounds", return isl_local_space_free(ls));
 561         offset = ls->div->n_col - ls->div->n_row;
 562         ls->div = isl_mat_swap_cols(ls->div, offset + a, offset + b);
 563         ls->div = isl_mat_swap_rows(ls->div, a, b);
 564         if (!ls->div)
 565                 return isl_local_space_free(ls);
 566         return ls;
 567 }
 568
 569 /* Construct a local space that contains all the divs in either
 570  * "ls1" or "ls2".
 571  */
 572 __isl_give isl_local_space *isl_local_space_intersect(
 573         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 574 {
 575         isl_ctx *ctx;
 576         int *exp1 = NULL;
 577         int *exp2 = NULL;
 578         isl_mat *div;
 579
 580         if (!ls1 || !ls2)
 581                 goto error;
 582
 583         ctx = isl_local_space_get_ctx(ls1);
 584         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 585                 isl_die(ctx, isl_error_invalid,
 586                         "spaces should be identical", goto error);
 587
 588         if (ls2->div->n_row == 0) {
 589                 isl_local_space_free(ls2);
 590                 return ls1;
 591         }
 592
 593         if (ls1->div->n_row == 0) {
 594                 isl_local_space_free(ls1);
 595                 return ls2;
 596         }
 597
 598         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 599         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 600         if (!exp1 || !exp2)
 601                 goto error;
 602
 603         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 604         if (!div)
 605                 goto error;
 606
 607         free(exp1);
 608         free(exp2);
 609         isl_local_space_free(ls2);
 610         isl_mat_free(ls1->div);
 611         ls1->div = div;
 612
 613         return ls1;
 614 error:
 615         free(exp1);
 616         free(exp2);
 617         isl_local_space_free(ls1);
 618         isl_local_space_free(ls2);
 619         return NULL;
 620 }
 621
 622 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 623 {
 624         int i;
 625
 626         if (!ls)
 627                 return -1;
 628
 629         for (i = 0; i < ls->div->n_row; ++i)
 630                 if (isl_int_is_zero(ls->div->row[i][0]))
 631                         return 0;
 632
 633         return 1;
 634 }
 635
 636 __isl_give isl_local_space *isl_local_space_domain(
 637         __isl_take isl_local_space *ls)
 638 {
 639         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 640                                         0, isl_local_space_dim(ls, isl_dim_out));
 641         ls = isl_local_space_cow(ls);
 642         if (!ls)
 643                 return NULL;
 644         ls->dim = isl_space_domain(ls->dim);
 645         if (!ls->dim)
 646                 return isl_local_space_free(ls);
 647         return ls;
 648 }
 649
 650 __isl_give isl_local_space *isl_local_space_range(
 651         __isl_take isl_local_space *ls)
 652 {
 653         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 654                                         0, isl_local_space_dim(ls, isl_dim_in));
 655         ls = isl_local_space_cow(ls);
 656         if (!ls)
 657                 return NULL;
 658
 659         ls->dim = isl_space_range(ls->dim);
 660         if (!ls->dim)
 661                 return isl_local_space_free(ls);
 662         return ls;
 663 }
 664
 665 /* Construct a local space for a map that has the given local
 666  * space as domain and that has a zero-dimensional range.
 667  */
 668 __isl_give isl_local_space *isl_local_space_from_domain(
 669         __isl_take isl_local_space *ls)
 670 {
 671         ls = isl_local_space_cow(ls);
 672         if (!ls)
 673                 return NULL;
 674         ls->dim = isl_space_from_domain(ls->dim);
 675         if (!ls->dim)
 676                 return isl_local_space_free(ls);
 677         return ls;
 678 }
 679
 680 __isl_give isl_local_space *isl_local_space_add_dims(
 681         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 682 {
 683         int pos;
 684
 685         if (!ls)
 686                 return NULL;
 687         pos = isl_local_space_dim(ls, type);
 688         return isl_local_space_insert_dims(ls, type, pos, n);
 689 }
 690
 691 /* Remove common factor of non-constant terms and denominator.
 692  */
 693 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 694 {
 695         isl_ctx *ctx = ls->div->ctx;
 696         unsigned total = ls->div->n_col - 2;
 697
 698         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 699         isl_int_gcd(ctx->normalize_gcd,
 700                     ctx->normalize_gcd, ls->div->row[div][0]);
 701         if (isl_int_is_one(ctx->normalize_gcd))
 702                 return;
 703
 704         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 705                             ctx->normalize_gcd, total);
 706         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 707                             ctx->normalize_gcd);
 708         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 709                             ctx->normalize_gcd);
 710 }
 711
 712 /* Exploit the equalities in "eq" to simplify the expressions of
 713  * the integer divisions in "ls".
