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 #define HAS_TYPE
 615
 616 #undef PW
 617 #define PW isl_pw_qpolynomial_fold
 618 #undef EL
 619 #define EL isl_qpolynomial_fold
 620 #undef EL_IS_ZERO
 621 #define EL_IS_ZERO is_empty
 622 #undef ZERO
 623 #define ZERO zero
 624 #undef IS_ZERO
 625 #define IS_ZERO is_zero
 626 #undef FIELD
 627 #define FIELD fold
 628
 629 #define NO_NEG
 630
 631 #include <isl_pw_templ.c>
 632
 633 #undef UNION
 634 #define UNION isl_union_pw_qpolynomial_fold
 635 #undef PART
 636 #define PART isl_pw_qpolynomial_fold
 637 #undef PARTS
 638 #define PARTS pw_qpolynomial_fold
 639 #define ALIGN_DOMAIN
 640
 641 #include <isl_union_templ.c>
 642
 643 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
 644         __isl_take isl_space *dim)
 645 {
 646         return qpolynomial_fold_alloc(type, dim, 0);
 647 }
 648
 649 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
 650         enum isl_fold type, __isl_take isl_qpolynomial *qp)
 651 {
 652         isl_qpolynomial_fold *fold;
 653
 654         if (!qp)
 655                 return NULL;
 656
 657         fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
 658         if (!fold)
 659                 goto error;
 660
 661         fold->qp[0] = qp;
 662         fold->n++;
 663
 664         return fold;
 665 error:
 666         isl_qpolynomial_fold_free(fold);
 667         isl_qpolynomial_free(qp);
 668         return NULL;
 669 }
 670
 671 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
 672         __isl_keep isl_qpolynomial_fold *fold)
 673 {
 674         if (!fold)
 675                 return NULL;
 676
 677         fold->ref++;
 678         return fold;
 679 }
 680
 681 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
 682         __isl_keep isl_qpolynomial_fold *fold)
 683 {
 684         int i;
 685         isl_qpolynomial_fold *dup;
 686
 687         if (!fold)
 688                 return NULL;
 689         dup = qpolynomial_fold_alloc(fold->type,
 690                                         isl_space_copy(fold->dim), fold->n);
 691         if (!dup)
 692                 return NULL;
 693
 694         dup->n = fold->n;
 695         for (i = 0; i < fold->n; ++i) {
 696                 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
 697                 if (!dup->qp[i])
 698                         goto error;
 699         }
 700
 701         return dup;
 702 error:
 703         isl_qpolynomial_fold_free(dup);
 704         return NULL;
 705 }
 706
 707 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
 708         __isl_take isl_qpolynomial_fold *fold)
 709 {
 710         if (!fold)
 711                 return NULL;
 712
 713         if (fold->ref == 1)
 714                 return fold;
 715         fold->ref--;
 716         return isl_qpolynomial_fold_dup(fold);
 717 }
 718
 719 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 720 {
 721         int i;
 722
 723         if (!fold)
 724                 return;
 725         if (--fold->ref > 0)
 726                 return;
 727
 728         for (i = 0; i < fold->n; ++i)
 729                 isl_qpolynomial_free(fold->qp[i]);
 730         isl_space_free(fold->dim);
 731         free(fold);
 732 }
 733
 734 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
 735 {
 736         if (!fold)
 737                 return -1;
 738
 739         return fold->n == 0;
 740 }
 741
 742 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
 743         __isl_take isl_qpolynomial_fold *fold1,
 744         __isl_take isl_qpolynomial_fold *fold2)
 745 {
 746         int i;
 747         struct isl_qpolynomial_fold *res = NULL;
 748
 749         if (!fold1 || !fold2)
 750                 goto error;
 751
 752         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 753         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 754                         goto error);
 755
 756         if (isl_qpolynomial_fold_is_empty(fold1)) {
 757                 isl_qpolynomial_fold_free(fold1);
 758                 return fold2;
 759         }
 760
 761         if (isl_qpolynomial_fold_is_empty(fold2)) {
 762                 isl_qpolynomial_fold_free(fold2);
 763                 return fold1;
 764         }
 765
 766         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 767                                         fold1->n + fold2->n);
 768         if (!res)
 769                 goto error;
 770
 771         for (i = 0; i < fold1->n; ++i) {
 772                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 773                 if (!res->qp[res->n])
 774                         goto error;
