isl_fold.c

   1 /*
   2  * Copyright 2010      INRIA Saclay
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   7  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   8  * 91893 Orsay, France
   9  */
  10
  11 #define ISL_DIM_H
  12 #include <isl_map_private.h>
  13 #include <isl_union_map_private.h>
  14 #include <isl_polynomial_private.h>
  15 #include <isl_point_private.h>
  16 #include <isl_space_private.h>
  17 #include <isl/lp.h>
  18 #include <isl/seq.h>
  19 #include <isl_mat_private.h>
  20 #include <isl_config.h>
  21
  22 enum isl_fold isl_fold_type_negate(enum isl_fold type)
  23 {
  24         switch (type) {
  25         case isl_fold_min:
  26                 return isl_fold_max;
  27         case isl_fold_max:
  28                 return isl_fold_min;
  29         case isl_fold_list:
  30                 return isl_fold_list;
  31         }
  32
  33         isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
  34 }
  35
  36 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
  37         enum isl_fold type, __isl_take isl_space *dim, int n)
  38 {
  39         isl_qpolynomial_fold *fold;
  40
  41         if (!dim)
  42                 goto error;
  43
  44         isl_assert(dim->ctx, n >= 0, goto error);
  45         fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
  46                         sizeof(struct isl_qpolynomial_fold) +
  47                         (n - 1) * sizeof(struct isl_qpolynomial *));
  48         if (!fold)
  49                 goto error;
  50
  51         fold->ref = 1;
  52         fold->size = n;
  53         fold->n = 0;
  54         fold->type = type;
  55         fold->dim = dim;
  56
  57         return fold;
  58 error:
  59         isl_space_free(dim);
  60         return NULL;
  61 }
  62
  63 isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
  64 {
  65         return fold ? fold->dim->ctx : NULL;
  66 }
  67
  68 __isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
  69         __isl_keep isl_qpolynomial_fold *fold)
  70 {
  71         return fold ? isl_space_copy(fold->dim) : NULL;
  72 }
  73
  74 __isl_give isl_space *isl_qpolynomial_fold_get_space(
  75         __isl_keep isl_qpolynomial_fold *fold)
  76 {
  77         isl_space *space;
  78         if (!fold)
  79                 return NULL;
  80         space = isl_space_copy(fold->dim);
  81         space = isl_space_from_domain(space);
  82         space = isl_space_add_dims(space, isl_dim_out, 1);
  83         return space;
  84 }
  85
  86 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
  87         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
  88 {
  89         int i;
  90
  91         fold = isl_qpolynomial_fold_cow(fold);
  92         if (!fold || !dim)
  93                 goto error;
  94
  95         for (i = 0; i < fold->n; ++i) {
  96                 fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
  97                                                         isl_space_copy(dim));
  98                 if (!fold->qp[i])
  99                         goto error;
 100         }
 101
 102         isl_space_free(fold->dim);
 103         fold->dim = dim;
 104
 105         return fold;
 106 error:
 107         isl_qpolynomial_fold_free(fold);
 108         isl_space_free(dim);
 109         return NULL;
 110 }
 111
 112 /* Reset the space of "fold".  This function is called from isl_pw_templ.c
 113  * and doesn't know if the space of an element object is represented
 114  * directly or through its domain.  It therefore passes along both.
 115  */
 116 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
 117         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
 118         __isl_take isl_space *domain)
 119 {
 120         isl_space_free(space);
 121         return isl_qpolynomial_fold_reset_domain_space(fold, domain);
 122 }
 123
 124 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
 125         enum isl_dim_type type, unsigned first, unsigned n)
 126 {
 127         int i;
 128
 129         if (!fold)
 130                 return -1;
 131         if (fold->n == 0 || n == 0)
 132                 return 0;
 133
 134         for (i = 0; i < fold->n; ++i) {
 135                 int involves = isl_qpolynomial_involves_dims(fold->qp[i],
 136                                                             type, first, n);
 137                 if (involves < 0 || involves)
 138                         return involves;
 139         }
 140         return 0;
 141 }
 142
 143 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
 144         __isl_take isl_qpolynomial_fold *fold,
 145         enum isl_dim_type type, unsigned pos, const char *s)
 146 {
 147         int i;
 148
 149         fold = isl_qpolynomial_fold_cow(fold);
 150         if (!fold)
 151                 return NULL;
 152         fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
 153         if (!fold->dim)
 154                 goto error;
 155
 156         for (i = 0; i < fold->n; ++i) {
 157                 fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
 158                                                             type, pos, s);
 159                 if (!fold->qp[i])
 160                         goto error;
 161         }
 162
 163         return fold;
 164 error:
 165         isl_qpolynomial_fold_free(fold);
 166         return NULL;
 167 }
 168
 169 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
 170         __isl_take isl_qpolynomial_fold *fold,
 171         enum isl_dim_type type, unsigned first, unsigned n)
 172 {
 173         int i;
 174         enum isl_dim_type set_type;
 175
 176         if (!fold)
 177                 return NULL;
 178         if (n == 0)
 179                 return fold;
 180
 181         set_type = type == isl_dim_in ? isl_dim_set : type;
 182
 183         fold = isl_qpolynomial_fold_cow(fold);
 184         if (!fold)
 185                 return NULL;
 186         fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
 187         if (!fold->dim)
 188                 goto error;
 189
 190         for (i = 0; i < fold->n; ++i) {
 191                 fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
 192                                                             type, first, n);
 193                 if (!fold->qp[i])
 194                         goto error;
 195         }
 196
 197         return fold;
 198 error:
