1/* 2 * Copyright 2008-2009 Katholieke Universiteit Leuven 3 * Copyright 2012 Ecole Normale Superieure 4 * 5 * Use of this software is governed by the MIT license 6 * 7 * Written by Sven Verdoolaege, K.U.Leuven, Departement 8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium 9 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France 10 */ 11 12#include <strings.h> 13#include <isl_ctx_private.h> 14#include <isl_map_private.h> 15#include "isl_equalities.h" 16#include <isl/map.h> 17#include <isl/seq.h> 18#include "isl_tab.h" 19#include <isl_space_private.h> 20#include <isl_mat_private.h> 21 22static void swap_equality(struct isl_basic_map *bmap, int a, int b) 23{ 24 isl_int *t = bmap->eq[a]; 25 bmap->eq[a] = bmap->eq[b]; 26 bmap->eq[b] = t; 27} 28 29static void swap_inequality(struct isl_basic_map *bmap, int a, int b) 30{ 31 if (a != b) { 32 isl_int *t = bmap->ineq[a]; 33 bmap->ineq[a] = bmap->ineq[b]; 34 bmap->ineq[b] = t; 35 } 36} 37 38static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem) 39{ 40 isl_seq_cpy(c, c + n, rem); 41 isl_seq_clr(c + rem, n); 42} 43 44/* Drop n dimensions starting at first. 45 * 46 * In principle, this frees up some extra variables as the number 47 * of columns remains constant, but we would have to extend 48 * the div array too as the number of rows in this array is assumed 49 * to be equal to extra. 50 */ 51struct isl_basic_set *isl_basic_set_drop_dims( 52 struct isl_basic_set *bset, unsigned first, unsigned n) 53{ 54 int i; 55 56 if (!bset) 57 goto error; 58 59 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error); 60 61 if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set)) 62 return bset; 63 64 bset = isl_basic_set_cow(bset); 65 if (!bset) 66 return NULL; 67 68 for (i = 0; i < bset->n_eq; ++i) 69 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n, 70 (bset->dim->n_out-first-n)+bset->extra); 71 72 for (i = 0; i < bset->n_ineq; ++i) 73 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n, 74 (bset->dim->n_out-first-n)+bset->extra); 75 76 for (i = 0; i < bset->n_div; ++i) 77 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n, 78 (bset->dim->n_out-first-n)+bset->extra); 79 80 bset->dim = isl_space_drop_outputs(bset->dim, first, n); 81 if (!bset->dim) 82 goto error; 83 84 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED); 85 bset = isl_basic_set_simplify(bset); 86 return isl_basic_set_finalize(bset); 87error: 88 isl_basic_set_free(bset); 89 return NULL; 90} 91 92struct isl_set *isl_set_drop_dims( 93 struct isl_set *set, unsigned first, unsigned n) 94{ 95 int i; 96 97 if (!set) 98 goto error; 99 100 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error); 101 102 if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set)) 103 return set; 104 set = isl_set_cow(set); 105 if (!set) 106 goto error; 107 set->dim = isl_space_drop_outputs(set->dim, first, n); 108 if (!set->dim) 109 goto error; 110 111 for (i = 0; i < set->n; ++i) { 112 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n); 113 if (!set->p[i]) 114 goto error; 115 } 116 117 ISL_F_CLR(set, ISL_SET_NORMALIZED); 118 return set; 119error: 120 isl_set_free(set); 121 return NULL; 122} 123 124/* Move "n" divs starting at "first" to the end of the list of divs. 125 */ 126static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap, 127 unsigned first, unsigned n) 128{ 129 isl_int **div; 130 int i; 131 132 if (first + n == bmap->n_div) 133 return bmap; 134 135 div = isl_alloc_array(bmap->ctx, isl_int *, n); 136 if (!div) 137 goto error; 138 for (i = 0; i < n; ++i) 139 div[i] = bmap->div[first + i]; 140 for (i = 0; i < bmap->n_div - first - n; ++i) 141 bmap->div[first + i] = bmap->div[first + n + i]; 142 for (i = 0; i < n; ++i) 143 bmap->div[bmap->n_div - n + i] = div[i]; 144 free(div); 145 return bmap; 146error: 147 isl_basic_map_free(bmap); 148 return NULL; 149} 150 151/* Drop "n" dimensions of type "type" starting at "first". 152 * 153 * In principle, this frees up some extra variables as the number 154 * of columns remains constant, but we would have to extend 155 * the div array too as the number of rows in this array is assumed 156 * to be equal to extra. 157 */ 158struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap, 159 enum isl_dim_type type, unsigned first, unsigned n) 160{ 161 int i; 162 unsigned dim; 163 unsigned offset; 164 unsigned left; 165 166 if (!bmap) 167 goto error; 168 169 dim = isl_basic_map_dim(bmap, type); 170 isl_assert(bmap->ctx, first + n <= dim, goto error); 171 172 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type)) 173 return bmap; 174 175 bmap = isl_basic_map_cow(bmap); 176 if (!bmap) 177 return NULL; 178 179 offset = isl_basic_map_offset(bmap, type) + first; 180 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n; 181 for (i = 0; i < bmap->n_eq; ++i) 182 constraint_drop_vars(bmap->eq[i]+offset, n, left); 183 184 for (i = 0; i < bmap->n_ineq; ++i) 185 constraint_drop_vars(bmap->ineq[i]+offset, n, left); 186 187 for (i = 0; i < bmap->n_div; ++i) 188 constraint_drop_vars(bmap->div[i]+1+offset, n, left); 189 190 if (type == isl_dim_div) { 191 bmap = move_divs_last(bmap, first, n); 192 if (!bmap) 193 goto error; 194 isl_basic_map_free_div(bmap, n); 195 } else 196 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n); 197 if (!bmap->dim) 198 goto error; 199 200 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); 201 bmap = isl_basic_map_simplify(bmap); 202 return isl_basic_map_finalize(bmap); 203error: 204 isl_basic_map_free(bmap); 205 return NULL; 206} 207 208__isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset, 209 enum isl_dim_type type, unsigned first, unsigned n) 210{ 211 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset, 212 type, first, n); 213} 214 215struct isl_basic_map *isl_basic_map_drop_inputs( 216 struct isl_basic_map *bmap, unsigned first, unsigned n) 217{ 218 return isl_basic_map_drop(bmap, isl_dim_in, first, n); 219} 220 221struct isl_map *isl_map_drop(struct isl_map *map, 222 enum isl_dim_type type, unsigned first, unsigned n) 223{ 224 int i; 225 226 if (!map) 227 goto error; 228 229 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error); 230 231 if (n == 0 && !isl_space_get_tuple_name(map->dim, type)) 232 return map; 233 map = isl_map_cow(map); 234 if (!map) 235 goto error; 236 map->dim = isl_space_drop_dims(map->dim, type, first, n); 237 if (!map->dim) 238 goto error; 239 240 for (i = 0; i < map->n; ++i) { 241 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n); 242 if (!map->p[i]) 243 goto error; 244 } 245 ISL_F_CLR(map, ISL_MAP_NORMALIZED); 246 247 return map; 248error: 249 isl_map_free(map); 250 return NULL; 251} 252 253struct isl_set *isl_set_drop(struct isl_set *set, 254 enum isl_dim_type type, unsigned first, unsigned n) 255{ 256 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n); 257} 258 259struct isl_map *isl_map_drop_inputs( 260 struct isl_map *map, unsigned first, unsigned n) 261{ 262 return isl_map_drop(map, isl_dim_in, first, n); 263} 264 265/* 266 * We don't cow, as the div is assumed to be redundant. 267 */ 268static struct isl_basic_map *isl_basic_map_drop_div( 269 struct isl_basic_map *bmap, unsigned div) 270{ 271 int i; 272 unsigned pos; 273 274 if (!bmap) 275 goto error; 276 277 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div; 278 279 isl_assert(bmap->ctx, div < bmap->n_div, goto error); 280 281 for (i = 0; i < bmap->n_eq; ++i) 282 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1); 283 284 for (i = 0; i < bmap->n_ineq; ++i) { 285 if (!isl_int_is_zero(bmap->ineq[i][pos])) { 286 isl_basic_map_drop_inequality(bmap, i); 287 --i; 288 continue; 289 } 290 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1); 291 } 292 293 for (i = 0; i < bmap->n_div; ++i) 294 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1); 295 296 if (div != bmap->n_div - 1) { 297 int j; 298 isl_int *t = bmap->div[div]; 299 300 for (j = div; j < bmap->n_div - 1; ++j) 301 bmap->div[j] = bmap->div[j+1]; 302 303 bmap->div[bmap->n_div - 1] = t; 304 } 305 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); 306 isl_basic_map_free_div(bmap, 1); 307 308 return bmap; 309error: 310 isl_basic_map_free(bmap); 311 return NULL; 312} 313 314struct isl_basic_map *isl_basic_map_normalize_constraints( 315 struct isl_basic_map *bmap) 316{ 317 int i; 318 isl_int gcd; 319 unsigned total = isl_basic_map_total_dim(bmap); 320 321 if (!bmap) 322 return NULL; 323 324 isl_int_init(gcd); 325 for (i = bmap->n_eq - 1; i >= 0; --i) { 326 isl_seq_gcd(bmap->eq[i]+1, total, &gcd); 327 if (isl_int_is_zero(gcd)) { 328 if (!isl_int_is_zero(bmap->eq[i][0])) { 329 bmap = isl_basic_map_set_to_empty(bmap); 330 break; 331 } 332 isl_basic_map_drop_equality(bmap, i); 333 continue; 334 } 335 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) 336 isl_int_gcd(gcd, gcd, bmap->eq[i][0]); 337 if (isl_int_is_one(gcd)) 338 continue; 339 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) { 340 bmap = isl_basic_map_set_to_empty(bmap); 341 break; 342 } 343 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total); 344 } 345 346 for (i = bmap->n_ineq - 1; i >= 0; --i) { 347 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd); 348 if (isl_int_is_zero(gcd)) { 349 if (isl_int_is_neg(bmap->ineq[i][0])) { 350 bmap = isl_basic_map_set_to_empty(bmap); 351 break; 352 } 353 isl_basic_map_drop_inequality(bmap, i); 354 continue; 355 } 356 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) 357 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]); 358 if (isl_int_is_one(gcd)) 359 continue; 360 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd); 361 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total); 362 } 363 isl_int_clear(gcd); 364 365 return bmap; 366} 367 368struct isl_basic_set *isl_basic_set_normalize_constraints( 369 struct isl_basic_set *bset) 370{ 371 return (struct isl_basic_set *)isl_basic_map_normalize_constraints( 372 (struct isl_basic_map *)bset); 373} 374 375/* Remove any common factor in numerator and denominator of the div expression, 376 * not taking into account the constant term. 377 * That is, if the div is of the form 378 * 379 * floor((a + m f(x))/(m d)) 380 * 381 * then replace it by 382 * 383 * floor((floor(a/m) + f(x))/d) 384 * 385 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d 386 * and can therefore not influence the result of the floor. 387 */ 388static void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div) 389{ 390 unsigned total = isl_basic_map_total_dim(bmap); 391 isl_ctx *ctx = bmap->ctx; 392 393 if (isl_int_is_zero(bmap->div[div][0])) 394 return; 395 isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd); 396 isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]); 397 if (isl_int_is_one(ctx->normalize_gcd)) 398 return; 399 isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1], 400 ctx->normalize_gcd); 401 isl_int_divexact(bmap->div[div][0], bmap->div[div][0], 402 ctx->normalize_gcd); 403 isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2, 404 ctx->normalize_gcd, total); 405} 406 407/* Remove any common factor in numerator and denominator of a div expression, 408 * not taking into account the constant term. 409 * That is, look for any div of the form 410 * 411 * floor((a + m f(x))/(m d)) 412 * 413 * and replace it by 414 * 415 * floor((floor(a/m) + f(x))/d) 416 * 417 * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d 418 * and can therefore not influence the result of the floor. 