 775                 res->n++;
 776         }
 777
 778         for (i = 0; i < fold2->n; ++i) {
 779                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 780                 if (!res->qp[res->n])
 781                         goto error;
 782                 res->n++;
 783         }
 784
 785         isl_qpolynomial_fold_free(fold1);
 786         isl_qpolynomial_fold_free(fold2);
 787
 788         return res;
 789 error:
 790         isl_qpolynomial_fold_free(res);
 791         isl_qpolynomial_fold_free(fold1);
 792         isl_qpolynomial_fold_free(fold2);
 793         return NULL;
 794 }
 795
 796 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
 797         __isl_take isl_pw_qpolynomial_fold *pw1,
 798         __isl_take isl_pw_qpolynomial_fold *pw2)
 799 {
 800         int i, j, n;
 801         struct isl_pw_qpolynomial_fold *res;
 802         isl_set *set;
 803
 804         if (!pw1 || !pw2)
 805                 goto error;
 806
 807         isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 808
 809         if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
 810                 isl_pw_qpolynomial_fold_free(pw1);
 811                 return pw2;
 812         }
 813
 814         if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
 815                 isl_pw_qpolynomial_fold_free(pw2);
 816                 return pw1;
 817         }
 818
 819         if (pw1->type != pw2->type)
 820                 isl_die(pw1->dim->ctx, isl_error_invalid,
 821                         "fold types don't match", goto error);
 822
 823         n = (pw1->n + 1) * (pw2->n + 1);
 824         res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
 825                                                 pw1->type, n);
 826
 827         for (i = 0; i < pw1->n; ++i) {
 828                 set = isl_set_copy(pw1->p[i].set);
 829                 for (j = 0; j < pw2->n; ++j) {
 830                         struct isl_set *common;
 831                         isl_qpolynomial_fold *sum;
 832                         set = isl_set_subtract(set,
 833                                         isl_set_copy(pw2->p[j].set));
 834                         common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 835                                                 isl_set_copy(pw2->p[j].set));
 836                         if (isl_set_plain_is_empty(common)) {
 837                                 isl_set_free(common);
 838                                 continue;
 839                         }
 840
 841                         sum = isl_qpolynomial_fold_fold_on_domain(common,
 842                                isl_qpolynomial_fold_copy(pw1->p[i].fold),
 843                                isl_qpolynomial_fold_copy(pw2->p[j].fold));
 844
 845                         res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
 846                 }
 847                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 848                         isl_qpolynomial_fold_copy(pw1->p[i].fold));
 849         }
 850
 851         for (j = 0; j < pw2->n; ++j) {
 852                 set = isl_set_copy(pw2->p[j].set);
 853                 for (i = 0; i < pw1->n; ++i)
 854                         set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
 855                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 856                                     isl_qpolynomial_fold_copy(pw2->p[j].fold));
 857         }
 858
 859         isl_pw_qpolynomial_fold_free(pw1);
 860         isl_pw_qpolynomial_fold_free(pw2);
 861
 862         return res;
 863 error:
 864         isl_pw_qpolynomial_fold_free(pw1);
 865         isl_pw_qpolynomial_fold_free(pw2);
 866         return NULL;
 867 }
 868
 869 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
 870         __isl_take isl_union_pw_qpolynomial_fold *u,
 871         __isl_take isl_pw_qpolynomial_fold *part)
 872 {
 873         uint32_t hash;
 874         struct isl_hash_table_entry *entry;
 875
 876         u = isl_union_pw_qpolynomial_fold_cow(u);
 877
 878         if (!part || !u)
 879                 goto error;
 880
 881         isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
 882                                               isl_dim_param), goto error);
 883
 884         hash = isl_space_get_hash(part->dim);
 885         entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
 886                                     &has_dim, part->dim, 1);
 887         if (!entry)
 888                 goto error;
 889
 890         if (!entry->data)
 891                 entry->data = part;
 892         else {
