1/* 2 * Copyright 2008-2009 Katholieke Universiteit Leuven 3 * Copyright 2010 INRIA Saclay 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 INRIA Saclay - Ile-de-France, Parc Club Orsay Universite, 10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 11 */ 12 13#include <isl_ctx_private.h> 14#include "isl_map_private.h" 15#include <isl/seq.h> 16#include "isl_tab.h" 17#include "isl_sample.h" 18#include <isl_mat_private.h> 19#include <isl_aff_private.h> 20#include <isl_options_private.h> 21#include <isl_config.h> 22 23/* 24 * The implementation of parametric integer linear programming in this file 25 * was inspired by the paper "Parametric Integer Programming" and the 26 * report "Solving systems of affine (in)equalities" by Paul Feautrier 27 * (and others). 28 * 29 * The strategy used for obtaining a feasible solution is different 30 * from the one used in isl_tab.c. In particular, in isl_tab.c, 31 * upon finding a constraint that is not yet satisfied, we pivot 32 * in a row that increases the constant term of the row holding the 33 * constraint, making sure the sample solution remains feasible 34 * for all the constraints it already satisfied. 35 * Here, we always pivot in the row holding the constraint, 36 * choosing a column that induces the lexicographically smallest 37 * increment to the sample solution. 38 * 39 * By starting out from a sample value that is lexicographically 40 * smaller than any integer point in the problem space, the first 41 * feasible integer sample point we find will also be the lexicographically 42 * smallest. If all variables can be assumed to be non-negative, 43 * then the initial sample value may be chosen equal to zero. 44 * However, we will not make this assumption. Instead, we apply 45 * the "big parameter" trick. Any variable x is then not directly 46 * used in the tableau, but instead it is represented by another 47 * variable x' = M + x, where M is an arbitrarily large (positive) 48 * value. x' is therefore always non-negative, whatever the value of x. 49 * Taking as initial sample value x' = 0 corresponds to x = -M, 50 * which is always smaller than any possible value of x. 51 * 52 * The big parameter trick is used in the main tableau and 53 * also in the context tableau if isl_context_lex is used. 54 * In this case, each tableaus has its own big parameter. 55 * Before doing any real work, we check if all the parameters 56 * happen to be non-negative. If so, we drop the column corresponding 57 * to M from the initial context tableau. 58 * If isl_context_gbr is used, then the big parameter trick is only 59 * used in the main tableau. 60 */ 61 62struct isl_context; 63struct isl_context_op { 64 /* detect nonnegative parameters in context and mark them in tab */ 65 struct isl_tab *(*detect_nonnegative_parameters)( 66 struct isl_context *context, struct isl_tab *tab); 67 /* return temporary reference to basic set representation of context */ 68 struct isl_basic_set *(*peek_basic_set)(struct isl_context *context); 69 /* return temporary reference to tableau representation of context */ 70 struct isl_tab *(*peek_tab)(struct isl_context *context); 71 /* add equality; check is 1 if eq may not be valid; 72 * update is 1 if we may want to call ineq_sign on context later. 73 */ 74 void (*add_eq)(struct isl_context *context, isl_int *eq, 75 int check, int update); 76 /* add inequality; check is 1 if ineq may not be valid; 77 * update is 1 if we may want to call ineq_sign on context later. 78 */ 79 void (*add_ineq)(struct isl_context *context, isl_int *ineq, 80 int check, int update); 81 /* check sign of ineq based on previous information. 82 * strict is 1 if saturation should be treated as a positive sign. 83 */ 84 enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context, 85 isl_int *ineq, int strict); 86 /* check if inequality maintains feasibility */ 87 int (*test_ineq)(struct isl_context *context, isl_int *ineq); 88 /* return index of a div that corresponds to "div" */ 89 int (*get_div)(struct isl_context *context, struct isl_tab *tab, 90 struct isl_vec *div); 91 /* add div "div" to context and return non-negativity */ 92 int (*add_div)(struct isl_context *context, struct isl_vec *div); 93 int (*detect_equalities)(struct isl_context *context, 94 struct isl_tab *tab); 95 /* return row index of "best" split */ 96 int (*best_split)(struct isl_context *context, struct isl_tab *tab); 97 /* check if context has already been determined to be empty */ 98 int (*is_empty)(struct isl_context *context); 99 /* check if context is still usable */ 100 int (*is_ok)(struct isl_context *context); 101 /* save a copy/snapshot of context */ 102 void *(*save)(struct isl_context *context); 103 /* restore saved context */ 104 void (*restore)(struct isl_context *context, void *); 105 /* discard saved context */ 106 void (*discard)(void *); 107 /* invalidate context */ 108 void (*invalidate)(struct isl_context *context); 109 /* free context */ 110 void (*free)(struct isl_context *context); 111}; 112 113struct isl_context { 114 struct isl_context_op *op; 115}; 116 117struct isl_context_lex { 118 struct isl_context context; 119 struct isl_tab *tab; 120}; 121 122/* A stack (linked list) of solutions of subtrees of the search space. 123 * 124 * "M" describes the solution in terms of the dimensions of "dom". 125 * The number of columns of "M" is one more than the total number 126 * of dimensions of "dom". 127 * 128 * If "M" is NULL, then there is no solution on "dom". 129 */ 130struct isl_partial_sol { 131 int level; 132 struct isl_basic_set *dom; 133 struct isl_mat *M; 134 135 struct isl_partial_sol *next; 136}; 137 138struct isl_sol; 139struct isl_sol_callback { 140 struct isl_tab_callback callback; 141 struct isl_sol *sol; 142}; 143 144/* isl_sol is an interface for constructing a solution to 145 * a parametric integer linear programming problem. 146 * Every time the algorithm reaches a state where a solution 147 * can be read off from the tableau (including cases where the tableau 148 * is empty), the function "add" is called on the isl_sol passed 149 * to find_solutions_main. 150 * 151 * The context tableau is owned by isl_sol and is updated incrementally. 152 * 153 * There are currently two implementations of this interface, 154 * isl_sol_map, which simply collects the solutions in an isl_map 155 * and (optionally) the parts of the context where there is no solution 156 * in an isl_set, and 157 * isl_sol_for, which calls a user-defined function for each part of 158 * the solution. 159 */ 160struct isl_sol { 161 int error; 162 int rational; 163 int level; 164 int max; 165 int n_out; 166 struct isl_context *context; 167 struct isl_partial_sol *partial; 168 void (*add)(struct isl_sol *sol, 169 struct isl_basic_set *dom, struct isl_mat *M); 170 void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset); 171 void (*free)(struct isl_sol *sol); 172 struct isl_sol_callback dec_level; 173}; 174 175static void sol_free(struct isl_sol *sol) 176{ 177 struct isl_partial_sol *partial, *next; 178 if (!sol) 179 return; 180 for (partial = sol->partial; partial; partial = next) { 181 next = partial->next; 182 isl_basic_set_free(partial->dom); 183 isl_mat_free(partial->M); 184 free(partial); 185 } 186 sol->free(sol); 187} 188 189/* Push a partial solution represented by a domain and mapping M 190 * onto the stack of partial solutions. 191 */ 192static void sol_push_sol(struct isl_sol *sol, 193 struct isl_basic_set *dom, struct isl_mat *M) 194{ 195 struct isl_partial_sol *partial; 196 197 if (sol->error || !dom) 198 goto error; 199 200 partial = isl_alloc_type(dom->ctx, struct isl_partial_sol); 201 if (!partial) 202 goto error; 203 204 partial->level = sol->level; 205 partial->dom = dom; 206 partial->M = M; 207 partial->next = sol->partial; 208 209 sol->partial = partial; 210 211 return; 212error: 213 isl_basic_set_free(dom); 214 isl_mat_free(M); 215 sol->error = 1; 216} 217 218/* Pop one partial solution from the partial solution stack and 219 * pass it on to sol->add or sol->add_empty. 220 */ 221static void sol_pop_one(struct isl_sol *sol) 222{ 223 struct isl_partial_sol *partial; 224 225 partial = sol->partial; 226 sol->partial = partial->next; 227 228 if (partial->M) 229 sol->add(sol, partial->dom, partial->M); 230 else 231 sol->add_empty(sol, partial->dom); 232 free(partial); 233} 234 235/* Return a fresh copy of the domain represented by the context tableau. 236 */ 237static struct isl_basic_set *sol_domain(struct isl_sol *sol) 238{ 239 struct isl_basic_set *bset; 240 241 if (sol->error) 242 return NULL; 243 244 bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context)); 245 bset = isl_basic_set_update_from_tab(bset, 246 sol->context->op->peek_tab(sol->context)); 247 248 return bset; 249} 250 251/* Check whether two partial solutions have the same mapping, where n_div 252 * is the number of divs that the two partial solutions have in common. 253 */ 254static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2, 255 unsigned n_div) 256{ 257 int i; 258 unsigned dim; 259 260 if (!s1->M != !s2->M) 261 return 0; 262 if (!s1->M) 263 return 1; 264 265 dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div; 266 267 for (i = 0; i < s1->M->n_row; ++i) { 268 if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div, 269 s1->M->n_col-1-dim-n_div) != -1) 270 return 0; 271 if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div, 272 s2->M->n_col-1-dim-n_div) != -1) 273 return 0; 274 if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div)) 275 return 0; 276 } 277 return 1; 278} 279 280/* Pop all solutions from the partial solution stack that were pushed onto 281 * the stack at levels that are deeper than the current level. 282 * If the two topmost elements on the stack have the same level 283 * and represent the same solution, then their domains are combined. 284 * This combined domain is the same as the current context domain 285 * as sol_pop is called each time we move back to a higher level. 286 */ 287static void sol_pop(struct isl_sol *sol) 288{ 289 struct isl_partial_sol *partial; 290 unsigned n_div; 291 292 if (sol->error) 293 return; 294 295 if (sol->level == 0) { 296 for (partial = sol->partial; partial; partial = sol->partial) 297 sol_pop_one(sol); 298 return; 299 } 300 301 partial = sol->partial; 302 if (!partial) 303 return; 304 305 if (partial->level <= sol->level) 306 return; 307 308 if (partial->next && partial->next->level == partial->level) { 309 n_div = isl_basic_set_dim( 310 sol->context->op->peek_basic_set(sol->context), 311 isl_dim_div); 312 313 if (!same_solution(partial, partial->next, n_div)) { 314 sol_pop_one(sol); 315 sol_pop_one(sol); 316 } else { 317 struct isl_basic_set *bset; 318 isl_mat *M; 319 unsigned n; 320 321 n = isl_basic_set_dim(partial->next->dom, isl_dim_div); 322 n -= n_div; 323 bset = sol_domain(sol); 324 isl_basic_set_free(partial->next->dom); 325 partial->next->dom = bset; 326 M = partial->next->M; 327 if (M) { 328 M = isl_mat_drop_cols(M, M->n_col - n, n); 329 partial->next->M = M; 330 if (!M) 331 goto error; 332 } 333 partial->next->level = sol->level; 334 335 if (!bset) 336 goto error; 337 338 sol->partial = partial->next; 339 isl_basic_set_free(partial->dom); 340 isl_mat_free(partial->M); 341 free(partial); 342 } 343 } else 344 sol_pop_one(sol); 345 346 if (0) 347error: sol->error = 1; 348} 349 350static void sol_dec_level(struct isl_sol *sol) 351{ 352 if (sol->error) 353 return; 354 355 sol->level--; 356 357 sol_pop(sol); 358} 359 360static int sol_dec_level_wrap(struct isl_tab_callback *cb) 361{ 362 struct isl_sol_callback *callback = (struct isl_sol_callback *)cb; 363 364 sol_dec_level(callback->sol); 365 366 return callback->sol->error ? -1 : 0; 367} 368 369/* Move down to next level and push callback onto context tableau 370 * to decrease the level again when it gets rolled back across 371 * the current state. That is, dec_level will be called with 372 * the context tableau in the same state as it is when inc_level 373 * is called. 374 */ 375static void sol_inc_level(struct isl_sol *sol) 376{ 377 struct isl_tab *tab; 378 379 if (sol->error) 380 return; 381 382 sol->level++; 383 tab = sol->context->op->peek_tab(sol->context); 384 if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0) 385 sol->error = 1; 386} 387 388static void scale_rows(struct isl_mat *mat, isl_int m, int n_row) 389{ 390 int i; 391 392 if (isl_int_is_one(m)) 393 return; 394 395 for (i = 0; i < n_row; ++i) 396 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col); 397} 398 399/* Add the solution identified by the tableau and the context tableau. 400 * 401 * The layout of the variables is as follows. 402 * tab->n_var is equal to the total number of variables in the input 403 * map (including divs that were copied from the context) 404 * + the number of extra divs constructed 405 * Of these, the first tab->n_param and the last tab->n_div variables 406 * correspond to the variables in the context, i.e., 407 * tab->n_param + tab->n_div = context_tab->n_var 408 * tab->n_param is equal to the number of parameters and input 409 * dimensions in the input map 410 * tab->n_div is equal to the number of divs in the context 411 * 412 * If there is no solution, then call add_empty with a basic set 413 * that corresponds to the context tableau. (If add_empty is NULL, 414 * then do nothing). 415 * 416 * If there is a solution, then first construct a matrix that maps 417 * all dimensions of the context to the output variables, i.e., 418 * the output dimensions in the input map. 419 * The divs in the input map (if any) that do not correspond to any 420 * div in the context do not appear in the solution. 421 * The algorithm will make sure that they have an integer value, 422 * but these values themselves are of no interest. 423 * We have to be careful not to drop or rearrange any divs in the 424 * context because that would change the meaning of the matrix. 425 * 426 * To extract the value of the output variables, it should be noted 427 * that we always use a big parameter M in the main tableau and so 428 * the variable stored in this tableau is not an output variable x itself, but 429 * x' = M + x (in case of minimization) 430 * or 431 * x' = M - x (in case of maximization) 432 * If x' appears in a column, then its optimal value is zero, 433 * which means that the optimal value of x is an unbounded number 434 * (-M for minimization and M for maximization). 435 * We currently assume that the output dimensions in the original map 436 * are bounded, so this cannot occur. 437 * Similarly, when x' appears in a row, then the coefficient of M in that 438 * row is necessarily 1. 439 * If the row in the tableau represents 440 * d x' = c + d M + e(y) 441 * then, in case of minimization, the corresponding row in the matrix 442 * will be 443 * a c + a e(y) 444 * with a d = m, the (updated) common denominator of the matrix. 445 * In case of maximization, the row will be 446 * -a c - a e(y) 447 */ 448static void sol_add(struct isl_sol *sol, struct isl_tab *tab) 449{ 450 struct isl_basic_set *bset = NULL; 451 struct isl_mat *mat = NULL; 452 unsigned off; 453 int row; 454 isl_int m; 455 456 if (sol->error || !tab) 457 goto error; 458 459 if (tab->empty && !sol->add_empty) 460 return; 461 if (sol->context->op->is_empty(sol->context)) 462 return; 463 464 bset = sol_domain(sol); 465 466 if (tab->empty) { 467 sol_push_sol(sol, bset, NULL); 468 return; 469 } 470 471 off = 2 + tab->M; 472 473 mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out, 474 1 + tab->n_param + tab->n_div); 475 if (!mat) 476 goto error; 477 478 isl_int_init(m); 479 480 isl_seq_clr(mat->row[0] + 1, mat->n_col - 1); 481 isl_int_set_si(mat->row[0][0], 1); 482 for (row = 0; row < sol->n_out; ++row) { 483 int i = tab->n_param + row; 484 int r, j; 485 486 isl_seq_clr(mat->row[1 + row], mat->n_col); 487 if (!tab->var[i].is_row) { 488 if (tab->M) 489 isl_die(mat->ctx, isl_error_invalid, 490 "unbounded optimum", goto error2); 491 continue; 492 } 493 494 r = tab->var[i].index; 495 if (tab->M && 496 isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0])) 497 isl_die(mat->ctx, isl_error_invalid, 498 "unbounded optimum", goto error2); 499 isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]); 500 isl_int_divexact(m, tab->mat->row[r][0], m); 501 scale_rows(mat, m, 1 + row); 502 isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]); 503 isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]); 504 for (j = 0; j < tab->n_param; ++j) { 505 int col; 506 if (tab->var[j].is_row) 507 continue; 508 col = tab->var[j].index; 509 isl_int_mul(mat->row[1 + row][1 + j], m, 510 tab->mat->row[r][off + col]); 511 } 512 for (j = 0; j < tab->n_div; ++j) { 513 int col; 514 if (tab->var[tab->n_var - tab->n_div+j].is_row) 515 continue; 516 col = tab->var[tab->n_var - tab->n_div+j].index; 517 isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m, 518 tab->mat->row[r][off + col]); 519 } 520 if (sol->max) 521 isl_seq_neg(mat->row[1 + row], mat->row[1 + row], 522 mat->n_col); 523 } 524 525 isl_int_clear(m); 526 527 sol_push_sol(sol, bset, mat); 528 return; 529error2: 530 isl_int_clear(m); 531error: 532 isl_basic_set_free(bset); 533 isl_mat_free(mat); 534 sol->error = 1; 535} 536 537struct isl_sol_map { 538 struct isl_sol sol; 539 struct isl_map *map; 540 struct isl_set *empty; 541}; 542 543static void sol_map_free(struct isl_sol_map *sol_map) 544{ 545 if (!sol_map) 546 return; 547 if (sol_map->sol.context) 548 sol_map->sol.context->op->free(sol_map->sol.context); 549 isl_map_free(sol_map->map); 550 isl_set_free(sol_map->empty); 551 free(sol_map); 552} 553 554static void sol_map_free_wrap(struct isl_sol *sol) 555{ 556 sol_map_free((struct isl_sol_map *)sol); 557} 558 559/* This function is called for parts of the context where there is 560 * no solution, with "bset" corresponding to the context tableau. 561 * Simply add the basic set to the set "empty". 562 */ 563static void sol_map_add_empty(struct isl_sol_map *sol, 564 struct isl_basic_set *bset) 565{ 566 if (!bset) 567 goto error; 568 isl_assert(bset->ctx, sol->empty, goto error); 569 570 sol->empty = isl_set_grow(sol->empty, 1); 571 bset = isl_basic_set_simplify(bset); 572 bset = isl_basic_set_finalize(bset); 573 sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset)); 574 if (!sol->empty) 575 goto error; 576 isl_basic_set_free(bset); 577 return; 578error: 579 isl_basic_set_free(bset); 580 sol->sol.error = 1; 581} 582 583static void sol_map_add_empty_wrap(struct isl_sol *sol, 584 struct isl_basic_set *bset) 585{ 586 sol_map_add_empty((struct isl_sol_map *)sol, bset); 587} 588 589/* Given a basic map "dom" that represents the context and an affine 590 * matrix "M" that maps the dimensions of the context to the 591 * output variables, construct a basic map with the same parameters 592 * and divs as the context, the dimensions of the context as input 593 * dimensions and a number of output dimensions that is equal to 594 * the number of output dimensions in the input map. 595 * 596 * The constraints and divs of the context are simply copied 597 * from "dom". For each row 598 * x = c + e(y) 599 * an equality 600 * c + e(y) - d x = 0 601 * is added, with d the common denominator of M. 602 */ 603static void sol_map_add(struct isl_sol_map *sol, 604 struct isl_basic_set *dom, struct isl_mat *M) 605{ 606 int i; 607 struct isl_basic_map *bmap = NULL; 608 unsigned n_eq; 609 unsigned n_ineq; 610 unsigned nparam; 611 unsigned total; 612 unsigned n_div; 613 unsigned n_out; 614 615 if (sol->sol.error || !dom || !M) 616 goto error; 617 618 n_out = sol->sol.n_out; 619 n_eq = dom->n_eq + n_out; 620 n_ineq = dom->n_ineq; 621 n_div = dom->n_div; 622 nparam = isl_basic_set_total_dim(dom) - n_div; 623 total = isl_map_dim(sol->map, isl_dim_all); 624 bmap = isl_basic_map_alloc_space(isl_map_get_space(sol->map), 625 n_div, n_eq, 2 * n_div + n_ineq); 626 if (!bmap) 627 goto error; 628 if (sol->sol.rational) 629 ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL); 630 for (i = 0; i < dom->n_div; ++i) { 631 int k = isl_basic_map_alloc_div(bmap); 632 if (k < 0) 633 goto error; 634 isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam); 635 isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam); 636 isl_seq_cpy(bmap->div[k] + 1 + 1 + total, 637 dom->div[i] + 1 + 1 + nparam, i); 638 } 639 for (i = 0; i < dom->n_eq; ++i) { 640 int k = isl_basic_map_alloc_equality(bmap); 641 if (k < 0) 642 goto error; 643 isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam); 644 isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam); 645 isl_seq_cpy(bmap->eq[k] + 1 + total, 646 dom->eq[i] + 1 + nparam, n_div); 647 } 648 for (i = 0; i < dom->n_ineq; ++i) { 649 int k = isl_basic_map_alloc_inequality(bmap); 650 if (k < 0) 651 goto error; 652 isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam); 653 isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam); 654 isl_seq_cpy(bmap->ineq[k] + 1 + total, 655 dom->ineq[i] + 1 + nparam, n_div); 656 } 657 for (i = 0; i < M->n_row - 1; ++i) { 658 int k = isl_basic_map_alloc_equality(bmap); 659 if (k < 0) 660 goto error; 661 isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam); 662 isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out); 663 isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]); 664 isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out, 665 M->row[1 + i] + 1 + nparam, n_div); 666 } 667 bmap = isl_basic_map_simplify(bmap); 668 bmap = isl_basic_map_finalize(bmap); 669 sol->map = isl_map_grow(sol->map, 1); 670 sol->map = isl_map_add_basic_map(sol->map, bmap); 671 isl_basic_set_free(dom); 672 isl_mat_free(M); 673 if (!sol->map) 674 sol->sol.error = 1; 675 return; 676error: 677 isl_basic_set_free(dom); 678 isl_mat_free(M); 679 isl_basic_map_free(bmap); 680 sol->sol.error = 1; 681} 682 683static void sol_map_add_wrap(struct isl_sol *sol, 684 struct isl_basic_set *dom, struct isl_mat *M) 685{ 686 sol_map_add((struct isl_sol_map *)sol, dom, M); 687} 688 689 690/* Store the "parametric constant" of row "row" of tableau "tab" in "line", 691 * i.e., the constant term and the coefficients of all variables that 692 * appear in the context tableau. 