419 */ 420static __isl_give isl_basic_map *normalize_div_expressions( 421 __isl_take isl_basic_map *bmap) 422{ 423 int i; 424 425 if (!bmap) 426 return NULL; 427 if (bmap->n_div == 0) 428 return bmap; 429 430 for (i = 0; i < bmap->n_div; ++i) 431 normalize_div_expression(bmap, i); 432 433 return bmap; 434} 435 436/* Assumes divs have been ordered if keep_divs is set. 437 */ 438static void eliminate_var_using_equality(struct isl_basic_map *bmap, 439 unsigned pos, isl_int *eq, int keep_divs, int *progress) 440{ 441 unsigned total; 442 unsigned space_total; 443 int k; 444 int last_div; 445 446 total = isl_basic_map_total_dim(bmap); 447 space_total = isl_space_dim(bmap->dim, isl_dim_all); 448 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div); 449 for (k = 0; k < bmap->n_eq; ++k) { 450 if (bmap->eq[k] == eq) 451 continue; 452 if (isl_int_is_zero(bmap->eq[k][1+pos])) 453 continue; 454 if (progress) 455 *progress = 1; 456 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL); 457 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total); 458 } 459 460 for (k = 0; k < bmap->n_ineq; ++k) { 461 if (isl_int_is_zero(bmap->ineq[k][1+pos])) 462 continue; 463 if (progress) 464 *progress = 1; 465 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL); 466 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total); 467 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); 468 } 469 470 for (k = 0; k < bmap->n_div; ++k) { 471 if (isl_int_is_zero(bmap->div[k][0])) 472 continue; 473 if (isl_int_is_zero(bmap->div[k][1+1+pos])) 474 continue; 475 if (progress) 476 *progress = 1; 477 /* We need to be careful about circular definitions, 478 * so for now we just remove the definition of div k 479 * if the equality contains any divs. 480 * If keep_divs is set, then the divs have been ordered 481 * and we can keep the definition as long as the result 482 * is still ordered. 483 */ 484 if (last_div == -1 || (keep_divs && last_div < k)) { 485 isl_seq_elim(bmap->div[k]+1, eq, 486 1+pos, 1+total, &bmap->div[k][0]); 487 normalize_div_expression(bmap, k); 488 } else 489 isl_seq_clr(bmap->div[k], 1 + total); 490 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); 491 } 492} 493 494/* Assumes divs have been ordered if keep_divs is set. 495 */ 496static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, 497 unsigned div, int keep_divs) 498{ 499 unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div; 500 501 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL); 502 503 isl_basic_map_drop_div(bmap, div); 504} 505 506/* Check if elimination of div "div" using equality "eq" would not 507 * result in a div depending on a later div. 508 */ 509static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq, 510 unsigned div) 511{ 512 int k; 513 int last_div; 514 unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all); 515 unsigned pos = space_total + div; 516 517 last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div); 518 if (last_div < 0 || last_div <= div) 519 return 1; 520 521 for (k = 0; k <= last_div; ++k) { 522 if (isl_int_is_zero(bmap->div[k][0])) 523 return 1; 524 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos])) 525 return 0; 526 } 527 528 return 1; 529} 530 531/* Elimininate divs based on equalities 532 */ 533static struct isl_basic_map *eliminate_divs_eq( 534 struct isl_basic_map *bmap, int *progress) 535{ 536 int d; 537 int i; 538 int modified = 0; 539 unsigned off; 540 541 bmap = isl_basic_map_order_divs(bmap); 542 543 if (!bmap) 544 return NULL; 545 546 off = 1 + isl_space_dim(bmap->dim, isl_dim_all); 547 548 for (d = bmap->n_div - 1; d >= 0 ; --d) { 549 for (i = 0; i < bmap->n_eq; ++i) { 550 if (!isl_int_is_one(bmap->eq[i][off + d]) && 551 !isl_int_is_negone(bmap->eq[i][off + d])) 552 continue; 553 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d)) 554 continue; 555 modified = 1; 556 *progress = 1; 557 eliminate_div(bmap, bmap->eq[i], d, 1); 558 isl_basic_map_drop_equality(bmap, i); 559 break; 560 } 561 } 562 if (modified) 563 return eliminate_divs_eq(bmap, progress); 564 return bmap; 565} 566 567/* Elimininate divs based on inequalities 568 */ 569static struct isl_basic_map *eliminate_divs_ineq( 570 struct isl_basic_map *bmap, int *progress) 571{ 572 int d; 573 int i; 574 unsigned off; 575 struct isl_ctx *ctx; 576 577 if (!bmap) 578 return NULL; 579 580 ctx = bmap->ctx; 581 off = 1 + isl_space_dim(bmap->dim, isl_dim_all); 582 583 for (d = bmap->n_div - 1; d >= 0 ; --d) { 584 for (i = 0; i < bmap->n_eq; ++i) 585 if (!isl_int_is_zero(bmap->eq[i][off + d])) 586 break; 587 if (i < bmap->n_eq) 588 continue; 589 for (i = 0; i < bmap->n_ineq; ++i) 590 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one)) 591 break; 592 if (i < bmap->n_ineq) 593 continue; 594 *progress = 1; 595 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1); 596 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) 597 break; 598 bmap = isl_basic_map_drop_div(bmap, d); 599 if (!bmap) 600 break; 601 } 602 return bmap; 603} 604 605struct isl_basic_map *isl_basic_map_gauss( 606 struct isl_basic_map *bmap, int *progress) 607{ 608 int k; 609 int done; 610 int last_var; 611 unsigned total_var; 612 unsigned total; 613 614 bmap = isl_basic_map_order_divs(bmap); 615 616 if (!bmap) 617 return NULL; 618 619 total = isl_basic_map_total_dim(bmap); 620 total_var = total - bmap->n_div; 621 622 last_var = total - 1; 623 for (done = 0; done < bmap->n_eq; ++done) { 624 for (; last_var >= 0; --last_var) { 625 for (k = done; k < bmap->n_eq; ++k) 626 if (!isl_int_is_zero(bmap->eq[k][1+last_var])) 627 break; 628 if (k < bmap->n_eq) 629 break; 630 } 631 if (last_var < 0) 632 break; 633 if (k != done) 634 swap_equality(bmap, k, done); 635 if (isl_int_is_neg(bmap->eq[done][1+last_var])) 636 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total); 637 638 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1, 639 progress); 640 641 if (last_var >= total_var && 642 isl_int_is_zero(bmap->div[last_var - total_var][0])) { 643 unsigned div = last_var - total_var; 644 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total); 645 isl_int_set_si(bmap->div[div][1+1+last_var], 0); 646 isl_int_set(bmap->div[div][0], 647 bmap->eq[done][1+last_var]); 648 if (progress) 649 *progress = 1; 650 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); 651 } 652 } 653 if (done == bmap->n_eq) 654 return bmap; 655 for (k = done; k < bmap->n_eq; ++k) { 656 if (isl_int_is_zero(bmap->eq[k][0])) 657 continue; 658 return isl_basic_map_set_to_empty(bmap); 659 } 660 isl_basic_map_free_equality(bmap, bmap->n_eq-done); 661 return bmap; 662} 663 664struct isl_basic_set *isl_basic_set_gauss( 665 struct isl_basic_set *bset, int *progress) 666{ 667 return (struct isl_basic_set*)isl_basic_map_gauss( 668 (struct isl_basic_map *)bset, progress); 669} 670 671 672static unsigned int round_up(unsigned int v) 673{ 674 int old_v = v; 675 676 while (v) { 677 old_v = v; 678 v ^= v & -v; 679 } 680 return old_v << 1; 681} 682 683static int hash_index(isl_int ***index, unsigned int size, int bits, 684 struct isl_basic_map *bmap, int k) 685{ 686 int h; 687 unsigned total = isl_basic_map_total_dim(bmap); 688 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits); 689 for (h = hash; index[h]; h = (h+1) % size) 690 if (&bmap->ineq[k] != index[h] && 691 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total)) 692 break; 693 return h; 694} 695 696static int set_hash_index(isl_int ***index, unsigned int size, int bits, 697 struct isl_basic_set *bset, int k) 698{ 699 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k); 700} 701 702/* If we can eliminate more than one div, then we need to make 703 * sure we do it from last div to first div, in order not to 704 * change the position of the other divs that still need to 705 * be removed. 706 */ 707static struct isl_basic_map *remove_duplicate_divs( 708 struct isl_basic_map *bmap, int *progress) 709{ 710 unsigned int size; 711 int *index; 712 int *elim_for; 713 int k, l, h; 714 int bits; 715 struct isl_blk eq; 716 unsigned total_var; 717 unsigned total; 718 struct isl_ctx *ctx; 719 720 bmap = isl_basic_map_order_divs(bmap); 721 if (!bmap || bmap->n_div <= 1) 722 return bmap; 723 724 total_var = isl_space_dim(bmap->dim, isl_dim_all); 725 total = total_var + bmap->n_div; 726 727 ctx = bmap->ctx; 728 for (k = bmap->n_div - 1; k >= 0; --k) 729 if (!isl_int_is_zero(bmap->div[k][0])) 730 break; 731 if (k <= 0) 732 return bmap; 733 734 elim_for = isl_calloc_array(ctx, int, bmap->n_div); 735 size = round_up(4 * bmap->n_div / 3 - 1); 736 bits = ffs(size) - 1; 737 index = isl_calloc_array(ctx, int, size); 738 if (!index) 739 return bmap; 740 eq = isl_blk_alloc(ctx, 1+total); 741 if (isl_blk_is_error(eq)) 742 goto out; 743 744 isl_seq_clr(eq.data, 1+total); 745 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1; 746 for (--k; k >= 0; --k) { 747 uint32_t hash; 748 749 if (isl_int_is_zero(bmap->div[k][0])) 750 continue; 751 752 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits); 753 for (h = hash; index[h]; h = (h+1) % size) 754 if (isl_seq_eq(bmap->div[k], 755 bmap->div[index[h]-1], 2+total)) 756 break; 757 if (index[h]) { 758 *progress = 1; 759 l = index[h] - 1; 760 elim_for[l] = k + 1; 761 } 762 index[h] = k+1; 763 } 764 for (l = bmap->n_div - 1; l >= 0; --l) { 765 if (!elim_for[l]) 766 continue; 767 k = elim_for[l] - 1; 768 isl_int_set_si(eq.data[1+total_var+k], -1); 769 isl_int_set_si(eq.data[1+total_var+l], 1); 770 eliminate_div(bmap, eq.data, l, 1); 771 isl_int_set_si(eq.data[1+total_var+k], 0); 772 isl_int_set_si(eq.data[1+total_var+l], 0); 773 } 774 775 isl_blk_free(ctx, eq); 776out: 777 free(index); 778 free(elim_for); 779 return bmap; 780} 781 782static int n_pure_div_eq(struct isl_basic_map *bmap) 783{ 784 int i, j; 785 unsigned total; 786 787 total = isl_space_dim(bmap->dim, isl_dim_all); 788 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) { 789 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j])) 790 --j; 791 if (j < 0) 792 break; 793 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1) 794 return 0; 795 } 796 return i; 797} 798 799/* Normalize divs that appear in equalities. 800 * 801 * In particular, we assume that bmap contains some equalities 802 * of the form 803 * 804 * a x = m * e_i 805 * 806 * and we want to replace the set of e_i by a minimal set and 807 * such that the new e_i have a canonical representation in terms 808 * of the vector x. 809 * If any of the equalities involves more than one divs, then 810 * we currently simply bail out. 811 * 812 * Let us first additionally assume that all equalities involve 813 * a div. The equalities then express modulo constraints on the 814 * remaining variables and we can use "parameter compression" 815 * to find a minimal set of constraints. The result is a transformation 816 * 817 * x = T(x') = x_0 + G x' 818 * 819 * with G a lower-triangular matrix with all elements below the diagonal 820 * non-negative and smaller than the diagonal element on the same row. 821 * We first normalize x_0 by making the same property hold in the affine 822 * T matrix. 823 * The rows i of G with a 1 on the diagonal do not impose any modulo 824 * constraint and simply express x_i = x'_i. 825 * For each of the remaining rows i, we introduce a div and a corresponding 826 * equality. In particular 827 * 828 * g_ii e_j = x_i - g_i(x') 829 * 830 * where each x'_k is replaced either by x_k (if g_kk = 1) or the 831 * corresponding div (if g_kk != 1). 