 714  * The integer divisions in "ls" are assumed to appear as regular
 715  * dimensions in "eq".
 716  */
 717 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 718         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 719 {
 720         int i, j, k;
 721         unsigned total;
 722         unsigned n_div;
 723
 724         if (!ls || !eq)
 725                 goto error;
 726
 727         total = isl_space_dim(eq->dim, isl_dim_all);
 728         if (isl_local_space_dim(ls, isl_dim_all) != total)
 729                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 730                         "spaces don't match", goto error);
 731         total++;
 732         n_div = eq->n_div;
 733         for (i = 0; i < eq->n_eq; ++i) {
 734                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 735                 if (j < 0 || j == 0 || j >= total)
 736                         continue;
 737
 738                 for (k = 0; k < ls->div->n_row; ++k) {
 739                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 740                                 continue;
 741                         ls = isl_local_space_cow(ls);
 742                         if (!ls)
 743                                 goto error;
 744                         ls->div = isl_mat_cow(ls->div);
 745                         if (!ls->div)
 746                                 goto error;
 747                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 748                                         &ls->div->row[k][0]);
 749                         normalize_div(ls, k);
 750                 }
 751         }
 752
 753         isl_basic_set_free(eq);
 754         return ls;
 755 error:
 756         isl_basic_set_free(eq);
 757         isl_local_space_free(ls);
 758         return NULL;
 759 }
 760
 761 /* Plug in the affine expressions "subs" of length "subs_len" (including
 762  * the denominator and the constant term) into the variable at position "pos"
 763  * of the "n" div expressions starting at "first".
 764  *
 765  * Let i be the dimension to replace and let "subs" be of the form
 766  *
 767  *      f/d
 768  *
 769  * Any integer division starting at "first" with a non-zero coefficient for i,
 770  *
 771  *      floor((a i + g)/m)
 772  *
 773  * is replaced by
 774  *
 775  *      floor((a f + d g)/(m d))
 776  */
 777 __isl_give isl_local_space *isl_local_space_substitute_seq(
 778         __isl_take isl_local_space *ls,
 779         enum isl_dim_type type, unsigned pos, isl_int *subs, int subs_len,
 780         int first, int n)
 781 {
 782         int i;
 783         isl_int v;
 784
 785         if (n == 0)
 786                 return ls;
 787         ls = isl_local_space_cow(ls);
 788         if (!ls)
 789                 return NULL;
 790         ls->div = isl_mat_cow(ls->div);
 791         if (!ls->div)
 792                 return isl_local_space_free(ls);
 793
 794         if (first + n > ls->div->n_row)
 795                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 796                         "index out of bounds", return isl_local_space_free(ls));
 797
 798         pos += isl_local_space_offset(ls, type);
 799
 800         isl_int_init(v);
 801         for (i = first; i < ls->div->n_row; ++i) {
 802                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 803                         continue;
 804                 isl_seq_substitute(ls->div->row[i], pos, subs,
 805                         ls->div->n_col, subs_len, v);
 806                 normalize_div(ls, i);
 807         }
 808         isl_int_clear(v);
 809
 810         return ls;
 811 }
 812
 813 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 814  * of "ls".