693 * Note that the coefficient of the big parameter M is NOT copied. 694 * The context tableau may not have a big parameter and even when it 695 * does, it is a different big parameter. 696 */ 697static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line) 698{ 699 int i; 700 unsigned off = 2 + tab->M; 701 702 isl_int_set(line[0], tab->mat->row[row][1]); 703 for (i = 0; i < tab->n_param; ++i) { 704 if (tab->var[i].is_row) 705 isl_int_set_si(line[1 + i], 0); 706 else { 707 int col = tab->var[i].index; 708 isl_int_set(line[1 + i], tab->mat->row[row][off + col]); 709 } 710 } 711 for (i = 0; i < tab->n_div; ++i) { 712 if (tab->var[tab->n_var - tab->n_div + i].is_row) 713 isl_int_set_si(line[1 + tab->n_param + i], 0); 714 else { 715 int col = tab->var[tab->n_var - tab->n_div + i].index; 716 isl_int_set(line[1 + tab->n_param + i], 717 tab->mat->row[row][off + col]); 718 } 719 } 720} 721 722/* Check if rows "row1" and "row2" have identical "parametric constants", 723 * as explained above. 724 * In this case, we also insist that the coefficients of the big parameter 725 * be the same as the values of the constants will only be the same 726 * if these coefficients are also the same. 727 */ 728static int identical_parameter_line(struct isl_tab *tab, int row1, int row2) 729{ 730 int i; 731 unsigned off = 2 + tab->M; 732 733 if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1])) 734 return 0; 735 736 if (tab->M && isl_int_ne(tab->mat->row[row1][2], 737 tab->mat->row[row2][2])) 738 return 0; 739 740 for (i = 0; i < tab->n_param + tab->n_div; ++i) { 741 int pos = i < tab->n_param ? i : 742 tab->n_var - tab->n_div + i - tab->n_param; 743 int col; 744 745 if (tab->var[pos].is_row) 746 continue; 747 col = tab->var[pos].index; 748 if (isl_int_ne(tab->mat->row[row1][off + col], 749 tab->mat->row[row2][off + col])) 750 return 0; 751 } 752 return 1; 753} 754 755/* Return an inequality that expresses that the "parametric constant" 756 * should be non-negative. 757 * This function is only called when the coefficient of the big parameter 758 * is equal to zero. 759 */ 760static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row) 761{ 762 struct isl_vec *ineq; 763 764 ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div); 765 if (!ineq) 766 return NULL; 767 768 get_row_parameter_line(tab, row, ineq->el); 769 if (ineq) 770 ineq = isl_vec_normalize(ineq); 771 772 return ineq; 773} 774 775/* Normalize a div expression of the form 776 * 777 * [(g*f(x) + c)/(g * m)] 778 * 779 * with c the constant term and f(x) the remaining coefficients, to 780 * 781 * [(f(x) + [c/g])/m] 782 */ 783static void normalize_div(__isl_keep isl_vec *div) 784{ 785 isl_ctx *ctx = isl_vec_get_ctx(div); 786 int len = div->size - 2; 787 788 isl_seq_gcd(div->el + 2, len, &ctx->normalize_gcd); 789 isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, div->el[0]); 790 791 if (isl_int_is_one(ctx->normalize_gcd)) 792 return; 793 794 isl_int_divexact(div->el[0], div->el[0], ctx->normalize_gcd); 795 isl_int_fdiv_q(div->el[1], div->el[1], ctx->normalize_gcd); 796 isl_seq_scale_down(div->el + 2, div->el + 2, ctx->normalize_gcd, len); 797} 798 799/* Return a integer division for use in a parametric cut based on the given row. 800 * In particular, let the parametric constant of the row be 801 * 802 * \sum_i a_i y_i 803 * 804 * where y_0 = 1, but none of the y_i corresponds to the big parameter M. 805 * The div returned is equal to 806 * 807 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d) 808 */ 809static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row) 810{ 811 struct isl_vec *div; 812 813 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div); 814 if (!div) 815 return NULL; 816 817 isl_int_set(div->el[0], tab->mat->row[row][0]); 818 get_row_parameter_line(tab, row, div->el + 1); 819 isl_seq_neg(div->el + 1, div->el + 1, div->size - 1); 820 normalize_div(div); 821 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1); 822 823 return div; 824} 825 826/* Return a integer division for use in transferring an integrality constraint 827 * to the context. 828 * In particular, let the parametric constant of the row be 829 * 830 * \sum_i a_i y_i 831 * 832 * where y_0 = 1, but none of the y_i corresponds to the big parameter M. 833 * The the returned div is equal to 834 * 835 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d) 836 */ 837static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row) 838{ 839 struct isl_vec *div; 840 841 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div); 842 if (!div) 843 return NULL; 844 845 isl_int_set(div->el[0], tab->mat->row[row][0]); 846 get_row_parameter_line(tab, row, div->el + 1); 847 normalize_div(div); 848 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1); 849 850 return div; 851} 852 853/* Construct and return an inequality that expresses an upper bound 854 * on the given div. 855 * In particular, if the div is given by 856 * 857 * d = floor(e/m) 858 * 859 * then the inequality expresses 860 * 861 * m d <= e 862 */ 863static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div) 864{ 865 unsigned total; 866 unsigned div_pos; 867 struct isl_vec *ineq; 868 869 if (!bset) 870 return NULL; 871 872 total = isl_basic_set_total_dim(bset); 873 div_pos = 1 + total - bset->n_div + div; 874 875 ineq = isl_vec_alloc(bset->ctx, 1 + total); 876 if (!ineq) 877 return NULL; 878 879 isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total); 880 isl_int_neg(ineq->el[div_pos], bset->div[div][0]); 881 return ineq; 882} 883 884/* Given a row in the tableau and a div that was created 885 * using get_row_split_div and that has been constrained to equality, i.e., 886 * 887 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i 888 * 889 * replace the expression "\sum_i {a_i} y_i" in the row by d, 890 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d. 891 * The coefficients of the non-parameters in the tableau have been 892 * verified to be integral. We can therefore simply replace coefficient b 893 * by floor(b). For the coefficients of the parameters we have 894 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have 895 * floor(b) = b. 896 */ 897static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div) 898{ 899 isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1, 900 tab->mat->row[row][0], 1 + tab->M + tab->n_col); 901 902 isl_int_set_si(tab->mat->row[row][0], 1); 903 904 if (tab->var[tab->n_var - tab->n_div + div].is_row) { 905 int drow = tab->var[tab->n_var - tab->n_div + div].index; 906 907 isl_assert(tab->mat->ctx, 908 isl_int_is_one(tab->mat->row[drow][0]), goto error); 909 isl_seq_combine(tab->mat->row[row] + 1, 910 tab->mat->ctx->one, tab->mat->row[row] + 1, 911 tab->mat->ctx->one, tab->mat->row[drow] + 1, 912 1 + tab->M + tab->n_col); 913 } else { 914 int dcol = tab->var[tab->n_var - tab->n_div + div].index; 915 916 isl_int_add_ui(tab->mat->row[row][2 + tab->M + dcol], 917 tab->mat->row[row][2 + tab->M + dcol], 1); 918 } 919 920 return tab; 921error: 922 isl_tab_free(tab); 923 return NULL; 924} 925 926/* Check if the (parametric) constant of the given row is obviously 927 * negative, meaning that we don't need to consult the context tableau. 928 * If there is a big parameter and its coefficient is non-zero, 929 * then this coefficient determines the outcome. 930 * Otherwise, we check whether the constant is negative and 931 * all non-zero coefficients of parameters are negative and 932 * belong to non-negative parameters. 933 */ 934static int is_obviously_neg(struct isl_tab *tab, int row) 935{ 936 int i; 937 int col; 938 unsigned off = 2 + tab->M; 939 940 if (tab->M) { 941 if (isl_int_is_pos(tab->mat->row[row][2])) 942 return 0; 943 if (isl_int_is_neg(tab->mat->row[row][2])) 944 return 1; 945 } 946 947 if (isl_int_is_nonneg(tab->mat->row[row][1])) 948 return 0; 949 for (i = 0; i < tab->n_param; ++i) { 950 /* Eliminated parameter */ 951 if (tab->var[i].is_row) 952 continue; 953 col = tab->var[i].index; 954 if (isl_int_is_zero(tab->mat->row[row][off + col])) 955 continue; 956 if (!tab->var[i].is_nonneg) 957 return 0; 958 if (isl_int_is_pos(tab->mat->row[row][off + col])) 959 return 0; 960 } 961 for (i = 0; i < tab->n_div; ++i) { 962 if (tab->var[tab->n_var - tab->n_div + i].is_row) 963 continue; 964 col = tab->var[tab->n_var - tab->n_div + i].index; 965 if (isl_int_is_zero(tab->mat->row[row][off + col])) 966 continue; 967 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg) 968 return 0; 969 if (isl_int_is_pos(tab->mat->row[row][off + col])) 970 return 0; 971 } 972 return 1; 973} 974 975/* Check if the (parametric) constant of the given row is obviously 976 * non-negative, meaning that we don't need to consult the context tableau. 977 * If there is a big parameter and its coefficient is non-zero, 978 * then this coefficient determines the outcome. 979 * Otherwise, we check whether the constant is non-negative and 980 * all non-zero coefficients of parameters are positive and 981 * belong to non-negative parameters. 982 */ 983static int is_obviously_nonneg(struct isl_tab *tab, int row) 984{ 985 int i; 986 int col; 987 unsigned off = 2 + tab->M; 988 989 if (tab->M) { 990 if (isl_int_is_pos(tab->mat->row[row][2])) 991 return 1; 992 if (isl_int_is_neg(tab->mat->row[row][2])) 993 return 0; 994 } 995 996 if (isl_int_is_neg(tab->mat->row[row][1])) 997 return 0; 998 for (i = 0; i < tab->n_param; ++i) { 999 /* Eliminated parameter */ 1000 if (tab->var[i].is_row) 1001 continue; 1002 col = tab->var[i].index; 1003 if (isl_int_is_zero(tab->mat->row[row][off + col])) 1004 continue; 1005 if (!tab->var[i].is_nonneg) 1006 return 0; 1007 if (isl_int_is_neg(tab->mat->row[row][off + col])) 1008 return 0; 1009 } 1010 for (i = 0; i < tab->n_div; ++i) { 1011 if (tab->var[tab->n_var - tab->n_div + i].is_row) 1012 continue; 1013 col = tab->var[tab->n_var - tab->n_div + i].index; 1014 if (isl_int_is_zero(tab->mat->row[row][off + col])) 1015 continue; 1016 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg) 1017 return 0; 1018 if (isl_int_is_neg(tab->mat->row[row][off + col])) 1019 return 0; 1020 } 1021 return 1; 1022} 1023 1024/* Given a row r and two columns, return the column that would 1025 * lead to the lexicographically smallest increment in the sample 1026 * solution when leaving the basis in favor of the row. 1027 * Pivoting with column c will increment the sample value by a non-negative 1028 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c 1029 * corresponding to the non-parametric variables. 1030 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v, 1031 * with all other entries in this virtual row equal to zero. 1032 * If variable v appears in a row, then a_{v,c} is the element in column c 1033 * of that row. 1034 * 1035 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}. 1036 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e., 1037 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal 1038 * increment. Otherwise, it's c2. 1039 */ 1040static int lexmin_col_pair(struct isl_tab *tab, 1041 int row, int col1, int col2, isl_int tmp) 1042{ 1043 int i; 1044 isl_int *tr; 1045 1046 tr = tab->mat->row[row] + 2 + tab->M; 1047 1048 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) { 1049 int s1, s2; 1050 isl_int *r; 1051 1052 if (!tab->var[i].is_row) { 1053 if (tab->var[i].index == col1) 1054 return col2; 1055 if (tab->var[i].index == col2) 1056 return col1; 1057 continue; 1058 } 1059 1060 if (tab->var[i].index == row) 1061 continue; 1062 1063 r = tab->mat->row[tab->var[i].index] + 2 + tab->M; 1064 s1 = isl_int_sgn(r[col1]); 1065 s2 = isl_int_sgn(r[col2]); 1066 if (s1 == 0 && s2 == 0) 1067 continue; 1068 if (s1 < s2) 1069 return col1; 1070 if (s2 < s1) 1071 return col2; 1072 1073 isl_int_mul(tmp, r[col2], tr[col1]); 1074 isl_int_submul(tmp, r[col1], tr[col2]); 1075 if (isl_int_is_pos(tmp)) 1076 return col1; 1077 if (isl_int_is_neg(tmp)) 1078 return col2; 1079 } 1080 return -1; 1081} 1082 1083/* Given a row in the tableau, find and return the column that would 1084 * result in the lexicographically smallest, but positive, increment 1085 * in the sample point. 1086 * If there is no such column, then return tab->n_col. 1087 * If anything goes wrong, return -1. 1088 */ 1089static int lexmin_pivot_col(struct isl_tab *tab, int row) 1090{ 1091 int j; 1092 int col = tab->n_col; 1093 isl_int *tr; 1094 isl_int tmp; 1095 1096 tr = tab->mat->row[row] + 2 + tab->M; 1097 1098 isl_int_init(tmp); 1099 1100 for (j = tab->n_dead; j < tab->n_col; ++j) { 1101 if (tab->col_var[j] >= 0 && 1102 (tab->col_var[j] < tab->n_param || 1103 tab->col_var[j] >= tab->n_var - tab->n_div)) 1104 continue; 1105 1106 if (!isl_int_is_pos(tr[j])) 1107 continue; 1108 1109 if (col == tab->n_col) 1110 col = j; 1111 else 1112 col = lexmin_col_pair(tab, row, col, j, tmp); 1113 isl_assert(tab->mat->ctx, col >= 0, goto error); 1114 } 1115 1116 isl_int_clear(tmp); 1117 return col; 1118error: 1119 isl_int_clear(tmp); 1120 return -1; 1121} 1122 1123/* Return the first known violated constraint, i.e., a non-negative 1124 * constraint that currently has an either obviously negative value 1125 * or a previously determined to be negative value. 1126 * 1127 * If any constraint has a negative coefficient for the big parameter, 1128 * if any, then we return one of these first. 1129 */ 1130static int first_neg(struct isl_tab *tab) 1131{ 1132 int row; 1133 1134 if (tab->M) 1135 for (row = tab->n_redundant; row < tab->n_row; ++row) { 1136 if (!isl_tab_var_from_row(tab, row)->is_nonneg) 1137 continue; 1138 if (!isl_int_is_neg(tab->mat->row[row][2])) 1139 continue; 1140 if (tab->row_sign) 1141 tab->row_sign[row] = isl_tab_row_neg; 1142 return row; 1143 } 1144 for (row = tab->n_redundant; row < tab->n_row; ++row) { 1145 if (!isl_tab_var_from_row(tab, row)->is_nonneg) 1146 continue; 1147 if (tab->row_sign) { 1148 if (tab->row_sign[row] == 0 && 1149 is_obviously_neg(tab, row)) 1150 tab->row_sign[row] = isl_tab_row_neg; 1151 if (tab->row_sign[row] != isl_tab_row_neg) 1152 continue; 1153 } else if (!is_obviously_neg(tab, row)) 1154 continue; 1155 return row; 1156 } 1157 return -1; 1158} 1159 1160/* Check whether the invariant that all columns are lexico-positive 1161 * is satisfied. This function is not called from the current code 1162 * but is useful during debugging. 1163 */ 1164static void check_lexpos(struct isl_tab *tab) __attribute__ ((unused)); 1165static void check_lexpos(struct isl_tab *tab) 1166{ 1167 unsigned off = 2 + tab->M; 1168 int col; 1169 int var; 1170 int row; 1171 1172 for (col = tab->n_dead; col < tab->n_col; ++col) { 1173 if (tab->col_var[col] >= 0 && 1174 (tab->col_var[col] < tab->n_param || 1175 tab->col_var[col] >= tab->n_var - tab->n_div)) 1176 continue; 1177 for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) { 1178 if (!tab->var[var].is_row) { 1179 if (tab->var[var].index == col) 1180 break; 1181 else 1182 continue; 1183 } 1184 row = tab->var[var].index; 1185 if (isl_int_is_zero(tab->mat->row[row][off + col])) 1186 continue; 1187 if (isl_int_is_pos(tab->mat->row[row][off + col])) 1188 break; 1189 fprintf(stderr, "lexneg column %d (row %d)\n", 1190 col, row); 1191 } 1192 if (var >= tab->n_var - tab->n_div) 1193 fprintf(stderr, "zero column %d\n", col); 1194 } 1195} 1196 1197/* Report to the caller that the given constraint is part of an encountered 1198 * conflict. 1199 */ 1200static int report_conflicting_constraint(struct isl_tab *tab, int con) 1201{ 1202 return tab->conflict(con, tab->conflict_user); 1203} 1204 1205/* Given a conflicting row in the tableau, report all constraints 1206 * involved in the row to the caller. That is, the row itself 1207 * (if it represents a constraint) and all constraint columns with 1208 * non-zero (and therefore negative) coefficients. 1209 */ 1210static int report_conflict(struct isl_tab *tab, int row) 1211{ 1212 int j; 1213 isl_int *tr; 1214 1215 if (!tab->conflict) 1216 return 0; 1217 1218 if (tab->row_var[row] < 0 && 1219 report_conflicting_constraint(tab, ~tab->row_var[row]) < 0) 1220 return -1; 1221 1222 tr = tab->mat->row[row] + 2 + tab->M; 1223 1224 for (j = tab->n_dead; j < tab->n_col; ++j) { 1225 if (tab->col_var[j] >= 0 && 1226 (tab->col_var[j] < tab->n_param || 1227 tab->col_var[j] >= tab->n_var - tab->n_div)) 1228 continue; 1229 1230 if (!isl_int_is_neg(tr[j])) 1231 continue; 1232 1233 if (tab->col_var[j] < 0 && 1234 report_conflicting_constraint(tab, ~tab->col_var[j]) < 0) 1235 return -1; 1236 } 1237 1238 return 0; 1239} 1240 1241/* Resolve all known or obviously violated constraints through pivoting. 1242 * In particular, as long as we can find any violated constraint, we 1243 * look for a pivoting column that would result in the lexicographically 1244 * smallest increment in the sample point. If there is no such column 1245 * then the tableau is infeasible. 1246 */ 1247static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED; 1248static int restore_lexmin(struct isl_tab *tab) 1249{ 1250 int row, col; 1251 1252 if (!tab) 1253 return -1; 1254 if (tab->empty) 1255 return 0; 1256 while ((row = first_neg(tab)) != -1) { 1257 col = lexmin_pivot_col(tab, row); 1258 if (col >= tab->n_col) { 1259 if (report_conflict(tab, row) < 0) 1260 return -1; 1261 if (isl_tab_mark_empty(tab) < 0) 1262 return -1; 1263 return 0; 1264 } 1265 if (col < 0) 1266 return -1; 1267 if (isl_tab_pivot(tab, row, col) < 0) 1268 return -1; 1269 } 1270 return 0; 1271} 1272 1273/* Given a row that represents an equality, look for an appropriate 1274 * pivoting column. 1275 * In particular, if there are any non-zero coefficients among 1276 * the non-parameter variables, then we take the last of these 1277 * variables. Eliminating this variable in terms of the other 1278 * variables and/or parameters does not influence the property 1279 * that all column in the initial tableau are lexicographically 1280 * positive. The row corresponding to the eliminated variable 1281 * will only have non-zero entries below the diagonal of the 1282 * initial tableau. That is, we transform 1283 * 1284 * I I 1285 * 1 into a 1286 * I I 1287 * 1288 * If there is no such non-parameter variable, then we are dealing with 1289 * pure parameter equality and we pick any parameter with coefficient 1 or -1 1290 * for elimination. This will ensure that the eliminated parameter 1291 * always has an integer value whenever all the other parameters are integral. 1292 * If there is no such parameter then we return -1. 1293 */ 1294static int last_var_col_or_int_par_col(struct isl_tab *tab, int row) 1295{ 1296 unsigned off = 2 + tab->M; 1297 int i; 1298 1299 for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) { 1300 int col; 1301 if (tab->var[i].is_row) 1302 continue; 1303 col = tab->var[i].index; 1304 if (col <= tab->n_dead) 1305 continue; 1306 if (!isl_int_is_zero(tab->mat->row[row][off + col])) 1307 return col; 1308 } 1309 for (i = tab->n_dead; i < tab->n_col; ++i) { 1310 if (isl_int_is_one(tab->mat->row[row][off + i])) 1311 return i; 1312 if (isl_int_is_negone(tab->mat->row[row][off + i])) 1313 return i; 1314 } 1315 return -1; 1316} 1317 1318/* Add an equality that is known to be valid to the tableau. 1319 * We first check if we can eliminate a variable or a parameter. 1320 * If not, we add the equality as two inequalities. 1321 * In this case, the equality was a pure parameter equality and there 1322 * is no need to resolve any constraint violations. 1323 */ 1324static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq) 1325{ 1326 int i; 1327 int r; 1328 1329 if (!tab) 1330 return NULL; 1331 r = isl_tab_add_row(tab, eq); 1332 if (r < 0) 1333 goto error; 1334 1335 r = tab->con[r].index; 1336 i = last_var_col_or_int_par_col(tab, r); 1337 if (i < 0) { 1338 tab->con[r].is_nonneg = 1; 1339 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) 1340 goto error; 1341 isl_seq_neg(eq, eq, 1 + tab->n_var); 1342 r = isl_tab_add_row(tab, eq); 1343 if (r < 0) 1344 goto error; 1345 tab->con[r].is_nonneg = 1; 1346 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) 1347 goto error; 1348 } else { 1349 if (isl_tab_pivot(tab, r, i) < 0) 1350 goto error; 1351 if (isl_tab_kill_col(tab, i) < 0) 1352 goto error; 1353 tab->n_eq++; 1354 } 1355 1356 return tab; 1357error: 1358 isl_tab_free(tab); 1359 return NULL; 1360} 1361 1362/* Check if the given row is a pure constant. 1363 */ 1364static int is_constant(struct isl_tab *tab, int row) 1365{ 1366 unsigned off = 2 + tab->M; 1367 1368 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead, 1369 tab->n_col - tab->n_dead) == -1; 1370} 1371 1372/* Add an equality that may or may not be valid to the tableau. 1373 * If the resulting row is a pure constant, then it must be zero. 1374 * Otherwise, the resulting tableau is empty. 1375 * 1376 * If the row is not a pure constant, then we add two inequalities, 1377 * each time checking that they can be satisfied. 1378 * In the end we try to use one of the two constraints to eliminate 1379 * a column. 