832 * 833 * If there are any equalities not involving any div, then we 834 * first apply a variable compression on the variables x: 835 * 836 * x = C x'' x'' = C_2 x 837 * 838 * and perform the above parameter compression on A C instead of on A. 839 * The resulting compression is then of the form 840 * 841 * x'' = T(x') = x_0 + G x' 842 * 843 * and in constructing the new divs and the corresponding equalities, 844 * we have to replace each x'', i.e., the x'_k with (g_kk = 1), 845 * by the corresponding row from C_2. 846 */ 847static struct isl_basic_map *normalize_divs( 848 struct isl_basic_map *bmap, int *progress) 849{ 850 int i, j, k; 851 int total; 852 int div_eq; 853 struct isl_mat *B; 854 struct isl_vec *d; 855 struct isl_mat *T = NULL; 856 struct isl_mat *C = NULL; 857 struct isl_mat *C2 = NULL; 858 isl_int v; 859 int *pos; 860 int dropped, needed; 861 862 if (!bmap) 863 return NULL; 864 865 if (bmap->n_div == 0) 866 return bmap; 867 868 if (bmap->n_eq == 0) 869 return bmap; 870 871 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS)) 872 return bmap; 873 874 total = isl_space_dim(bmap->dim, isl_dim_all); 875 div_eq = n_pure_div_eq(bmap); 876 if (div_eq == 0) 877 return bmap; 878 879 if (div_eq < bmap->n_eq) { 880 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq, 881 bmap->n_eq - div_eq, 0, 1 + total); 882 C = isl_mat_variable_compression(B, &C2); 883 if (!C || !C2) 884 goto error; 885 if (C->n_col == 0) { 886 bmap = isl_basic_map_set_to_empty(bmap); 887 isl_mat_free(C); 888 isl_mat_free(C2); 889 goto done; 890 } 891 } 892 893 d = isl_vec_alloc(bmap->ctx, div_eq); 894 if (!d) 895 goto error; 896 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) { 897 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j])) 898 --j; 899 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]); 900 } 901 B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total); 902 903 if (C) { 904 B = isl_mat_product(B, C); 905 C = NULL; 906 } 907 908 T = isl_mat_parameter_compression(B, d); 909 if (!T) 910 goto error; 911 if (T->n_col == 0) { 912 bmap = isl_basic_map_set_to_empty(bmap); 913 isl_mat_free(C2); 914 isl_mat_free(T); 915 goto done; 916 } 917 isl_int_init(v); 918 for (i = 0; i < T->n_row - 1; ++i) { 919 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]); 920 if (isl_int_is_zero(v)) 921 continue; 922 isl_mat_col_submul(T, 0, v, 1 + i); 923 } 924 isl_int_clear(v); 925 pos = isl_alloc_array(bmap->ctx, int, T->n_row); 926 if (!pos) 927 goto error; 928 /* We have to be careful because dropping equalities may reorder them */ 929 dropped = 0; 930 for (j = bmap->n_div - 1; j >= 0; --j) { 931 for (i = 0; i < bmap->n_eq; ++i) 932 if (!isl_int_is_zero(bmap->eq[i][1 + total + j])) 933 break; 934 if (i < bmap->n_eq) { 935 bmap = isl_basic_map_drop_div(bmap, j); 936 isl_basic_map_drop_equality(bmap, i); 937 ++dropped; 938 } 939 } 940 pos[0] = 0; 941 needed = 0; 942 for (i = 1; i < T->n_row; ++i) { 943 if (isl_int_is_one(T->row[i][i])) 944 pos[i] = i; 945 else 946 needed++; 947 } 948 if (needed > dropped) { 949 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 950 needed, needed, 0); 951 if (!bmap) 952 goto error; 953 } 954 for (i = 1; i < T->n_row; ++i) { 955 if (isl_int_is_one(T->row[i][i])) 956 continue; 957 k = isl_basic_map_alloc_div(bmap); 958 pos[i] = 1 + total + k; 959 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div); 960 isl_int_set(bmap->div[k][0], T->row[i][i]); 961 if (C2) 962 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total); 963 else 964 isl_int_set_si(bmap->div[k][1 + i], 1); 965 for (j = 0; j < i; ++j) { 966 if (isl_int_is_zero(T->row[i][j])) 967 continue; 968 if (pos[j] < T->n_row && C2) 969 isl_seq_submul(bmap->div[k] + 1, T->row[i][j], 970 C2->row[pos[j]], 1 + total); 971 else 972 isl_int_neg(bmap->div[k][1 + pos[j]], 973 T->row[i][j]); 974 } 975 j = isl_basic_map_alloc_equality(bmap); 976 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div); 977 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]); 978 } 979 free(pos); 980 isl_mat_free(C2); 981 isl_mat_free(T); 982 983 if (progress) 984 *progress = 1; 985done: 986 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS); 987 988 return bmap; 989error: 990 isl_mat_free(C); 991 isl_mat_free(C2); 992 isl_mat_free(T); 993 return bmap; 994} 995 996static struct isl_basic_map *set_div_from_lower_bound( 997 struct isl_basic_map *bmap, int div, int ineq) 998{ 999 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); 1000 1001 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div); 1002 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]); 1003 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]); 1004 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1); 1005 isl_int_set_si(bmap->div[div][1 + total + div], 0); 1006 1007 return bmap; 1008} 1009 1010/* Check whether it is ok to define a div based on an inequality. 1011 * To avoid the introduction of circular definitions of divs, we 1012 * do not allow such a definition if the resulting expression would refer to 1013 * any other undefined divs or if any known div is defined in 1014 * terms of the unknown div. 1015 */ 1016static int ok_to_set_div_from_bound(struct isl_basic_map *bmap, 1017 int div, int ineq) 1018{ 1019 int j; 1020 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); 1021 1022 /* Not defined in terms of unknown divs */ 1023 for (j = 0; j < bmap->n_div; ++j) { 1024 if (div == j) 1025 continue; 1026 if (isl_int_is_zero(bmap->ineq[ineq][total + j])) 1027 continue; 1028 if (isl_int_is_zero(bmap->div[j][0])) 1029 return 0; 1030 } 1031 1032 /* No other div defined in terms of this one => avoid loops */ 1033 for (j = 0; j < bmap->n_div; ++j) { 1034 if (div == j) 1035 continue; 1036 if (isl_int_is_zero(bmap->div[j][0])) 1037 continue; 1038 if (!isl_int_is_zero(bmap->div[j][1 + total + div])) 1039 return 0; 1040 } 1041 1042 return 1; 1043} 1044 1045/* Would an expression for div "div" based on inequality "ineq" of "bmap" 1046 * be a better expression than the current one? 1047 * 1048 * If we do not have any expression yet, then any expression would be better. 1049 * Otherwise we check if the last variable involved in the inequality 1050 * (disregarding the div that it would define) is in an earlier position 1051 * than the last variable involved in the current div expression. 1052 */ 1053static int better_div_constraint(__isl_keep isl_basic_map *bmap, 1054 int div, int ineq) 1055{ 1056 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); 1057 int last_div; 1058 int last_ineq; 1059 1060 if (isl_int_is_zero(bmap->div[div][0])) 1061 return 1; 1062 1063 if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1, 1064 bmap->n_div - (div + 1)) >= 0) 1065 return 0; 1066 1067 last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div); 1068 last_div = isl_seq_last_non_zero(bmap->div[div] + 1, 1069 total + bmap->n_div); 1070 1071 return last_ineq < last_div; 1072} 1073 1074/* Given two constraints "k" and "l" that are opposite to each other, 1075 * except for the constant term, check if we can use them 1076 * to obtain an expression for one of the hitherto unknown divs or 1077 * a "better" expression for a div for which we already have an expression. 1078 * "sum" is the sum of the constant terms of the constraints. 1079 * If this sum is strictly smaller than the coefficient of one 1080 * of the divs, then this pair can be used define the div. 1081 * To avoid the introduction of circular definitions of divs, we 1082 * do not use the pair if the resulting expression would refer to 1083 * any other undefined divs or if any known div is defined in 1084 * terms of the unknown div. 1085 */ 1086static struct isl_basic_map *check_for_div_constraints( 1087 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress) 1088{ 1089 int i; 1090 unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all); 1091 1092 for (i = 0; i < bmap->n_div; ++i) { 1093 if (isl_int_is_zero(bmap->ineq[k][total + i])) 1094 continue; 1095 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i])) 1096 continue; 1097 if (!better_div_constraint(bmap, i, k)) 1098 continue; 1099 if (!ok_to_set_div_from_bound(bmap, i, k)) 1100 break; 1101 if (isl_int_is_pos(bmap->ineq[k][total + i])) 1102 bmap = set_div_from_lower_bound(bmap, i, k); 1103 else 1104 bmap = set_div_from_lower_bound(bmap, i, l); 1105 if (progress) 1106 *progress = 1; 1107 break; 1108 } 1109 return bmap; 1110} 1111 1112static struct isl_basic_map *remove_duplicate_constraints( 1113 struct isl_basic_map *bmap, int *progress, int detect_divs) 1114{ 1115 unsigned int size; 1116 isl_int ***index; 1117 int k, l, h; 1118 int bits; 1119 unsigned total = isl_basic_map_total_dim(bmap); 1120 isl_int sum; 1121 isl_ctx *ctx; 1122 1123 if (!bmap || bmap->n_ineq <= 1) 1124 return bmap; 1125 1126 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1); 1127 bits = ffs(size) - 1; 1128 ctx = isl_basic_map_get_ctx(bmap); 1129 index = isl_calloc_array(ctx, isl_int **, size); 1130 if (!index) 1131 return bmap; 1132 1133 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0]; 1134 for (k = 1; k < bmap->n_ineq; ++k) { 1135 h = hash_index(index, size, bits, bmap, k); 1136 if (!index[h]) { 1137 index[h] = &bmap->ineq[k]; 1138 continue; 1139 } 1140 if (progress) 1141 *progress = 1; 1142 l = index[h] - &bmap->ineq[0]; 1143 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0])) 1144 swap_inequality(bmap, k, l); 1145 isl_basic_map_drop_inequality(bmap, k); 1146 --k; 1147 } 1148 isl_int_init(sum); 1149 for (k = 0; k < bmap->n_ineq-1; ++k) { 1150 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); 1151 h = hash_index(index, size, bits, bmap, k); 1152 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total); 1153 if (!index[h]) 1154 continue; 1155 l = index[h] - &bmap->ineq[0]; 1156 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]); 1157 if (isl_int_is_pos(sum)) { 1158 if (detect_divs) 1159 bmap = check_for_div_constraints(bmap, k, l, 1160 sum, progress); 1161 continue; 1162 } 1163 if (isl_int_is_zero(sum)) { 1164 /* We need to break out of the loop after these 1165 * changes since the contents of the hash 1166 * will no longer be valid. 1167 * Plus, we probably we want to regauss first. 1168 */ 1169 if (progress) 1170 *progress = 1; 1171 isl_basic_map_drop_inequality(bmap, l); 1172 isl_basic_map_inequality_to_equality(bmap, k); 1173 } else 1174 bmap = isl_basic_map_set_to_empty(bmap); 1175 break; 1176 } 1177 isl_int_clear(sum); 1178 1179 free(index); 1180 return bmap; 1181} 1182 1183 1184/* Eliminate knowns divs from constraints where they appear with 1185 * a (positive or negative) unit coefficient. 1186 * 1187 * That is, replace 1188 * 1189 * floor(e/m) + f >= 0 1190 * 1191 * by 1192 * 1193 * e + m f >= 0 1194 * 1195 * and 1196 * 1197 * -floor(e/m) + f >= 0 1198 * 1199 * by 1200 * 1201 * -e + m f + m - 1 >= 0 1202 * 1203 * The first conversion is valid because floor(e/m) >= -f is equivalent 1204 * to e/m >= -f because -f is an integral expression. 1205 * The second conversion follows from the fact that 1206 * 1207 * -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m) 1208 * 1209 * 1210 * Note that one of the div constraints may have been eliminated 1211 * due to being redundant with respect to the constraint that is 1212 * being modified by this function. The modified constraint may 1213 * no longer imply this div constraint, so we add it back to make 1214 * sure we do not lose any information. 1215 * 1216 * We skip integral divs, i.e., those with denominator 1, as we would 1217 * risk eliminating the div from the div constraints. We do not need 1218 * to handle those divs here anyway since the div constraints will turn 1219 * out to form an equality and this equality can then be use to eliminate 1220 * the div from all constraints. 