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 21isl_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; 45error: 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 104void *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 */ 122int 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 */ 130int 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 150int 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 162unsigned 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 */ 183int 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 189const 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 195int 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; 280error: 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 */ 290static __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; 316error: 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; 341error: 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; 368error: 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; 385error: 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 */ 394static 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 */ 413static 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 */ 442int 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 */ 449static 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; 614error: 615 free(exp1); 616 free(exp2); 617 isl_local_space_free(ls1); 618 isl_local_space_free(ls2); 619 return NULL; 620} 621 622int 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 */ 693static 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; 755error: 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 848int 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 */ 937int 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 */ 980int *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 (total && !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; 1127error: 1128 isl_local_space_free(ls); 1129 isl_multi_aff_free(ma); 1130 isl_local_space_free(res); 1131 return NULL; 1132} 1133