1380 */ 1381static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED; 1382static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) 1383{ 1384 int r1, r2; 1385 int row; 1386 struct isl_tab_undo *snap; 1387 1388 if (!tab) 1389 return -1; 1390 snap = isl_tab_snap(tab); 1391 r1 = isl_tab_add_row(tab, eq); 1392 if (r1 < 0) 1393 return -1; 1394 tab->con[r1].is_nonneg = 1; 1395 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0) 1396 return -1; 1397 1398 row = tab->con[r1].index; 1399 if (is_constant(tab, row)) { 1400 if (!isl_int_is_zero(tab->mat->row[row][1]) || 1401 (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) { 1402 if (isl_tab_mark_empty(tab) < 0) 1403 return -1; 1404 return 0; 1405 } 1406 if (isl_tab_rollback(tab, snap) < 0) 1407 return -1; 1408 return 0; 1409 } 1410 1411 if (restore_lexmin(tab) < 0) 1412 return -1; 1413 if (tab->empty) 1414 return 0; 1415 1416 isl_seq_neg(eq, eq, 1 + tab->n_var); 1417 1418 r2 = isl_tab_add_row(tab, eq); 1419 if (r2 < 0) 1420 return -1; 1421 tab->con[r2].is_nonneg = 1; 1422 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0) 1423 return -1; 1424 1425 if (restore_lexmin(tab) < 0) 1426 return -1; 1427 if (tab->empty) 1428 return 0; 1429 1430 if (!tab->con[r1].is_row) { 1431 if (isl_tab_kill_col(tab, tab->con[r1].index) < 0) 1432 return -1; 1433 } else if (!tab->con[r2].is_row) { 1434 if (isl_tab_kill_col(tab, tab->con[r2].index) < 0) 1435 return -1; 1436 } 1437 1438 if (tab->bmap) { 1439 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq); 1440 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0) 1441 return -1; 1442 isl_seq_neg(eq, eq, 1 + tab->n_var); 1443 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq); 1444 isl_seq_neg(eq, eq, 1 + tab->n_var); 1445 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0) 1446 return -1; 1447 if (!tab->bmap) 1448 return -1; 1449 } 1450 1451 return 0; 1452} 1453 1454/* Add an inequality to the tableau, resolving violations using 1455 * restore_lexmin. 1456 */ 1457static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq) 1458{ 1459 int r; 1460 1461 if (!tab) 1462 return NULL; 1463 if (tab->bmap) { 1464 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq); 1465 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0) 1466 goto error; 1467 if (!tab->bmap) 1468 goto error; 1469 } 1470 r = isl_tab_add_row(tab, ineq); 1471 if (r < 0) 1472 goto error; 1473 tab->con[r].is_nonneg = 1; 1474 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) 1475 goto error; 1476 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) { 1477 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0) 1478 goto error; 1479 return tab; 1480 } 1481 1482 if (restore_lexmin(tab) < 0) 1483 goto error; 1484 if (!tab->empty && tab->con[r].is_row && 1485 isl_tab_row_is_redundant(tab, tab->con[r].index)) 1486 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0) 1487 goto error; 1488 return tab; 1489error: 1490 isl_tab_free(tab); 1491 return NULL; 1492} 1493 1494/* Check if the coefficients of the parameters are all integral. 1495 */ 1496static int integer_parameter(struct isl_tab *tab, int row) 1497{ 1498 int i; 1499 int col; 1500 unsigned off = 2 + tab->M; 1501 1502 for (i = 0; i < tab->n_param; ++i) { 1503 /* Eliminated parameter */ 1504 if (tab->var[i].is_row) 1505 continue; 1506 col = tab->var[i].index; 1507 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col], 1508 tab->mat->row[row][0])) 1509 return 0; 1510 } 1511 for (i = 0; i < tab->n_div; ++i) { 1512 if (tab->var[tab->n_var - tab->n_div + i].is_row) 1513 continue; 1514 col = tab->var[tab->n_var - tab->n_div + i].index; 1515 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col], 1516 tab->mat->row[row][0])) 1517 return 0; 1518 } 1519 return 1; 1520} 1521 1522/* Check if the coefficients of the non-parameter variables are all integral. 1523 */ 1524static int integer_variable(struct isl_tab *tab, int row) 1525{ 1526 int i; 1527 unsigned off = 2 + tab->M; 1528 1529 for (i = tab->n_dead; i < tab->n_col; ++i) { 1530 if (tab->col_var[i] >= 0 && 1531 (tab->col_var[i] < tab->n_param || 1532 tab->col_var[i] >= tab->n_var - tab->n_div)) 1533 continue; 1534 if (!isl_int_is_divisible_by(tab->mat->row[row][off + i], 1535 tab->mat->row[row][0])) 1536 return 0; 1537 } 1538 return 1; 1539} 1540 1541/* Check if the constant term is integral. 1542 */ 1543static int integer_constant(struct isl_tab *tab, int row) 1544{ 1545 return isl_int_is_divisible_by(tab->mat->row[row][1], 1546 tab->mat->row[row][0]); 1547} 1548 1549#define I_CST 1 << 0 1550#define I_PAR 1 << 1 1551#define I_VAR 1 << 2 1552 1553/* Check for next (non-parameter) variable after "var" (first if var == -1) 1554 * that is non-integer and therefore requires a cut and return 1555 * the index of the variable. 1556 * For parametric tableaus, there are three parts in a row, 1557 * the constant, the coefficients of the parameters and the rest. 1558 * For each part, we check whether the coefficients in that part 1559 * are all integral and if so, set the corresponding flag in *f. 1560 * If the constant and the parameter part are integral, then the 1561 * current sample value is integral and no cut is required 1562 * (irrespective of whether the variable part is integral). 1563 */ 1564static int next_non_integer_var(struct isl_tab *tab, int var, int *f) 1565{ 1566 var = var < 0 ? tab->n_param : var + 1; 1567 1568 for (; var < tab->n_var - tab->n_div; ++var) { 1569 int flags = 0; 1570 int row; 1571 if (!tab->var[var].is_row) 1572 continue; 1573 row = tab->var[var].index; 1574 if (integer_constant(tab, row)) 1575 ISL_FL_SET(flags, I_CST); 1576 if (integer_parameter(tab, row)) 1577 ISL_FL_SET(flags, I_PAR); 1578 if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR)) 1579 continue; 1580 if (integer_variable(tab, row)) 1581 ISL_FL_SET(flags, I_VAR); 1582 *f = flags; 1583 return var; 1584 } 1585 return -1; 1586} 1587 1588/* Check for first (non-parameter) variable that is non-integer and 1589 * therefore requires a cut and return the corresponding row. 1590 * For parametric tableaus, there are three parts in a row, 1591 * the constant, the coefficients of the parameters and the rest. 1592 * For each part, we check whether the coefficients in that part 1593 * are all integral and if so, set the corresponding flag in *f. 1594 * If the constant and the parameter part are integral, then the 1595 * current sample value is integral and no cut is required 1596 * (irrespective of whether the variable part is integral). 1597 */ 1598static int first_non_integer_row(struct isl_tab *tab, int *f) 1599{ 1600 int var = next_non_integer_var(tab, -1, f); 1601 1602 return var < 0 ? -1 : tab->var[var].index; 1603} 1604 1605/* Add a (non-parametric) cut to cut away the non-integral sample 1606 * value of the given row. 1607 * 1608 * If the row is given by 1609 * 1610 * m r = f + \sum_i a_i y_i 1611 * 1612 * then the cut is 1613 * 1614 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0 1615 * 1616 * The big parameter, if any, is ignored, since it is assumed to be big 1617 * enough to be divisible by any integer. 1618 * If the tableau is actually a parametric tableau, then this function 1619 * is only called when all coefficients of the parameters are integral. 1620 * The cut therefore has zero coefficients for the parameters. 1621 * 1622 * The current value is known to be negative, so row_sign, if it 1623 * exists, is set accordingly. 1624 * 1625 * Return the row of the cut or -1. 1626 */ 1627static int add_cut(struct isl_tab *tab, int row) 1628{ 1629 int i; 1630 int r; 1631 isl_int *r_row; 1632 unsigned off = 2 + tab->M; 1633 1634 if (isl_tab_extend_cons(tab, 1) < 0) 1635 return -1; 1636 r = isl_tab_allocate_con(tab); 1637 if (r < 0) 1638 return -1; 1639 1640 r_row = tab->mat->row[tab->con[r].index]; 1641 isl_int_set(r_row[0], tab->mat->row[row][0]); 1642 isl_int_neg(r_row[1], tab->mat->row[row][1]); 1643 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]); 1644 isl_int_neg(r_row[1], r_row[1]); 1645 if (tab->M) 1646 isl_int_set_si(r_row[2], 0); 1647 for (i = 0; i < tab->n_col; ++i) 1648 isl_int_fdiv_r(r_row[off + i], 1649 tab->mat->row[row][off + i], tab->mat->row[row][0]); 1650 1651 tab->con[r].is_nonneg = 1; 1652 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) 1653 return -1; 1654 if (tab->row_sign) 1655 tab->row_sign[tab->con[r].index] = isl_tab_row_neg; 1656 1657 return tab->con[r].index; 1658} 1659 1660#define CUT_ALL 1 1661#define CUT_ONE 0 1662 1663/* Given a non-parametric tableau, add cuts until an integer 1664 * sample point is obtained or until the tableau is determined 1665 * to be integer infeasible. 1666 * As long as there is any non-integer value in the sample point, 1667 * we add appropriate cuts, if possible, for each of these 1668 * non-integer values and then resolve the violated 1669 * cut constraints using restore_lexmin. 1670 * If one of the corresponding rows is equal to an integral 1671 * combination of variables/constraints plus a non-integral constant, 1672 * then there is no way to obtain an integer point and we return 1673 * a tableau that is marked empty. 1674 * The parameter cutting_strategy controls the strategy used when adding cuts 1675 * to remove non-integer points. CUT_ALL adds all possible cuts 1676 * before continuing the search. CUT_ONE adds only one cut at a time. 1677 */ 1678static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab, 1679 int cutting_strategy) 1680{ 1681 int var; 1682 int row; 1683 int flags; 1684 1685 if (!tab) 1686 return NULL; 1687 if (tab->empty) 1688 return tab; 1689 1690 while ((var = next_non_integer_var(tab, -1, &flags)) != -1) { 1691 do { 1692 if (ISL_FL_ISSET(flags, I_VAR)) { 1693 if (isl_tab_mark_empty(tab) < 0) 1694 goto error; 1695 return tab; 1696 } 1697 row = tab->var[var].index; 1698 row = add_cut(tab, row); 1699 if (row < 0) 1700 goto error; 1701 if (cutting_strategy == CUT_ONE) 1702 break; 1703 } while ((var = next_non_integer_var(tab, var, &flags)) != -1); 1704 if (restore_lexmin(tab) < 0) 1705 goto error; 1706 if (tab->empty) 1707 break; 1708 } 1709 return tab; 1710error: 1711 isl_tab_free(tab); 1712 return NULL; 1713} 1714 1715/* Check whether all the currently active samples also satisfy the inequality 1716 * "ineq" (treated as an equality if eq is set). 1717 * Remove those samples that do not. 1718 */ 1719static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq) 1720{ 1721 int i; 1722 isl_int v; 1723 1724 if (!tab) 1725 return NULL; 1726 1727 isl_assert(tab->mat->ctx, tab->bmap, goto error); 1728 isl_assert(tab->mat->ctx, tab->samples, goto error); 1729 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error); 1730 1731 isl_int_init(v); 1732 for (i = tab->n_outside; i < tab->n_sample; ++i) { 1733 int sgn; 1734 isl_seq_inner_product(ineq, tab->samples->row[i], 1735 1 + tab->n_var, &v); 1736 sgn = isl_int_sgn(v); 1737 if (eq ? (sgn == 0) : (sgn >= 0)) 1738 continue; 1739 tab = isl_tab_drop_sample(tab, i); 1740 if (!tab) 1741 break; 1742 } 1743 isl_int_clear(v); 1744 1745 return tab; 1746error: 1747 isl_tab_free(tab); 1748 return NULL; 1749} 1750 1751/* Check whether the sample value of the tableau is finite, 1752 * i.e., either the tableau does not use a big parameter, or 1753 * all values of the variables are equal to the big parameter plus 1754 * some constant. This constant is the actual sample value. 1755 */ 1756static int sample_is_finite(struct isl_tab *tab) 1757{ 1758 int i; 1759 1760 if (!tab->M) 1761 return 1; 1762 1763 for (i = 0; i < tab->n_var; ++i) { 1764 int row; 1765 if (!tab->var[i].is_row) 1766 return 0; 1767 row = tab->var[i].index; 1768 if (isl_int_ne(tab->mat->row[row][0], tab->mat->row[row][2])) 1769 return 0; 1770 } 1771 return 1; 1772} 1773 1774/* Check if the context tableau of sol has any integer points. 1775 * Leave tab in empty state if no integer point can be found. 1776 * If an integer point can be found and if moreover it is finite, 1777 * then it is added to the list of sample values. 1778 * 1779 * This function is only called when none of the currently active sample 1780 * values satisfies the most recently added constraint. 1781 */ 1782static struct isl_tab *check_integer_feasible(struct isl_tab *tab) 1783{ 1784 struct isl_tab_undo *snap; 1785 1786 if (!tab) 1787 return NULL; 1788 1789 snap = isl_tab_snap(tab); 1790 if (isl_tab_push_basis(tab) < 0) 1791 goto error; 1792 1793 tab = cut_to_integer_lexmin(tab, CUT_ALL); 1794 if (!tab) 1795 goto error; 1796 1797 if (!tab->empty && sample_is_finite(tab)) { 1798 struct isl_vec *sample; 1799 1800 sample = isl_tab_get_sample_value(tab); 1801 1802 tab = isl_tab_add_sample(tab, sample); 1803 } 1804 1805 if (!tab->empty && isl_tab_rollback(tab, snap) < 0) 1806 goto error; 1807 1808 return tab; 1809error: 1810 isl_tab_free(tab); 1811 return NULL; 1812} 1813 1814/* Check if any of the currently active sample values satisfies 1815 * the inequality "ineq" (an equality if eq is set). 1816 */ 1817static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq) 1818{ 1819 int i; 1820 isl_int v; 1821 1822 if (!tab) 1823 return -1; 1824 1825 isl_assert(tab->mat->ctx, tab->bmap, return -1); 1826 isl_assert(tab->mat->ctx, tab->samples, return -1); 1827 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1); 1828 1829 isl_int_init(v); 1830 for (i = tab->n_outside; i < tab->n_sample; ++i) { 1831 int sgn; 1832 isl_seq_inner_product(ineq, tab->samples->row[i], 1833 1 + tab->n_var, &v); 1834 sgn = isl_int_sgn(v); 1835 if (eq ? (sgn == 0) : (sgn >= 0)) 1836 break; 1837 } 1838 isl_int_clear(v); 1839 1840 return i < tab->n_sample; 1841} 1842 1843/* Add a div specified by "div" to the tableau "tab" and return 1844 * 1 if the div is obviously non-negative. 1845 */ 1846static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div, 1847 int (*add_ineq)(void *user, isl_int *), void *user) 1848{ 1849 int i; 1850 int r; 1851 struct isl_mat *samples; 1852 int nonneg; 1853 1854 r = isl_tab_add_div(tab, div, add_ineq, user); 1855 if (r < 0) 1856 return -1; 1857 nonneg = tab->var[r].is_nonneg; 1858 tab->var[r].frozen = 1; 1859 1860 samples = isl_mat_extend(tab->samples, 1861 tab->n_sample, 1 + tab->n_var); 1862 tab->samples = samples; 1863 if (!samples) 1864 return -1; 1865 for (i = tab->n_outside; i < samples->n_row; ++i) { 1866 isl_seq_inner_product(div->el + 1, samples->row[i], 1867 div->size - 1, &samples->row[i][samples->n_col - 1]); 1868 isl_int_fdiv_q(samples->row[i][samples->n_col - 1], 1869 samples->row[i][samples->n_col - 1], div->el[0]); 1870 } 1871 1872 return nonneg; 1873} 1874 1875/* Add a div specified by "div" to both the main tableau and 1876 * the context tableau. In case of the main tableau, we only 1877 * need to add an extra div. In the context tableau, we also 1878 * need to express the meaning of the div. 1879 * Return the index of the div or -1 if anything went wrong. 1880 */ 1881static int add_div(struct isl_tab *tab, struct isl_context *context, 1882 struct isl_vec *div) 1883{ 1884 int r; 1885 int nonneg; 1886 1887 if ((nonneg = context->op->add_div(context, div)) < 0) 1888 goto error; 1889 1890 if (!context->op->is_ok(context)) 1891 goto error; 1892 1893 if (isl_tab_extend_vars(tab, 1) < 0) 1894 goto error; 1895 r = isl_tab_allocate_var(tab); 1896 if (r < 0) 1897 goto error; 1898 if (nonneg) 1899 tab->var[r].is_nonneg = 1; 1900 tab->var[r].frozen = 1; 1901 tab->n_div++; 1902 1903 return tab->n_div - 1; 1904error: 1905 context->op->invalidate(context); 1906 return -1; 1907} 1908 1909static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom) 1910{ 1911 int i; 1912 unsigned total = isl_basic_map_total_dim(tab->bmap); 1913 1914 for (i = 0; i < tab->bmap->n_div; ++i) { 1915 if (isl_int_ne(tab->bmap->div[i][0], denom)) 1916 continue; 1917 if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total)) 1918 continue; 1919 return i; 1920 } 1921 return -1; 1922} 1923 1924/* Return the index of a div that corresponds to "div". 1925 * We first check if we already have such a div and if not, we create one. 1926 */ 1927static int get_div(struct isl_tab *tab, struct isl_context *context, 1928 struct isl_vec *div) 1929{ 1930 int d; 1931 struct isl_tab *context_tab = context->op->peek_tab(context); 1932 1933 if (!context_tab) 1934 return -1; 1935 1936 d = find_div(context_tab, div->el + 1, div->el[0]); 1937 if (d != -1) 1938 return d; 1939 1940 return add_div(tab, context, div); 1941} 1942 1943/* Add a parametric cut to cut away the non-integral sample value 1944 * of the give row. 1945 * Let a_i be the coefficients of the constant term and the parameters 1946 * and let b_i be the coefficients of the variables or constraints 1947 * in basis of the tableau. 1948 * Let q be the div q = floor(\sum_i {-a_i} y_i). 1949 * 1950 * The cut is expressed as 1951 * 1952 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0 1953 * 1954 * If q did not already exist in the context tableau, then it is added first. 1955 * If q is in a column of the main tableau then the "+ q" can be accomplished 1956 * by setting the corresponding entry to the denominator of the constraint. 1957 * If q happens to be in a row of the main tableau, then the corresponding 1958 * row needs to be added instead (taking care of the denominators). 1959 * Note that this is very unlikely, but perhaps not entirely impossible. 1960 * 1961 * The current value of the cut is known to be negative (or at least 1962 * non-positive), so row_sign is set accordingly. 1963 * 1964 * Return the row of the cut or -1. 1965 */ 1966static int add_parametric_cut(struct isl_tab *tab, int row, 1967 struct isl_context *context) 1968{ 1969 struct isl_vec *div; 1970 int d; 1971 int i; 1972 int r; 1973 isl_int *r_row; 1974 int col; 1975 int n; 1976 unsigned off = 2 + tab->M; 1977 1978 if (!context) 1979 return -1; 1980 1981 div = get_row_parameter_div(tab, row); 1982 if (!div) 1983 return -1; 1984 1985 n = tab->n_div; 1986 d = context->op->get_div(context, tab, div); 1987 isl_vec_free(div); 1988 if (d < 0) 1989 return -1; 1990 1991 if (isl_tab_extend_cons(tab, 1) < 0) 1992 return -1; 1993 r = isl_tab_allocate_con(tab); 1994 if (r < 0) 1995 return -1; 1996 1997 r_row = tab->mat->row[tab->con[r].index]; 1998 isl_int_set(r_row[0], tab->mat->row[row][0]); 1999 isl_int_neg(r_row[1], tab->mat->row[row][1]); 2000 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]); 2001 isl_int_neg(r_row[1], r_row[1]); 2002 if (tab->M) 2003 isl_int_set_si(r_row[2], 0); 2004 for (i = 0; i < tab->n_param; ++i) { 2005 if (tab->var[i].is_row) 2006 continue; 2007 col = tab->var[i].index; 2008 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]); 2009 isl_int_fdiv_r(r_row[off + col], r_row[off + col], 2010 tab->mat->row[row][0]); 2011 isl_int_neg(r_row[off + col], r_row[off + col]); 2012 } 2013 for (i = 0; i < tab->n_div; ++i) { 2014 if (tab->var[tab->n_var - tab->n_div + i].is_row) 2015 continue; 2016 col = tab->var[tab->n_var - tab->n_div + i].index; 2017 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]); 2018 isl_int_fdiv_r(r_row[off + col], r_row[off + col], 2019 tab->mat->row[row][0]); 2020 isl_int_neg(r_row[off + col], r_row[off + col]); 2021 } 2022 for (i = 0; i < tab->n_col; ++i) { 2023 if (tab->col_var[i] >= 0 && 2024 (tab->col_var[i] < tab->n_param || 2025 tab->col_var[i] >= tab->n_var - tab->n_div)) 2026 continue; 2027 isl_int_fdiv_r(r_row[off + i], 2028 tab->mat->row[row][off + i], tab->mat->row[row][0]); 2029 } 2030 if (tab->var[tab->n_var - tab->n_div + d].is_row) { 2031 isl_int gcd; 2032 int d_row = tab->var[tab->n_var - tab->n_div + d].index; 2033 isl_int_init(gcd); 2034 isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]); 2035 isl_int_divexact(r_row[0], r_row[0], gcd); 2036 isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd); 2037 isl_seq_combine(r_row + 1, gcd, r_row + 1, 2038 r_row[0], tab->mat->row[d_row] + 1, 2039 off - 1 + tab->n_col); 2040 isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]); 2041 isl_int_clear(gcd); 2042 } else { 2043 col = tab->var[tab->n_var - tab->n_div + d].index; 2044 isl_int_set(r_row[off + col], tab->mat->row[row][0]); 2045 } 2046 2047 tab->con[r].is_nonneg = 1; 2048 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) 2049 return -1; 2050 if (tab->row_sign) 2051 tab->row_sign[tab->con[r].index] = isl_tab_row_neg; 2052 2053 row = tab->con[r].index; 2054 2055 if (d >= n && context->op->detect_equalities(context, tab) < 0) 2056 return -1; 2057 2058 return row; 2059} 2060 2061/* Construct a tableau for bmap that can be used for computing 2062 * the lexicographic minimum (or maximum) of bmap. 2063 * If not NULL, then dom is the domain where the minimum 2064 * should be computed. In this case, we set up a parametric 2065 * tableau with row signs (initialized to "unknown"). 2066 * If M is set, then the tableau will use a big parameter. 2067 * If max is set, then a maximum should be computed instead of a minimum. 2068 * This means that for each variable x, the tableau will contain the variable 2069 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient 2070 * of the variables in all constraints are negated prior to adding them 2071 * to the tableau. 2072 */ 2073static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap, 2074 struct isl_basic_set *dom, unsigned M, int max) 2075{ 2076 int i; 2077 struct isl_tab *tab; 2078 2079 tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1, 2080 isl_basic_map_total_dim(bmap), M); 2081 if (!tab) 2082 return NULL; 2083 2084 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); 2085 if (dom) { 2086 tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div; 2087 tab->n_div = dom->n_div; 2088 tab->row_sign = isl_calloc_array(bmap->ctx, 2089 enum isl_tab_row_sign, tab->mat->n_row); 2090 if (tab->mat->n_row && !tab->row_sign) 2091 goto error; 2092 } 2093 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) { 2094 if (isl_tab_mark_empty(tab) < 0) 2095 goto error; 2096 return tab; 2097 } 2098 2099 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) { 2100 tab->var[i].is_nonneg = 1; 2101 tab->var[i].frozen = 1; 2102 } 2103 for (i = 0; i < bmap->n_eq; ++i) { 2104 if (max) 2105 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param, 2106 bmap->eq[i] + 1 + tab->n_param, 2107 tab->n_var - tab->n_param - tab->n_div); 2108 tab = add_lexmin_valid_eq(tab, bmap->eq[i]); 2109 if (max) 2110 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param, 2111 bmap->eq[i] + 1 + tab->n_param, 2112 tab->n_var - tab->n_param - tab->n_div); 2113 if (!tab || tab->empty) 2114 return tab; 2115 } 2116 if (bmap->n_eq && restore_lexmin(tab) < 0) 2117 goto error; 2118 for (i = 0; i < bmap->n_ineq; ++i) { 2119 if (max) 2120 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param, 2121 bmap->ineq[i] + 1 + tab->n_param, 2122 tab->n_var - tab->n_param - tab->n_div); 2123 tab = add_lexmin_ineq(tab, bmap->ineq[i]); 2124 if (max) 2125 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param, 2126 bmap->ineq[i] + 1 + tab->n_param, 2127 tab->n_var - tab->n_param - tab->n_div); 2128 if (!tab || tab->empty) 2129 return tab; 2130 } 2131 return tab; 2132error: 2133 isl_tab_free(tab); 2134 return NULL; 2135} 2136 2137/* Given a main tableau where more than one row requires a split, 2138 * determine and return the "best" row to split on. 2139 * 2140 * Given two rows in the main tableau, if the inequality corresponding 2141 * to the first row is redundant with respect to that of the second row 2142 * in the current tableau, then it is better to split on the second row, 2143 * since in the positive part, both row will be positive. 