 199         isl_qpolynomial_fold_free(fold);
 200         return NULL;
 201 }
 202
 203 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
 204         __isl_take isl_qpolynomial_fold *fold,
 205         enum isl_dim_type type, unsigned first, unsigned n)
 206 {
 207         int i;
 208
 209         if (!fold)
 210                 return NULL;
 211         if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
 212                 return fold;
 213
 214         fold = isl_qpolynomial_fold_cow(fold);
 215         if (!fold)
 216                 return NULL;
 217         fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
 218         if (!fold->dim)
 219                 goto error;
 220
 221         for (i = 0; i < fold->n; ++i) {
 222                 fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
 223                                                             type, first, n);
 224                 if (!fold->qp[i])
 225                         goto error;
 226         }
 227
 228         return fold;
 229 error:
 230         isl_qpolynomial_fold_free(fold);
 231         return NULL;
 232 }
 233
 234 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
 235 {
 236         struct isl_upoly_cst *cst;
 237
 238         cst = isl_upoly_as_cst(qp->upoly);
 239         if (!cst)
 240                 return 0;
 241
 242         return isl_int_sgn(cst->n) < 0 ? -1 : 1;
 243 }
 244
 245 static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
 246         __isl_keep isl_qpolynomial *qp)
 247 {
 248         enum isl_lp_result res;
 249         isl_vec *aff;
 250         isl_int opt;
 251         int sgn = 0;
 252
 253         aff = isl_qpolynomial_extract_affine(qp);
 254         if (!aff)
 255                 return 0;
 256
 257         isl_int_init(opt);
 258
 259         res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
 260                                 &opt, NULL, NULL);
 261         if (res == isl_lp_error)
 262                 goto done;
 263         if (res == isl_lp_empty ||
 264             (res == isl_lp_ok && !isl_int_is_neg(opt))) {
 265                 sgn = 1;
 266                 goto done;
 267         }
 268
 269         res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
 270                                 &opt, NULL, NULL);
 271         if (res == isl_lp_ok && !isl_int_is_pos(opt))
 272                 sgn = -1;
 273
 274 done:
 275         isl_int_clear(opt);
 276         isl_vec_free(aff);
 277         return sgn;
 278 }
 279
 280 /* Determine, if possible, the sign of the quasipolynomial "qp" on
 281  * the domain "set".
 282  *
 283  * If qp is a constant, then the problem is trivial.
 284  * If qp is linear, then we check if the minimum of the corresponding
 285  * affine constraint is non-negative or if the maximum is non-positive.
 286  *
 287  * Otherwise, we check if the outermost variable "v" has a lower bound "l"
 288  * in "set".  If so, we write qp(v,v') as
 289  *
 290  *      q(v,v') * (v - l) + r(v')
 291  *
 292  * if q(v,v') and r(v') have the same known sign, then the original
 293  * quasipolynomial has the same sign as well.
 294  *
 295  * Return
 296  *      -1 if qp <= 0
 297  *       1 if qp >= 0
 298  *       0 if unknown
 299  */
 300 static int isl_qpolynomial_sign(__isl_keep isl_set *set,
 301         __isl_keep isl_qpolynomial *qp)
 302 {
 303         int d;
 304         int i;
 305         int is;
 306         struct isl_upoly_rec *rec;
 307         isl_vec *v;
 308         isl_int l;
 309         enum isl_lp_result res;
 310         int sgn = 0;
 311
 312         is = isl_qpolynomial_is_cst(qp, NULL, NULL);
 313         if (is < 0)
 314                 return 0;
 315         if (is)
 316                 return isl_qpolynomial_cst_sign(qp);
 317
 318         is = isl_qpolynomial_is_affine(qp);
 319         if (is < 0)
 320                 return 0;
 321         if (is)
 322                 return isl_qpolynomial_aff_sign(set, qp);
 323
 324         if (qp->div->n_row > 0)
 325                 return 0;
 326
 327         rec = isl_upoly_as_rec(qp->upoly);
 328         if (!rec)
 329                 return 0;
 330
 331         d = isl_space_dim(qp->dim, isl_dim_all);
 332         v = isl_vec_alloc(set->ctx, 2 + d);
 333         if (!v)
 334                 return 0;
 335
 336         isl_seq_clr(v->el + 1, 1 + d);
 337         isl_int_set_si(v->el[0], 1);
 338         isl_int_set_si(v->el[2 + qp->upoly->var], 1);
 339
 340         isl_int_init(l);
 341
 342         res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
 343         if (res == isl_lp_ok) {
 344                 isl_qpolynomial *min;
 345                 isl_qpolynomial *base;
 346                 isl_qpolynomial *r, *q;
 347                 isl_qpolynomial *t;
 348
 349                 min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
 350                 base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
 351                                                 qp->upoly->var, 1);
 352
 353                 r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
 354                                           isl_upoly_copy(rec->p[rec->n - 1]));
 355                 q = isl_qpolynomial_copy(r);
 356
 357                 for (i = rec->n - 2; i >= 0; --i) {
 358                         r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
 359                         t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
 360                                                   isl_upoly_copy(rec->p[i]));
 361                         r = isl_qpolynomial_add(r, t);
 362                         if (i == 0)
 363                                 break;
 364                         q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
 365                         q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
 366                 }
 367
 368                 if (isl_qpolynomial_is_zero(q))
 369                         sgn = isl_qpolynomial_sign(set, r);
 370                 else if (isl_qpolynomial_is_zero(r))
 371                         sgn = isl_qpolynomial_sign(set, q);
 372                 else {
 373                         int sgn_q, sgn_r;
 374                         sgn_r = isl_qpolynomial_sign(set, r);
 375                         sgn_q = isl_qpolynomial_sign(set, q);
 376                         if (sgn_r == sgn_q)
 377                                 sgn = sgn_r;