1221 */ 1222static __isl_give isl_basic_map *eliminate_unit_divs( 1223 __isl_take isl_basic_map *bmap, int *progress) 1224{ 1225 int i, j; 1226 isl_ctx *ctx; 1227 unsigned total; 1228 1229 if (!bmap) 1230 return NULL; 1231 1232 ctx = isl_basic_map_get_ctx(bmap); 1233 total = 1 + isl_space_dim(bmap->dim, isl_dim_all); 1234 1235 for (i = 0; i < bmap->n_div; ++i) { 1236 if (isl_int_is_zero(bmap->div[i][0])) 1237 continue; 1238 if (isl_int_is_one(bmap->div[i][0])) 1239 continue; 1240 for (j = 0; j < bmap->n_ineq; ++j) { 1241 int s; 1242 1243 if (!isl_int_is_one(bmap->ineq[j][total + i]) && 1244 !isl_int_is_negone(bmap->ineq[j][total + i])) 1245 continue; 1246 1247 *progress = 1; 1248 1249 s = isl_int_sgn(bmap->ineq[j][total + i]); 1250 isl_int_set_si(bmap->ineq[j][total + i], 0); 1251 if (s < 0) 1252 isl_seq_combine(bmap->ineq[j], 1253 ctx->negone, bmap->div[i] + 1, 1254 bmap->div[i][0], bmap->ineq[j], 1255 total + bmap->n_div); 1256 else 1257 isl_seq_combine(bmap->ineq[j], 1258 ctx->one, bmap->div[i] + 1, 1259 bmap->div[i][0], bmap->ineq[j], 1260 total + bmap->n_div); 1261 if (s < 0) { 1262 isl_int_add(bmap->ineq[j][0], 1263 bmap->ineq[j][0], bmap->div[i][0]); 1264 isl_int_sub_ui(bmap->ineq[j][0], 1265 bmap->ineq[j][0], 1); 1266 } 1267 1268 bmap = isl_basic_map_extend_constraints(bmap, 0, 1); 1269 if (isl_basic_map_add_div_constraint(bmap, i, s) < 0) 1270 return isl_basic_map_free(bmap); 1271 } 1272 } 1273 1274 return bmap; 1275} 1276 1277struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap) 1278{ 1279 int progress = 1; 1280 if (!bmap) 1281 return NULL; 1282 while (progress) { 1283 progress = 0; 1284 if (!bmap) 1285 break; 1286 if (isl_basic_map_plain_is_empty(bmap)) 1287 break; 1288 bmap = isl_basic_map_normalize_constraints(bmap); 1289 bmap = normalize_div_expressions(bmap); 1290 bmap = remove_duplicate_divs(bmap, &progress); 1291 bmap = eliminate_unit_divs(bmap, &progress); 1292 bmap = eliminate_divs_eq(bmap, &progress); 1293 bmap = eliminate_divs_ineq(bmap, &progress); 1294 bmap = isl_basic_map_gauss(bmap, &progress); 1295 /* requires equalities in normal form */ 1296 bmap = normalize_divs(bmap, &progress); 1297 bmap = remove_duplicate_constraints(bmap, &progress, 1); 1298 } 1299 return bmap; 1300} 1301 1302struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset) 1303{ 1304 return (struct isl_basic_set *) 1305 isl_basic_map_simplify((struct isl_basic_map *)bset); 1306} 1307 1308 1309int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap, 1310 isl_int *constraint, unsigned div) 1311{ 1312 unsigned pos; 1313 1314 if (!bmap) 1315 return -1; 1316 1317 pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div; 1318 1319 if (isl_int_eq(constraint[pos], bmap->div[div][0])) { 1320 int neg; 1321 isl_int_sub(bmap->div[div][1], 1322 bmap->div[div][1], bmap->div[div][0]); 1323 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1); 1324 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos); 1325 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1); 1326 isl_int_add(bmap->div[div][1], 1327 bmap->div[div][1], bmap->div[div][0]); 1328 if (!neg) 1329 return 0; 1330 if (isl_seq_first_non_zero(constraint+pos+1, 1331 bmap->n_div-div-1) != -1) 1332 return 0; 1333 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) { 1334 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos)) 1335 return 0; 1336 if (isl_seq_first_non_zero(constraint+pos+1, 1337 bmap->n_div-div-1) != -1) 1338 return 0; 1339 } else 1340 return 0; 1341 1342 return 1; 1343} 1344 1345int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset, 1346 isl_int *constraint, unsigned div) 1347{ 1348 return isl_basic_map_is_div_constraint(bset, constraint, div); 1349} 1350 1351 1352/* If the only constraints a div d=floor(f/m) 1353 * appears in are its two defining constraints 1354 * 1355 * f - m d >=0 1356 * -(f - (m - 1)) + m d >= 0 1357 * 1358 * then it can safely be removed. 1359 */ 1360static int div_is_redundant(struct isl_basic_map *bmap, int div) 1361{ 1362 int i; 1363 unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div; 1364 1365 for (i = 0; i < bmap->n_eq; ++i) 1366 if (!isl_int_is_zero(bmap->eq[i][pos])) 1367 return 0; 1368 1369 for (i = 0; i < bmap->n_ineq; ++i) { 1370 if (isl_int_is_zero(bmap->ineq[i][pos])) 1371 continue; 1372 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div)) 1373 return 0; 1374 } 1375 1376 for (i = 0; i < bmap->n_div; ++i) { 1377 if (isl_int_is_zero(bmap->div[i][0])) 1378 continue; 1379 if (!isl_int_is_zero(bmap->div[i][1+pos])) 1380 return 0; 1381 } 1382 1383 return 1; 1384} 1385 1386/* 1387 * Remove divs that don't occur in any of the constraints or other divs. 1388 * These can arise when dropping some of the variables in a quast 1389 * returned by piplib. 1390 */ 1391static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap) 1392{ 1393 int i; 1394 1395 if (!bmap) 1396 return NULL; 1397 1398 for (i = bmap->n_div-1; i >= 0; --i) { 1399 if (!div_is_redundant(bmap, i)) 1400 continue; 1401 bmap = isl_basic_map_drop_div(bmap, i); 1402 } 1403 return bmap; 1404} 1405 1406struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap) 1407{ 1408 bmap = remove_redundant_divs(bmap); 1409 if (!bmap) 1410 return NULL; 1411 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL); 1412 return bmap; 1413} 1414 1415struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset) 1416{ 1417 return (struct isl_basic_set *) 1418 isl_basic_map_finalize((struct isl_basic_map *)bset); 1419} 1420 1421struct isl_set *isl_set_finalize(struct isl_set *set) 1422{ 1423 int i; 1424 1425 if (!set) 1426 return NULL; 1427 for (i = 0; i < set->n; ++i) { 1428 set->p[i] = isl_basic_set_finalize(set->p[i]); 1429 if (!set->p[i]) 1430 goto error; 1431 } 1432 return set; 1433error: 1434 isl_set_free(set); 1435 return NULL; 1436} 1437 1438struct isl_map *isl_map_finalize(struct isl_map *map) 1439{ 1440 int i; 1441 1442 if (!map) 1443 return NULL; 1444 for (i = 0; i < map->n; ++i) { 1445 map->p[i] = isl_basic_map_finalize(map->p[i]); 1446 if (!map->p[i]) 1447 goto error; 1448 } 1449 ISL_F_CLR(map, ISL_MAP_NORMALIZED); 1450 return map; 1451error: 1452 isl_map_free(map); 1453 return NULL; 1454} 1455 1456 1457/* Remove definition of any div that is defined in terms of the given variable. 1458 * The div itself is not removed. Functions such as 1459 * eliminate_divs_ineq depend on the other divs remaining in place. 1460 */ 1461static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap, 1462 int pos) 1463{ 1464 int i; 1465 1466 if (!bmap) 1467 return NULL; 1468 1469 for (i = 0; i < bmap->n_div; ++i) { 1470 if (isl_int_is_zero(bmap->div[i][0])) 1471 continue; 1472 if (isl_int_is_zero(bmap->div[i][1+1+pos])) 1473 continue; 1474 isl_int_set_si(bmap->div[i][0], 0); 1475 } 1476 return bmap; 1477} 1478 1479/* Eliminate the specified variables from the constraints using 1480 * Fourier-Motzkin. The variables themselves are not removed. 1481 */ 1482struct isl_basic_map *isl_basic_map_eliminate_vars( 1483 struct isl_basic_map *bmap, unsigned pos, unsigned n) 1484{ 1485 int d; 1486 int i, j, k; 1487 unsigned total; 1488 int need_gauss = 0; 1489 1490 if (n == 0) 1491 return bmap; 1492 if (!bmap) 1493 return NULL; 1494 total = isl_basic_map_total_dim(bmap); 1495 1496 bmap = isl_basic_map_cow(bmap); 1497 for (d = pos + n - 1; d >= 0 && d >= pos; --d) 1498 bmap = remove_dependent_vars(bmap, d); 1499 if (!bmap) 1500 return NULL; 1501 1502 for (d = pos + n - 1; 1503 d >= 0 && d >= total - bmap->n_div && d >= pos; --d) 1504 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total); 1505 for (d = pos + n - 1; d >= 0 && d >= pos; --d) { 1506 int n_lower, n_upper; 1507 if (!bmap) 1508 return NULL; 1509 for (i = 0; i < bmap->n_eq; ++i) { 1510 if (isl_int_is_zero(bmap->eq[i][1+d])) 1511 continue; 1512 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL); 1513 isl_basic_map_drop_equality(bmap, i); 1514 need_gauss = 1; 1515 break; 1516 } 1517 if (i < bmap->n_eq) 1518 continue; 1519 n_lower = 0; 1520 n_upper = 0; 1521 for (i = 0; i < bmap->n_ineq; ++i) { 1522 if (isl_int_is_pos(bmap->ineq[i][1+d])) 1523 n_lower++; 1524 else if (isl_int_is_neg(bmap->ineq[i][1+d])) 1525 n_upper++; 1526 } 1527 bmap = isl_basic_map_extend_constraints(bmap, 1528 0, n_lower * n_upper); 1529 if (!bmap) 1530 goto error; 1531 for (i = bmap->n_ineq - 1; i >= 0; --i) { 1532 int last; 1533 if (isl_int_is_zero(bmap->ineq[i][1+d])) 1534 continue; 1535 last = -1; 1536 for (j = 0; j < i; ++j) { 1537 if (isl_int_is_zero(bmap->ineq[j][1+d])) 1538 continue; 1539 last = j; 1540 if (isl_int_sgn(bmap->ineq[i][1+d]) == 1541 isl_int_sgn(bmap->ineq[j][1+d])) 1542 continue; 1543 k = isl_basic_map_alloc_inequality(bmap); 1544 if (k < 0) 1545 goto error; 1546 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i], 1547 1+total); 1548 isl_seq_elim(bmap->ineq[k], bmap->ineq[j], 1549 1+d, 1+total, NULL); 1550 } 1551 isl_basic_map_drop_inequality(bmap, i); 1552 i = last + 1; 1553 } 1554 if (n_lower > 0 && n_upper > 0) { 1555 bmap = isl_basic_map_normalize_constraints(bmap); 1556 bmap = remove_duplicate_constraints(bmap, NULL, 0); 1557 bmap = isl_basic_map_gauss(bmap, NULL); 1558 bmap = isl_basic_map_remove_redundancies(bmap); 1559 need_gauss = 0; 1560 if (!bmap) 1561 goto error; 1562 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) 1563 break; 1564 } 1565 } 1566 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED); 1567 if (need_gauss) 1568 bmap = isl_basic_map_gauss(bmap, NULL); 1569 return bmap; 1570error: 1571 isl_basic_map_free(bmap); 1572 return NULL; 1573} 1574 1575struct isl_basic_set *isl_basic_set_eliminate_vars( 1576 struct isl_basic_set *bset, unsigned pos, unsigned n) 1577{ 1578 return (struct isl_basic_set *)isl_basic_map_eliminate_vars( 1579 (struct isl_basic_map *)bset, pos, n); 1580} 1581 1582/* Eliminate the specified n dimensions starting at first from the 1583 * constraints, without removing the dimensions from the space. 1584 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin. 1585 * Otherwise, they are projected out and the original space is restored. 