 893                 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
 894                                             isl_pw_qpolynomial_fold_copy(part));
 895                 if (!entry->data)
 896                         goto error;
 897                 isl_pw_qpolynomial_fold_free(part);
 898         }
 899
 900         return u;
 901 error:
 902         isl_pw_qpolynomial_fold_free(part);
 903         isl_union_pw_qpolynomial_fold_free(u);
 904         return NULL;
 905 }
 906
 907 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
 908 {
 909         isl_union_pw_qpolynomial_fold **u;
 910         u = (isl_union_pw_qpolynomial_fold **)user;
 911
 912         *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 913
 914         return 0;
 915 }
 916
 917 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
 918         __isl_take isl_union_pw_qpolynomial_fold *u1,
 919         __isl_take isl_union_pw_qpolynomial_fold *u2)
 920 {
 921         u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 922
 923         if (!u1 || !u2)
 924                 goto error;
 925
 926         if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
 927                                                         &fold_part, &u1) < 0)
 928                 goto error;
 929
 930         isl_union_pw_qpolynomial_fold_free(u2);
 931
 932         return u1;
 933 error:
 934         isl_union_pw_qpolynomial_fold_free(u1);
 935         isl_union_pw_qpolynomial_fold_free(u2);
 936         return NULL;
 937 }
 938
 939 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
 940         enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 941 {
 942         int i;
 943         isl_pw_qpolynomial_fold *pwf;
 944
 945         if (!pwqp)
 946                 return NULL;
 947
 948         pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
 949                                                 type, pwqp->n);
 950
 951         for (i = 0; i < pwqp->n; ++i)
 952                 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
 953                         isl_set_copy(pwqp->p[i].set),
 954                         isl_qpolynomial_fold_alloc(type,
 955                                 isl_qpolynomial_copy(pwqp->p[i].qp)));
 956
 957         isl_pw_qpolynomial_free(pwqp);
 958
 959         return pwf;
 960 }
 961
 962 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 963         __isl_keep isl_qpolynomial_fold *fold2)
 964 {
 965         int i;
 966
 967         if (!fold1 || !fold2)
 968                 return -1;
 969
 970         if (fold1->n != fold2->n)
 971                 return 0;
 972
 973         /* We probably want to sort the qps first... */
 974         for (i = 0; i < fold1->n; ++i) {
 975                 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
 976                 if (eq < 0 || !eq)
 977                         return eq;
 978         }
 979
 980         return 1;
 981 }
 982
 983 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
 984         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
 985 {
 986         isl_qpolynomial *qp;
 987
 988         if (!fold || !pnt)
 989                 goto error;
 990         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
 991         isl_assert(pnt->dim->ctx,
 992                 fold->type == isl_fold_max || fold->type == isl_fold_min,
 993                 goto error);
 994
 995         if (fold->n == 0)
 996                 qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
 997         else {
 998                 int i;
 999                 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
1000                                                 isl_point_copy(pnt));
1001                 for (i = 1; i < fold->n; ++i) {
1002                         isl_qpolynomial *qp_i;
1003                         qp_i = isl_qpolynomial_eval(
1004                                             isl_qpolynomial_copy(fold->qp[i]),
1005                                             isl_point_copy(pnt));
1006                         if (fold->type == isl_fold_max)
1007                                 qp = isl_qpolynomial_max_cst(qp, qp_i);
1008                         else
1009                                 qp = isl_qpolynomial_min_cst(qp, qp_i);
1010                 }
1011         }
1012         isl_qpolynomial_fold_free(fold);
1013         isl_point_free(pnt);
1014
1015         return qp;
1016 error:
1017         isl_qpolynomial_fold_free(fold);
1018         isl_point_free(pnt);
1019         return NULL;
1020 }
1021
1022 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
1023 {
1024         int i;