2144 * (In the negative part a pivot will have to be performed and just about 2145 * anything can happen to the sign of the other row.) 2146 * 2147 * As a simple heuristic, we therefore select the row that makes the most 2148 * of the other rows redundant. 2149 * 2150 * Perhaps it would also be useful to look at the number of constraints 2151 * that conflict with any given constraint. 2152 */ 2153static int best_split(struct isl_tab *tab, struct isl_tab *context_tab) 2154{ 2155 struct isl_tab_undo *snap; 2156 int split; 2157 int row; 2158 int best = -1; 2159 int best_r; 2160 2161 if (isl_tab_extend_cons(context_tab, 2) < 0) 2162 return -1; 2163 2164 snap = isl_tab_snap(context_tab); 2165 2166 for (split = tab->n_redundant; split < tab->n_row; ++split) { 2167 struct isl_tab_undo *snap2; 2168 struct isl_vec *ineq = NULL; 2169 int r = 0; 2170 int ok; 2171 2172 if (!isl_tab_var_from_row(tab, split)->is_nonneg) 2173 continue; 2174 if (tab->row_sign[split] != isl_tab_row_any) 2175 continue; 2176 2177 ineq = get_row_parameter_ineq(tab, split); 2178 if (!ineq) 2179 return -1; 2180 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0; 2181 isl_vec_free(ineq); 2182 if (!ok) 2183 return -1; 2184 2185 snap2 = isl_tab_snap(context_tab); 2186 2187 for (row = tab->n_redundant; row < tab->n_row; ++row) { 2188 struct isl_tab_var *var; 2189 2190 if (row == split) 2191 continue; 2192 if (!isl_tab_var_from_row(tab, row)->is_nonneg) 2193 continue; 2194 if (tab->row_sign[row] != isl_tab_row_any) 2195 continue; 2196 2197 ineq = get_row_parameter_ineq(tab, row); 2198 if (!ineq) 2199 return -1; 2200 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0; 2201 isl_vec_free(ineq); 2202 if (!ok) 2203 return -1; 2204 var = &context_tab->con[context_tab->n_con - 1]; 2205 if (!context_tab->empty && 2206 !isl_tab_min_at_most_neg_one(context_tab, var)) 2207 r++; 2208 if (isl_tab_rollback(context_tab, snap2) < 0) 2209 return -1; 2210 } 2211 if (best == -1 || r > best_r) { 2212 best = split; 2213 best_r = r; 2214 } 2215 if (isl_tab_rollback(context_tab, snap) < 0) 2216 return -1; 2217 } 2218 2219 return best; 2220} 2221 2222static struct isl_basic_set *context_lex_peek_basic_set( 2223 struct isl_context *context) 2224{ 2225 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2226 if (!clex->tab) 2227 return NULL; 2228 return isl_tab_peek_bset(clex->tab); 2229} 2230 2231static struct isl_tab *context_lex_peek_tab(struct isl_context *context) 2232{ 2233 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2234 return clex->tab; 2235} 2236 2237static void context_lex_add_eq(struct isl_context *context, isl_int *eq, 2238 int check, int update) 2239{ 2240 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2241 if (isl_tab_extend_cons(clex->tab, 2) < 0) 2242 goto error; 2243 if (add_lexmin_eq(clex->tab, eq) < 0) 2244 goto error; 2245 if (check) { 2246 int v = tab_has_valid_sample(clex->tab, eq, 1); 2247 if (v < 0) 2248 goto error; 2249 if (!v) 2250 clex->tab = check_integer_feasible(clex->tab); 2251 } 2252 if (update) 2253 clex->tab = check_samples(clex->tab, eq, 1); 2254 return; 2255error: 2256 isl_tab_free(clex->tab); 2257 clex->tab = NULL; 2258} 2259 2260static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq, 2261 int check, int update) 2262{ 2263 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2264 if (isl_tab_extend_cons(clex->tab, 1) < 0) 2265 goto error; 2266 clex->tab = add_lexmin_ineq(clex->tab, ineq); 2267 if (check) { 2268 int v = tab_has_valid_sample(clex->tab, ineq, 0); 2269 if (v < 0) 2270 goto error; 2271 if (!v) 2272 clex->tab = check_integer_feasible(clex->tab); 2273 } 2274 if (update) 2275 clex->tab = check_samples(clex->tab, ineq, 0); 2276 return; 2277error: 2278 isl_tab_free(clex->tab); 2279 clex->tab = NULL; 2280} 2281 2282static int context_lex_add_ineq_wrap(void *user, isl_int *ineq) 2283{ 2284 struct isl_context *context = (struct isl_context *)user; 2285 context_lex_add_ineq(context, ineq, 0, 0); 2286 return context->op->is_ok(context) ? 0 : -1; 2287} 2288 2289/* Check which signs can be obtained by "ineq" on all the currently 2290 * active sample values. See row_sign for more information. 2291 */ 2292static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq, 2293 int strict) 2294{ 2295 int i; 2296 int sgn; 2297 isl_int tmp; 2298 enum isl_tab_row_sign res = isl_tab_row_unknown; 2299 2300 isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown); 2301 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, 2302 return isl_tab_row_unknown); 2303 2304 isl_int_init(tmp); 2305 for (i = tab->n_outside; i < tab->n_sample; ++i) { 2306 isl_seq_inner_product(tab->samples->row[i], ineq, 2307 1 + tab->n_var, &tmp); 2308 sgn = isl_int_sgn(tmp); 2309 if (sgn > 0 || (sgn == 0 && strict)) { 2310 if (res == isl_tab_row_unknown) 2311 res = isl_tab_row_pos; 2312 if (res == isl_tab_row_neg) 2313 res = isl_tab_row_any; 2314 } 2315 if (sgn < 0) { 2316 if (res == isl_tab_row_unknown) 2317 res = isl_tab_row_neg; 2318 if (res == isl_tab_row_pos) 2319 res = isl_tab_row_any; 2320 } 2321 if (res == isl_tab_row_any) 2322 break; 2323 } 2324 isl_int_clear(tmp); 2325 2326 return res; 2327} 2328 2329static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context, 2330 isl_int *ineq, int strict) 2331{ 2332 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2333 return tab_ineq_sign(clex->tab, ineq, strict); 2334} 2335 2336/* Check whether "ineq" can be added to the tableau without rendering 2337 * it infeasible. 2338 */ 2339static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq) 2340{ 2341 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2342 struct isl_tab_undo *snap; 2343 int feasible; 2344 2345 if (!clex->tab) 2346 return -1; 2347 2348 if (isl_tab_extend_cons(clex->tab, 1) < 0) 2349 return -1; 2350 2351 snap = isl_tab_snap(clex->tab); 2352 if (isl_tab_push_basis(clex->tab) < 0) 2353 return -1; 2354 clex->tab = add_lexmin_ineq(clex->tab, ineq); 2355 clex->tab = check_integer_feasible(clex->tab); 2356 if (!clex->tab) 2357 return -1; 2358 feasible = !clex->tab->empty; 2359 if (isl_tab_rollback(clex->tab, snap) < 0) 2360 return -1; 2361 2362 return feasible; 2363} 2364 2365static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab, 2366 struct isl_vec *div) 2367{ 2368 return get_div(tab, context, div); 2369} 2370 2371/* Add a div specified by "div" to the context tableau and return 2372 * 1 if the div is obviously non-negative. 2373 * context_tab_add_div will always return 1, because all variables 2374 * in a isl_context_lex tableau are non-negative. 2375 * However, if we are using a big parameter in the context, then this only 2376 * reflects the non-negativity of the variable used to _encode_ the 2377 * div, i.e., div' = M + div, so we can't draw any conclusions. 2378 */ 2379static int context_lex_add_div(struct isl_context *context, struct isl_vec *div) 2380{ 2381 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2382 int nonneg; 2383 nonneg = context_tab_add_div(clex->tab, div, 2384 context_lex_add_ineq_wrap, context); 2385 if (nonneg < 0) 2386 return -1; 2387 if (clex->tab->M) 2388 return 0; 2389 return nonneg; 2390} 2391 2392static int context_lex_detect_equalities(struct isl_context *context, 2393 struct isl_tab *tab) 2394{ 2395 return 0; 2396} 2397 2398static int context_lex_best_split(struct isl_context *context, 2399 struct isl_tab *tab) 2400{ 2401 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2402 struct isl_tab_undo *snap; 2403 int r; 2404 2405 snap = isl_tab_snap(clex->tab); 2406 if (isl_tab_push_basis(clex->tab) < 0) 2407 return -1; 2408 r = best_split(tab, clex->tab); 2409 2410 if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0) 2411 return -1; 2412 2413 return r; 2414} 2415 2416static int context_lex_is_empty(struct isl_context *context) 2417{ 2418 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2419 if (!clex->tab) 2420 return -1; 2421 return clex->tab->empty; 2422} 2423 2424static void *context_lex_save(struct isl_context *context) 2425{ 2426 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2427 struct isl_tab_undo *snap; 2428 2429 snap = isl_tab_snap(clex->tab); 2430 if (isl_tab_push_basis(clex->tab) < 0) 2431 return NULL; 2432 if (isl_tab_save_samples(clex->tab) < 0) 2433 return NULL; 2434 2435 return snap; 2436} 2437 2438static void context_lex_restore(struct isl_context *context, void *save) 2439{ 2440 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2441 if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) { 2442 isl_tab_free(clex->tab); 2443 clex->tab = NULL; 2444 } 2445} 2446 2447static void context_lex_discard(void *save) 2448{ 2449} 2450 2451static int context_lex_is_ok(struct isl_context *context) 2452{ 2453 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2454 return !!clex->tab; 2455} 2456 2457/* For each variable in the context tableau, check if the variable can 2458 * only attain non-negative values. If so, mark the parameter as non-negative 2459 * in the main tableau. This allows for a more direct identification of some 2460 * cases of violated constraints. 2461 */ 2462static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab, 2463 struct isl_tab *context_tab) 2464{ 2465 int i; 2466 struct isl_tab_undo *snap; 2467 struct isl_vec *ineq = NULL; 2468 struct isl_tab_var *var; 2469 int n; 2470 2471 if (context_tab->n_var == 0) 2472 return tab; 2473 2474 ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var); 2475 if (!ineq) 2476 goto error; 2477 2478 if (isl_tab_extend_cons(context_tab, 1) < 0) 2479 goto error; 2480 2481 snap = isl_tab_snap(context_tab); 2482 2483 n = 0; 2484 isl_seq_clr(ineq->el, ineq->size); 2485 for (i = 0; i < context_tab->n_var; ++i) { 2486 isl_int_set_si(ineq->el[1 + i], 1); 2487 if (isl_tab_add_ineq(context_tab, ineq->el) < 0) 2488 goto error; 2489 var = &context_tab->con[context_tab->n_con - 1]; 2490 if (!context_tab->empty && 2491 !isl_tab_min_at_most_neg_one(context_tab, var)) { 2492 int j = i; 2493 if (i >= tab->n_param) 2494 j = i - tab->n_param + tab->n_var - tab->n_div; 2495 tab->var[j].is_nonneg = 1; 2496 n++; 2497 } 2498 isl_int_set_si(ineq->el[1 + i], 0); 2499 if (isl_tab_rollback(context_tab, snap) < 0) 2500 goto error; 2501 } 2502 2503 if (context_tab->M && n == context_tab->n_var) { 2504 context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1); 2505 context_tab->M = 0; 2506 } 2507 2508 isl_vec_free(ineq); 2509 return tab; 2510error: 2511 isl_vec_free(ineq); 2512 isl_tab_free(tab); 2513 return NULL; 2514} 2515 2516static struct isl_tab *context_lex_detect_nonnegative_parameters( 2517 struct isl_context *context, struct isl_tab *tab) 2518{ 2519 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2520 struct isl_tab_undo *snap; 2521 2522 if (!tab) 2523 return NULL; 2524 2525 snap = isl_tab_snap(clex->tab); 2526 if (isl_tab_push_basis(clex->tab) < 0) 2527 goto error; 2528 2529 tab = tab_detect_nonnegative_parameters(tab, clex->tab); 2530 2531 if (isl_tab_rollback(clex->tab, snap) < 0) 2532 goto error; 2533 2534 return tab; 2535error: 2536 isl_tab_free(tab); 2537 return NULL; 2538} 2539 2540static void context_lex_invalidate(struct isl_context *context) 2541{ 2542 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2543 isl_tab_free(clex->tab); 2544 clex->tab = NULL; 2545} 2546 2547static void context_lex_free(struct isl_context *context) 2548{ 2549 struct isl_context_lex *clex = (struct isl_context_lex *)context; 2550 isl_tab_free(clex->tab); 2551 free(clex); 2552} 2553 2554struct isl_context_op isl_context_lex_op = { 2555 context_lex_detect_nonnegative_parameters, 2556 context_lex_peek_basic_set, 2557 context_lex_peek_tab, 2558 context_lex_add_eq, 2559 context_lex_add_ineq, 2560 context_lex_ineq_sign, 2561 context_lex_test_ineq, 2562 context_lex_get_div, 2563 context_lex_add_div, 2564 context_lex_detect_equalities, 2565 context_lex_best_split, 2566 context_lex_is_empty, 2567 context_lex_is_ok, 2568 context_lex_save, 2569 context_lex_restore, 2570 context_lex_discard, 2571 context_lex_invalidate, 2572 context_lex_free, 2573}; 2574 2575static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset) 2576{ 2577 struct isl_tab *tab; 2578 2579 if (!bset) 2580 return NULL; 2581 tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0); 2582 if (!tab) 2583 goto error; 2584 if (isl_tab_track_bset(tab, bset) < 0) 2585 goto error; 2586 tab = isl_tab_init_samples(tab); 2587 return tab; 2588error: 2589 isl_basic_set_free(bset); 2590 return NULL; 2591} 2592 2593static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom) 2594{ 2595 struct isl_context_lex *clex; 2596 2597 if (!dom) 2598 return NULL; 2599 2600 clex = isl_alloc_type(dom->ctx, struct isl_context_lex); 2601 if (!clex) 2602 return NULL; 2603 2604 clex->context.op = &isl_context_lex_op; 2605 2606 clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom)); 2607 if (restore_lexmin(clex->tab) < 0) 2608 goto error; 2609 clex->tab = check_integer_feasible(clex->tab); 2610 if (!clex->tab) 2611 goto error; 2612 2613 return &clex->context; 2614error: 2615 clex->context.op->free(&clex->context); 2616 return NULL; 2617} 2618 2619/* Representation of the context when using generalized basis reduction. 2620 * 2621 * "shifted" contains the offsets of the unit hypercubes that lie inside the 2622 * context. Any rational point in "shifted" can therefore be rounded 2623 * up to an integer point in the context. 2624 * If the context is constrained by any equality, then "shifted" is not used 2625 * as it would be empty. 2626 */ 2627struct isl_context_gbr { 2628 struct isl_context context; 2629 struct isl_tab *tab; 2630 struct isl_tab *shifted; 2631 struct isl_tab *cone; 2632}; 2633 2634static struct isl_tab *context_gbr_detect_nonnegative_parameters( 2635 struct isl_context *context, struct isl_tab *tab) 2636{ 2637 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2638 if (!tab) 2639 return NULL; 2640 return tab_detect_nonnegative_parameters(tab, cgbr->tab); 2641} 2642 2643static struct isl_basic_set *context_gbr_peek_basic_set( 2644 struct isl_context *context) 2645{ 2646 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2647 if (!cgbr->tab) 2648 return NULL; 2649 return isl_tab_peek_bset(cgbr->tab); 2650} 2651 2652static struct isl_tab *context_gbr_peek_tab(struct isl_context *context) 2653{ 2654 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2655 return cgbr->tab; 2656} 2657 2658/* Initialize the "shifted" tableau of the context, which 2659 * contains the constraints of the original tableau shifted 2660 * by the sum of all negative coefficients. This ensures 2661 * that any rational point in the shifted tableau can 2662 * be rounded up to yield an integer point in the original tableau. 2663 */ 2664static void gbr_init_shifted(struct isl_context_gbr *cgbr) 2665{ 2666 int i, j; 2667 struct isl_vec *cst; 2668 struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab); 2669 unsigned dim = isl_basic_set_total_dim(bset); 2670 2671 cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq); 2672 if (!cst) 2673 return; 2674 2675 for (i = 0; i < bset->n_ineq; ++i) { 2676 isl_int_set(cst->el[i], bset->ineq[i][0]); 2677 for (j = 0; j < dim; ++j) { 2678 if (!isl_int_is_neg(bset->ineq[i][1 + j])) 2679 continue; 2680 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], 2681 bset->ineq[i][1 + j]); 2682 } 2683 } 2684 2685 cgbr->shifted = isl_tab_from_basic_set(bset, 0); 2686 2687 for (i = 0; i < bset->n_ineq; ++i) 2688 isl_int_set(bset->ineq[i][0], cst->el[i]); 2689 2690 isl_vec_free(cst); 2691} 2692 2693/* Check if the shifted tableau is non-empty, and if so 2694 * use the sample point to construct an integer point 2695 * of the context tableau. 2696 */ 2697static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr) 2698{ 2699 struct isl_vec *sample; 2700 2701 if (!cgbr->shifted) 2702 gbr_init_shifted(cgbr); 2703 if (!cgbr->shifted) 2704 return NULL; 2705 if (cgbr->shifted->empty) 2706 return isl_vec_alloc(cgbr->tab->mat->ctx, 0); 2707 2708 sample = isl_tab_get_sample_value(cgbr->shifted); 2709 sample = isl_vec_ceil(sample); 2710 2711 return sample; 2712} 2713 2714static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset) 2715{ 2716 int i; 2717 2718 if (!bset) 2719 return NULL; 2720 2721 for (i = 0; i < bset->n_eq; ++i) 2722 isl_int_set_si(bset->eq[i][0], 0); 2723 2724 for (i = 0; i < bset->n_ineq; ++i) 2725 isl_int_set_si(bset->ineq[i][0], 0); 2726 2727 return bset; 2728} 2729 2730static int use_shifted(struct isl_context_gbr *cgbr) 2731{ 2732 if (!cgbr->tab) 2733 return 0; 2734 return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0; 2735} 2736 2737static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr) 2738{ 2739 struct isl_basic_set *bset; 2740 struct isl_basic_set *cone; 2741 2742 if (isl_tab_sample_is_integer(cgbr->tab)) 2743 return isl_tab_get_sample_value(cgbr->tab); 2744 2745 if (use_shifted(cgbr)) { 2746 struct isl_vec *sample; 2747 2748 sample = gbr_get_shifted_sample(cgbr); 2749 if (!sample || sample->size > 0) 2750 return sample; 2751 2752 isl_vec_free(sample); 2753 } 2754 2755 if (!cgbr->cone) { 2756 bset = isl_tab_peek_bset(cgbr->tab); 2757 cgbr->cone = isl_tab_from_recession_cone(bset, 0); 2758 if (!cgbr->cone) 2759 return NULL; 2760 if (isl_tab_track_bset(cgbr->cone, 2761 isl_basic_set_copy(bset)) < 0) 2762 return NULL; 2763 } 2764 if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0) 2765 return NULL; 2766 2767 if (cgbr->cone->n_dead == cgbr->cone->n_col) { 2768 struct isl_vec *sample; 2769 struct isl_tab_undo *snap; 2770 2771 if (cgbr->tab->basis) { 2772 if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) { 2773 isl_mat_free(cgbr->tab->basis); 2774 cgbr->tab->basis = NULL; 2775 } 2776 cgbr->tab->n_zero = 0; 2777 cgbr->tab->n_unbounded = 0; 2778 } 2779 2780 snap = isl_tab_snap(cgbr->tab); 2781 2782 sample = isl_tab_sample(cgbr->tab); 2783 2784 if (isl_tab_rollback(cgbr->tab, snap) < 0) { 2785 isl_vec_free(sample); 2786 return NULL; 2787 } 2788 2789 return sample; 2790 } 2791 2792 cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone)); 2793 cone = drop_constant_terms(cone); 2794 cone = isl_basic_set_update_from_tab(cone, cgbr->cone); 2795 cone = isl_basic_set_underlying_set(cone); 2796 cone = isl_basic_set_gauss(cone, NULL); 2797 2798 bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab)); 2799 bset = isl_basic_set_update_from_tab(bset, cgbr->tab); 2800 bset = isl_basic_set_underlying_set(bset); 2801 bset = isl_basic_set_gauss(bset, NULL); 2802 2803 return isl_basic_set_sample_with_cone(bset, cone); 2804} 2805 2806static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr) 2807{ 2808 struct isl_vec *sample; 2809 2810 if (!cgbr->tab) 2811 return; 2812 2813 if (cgbr->tab->empty) 2814 return; 2815 2816 sample = gbr_get_sample(cgbr); 2817 if (!sample) 2818 goto error; 2819 2820 if (sample->size == 0) { 2821 isl_vec_free(sample); 2822 if (isl_tab_mark_empty(cgbr->tab) < 0) 2823 goto error; 2824 return; 2825 } 2826 2827 cgbr->tab = isl_tab_add_sample(cgbr->tab, sample); 2828 2829 return; 2830error: 2831 isl_tab_free(cgbr->tab); 2832 cgbr->tab = NULL; 2833} 2834 2835static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq) 2836{ 2837 if (!tab) 2838 return NULL; 2839 2840 if (isl_tab_extend_cons(tab, 2) < 0) 2841 goto error; 2842 2843 if (isl_tab_add_eq(tab, eq) < 0) 2844 goto error; 2845 2846 return tab; 2847error: 2848 isl_tab_free(tab); 2849 return NULL; 2850} 2851 2852/* Add the equality described by "eq" to the context. 2853 * If "check" is set, then we check if the context is empty after 2854 * adding the equality. 2855 * If "update" is set, then we check if the samples are still valid. 2856 * 2857 * We do not explicitly add shifted copies of the equality to 2858 * cgbr->shifted since they would conflict with each other. 2859 * Instead, we directly mark cgbr->shifted empty. 