 378                 }
 379
 380                 isl_qpolynomial_free(min);
 381                 isl_qpolynomial_free(base);
 382                 isl_qpolynomial_free(q);
 383                 isl_qpolynomial_free(r);
 384         }
 385
 386         isl_int_clear(l);
 387
 388         isl_vec_free(v);
 389
 390         return sgn;
 391 }
 392
 393 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
 394         __isl_keep isl_set *set,
 395         __isl_take isl_qpolynomial_fold *fold1,
 396         __isl_take isl_qpolynomial_fold *fold2)
 397 {
 398         int i, j;
 399         int n1;
 400         struct isl_qpolynomial_fold *res = NULL;
 401         int better;
 402
 403         if (!fold1 || !fold2)
 404                 goto error;
 405
 406         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 407         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 408                         goto error);
 409
 410         better = fold1->type == isl_fold_max ? -1 : 1;
 411
 412         if (isl_qpolynomial_fold_is_empty(fold1)) {
 413                 isl_qpolynomial_fold_free(fold1);
 414                 return fold2;
 415         }
 416
 417         if (isl_qpolynomial_fold_is_empty(fold2)) {
 418                 isl_qpolynomial_fold_free(fold2);
 419                 return fold1;
 420         }
 421
 422         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 423                                         fold1->n + fold2->n);
 424         if (!res)
 425                 goto error;
 426
 427         for (i = 0; i < fold1->n; ++i) {
 428                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 429                 if (!res->qp[res->n])
 430                         goto error;
 431                 res->n++;
 432         }
 433         n1 = res->n;
 434
 435         for (i = 0; i < fold2->n; ++i) {
 436                 for (j = n1 - 1; j >= 0; --j) {
 437                         isl_qpolynomial *d;
 438                         int sgn;
 439                         d = isl_qpolynomial_sub(
 440                                 isl_qpolynomial_copy(res->qp[j]),
 441                                 isl_qpolynomial_copy(fold2->qp[i]));
 442                         sgn = isl_qpolynomial_sign(set, d);
 443                         isl_qpolynomial_free(d);
 444                         if (sgn == 0)
 445                                 continue;
 446                         if (sgn != better)
 447                                 break;
 448                         isl_qpolynomial_free(res->qp[j]);
 449                         if (j != n1 - 1)
 450                                 res->qp[j] = res->qp[n1 - 1];
 451                         n1--;
 452                         if (n1 != res->n - 1)
 453                                 res->qp[n1] = res->qp[res->n - 1];
 454                         res->n--;
 455                 }
 456                 if (j >= 0)
 457                         continue;
 458                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 459                 if (!res->qp[res->n])
 460                         goto error;
 461                 res->n++;
 462         }
 463
 464         isl_qpolynomial_fold_free(fold1);
 465         isl_qpolynomial_fold_free(fold2);
 466
 467         return res;
 468 error:
 469         isl_qpolynomial_fold_free(res);
 470         isl_qpolynomial_fold_free(fold1);
 471         isl_qpolynomial_fold_free(fold2);
 472         return NULL;
 473 }
 474
 475 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
 476         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
 477 {
 478         int i;
 479
 480         if (!fold || !qp)
 481                 goto error;
 482
 483         if (isl_qpolynomial_is_zero(qp)) {
 484                 isl_qpolynomial_free(qp);
 485                 return fold;
 486         }
 487
 488         fold = isl_qpolynomial_fold_cow(fold);
 489         if (!fold)
 490                 goto error;
 491
 492         for (i = 0; i < fold->n; ++i) {
 493                 fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
 494                                                 isl_qpolynomial_copy(qp));
 495                 if (!fold->qp[i])
 496                         goto error;
 497         }
 498
 499         isl_qpolynomial_free(qp);
 500         return fold;
 501 error:
 502         isl_qpolynomial_fold_free(fold);
 503         isl_qpolynomial_free(qp);
 504         return NULL;
 505 }
 506
 507 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
 508         __isl_keep isl_set *dom,
 509         __isl_take isl_qpolynomial_fold *fold1,
 510         __isl_take isl_qpolynomial_fold *fold2)
 511 {
 512         int i;
 513         isl_qpolynomial_fold *res = NULL;
 514
 515         if (!fold1 || !fold2)
 516                 goto error;
 517
 518         if (isl_qpolynomial_fold_is_empty(fold1)) {
 519                 isl_qpolynomial_fold_free(fold1);
 520                 return fold2;
 521         }
 522
 523         if (isl_qpolynomial_fold_is_empty(fold2)) {
 524                 isl_qpolynomial_fold_free(fold2);
 525                 return fold1;
 526         }
 527
 528         if (fold1->n == 1 && fold2->n != 1)
 529                 return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
 530
 531         if (fold2->n == 1) {
 532                 res = isl_qpolynomial_fold_add_qpolynomial(fold1,
 533                                         isl_qpolynomial_copy(fold2->qp[0]));
 534                 isl_qpolynomial_fold_free(fold2);
 535                 return res;
 536         }
 537
 538         res = isl_qpolynomial_fold_add_qpolynomial(
 539                                 isl_qpolynomial_fold_copy(fold1),
 540                                 isl_qpolynomial_copy(fold2->qp[0]));
 541
 542         for (i = 1; i < fold2->n; ++i) {
 543                 isl_qpolynomial_fold *res_i;
 544                 res_i = isl_qpolynomial_fold_add_qpolynomial(
 545                                         isl_qpolynomial_fold_copy(fold1),
 546                                         isl_qpolynomial_copy(fold2->qp[i]));
 547                 res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
 548         }
 549
 550         isl_qpolynomial_fold_free(fold1);
 551         isl_qpolynomial_fold_free(fold2);
 552         return res;
 553 error:
 554         isl_qpolynomial_fold_free(res);
 555         isl_qpolynomial_fold_free(fold1);