1025         size_t n = 0;
1026
1027         for (i = 0; i < pwf->n; ++i)
1028                 n += pwf->p[i].fold->n;
1029
1030         return n;
1031 }
1032
1033 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1034         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1035 {
1036         int i;
1037         isl_qpolynomial *opt;
1038
1039         if (!set || !fold)
1040                 goto error;
1041
1042         if (fold->n == 0) {
1043                 isl_space *dim = isl_space_copy(fold->dim);
1044                 isl_set_free(set);
1045                 isl_qpolynomial_fold_free(fold);
1046                 return isl_qpolynomial_zero_on_domain(dim);
1047         }
1048
1049         opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1050                                                 isl_set_copy(set), max);
1051         for (i = 1; i < fold->n; ++i) {
1052                 isl_qpolynomial *opt_i;
1053                 opt_i = isl_qpolynomial_opt_on_domain(
1054                                 isl_qpolynomial_copy(fold->qp[i]),
1055                                 isl_set_copy(set), max);
1056                 if (max)
1057                         opt = isl_qpolynomial_max_cst(opt, opt_i);
1058                 else
1059                         opt = isl_qpolynomial_min_cst(opt, opt_i);
1060         }
1061
1062         isl_set_free(set);
1063         isl_qpolynomial_fold_free(fold);
1064
1065         return opt;
1066 error:
1067         isl_set_free(set);
1068         isl_qpolynomial_fold_free(fold);
1069         return NULL;
1070 }
1071
1072 /* Check whether for each quasi-polynomial in "fold2" there is
1073  * a quasi-polynomial in "fold1" that dominates it on "set".
1074  */
1075 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1076         __isl_keep isl_qpolynomial_fold *fold1,
1077         __isl_keep isl_qpolynomial_fold *fold2)
1078 {
1079         int i, j;
1080         int covers;
1081
1082         if (!set || !fold1 || !fold2)
1083                 return -1;
1084
1085         covers = fold1->type == isl_fold_max ? 1 : -1;
1086
1087         for (i = 0; i < fold2->n; ++i) {
1088                 for (j = 0; j < fold1->n; ++j) {
1089                         isl_qpolynomial *d;
1090                         int sgn;
1091
1092                         d = isl_qpolynomial_sub(
1093                                 isl_qpolynomial_copy(fold1->qp[j]),
1094                                 isl_qpolynomial_copy(fold2->qp[i]));
1095                         sgn = isl_qpolynomial_sign(set, d);
1096                         isl_qpolynomial_free(d);
1097                         if (sgn == covers)
1098                                 break;
1099                 }
1100                 if (j >= fold1->n)
1101                         return 0;
1102         }
1103
1104         return 1;
1105 }
1106
1107 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1108  * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1109  * that of pwf2.
1110  */
1111 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1112         __isl_keep isl_pw_qpolynomial_fold *pwf2)
1113 {
1114         int i, j;
1115         isl_set *dom1, *dom2;
1116         int is_subset;
1117
1118         if (!pwf1 || !pwf2)
1119                 return -1;
1120
1121         if (pwf2->n == 0)
1122                 return 1;
1123         if (pwf1->n == 0)
1124                 return 0;
1125
1126         dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1127         dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1128         is_subset = isl_set_is_subset(dom2, dom1);
1129         isl_set_free(dom1);
1130         isl_set_free(dom2);
1131
1132         if (is_subset < 0 || !is_subset)
1133                 return is_subset;
1134
1135         for (i = 0; i < pwf2->n; ++i) {
1136                 for (j = 0; j < pwf1->n; ++j) {
1137                         int is_empty;
1138                         isl_set *common;
1139                         int covers;
1140
1141                         common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1142                                                    isl_set_copy(pwf2->p[i].set));
1143                         is_empty = isl_set_is_empty(common);
1144                         if (is_empty < 0 || is_empty) {
1145                                 isl_set_free(common);
1146                                 if (is_empty < 0)
1147                                         return -1;
1148                                 continue;
1149                         }
1150                         covers = qpolynomial_fold_covers_on_domain(common,