 815  *
 816  * Let i be the dimension to replace and let "subs" be of the form
 817  *
 818  *      f/d
 819  *
 820  * Any integer division with a non-zero coefficient for i,
 821  *
 822  *      floor((a i + g)/m)
 823  *
 824  * is replaced by
 825  *
 826  *      floor((a f + d g)/(m d))
 827  */
 828 __isl_give isl_local_space *isl_local_space_substitute(
 829         __isl_take isl_local_space *ls,
 830         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 831 {
 832         ls = isl_local_space_cow(ls);
 833         if (!ls || !subs)
 834                 return isl_local_space_free(ls);
 835
 836         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 837                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 838                         "spaces don't match", return isl_local_space_free(ls));
 839         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 840                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 841                         "cannot handle divs yet",
 842                         return isl_local_space_free(ls));
 843
 844         return isl_local_space_substitute_seq(ls, type, pos, subs->v->el,
 845                                             subs->v->size, 0, ls->div->n_row);
 846 }
 847
 848 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 849         enum isl_dim_type type)
 850 {
 851         if (!ls)
 852                 return -1;
 853         return isl_space_is_named_or_nested(ls->dim, type);
 854 }
 855
 856 __isl_give isl_local_space *isl_local_space_drop_dims(
 857         __isl_take isl_local_space *ls,
 858         enum isl_dim_type type, unsigned first, unsigned n)
 859 {
 860         isl_ctx *ctx;
 861
 862         if (!ls)
 863                 return NULL;
 864         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 865                 return ls;
 866
 867         ctx = isl_local_space_get_ctx(ls);
 868         if (first + n > isl_local_space_dim(ls, type))
 869                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 870                         return isl_local_space_free(ls));
 871
 872         ls = isl_local_space_cow(ls);
 873         if (!ls)
 874                 return NULL;
 875
 876         if (type == isl_dim_div) {
 877                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 878         } else {
 879                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 880                 if (!ls->dim)
 881                         return isl_local_space_free(ls);
 882         }
 883
 884         first += 1 + isl_local_space_offset(ls, type);
 885         ls->div = isl_mat_drop_cols(ls->div, first, n);
 886         if (!ls->div)
 887                 return isl_local_space_free(ls);
 888
 889         return ls;
 890 }
 891
 892 __isl_give isl_local_space *isl_local_space_insert_dims(
 893         __isl_take isl_local_space *ls,
 894         enum isl_dim_type type, unsigned first, unsigned n)
 895 {
 896         isl_ctx *ctx;
 897
 898         if (!ls)
 899                 return NULL;
 900         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 901                 return ls;
 902
 903         ctx = isl_local_space_get_ctx(ls);
 904         if (first > isl_local_space_dim(ls, type))
 905                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 906                         return isl_local_space_free(ls));
 907
 908         ls = isl_local_space_cow(ls);
 909         if (!ls)
 910                 return NULL;
 911
 912         if (type == isl_dim_div) {
 913                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 914         } else {
 915                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 916                 if (!ls->dim)
 917                         return isl_local_space_free(ls);
 918         }
 919
 920         first += 1 + isl_local_space_offset(ls, type);
 921         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 922         if (!ls->div)
 923                 return isl_local_space_free(ls);
 924
 925         return ls;
 926 }
 927
 928 /* Check if the constraints pointed to by "constraint" is a div
 929  * constraint corresponding to div "div" in "ls".
 930  *
 931  * That is, if div = floor(f/m), then check if the constraint is
 932  *
 933  *              f - m d >= 0
 934  * or
 935  *              -(f-(m-1)) + m d >= 0
 936  */
 937 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 938         isl_int *constraint, unsigned div)
 939 {
 940         unsigned pos;
 941
 942         if (!ls)
 943                 return -1;
 944
 945         if (isl_int_is_zero(ls->div->row[div][0]))
 946                 return 0;
 947
 948         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 949
 950         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 951                 int neg;
 952                 isl_int_sub(ls->div->row[div][1],
 953                                 ls->div->row[div][1], ls->div->row[div][0]);
 954                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 955                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 956                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 957                 isl_int_add(ls->div->row[div][1],
 958                                 ls->div->row[div][1], ls->div->row[div][0]);
 959                 if (!neg)
 960                         return 0;
 961                 if (isl_seq_first_non_zero(constraint+pos+1,
 962                                             ls->div->n_row-div-1) != -1)
 963                         return 0;
 964         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 965                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 966                         return 0;
 967                 if (isl_seq_first_non_zero(constraint+pos+1,
 968                                             ls->div->n_row-div-1) != -1)
 969                         return 0;
 970         } else
 971                 return 0;
 972
 973         return 1;
 974 }
 975
 976 /*
 977  * Set active[i] to 1 if the dimension at position i is involved
 978  * in the linear expression l.
 979  */
 980 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 981 {
 982         int i, j;
 983         isl_ctx *ctx;
 984         int *active = NULL;
 985         unsigned total;
 986         unsigned offset;
 987
 988         ctx = isl_local_space_get_ctx(ls);
 989         total = isl_local_space_dim(ls, isl_dim_all);
 990         active = isl_calloc_array(ctx, int, total);
 991         if (!active)
 992                 return NULL;
 993
 994         for (i = 0; i < total; ++i)
 995                 active[i] = !isl_int_is_zero(l[i]);
 996
 997         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 998         for (i = ls->div->n_row - 1; i >= 0; --i) {
 999                 if (!active[offset + i])
1000                         continue;
1001                 for (j = 0; j < total; ++j)
1002                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
1003         }
1004
1005         return active;
1006 }
1007
1008 /* Given a local space "ls" of a set, create a local space
1009  * for the lift of the set.  In particular, the result
1010  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
1011  * range of the wrapped map.