1586 */ 1587__isl_give isl_basic_map *isl_basic_map_eliminate( 1588 __isl_take isl_basic_map *bmap, 1589 enum isl_dim_type type, unsigned first, unsigned n) 1590{ 1591 isl_space *space; 1592 1593 if (!bmap) 1594 return NULL; 1595 if (n == 0) 1596 return bmap; 1597 1598 if (first + n > isl_basic_map_dim(bmap, type) || first + n < first) 1599 isl_die(bmap->ctx, isl_error_invalid, 1600 "index out of bounds", goto error); 1601 1602 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) { 1603 first += isl_basic_map_offset(bmap, type) - 1; 1604 bmap = isl_basic_map_eliminate_vars(bmap, first, n); 1605 return isl_basic_map_finalize(bmap); 1606 } 1607 1608 space = isl_basic_map_get_space(bmap); 1609 bmap = isl_basic_map_project_out(bmap, type, first, n); 1610 bmap = isl_basic_map_insert_dims(bmap, type, first, n); 1611 bmap = isl_basic_map_reset_space(bmap, space); 1612 return bmap; 1613error: 1614 isl_basic_map_free(bmap); 1615 return NULL; 1616} 1617 1618__isl_give isl_basic_set *isl_basic_set_eliminate( 1619 __isl_take isl_basic_set *bset, 1620 enum isl_dim_type type, unsigned first, unsigned n) 1621{ 1622 return isl_basic_map_eliminate(bset, type, first, n); 1623} 1624 1625/* Don't assume equalities are in order, because align_divs 1626 * may have changed the order of the divs. 1627 */ 1628static void compute_elimination_index(struct isl_basic_map *bmap, int *elim) 1629{ 1630 int d, i; 1631 unsigned total; 1632 1633 total = isl_space_dim(bmap->dim, isl_dim_all); 1634 for (d = 0; d < total; ++d) 1635 elim[d] = -1; 1636 for (i = 0; i < bmap->n_eq; ++i) { 1637 for (d = total - 1; d >= 0; --d) { 1638 if (isl_int_is_zero(bmap->eq[i][1+d])) 1639 continue; 1640 elim[d] = i; 1641 break; 1642 } 1643 } 1644} 1645 1646static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim) 1647{ 1648 compute_elimination_index((struct isl_basic_map *)bset, elim); 1649} 1650 1651static int reduced_using_equalities(isl_int *dst, isl_int *src, 1652 struct isl_basic_map *bmap, int *elim) 1653{ 1654 int d; 1655 int copied = 0; 1656 unsigned total; 1657 1658 total = isl_space_dim(bmap->dim, isl_dim_all); 1659 for (d = total - 1; d >= 0; --d) { 1660 if (isl_int_is_zero(src[1+d])) 1661 continue; 1662 if (elim[d] == -1) 1663 continue; 1664 if (!copied) { 1665 isl_seq_cpy(dst, src, 1 + total); 1666 copied = 1; 1667 } 1668 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL); 1669 } 1670 return copied; 1671} 1672 1673static int set_reduced_using_equalities(isl_int *dst, isl_int *src, 1674 struct isl_basic_set *bset, int *elim) 1675{ 1676 return reduced_using_equalities(dst, src, 1677 (struct isl_basic_map *)bset, elim); 1678} 1679 1680static struct isl_basic_set *isl_basic_set_reduce_using_equalities( 1681 struct isl_basic_set *bset, struct isl_basic_set *context) 1682{ 1683 int i; 1684 int *elim; 1685 1686 if (!bset || !context) 1687 goto error; 1688 1689 if (context->n_eq == 0) { 1690 isl_basic_set_free(context); 1691 return bset; 1692 } 1693 1694 bset = isl_basic_set_cow(bset); 1695 if (!bset) 1696 goto error; 1697 1698 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset)); 1699 if (!elim) 1700 goto error; 1701 set_compute_elimination_index(context, elim); 1702 for (i = 0; i < bset->n_eq; ++i) 1703 set_reduced_using_equalities(bset->eq[i], bset->eq[i], 1704 context, elim); 1705 for (i = 0; i < bset->n_ineq; ++i) 1706 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i], 1707 context, elim); 1708 isl_basic_set_free(context); 1709 free(elim); 1710 bset = isl_basic_set_simplify(bset); 1711 bset = isl_basic_set_finalize(bset); 1712 return bset; 1713error: 1714 isl_basic_set_free(bset); 1715 isl_basic_set_free(context); 1716 return NULL; 1717} 1718 1719static struct isl_basic_set *remove_shifted_constraints( 1720 struct isl_basic_set *bset, struct isl_basic_set *context) 1721{ 1722 unsigned int size; 1723 isl_int ***index; 1724 int bits; 1725 int k, h, l; 1726 isl_ctx *ctx; 1727 1728 if (!bset) 1729 return NULL; 1730 1731 size = round_up(4 * (context->n_ineq+1) / 3 - 1); 1732 bits = ffs(size) - 1; 1733 ctx = isl_basic_set_get_ctx(bset); 1734 index = isl_calloc_array(ctx, isl_int **, size); 1735 if (!index) 1736 return bset; 1737 1738 for (k = 0; k < context->n_ineq; ++k) { 1739 h = set_hash_index(index, size, bits, context, k); 1740 index[h] = &context->ineq[k]; 1741 } 1742 for (k = 0; k < bset->n_ineq; ++k) { 1743 h = set_hash_index(index, size, bits, bset, k); 1744 if (!index[h]) 1745 continue; 1746 l = index[h] - &context->ineq[0]; 1747 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0])) 1748 continue; 1749 bset = isl_basic_set_cow(bset); 1750 if (!bset) 1751 goto error; 1752 isl_basic_set_drop_inequality(bset, k); 1753 --k; 1754 } 1755 free(index); 1756 return bset; 1757error: 1758 free(index); 1759 return bset; 1760} 1761 1762/* Does the (linear part of a) constraint "c" involve any of the "len" 1763 * "relevant" dimensions? 1764 */ 1765static int is_related(isl_int *c, int len, int *relevant) 1766{ 1767 int i; 1768 1769 for (i = 0; i < len; ++i) { 1770 if (!relevant[i]) 1771 continue; 1772 if (!isl_int_is_zero(c[i])) 1773 return 1; 1774 } 1775 1776 return 0; 1777} 1778 1779/* Drop constraints from "bset" that do not involve any of 1780 * the dimensions marked "relevant". 1781 */ 1782static __isl_give isl_basic_set *drop_unrelated_constraints( 1783 __isl_take isl_basic_set *bset, int *relevant) 1784{ 1785 int i, dim; 1786 1787 dim = isl_basic_set_dim(bset, isl_dim_set); 1788 for (i = 0; i < dim; ++i) 1789 if (!relevant[i]) 1790 break; 1791 if (i >= dim) 1792 return bset; 1793 1794 for (i = bset->n_eq - 1; i >= 0; --i) 1795 if (!is_related(bset->eq[i] + 1, dim, relevant)) 1796 isl_basic_set_drop_equality(bset, i); 1797 1798 for (i = bset->n_ineq - 1; i >= 0; --i) 1799 if (!is_related(bset->ineq[i] + 1, dim, relevant)) 1800 isl_basic_set_drop_inequality(bset, i); 1801 1802 return bset; 1803} 1804 1805/* Update the groups in "group" based on the (linear part of a) constraint "c". 1806 * 1807 * In particular, for any variable involved in the constraint, 1808 * find the actual group id from before and replace the group 1809 * of the corresponding variable by the minimal group of all 1810 * the variables involved in the constraint considered so far 1811 * (if this minimum is smaller) or replace the minimum by this group 1812 * (if the minimum is larger). 1813 * 1814 * At the end, all the variables in "c" will (indirectly) point 1815 * to the minimal of the groups that they referred to originally. 1816 */ 1817static void update_groups(int dim, int *group, isl_int *c) 1818{ 1819 int j; 1820 int min = dim; 1821 1822 for (j = 0; j < dim; ++j) { 1823 if (isl_int_is_zero(c[j])) 1824 continue; 1825 while (group[j] >= 0 && group[group[j]] != group[j]) 1826 group[j] = group[group[j]]; 1827 if (group[j] == min) 1828 continue; 1829 if (group[j] < min) { 1830 if (min >= 0 && min < dim) 1831 group[min] = group[j]; 1832 min = group[j]; 1833 } else 1834 group[group[j]] = min; 1835 } 1836} 1837 1838/* Drop constraints from "context" that are irrelevant for computing 1839 * the gist of "bset". 1840 * 1841 * In particular, drop constraints in variables that are not related 1842 * to any of the variables involved in the constraints of "bset" 1843 * in the sense that there is no sequence of constraints that connects them. 1844 * 1845 * We construct groups of variables that collect variables that 1846 * (indirectly) appear in some common constraint of "context". 1847 * Each group is identified by the first variable in the group, 1848 * except for the special group of variables that appear in "bset" 1849 * (or are related to those variables), which is identified by -1. 1850 * If group[i] is equal to i (or -1), then the group of i is i (or -1), 1851 * otherwise the group of i is the group of group[i]. 1852 * 1853 * We first initialize the -1 group with the variables that appear in "bset". 1854 * Then we initialize groups for the remaining variables. 1855 * Then we iterate over the constraints of "context" and update the 1856 * group of the variables in the constraint by the smallest group. 1857 * Finally, we resolve indirect references to groups by running over 1858 * the variables. 1859 * 1860 * After computing the groups, we drop constraints that do not involve 1861 * any variables in the -1 group. 1862 */ 1863static __isl_give isl_basic_set *drop_irrelevant_constraints( 1864 __isl_take isl_basic_set *context, __isl_keep isl_basic_set *bset) 1865{ 1866 isl_ctx *ctx; 1867 int *group; 1868 int dim; 1869 int i, j; 1870 int last; 1871 1872 if (!context || !bset) 1873 return isl_basic_set_free(context); 1874 1875 dim = isl_basic_set_dim(bset, isl_dim_set); 1876 ctx = isl_basic_set_get_ctx(bset); 1877 group = isl_calloc_array(ctx, int, dim); 1878 1879 if (!group) 1880 goto error; 1881 1882 for (i = 0; i < dim; ++i) { 1883 for (j = 0; j < bset->n_eq; ++j) 1884 if (!isl_int_is_zero(bset->eq[j][1 + i])) 1885 break; 1886 if (j < bset->n_eq) { 1887 group[i] = -1; 1888 continue; 1889 } 1890 for (j = 0; j < bset->n_ineq; ++j) 1891 if (!isl_int_is_zero(bset->ineq[j][1 + i])) 1892 break; 1893 if (j < bset->n_ineq) 1894 group[i] = -1; 1895 } 1896 1897 last = -1; 1898 for (i = 0; i < dim; ++i) 1899 if (group[i] >= 0) 1900 last = group[i] = i; 1901 if (last < 0) { 1902 free(group); 1903 return context; 1904 } 1905 1906 for (i = 0; i < context->n_eq; ++i) 1907 update_groups(dim, group, context->eq[i] + 1); 1908 for (i = 0; i < context->n_ineq; ++i) 1909 update_groups(dim, group, context->ineq[i] + 1); 1910 1911 for (i = 0; i < dim; ++i) 1912 if (group[i] >= 0) 1913 group[i] = group[group[i]]; 1914 1915 for (i = 0; i < dim; ++i) 1916 group[i] = group[i] == -1; 1917 1918 context = drop_unrelated_constraints(context, group); 1919 1920 free(group); 1921 return context; 1922error: 1923 free(group); 1924 return isl_basic_set_free(context); 1925} 1926 1927/* Remove all information from bset that is redundant in the context 1928 * of context. Both bset and context are assumed to be full-dimensional. 1929 * 1930 * We first remove the inequalities from "bset" 1931 * that are obviously redundant with respect to some inequality in "context". 1932 * Then we remove those constraints from "context" that have become 1933 * irrelevant for computing the gist of "bset". 1934 * Note that this removal of constraints cannot be replaced by 1935 * a factorization because factors in "bset" may still be connected 1936 * to each other through constraints in "context". 1937 * 1938 * If there are any inequalities left, we construct a tableau for 1939 * the context and then add the inequalities of "bset". 1940 * Before adding these inequalities, we freeze all constraints such that 1941 * they won't be considered redundant in terms of the constraints of "bset". 1942 * Then we detect all redundant constraints (among the 1943 * constraints that weren't frozen), first by checking for redundancy in the 1944 * the tableau and then by checking if replacing a constraint by its negation 1945 * would lead to an empty set. This last step is fairly expensive 1946 * and could be optimized by more reuse of the tableau. 1947 * Finally, we update bset according to the results. 1948 */ 1949static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset, 1950 __isl_take isl_basic_set *context) 1951{ 1952 int i, k; 1953 isl_basic_set *combined = NULL; 1954 struct isl_tab *tab = NULL; 1955 unsigned context_ineq; 1956 unsigned total; 1957 1958 if (!bset || !context) 1959 goto error; 1960 1961 if (isl_basic_set_is_universe(bset)) { 1962 isl_basic_set_free(context); 1963 return bset; 1964 } 1965 1966 if (isl_basic_set_is_universe(context)) { 1967 isl_basic_set_free(context); 1968 return bset; 1969 } 1970 1971 bset = remove_shifted_constraints(bset, context); 1972 if (!bset) 1973 goto error; 1974 if (bset->n_ineq == 0) 1975 goto done; 1976 1977 context = drop_irrelevant_constraints(context, bset); 1978 if (!context) 1979 goto error; 1980 if (isl_basic_set_is_universe(context)) { 1981 isl_basic_set_free(context); 1982 return bset; 1983 } 1984 1985 context_ineq = context->n_ineq; 1986 combined = isl_basic_set_cow(isl_basic_set_copy(context)); 1987 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq); 1988 tab = isl_tab_from_basic_set(combined, 0); 1989 for (i = 0; i < context_ineq; ++i) 1990 if (isl_tab_freeze_constraint(tab, i) < 0) 1991 goto error; 1992 tab = isl_tab_extend(tab, bset->n_ineq); 1993 for (i = 0; i < bset->n_ineq; ++i) 1994 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0) 1995 goto error; 1996 bset = isl_basic_set_add_constraints(combined, bset, 0); 1997 combined = NULL; 1998 if (!bset) 1999 goto error; 2000 if (isl_tab_detect_redundant(tab) < 0) 2001 goto error; 2002 total = isl_basic_set_total_dim(bset); 2003 for (i = context_ineq; i < bset->n_ineq; ++i) { 2004 int is_empty; 2005 if (tab->con[i].is_redundant) 2006 continue; 2007 tab->con[i].is_redundant = 1; 2008 combined = isl_basic_set_dup(bset); 2009 combined = isl_basic_set_update_from_tab(combined, tab); 2010 combined = isl_basic_set_extend_constraints(combined, 0, 1); 2011 k = isl_basic_set_alloc_inequality(combined); 2012 if (k < 0) 2013 goto error; 2014 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total); 2015 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1); 2016 is_empty = isl_basic_set_is_empty(combined); 2017 if (is_empty < 0) 2018 goto error; 2019 isl_basic_set_free(combined); 2020 combined = NULL; 2021 if (!is_empty) 2022 tab->con[i].is_redundant = 0; 2023 } 2024 for (i = 0; i < context_ineq; ++i) 2025 tab->con[i].is_redundant = 1; 2026 bset = isl_basic_set_update_from_tab(bset, tab); 2027 if (bset) { 2028 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT); 2029 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT); 2030 } 2031 2032 isl_tab_free(tab); 2033done: 2034 bset = isl_basic_set_simplify(bset); 2035 bset = isl_basic_set_finalize(bset); 2036 isl_basic_set_free(context); 2037 return bset; 2038error: 2039 isl_tab_free(tab); 2040 isl_basic_set_free(combined); 2041 isl_basic_set_free(context); 2042 isl_basic_set_free(bset); 2043 return NULL; 2044} 2045 2046/* Remove all information from bset that is redundant in the context 2047 * of context. In particular, equalities that are linear combinations 2048 * of those in context are removed. Then the inequalities that are 2049 * redundant in the context of the equalities and inequalities of 2050 * context are removed. 