1151                                         pwf1->p[j].fold, pwf2->p[i].fold);
1152                         isl_set_free(common);
1153                         if (covers < 0 || !covers)
1154                                 return covers;
1155                 }
1156         }
1157
1158         return 1;
1159 }
1160
1161 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
1162         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1163 {
1164         int i;
1165         isl_ctx *ctx;
1166
1167         if (!fold || !morph)
1168                 goto error;
1169
1170         ctx = fold->dim->ctx;
1171         isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
1172
1173         fold = isl_qpolynomial_fold_cow(fold);
1174         if (!fold)
1175                 goto error;
1176
1177         isl_space_free(fold->dim);
1178         fold->dim = isl_space_copy(morph->ran->dim);
1179         if (!fold->dim)
1180                 goto error;
1181
1182         for (i = 0; i < fold->n; ++i) {
1183                 fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
1184                                                 isl_morph_copy(morph));
1185                 if (!fold->qp[i])
1186                         goto error;
1187         }
1188
1189         isl_morph_free(morph);
1190
1191         return fold;
1192 error:
1193         isl_qpolynomial_fold_free(fold);
1194         isl_morph_free(morph);
1195         return NULL;
1196 }
1197
1198 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1199 {
1200         if (!fold)
1201                 return isl_fold_list;
1202         return fold->type;
1203 }
1204
1205 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1206         __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1207 {
1208         if (!upwf)
1209                 return isl_fold_list;
1210         return upwf->type;
1211 }
1212
1213 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1214         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
1215 {
1216         int i;
1217
1218         if (!fold || !dim)
1219                 goto error;
1220
1221         if (isl_space_is_equal(fold->dim, dim)) {
1222                 isl_space_free(dim);
1223                 return fold;
1224         }
1225
1226         fold = isl_qpolynomial_fold_cow(fold);
1227         if (!fold)
1228                 goto error;
1229
1230         isl_space_free(fold->dim);
1231         fold->dim = isl_space_copy(dim);
1232         if (!fold->dim)
1233                 goto error;
1234
1235         for (i = 0; i < fold->n; ++i) {
1236                 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1237                                                 isl_space_copy(dim));
1238                 if (!fold->qp[i])
1239                         goto error;
1240         }
1241
1242         isl_space_free(dim);
1243
1244         return fold;
1245 error:
1246         isl_qpolynomial_fold_free(fold);
1247         isl_space_free(dim);
1248         return NULL;
1249 }
1250
1251 int isl_qpolynomial_fold_foreach_qpolynomial(
1252         __isl_keep isl_qpolynomial_fold *fold,
1253         int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1254 {
1255         int i;
1256
1257         if (!fold)
1258                 return -1;
1259
1260         for (i = 0; i < fold->n; ++i)
1261                 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1262                         return -1;
1263
1264         return 0;
1265 }
1266
1267 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1268         __isl_take isl_qpolynomial_fold *fold,
1269         enum isl_dim_type dst_type, unsigned dst_pos,
1270         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1271 {
1272         int i;
1273
1274         if (n == 0)
1275                 return fold;
1276
1277         fold = isl_qpolynomial_fold_cow(fold);
1278         if (!fold)
1279                 return NULL;
1280
1281         fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
1282                                                 src_type, src_pos, n);
1283         if (!fold->dim)
1284                 goto error;
1285
1286         for (i = 0; i < fold->n; ++i) {
1287                 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1288                                 dst_type, dst_pos, src_type, src_pos, n);
1289                 if (!fold->qp[i])
1290                         goto error;
1291         }
1292
1293         return fold;
1294 error:
1295         isl_qpolynomial_fold_free(fold);
1296         return NULL;
1297 }
1298
1299 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1300  * in fold->qp[k] by subs[i].