 556         isl_qpolynomial_fold_free(fold2);
 557         return NULL;
 558 }
 559
 560 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
 561         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
 562 {
 563         int i;
 564
 565         if (!fold || !eq)
 566                 goto error;
 567
 568         fold = isl_qpolynomial_fold_cow(fold);
 569         if (!fold)
 570                 return NULL;
 571
 572         for (i = 0; i < fold->n; ++i) {
 573                 fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
 574                                                         isl_basic_set_copy(eq));
 575                 if (!fold->qp[i])
 576                         goto error;
 577         }
 578
 579         isl_basic_set_free(eq);
 580         return fold;
 581 error:
 582         isl_basic_set_free(eq);
 583         isl_qpolynomial_fold_free(fold);
 584         return NULL;
 585 }
 586
 587 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
 588         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 589 {
 590         int i;
 591
 592         if (!fold || !context)
 593                 goto error;
 594
 595         fold = isl_qpolynomial_fold_cow(fold);
 596         if (!fold)
 597                 return NULL;
 598
 599         for (i = 0; i < fold->n; ++i) {
 600                 fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
 601                                                         isl_set_copy(context));
 602                 if (!fold->qp[i])
 603                         goto error;
 604         }
 605
 606         isl_set_free(context);
 607         return fold;
 608 error:
 609         isl_set_free(context);
 610         isl_qpolynomial_fold_free(fold);
 611         return NULL;
 612 }
 613
 614 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
 615         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 616 {
 617         isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
 618         isl_set *dom_context = isl_set_universe(space);
 619         dom_context = isl_set_intersect_params(dom_context, context);
 620         return isl_qpolynomial_fold_gist(fold, dom_context);
 621 }
 622
 623 #define HAS_TYPE
 624
 625 #undef PW
 626 #define PW isl_pw_qpolynomial_fold
 627 #undef EL
 628 #define EL isl_qpolynomial_fold
 629 #undef EL_IS_ZERO
 630 #define EL_IS_ZERO is_empty
 631 #undef ZERO
 632 #define ZERO zero
 633 #undef IS_ZERO
 634 #define IS_ZERO is_zero
 635 #undef FIELD
 636 #define FIELD fold
 637
 638 #define NO_NEG
 639
 640 #include <isl_pw_templ.c>
 641
 642 #undef UNION
 643 #define UNION isl_union_pw_qpolynomial_fold
 644 #undef PART
 645 #define PART isl_pw_qpolynomial_fold
 646 #undef PARTS
 647 #define PARTS pw_qpolynomial_fold
 648 #define ALIGN_DOMAIN
 649
 650 #include <isl_union_templ.c>
 651
 652 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
 653         __isl_take isl_space *dim)
 654 {
 655         return qpolynomial_fold_alloc(type, dim, 0);
 656 }
 657
 658 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
 659         enum isl_fold type, __isl_take isl_qpolynomial *qp)
 660 {
 661         isl_qpolynomial_fold *fold;
 662
 663         if (!qp)
 664                 return NULL;
 665
 666         fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
 667         if (!fold)
 668                 goto error;
 669
 670         fold->qp[0] = qp;
 671         fold->n++;
 672
 673         return fold;
 674 error:
 675         isl_qpolynomial_fold_free(fold);
 676         isl_qpolynomial_free(qp);
 677         return NULL;
 678 }
 679
 680 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
 681         __isl_keep isl_qpolynomial_fold *fold)
 682 {
 683         if (!fold)
 684                 return NULL;
 685
 686         fold->ref++;
 687         return fold;
 688 }
 689
 690 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
 691         __isl_keep isl_qpolynomial_fold *fold)
 692 {
 693         int i;
 694         isl_qpolynomial_fold *dup;
 695
 696         if (!fold)
 697                 return NULL;
 698         dup = qpolynomial_fold_alloc(fold->type,
 699                                         isl_space_copy(fold->dim), fold->n);
 700         if (!dup)
 701                 return NULL;
 702
 703         dup->n = fold->n;
 704         for (i = 0; i < fold->n; ++i) {
 705                 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
 706                 if (!dup->qp[i])
 707                         goto error;
 708         }
 709
 710         return dup;
 711 error:
 712         isl_qpolynomial_fold_free(dup);
 713         return NULL;
 714 }
 715
 716 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
 717         __isl_take isl_qpolynomial_fold *fold)
 718 {
 719         if (!fold)
 720                 return NULL;
 721
 722         if (fold->ref == 1)
 723                 return fold;
 724         fold->ref--;
 725         return isl_qpolynomial_fold_dup(fold);
 726 }
 727
 728 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 729 {
 730         int i;
 731
 732         if (!fold)
 733                 return;
 734         if (--fold->ref > 0)
 735                 return;
 736
 737         for (i = 0; i < fold->n; ++i)
 738                 isl_qpolynomial_free(fold->qp[i]);
 739         isl_space_free(fold->dim);
 740         free(fold);
 741 }
 742
 743 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
 744 {
 745         if (!fold)
 746                 return -1;
 747
 748         return fold->n == 0;
 749 }
 750
 751 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
 752         __isl_take isl_qpolynomial_fold *fold1,
 753         __isl_take isl_qpolynomial_fold *fold2)
 754 {
 755         int i;
 756         struct isl_qpolynomial_fold *res = NULL;
 757
 758         if (!fold1 || !fold2)
 759                 goto error;
 760
 761         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 762         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 763                         goto error);
 764
 765         if (isl_qpolynomial_fold_is_empty(fold1)) {
 766                 isl_qpolynomial_fold_free(fold1);
 767                 return fold2;
 768         }
 769
 770         if (isl_qpolynomial_fold_is_empty(fold2)) {
 771                 isl_qpolynomial_fold_free(fold2);
 772                 return fold1;
 773         }
 774