2051 * 2052 * First of all, we drop those constraints from "context" 2053 * that are irrelevant for computing the gist of "bset". 2054 * Alternatively, we could factorize the intersection of "context" and "bset". 2055 * 2056 * We first compute the integer affine hull of the intersection, 2057 * compute the gist inside this affine hull and then add back 2058 * those equalities that are not implied by the context. 2059 * 2060 * If two constraints are mutually redundant, then uset_gist_full 2061 * will remove the second of those constraints. We therefore first 2062 * sort the constraints so that constraints not involving existentially 2063 * quantified variables are given precedence over those that do. 2064 * We have to perform this sorting before the variable compression, 2065 * because that may effect the order of the variables. 2066 */ 2067static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset, 2068 __isl_take isl_basic_set *context) 2069{ 2070 isl_mat *eq; 2071 isl_mat *T, *T2; 2072 isl_basic_set *aff; 2073 isl_basic_set *aff_context; 2074 unsigned total; 2075 2076 if (!bset || !context) 2077 goto error; 2078 2079 context = drop_irrelevant_constraints(context, bset); 2080 2081 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context)); 2082 if (isl_basic_set_plain_is_empty(bset)) { 2083 isl_basic_set_free(context); 2084 return bset; 2085 } 2086 bset = isl_basic_set_sort_constraints(bset); 2087 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset)); 2088 if (!aff) 2089 goto error; 2090 if (isl_basic_set_plain_is_empty(aff)) { 2091 isl_basic_set_free(aff); 2092 isl_basic_set_free(context); 2093 return bset; 2094 } 2095 if (aff->n_eq == 0) { 2096 isl_basic_set_free(aff); 2097 return uset_gist_full(bset, context); 2098 } 2099 total = isl_basic_set_total_dim(bset); 2100 eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total); 2101 eq = isl_mat_cow(eq); 2102 T = isl_mat_variable_compression(eq, &T2); 2103 if (T && T->n_col == 0) { 2104 isl_mat_free(T); 2105 isl_mat_free(T2); 2106 isl_basic_set_free(context); 2107 isl_basic_set_free(aff); 2108 return isl_basic_set_set_to_empty(bset); 2109 } 2110 2111 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context)); 2112 2113 bset = isl_basic_set_preimage(bset, isl_mat_copy(T)); 2114 context = isl_basic_set_preimage(context, T); 2115 2116 bset = uset_gist_full(bset, context); 2117 bset = isl_basic_set_preimage(bset, T2); 2118 bset = isl_basic_set_intersect(bset, aff); 2119 bset = isl_basic_set_reduce_using_equalities(bset, aff_context); 2120 2121 if (bset) { 2122 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT); 2123 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT); 2124 } 2125 2126 return bset; 2127error: 2128 isl_basic_set_free(bset); 2129 isl_basic_set_free(context); 2130 return NULL; 2131} 2132 2133/* Normalize the divs in "bmap" in the context of the equalities in "context". 2134 * We simply add the equalities in context to bmap and then do a regular 2135 * div normalizations. Better results can be obtained by normalizing 2136 * only the divs in bmap than do not also appear in context. 2137 * We need to be careful to reduce the divs using the equalities 2138 * so that later calls to isl_basic_map_overlying_set wouldn't introduce 2139 * spurious constraints. 2140 */ 2141static struct isl_basic_map *normalize_divs_in_context( 2142 struct isl_basic_map *bmap, struct isl_basic_map *context) 2143{ 2144 int i; 2145 unsigned total_context; 2146 int div_eq; 2147 2148 div_eq = n_pure_div_eq(bmap); 2149 if (div_eq == 0) 2150 return bmap; 2151 2152 if (context->n_div > 0) 2153 bmap = isl_basic_map_align_divs(bmap, context); 2154 2155 total_context = isl_basic_map_total_dim(context); 2156 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0); 2157 for (i = 0; i < context->n_eq; ++i) { 2158 int k; 2159 k = isl_basic_map_alloc_equality(bmap); 2160 if (k < 0) 2161 return isl_basic_map_free(bmap); 2162 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context); 2163 isl_seq_clr(bmap->eq[k] + 1 + total_context, 2164 isl_basic_map_total_dim(bmap) - total_context); 2165 } 2166 bmap = isl_basic_map_gauss(bmap, NULL); 2167 bmap = normalize_divs(bmap, NULL); 2168 bmap = isl_basic_map_gauss(bmap, NULL); 2169 return bmap; 2170} 2171 2172struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap, 2173 struct isl_basic_map *context) 2174{ 2175 struct isl_basic_set *bset; 2176 2177 if (!bmap || !context) 2178 goto error; 2179 2180 if (isl_basic_map_is_universe(bmap)) { 2181 isl_basic_map_free(context); 2182 return bmap; 2183 } 2184 if (isl_basic_map_plain_is_empty(context)) { 2185 isl_basic_map_free(bmap); 2186 return context; 2187 } 2188 if (isl_basic_map_plain_is_empty(bmap)) { 2189 isl_basic_map_free(context); 2190 return bmap; 2191 } 2192 2193 bmap = isl_basic_map_remove_redundancies(bmap); 2194 context = isl_basic_map_remove_redundancies(context); 2195 if (!context) 2196 goto error; 2197 2198 if (context->n_eq) 2199 bmap = normalize_divs_in_context(bmap, context); 2200 2201 context = isl_basic_map_align_divs(context, bmap); 2202 bmap = isl_basic_map_align_divs(bmap, context); 2203 2204 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)), 2205 isl_basic_map_underlying_set(context)); 2206 2207 return isl_basic_map_overlying_set(bset, bmap); 2208error: 2209 isl_basic_map_free(bmap); 2210 isl_basic_map_free(context); 2211 return NULL; 2212} 2213 2214/* 2215 * Assumes context has no implicit divs. 2216 */ 2217__isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map, 2218 __isl_take isl_basic_map *context) 2219{ 2220 int i; 2221 2222 if (!map || !context) 2223 goto error;; 2224 2225 if (isl_basic_map_plain_is_empty(context)) { 2226 isl_map_free(map); 2227 return isl_map_from_basic_map(context); 2228 } 2229 2230 context = isl_basic_map_remove_redundancies(context); 2231 map = isl_map_cow(map); 2232 if (!map || !context) 2233 goto error;; 2234 isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error); 2235 map = isl_map_compute_divs(map); 2236 if (!map) 2237 goto error; 2238 for (i = map->n - 1; i >= 0; --i) { 2239 map->p[i] = isl_basic_map_gist(map->p[i], 2240 isl_basic_map_copy(context)); 2241 if (!map->p[i]) 2242 goto error; 2243 if (isl_basic_map_plain_is_empty(map->p[i])) { 2244 isl_basic_map_free(map->p[i]); 2245 if (i != map->n - 1) 2246 map->p[i] = map->p[map->n - 1]; 2247 map->n--; 2248 } 2249 } 2250 isl_basic_map_free(context); 2251 ISL_F_CLR(map, ISL_MAP_NORMALIZED); 2252 return map; 2253error: 2254 isl_map_free(map); 2255 isl_basic_map_free(context); 2256 return NULL; 2257} 2258 2259/* Return a map that has the same intersection with "context" as "map" 2260 * and that as "simple" as possible. 2261 * 2262 * If "map" is already the universe, then we cannot make it any simpler. 2263 * Similarly, if "context" is the universe, then we cannot exploit it 2264 * to simplify "map" 2265 * If "map" and "context" are identical to each other, then we can 2266 * return the corresponding universe. 2267 * 2268 * If none of these cases apply, we have to work a bit harder. 2269 */ 2270static __isl_give isl_map *map_gist(__isl_take isl_map *map, 2271 __isl_take isl_map *context) 2272{ 2273 int equal; 2274 int is_universe; 2275 2276 is_universe = isl_map_plain_is_universe(map); 2277 if (is_universe >= 0 && !is_universe) 2278 is_universe = isl_map_plain_is_universe(context); 2279 if (is_universe < 0) 2280 goto error; 2281 if (is_universe) { 2282 isl_map_free(context); 2283 return map; 2284 } 2285 2286 equal = isl_map_plain_is_equal(map, context); 2287 if (equal < 0) 2288 goto error; 2289 if (equal) { 2290 isl_map *res = isl_map_universe(isl_map_get_space(map)); 2291 isl_map_free(map); 2292 isl_map_free(context); 2293 return res; 2294 } 2295 2296 context = isl_map_compute_divs(context); 2297 return isl_map_gist_basic_map(map, isl_map_simple_hull(context)); 2298error: 2299 isl_map_free(map); 2300 isl_map_free(context); 2301 return NULL; 2302} 2303 2304__isl_give isl_map *isl_map_gist(__isl_take isl_map *map, 2305 __isl_take isl_map *context) 2306{ 2307 return isl_map_align_params_map_map_and(map, context, &map_gist); 2308} 2309 2310struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset, 2311 struct isl_basic_set *context) 2312{ 2313 return (struct isl_basic_set *)isl_basic_map_gist( 2314 (struct isl_basic_map *)bset, (struct isl_basic_map *)context); 2315} 2316 2317__isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set, 2318 __isl_take isl_basic_set *context) 2319{ 2320 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set, 2321 (struct isl_basic_map *)context); 2322} 2323 2324__isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set, 2325 __isl_take isl_basic_set *context) 2326{ 2327 isl_space *space = isl_set_get_space(set); 2328 isl_basic_set *dom_context = isl_basic_set_universe(space); 2329 dom_context = isl_basic_set_intersect_params(dom_context, context); 2330 return isl_set_gist_basic_set(set, dom_context); 2331} 2332 2333__isl_give isl_set *isl_set_gist(__isl_take isl_set *set, 2334 __isl_take isl_set *context) 2335{ 2336 return (struct isl_set *)isl_map_gist((struct isl_map *)set, 2337 (struct isl_map *)context); 2338} 2339 2340__isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map, 2341 __isl_take isl_set *context) 2342{ 2343 isl_map *map_context = isl_map_universe(isl_map_get_space(map)); 2344 map_context = isl_map_intersect_domain(map_context, context); 2345 return isl_map_gist(map, map_context); 2346} 2347 2348__isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map, 2349 __isl_take isl_set *context) 2350{ 2351 isl_map *map_context = isl_map_universe(isl_map_get_space(map)); 2352 map_context = isl_map_intersect_range(map_context, context); 2353 return isl_map_gist(map, map_context); 2354} 2355 2356__isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map, 2357 __isl_take isl_set *context) 2358{ 2359 isl_map *map_context = isl_map_universe(isl_map_get_space(map)); 2360 map_context = isl_map_intersect_params(map_context, context); 2361 return isl_map_gist(map, map_context); 2362} 2363 2364__isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set, 2365 __isl_take isl_set *context) 2366{ 2367 return isl_map_gist_params(set, context); 2368} 2369 2370/* Quick check to see if two basic maps are disjoint. 