2860 */ 2861static void context_gbr_add_eq(struct isl_context *context, isl_int *eq, 2862 int check, int update) 2863{ 2864 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2865 2866 cgbr->tab = add_gbr_eq(cgbr->tab, eq); 2867 2868 if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) { 2869 if (isl_tab_mark_empty(cgbr->shifted) < 0) 2870 goto error; 2871 } 2872 2873 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) { 2874 if (isl_tab_extend_cons(cgbr->cone, 2) < 0) 2875 goto error; 2876 if (isl_tab_add_eq(cgbr->cone, eq) < 0) 2877 goto error; 2878 } 2879 2880 if (check) { 2881 int v = tab_has_valid_sample(cgbr->tab, eq, 1); 2882 if (v < 0) 2883 goto error; 2884 if (!v) 2885 check_gbr_integer_feasible(cgbr); 2886 } 2887 if (update) 2888 cgbr->tab = check_samples(cgbr->tab, eq, 1); 2889 return; 2890error: 2891 isl_tab_free(cgbr->tab); 2892 cgbr->tab = NULL; 2893} 2894 2895static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq) 2896{ 2897 if (!cgbr->tab) 2898 return; 2899 2900 if (isl_tab_extend_cons(cgbr->tab, 1) < 0) 2901 goto error; 2902 2903 if (isl_tab_add_ineq(cgbr->tab, ineq) < 0) 2904 goto error; 2905 2906 if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) { 2907 int i; 2908 unsigned dim; 2909 dim = isl_basic_map_total_dim(cgbr->tab->bmap); 2910 2911 if (isl_tab_extend_cons(cgbr->shifted, 1) < 0) 2912 goto error; 2913 2914 for (i = 0; i < dim; ++i) { 2915 if (!isl_int_is_neg(ineq[1 + i])) 2916 continue; 2917 isl_int_add(ineq[0], ineq[0], ineq[1 + i]); 2918 } 2919 2920 if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0) 2921 goto error; 2922 2923 for (i = 0; i < dim; ++i) { 2924 if (!isl_int_is_neg(ineq[1 + i])) 2925 continue; 2926 isl_int_sub(ineq[0], ineq[0], ineq[1 + i]); 2927 } 2928 } 2929 2930 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) { 2931 if (isl_tab_extend_cons(cgbr->cone, 1) < 0) 2932 goto error; 2933 if (isl_tab_add_ineq(cgbr->cone, ineq) < 0) 2934 goto error; 2935 } 2936 2937 return; 2938error: 2939 isl_tab_free(cgbr->tab); 2940 cgbr->tab = NULL; 2941} 2942 2943static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq, 2944 int check, int update) 2945{ 2946 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2947 2948 add_gbr_ineq(cgbr, ineq); 2949 if (!cgbr->tab) 2950 return; 2951 2952 if (check) { 2953 int v = tab_has_valid_sample(cgbr->tab, ineq, 0); 2954 if (v < 0) 2955 goto error; 2956 if (!v) 2957 check_gbr_integer_feasible(cgbr); 2958 } 2959 if (update) 2960 cgbr->tab = check_samples(cgbr->tab, ineq, 0); 2961 return; 2962error: 2963 isl_tab_free(cgbr->tab); 2964 cgbr->tab = NULL; 2965} 2966 2967static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq) 2968{ 2969 struct isl_context *context = (struct isl_context *)user; 2970 context_gbr_add_ineq(context, ineq, 0, 0); 2971 return context->op->is_ok(context) ? 0 : -1; 2972} 2973 2974static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context, 2975 isl_int *ineq, int strict) 2976{ 2977 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2978 return tab_ineq_sign(cgbr->tab, ineq, strict); 2979} 2980 2981/* Check whether "ineq" can be added to the tableau without rendering 2982 * it infeasible. 2983 */ 2984static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq) 2985{ 2986 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 2987 struct isl_tab_undo *snap; 2988 struct isl_tab_undo *shifted_snap = NULL; 2989 struct isl_tab_undo *cone_snap = NULL; 2990 int feasible; 2991 2992 if (!cgbr->tab) 2993 return -1; 2994 2995 if (isl_tab_extend_cons(cgbr->tab, 1) < 0) 2996 return -1; 2997 2998 snap = isl_tab_snap(cgbr->tab); 2999 if (cgbr->shifted) 3000 shifted_snap = isl_tab_snap(cgbr->shifted); 3001 if (cgbr->cone) 3002 cone_snap = isl_tab_snap(cgbr->cone); 3003 add_gbr_ineq(cgbr, ineq); 3004 check_gbr_integer_feasible(cgbr); 3005 if (!cgbr->tab) 3006 return -1; 3007 feasible = !cgbr->tab->empty; 3008 if (isl_tab_rollback(cgbr->tab, snap) < 0) 3009 return -1; 3010 if (shifted_snap) { 3011 if (isl_tab_rollback(cgbr->shifted, shifted_snap)) 3012 return -1; 3013 } else if (cgbr->shifted) { 3014 isl_tab_free(cgbr->shifted); 3015 cgbr->shifted = NULL; 3016 } 3017 if (cone_snap) { 3018 if (isl_tab_rollback(cgbr->cone, cone_snap)) 3019 return -1; 3020 } else if (cgbr->cone) { 3021 isl_tab_free(cgbr->cone); 3022 cgbr->cone = NULL; 3023 } 3024 3025 return feasible; 3026} 3027 3028/* Return the column of the last of the variables associated to 3029 * a column that has a non-zero coefficient. 3030 * This function is called in a context where only coefficients 3031 * of parameters or divs can be non-zero. 3032 */ 3033static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p) 3034{ 3035 int i; 3036 int col; 3037 3038 if (tab->n_var == 0) 3039 return -1; 3040 3041 for (i = tab->n_var - 1; i >= 0; --i) { 3042 if (i >= tab->n_param && i < tab->n_var - tab->n_div) 3043 continue; 3044 if (tab->var[i].is_row) 3045 continue; 3046 col = tab->var[i].index; 3047 if (!isl_int_is_zero(p[col])) 3048 return col; 3049 } 3050 3051 return -1; 3052} 3053 3054/* Look through all the recently added equalities in the context 3055 * to see if we can propagate any of them to the main tableau. 3056 * 3057 * The newly added equalities in the context are encoded as pairs 3058 * of inequalities starting at inequality "first". 3059 * 3060 * We tentatively add each of these equalities to the main tableau 3061 * and if this happens to result in a row with a final coefficient 3062 * that is one or negative one, we use it to kill a column 3063 * in the main tableau. Otherwise, we discard the tentatively 3064 * added row. 3065 */ 3066static void propagate_equalities(struct isl_context_gbr *cgbr, 3067 struct isl_tab *tab, unsigned first) 3068{ 3069 int i; 3070 struct isl_vec *eq = NULL; 3071 3072 eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var); 3073 if (!eq) 3074 goto error; 3075 3076 if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0) 3077 goto error; 3078 3079 isl_seq_clr(eq->el + 1 + tab->n_param, 3080 tab->n_var - tab->n_param - tab->n_div); 3081 for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) { 3082 int j; 3083 int r; 3084 struct isl_tab_undo *snap; 3085 snap = isl_tab_snap(tab); 3086 3087 isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param); 3088 isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div, 3089 cgbr->tab->bmap->ineq[i] + 1 + tab->n_param, 3090 tab->n_div); 3091 3092 r = isl_tab_add_row(tab, eq->el); 3093 if (r < 0) 3094 goto error; 3095 r = tab->con[r].index; 3096 j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M); 3097 if (j < 0 || j < tab->n_dead || 3098 !isl_int_is_one(tab->mat->row[r][0]) || 3099 (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) && 3100 !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) { 3101 if (isl_tab_rollback(tab, snap) < 0) 3102 goto error; 3103 continue; 3104 } 3105 if (isl_tab_pivot(tab, r, j) < 0) 3106 goto error; 3107 if (isl_tab_kill_col(tab, j) < 0) 3108 goto error; 3109 3110 if (restore_lexmin(tab) < 0) 3111 goto error; 3112 } 3113 3114 isl_vec_free(eq); 3115 3116 return; 3117error: 3118 isl_vec_free(eq); 3119 isl_tab_free(cgbr->tab); 3120 cgbr->tab = NULL; 3121} 3122 3123static int context_gbr_detect_equalities(struct isl_context *context, 3124 struct isl_tab *tab) 3125{ 3126 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3127 struct isl_ctx *ctx; 3128 unsigned n_ineq; 3129 3130 ctx = cgbr->tab->mat->ctx; 3131 3132 if (!cgbr->cone) { 3133 struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab); 3134 cgbr->cone = isl_tab_from_recession_cone(bset, 0); 3135 if (!cgbr->cone) 3136 goto error; 3137 if (isl_tab_track_bset(cgbr->cone, 3138 isl_basic_set_copy(bset)) < 0) 3139 goto error; 3140 } 3141 if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0) 3142 goto error; 3143 3144 n_ineq = cgbr->tab->bmap->n_ineq; 3145 cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone); 3146 if (!cgbr->tab) 3147 return -1; 3148 if (cgbr->tab->bmap->n_ineq > n_ineq) 3149 propagate_equalities(cgbr, tab, n_ineq); 3150 3151 return 0; 3152error: 3153 isl_tab_free(cgbr->tab); 3154 cgbr->tab = NULL; 3155 return -1; 3156} 3157 3158static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab, 3159 struct isl_vec *div) 3160{ 3161 return get_div(tab, context, div); 3162} 3163 3164static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div) 3165{ 3166 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3167 if (cgbr->cone) { 3168 int k; 3169 3170 if (isl_tab_extend_cons(cgbr->cone, 3) < 0) 3171 return -1; 3172 if (isl_tab_extend_vars(cgbr->cone, 1) < 0) 3173 return -1; 3174 if (isl_tab_allocate_var(cgbr->cone) <0) 3175 return -1; 3176 3177 cgbr->cone->bmap = isl_basic_map_extend_space(cgbr->cone->bmap, 3178 isl_basic_map_get_space(cgbr->cone->bmap), 1, 0, 2); 3179 k = isl_basic_map_alloc_div(cgbr->cone->bmap); 3180 if (k < 0) 3181 return -1; 3182 isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size); 3183 if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0) 3184 return -1; 3185 } 3186 return context_tab_add_div(cgbr->tab, div, 3187 context_gbr_add_ineq_wrap, context); 3188} 3189 3190static int context_gbr_best_split(struct isl_context *context, 3191 struct isl_tab *tab) 3192{ 3193 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3194 struct isl_tab_undo *snap; 3195 int r; 3196 3197 snap = isl_tab_snap(cgbr->tab); 3198 r = best_split(tab, cgbr->tab); 3199 3200 if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0) 3201 return -1; 3202 3203 return r; 3204} 3205 3206static int context_gbr_is_empty(struct isl_context *context) 3207{ 3208 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3209 if (!cgbr->tab) 3210 return -1; 3211 return cgbr->tab->empty; 3212} 3213 3214struct isl_gbr_tab_undo { 3215 struct isl_tab_undo *tab_snap; 3216 struct isl_tab_undo *shifted_snap; 3217 struct isl_tab_undo *cone_snap; 3218}; 3219 3220static void *context_gbr_save(struct isl_context *context) 3221{ 3222 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3223 struct isl_gbr_tab_undo *snap; 3224 3225 if (!cgbr->tab) 3226 return NULL; 3227 3228 snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo); 3229 if (!snap) 3230 return NULL; 3231 3232 snap->tab_snap = isl_tab_snap(cgbr->tab); 3233 if (isl_tab_save_samples(cgbr->tab) < 0) 3234 goto error; 3235 3236 if (cgbr->shifted) 3237 snap->shifted_snap = isl_tab_snap(cgbr->shifted); 3238 else 3239 snap->shifted_snap = NULL; 3240 3241 if (cgbr->cone) 3242 snap->cone_snap = isl_tab_snap(cgbr->cone); 3243 else 3244 snap->cone_snap = NULL; 3245 3246 return snap; 3247error: 3248 free(snap); 3249 return NULL; 3250} 3251 3252static void context_gbr_restore(struct isl_context *context, void *save) 3253{ 3254 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3255 struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save; 3256 if (!snap) 3257 goto error; 3258 if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) { 3259 isl_tab_free(cgbr->tab); 3260 cgbr->tab = NULL; 3261 } 3262 3263 if (snap->shifted_snap) { 3264 if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0) 3265 goto error; 3266 } else if (cgbr->shifted) { 3267 isl_tab_free(cgbr->shifted); 3268 cgbr->shifted = NULL; 3269 } 3270 3271 if (snap->cone_snap) { 3272 if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0) 3273 goto error; 3274 } else if (cgbr->cone) { 3275 isl_tab_free(cgbr->cone); 3276 cgbr->cone = NULL; 3277 } 3278 3279 free(snap); 3280 3281 return; 3282error: 3283 free(snap); 3284 isl_tab_free(cgbr->tab); 3285 cgbr->tab = NULL; 3286} 3287 3288static void context_gbr_discard(void *save) 3289{ 3290 struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save; 3291 free(snap); 3292} 3293 3294static int context_gbr_is_ok(struct isl_context *context) 3295{ 3296 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3297 return !!cgbr->tab; 3298} 3299 3300static void context_gbr_invalidate(struct isl_context *context) 3301{ 3302 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3303 isl_tab_free(cgbr->tab); 3304 cgbr->tab = NULL; 3305} 3306 3307static void context_gbr_free(struct isl_context *context) 3308{ 3309 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; 3310 isl_tab_free(cgbr->tab); 3311 isl_tab_free(cgbr->shifted); 3312 isl_tab_free(cgbr->cone); 3313 free(cgbr); 3314} 3315 3316struct isl_context_op isl_context_gbr_op = { 3317 context_gbr_detect_nonnegative_parameters, 3318 context_gbr_peek_basic_set, 3319 context_gbr_peek_tab, 3320 context_gbr_add_eq, 3321 context_gbr_add_ineq, 3322 context_gbr_ineq_sign, 3323 context_gbr_test_ineq, 3324 context_gbr_get_div, 3325 context_gbr_add_div, 3326 context_gbr_detect_equalities, 3327 context_gbr_best_split, 3328 context_gbr_is_empty, 3329 context_gbr_is_ok, 3330 context_gbr_save, 3331 context_gbr_restore, 3332 context_gbr_discard, 3333 context_gbr_invalidate, 3334 context_gbr_free, 3335}; 3336 3337static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom) 3338{ 3339 struct isl_context_gbr *cgbr; 3340 3341 if (!dom) 3342 return NULL; 3343 3344 cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr); 3345 if (!cgbr) 3346 return NULL; 3347 3348 cgbr->context.op = &isl_context_gbr_op; 3349 3350 cgbr->shifted = NULL; 3351 cgbr->cone = NULL; 3352 cgbr->tab = isl_tab_from_basic_set(dom, 1); 3353 cgbr->tab = isl_tab_init_samples(cgbr->tab); 3354 if (!cgbr->tab) 3355 goto error; 3356 check_gbr_integer_feasible(cgbr); 3357 3358 return &cgbr->context; 3359error: 3360 cgbr->context.op->free(&cgbr->context); 3361 return NULL; 3362} 3363 3364static struct isl_context *isl_context_alloc(struct isl_basic_set *dom) 3365{ 3366 if (!dom) 3367 return NULL; 3368 3369 if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN) 3370 return isl_context_lex_alloc(dom); 3371 else 3372 return isl_context_gbr_alloc(dom); 3373} 3374 3375/* Construct an isl_sol_map structure for accumulating the solution. 3376 * If track_empty is set, then we also keep track of the parts 3377 * of the context where there is no solution. 3378 * If max is set, then we are solving a maximization, rather than 3379 * a minimization problem, which means that the variables in the 3380 * tableau have value "M - x" rather than "M + x". 3381 */ 3382static struct isl_sol *sol_map_init(struct isl_basic_map *bmap, 3383 struct isl_basic_set *dom, int track_empty, int max) 3384{ 3385 struct isl_sol_map *sol_map = NULL; 3386 3387 if (!bmap) 3388 goto error; 3389 3390 sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map); 3391 if (!sol_map) 3392 goto error; 3393 3394 sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); 3395 sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap; 3396 sol_map->sol.dec_level.sol = &sol_map->sol; 3397 sol_map->sol.max = max; 3398 sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out); 3399 sol_map->sol.add = &sol_map_add_wrap; 3400 sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL; 3401 sol_map->sol.free = &sol_map_free_wrap; 3402 sol_map->map = isl_map_alloc_space(isl_basic_map_get_space(bmap), 1, 3403 ISL_MAP_DISJOINT); 3404 if (!sol_map->map) 3405 goto error; 3406 3407 sol_map->sol.context = isl_context_alloc(dom); 3408 if (!sol_map->sol.context) 3409 goto error; 3410 3411 if (track_empty) { 3412 sol_map->empty = isl_set_alloc_space(isl_basic_set_get_space(dom), 3413 1, ISL_SET_DISJOINT); 3414 if (!sol_map->empty) 3415 goto error; 3416 } 3417 3418 isl_basic_set_free(dom); 3419 return &sol_map->sol; 3420error: 3421 isl_basic_set_free(dom); 3422 sol_map_free(sol_map); 3423 return NULL; 3424} 3425 3426/* Check whether all coefficients of (non-parameter) variables 3427 * are non-positive, meaning that no pivots can be performed on the row. 3428 */ 3429static int is_critical(struct isl_tab *tab, int row) 3430{ 3431 int j; 3432 unsigned off = 2 + tab->M; 3433 3434 for (j = tab->n_dead; j < tab->n_col; ++j) { 3435 if (tab->col_var[j] >= 0 && 3436 (tab->col_var[j] < tab->n_param || 3437 tab->col_var[j] >= tab->n_var - tab->n_div)) 3438 continue; 3439 3440 if (isl_int_is_pos(tab->mat->row[row][off + j])) 3441 return 0; 3442 } 3443 3444 return 1; 3445} 3446 3447/* Check whether the inequality represented by vec is strict over the integers, 3448 * i.e., there are no integer values satisfying the constraint with 3449 * equality. This happens if the gcd of the coefficients is not a divisor 3450 * of the constant term. If so, scale the constraint down by the gcd 3451 * of the coefficients. 3452 */ 3453static int is_strict(struct isl_vec *vec) 3454{ 3455 isl_int gcd; 3456 int strict = 0; 3457 3458 isl_int_init(gcd); 3459 isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd); 3460 if (!isl_int_is_one(gcd)) { 3461 strict = !isl_int_is_divisible_by(vec->el[0], gcd); 3462 isl_int_fdiv_q(vec->el[0], vec->el[0], gcd); 3463 isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1); 3464 } 3465 isl_int_clear(gcd); 3466 3467 return strict; 3468} 3469 3470/* Determine the sign of the given row of the main tableau. 3471 * The result is one of 3472 * isl_tab_row_pos: always non-negative; no pivot needed 3473 * isl_tab_row_neg: always non-positive; pivot 3474 * isl_tab_row_any: can be both positive and negative; split 3475 * 3476 * We first handle some simple cases 3477 * - the row sign may be known already 3478 * - the row may be obviously non-negative 3479 * - the parametric constant may be equal to that of another row 3480 * for which we know the sign. This sign will be either "pos" or 3481 * "any". If it had been "neg" then we would have pivoted before. 3482 * 3483 * If none of these cases hold, we check the value of the row for each 3484 * of the currently active samples. Based on the signs of these values 3485 * we make an initial determination of the sign of the row. 3486 * 3487 * all zero -> unk(nown) 3488 * all non-negative -> pos 3489 * all non-positive -> neg 3490 * both negative and positive -> all 3491 * 3492 * If we end up with "all", we are done. 3493 * Otherwise, we perform a check for positive and/or negative 3494 * values as follows. 3495 * 3496 * samples neg unk pos 3497 * <0 ? Y N Y N 3498 * pos any pos 3499 * >0 ? Y N Y N 3500 * any neg any neg 3501 * 3502 * There is no special sign for "zero", because we can usually treat zero 3503 * as either non-negative or non-positive, whatever works out best. 3504 * However, if the row is "critical", meaning that pivoting is impossible 3505 * then we don't want to limp zero with the non-positive case, because 3506 * then we we would lose the solution for those values of the parameters 3507 * where the value of the row is zero. Instead, we treat 0 as non-negative 3508 * ensuring a split if the row can attain both zero and negative values. 3509 * The same happens when the original constraint was one that could not 3510 * be satisfied with equality by any integer values of the parameters. 3511 * In this case, we normalize the constraint, but then a value of zero 3512 * for the normalized constraint is actually a positive value for the 3513 * original constraint, so again we need to treat zero as non-negative. 3514 * In both these cases, we have the following decision tree instead: 3515 * 3516 * all non-negative -> pos 3517 * all negative -> neg 3518 * both negative and non-negative -> all 3519 * 3520 * samples neg pos 3521 * <0 ? Y N 3522 * any pos 3523 * >=0 ? Y N 3524 * any neg 3525 */ 3526static enum isl_tab_row_sign row_sign(struct isl_tab *tab, 3527 struct isl_sol *sol, int row) 3528{ 3529 struct isl_vec *ineq = NULL; 3530 enum isl_tab_row_sign res = isl_tab_row_unknown; 3531 int critical; 3532 int strict; 3533 int row2; 3534 3535 if (tab->row_sign[row] != isl_tab_row_unknown) 3536 return tab->row_sign[row]; 3537 if (is_obviously_nonneg(tab, row)) 3538 return isl_tab_row_pos; 3539 for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) { 3540 if (tab->row_sign[row2] == isl_tab_row_unknown) 3541 continue; 3542 if (identical_parameter_line(tab, row, row2)) 3543 return tab->row_sign[row2]; 3544 } 3545 3546 critical = is_critical(tab, row); 3547 3548 ineq = get_row_parameter_ineq(tab, row); 3549 if (!ineq) 3550 goto error; 3551 3552 strict = is_strict(ineq); 3553 3554 res = sol->context->op->ineq_sign(sol->context, ineq->el, 3555 critical || strict); 3556 3557 if (res == isl_tab_row_unknown || res == isl_tab_row_pos) { 3558 /* test for negative values */ 3559 int feasible; 3560 isl_seq_neg(ineq->el, ineq->el, ineq->size); 3561 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); 3562 3563 feasible = sol->context->op->test_ineq(sol->context, ineq->el); 3564 if (feasible < 0) 3565 goto error; 3566 if (!feasible) 3567 res = isl_tab_row_pos; 3568 else 3569 res = (res == isl_tab_row_unknown) ? isl_tab_row_neg 3570 : isl_tab_row_any; 3571 if (res == isl_tab_row_neg) { 3572 isl_seq_neg(ineq->el, ineq->el, ineq->size); 3573 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); 3574 } 3575 } 3576 3577 if (res == isl_tab_row_neg) { 3578 /* test for positive values */ 3579 int feasible; 3580 if (!critical && !strict) 3581 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); 3582 3583 feasible = sol->context->op->test_ineq(sol->context, ineq->el); 3584 if (feasible < 0) 3585 goto error; 3586 if (feasible) 3587 res = isl_tab_row_any; 3588 } 3589 3590 isl_vec_free(ineq); 3591 return res; 3592error: 3593 isl_vec_free(ineq); 3594 return isl_tab_row_unknown; 3595} 3596 3597static void find_solutions(struct isl_sol *sol, struct isl_tab *tab); 3598 3599/* Find solutions for values of the parameters that satisfy the given 3600 * inequality. 3601 * 3602 * We currently take a snapshot of the context tableau that is reset 3603 * when we return from this function, while we make a copy of the main 3604 * tableau, leaving the original main tableau untouched. 3605 * These are fairly arbitrary choices. Making a copy also of the context 3606 * tableau would obviate the need to undo any changes made to it later, 3607 * while taking a snapshot of the main tableau could reduce memory usage. 3608 * If we were to switch to taking a snapshot of the main tableau, 3609 * we would have to keep in mind that we need to save the row signs 3610 * and that we need to do this before saving the current basis 3611 * such that the basis has been restore before we restore the row signs. 3612 */ 3613static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq) 3614{ 3615 void *saved; 3616 3617 if (!sol->context) 3618 goto error; 3619 saved = sol->context->op->save(sol->context); 3620 3621 tab = isl_tab_dup(tab); 3622 if (!tab) 3623 goto error; 3624 3625 sol->context->op->add_ineq(sol->context, ineq, 0, 1); 3626 3627 find_solutions(sol, tab); 3628 3629 if (!sol->error) 3630 sol->context->op->restore(sol->context, saved); 3631 else 3632 sol->context->op->discard(saved); 3633 return; 3634error: 3635 sol->error = 1; 3636} 3637 3638/* Record the absence of solutions for those values of the parameters 3639 * that do not satisfy the given inequality with equality. 