 775         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 776                                         fold1->n + fold2->n);
 777         if (!res)
 778                 goto error;
 779
 780         for (i = 0; i < fold1->n; ++i) {
 781                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 782                 if (!res->qp[res->n])
 783                         goto error;
 784                 res->n++;
 785         }
 786
 787         for (i = 0; i < fold2->n; ++i) {
 788                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 789                 if (!res->qp[res->n])
 790                         goto error;
 791                 res->n++;
 792         }
 793
 794         isl_qpolynomial_fold_free(fold1);
 795         isl_qpolynomial_fold_free(fold2);
 796
 797         return res;
 798 error:
 799         isl_qpolynomial_fold_free(res);
 800         isl_qpolynomial_fold_free(fold1);
 801         isl_qpolynomial_fold_free(fold2);
 802         return NULL;
 803 }
 804
 805 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
 806         __isl_take isl_pw_qpolynomial_fold *pw1,
 807         __isl_take isl_pw_qpolynomial_fold *pw2)
 808 {
 809         int i, j, n;
 810         struct isl_pw_qpolynomial_fold *res;
 811         isl_set *set;
 812
 813         if (!pw1 || !pw2)
 814                 goto error;
 815
 816         isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 817
 818         if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
 819                 isl_pw_qpolynomial_fold_free(pw1);
 820                 return pw2;
 821         }
 822
 823         if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
 824                 isl_pw_qpolynomial_fold_free(pw2);
 825                 return pw1;
 826         }
 827
 828         if (pw1->type != pw2->type)
 829                 isl_die(pw1->dim->ctx, isl_error_invalid,
 830                         "fold types don't match", goto error);
 831
 832         n = (pw1->n + 1) * (pw2->n + 1);
 833         res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
 834                                                 pw1->type, n);
 835
 836         for (i = 0; i < pw1->n; ++i) {
 837                 set = isl_set_copy(pw1->p[i].set);
 838                 for (j = 0; j < pw2->n; ++j) {
 839                         struct isl_set *common;
 840                         isl_qpolynomial_fold *sum;
 841                         set = isl_set_subtract(set,
 842                                         isl_set_copy(pw2->p[j].set));
 843                         common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 844                                                 isl_set_copy(pw2->p[j].set));
 845                         if (isl_set_plain_is_empty(common)) {
 846                                 isl_set_free(common);
 847                                 continue;
 848                         }
 849
 850                         sum = isl_qpolynomial_fold_fold_on_domain(common,
 851                                isl_qpolynomial_fold_copy(pw1->p[i].fold),
 852                                isl_qpolynomial_fold_copy(pw2->p[j].fold));
 853
 854                         res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
 855                 }
 856                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 857                         isl_qpolynomial_fold_copy(pw1->p[i].fold));
 858         }
 859
 860         for (j = 0; j < pw2->n; ++j) {
 861                 set = isl_set_copy(pw2->p[j].set);
 862                 for (i = 0; i < pw1->n; ++i)
 863                         set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
 864                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 865                                     isl_qpolynomial_fold_copy(pw2->p[j].fold));
 866         }
 867
 868         isl_pw_qpolynomial_fold_free(pw1);
 869         isl_pw_qpolynomial_fold_free(pw2);
 870
 871         return res;
 872 error:
 873         isl_pw_qpolynomial_fold_free(pw1);
 874         isl_pw_qpolynomial_fold_free(pw2);
 875         return NULL;
 876 }
 877
 878 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
 879         __isl_take isl_union_pw_qpolynomial_fold *u,
 880         __isl_take isl_pw_qpolynomial_fold *part)
 881 {
 882         uint32_t hash;
 883         struct isl_hash_table_entry *entry;
 884
 885         u = isl_union_pw_qpolynomial_fold_cow(u);
 886
 887         if (!part || !u)
 888                 goto error;
 889
 890         isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
 891                                               isl_dim_param), goto error);
 892
 893         hash = isl_space_get_hash(part->dim);
 894         entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
 895                                     &has_dim, part->dim, 1);
 896         if (!entry)
 897                 goto error;
 898
 899         if (!entry->data)
 900                 entry->data = part;
 901         else {
 902                 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
 903                                             isl_pw_qpolynomial_fold_copy(part));
 904                 if (!entry->data)
 905                         goto error;
 906                 isl_pw_qpolynomial_fold_free(part);
 907         }
 908
 909         return u;
 910 error:
 911         isl_pw_qpolynomial_fold_free(part);
 912         isl_union_pw_qpolynomial_fold_free(u);
 913         return NULL;
 914 }
 915
 916 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
 917 {
 918         isl_union_pw_qpolynomial_fold **u;
 919         u = (isl_union_pw_qpolynomial_fold **)user;
 920
 921         *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 922
 923         return 0;
 924 }
 925
 926 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
 927         __isl_take isl_union_pw_qpolynomial_fold *u1,
 928         __isl_take isl_union_pw_qpolynomial_fold *u2)
 929 {
 930         u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 931
 932         if (!u1 || !u2)
 933                 goto error;
 934
 935         if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
 936                                                         &fold_part, &u1) < 0)
 937                 goto error;
 938
 939         isl_union_pw_qpolynomial_fold_free(u2);
 940
 941         return u1;
 942 error:
 943         isl_union_pw_qpolynomial_fold_free(u1);
 944         isl_union_pw_qpolynomial_fold_free(u2);