2371 * In particular, we reduce the equalities and inequalities of 2372 * one basic map in the context of the equalities of the other 2373 * basic map and check if we get a contradiction. 2374 */ 2375int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1, 2376 __isl_keep isl_basic_map *bmap2) 2377{ 2378 struct isl_vec *v = NULL; 2379 int *elim = NULL; 2380 unsigned total; 2381 int i; 2382 2383 if (!bmap1 || !bmap2) 2384 return -1; 2385 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), 2386 return -1); 2387 if (bmap1->n_div || bmap2->n_div) 2388 return 0; 2389 if (!bmap1->n_eq && !bmap2->n_eq) 2390 return 0; 2391 2392 total = isl_space_dim(bmap1->dim, isl_dim_all); 2393 if (total == 0) 2394 return 0; 2395 v = isl_vec_alloc(bmap1->ctx, 1 + total); 2396 if (!v) 2397 goto error; 2398 elim = isl_alloc_array(bmap1->ctx, int, total); 2399 if (!elim) 2400 goto error; 2401 compute_elimination_index(bmap1, elim); 2402 for (i = 0; i < bmap2->n_eq; ++i) { 2403 int reduced; 2404 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i], 2405 bmap1, elim); 2406 if (reduced && !isl_int_is_zero(v->block.data[0]) && 2407 isl_seq_first_non_zero(v->block.data + 1, total) == -1) 2408 goto disjoint; 2409 } 2410 for (i = 0; i < bmap2->n_ineq; ++i) { 2411 int reduced; 2412 reduced = reduced_using_equalities(v->block.data, 2413 bmap2->ineq[i], bmap1, elim); 2414 if (reduced && isl_int_is_neg(v->block.data[0]) && 2415 isl_seq_first_non_zero(v->block.data + 1, total) == -1) 2416 goto disjoint; 2417 } 2418 compute_elimination_index(bmap2, elim); 2419 for (i = 0; i < bmap1->n_ineq; ++i) { 2420 int reduced; 2421 reduced = reduced_using_equalities(v->block.data, 2422 bmap1->ineq[i], bmap2, elim); 2423 if (reduced && isl_int_is_neg(v->block.data[0]) && 2424 isl_seq_first_non_zero(v->block.data + 1, total) == -1) 2425 goto disjoint; 2426 } 2427 isl_vec_free(v); 2428 free(elim); 2429 return 0; 2430disjoint: 2431 isl_vec_free(v); 2432 free(elim); 2433 return 1; 2434error: 2435 isl_vec_free(v); 2436 free(elim); 2437 return -1; 2438} 2439 2440int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1, 2441 __isl_keep isl_basic_set *bset2) 2442{ 2443 return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1, 2444 (struct isl_basic_map *)bset2); 2445} 2446 2447/* Are "map1" and "map2" obviously disjoint? 2448 * 2449 * If they have different parameters, then we skip any further tests. 2450 * In particular, the outcome of the subsequent calls to 2451 * isl_space_tuple_match may be affected by the different parameters 2452 * in nested spaces. 2453 * 2454 * If one of them is empty or if they live in different spaces (assuming 2455 * they have the same parameters), then they are clearly disjoint. 2456 * 2457 * If they are obviously equal, but not obviously empty, then we will 2458 * not be able to detect if they are disjoint. 2459 * 2460 * Otherwise we check if each basic map in "map1" is obviously disjoint 2461 * from each basic map in "map2". 2462 */ 2463int isl_map_plain_is_disjoint(__isl_keep isl_map *map1, 2464 __isl_keep isl_map *map2) 2465{ 2466 int i, j; 2467 int disjoint; 2468 int intersect; 2469 int match; 2470 2471 if (!map1 || !map2) 2472 return -1; 2473 2474 disjoint = isl_map_plain_is_empty(map1); 2475 if (disjoint < 0 || disjoint) 2476 return disjoint; 2477 2478 disjoint = isl_map_plain_is_empty(map2); 2479 if (disjoint < 0 || disjoint) 2480 return disjoint; 2481 2482 match = isl_space_match(map1->dim, isl_dim_param, 2483 map2->dim, isl_dim_param); 2484 if (match < 0 || !match) 2485 return match < 0 ? -1 : 0; 2486 2487 match = isl_space_tuple_match(map1->dim, isl_dim_in, 2488 map2->dim, isl_dim_in); 2489 if (match < 0 || !match) 2490 return match < 0 ? -1 : 1; 2491 2492 match = isl_space_tuple_match(map1->dim, isl_dim_out, 2493 map2->dim, isl_dim_out); 2494 if (match < 0 || !match) 2495 return match < 0 ? -1 : 1; 2496 2497 intersect = isl_map_plain_is_equal(map1, map2); 2498 if (intersect < 0 || intersect) 2499 return intersect < 0 ? -1 : 0; 2500 2501 for (i = 0; i < map1->n; ++i) { 2502 for (j = 0; j < map2->n; ++j) { 2503 int d = isl_basic_map_plain_is_disjoint(map1->p[i], 2504 map2->p[j]); 2505 if (d != 1) 2506 return d; 2507 } 2508 } 2509 return 1; 2510} 2511 2512/* Are "map1" and "map2" disjoint? 2513 * 2514 * They are disjoint if they are "obviously disjoint" or if one of them 2515 * is empty. Otherwise, they are not disjoint if one of them is universal. 2516 * If none of these cases apply, we compute the intersection and see if 2517 * the result is empty. 2518 */ 2519int isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2) 2520{ 2521 int disjoint; 2522 int intersect; 2523 isl_map *test; 2524 2525 disjoint = isl_map_plain_is_disjoint(map1, map2); 2526 if (disjoint < 0 || disjoint) 2527 return disjoint; 2528 2529 disjoint = isl_map_is_empty(map1); 2530 if (disjoint < 0 || disjoint) 2531 return disjoint; 2532 2533 disjoint = isl_map_is_empty(map2); 2534 if (disjoint < 0 || disjoint) 2535 return disjoint; 2536 2537 intersect = isl_map_plain_is_universe(map1); 2538 if (intersect < 0 || intersect) 2539 return intersect < 0 ? -1 : 0; 2540 2541 intersect = isl_map_plain_is_universe(map2); 2542 if (intersect < 0 || intersect) 2543 return intersect < 0 ? -1 : 0; 2544 2545 test = isl_map_intersect(isl_map_copy(map1), isl_map_copy(map2)); 2546 disjoint = isl_map_is_empty(test); 2547 isl_map_free(test); 2548 2549 return disjoint; 2550} 2551 2552int isl_set_plain_is_disjoint(__isl_keep isl_set *set1, 2553 __isl_keep isl_set *set2) 2554{ 2555 return isl_map_plain_is_disjoint((struct isl_map *)set1, 2556 (struct isl_map *)set2); 2557} 2558 2559/* Are "set1" and "set2" disjoint? 2560 */ 2561int isl_set_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2) 2562{ 2563 return isl_map_is_disjoint(set1, set2); 2564} 2565 2566int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2) 2567{ 2568 return isl_set_plain_is_disjoint(set1, set2); 2569} 2570 2571/* Check if we can combine a given div with lower bound l and upper 2572 * bound u with some other div and if so return that other div. 2573 * Otherwise return -1. 2574 * 2575 * We first check that 2576 * - the bounds are opposites of each other (except for the constant 2577 * term) 2578 * - the bounds do not reference any other div 2579 * - no div is defined in terms of this div 2580 * 2581 * Let m be the size of the range allowed on the div by the bounds. 2582 * That is, the bounds are of the form 2583 * 2584 * e <= a <= e + m - 1 2585 * 2586 * with e some expression in the other variables. 2587 * We look for another div b such that no third div is defined in terms 2588 * of this second div b and such that in any constraint that contains 2589 * a (except for the given lower and upper bound), also contains b 2590 * with a coefficient that is m times that of b. 2591 * That is, all constraints (execpt for the lower and upper bound) 2592 * are of the form 2593 * 2594 * e + f (a + m b) >= 0 2595 * 2596 * If so, we return b so that "a + m b" can be replaced by 2597 * a single div "c = a + m b". 2598 */ 2599static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs, 2600 unsigned div, unsigned l, unsigned u) 2601{ 2602 int i, j; 2603 unsigned dim; 2604 int coalesce = -1; 2605 2606 if (bmap->n_div <= 1) 2607 return -1; 2608 dim = isl_space_dim(bmap->dim, isl_dim_all); 2609 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1) 2610 return -1; 2611 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1, 2612 bmap->n_div - div - 1) != -1) 2613 return -1; 2614 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1, 2615 dim + bmap->n_div)) 2616 return -1; 2617 2618 for (i = 0; i < bmap->n_div; ++i) { 2619 if (isl_int_is_zero(bmap->div[i][0])) 2620 continue; 2621 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div])) 2622 return -1; 2623 } 2624 2625 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]); 2626 if (isl_int_is_neg(bmap->ineq[l][0])) { 2627 isl_int_sub(bmap->ineq[l][0], 2628 bmap->ineq[l][0], bmap->ineq[u][0]); 2629 bmap = isl_basic_map_copy(bmap); 2630 bmap = isl_basic_map_set_to_empty(bmap); 2631 isl_basic_map_free(bmap); 2632 return -1; 2633 } 2634 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1); 2635 for (i = 0; i < bmap->n_div; ++i) { 2636 if (i == div) 2637 continue; 2638 if (!pairs[i]) 2639 continue; 2640 for (j = 0; j < bmap->n_div; ++j) { 2641 if (isl_int_is_zero(bmap->div[j][0])) 2642 continue; 2643 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i])) 2644 break; 2645 } 2646 if (j < bmap->n_div) 2647 continue; 2648 for (j = 0; j < bmap->n_ineq; ++j) { 2649 int valid; 2650 if (j == l || j == u) 2651 continue; 2652 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div])) 2653 continue; 2654 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i])) 2655 break; 2656 isl_int_mul(bmap->ineq[j][1 + dim + div], 2657 bmap->ineq[j][1 + dim + div], 2658 bmap->ineq[l][0]); 2659 valid = isl_int_eq(bmap->ineq[j][1 + dim + div], 2660 bmap->ineq[j][1 + dim + i]); 2661 isl_int_divexact(bmap->ineq[j][1 + dim + div], 2662 bmap->ineq[j][1 + dim + div], 2663 bmap->ineq[l][0]); 2664 if (!valid) 2665 break; 2666 } 2667 if (j < bmap->n_ineq) 2668 continue; 2669 coalesce = i; 2670 break; 2671 } 2672 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1); 2673 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]); 2674 return coalesce; 2675} 2676 2677/* Given a lower and an upper bound on div i, construct an inequality 2678 * that when nonnegative ensures that this pair of bounds always allows 2679 * for an integer value of the given div. 2680 * The lower bound is inequality l, while the upper bound is inequality u. 2681 * The constructed inequality is stored in ineq. 2682 * g, fl, fu are temporary scalars. 2683 * 2684 * Let the upper bound be 2685 * 2686 * -n_u a + e_u >= 0 2687 * 2688 * and the lower bound 2689 * 2690 * n_l a + e_l >= 0 2691 * 2692 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l). 2693 * We have 2694 * 2695 * - f_u e_l <= f_u f_l g a <= f_l e_u 2696 * 2697 * Since all variables are integer valued, this is equivalent to 2698 * 2699 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1) 2700 * 2701 * If this interval is at least f_u f_l g, then it contains at least 2702 * one integer value for a. 2703 * That is, the test constraint is 2704 * 2705 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g 2706 */ 2707static void construct_test_ineq(struct isl_basic_map *bmap, int i, 2708 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu) 2709{ 2710 unsigned dim; 2711 dim = isl_space_dim(bmap->dim, isl_dim_all); 2712 2713 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]); 2714 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g); 2715 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g); 2716 isl_int_neg(fu, fu); 2717 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l], 2718 1 + dim + bmap->n_div); 2719 isl_int_add(ineq[0], ineq[0], fl); 2720 isl_int_add(ineq[0], ineq[0], fu); 2721 isl_int_sub_ui(ineq[0], ineq[0], 1); 2722 isl_int_mul(g, g, fl); 2723 isl_int_mul(g, g, fu); 2724 isl_int_sub(ineq[0], ineq[0], g); 2725} 2726 2727/* Remove more kinds of divs that are not strictly needed. 