3640 */ 3641static void no_sol_in_strict(struct isl_sol *sol, 3642 struct isl_tab *tab, struct isl_vec *ineq) 3643{ 3644 int empty; 3645 void *saved; 3646 3647 if (!sol->context || sol->error) 3648 goto error; 3649 saved = sol->context->op->save(sol->context); 3650 3651 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); 3652 3653 sol->context->op->add_ineq(sol->context, ineq->el, 1, 0); 3654 if (!sol->context) 3655 goto error; 3656 3657 empty = tab->empty; 3658 tab->empty = 1; 3659 sol_add(sol, tab); 3660 tab->empty = empty; 3661 3662 isl_int_add_ui(ineq->el[0], ineq->el[0], 1); 3663 3664 sol->context->op->restore(sol->context, saved); 3665 return; 3666error: 3667 sol->error = 1; 3668} 3669 3670/* Compute the lexicographic minimum of the set represented by the main 3671 * tableau "tab" within the context "sol->context_tab". 3672 * On entry the sample value of the main tableau is lexicographically 3673 * less than or equal to this lexicographic minimum. 3674 * Pivots are performed until a feasible point is found, which is then 3675 * necessarily equal to the minimum, or until the tableau is found to 3676 * be infeasible. Some pivots may need to be performed for only some 3677 * feasible values of the context tableau. If so, the context tableau 3678 * is split into a part where the pivot is needed and a part where it is not. 3679 * 3680 * Whenever we enter the main loop, the main tableau is such that no 3681 * "obvious" pivots need to be performed on it, where "obvious" means 3682 * that the given row can be seen to be negative without looking at 3683 * the context tableau. In particular, for non-parametric problems, 3684 * no pivots need to be performed on the main tableau. 3685 * The caller of find_solutions is responsible for making this property 3686 * hold prior to the first iteration of the loop, while restore_lexmin 3687 * is called before every other iteration. 3688 * 3689 * Inside the main loop, we first examine the signs of the rows of 3690 * the main tableau within the context of the context tableau. 3691 * If we find a row that is always non-positive for all values of 3692 * the parameters satisfying the context tableau and negative for at 3693 * least one value of the parameters, we perform the appropriate pivot 3694 * and start over. An exception is the case where no pivot can be 3695 * performed on the row. In this case, we require that the sign of 3696 * the row is negative for all values of the parameters (rather than just 3697 * non-positive). This special case is handled inside row_sign, which 3698 * will say that the row can have any sign if it determines that it can 3699 * attain both negative and zero values. 3700 * 3701 * If we can't find a row that always requires a pivot, but we can find 3702 * one or more rows that require a pivot for some values of the parameters 3703 * (i.e., the row can attain both positive and negative signs), then we split 3704 * the context tableau into two parts, one where we force the sign to be 3705 * non-negative and one where we force is to be negative. 3706 * The non-negative part is handled by a recursive call (through find_in_pos). 3707 * Upon returning from this call, we continue with the negative part and 3708 * perform the required pivot. 3709 * 3710 * If no such rows can be found, all rows are non-negative and we have 3711 * found a (rational) feasible point. If we only wanted a rational point 3712 * then we are done. 3713 * Otherwise, we check if all values of the sample point of the tableau 3714 * are integral for the variables. If so, we have found the minimal 3715 * integral point and we are done. 3716 * If the sample point is not integral, then we need to make a distinction 3717 * based on whether the constant term is non-integral or the coefficients 3718 * of the parameters. Furthermore, in order to decide how to handle 3719 * the non-integrality, we also need to know whether the coefficients 3720 * of the other columns in the tableau are integral. This leads 3721 * to the following table. The first two rows do not correspond 3722 * to a non-integral sample point and are only mentioned for completeness. 3723 * 3724 * constant parameters other 3725 * 3726 * int int int | 3727 * int int rat | -> no problem 3728 * 3729 * rat int int -> fail 3730 * 3731 * rat int rat -> cut 3732 * 3733 * int rat rat | 3734 * rat rat rat | -> parametric cut 3735 * 3736 * int rat int | 3737 * rat rat int | -> split context 3738 * 3739 * If the parametric constant is completely integral, then there is nothing 3740 * to be done. If the constant term is non-integral, but all the other 3741 * coefficient are integral, then there is nothing that can be done 3742 * and the tableau has no integral solution. 3743 * If, on the other hand, one or more of the other columns have rational 3744 * coefficients, but the parameter coefficients are all integral, then 3745 * we can perform a regular (non-parametric) cut. 3746 * Finally, if there is any parameter coefficient that is non-integral, 3747 * then we need to involve the context tableau. There are two cases here. 3748 * If at least one other column has a rational coefficient, then we 3749 * can perform a parametric cut in the main tableau by adding a new 3750 * integer division in the context tableau. 3751 * If all other columns have integral coefficients, then we need to 3752 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m 3753 * is always integral. We do this by introducing an integer division 3754 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should 3755 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i. 3756 * Since q is expressed in the tableau as 3757 * c + \sum a_i y_i - m q >= 0 3758 * -c - \sum a_i y_i + m q + m - 1 >= 0 3759 * it is sufficient to add the inequality 3760 * -c - \sum a_i y_i + m q >= 0 3761 * In the part of the context where this inequality does not hold, the 3762 * main tableau is marked as being empty. 3763 */ 3764static void find_solutions(struct isl_sol *sol, struct isl_tab *tab) 3765{ 3766 struct isl_context *context; 3767 int r; 3768 3769 if (!tab || sol->error) 3770 goto error; 3771 3772 context = sol->context; 3773 3774 if (tab->empty) 3775 goto done; 3776 if (context->op->is_empty(context)) 3777 goto done; 3778 3779 for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) { 3780 int flags; 3781 int row; 3782 enum isl_tab_row_sign sgn; 3783 int split = -1; 3784 int n_split = 0; 3785 3786 for (row = tab->n_redundant; row < tab->n_row; ++row) { 3787 if (!isl_tab_var_from_row(tab, row)->is_nonneg) 3788 continue; 3789 sgn = row_sign(tab, sol, row); 3790 if (!sgn) 3791 goto error; 3792 tab->row_sign[row] = sgn; 3793 if (sgn == isl_tab_row_any) 3794 n_split++; 3795 if (sgn == isl_tab_row_any && split == -1) 3796 split = row; 3797 if (sgn == isl_tab_row_neg) 3798 break; 3799 } 3800 if (row < tab->n_row) 3801 continue; 3802 if (split != -1) { 3803 struct isl_vec *ineq; 3804 if (n_split != 1) 3805 split = context->op->best_split(context, tab); 3806 if (split < 0) 3807 goto error; 3808 ineq = get_row_parameter_ineq(tab, split); 3809 if (!ineq) 3810 goto error; 3811 is_strict(ineq); 3812 for (row = tab->n_redundant; row < tab->n_row; ++row) { 3813 if (!isl_tab_var_from_row(tab, row)->is_nonneg) 3814 continue; 3815 if (tab->row_sign[row] == isl_tab_row_any) 3816 tab->row_sign[row] = isl_tab_row_unknown; 3817 } 3818 tab->row_sign[split] = isl_tab_row_pos; 3819 sol_inc_level(sol); 3820 find_in_pos(sol, tab, ineq->el); 3821 tab->row_sign[split] = isl_tab_row_neg; 3822 row = split; 3823 isl_seq_neg(ineq->el, ineq->el, ineq->size); 3824 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); 3825 if (!sol->error) 3826 context->op->add_ineq(context, ineq->el, 0, 1); 3827 isl_vec_free(ineq); 3828 if (sol->error) 3829 goto error; 3830 continue; 3831 } 3832 if (tab->rational) 3833 break; 3834 row = first_non_integer_row(tab, &flags); 3835 if (row < 0) 3836 break; 3837 if (ISL_FL_ISSET(flags, I_PAR)) { 3838 if (ISL_FL_ISSET(flags, I_VAR)) { 3839 if (isl_tab_mark_empty(tab) < 0) 3840 goto error; 3841 break; 3842 } 3843 row = add_cut(tab, row); 3844 } else if (ISL_FL_ISSET(flags, I_VAR)) { 3845 struct isl_vec *div; 3846 struct isl_vec *ineq; 3847 int d; 3848 div = get_row_split_div(tab, row); 3849 if (!div) 3850 goto error; 3851 d = context->op->get_div(context, tab, div); 3852 isl_vec_free(div); 3853 if (d < 0) 3854 goto error; 3855 ineq = ineq_for_div(context->op->peek_basic_set(context), d); 3856 if (!ineq) 3857 goto error; 3858 sol_inc_level(sol); 3859 no_sol_in_strict(sol, tab, ineq); 3860 isl_seq_neg(ineq->el, ineq->el, ineq->size); 3861 context->op->add_ineq(context, ineq->el, 1, 1); 3862 isl_vec_free(ineq); 3863 if (sol->error || !context->op->is_ok(context)) 3864 goto error; 3865 tab = set_row_cst_to_div(tab, row, d); 3866 if (context->op->is_empty(context)) 3867 break; 3868 } else 3869 row = add_parametric_cut(tab, row, context); 3870 if (row < 0) 3871 goto error; 3872 } 3873 if (r < 0) 3874 goto error; 3875done: 3876 sol_add(sol, tab); 3877 isl_tab_free(tab); 3878 return; 3879error: 3880 isl_tab_free(tab); 3881 sol->error = 1; 3882} 3883 3884/* Does "sol" contain a pair of partial solutions that could potentially 3885 * be merged? 3886 * 3887 * We currently only check that "sol" is not in an error state 3888 * and that there are at least two partial solutions of which the final two 3889 * are defined at the same level. 3890 */ 3891static int sol_has_mergeable_solutions(struct isl_sol *sol) 3892{ 3893 if (sol->error) 3894 return 0; 3895 if (!sol->partial) 3896 return 0; 3897 if (!sol->partial->next) 3898 return 0; 3899 return sol->partial->level == sol->partial->next->level; 3900} 3901 3902/* Compute the lexicographic minimum of the set represented by the main 3903 * tableau "tab" within the context "sol->context_tab". 3904 * 3905 * As a preprocessing step, we first transfer all the purely parametric 3906 * equalities from the main tableau to the context tableau, i.e., 3907 * parameters that have been pivoted to a row. 3908 * These equalities are ignored by the main algorithm, because the 3909 * corresponding rows may not be marked as being non-negative. 3910 * In parts of the context where the added equality does not hold, 3911 * the main tableau is marked as being empty. 3912 * 3913 * Before we embark on the actual computation, we save a copy 3914 * of the context. When we return, we check if there are any 3915 * partial solutions that can potentially be merged. If so, 3916 * we perform a rollback to the initial state of the context. 3917 * The merging of partial solutions happens inside calls to 3918 * sol_dec_level that are pushed onto the undo stack of the context. 3919 * If there are no partial solutions that can potentially be merged 3920 * then the rollback is skipped as it would just be wasted effort. 3921 */ 3922static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab) 3923{ 3924 int row; 3925 void *saved; 3926 3927 if (!tab) 3928 goto error; 3929 3930 sol->level = 0; 3931 3932 for (row = tab->n_redundant; row < tab->n_row; ++row) { 3933 int p; 3934 struct isl_vec *eq; 3935 3936 if (tab->row_var[row] < 0) 3937 continue; 3938 if (tab->row_var[row] >= tab->n_param && 3939 tab->row_var[row] < tab->n_var - tab->n_div) 3940 continue; 3941 if (tab->row_var[row] < tab->n_param) 3942 p = tab->row_var[row]; 3943 else 3944 p = tab->row_var[row] 3945 + tab->n_param - (tab->n_var - tab->n_div); 3946 3947 eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div); 3948 if (!eq) 3949 goto error; 3950 get_row_parameter_line(tab, row, eq->el); 3951 isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]); 3952 eq = isl_vec_normalize(eq); 3953 3954 sol_inc_level(sol); 3955 no_sol_in_strict(sol, tab, eq); 3956 3957 isl_seq_neg(eq->el, eq->el, eq->size); 3958 sol_inc_level(sol); 3959 no_sol_in_strict(sol, tab, eq); 3960 isl_seq_neg(eq->el, eq->el, eq->size); 3961 3962 sol->context->op->add_eq(sol->context, eq->el, 1, 1); 3963 3964 isl_vec_free(eq); 3965 3966 if (isl_tab_mark_redundant(tab, row) < 0) 3967 goto error; 3968 3969 if (sol->context->op->is_empty(sol->context)) 3970 break; 3971 3972 row = tab->n_redundant - 1; 3973 } 3974 3975 saved = sol->context->op->save(sol->context); 3976 3977 find_solutions(sol, tab); 3978 3979 if (sol_has_mergeable_solutions(sol)) 3980 sol->context->op->restore(sol->context, saved); 3981 else 3982 sol->context->op->discard(saved); 3983 3984 sol->level = 0; 3985 sol_pop(sol); 3986 3987 return; 3988error: 3989 isl_tab_free(tab); 3990 sol->error = 1; 3991} 3992 3993/* Check if integer division "div" of "dom" also occurs in "bmap". 3994 * If so, return its position within the divs. 3995 * If not, return -1. 3996 */ 3997static int find_context_div(struct isl_basic_map *bmap, 3998 struct isl_basic_set *dom, unsigned div) 3999{ 4000 int i; 4001 unsigned b_dim = isl_space_dim(bmap->dim, isl_dim_all); 4002 unsigned d_dim = isl_space_dim(dom->dim, isl_dim_all); 4003 4004 if (isl_int_is_zero(dom->div[div][0])) 4005 return -1; 4006 if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1) 4007 return -1; 4008 4009 for (i = 0; i < bmap->n_div; ++i) { 4010 if (isl_int_is_zero(bmap->div[i][0])) 4011 continue; 4012 if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim, 4013 (b_dim - d_dim) + bmap->n_div) != -1) 4014 continue; 4015 if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim)) 4016 return i; 4017 } 4018 return -1; 4019} 4020 4021/* The correspondence between the variables in the main tableau, 4022 * the context tableau, and the input map and domain is as follows. 4023 * The first n_param and the last n_div variables of the main tableau 4024 * form the variables of the context tableau. 4025 * In the basic map, these n_param variables correspond to the 4026 * parameters and the input dimensions. In the domain, they correspond 4027 * to the parameters and the set dimensions. 4028 * The n_div variables correspond to the integer divisions in the domain. 4029 * To ensure that everything lines up, we may need to copy some of the 4030 * integer divisions of the domain to the map. These have to be placed 4031 * in the same order as those in the context and they have to be placed 4032 * after any other integer divisions that the map may have. 4033 * This function performs the required reordering. 4034 */ 4035static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap, 4036 struct isl_basic_set *dom) 4037{ 4038 int i; 4039 int common = 0; 4040 int other; 4041 4042 for (i = 0; i < dom->n_div; ++i) 4043 if (find_context_div(bmap, dom, i) != -1) 4044 common++; 4045 other = bmap->n_div - common; 4046 if (dom->n_div - common > 0) { 4047 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 4048 dom->n_div - common, 0, 0); 4049 if (!bmap) 4050 return NULL; 4051 } 4052 for (i = 0; i < dom->n_div; ++i) { 4053 int pos = find_context_div(bmap, dom, i); 4054 if (pos < 0) { 4055 pos = isl_basic_map_alloc_div(bmap); 4056 if (pos < 0) 4057 goto error; 4058 isl_int_set_si(bmap->div[pos][0], 0); 4059 } 4060 if (pos != other + i) 4061 isl_basic_map_swap_div(bmap, pos, other + i); 4062 } 4063 return bmap; 4064error: 4065 isl_basic_map_free(bmap); 4066 return NULL; 4067} 4068 4069/* Base case of isl_tab_basic_map_partial_lexopt, after removing 4070 * some obvious symmetries. 4071 * 4072 * We make sure the divs in the domain are properly ordered, 4073 * because they will be added one by one in the given order 4074 * during the construction of the solution map. 4075 */ 4076static struct isl_sol *basic_map_partial_lexopt_base( 4077 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4078 __isl_give isl_set **empty, int max, 4079 struct isl_sol *(*init)(__isl_keep isl_basic_map *bmap, 4080 __isl_take isl_basic_set *dom, int track_empty, int max)) 4081{ 4082 struct isl_tab *tab; 4083 struct isl_sol *sol = NULL; 4084 struct isl_context *context; 4085 4086 if (dom->n_div) { 4087 dom = isl_basic_set_order_divs(dom); 4088 bmap = align_context_divs(bmap, dom); 4089 } 4090 sol = init(bmap, dom, !!empty, max); 4091 if (!sol) 4092 goto error; 4093 4094 context = sol->context; 4095 if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context))) 4096 /* nothing */; 4097 else if (isl_basic_map_plain_is_empty(bmap)) { 4098 if (sol->add_empty) 4099 sol->add_empty(sol, 4100 isl_basic_set_copy(context->op->peek_basic_set(context))); 4101 } else { 4102 tab = tab_for_lexmin(bmap, 4103 context->op->peek_basic_set(context), 1, max); 4104 tab = context->op->detect_nonnegative_parameters(context, tab); 4105 find_solutions_main(sol, tab); 4106 } 4107 if (sol->error) 4108 goto error; 4109 4110 isl_basic_map_free(bmap); 4111 return sol; 4112error: 4113 sol_free(sol); 4114 isl_basic_map_free(bmap); 4115 return NULL; 4116} 4117 4118/* Base case of isl_tab_basic_map_partial_lexopt, after removing 4119 * some obvious symmetries. 4120 * 4121 * We call basic_map_partial_lexopt_base and extract the results. 4122 */ 4123static __isl_give isl_map *basic_map_partial_lexopt_base_map( 4124 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4125 __isl_give isl_set **empty, int max) 4126{ 4127 isl_map *result = NULL; 4128 struct isl_sol *sol; 4129 struct isl_sol_map *sol_map; 4130 4131 sol = basic_map_partial_lexopt_base(bmap, dom, empty, max, 4132 &sol_map_init); 4133 if (!sol) 4134 return NULL; 4135 sol_map = (struct isl_sol_map *) sol; 4136 4137 result = isl_map_copy(sol_map->map); 4138 if (empty) 4139 *empty = isl_set_copy(sol_map->empty); 4140 sol_free(&sol_map->sol); 4141 return result; 4142} 4143 4144/* Structure used during detection of parallel constraints. 4145 * n_in: number of "input" variables: isl_dim_param + isl_dim_in 4146 * n_out: number of "output" variables: isl_dim_out + isl_dim_div 4147 * val: the coefficients of the output variables 4148 */ 4149struct isl_constraint_equal_info { 4150 isl_basic_map *bmap; 4151 unsigned n_in; 4152 unsigned n_out; 4153 isl_int *val; 4154}; 4155 4156/* Check whether the coefficients of the output variables 4157 * of the constraint in "entry" are equal to info->val. 4158 */ 4159static int constraint_equal(const void *entry, const void *val) 4160{ 4161 isl_int **row = (isl_int **)entry; 4162 const struct isl_constraint_equal_info *info = val; 4163 4164 return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out); 4165} 4166 4167/* Check whether "bmap" has a pair of constraints that have 4168 * the same coefficients for the output variables. 4169 * Note that the coefficients of the existentially quantified 4170 * variables need to be zero since the existentially quantified 4171 * of the result are usually not the same as those of the input. 4172 * the isl_dim_out and isl_dim_div dimensions. 4173 * If so, return 1 and return the row indices of the two constraints 4174 * in *first and *second. 4175 */ 4176static int parallel_constraints(__isl_keep isl_basic_map *bmap, 4177 int *first, int *second) 4178{ 4179 int i; 4180 isl_ctx *ctx = isl_basic_map_get_ctx(bmap); 4181 struct isl_hash_table *table = NULL; 4182 struct isl_hash_table_entry *entry; 4183 struct isl_constraint_equal_info info; 4184 unsigned n_out; 4185 unsigned n_div; 4186 4187 ctx = isl_basic_map_get_ctx(bmap); 4188 table = isl_hash_table_alloc(ctx, bmap->n_ineq); 4189 if (!table) 4190 goto error; 4191 4192 info.n_in = isl_basic_map_dim(bmap, isl_dim_param) + 4193 isl_basic_map_dim(bmap, isl_dim_in); 4194 info.bmap = bmap; 4195 n_out = isl_basic_map_dim(bmap, isl_dim_out); 4196 n_div = isl_basic_map_dim(bmap, isl_dim_div); 4197 info.n_out = n_out + n_div; 4198 for (i = 0; i < bmap->n_ineq; ++i) { 4199 uint32_t hash; 4200 4201 info.val = bmap->ineq[i] + 1 + info.n_in; 4202 if (isl_seq_first_non_zero(info.val, n_out) < 0) 4203 continue; 4204 if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0) 4205 continue; 4206 hash = isl_seq_get_hash(info.val, info.n_out); 4207 entry = isl_hash_table_find(ctx, table, hash, 4208 constraint_equal, &info, 1); 4209 if (!entry) 4210 goto error; 4211 if (entry->data) 4212 break; 4213 entry->data = &bmap->ineq[i]; 4214 } 4215 4216 if (i < bmap->n_ineq) { 4217 *first = ((isl_int **)entry->data) - bmap->ineq; 4218 *second = i; 4219 } 4220 4221 isl_hash_table_free(ctx, table); 4222 4223 return i < bmap->n_ineq; 4224error: 4225 isl_hash_table_free(ctx, table); 4226 return -1; 4227} 4228 4229/* Given a set of upper bounds in "var", add constraints to "bset" 4230 * that make the i-th bound smallest. 4231 * 4232 * In particular, if there are n bounds b_i, then add the constraints 4233 * 4234 * b_i <= b_j for j > i 4235 * b_i < b_j for j < i 4236 */ 4237static __isl_give isl_basic_set *select_minimum(__isl_take isl_basic_set *bset, 4238 __isl_keep isl_mat *var, int i) 4239{ 4240 isl_ctx *ctx; 4241 int j, k; 4242 4243 ctx = isl_mat_get_ctx(var); 4244 4245 for (j = 0; j < var->n_row; ++j) { 4246 if (j == i) 4247 continue; 4248 k = isl_basic_set_alloc_inequality(bset); 4249 if (k < 0) 4250 goto error; 4251 isl_seq_combine(bset->ineq[k], ctx->one, var->row[j], 4252 ctx->negone, var->row[i], var->n_col); 4253 isl_int_set_si(bset->ineq[k][var->n_col], 0); 4254 if (j < i) 4255 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1); 4256 } 4257 4258 bset = isl_basic_set_finalize(bset); 4259 4260 return bset; 4261error: 4262 isl_basic_set_free(bset); 4263 return NULL; 4264} 4265 4266/* Given a set of upper bounds on the last "input" variable m, 4267 * construct a set that assigns the minimal upper bound to m, i.e., 4268 * construct a set that divides the space into cells where one 4269 * of the upper bounds is smaller than all the others and assign 4270 * this upper bound to m. 4271 * 4272 * In particular, if there are n bounds b_i, then the result 4273 * consists of n basic sets, each one of the form 4274 * 4275 * m = b_i 4276 * b_i <= b_j for j > i 4277 * b_i < b_j for j < i 4278 */ 4279static __isl_give isl_set *set_minimum(__isl_take isl_space *dim, 4280 __isl_take isl_mat *var) 4281{ 4282 int i, k; 4283 isl_basic_set *bset = NULL; 4284 isl_ctx *ctx; 4285 isl_set *set = NULL; 4286 4287 if (!dim || !var) 4288 goto error; 4289 4290 ctx = isl_space_get_ctx(dim); 4291 set = isl_set_alloc_space(isl_space_copy(dim), 4292 var->n_row, ISL_SET_DISJOINT); 4293 4294 for (i = 0; i < var->n_row; ++i) { 4295 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 4296 1, var->n_row - 1); 4297 k = isl_basic_set_alloc_equality(bset); 4298 if (k < 0) 4299 goto error; 4300 isl_seq_cpy(bset->eq[k], var->row[i], var->n_col); 4301 isl_int_set_si(bset->eq[k][var->n_col], -1); 4302 bset = select_minimum(bset, var, i); 4303 set = isl_set_add_basic_set(set, bset); 4304 } 4305 4306 isl_space_free(dim); 4307 isl_mat_free(var); 4308 return set; 4309error: 4310 isl_basic_set_free(bset); 4311 isl_set_free(set); 4312 isl_space_free(dim); 4313 isl_mat_free(var); 4314 return NULL; 4315} 4316 4317/* Given that the last input variable of "bmap" represents the minimum 4318 * of the bounds in "cst", check whether we need to split the domain 4319 * based on which bound attains the minimum. 