 945         return NULL;
 946 }
 947
 948 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
 949         enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 950 {
 951         int i;
 952         isl_pw_qpolynomial_fold *pwf;
 953
 954         if (!pwqp)
 955                 return NULL;
 956
 957         pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
 958                                                 type, pwqp->n);
 959
 960         for (i = 0; i < pwqp->n; ++i)
 961                 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
 962                         isl_set_copy(pwqp->p[i].set),
 963                         isl_qpolynomial_fold_alloc(type,
 964                                 isl_qpolynomial_copy(pwqp->p[i].qp)));
 965
 966         isl_pw_qpolynomial_free(pwqp);
 967
 968         return pwf;
 969 }
 970
 971 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
 972         __isl_take isl_pw_qpolynomial_fold *pwf1,
 973         __isl_take isl_pw_qpolynomial_fold *pwf2)
 974 {
 975         return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
 976 }
 977
 978 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 979         __isl_keep isl_qpolynomial_fold *fold2)
 980 {
 981         int i;
 982
 983         if (!fold1 || !fold2)
 984                 return -1;
 985
 986         if (fold1->n != fold2->n)
 987                 return 0;
 988
 989         /* We probably want to sort the qps first... */
 990         for (i = 0; i < fold1->n; ++i) {
 991                 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
 992                 if (eq < 0 || !eq)
 993                         return eq;
 994         }
 995
 996         return 1;
 997 }
 998
 999 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
1000         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
1001 {
1002         isl_qpolynomial *qp;
1003
1004         if (!fold || !pnt)
1005                 goto error;
1006         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
1007         isl_assert(pnt->dim->ctx,
1008                 fold->type == isl_fold_max || fold->type == isl_fold_min,
1009                 goto error);
1010
1011         if (fold->n == 0)
1012                 qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
1013         else {
1014                 int i;
1015                 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
1016                                                 isl_point_copy(pnt));
1017                 for (i = 1; i < fold->n; ++i) {
1018                         isl_qpolynomial *qp_i;
1019                         qp_i = isl_qpolynomial_eval(
1020                                             isl_qpolynomial_copy(fold->qp[i]),
1021                                             isl_point_copy(pnt));
1022                         if (fold->type == isl_fold_max)
1023                                 qp = isl_qpolynomial_max_cst(qp, qp_i);
1024                         else
1025                                 qp = isl_qpolynomial_min_cst(qp, qp_i);
1026                 }
1027         }
1028         isl_qpolynomial_fold_free(fold);
1029         isl_point_free(pnt);
1030
1031         return qp;
1032 error:
1033         isl_qpolynomial_fold_free(fold);
1034         isl_point_free(pnt);
1035         return NULL;
1036 }
1037
1038 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
1039 {
1040         int i;
1041         size_t n = 0;
1042
1043         for (i = 0; i < pwf->n; ++i)
1044                 n += pwf->p[i].fold->n;
1045
1046         return n;
1047 }
1048
1049 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1050         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1051 {
1052         int i;
1053         isl_qpolynomial *opt;
1054
1055         if (!set || !fold)
1056                 goto error;
1057
1058         if (fold->n == 0) {
1059                 isl_space *dim = isl_space_copy(fold->dim);
1060                 isl_set_free(set);
1061                 isl_qpolynomial_fold_free(fold);
1062                 return isl_qpolynomial_zero_on_domain(dim);
1063         }
1064
1065         opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1066                                                 isl_set_copy(set), max);
1067         for (i = 1; i < fold->n; ++i) {
1068                 isl_qpolynomial *opt_i;
1069                 opt_i = isl_qpolynomial_opt_on_domain(
1070                                 isl_qpolynomial_copy(fold->qp[i]),
1071                                 isl_set_copy(set), max);
1072                 if (max)
1073                         opt = isl_qpolynomial_max_cst(opt, opt_i);
1074                 else
1075                         opt = isl_qpolynomial_min_cst(opt, opt_i);
1076         }
1077
1078         isl_set_free(set);
1079         isl_qpolynomial_fold_free(fold);
1080
1081         return opt;
1082 error:
1083         isl_set_free(set);
1084         isl_qpolynomial_fold_free(fold);
1085         return NULL;
1086 }
1087
1088 /* Check whether for each quasi-polynomial in "fold2" there is
1089  * a quasi-polynomial in "fold1" that dominates it on "set".
1090  */
1091 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1092         __isl_keep isl_qpolynomial_fold *fold1,
1093         __isl_keep isl_qpolynomial_fold *fold2)
1094 {
1095         int i, j;
1096         int covers;
1097
1098         if (!set || !fold1 || !fold2)
1099                 return -1;
1100
1101         covers = fold1->type == isl_fold_max ? 1 : -1;
1102
1103         for (i = 0; i < fold2->n; ++i) {
1104                 for (j = 0; j < fold1->n; ++j) {
1105                         isl_qpolynomial *d;
1106                         int sgn;
1107
1108                         d = isl_qpolynomial_sub(
1109                                 isl_qpolynomial_copy(fold1->qp[j]),
1110                                 isl_qpolynomial_copy(fold2->qp[i]));
1111                         sgn = isl_qpolynomial_sign(set, d);
1112                         isl_qpolynomial_free(d);
1113                         if (sgn == covers)
1114                                 break;
1115                 }
1116                 if (j >= fold1->n)
1117                         return 0;
1118         }
1119
1120         return 1;
1121 }
1122
1123 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1124  * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1125  * that of pwf2.