1301  */
1302 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1303         __isl_take isl_qpolynomial_fold *fold,
1304         enum isl_dim_type type, unsigned first, unsigned n,
1305         __isl_keep isl_qpolynomial **subs)
1306 {
1307         int i;
1308
1309         if (n == 0)
1310                 return fold;
1311
1312         fold = isl_qpolynomial_fold_cow(fold);
1313         if (!fold)
1314                 return NULL;
1315
1316         for (i = 0; i < fold->n; ++i) {
1317                 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1318                                 type, first, n, subs);
1319                 if (!fold->qp[i])
1320                         goto error;
1321         }
1322
1323         return fold;
1324 error:
1325         isl_qpolynomial_fold_free(fold);
1326         return NULL;
1327 }
1328
1329 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1330 {
1331         isl_ctx *ctx;
1332         isl_pw_qpolynomial_fold *pwf;
1333         isl_union_pw_qpolynomial_fold **upwf;
1334         uint32_t hash;
1335         struct isl_hash_table_entry *entry;
1336
1337         upwf = (isl_union_pw_qpolynomial_fold **)user;
1338
1339         ctx = pwqp->dim->ctx;
1340         hash = isl_space_get_hash(pwqp->dim);
1341         entry = isl_hash_table_find(ctx, &(*upwf)->table,
1342                                      hash, &has_dim, pwqp->dim, 1);
1343         if (!entry)
1344                 goto error;
1345
1346         pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1347         if (!entry->data)
1348                 entry->data = pwf;
1349         else {
1350                 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1351                 if (!entry->data)
1352                         return -1;
1353                 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1354                         isl_pw_qpolynomial_fold_free(entry->data);
1355                         isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1356                 }
1357         }
1358
1359         return 0;
1360 error:
1361         isl_pw_qpolynomial_free(pwqp);
1362         return -1;
1363 }
1364
1365 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1366         __isl_take isl_union_pw_qpolynomial_fold *upwf,
1367         __isl_take isl_union_pw_qpolynomial *upwqp)
1368 {
1369         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1370                                 isl_union_pw_qpolynomial_get_space(upwqp));
1371         upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1372                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1373
1374         upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1375         if (!upwf || !upwqp)
1376                 goto error;
1377
1378         if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1379                                                          &upwf) < 0)
1380                 goto error;
1381
1382         isl_union_pw_qpolynomial_free(upwqp);
1383
1384         return upwf;
1385 error:
1386         isl_union_pw_qpolynomial_fold_free(upwf);
1387         isl_union_pw_qpolynomial_free(upwqp);
1388         return NULL;
1389 }
1390
1391 static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
1392 {
1393         int m;
1394         m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
1395         if (m < 0 || !m)
1396                 return m;
1397         return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
1398 }
1399
1400 /* Compute the intersection of the range of the map and the domain
1401  * of the piecewise quasipolynomial reduction and then compute a bound
1402  * on the associated quasipolynomial reduction over all elements
1403  * in this intersection.
1404  *
1405  * We first introduce some unconstrained dimensions in the
1406  * piecewise quasipolynomial, intersect the resulting domain
1407  * with the wrapped map and the compute the sum.
1408  */
1409 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1410         __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1411         int *tight)
1412 {
1413         isl_ctx *ctx;
1414         isl_set *dom;
1415         isl_space *map_dim;
1416         isl_space *pwf_dim;
1417         unsigned n_in;
1418         int ok;
1419
1420         ctx = isl_map_get_ctx(map);
1421         if (!ctx)
1422                 goto error;
1423
1424         map_dim = isl_map_get_space(map);
1425         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1426         ok = join_compatible(map_dim, pwf_dim);
1427         isl_space_free(map_dim);
1428         isl_space_free(pwf_dim);
1429         if (!ok)
1430                 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1431                         goto error);
1432
1433         n_in = isl_map_dim(map, isl_dim_in);
1434         pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
1435
1436         dom = isl_map_wrap(map);
1437         pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
1438                                                 isl_set_get_space(dom));
1439
1440         pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1441         pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1442
1443         return pwf;
1444 error:
1445         isl_map_free(map);
1446         isl_pw_qpolynomial_fold_free(pwf);
1447         return NULL;
1448 }
1449
1450 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1451         __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1452         int *tight)
1453 {