4320 * 4321 * A split is needed when the minimum appears in an integer division 4322 * or in an equality. Otherwise, it is only needed if it appears in 4323 * an upper bound that is different from the upper bounds on which it 4324 * is defined. 4325 */ 4326static int need_split_basic_map(__isl_keep isl_basic_map *bmap, 4327 __isl_keep isl_mat *cst) 4328{ 4329 int i, j; 4330 unsigned total; 4331 unsigned pos; 4332 4333 pos = cst->n_col - 1; 4334 total = isl_basic_map_dim(bmap, isl_dim_all); 4335 4336 for (i = 0; i < bmap->n_div; ++i) 4337 if (!isl_int_is_zero(bmap->div[i][2 + pos])) 4338 return 1; 4339 4340 for (i = 0; i < bmap->n_eq; ++i) 4341 if (!isl_int_is_zero(bmap->eq[i][1 + pos])) 4342 return 1; 4343 4344 for (i = 0; i < bmap->n_ineq; ++i) { 4345 if (isl_int_is_nonneg(bmap->ineq[i][1 + pos])) 4346 continue; 4347 if (!isl_int_is_negone(bmap->ineq[i][1 + pos])) 4348 return 1; 4349 if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1, 4350 total - pos - 1) >= 0) 4351 return 1; 4352 4353 for (j = 0; j < cst->n_row; ++j) 4354 if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col)) 4355 break; 4356 if (j >= cst->n_row) 4357 return 1; 4358 } 4359 4360 return 0; 4361} 4362 4363/* Given that the last set variable of "bset" represents the minimum 4364 * of the bounds in "cst", check whether we need to split the domain 4365 * based on which bound attains the minimum. 4366 * 4367 * We simply call need_split_basic_map here. This is safe because 4368 * the position of the minimum is computed from "cst" and not 4369 * from "bmap". 4370 */ 4371static int need_split_basic_set(__isl_keep isl_basic_set *bset, 4372 __isl_keep isl_mat *cst) 4373{ 4374 return need_split_basic_map((isl_basic_map *)bset, cst); 4375} 4376 4377/* Given that the last set variable of "set" represents the minimum 4378 * of the bounds in "cst", check whether we need to split the domain 4379 * based on which bound attains the minimum. 4380 */ 4381static int need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst) 4382{ 4383 int i; 4384 4385 for (i = 0; i < set->n; ++i) 4386 if (need_split_basic_set(set->p[i], cst)) 4387 return 1; 4388 4389 return 0; 4390} 4391 4392/* Given a set of which the last set variable is the minimum 4393 * of the bounds in "cst", split each basic set in the set 4394 * in pieces where one of the bounds is (strictly) smaller than the others. 4395 * This subdivision is given in "min_expr". 4396 * The variable is subsequently projected out. 4397 * 4398 * We only do the split when it is needed. 4399 * For example if the last input variable m = min(a,b) and the only 4400 * constraints in the given basic set are lower bounds on m, 4401 * i.e., l <= m = min(a,b), then we can simply project out m 4402 * to obtain l <= a and l <= b, without having to split on whether 4403 * m is equal to a or b. 4404 */ 4405static __isl_give isl_set *split(__isl_take isl_set *empty, 4406 __isl_take isl_set *min_expr, __isl_take isl_mat *cst) 4407{ 4408 int n_in; 4409 int i; 4410 isl_space *dim; 4411 isl_set *res; 4412 4413 if (!empty || !min_expr || !cst) 4414 goto error; 4415 4416 n_in = isl_set_dim(empty, isl_dim_set); 4417 dim = isl_set_get_space(empty); 4418 dim = isl_space_drop_dims(dim, isl_dim_set, n_in - 1, 1); 4419 res = isl_set_empty(dim); 4420 4421 for (i = 0; i < empty->n; ++i) { 4422 isl_set *set; 4423 4424 set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i])); 4425 if (need_split_basic_set(empty->p[i], cst)) 4426 set = isl_set_intersect(set, isl_set_copy(min_expr)); 4427 set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1); 4428 4429 res = isl_set_union_disjoint(res, set); 4430 } 4431 4432 isl_set_free(empty); 4433 isl_set_free(min_expr); 4434 isl_mat_free(cst); 4435 return res; 4436error: 4437 isl_set_free(empty); 4438 isl_set_free(min_expr); 4439 isl_mat_free(cst); 4440 return NULL; 4441} 4442 4443/* Given a map of which the last input variable is the minimum 4444 * of the bounds in "cst", split each basic set in the set 4445 * in pieces where one of the bounds is (strictly) smaller than the others. 4446 * This subdivision is given in "min_expr". 4447 * The variable is subsequently projected out. 4448 * 4449 * The implementation is essentially the same as that of "split". 4450 */ 4451static __isl_give isl_map *split_domain(__isl_take isl_map *opt, 4452 __isl_take isl_set *min_expr, __isl_take isl_mat *cst) 4453{ 4454 int n_in; 4455 int i; 4456 isl_space *dim; 4457 isl_map *res; 4458 4459 if (!opt || !min_expr || !cst) 4460 goto error; 4461 4462 n_in = isl_map_dim(opt, isl_dim_in); 4463 dim = isl_map_get_space(opt); 4464 dim = isl_space_drop_dims(dim, isl_dim_in, n_in - 1, 1); 4465 res = isl_map_empty(dim); 4466 4467 for (i = 0; i < opt->n; ++i) { 4468 isl_map *map; 4469 4470 map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i])); 4471 if (need_split_basic_map(opt->p[i], cst)) 4472 map = isl_map_intersect_domain(map, 4473 isl_set_copy(min_expr)); 4474 map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1); 4475 4476 res = isl_map_union_disjoint(res, map); 4477 } 4478 4479 isl_map_free(opt); 4480 isl_set_free(min_expr); 4481 isl_mat_free(cst); 4482 return res; 4483error: 4484 isl_map_free(opt); 4485 isl_set_free(min_expr); 4486 isl_mat_free(cst); 4487 return NULL; 4488} 4489 4490static __isl_give isl_map *basic_map_partial_lexopt( 4491 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4492 __isl_give isl_set **empty, int max); 4493 4494union isl_lex_res { 4495 void *p; 4496 isl_map *map; 4497 isl_pw_multi_aff *pma; 4498}; 4499 4500/* This function is called from basic_map_partial_lexopt_symm. 4501 * The last variable of "bmap" and "dom" corresponds to the minimum 4502 * of the bounds in "cst". "map_space" is the space of the original 4503 * input relation (of basic_map_partial_lexopt_symm) and "set_space" 4504 * is the space of the original domain. 4505 * 4506 * We recursively call basic_map_partial_lexopt and then plug in 4507 * the definition of the minimum in the result. 4508 */ 4509static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_map_core( 4510 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4511 __isl_give isl_set **empty, int max, __isl_take isl_mat *cst, 4512 __isl_take isl_space *map_space, __isl_take isl_space *set_space) 4513{ 4514 isl_map *opt; 4515 isl_set *min_expr; 4516 union isl_lex_res res; 4517 4518 min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst)); 4519 4520 opt = basic_map_partial_lexopt(bmap, dom, empty, max); 4521 4522 if (empty) { 4523 *empty = split(*empty, 4524 isl_set_copy(min_expr), isl_mat_copy(cst)); 4525 *empty = isl_set_reset_space(*empty, set_space); 4526 } 4527 4528 opt = split_domain(opt, min_expr, cst); 4529 opt = isl_map_reset_space(opt, map_space); 4530 4531 res.map = opt; 4532 return res; 4533} 4534 4535/* Given a basic map with at least two parallel constraints (as found 4536 * by the function parallel_constraints), first look for more constraints 4537 * parallel to the two constraint and replace the found list of parallel 4538 * constraints by a single constraint with as "input" part the minimum 4539 * of the input parts of the list of constraints. Then, recursively call 4540 * basic_map_partial_lexopt (possibly finding more parallel constraints) 4541 * and plug in the definition of the minimum in the result. 4542 * 4543 * More specifically, given a set of constraints 4544 * 4545 * a x + b_i(p) >= 0 4546 * 4547 * Replace this set by a single constraint 4548 * 4549 * a x + u >= 0 4550 * 4551 * with u a new parameter with constraints 4552 * 4553 * u <= b_i(p) 4554 * 4555 * Any solution to the new system is also a solution for the original system 4556 * since 4557 * 4558 * a x >= -u >= -b_i(p) 4559 * 4560 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can 4561 * therefore be plugged into the solution. 4562 */ 4563static union isl_lex_res basic_map_partial_lexopt_symm( 4564 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4565 __isl_give isl_set **empty, int max, int first, int second, 4566 __isl_give union isl_lex_res (*core)(__isl_take isl_basic_map *bmap, 4567 __isl_take isl_basic_set *dom, 4568 __isl_give isl_set **empty, 4569 int max, __isl_take isl_mat *cst, 4570 __isl_take isl_space *map_space, 4571 __isl_take isl_space *set_space)) 4572{ 4573 int i, n, k; 4574 int *list = NULL; 4575 unsigned n_in, n_out, n_div; 4576 isl_ctx *ctx; 4577 isl_vec *var = NULL; 4578 isl_mat *cst = NULL; 4579 isl_space *map_space, *set_space; 4580 union isl_lex_res res; 4581 4582 map_space = isl_basic_map_get_space(bmap); 4583 set_space = empty ? isl_basic_set_get_space(dom) : NULL; 4584 4585 n_in = isl_basic_map_dim(bmap, isl_dim_param) + 4586 isl_basic_map_dim(bmap, isl_dim_in); 4587 n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in; 4588 4589 ctx = isl_basic_map_get_ctx(bmap); 4590 list = isl_alloc_array(ctx, int, bmap->n_ineq); 4591 var = isl_vec_alloc(ctx, n_out); 4592 if ((bmap->n_ineq && !list) || (n_out && !var)) 4593 goto error; 4594 4595 list[0] = first; 4596 list[1] = second; 4597 isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out); 4598 for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) { 4599 if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out)) 4600 list[n++] = i; 4601 } 4602 4603 cst = isl_mat_alloc(ctx, n, 1 + n_in); 4604 if (!cst) 4605 goto error; 4606 4607 for (i = 0; i < n; ++i) 4608 isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in); 4609 4610 bmap = isl_basic_map_cow(bmap); 4611 if (!bmap) 4612 goto error; 4613 for (i = n - 1; i >= 0; --i) 4614 if (isl_basic_map_drop_inequality(bmap, list[i]) < 0) 4615 goto error; 4616 4617 bmap = isl_basic_map_add(bmap, isl_dim_in, 1); 4618 bmap = isl_basic_map_extend_constraints(bmap, 0, 1); 4619 k = isl_basic_map_alloc_inequality(bmap); 4620 if (k < 0) 4621 goto error; 4622 isl_seq_clr(bmap->ineq[k], 1 + n_in); 4623 isl_int_set_si(bmap->ineq[k][1 + n_in], 1); 4624 isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out); 4625 bmap = isl_basic_map_finalize(bmap); 4626 4627 n_div = isl_basic_set_dim(dom, isl_dim_div); 4628 dom = isl_basic_set_add_dims(dom, isl_dim_set, 1); 4629 dom = isl_basic_set_extend_constraints(dom, 0, n); 4630 for (i = 0; i < n; ++i) { 4631 k = isl_basic_set_alloc_inequality(dom); 4632 if (k < 0) 4633 goto error; 4634 isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in); 4635 isl_int_set_si(dom->ineq[k][1 + n_in], -1); 4636 isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div); 4637 } 4638 4639 isl_vec_free(var); 4640 free(list); 4641 4642 return core(bmap, dom, empty, max, cst, map_space, set_space); 4643error: 4644 isl_space_free(map_space); 4645 isl_space_free(set_space); 4646 isl_mat_free(cst); 4647 isl_vec_free(var); 4648 free(list); 4649 isl_basic_set_free(dom); 4650 isl_basic_map_free(bmap); 4651 res.p = NULL; 4652 return res; 4653} 4654 4655static __isl_give isl_map *basic_map_partial_lexopt_symm_map( 4656 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4657 __isl_give isl_set **empty, int max, int first, int second) 4658{ 4659 return basic_map_partial_lexopt_symm(bmap, dom, empty, max, 4660 first, second, &basic_map_partial_lexopt_symm_map_core).map; 4661} 4662 4663/* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting 4664 * equalities and removing redundant constraints. 4665 * 4666 * We first check if there are any parallel constraints (left). 4667 * If not, we are in the base case. 4668 * If there are parallel constraints, we replace them by a single 4669 * constraint in basic_map_partial_lexopt_symm and then call 4670 * this function recursively to look for more parallel constraints. 4671 */ 4672static __isl_give isl_map *basic_map_partial_lexopt( 4673 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 4674 __isl_give isl_set **empty, int max) 4675{ 4676 int par = 0; 4677 int first, second; 4678 4679 if (!bmap) 4680 goto error; 4681 4682 if (bmap->ctx->opt->pip_symmetry) 4683 par = parallel_constraints(bmap, &first, &second); 4684 if (par < 0) 4685 goto error; 4686 if (!par) 4687 return basic_map_partial_lexopt_base_map(bmap, dom, empty, max); 4688 4689 return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max, 4690 first, second); 4691error: 4692 isl_basic_set_free(dom); 4693 isl_basic_map_free(bmap); 4694 return NULL; 4695} 4696 4697/* Compute the lexicographic minimum (or maximum if "max" is set) 4698 * of "bmap" over the domain "dom" and return the result as a map. 4699 * If "empty" is not NULL, then *empty is assigned a set that 4700 * contains those parts of the domain where there is no solution. 4701 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL), 4702 * then we compute the rational optimum. Otherwise, we compute 4703 * the integral optimum. 4704 * 4705 * We perform some preprocessing. As the PILP solver does not 4706 * handle implicit equalities very well, we first make sure all 4707 * the equalities are explicitly available. 4708 * 4709 * We also add context constraints to the basic map and remove 4710 * redundant constraints. This is only needed because of the 4711 * way we handle simple symmetries. In particular, we currently look 4712 * for symmetries on the constraints, before we set up the main tableau. 4713 * It is then no good to look for symmetries on possibly redundant constraints. 4714 */ 4715struct isl_map *isl_tab_basic_map_partial_lexopt( 4716 struct isl_basic_map *bmap, struct isl_basic_set *dom, 4717 struct isl_set **empty, int max) 4718{ 4719 if (empty) 4720 *empty = NULL; 4721 if (!bmap || !dom) 4722 goto error; 4723 4724 isl_assert(bmap->ctx, 4725 isl_basic_map_compatible_domain(bmap, dom), goto error); 4726 4727 if (isl_basic_set_dim(dom, isl_dim_all) == 0) 4728 return basic_map_partial_lexopt(bmap, dom, empty, max); 4729 4730 bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom)); 4731 bmap = isl_basic_map_detect_equalities(bmap); 4732 bmap = isl_basic_map_remove_redundancies(bmap); 4733 4734 return basic_map_partial_lexopt(bmap, dom, empty, max); 4735error: 4736 isl_basic_set_free(dom); 4737 isl_basic_map_free(bmap); 4738 return NULL; 4739} 4740 4741struct isl_sol_for { 4742 struct isl_sol sol; 4743 int (*fn)(__isl_take isl_basic_set *dom, 4744 __isl_take isl_aff_list *list, void *user); 4745 void *user; 4746}; 4747 4748static void sol_for_free(struct isl_sol_for *sol_for) 4749{ 4750 if (sol_for->sol.context) 4751 sol_for->sol.context->op->free(sol_for->sol.context); 4752 free(sol_for); 4753} 4754 4755static void sol_for_free_wrap(struct isl_sol *sol) 4756{ 4757 sol_for_free((struct isl_sol_for *)sol); 4758} 4759 4760/* Add the solution identified by the tableau and the context tableau. 4761 * 4762 * See documentation of sol_add for more details. 4763 * 4764 * Instead of constructing a basic map, this function calls a user 4765 * defined function with the current context as a basic set and 4766 * a list of affine expressions representing the relation between 4767 * the input and output. The space over which the affine expressions 4768 * are defined is the same as that of the domain. The number of 4769 * affine expressions in the list is equal to the number of output variables. 4770 */ 4771static void sol_for_add(struct isl_sol_for *sol, 4772 struct isl_basic_set *dom, struct isl_mat *M) 4773{ 4774 int i; 4775 isl_ctx *ctx; 4776 isl_local_space *ls; 4777 isl_aff *aff; 4778 isl_aff_list *list; 4779 4780 if (sol->sol.error || !dom || !M) 4781 goto error; 4782 4783 ctx = isl_basic_set_get_ctx(dom); 4784 ls = isl_basic_set_get_local_space(dom); 4785 list = isl_aff_list_alloc(ctx, M->n_row - 1); 4786 for (i = 1; i < M->n_row; ++i) { 4787 aff = isl_aff_alloc(isl_local_space_copy(ls)); 4788 if (aff) { 4789 isl_int_set(aff->v->el[0], M->row[0][0]); 4790 isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col); 4791 } 4792 aff = isl_aff_normalize(aff); 4793 list = isl_aff_list_add(list, aff); 4794 } 4795 isl_local_space_free(ls); 4796 4797 dom = isl_basic_set_finalize(dom); 4798 4799 if (sol->fn(isl_basic_set_copy(dom), list, sol->user) < 0) 4800 goto error; 4801 4802 isl_basic_set_free(dom); 4803 isl_mat_free(M); 4804 return; 4805error: 4806 isl_basic_set_free(dom); 4807 isl_mat_free(M); 4808 sol->sol.error = 1; 4809} 4810 4811static void sol_for_add_wrap(struct isl_sol *sol, 4812 struct isl_basic_set *dom, struct isl_mat *M) 4813{ 4814 sol_for_add((struct isl_sol_for *)sol, dom, M); 4815} 4816 4817static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max, 4818 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list, 4819 void *user), 4820 void *user) 4821{ 4822 struct isl_sol_for *sol_for = NULL; 4823 isl_space *dom_dim; 4824 struct isl_basic_set *dom = NULL; 4825 4826 sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for); 4827 if (!sol_for) 4828 goto error; 4829 4830 dom_dim = isl_space_domain(isl_space_copy(bmap->dim)); 4831 dom = isl_basic_set_universe(dom_dim); 4832 4833 sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); 4834 sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap; 4835 sol_for->sol.dec_level.sol = &sol_for->sol; 4836 sol_for->fn = fn; 4837 sol_for->user = user; 4838 sol_for->sol.max = max; 4839 sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out); 4840 sol_for->sol.add = &sol_for_add_wrap; 4841 sol_for->sol.add_empty = NULL; 4842 sol_for->sol.free = &sol_for_free_wrap; 4843 4844 sol_for->sol.context = isl_context_alloc(dom); 4845 if (!sol_for->sol.context) 4846 goto error; 4847 4848 isl_basic_set_free(dom); 4849 return sol_for; 4850error: 4851 isl_basic_set_free(dom); 4852 sol_for_free(sol_for); 4853 return NULL; 4854} 4855 4856static void sol_for_find_solutions(struct isl_sol_for *sol_for, 4857 struct isl_tab *tab) 4858{ 4859 find_solutions_main(&sol_for->sol, tab); 4860} 4861 4862int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max, 4863 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list, 4864 void *user), 4865 void *user) 4866{ 4867 struct isl_sol_for *sol_for = NULL; 4868 4869 bmap = isl_basic_map_copy(bmap); 4870 bmap = isl_basic_map_detect_equalities(bmap); 4871 if (!bmap) 4872 return -1; 4873 4874 sol_for = sol_for_init(bmap, max, fn, user); 4875 if (!sol_for) 4876 goto error; 4877 4878 if (isl_basic_map_plain_is_empty(bmap)) 4879 /* nothing */; 4880 else { 4881 struct isl_tab *tab; 4882 struct isl_context *context = sol_for->sol.context; 4883 tab = tab_for_lexmin(bmap, 4884 context->op->peek_basic_set(context), 1, max); 4885 tab = context->op->detect_nonnegative_parameters(context, tab); 4886 sol_for_find_solutions(sol_for, tab); 4887 if (sol_for->sol.error) 4888 goto error; 4889 } 4890 4891 sol_free(&sol_for->sol); 4892 isl_basic_map_free(bmap); 4893 return 0; 4894error: 4895 sol_free(&sol_for->sol); 4896 isl_basic_map_free(bmap); 4897 return -1; 4898} 4899 4900int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set *bset, int max, 4901 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list, 4902 void *user), 4903 void *user) 4904{ 4905 return isl_basic_map_foreach_lexopt(bset, max, fn, user); 4906} 4907 4908/* Check if the given sequence of len variables starting at pos 4909 * represents a trivial (i.e., zero) solution. 4910 * The variables are assumed to be non-negative and to come in pairs, 4911 * with each pair representing a variable of unrestricted sign. 4912 * The solution is trivial if each such pair in the sequence consists 4913 * of two identical values, meaning that the variable being represented 4914 * has value zero. 4915 */ 4916static int region_is_trivial(struct isl_tab *tab, int pos, int len) 4917{ 4918 int i; 4919 4920 if (len == 0) 4921 return 0; 4922 4923 for (i = 0; i < len; i += 2) { 4924 int neg_row; 4925 int pos_row; 4926 4927 neg_row = tab->var[pos + i].is_row ? 4928 tab->var[pos + i].index : -1; 4929 pos_row = tab->var[pos + i + 1].is_row ? 4930 tab->var[pos + i + 1].index : -1; 4931 4932 if ((neg_row < 0 || 4933 isl_int_is_zero(tab->mat->row[neg_row][1])) && 4934 (pos_row < 0 || 4935 isl_int_is_zero(tab->mat->row[pos_row][1]))) 4936 continue; 4937 4938 if (neg_row < 0 || pos_row < 0) 4939 return 0; 4940 if (isl_int_ne(tab->mat->row[neg_row][1], 4941 tab->mat->row[pos_row][1])) 4942 return 0; 4943 } 4944 4945 return 1; 4946} 4947 4948/* Return the index of the first trivial region or -1 if all regions 4949 * are non-trivial. 4950 */ 4951static int first_trivial_region(struct isl_tab *tab, 4952 int n_region, struct isl_region *region) 4953{ 4954 int i; 4955 4956 for (i = 0; i < n_region; ++i) { 4957 if (region_is_trivial(tab, region[i].pos, region[i].len)) 4958 return i; 4959 } 4960 4961 return -1; 4962} 4963 4964/* Check if the solution is optimal, i.e., whether the first 4965 * n_op entries are zero. 4966 */ 4967static int is_optimal(__isl_keep isl_vec *sol, int n_op) 4968{ 4969 int i; 4970 4971 for (i = 0; i < n_op; ++i) 4972 if (!isl_int_is_zero(sol->el[1 + i])) 4973 return 0; 4974 return 1; 4975} 4976 4977/* Add constraints to "tab" that ensure that any solution is significantly 4978 * better that that represented by "sol". That is, find the first 4979 * relevant (within first n_op) non-zero coefficient and force it (along 4980 * with all previous coefficients) to be zero. 4981 * If the solution is already optimal (all relevant coefficients are zero), 4982 * then just mark the table as empty. 