1126  */
1127 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1128         __isl_keep isl_pw_qpolynomial_fold *pwf2)
1129 {
1130         int i, j;
1131         isl_set *dom1, *dom2;
1132         int is_subset;
1133
1134         if (!pwf1 || !pwf2)
1135                 return -1;
1136
1137         if (pwf2->n == 0)
1138                 return 1;
1139         if (pwf1->n == 0)
1140                 return 0;
1141
1142         dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1143         dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1144         is_subset = isl_set_is_subset(dom2, dom1);
1145         isl_set_free(dom1);
1146         isl_set_free(dom2);
1147
1148         if (is_subset < 0 || !is_subset)
1149                 return is_subset;
1150
1151         for (i = 0; i < pwf2->n; ++i) {
1152                 for (j = 0; j < pwf1->n; ++j) {
1153                         int is_empty;
1154                         isl_set *common;
1155                         int covers;
1156
1157                         common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1158                                                    isl_set_copy(pwf2->p[i].set));
1159                         is_empty = isl_set_is_empty(common);
1160                         if (is_empty < 0 || is_empty) {
1161                                 isl_set_free(common);
1162                                 if (is_empty < 0)
1163                                         return -1;
1164                                 continue;
1165                         }
1166                         covers = qpolynomial_fold_covers_on_domain(common,
1167                                         pwf1->p[j].fold, pwf2->p[i].fold);
1168                         isl_set_free(common);
1169                         if (covers < 0 || !covers)
1170                                 return covers;
1171                 }
1172         }
1173
1174         return 1;
1175 }
1176
1177 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
1178         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1179 {
1180         int i;
1181         isl_ctx *ctx;
1182
1183         if (!fold || !morph)
1184                 goto error;
1185
1186         ctx = fold->dim->ctx;
1187         isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
1188
1189         fold = isl_qpolynomial_fold_cow(fold);
1190         if (!fold)
1191                 goto error;
1192
1193         isl_space_free(fold->dim);
1194         fold->dim = isl_space_copy(morph->ran->dim);
1195         if (!fold->dim)
1196                 goto error;
1197
1198         for (i = 0; i < fold->n; ++i) {
1199                 fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
1200                                                 isl_morph_copy(morph));
1201                 if (!fold->qp[i])
1202                         goto error;
1203         }
1204
1205         isl_morph_free(morph);
1206
1207         return fold;
1208 error:
1209         isl_qpolynomial_fold_free(fold);
1210         isl_morph_free(morph);
1211         return NULL;
1212 }
1213
1214 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1215 {
1216         if (!fold)
1217                 return isl_fold_list;
1218         return fold->type;
1219 }
1220
1221 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1222         __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1223 {
1224         if (!upwf)
1225                 return isl_fold_list;
1226         return upwf->type;
1227 }
1228
1229 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1230         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
1231 {
1232         int i;
1233
1234         if (!fold || !dim)
1235                 goto error;
1236
1237         if (isl_space_is_equal(fold->dim, dim)) {
1238                 isl_space_free(dim);
1239                 return fold;
1240         }
1241
1242         fold = isl_qpolynomial_fold_cow(fold);
1243         if (!fold)
1244                 goto error;
1245
1246         isl_space_free(fold->dim);
1247         fold->dim = isl_space_copy(dim);
1248         if (!fold->dim)
1249                 goto error;
1250
1251         for (i = 0; i < fold->n; ++i) {
1252                 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1253                                                 isl_space_copy(dim));
1254                 if (!fold->qp[i])
1255                         goto error;
1256         }
1257
1258         isl_space_free(dim);
1259
1260         return fold;
1261 error:
1262         isl_qpolynomial_fold_free(fold);
1263         isl_space_free(dim);
1264         return NULL;
1265 }
1266
1267 int isl_qpolynomial_fold_foreach_qpolynomial(
1268         __isl_keep isl_qpolynomial_fold *fold,
1269         int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1270 {
1271         int i;
1272
1273         if (!fold)
1274                 return -1;
1275
1276         for (i = 0; i < fold->n; ++i)
1277                 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1278                         return -1;
1279
1280         return 0;
1281 }
1282
1283 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1284         __isl_take isl_qpolynomial_fold *fold,
1285         enum isl_dim_type dst_type, unsigned dst_pos,
1286         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1287 {
1288         int i;
1289
1290         if (n == 0)
1291                 return fold;
1292
1293         fold = isl_qpolynomial_fold_cow(fold);
1294         if (!fold)
1295                 return NULL;
1296
1297         fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
1298                                                 src_type, src_pos, n);
1299         if (!fold->dim)
1300                 goto error;
1301
1302         for (i = 0; i < fold->n; ++i) {
1303                 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1304                                 dst_type, dst_pos, src_type, src_pos, n);
1305                 if (!fold->qp[i])
1306                         goto error;
1307         }
1308
1309         return fold;
1310 error:
1311         isl_qpolynomial_fold_free(fold);
1312         return NULL;
1313 }
1314
1315 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1316  * in fold->qp[k] by subs[i].
1317  */
1318 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1319         __isl_take isl_qpolynomial_fold *fold,
1320         enum isl_dim_type type, unsigned first, unsigned n,
1321         __isl_keep isl_qpolynomial **subs)
1322 {
1323         int i;
1324
1325         if (n == 0)
1326                 return fold;
1327
1328         fold = isl_qpolynomial_fold_cow(fold);
1329         if (!fold)
1330                 return NULL;
1331
1332         for (i = 0; i < fold->n; ++i) {
1333                 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1334                                 type, first, n, subs);
1335                 if (!fold->qp[i])
1336                         goto error;
1337         }
1338
1339         return fold;
1340 error:
1341         isl_qpolynomial_fold_free(fold);
1342         return NULL;
1343 }
1344
1345 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1346 {
1347         isl_ctx *ctx;
1348         isl_pw_qpolynomial_fold *pwf;
1349         isl_union_pw_qpolynomial_fold **upwf;
1350         uint32_t hash;
1351         struct isl_hash_table_entry *entry;
1352
1353         upwf = (isl_union_pw_qpolynomial_fold **)user;
1354
1355         ctx = pwqp->dim->ctx;
1356         hash = isl_space_get_hash(pwqp->dim);
1357         entry = isl_hash_table_find(ctx, &(*upwf)->table,
1358                                      hash, &has_dim, pwqp->dim, 1);
1359         if (!entry)
1360                 goto error;
1361
1362         pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1363         if (!entry->data)
1364                 entry->data = pwf;
1365         else {
1366                 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1367                 if (!entry->data)
1368                         return -1;
1369                 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1370                         isl_pw_qpolynomial_fold_free(entry->data);
1371                         isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1372                 }
1373         }
1374
1375         return 0;
1376 error:
1377         isl_pw_qpolynomial_free(pwqp);
1378         return -1;
1379 }
1380
1381 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1382         __isl_take isl_union_pw_qpolynomial_fold *upwf,
1383         __isl_take isl_union_pw_qpolynomial *upwqp)
1384 {
1385         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1386                                 isl_union_pw_qpolynomial_get_space(upwqp));
1387         upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1388                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1389
1390         upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1391         if (!upwf || !upwqp)
1392                 goto error;
1393
1394         if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1395                                                          &upwf) < 0)
1396                 goto error;
1397
1398         isl_union_pw_qpolynomial_free(upwqp);
1399
1400         return upwf;
1401 error:
1402         isl_union_pw_qpolynomial_fold_free(upwf);
1403         isl_union_pw_qpolynomial_free(upwqp);
1404         return NULL;
1405 }
1406
1407 static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
1408 {
1409         int m;
1410         m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
1411         if (m < 0 || !m)
1412                 return m;
1413         return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
1414 }
1415
1416 /* Compute the intersection of the range of the map and the domain
1417  * of the piecewise quasipolynomial reduction and then compute a bound
1418  * on the associated quasipolynomial reduction over all elements
1419  * in this intersection.