1454         return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
1455 }
1456
1457 struct isl_apply_fold_data {
1458         isl_union_pw_qpolynomial_fold *upwf;
1459         isl_union_pw_qpolynomial_fold *res;
1460         isl_map *map;
1461         int tight;
1462 };
1463
1464 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1465         void *user)
1466 {
1467         isl_space *map_dim;
1468         isl_space *pwf_dim;
1469         struct isl_apply_fold_data *data = user;
1470         int ok;
1471
1472         map_dim = isl_map_get_space(data->map);
1473         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1474         ok = join_compatible(map_dim, pwf_dim);
1475         isl_space_free(map_dim);
1476         isl_space_free(pwf_dim);
1477
1478         if (ok) {
1479                 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1480                                     pwf, data->tight ? &data->tight : NULL);
1481                 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1482                                                         data->res, pwf);
1483         } else
1484                 isl_pw_qpolynomial_fold_free(pwf);
1485
1486         return 0;
1487 }
1488
1489 static int map_apply(__isl_take isl_map *map, void *user)
1490 {
1491         struct isl_apply_fold_data *data = user;
1492         int r;
1493
1494         data->map = map;
1495         r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1496                                 data->upwf, &pw_qpolynomial_fold_apply, data);
1497
1498         isl_map_free(map);
1499         return r;
1500 }
1501
1502 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1503         __isl_take isl_union_map *umap,
1504         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1505 {
1506         isl_space *dim;
1507         enum isl_fold type;
1508         struct isl_apply_fold_data data;
1509
1510         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1511                                 isl_union_map_get_space(umap));
1512         umap = isl_union_map_align_params(umap,
1513                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1514
1515         data.upwf = upwf;
1516         data.tight = tight ? 1 : 0;
1517         dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
1518         type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1519         data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1520         if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1521                 goto error;
1522
1523         isl_union_map_free(umap);
1524         isl_union_pw_qpolynomial_fold_free(upwf);
1525
1526         if (tight)
1527                 *tight = data.tight;
1528
1529         return data.res;
1530 error:
1531         isl_union_map_free(umap);
1532         isl_union_pw_qpolynomial_fold_free(upwf);
1533         isl_union_pw_qpolynomial_fold_free(data.res);
1534         return NULL;
1535 }
1536
1537 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1538         __isl_take isl_union_set *uset,
1539         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1540 {
1541         return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1542 }
1543
1544 /* Reorder the dimension of "fold" according to the given reordering.
1545  */
1546 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
1547         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1548 {
1549         int i;
1550
1551         fold = isl_qpolynomial_fold_cow(fold);
1552         if (!fold || !r)
1553                 goto error;
1554
1555         for (i = 0; i < fold->n; ++i) {
1556                 fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
1557                                                     isl_reordering_copy(r));
1558                 if (!fold->qp[i])
1559                         goto error;
1560         }
1561
1562         fold = isl_qpolynomial_fold_reset_domain_space(fold,
1563                                                     isl_space_copy(r->dim));
1564
1565         isl_reordering_free(r);
1566
1567         return fold;
1568 error:
1569         isl_qpolynomial_fold_free(fold);
1570         isl_reordering_free(r);
1571         return NULL;
1572 }
1573
1574 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1575         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1576 {
1577         int i;
1578
1579         if (isl_int_is_one(v))
1580                 return fold;
1581         if (fold && isl_int_is_zero(v)) {
1582                 isl_qpolynomial_fold *zero;
1583                 isl_space *dim = isl_space_copy(fold->dim);
1584                 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1585                 isl_qpolynomial_fold_free(fold);
1586                 return zero;
1587         }
1588
1589         fold = isl_qpolynomial_fold_cow(fold);
1590         if (!fold)
1591                 return NULL;
1592
1593         if (isl_int_is_neg(v))
1594                 fold->type = isl_fold_type_negate(fold->type);
1595         for (i = 0; i < fold->n; ++i) {
1596                 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1597                 if (!fold->qp[i])
1598                         goto error;
1599         }
1600
1601         return fold;
1602 error:
1603         isl_qpolynomial_fold_free(fold);
1604         return NULL;
1605 }
1606
1607 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1608         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1609 {
1610         return isl_qpolynomial_fold_mul_isl_int(fold, v);
1611 }