1012  */
1013 __isl_give isl_local_space *isl_local_space_lift(
1014         __isl_take isl_local_space *ls)
1015 {
1016         ls = isl_local_space_cow(ls);
1017         if (!ls)
1018                 return NULL;
1019
1020         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
1021         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
1022         if (!ls->dim || !ls->div)
1023                 return isl_local_space_free(ls);
1024
1025         return ls;
1026 }
1027
1028 /* Construct a basic map that maps a set living in local space "ls"
1029  * to the corresponding lifted local space.
1030  */
1031 __isl_give isl_basic_map *isl_local_space_lifting(
1032         __isl_take isl_local_space *ls)
1033 {
1034         isl_basic_map *lifting;
1035         isl_basic_set *bset;
1036
1037         if (!ls)
1038                 return NULL;
1039         if (!isl_local_space_is_set(ls))
1040                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1041                         "lifting only defined on set spaces",
1042                         return isl_local_space_free(ls));
1043
1044         bset = isl_basic_set_from_local_space(ls);
1045         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
1046         lifting = isl_basic_map_domain_map(lifting);
1047         lifting = isl_basic_map_reverse(lifting);
1048
1049         return lifting;
1050 }
1051
1052 /* Compute the preimage of "ls" under the function represented by "ma".
1053  * In other words, plug in "ma" in "ls".  The result is a local space
1054  * that is part of the domain space of "ma".
1055  *
1056  * If the divs in "ls" are represented as
1057  *
1058  *      floor((a_i(p) + b_i x + c_i(divs))/n_i)
1059  *
1060  * and ma is represented by
1061  *
1062  *      x = D(p) + F(y) + G(divs')
1063  *
1064  * then the resulting divs are
1065  *
1066  *      floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
1067  *
1068  * We first copy over the divs from "ma" and then
1069  * we add the modified divs from "ls".
1070  */
1071 __isl_give isl_local_space *isl_local_space_preimage_multi_aff(
1072         __isl_take isl_local_space *ls, __isl_take isl_multi_aff *ma)
1073 {
1074         int i;
1075         isl_space *space;
1076         isl_local_space *res = NULL;
1077         int n_div_ls, n_div_ma;
1078         isl_int f, c1, c2, g;
1079
1080         ma = isl_multi_aff_align_divs(ma);
1081         if (!ls || !ma)
1082                 goto error;
1083         if (!isl_space_is_range_internal(ls->dim, ma->space))
1084                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
1085                         "spaces don't match", goto error);
1086
1087         n_div_ls = isl_local_space_dim(ls, isl_dim_div);
1088         n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
1089
1090         space = isl_space_domain(isl_multi_aff_get_space(ma));
1091         res = isl_local_space_alloc(space, n_div_ma + n_div_ls);
1092         if (!res)
1093                 goto error;
1094
1095         if (n_div_ma) {
1096                 isl_mat_free(res->div);
1097                 res->div = isl_mat_copy(ma->p[0]->ls->div);
1098                 res->div = isl_mat_add_zero_cols(res->div, n_div_ls);
1099                 res->div = isl_mat_add_rows(res->div, n_div_ls);
1100                 if (!res->div)
1101                         goto error;
1102         }
1103
1104         isl_int_init(f);
1105         isl_int_init(c1);
1106         isl_int_init(c2);
1107         isl_int_init(g);
1108
1109         for (i = 0; i < ls->div->n_row; ++i) {
1110                 if (isl_int_is_zero(ls->div->row[i][0])) {
1111                         isl_int_set_si(res->div->row[n_div_ma + i][0], 0);
1112                         continue;
1113                 }
1114                 isl_seq_preimage(res->div->row[n_div_ma + i], ls->div->row[i],
1115                                 ma, 0, 0, n_div_ma, n_div_ls, f, c1, c2, g, 1);
1116                 normalize_div(res, n_div_ma + i);
1117         }
1118
1119         isl_int_clear(f);
1120         isl_int_clear(c1);
1121         isl_int_clear(c2);
1122         isl_int_clear(g);
1123
1124         isl_local_space_free(ls);
1125         isl_multi_aff_free(ma);
1126         return res;
1127 error:
1128         isl_local_space_free(ls);
1129         isl_multi_aff_free(ma);
1130         isl_local_space_free(res);
1131         return NULL;
1132 }