2728 * In particular, if all pairs of lower and upper bounds on a div 2729 * are such that they allow at least one integer value of the div, 2730 * the we can eliminate the div using Fourier-Motzkin without 2731 * introducing any spurious solutions. 2732 */ 2733static struct isl_basic_map *drop_more_redundant_divs( 2734 struct isl_basic_map *bmap, int *pairs, int n) 2735{ 2736 struct isl_tab *tab = NULL; 2737 struct isl_vec *vec = NULL; 2738 unsigned dim; 2739 int remove = -1; 2740 isl_int g, fl, fu; 2741 2742 isl_int_init(g); 2743 isl_int_init(fl); 2744 isl_int_init(fu); 2745 2746 if (!bmap) 2747 goto error; 2748 2749 dim = isl_space_dim(bmap->dim, isl_dim_all); 2750 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div); 2751 if (!vec) 2752 goto error; 2753 2754 tab = isl_tab_from_basic_map(bmap, 0); 2755 2756 while (n > 0) { 2757 int i, l, u; 2758 int best = -1; 2759 enum isl_lp_result res; 2760 2761 for (i = 0; i < bmap->n_div; ++i) { 2762 if (!pairs[i]) 2763 continue; 2764 if (best >= 0 && pairs[best] <= pairs[i]) 2765 continue; 2766 best = i; 2767 } 2768 2769 i = best; 2770 for (l = 0; l < bmap->n_ineq; ++l) { 2771 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i])) 2772 continue; 2773 for (u = 0; u < bmap->n_ineq; ++u) { 2774 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i])) 2775 continue; 2776 construct_test_ineq(bmap, i, l, u, 2777 vec->el, g, fl, fu); 2778 res = isl_tab_min(tab, vec->el, 2779 bmap->ctx->one, &g, NULL, 0); 2780 if (res == isl_lp_error) 2781 goto error; 2782 if (res == isl_lp_empty) { 2783 bmap = isl_basic_map_set_to_empty(bmap); 2784 break; 2785 } 2786 if (res != isl_lp_ok || isl_int_is_neg(g)) 2787 break; 2788 } 2789 if (u < bmap->n_ineq) 2790 break; 2791 } 2792 if (l == bmap->n_ineq) { 2793 remove = i; 2794 break; 2795 } 2796 pairs[i] = 0; 2797 --n; 2798 } 2799 2800 isl_tab_free(tab); 2801 isl_vec_free(vec); 2802 2803 isl_int_clear(g); 2804 isl_int_clear(fl); 2805 isl_int_clear(fu); 2806 2807 free(pairs); 2808 2809 if (remove < 0) 2810 return bmap; 2811 2812 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1); 2813 return isl_basic_map_drop_redundant_divs(bmap); 2814error: 2815 free(pairs); 2816 isl_basic_map_free(bmap); 2817 isl_tab_free(tab); 2818 isl_vec_free(vec); 2819 isl_int_clear(g); 2820 isl_int_clear(fl); 2821 isl_int_clear(fu); 2822 return NULL; 2823} 2824 2825/* Given a pair of divs div1 and div2 such that, expect for the lower bound l 2826 * and the upper bound u, div1 always occurs together with div2 in the form 2827 * (div1 + m div2), where m is the constant range on the variable div1 2828 * allowed by l and u, replace the pair div1 and div2 by a single 2829 * div that is equal to div1 + m div2. 2830 * 2831 * The new div will appear in the location that contains div2. 2832 * We need to modify all constraints that contain 2833 * div2 = (div - div1) / m 2834 * (If a constraint does not contain div2, it will also not contain div1.) 2835 * If the constraint also contains div1, then we know they appear 2836 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div, 2837 * i.e., the coefficient of div is f. 2838 * 2839 * Otherwise, we first need to introduce div1 into the constraint. 2840 * Let the l be 2841 * 2842 * div1 + f >=0 2843 * 2844 * and u 2845 * 2846 * -div1 + f' >= 0 2847 * 2848 * A lower bound on div2 2849 * 2850 * n div2 + t >= 0 2851 * 2852 * can be replaced by 2853 * 2854 * (n * (m div 2 + div1) + m t + n f)/g >= 0 2855 * 2856 * with g = gcd(m,n). 2857 * An upper bound 2858 * 2859 * -n div2 + t >= 0 2860 * 2861 * can be replaced by 2862 * 2863 * (-n * (m div2 + div1) + m t + n f')/g >= 0 2864 * 2865 * These constraint are those that we would obtain from eliminating 2866 * div1 using Fourier-Motzkin. 2867 * 2868 * After all constraints have been modified, we drop the lower and upper 2869 * bound and then drop div1. 2870 */ 2871static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap, 2872 unsigned div1, unsigned div2, unsigned l, unsigned u) 2873{ 2874 isl_int a; 2875 isl_int b; 2876 isl_int m; 2877 unsigned dim, total; 2878 int i; 2879 2880 dim = isl_space_dim(bmap->dim, isl_dim_all); 2881 total = 1 + dim + bmap->n_div; 2882 2883 isl_int_init(a); 2884 isl_int_init(b); 2885 isl_int_init(m); 2886 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]); 2887 isl_int_add_ui(m, m, 1); 2888 2889 for (i = 0; i < bmap->n_ineq; ++i) { 2890 if (i == l || i == u) 2891 continue; 2892 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2])) 2893 continue; 2894 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) { 2895 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]); 2896 isl_int_divexact(a, m, b); 2897 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b); 2898 if (isl_int_is_pos(b)) { 2899 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i], 2900 b, bmap->ineq[l], total); 2901 } else { 2902 isl_int_neg(b, b); 2903 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i], 2904 b, bmap->ineq[u], total); 2905 } 2906 } 2907 isl_int_set(bmap->ineq[i][1 + dim + div2], 2908 bmap->ineq[i][1 + dim + div1]); 2909 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0); 2910 } 2911 2912 isl_int_clear(a); 2913 isl_int_clear(b); 2914 isl_int_clear(m); 2915 if (l > u) { 2916 isl_basic_map_drop_inequality(bmap, l); 2917 isl_basic_map_drop_inequality(bmap, u); 2918 } else { 2919 isl_basic_map_drop_inequality(bmap, u); 2920 isl_basic_map_drop_inequality(bmap, l); 2921 } 2922 bmap = isl_basic_map_drop_div(bmap, div1); 2923 return bmap; 2924} 2925 2926/* First check if we can coalesce any pair of divs and 2927 * then continue with dropping more redundant divs. 2928 * 2929 * We loop over all pairs of lower and upper bounds on a div 2930 * with coefficient 1 and -1, respectively, check if there 2931 * is any other div "c" with which we can coalesce the div 2932 * and if so, perform the coalescing. 2933 */ 2934static struct isl_basic_map *coalesce_or_drop_more_redundant_divs( 2935 struct isl_basic_map *bmap, int *pairs, int n) 2936{ 2937 int i, l, u; 2938 unsigned dim; 2939 2940 dim = isl_space_dim(bmap->dim, isl_dim_all); 2941 2942 for (i = 0; i < bmap->n_div; ++i) { 2943 if (!pairs[i]) 2944 continue; 2945 for (l = 0; l < bmap->n_ineq; ++l) { 2946 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i])) 2947 continue; 2948 for (u = 0; u < bmap->n_ineq; ++u) { 2949 int c; 2950 2951 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i])) 2952 continue; 2953 c = div_find_coalesce(bmap, pairs, i, l, u); 2954 if (c < 0) 2955 continue; 2956 free(pairs); 2957 bmap = coalesce_divs(bmap, i, c, l, u); 2958 return isl_basic_map_drop_redundant_divs(bmap); 2959 } 2960 } 2961 } 2962 2963 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) 2964 return bmap; 2965 2966 return drop_more_redundant_divs(bmap, pairs, n); 2967} 2968 2969/* Remove divs that are not strictly needed. 2970 * In particular, if a div only occurs positively (or negatively) 2971 * in constraints, then it can simply be dropped. 2972 * Also, if a div occurs in only two constraints and if moreover 2973 * those two constraints are opposite to each other, except for the constant 2974 * term and if the sum of the constant terms is such that for any value 2975 * of the other values, there is always at least one integer value of the 2976 * div, i.e., if one plus this sum is greater than or equal to 2977 * the (absolute value) of the coefficent of the div in the constraints, 2978 * then we can also simply drop the div. 2979 * 2980 * We skip divs that appear in equalities or in the definition of other divs. 2981 * Divs that appear in the definition of other divs usually occur in at least 2982 * 4 constraints, but the constraints may have been simplified. 2983 * 2984 * If any divs are left after these simple checks then we move on 2985 * to more complicated cases in drop_more_redundant_divs. 2986 */ 2987struct isl_basic_map *isl_basic_map_drop_redundant_divs( 2988 struct isl_basic_map *bmap) 2989{ 2990 int i, j; 2991 unsigned off; 2992 int *pairs = NULL; 2993 int n = 0; 2994 2995 if (!bmap) 2996 goto error; 2997 if (bmap->n_div == 0) 2998 return bmap; 2999 3000 off = isl_space_dim(bmap->dim, isl_dim_all); 3001 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div); 3002 if (!pairs) 3003 goto error; 3004 3005 for (i = 0; i < bmap->n_div; ++i) { 3006 int pos, neg; 3007 int last_pos, last_neg; 3008 int redundant; 3009 int defined; 3010 3011 defined = !isl_int_is_zero(bmap->div[i][0]); 3012 for (j = i; j < bmap->n_div; ++j) 3013 if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i])) 3014 break; 3015 if (j < bmap->n_div) 3016 continue; 3017 for (j = 0; j < bmap->n_eq; ++j) 3018 if (!isl_int_is_zero(bmap->eq[j][1 + off + i])) 3019 break; 3020 if (j < bmap->n_eq) 3021 continue; 3022 ++n; 3023 pos = neg = 0; 3024 for (j = 0; j < bmap->n_ineq; ++j) { 3025 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) { 3026 last_pos = j; 3027 ++pos; 3028 } 3029 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) { 3030 last_neg = j; 3031 ++neg; 3032 } 3033 } 3034 pairs[i] = pos * neg; 3035 if (pairs[i] == 0) { 3036 for (j = bmap->n_ineq - 1; j >= 0; --j) 3037 if (!isl_int_is_zero(bmap->ineq[j][1+off+i])) 3038 isl_basic_map_drop_inequality(bmap, j); 3039 bmap = isl_basic_map_drop_div(bmap, i); 3040 free(pairs); 3041 return isl_basic_map_drop_redundant_divs(bmap); 3042 } 3043 if (pairs[i] != 1) 3044 continue; 3045 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1, 3046 bmap->ineq[last_neg] + 1, 3047 off + bmap->n_div)) 3048 continue; 3049 3050 isl_int_add(bmap->ineq[last_pos][0], 3051 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]); 3052 isl_int_add_ui(bmap->ineq[last_pos][0], 3053 bmap->ineq[last_pos][0], 1); 3054 redundant = isl_int_ge(bmap->ineq[last_pos][0], 3055 bmap->ineq[last_pos][1+off+i]); 3056 isl_int_sub_ui(bmap->ineq[last_pos][0], 3057 bmap->ineq[last_pos][0], 1); 3058 isl_int_sub(bmap->ineq[last_pos][0], 3059 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]); 3060 if (!redundant) { 3061 if (defined || 3062 !ok_to_set_div_from_bound(bmap, i, last_pos)) { 3063 pairs[i] = 0; 3064 --n; 3065 continue; 3066 } 3067 bmap = set_div_from_lower_bound(bmap, i, last_pos); 3068 bmap = isl_basic_map_simplify(bmap); 3069 free(pairs); 3070 return isl_basic_map_drop_redundant_divs(bmap); 3071 } 3072 if (last_pos > last_neg) { 3073 isl_basic_map_drop_inequality(bmap, last_pos); 3074 isl_basic_map_drop_inequality(bmap, last_neg); 3075 } else { 3076 isl_basic_map_drop_inequality(bmap, last_neg); 3077 isl_basic_map_drop_inequality(bmap, last_pos); 3078 } 3079 bmap = isl_basic_map_drop_div(bmap, i); 3080 free(pairs); 3081 return isl_basic_map_drop_redundant_divs(bmap); 3082 } 3083 3084 if (n > 0) 3085 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n); 3086 3087 free(pairs); 3088 return bmap; 3089error: 3090 free(pairs); 3091 isl_basic_map_free(bmap); 3092 return NULL; 3093} 3094 3095struct isl_basic_set *isl_basic_set_drop_redundant_divs( 3096 struct isl_basic_set *bset) 3097{ 3098 return (struct isl_basic_set *) 3099 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset); 3100} 3101 3102struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map) 3103{ 3104 int i; 3105 3106 if (!map) 3107 return NULL; 3108 for (i = 0; i < map->n; ++i) { 3109 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]); 3110 if (!map->p[i]) 3111 goto error; 3112 } 3113 ISL_F_CLR(map, ISL_MAP_NORMALIZED); 3114 return map; 3115error: 3116 isl_map_free(map); 3117 return NULL; 3118} 3119 3120struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set) 3121{ 3122 return (struct isl_set *) 3123 isl_map_drop_redundant_divs((struct isl_map *)set); 3124} 3125