4983 */ 4984static int force_better_solution(struct isl_tab *tab, 4985 __isl_keep isl_vec *sol, int n_op) 4986{ 4987 int i; 4988 isl_ctx *ctx; 4989 isl_vec *v = NULL; 4990 4991 if (!sol) 4992 return -1; 4993 4994 for (i = 0; i < n_op; ++i) 4995 if (!isl_int_is_zero(sol->el[1 + i])) 4996 break; 4997 4998 if (i == n_op) { 4999 if (isl_tab_mark_empty(tab) < 0) 5000 return -1; 5001 return 0; 5002 } 5003 5004 ctx = isl_vec_get_ctx(sol); 5005 v = isl_vec_alloc(ctx, 1 + tab->n_var); 5006 if (!v) 5007 return -1; 5008 5009 for (; i >= 0; --i) { 5010 v = isl_vec_clr(v); 5011 isl_int_set_si(v->el[1 + i], -1); 5012 if (add_lexmin_eq(tab, v->el) < 0) 5013 goto error; 5014 } 5015 5016 isl_vec_free(v); 5017 return 0; 5018error: 5019 isl_vec_free(v); 5020 return -1; 5021} 5022 5023struct isl_trivial { 5024 int update; 5025 int region; 5026 int side; 5027 struct isl_tab_undo *snap; 5028}; 5029 5030/* Return the lexicographically smallest non-trivial solution of the 5031 * given ILP problem. 5032 * 5033 * All variables are assumed to be non-negative. 5034 * 5035 * n_op is the number of initial coordinates to optimize. 5036 * That is, once a solution has been found, we will only continue looking 5037 * for solution that result in significantly better values for those 5038 * initial coordinates. That is, we only continue looking for solutions 5039 * that increase the number of initial zeros in this sequence. 5040 * 5041 * A solution is non-trivial, if it is non-trivial on each of the 5042 * specified regions. Each region represents a sequence of pairs 5043 * of variables. A solution is non-trivial on such a region if 5044 * at least one of these pairs consists of different values, i.e., 5045 * such that the non-negative variable represented by the pair is non-zero. 5046 * 5047 * Whenever a conflict is encountered, all constraints involved are 5048 * reported to the caller through a call to "conflict". 5049 * 5050 * We perform a simple branch-and-bound backtracking search. 5051 * Each level in the search represents initially trivial region that is forced 5052 * to be non-trivial. 5053 * At each level we consider n cases, where n is the length of the region. 5054 * In terms of the n/2 variables of unrestricted signs being encoded by 5055 * the region, we consider the cases 5056 * x_0 >= 1 5057 * x_0 <= -1 5058 * x_0 = 0 and x_1 >= 1 5059 * x_0 = 0 and x_1 <= -1 5060 * x_0 = 0 and x_1 = 0 and x_2 >= 1 5061 * x_0 = 0 and x_1 = 0 and x_2 <= -1 5062 * ... 5063 * The cases are considered in this order, assuming that each pair 5064 * x_i_a x_i_b represents the value x_i_b - x_i_a. 5065 * That is, x_0 >= 1 is enforced by adding the constraint 5066 * x_0_b - x_0_a >= 1 5067 */ 5068__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin( 5069 __isl_take isl_basic_set *bset, int n_op, int n_region, 5070 struct isl_region *region, 5071 int (*conflict)(int con, void *user), void *user) 5072{ 5073 int i, j; 5074 int r; 5075 isl_ctx *ctx; 5076 isl_vec *v = NULL; 5077 isl_vec *sol = NULL; 5078 struct isl_tab *tab; 5079 struct isl_trivial *triv = NULL; 5080 int level, init; 5081 5082 if (!bset) 5083 return NULL; 5084 5085 ctx = isl_basic_set_get_ctx(bset); 5086 sol = isl_vec_alloc(ctx, 0); 5087 5088 tab = tab_for_lexmin(bset, NULL, 0, 0); 5089 if (!tab) 5090 goto error; 5091 tab->conflict = conflict; 5092 tab->conflict_user = user; 5093 5094 v = isl_vec_alloc(ctx, 1 + tab->n_var); 5095 triv = isl_calloc_array(ctx, struct isl_trivial, n_region); 5096 if (!v || (n_region && !triv)) 5097 goto error; 5098 5099 level = 0; 5100 init = 1; 5101 5102 while (level >= 0) { 5103 int side, base; 5104 5105 if (init) { 5106 tab = cut_to_integer_lexmin(tab, CUT_ONE); 5107 if (!tab) 5108 goto error; 5109 if (tab->empty) 5110 goto backtrack; 5111 r = first_trivial_region(tab, n_region, region); 5112 if (r < 0) { 5113 for (i = 0; i < level; ++i) 5114 triv[i].update = 1; 5115 isl_vec_free(sol); 5116 sol = isl_tab_get_sample_value(tab); 5117 if (!sol) 5118 goto error; 5119 if (is_optimal(sol, n_op)) 5120 break; 5121 goto backtrack; 5122 } 5123 if (level >= n_region) 5124 isl_die(ctx, isl_error_internal, 5125 "nesting level too deep", goto error); 5126 if (isl_tab_extend_cons(tab, 5127 2 * region[r].len + 2 * n_op) < 0) 5128 goto error; 5129 triv[level].region = r; 5130 triv[level].side = 0; 5131 } 5132 5133 r = triv[level].region; 5134 side = triv[level].side; 5135 base = 2 * (side/2); 5136 5137 if (side >= region[r].len) { 5138backtrack: 5139 level--; 5140 init = 0; 5141 if (level >= 0) 5142 if (isl_tab_rollback(tab, triv[level].snap) < 0) 5143 goto error; 5144 continue; 5145 } 5146 5147 if (triv[level].update) { 5148 if (force_better_solution(tab, sol, n_op) < 0) 5149 goto error; 5150 triv[level].update = 0; 5151 } 5152 5153 if (side == base && base >= 2) { 5154 for (j = base - 2; j < base; ++j) { 5155 v = isl_vec_clr(v); 5156 isl_int_set_si(v->el[1 + region[r].pos + j], 1); 5157 if (add_lexmin_eq(tab, v->el) < 0) 5158 goto error; 5159 } 5160 } 5161 5162 triv[level].snap = isl_tab_snap(tab); 5163 if (isl_tab_push_basis(tab) < 0) 5164 goto error; 5165 5166 v = isl_vec_clr(v); 5167 isl_int_set_si(v->el[0], -1); 5168 isl_int_set_si(v->el[1 + region[r].pos + side], -1); 5169 isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1); 5170 tab = add_lexmin_ineq(tab, v->el); 5171 5172 triv[level].side++; 5173 level++; 5174 init = 1; 5175 } 5176 5177 free(triv); 5178 isl_vec_free(v); 5179 isl_tab_free(tab); 5180 isl_basic_set_free(bset); 5181 5182 return sol; 5183error: 5184 free(triv); 5185 isl_vec_free(v); 5186 isl_tab_free(tab); 5187 isl_basic_set_free(bset); 5188 isl_vec_free(sol); 5189 return NULL; 5190} 5191 5192/* Return the lexicographically smallest rational point in "bset", 5193 * assuming that all variables are non-negative. 5194 * If "bset" is empty, then return a zero-length vector. 5195 */ 5196__isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin( 5197 __isl_take isl_basic_set *bset) 5198{ 5199 struct isl_tab *tab; 5200 isl_ctx *ctx = isl_basic_set_get_ctx(bset); 5201 isl_vec *sol; 5202 5203 if (!bset) 5204 return NULL; 5205 5206 tab = tab_for_lexmin(bset, NULL, 0, 0); 5207 if (!tab) 5208 goto error; 5209 if (tab->empty) 5210 sol = isl_vec_alloc(ctx, 0); 5211 else 5212 sol = isl_tab_get_sample_value(tab); 5213 isl_tab_free(tab); 5214 isl_basic_set_free(bset); 5215 return sol; 5216error: 5217 isl_tab_free(tab); 5218 isl_basic_set_free(bset); 5219 return NULL; 5220} 5221 5222struct isl_sol_pma { 5223 struct isl_sol sol; 5224 isl_pw_multi_aff *pma; 5225 isl_set *empty; 5226}; 5227 5228static void sol_pma_free(struct isl_sol_pma *sol_pma) 5229{ 5230 if (!sol_pma) 5231 return; 5232 if (sol_pma->sol.context) 5233 sol_pma->sol.context->op->free(sol_pma->sol.context); 5234 isl_pw_multi_aff_free(sol_pma->pma); 5235 isl_set_free(sol_pma->empty); 5236 free(sol_pma); 5237} 5238 5239/* This function is called for parts of the context where there is 5240 * no solution, with "bset" corresponding to the context tableau. 5241 * Simply add the basic set to the set "empty". 5242 */ 5243static void sol_pma_add_empty(struct isl_sol_pma *sol, 5244 __isl_take isl_basic_set *bset) 5245{ 5246 if (!bset) 5247 goto error; 5248 isl_assert(bset->ctx, sol->empty, goto error); 5249 5250 sol->empty = isl_set_grow(sol->empty, 1); 5251 bset = isl_basic_set_simplify(bset); 5252 bset = isl_basic_set_finalize(bset); 5253 sol->empty = isl_set_add_basic_set(sol->empty, bset); 5254 if (!sol->empty) 5255 sol->sol.error = 1; 5256 return; 5257error: 5258 isl_basic_set_free(bset); 5259 sol->sol.error = 1; 5260} 5261 5262/* Given a basic map "dom" that represents the context and an affine 5263 * matrix "M" that maps the dimensions of the context to the 5264 * output variables, construct an isl_pw_multi_aff with a single 5265 * cell corresponding to "dom" and affine expressions copied from "M". 5266 */ 5267static void sol_pma_add(struct isl_sol_pma *sol, 5268 __isl_take isl_basic_set *dom, __isl_take isl_mat *M) 5269{ 5270 int i; 5271 isl_local_space *ls; 5272 isl_aff *aff; 5273 isl_multi_aff *maff; 5274 isl_pw_multi_aff *pma; 5275 5276 maff = isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol->pma)); 5277 ls = isl_basic_set_get_local_space(dom); 5278 for (i = 1; i < M->n_row; ++i) { 5279 aff = isl_aff_alloc(isl_local_space_copy(ls)); 5280 if (aff) { 5281 isl_int_set(aff->v->el[0], M->row[0][0]); 5282 isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col); 5283 } 5284 aff = isl_aff_normalize(aff); 5285 maff = isl_multi_aff_set_aff(maff, i - 1, aff); 5286 } 5287 isl_local_space_free(ls); 5288 isl_mat_free(M); 5289 dom = isl_basic_set_simplify(dom); 5290 dom = isl_basic_set_finalize(dom); 5291 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom), maff); 5292 sol->pma = isl_pw_multi_aff_add_disjoint(sol->pma, pma); 5293 if (!sol->pma) 5294 sol->sol.error = 1; 5295} 5296 5297static void sol_pma_free_wrap(struct isl_sol *sol) 5298{ 5299 sol_pma_free((struct isl_sol_pma *)sol); 5300} 5301 5302static void sol_pma_add_empty_wrap(struct isl_sol *sol, 5303 __isl_take isl_basic_set *bset) 5304{ 5305 sol_pma_add_empty((struct isl_sol_pma *)sol, bset); 5306} 5307 5308static void sol_pma_add_wrap(struct isl_sol *sol, 5309 __isl_take isl_basic_set *dom, __isl_take isl_mat *M) 5310{ 5311 sol_pma_add((struct isl_sol_pma *)sol, dom, M); 5312} 5313 5314/* Construct an isl_sol_pma structure for accumulating the solution. 5315 * If track_empty is set, then we also keep track of the parts 5316 * of the context where there is no solution. 5317 * If max is set, then we are solving a maximization, rather than 5318 * a minimization problem, which means that the variables in the 5319 * tableau have value "M - x" rather than "M + x". 5320 */ 5321static struct isl_sol *sol_pma_init(__isl_keep isl_basic_map *bmap, 5322 __isl_take isl_basic_set *dom, int track_empty, int max) 5323{ 5324 struct isl_sol_pma *sol_pma = NULL; 5325 5326 if (!bmap) 5327 goto error; 5328 5329 sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma); 5330 if (!sol_pma) 5331 goto error; 5332 5333 sol_pma->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); 5334 sol_pma->sol.dec_level.callback.run = &sol_dec_level_wrap; 5335 sol_pma->sol.dec_level.sol = &sol_pma->sol; 5336 sol_pma->sol.max = max; 5337 sol_pma->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out); 5338 sol_pma->sol.add = &sol_pma_add_wrap; 5339 sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL; 5340 sol_pma->sol.free = &sol_pma_free_wrap; 5341 sol_pma->pma = isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap)); 5342 if (!sol_pma->pma) 5343 goto error; 5344 5345 sol_pma->sol.context = isl_context_alloc(dom); 5346 if (!sol_pma->sol.context) 5347 goto error; 5348 5349 if (track_empty) { 5350 sol_pma->empty = isl_set_alloc_space(isl_basic_set_get_space(dom), 5351 1, ISL_SET_DISJOINT); 5352 if (!sol_pma->empty) 5353 goto error; 5354 } 5355 5356 isl_basic_set_free(dom); 5357 return &sol_pma->sol; 5358error: 5359 isl_basic_set_free(dom); 5360 sol_pma_free(sol_pma); 5361 return NULL; 5362} 5363 5364/* Base case of isl_tab_basic_map_partial_lexopt, after removing 5365 * some obvious symmetries. 5366 * 5367 * We call basic_map_partial_lexopt_base and extract the results. 5368 */ 5369static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pma( 5370 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 5371 __isl_give isl_set **empty, int max) 5372{ 5373 isl_pw_multi_aff *result = NULL; 5374 struct isl_sol *sol; 5375 struct isl_sol_pma *sol_pma; 5376 5377 sol = basic_map_partial_lexopt_base(bmap, dom, empty, max, 5378 &sol_pma_init); 5379 if (!sol) 5380 return NULL; 5381 sol_pma = (struct isl_sol_pma *) sol; 5382 5383 result = isl_pw_multi_aff_copy(sol_pma->pma); 5384 if (empty) 5385 *empty = isl_set_copy(sol_pma->empty); 5386 sol_free(&sol_pma->sol); 5387 return result; 5388} 5389 5390/* Given that the last input variable of "maff" represents the minimum 5391 * of some bounds, check whether we need to plug in the expression 5392 * of the minimum. 5393 * 5394 * In particular, check if the last input variable appears in any 5395 * of the expressions in "maff". 5396 */ 5397static int need_substitution(__isl_keep isl_multi_aff *maff) 5398{ 5399 int i; 5400 unsigned pos; 5401 5402 pos = isl_multi_aff_dim(maff, isl_dim_in) - 1; 5403 5404 for (i = 0; i < maff->n; ++i) 5405 if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1)) 5406 return 1; 5407 5408 return 0; 5409} 5410 5411/* Given a set of upper bounds on the last "input" variable m, 5412 * construct a piecewise affine expression that selects 5413 * the minimal upper bound to m, i.e., 5414 * divide the space into cells where one 5415 * of the upper bounds is smaller than all the others and select 5416 * this upper bound on that cell. 5417 * 5418 * In particular, if there are n bounds b_i, then the result 5419 * consists of n cell, each one of the form 5420 * 5421 * b_i <= b_j for j > i 5422 * b_i < b_j for j < i 5423 * 5424 * The affine expression on this cell is 5425 * 5426 * b_i 5427 */ 5428static __isl_give isl_pw_aff *set_minimum_pa(__isl_take isl_space *space, 5429 __isl_take isl_mat *var) 5430{ 5431 int i; 5432 isl_aff *aff = NULL; 5433 isl_basic_set *bset = NULL; 5434 isl_ctx *ctx; 5435 isl_pw_aff *paff = NULL; 5436 isl_space *pw_space; 5437 isl_local_space *ls = NULL; 5438 5439 if (!space || !var) 5440 goto error; 5441 5442 ctx = isl_space_get_ctx(space); 5443 ls = isl_local_space_from_space(isl_space_copy(space)); 5444 pw_space = isl_space_copy(space); 5445 pw_space = isl_space_from_domain(pw_space); 5446 pw_space = isl_space_add_dims(pw_space, isl_dim_out, 1); 5447 paff = isl_pw_aff_alloc_size(pw_space, var->n_row); 5448 5449 for (i = 0; i < var->n_row; ++i) { 5450 isl_pw_aff *paff_i; 5451 5452 aff = isl_aff_alloc(isl_local_space_copy(ls)); 5453 bset = isl_basic_set_alloc_space(isl_space_copy(space), 0, 5454 0, var->n_row - 1); 5455 if (!aff || !bset) 5456 goto error; 5457 isl_int_set_si(aff->v->el[0], 1); 5458 isl_seq_cpy(aff->v->el + 1, var->row[i], var->n_col); 5459 isl_int_set_si(aff->v->el[1 + var->n_col], 0); 5460 bset = select_minimum(bset, var, i); 5461 paff_i = isl_pw_aff_alloc(isl_set_from_basic_set(bset), aff); 5462 paff = isl_pw_aff_add_disjoint(paff, paff_i); 5463 } 5464 5465 isl_local_space_free(ls); 5466 isl_space_free(space); 5467 isl_mat_free(var); 5468 return paff; 5469error: 5470 isl_aff_free(aff); 5471 isl_basic_set_free(bset); 5472 isl_pw_aff_free(paff); 5473 isl_local_space_free(ls); 5474 isl_space_free(space); 5475 isl_mat_free(var); 5476 return NULL; 5477} 5478 5479/* Given a piecewise multi-affine expression of which the last input variable 5480 * is the minimum of the bounds in "cst", plug in the value of the minimum. 5481 * This minimum expression is given in "min_expr_pa". 5482 * The set "min_expr" contains the same information, but in the form of a set. 5483 * The variable is subsequently projected out. 5484 * 5485 * The implementation is similar to those of "split" and "split_domain". 5486 * If the variable appears in a given expression, then minimum expression 5487 * is plugged in. Otherwise, if the variable appears in the constraints 5488 * and a split is required, then the domain is split. Otherwise, no split 5489 * is performed. 5490 */ 5491static __isl_give isl_pw_multi_aff *split_domain_pma( 5492 __isl_take isl_pw_multi_aff *opt, __isl_take isl_pw_aff *min_expr_pa, 5493 __isl_take isl_set *min_expr, __isl_take isl_mat *cst) 5494{ 5495 int n_in; 5496 int i; 5497 isl_space *space; 5498 isl_pw_multi_aff *res; 5499 5500 if (!opt || !min_expr || !cst) 5501 goto error; 5502 5503 n_in = isl_pw_multi_aff_dim(opt, isl_dim_in); 5504 space = isl_pw_multi_aff_get_space(opt); 5505 space = isl_space_drop_dims(space, isl_dim_in, n_in - 1, 1); 5506 res = isl_pw_multi_aff_empty(space); 5507 5508 for (i = 0; i < opt->n; ++i) { 5509 isl_pw_multi_aff *pma; 5510 5511 pma = isl_pw_multi_aff_alloc(isl_set_copy(opt->p[i].set), 5512 isl_multi_aff_copy(opt->p[i].maff)); 5513 if (need_substitution(opt->p[i].maff)) 5514 pma = isl_pw_multi_aff_substitute(pma, 5515 isl_dim_in, n_in - 1, min_expr_pa); 5516 else if (need_split_set(opt->p[i].set, cst)) 5517 pma = isl_pw_multi_aff_intersect_domain(pma, 5518 isl_set_copy(min_expr)); 5519 pma = isl_pw_multi_aff_project_out(pma, 5520 isl_dim_in, n_in - 1, 1); 5521 5522 res = isl_pw_multi_aff_add_disjoint(res, pma); 5523 } 5524 5525 isl_pw_multi_aff_free(opt); 5526 isl_pw_aff_free(min_expr_pa); 5527 isl_set_free(min_expr); 5528 isl_mat_free(cst); 5529 return res; 5530error: 5531 isl_pw_multi_aff_free(opt); 5532 isl_pw_aff_free(min_expr_pa); 5533 isl_set_free(min_expr); 5534 isl_mat_free(cst); 5535 return NULL; 5536} 5537 5538static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma( 5539 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 5540 __isl_give isl_set **empty, int max); 5541 5542/* This function is called from basic_map_partial_lexopt_symm. 5543 * The last variable of "bmap" and "dom" corresponds to the minimum 5544 * of the bounds in "cst". "map_space" is the space of the original 5545 * input relation (of basic_map_partial_lexopt_symm) and "set_space" 5546 * is the space of the original domain. 5547 * 5548 * We recursively call basic_map_partial_lexopt and then plug in 5549 * the definition of the minimum in the result. 5550 */ 5551static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_pma_core( 5552 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 5553 __isl_give isl_set **empty, int max, __isl_take isl_mat *cst, 5554 __isl_take isl_space *map_space, __isl_take isl_space *set_space) 5555{ 5556 isl_pw_multi_aff *opt; 5557 isl_pw_aff *min_expr_pa; 5558 isl_set *min_expr; 5559 union isl_lex_res res; 5560 5561 min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst)); 5562 min_expr_pa = set_minimum_pa(isl_basic_set_get_space(dom), 5563 isl_mat_copy(cst)); 5564 5565 opt = basic_map_partial_lexopt_pma(bmap, dom, empty, max); 5566 5567 if (empty) { 5568 *empty = split(*empty, 5569 isl_set_copy(min_expr), isl_mat_copy(cst)); 5570 *empty = isl_set_reset_space(*empty, set_space); 5571 } 5572 5573 opt = split_domain_pma(opt, min_expr_pa, min_expr, cst); 5574 opt = isl_pw_multi_aff_reset_space(opt, map_space); 5575 5576 res.pma = opt; 5577 return res; 5578} 5579 5580static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_symm_pma( 5581 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 5582 __isl_give isl_set **empty, int max, int first, int second) 5583{ 5584 return basic_map_partial_lexopt_symm(bmap, dom, empty, max, 5585 first, second, &basic_map_partial_lexopt_symm_pma_core).pma; 5586} 5587 5588/* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting 5589 * equalities and removing redundant constraints. 5590 * 5591 * We first check if there are any parallel constraints (left). 5592 * If not, we are in the base case. 5593 * If there are parallel constraints, we replace them by a single 5594 * constraint in basic_map_partial_lexopt_symm_pma and then call 5595 * this function recursively to look for more parallel constraints. 5596 */ 5597static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma( 5598 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 5599 __isl_give isl_set **empty, int max) 5600{ 5601 int par = 0; 5602 int first, second; 5603 5604 if (!bmap) 5605 goto error; 5606 5607 if (bmap->ctx->opt->pip_symmetry) 5608 par = parallel_constraints(bmap, &first, &second); 5609 if (par < 0) 5610 goto error; 5611 if (!par) 5612 return basic_map_partial_lexopt_base_pma(bmap, dom, empty, max); 5613 5614 return basic_map_partial_lexopt_symm_pma(bmap, dom, empty, max, 5615 first, second); 5616error: 5617 isl_basic_set_free(dom); 5618 isl_basic_map_free(bmap); 5619 return NULL; 5620} 5621 5622/* Compute the lexicographic minimum (or maximum if "max" is set) 5623 * of "bmap" over the domain "dom" and return the result as a piecewise 5624 * multi-affine expression. 5625 * If "empty" is not NULL, then *empty is assigned a set that 5626 * contains those parts of the domain where there is no solution. 5627 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL), 5628 * then we compute the rational optimum. Otherwise, we compute 5629 * the integral optimum. 5630 * 5631 * We perform some preprocessing. As the PILP solver does not 5632 * handle implicit equalities very well, we first make sure all 5633 * the equalities are explicitly available. 5634 * 5635 * We also add context constraints to the basic map and remove 5636 * redundant constraints. This is only needed because of the 5637 * way we handle simple symmetries. In particular, we currently look 5638 * for symmetries on the constraints, before we set up the main tableau. 5639 * It is then no good to look for symmetries on possibly redundant constraints. 5640 */ 5641__isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff( 5642 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 5643 __isl_give isl_set **empty, int max) 5644{ 5645 if (empty) 5646 *empty = NULL; 5647 if (!bmap || !dom) 5648 goto error; 5649 5650 isl_assert(bmap->ctx, 5651 isl_basic_map_compatible_domain(bmap, dom), goto error); 5652 5653 if (isl_basic_set_dim(dom, isl_dim_all) == 0) 5654 return basic_map_partial_lexopt_pma(bmap, dom, empty, max); 5655 5656 bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom)); 5657 bmap = isl_basic_map_detect_equalities(bmap); 5658 bmap = isl_basic_map_remove_redundancies(bmap); 5659 5660 return basic_map_partial_lexopt_pma(bmap, dom, empty, max); 5661error: 5662 isl_basic_set_free(dom); 5663 isl_basic_map_free(bmap); 5664 return NULL; 5665} 5666