1420  *
1421  * We first introduce some unconstrained dimensions in the
1422  * piecewise quasipolynomial, intersect the resulting domain
1423  * with the wrapped map and the compute the sum.
1424  */
1425 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1426         __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1427         int *tight)
1428 {
1429         isl_ctx *ctx;
1430         isl_set *dom;
1431         isl_space *map_dim;
1432         isl_space *pwf_dim;
1433         unsigned n_in;
1434         int ok;
1435
1436         ctx = isl_map_get_ctx(map);
1437         if (!ctx)
1438                 goto error;
1439
1440         map_dim = isl_map_get_space(map);
1441         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1442         ok = join_compatible(map_dim, pwf_dim);
1443         isl_space_free(map_dim);
1444         isl_space_free(pwf_dim);
1445         if (!ok)
1446                 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1447                         goto error);
1448
1449         n_in = isl_map_dim(map, isl_dim_in);
1450         pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
1451
1452         dom = isl_map_wrap(map);
1453         pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
1454                                                 isl_set_get_space(dom));
1455
1456         pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1457         pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1458
1459         return pwf;
1460 error:
1461         isl_map_free(map);
1462         isl_pw_qpolynomial_fold_free(pwf);
1463         return NULL;
1464 }
1465
1466 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1467         __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1468         int *tight)
1469 {
1470         return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
1471 }
1472
1473 struct isl_apply_fold_data {
1474         isl_union_pw_qpolynomial_fold *upwf;
1475         isl_union_pw_qpolynomial_fold *res;
1476         isl_map *map;
1477         int tight;
1478 };
1479
1480 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1481         void *user)
1482 {
1483         isl_space *map_dim;
1484         isl_space *pwf_dim;
1485         struct isl_apply_fold_data *data = user;
1486         int ok;
1487
1488         map_dim = isl_map_get_space(data->map);
1489         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1490         ok = join_compatible(map_dim, pwf_dim);
1491         isl_space_free(map_dim);
1492         isl_space_free(pwf_dim);
1493
1494         if (ok) {
1495                 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1496                                     pwf, data->tight ? &data->tight : NULL);
1497                 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1498                                                         data->res, pwf);
1499         } else
1500                 isl_pw_qpolynomial_fold_free(pwf);
1501
1502         return 0;
1503 }
1504
1505 static int map_apply(__isl_take isl_map *map, void *user)
1506 {
1507         struct isl_apply_fold_data *data = user;
1508         int r;
1509
1510         data->map = map;
1511         r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1512                                 data->upwf, &pw_qpolynomial_fold_apply, data);
1513
1514         isl_map_free(map);
1515         return r;
1516 }
1517
1518 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1519         __isl_take isl_union_map *umap,
1520         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1521 {
1522         isl_space *dim;
1523         enum isl_fold type;
1524         struct isl_apply_fold_data data;
1525
1526         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1527                                 isl_union_map_get_space(umap));
1528         umap = isl_union_map_align_params(umap,
1529                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1530
1531         data.upwf = upwf;
1532         data.tight = tight ? 1 : 0;
1533         dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
1534         type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1535         data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1536         if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1537                 goto error;
1538
1539         isl_union_map_free(umap);
1540         isl_union_pw_qpolynomial_fold_free(upwf);
1541
1542         if (tight)
1543                 *tight = data.tight;
1544
1545         return data.res;
1546 error:
1547         isl_union_map_free(umap);
1548         isl_union_pw_qpolynomial_fold_free(upwf);
1549         isl_union_pw_qpolynomial_fold_free(data.res);
1550         return NULL;
1551 }
1552
1553 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1554         __isl_take isl_union_set *uset,
1555         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1556 {
1557         return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1558 }
1559
1560 /* Reorder the dimension of "fold" according to the given reordering.
1561  */
1562 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
1563         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1564 {
1565         int i;
1566
1567         fold = isl_qpolynomial_fold_cow(fold);
1568         if (!fold || !r)
1569                 goto error;
1570
1571         for (i = 0; i < fold->n; ++i) {
1572                 fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
1573                                                     isl_reordering_copy(r));
1574                 if (!fold->qp[i])
1575                         goto error;
1576         }
1577
1578         fold = isl_qpolynomial_fold_reset_domain_space(fold,
1579                                                     isl_space_copy(r->dim));
1580
1581         isl_reordering_free(r);
1582
1583         return fold;
1584 error:
1585         isl_qpolynomial_fold_free(fold);
1586         isl_reordering_free(r);
1587         return NULL;
1588 }
1589
1590 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1591         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1592 {
1593         int i;
1594
1595         if (isl_int_is_one(v))
1596                 return fold;
1597         if (fold && isl_int_is_zero(v)) {
1598                 isl_qpolynomial_fold *zero;
1599                 isl_space *dim = isl_space_copy(fold->dim);
1600                 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1601                 isl_qpolynomial_fold_free(fold);
1602                 return zero;
1603         }
1604
1605         fold = isl_qpolynomial_fold_cow(fold);
1606         if (!fold)
1607                 return NULL;
1608
1609         if (isl_int_is_neg(v))
1610                 fold->type = isl_fold_type_negate(fold->type);
1611         for (i = 0; i < fold->n; ++i) {
1612                 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1613                 if (!fold->qp[i])
1614                         goto error;
1615         }
1616
1617         return fold;
1618 error:
1619         isl_qpolynomial_fold_free(fold);
1620         return NULL;
1621 }
1622
1623 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1624         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1625 {
1626         return isl_qpolynomial_fold_mul_isl_int(fold, v);
1627 }