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 #undef DEFAULT_IS_ZERO
 629 #define DEFAULT_IS_ZERO 1
 630
 631 #define NO_NEG
 632
 633 #include <isl_pw_templ.c>
 634
 635 #undef UNION
 636 #define UNION isl_union_pw_qpolynomial_fold
 637 #undef PART
 638 #define PART isl_pw_qpolynomial_fold
 639 #undef PARTS
 640 #define PARTS pw_qpolynomial_fold
 641 #define ALIGN_DOMAIN
 642
 643 #include <isl_union_templ.c>
 644
 645 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
 646         __isl_take isl_space *dim)
 647 {
 648         return qpolynomial_fold_alloc(type, dim, 0);
 649 }
 650
 651 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
 652         enum isl_fold type, __isl_take isl_qpolynomial *qp)
 653 {
 654         isl_qpolynomial_fold *fold;
 655
 656         if (!qp)
 657                 return NULL;
 658
 659         fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
 660         if (!fold)
 661                 goto error;
 662
 663         fold->qp[0] = qp;
 664         fold->n++;
 665
 666         return fold;
 667 error:
 668         isl_qpolynomial_fold_free(fold);
 669         isl_qpolynomial_free(qp);
 670         return NULL;
 671 }
 672
 673 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
 674         __isl_keep isl_qpolynomial_fold *fold)
 675 {
 676         if (!fold)
 677                 return NULL;
 678
 679         fold->ref++;
 680         return fold;
 681 }
 682
 683 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
 684         __isl_keep isl_qpolynomial_fold *fold)
 685 {
 686         int i;
 687         isl_qpolynomial_fold *dup;
 688
 689         if (!fold)
 690                 return NULL;
 691         dup = qpolynomial_fold_alloc(fold->type,
 692                                         isl_space_copy(fold->dim), fold->n);
 693         if (!dup)
 694                 return NULL;
 695
 696         dup->n = fold->n;
 697         for (i = 0; i < fold->n; ++i) {
 698                 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
 699                 if (!dup->qp[i])
 700                         goto error;
 701         }
 702
 703         return dup;
 704 error:
 705         isl_qpolynomial_fold_free(dup);
 706         return NULL;
 707 }
 708
 709 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
 710         __isl_take isl_qpolynomial_fold *fold)
 711 {
 712         if (!fold)
 713                 return NULL;
 714
 715         if (fold->ref == 1)
 716                 return fold;
 717         fold->ref--;
 718         return isl_qpolynomial_fold_dup(fold);
 719 }
 720
 721 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 722 {
 723         int i;
 724
 725         if (!fold)
 726                 return;
 727         if (--fold->ref > 0)
 728                 return;
 729
 730         for (i = 0; i < fold->n; ++i)
 731                 isl_qpolynomial_free(fold->qp[i]);
 732         isl_space_free(fold->dim);
 733         free(fold);
 734 }
 735
 736 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
 737 {
 738         if (!fold)
 739                 return -1;
 740
 741         return fold->n == 0;
 742 }
 743
 744 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
 745         __isl_take isl_qpolynomial_fold *fold1,
 746         __isl_take isl_qpolynomial_fold *fold2)
 747 {
 748         int i;
 749         struct isl_qpolynomial_fold *res = NULL;
 750
 751         if (!fold1 || !fold2)
 752                 goto error;
 753
 754         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 755         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 756                         goto error);
 757
 758         if (isl_qpolynomial_fold_is_empty(fold1)) {
 759                 isl_qpolynomial_fold_free(fold1);
 760                 return fold2;
 761         }
 762
 763         if (isl_qpolynomial_fold_is_empty(fold2)) {
 764                 isl_qpolynomial_fold_free(fold2);
 765                 return fold1;
 766         }
 767
 768         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 769                                         fold1->n + fold2->n);
 770         if (!res)
 771                 goto error;
 772
 773         for (i = 0; i < fold1->n; ++i) {
 774                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 775                 if (!res->qp[res->n])
 776                         goto error;
 777                 res->n++;
 778         }
 779
 780         for (i = 0; i < fold2->n; ++i) {
 781                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 782                 if (!res->qp[res->n])
 783                         goto error;
 784                 res->n++;
 785         }
 786
 787         isl_qpolynomial_fold_free(fold1);
 788         isl_qpolynomial_fold_free(fold2);
 789
 790         return res;
 791 error:
 792         isl_qpolynomial_fold_free(res);
 793         isl_qpolynomial_fold_free(fold1);
 794         isl_qpolynomial_fold_free(fold2);
 795         return NULL;
 796 }
 797
 798 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
 799         __isl_take isl_pw_qpolynomial_fold *pw1,
 800         __isl_take isl_pw_qpolynomial_fold *pw2)
 801 {
 802         int i, j, n;
 803         struct isl_pw_qpolynomial_fold *res;
 804         isl_set *set;
 805
 806         if (!pw1 || !pw2)
 807                 goto error;
 808
 809         isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 810
 811         if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
 812                 isl_pw_qpolynomial_fold_free(pw1);
 813                 return pw2;
 814         }
 815
 816         if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
 817                 isl_pw_qpolynomial_fold_free(pw2);
 818                 return pw1;
 819         }
 820
 821         if (pw1->type != pw2->type)
 822                 isl_die(pw1->dim->ctx, isl_error_invalid,
 823                         "fold types don't match", goto error);
 824
 825         n = (pw1->n + 1) * (pw2->n + 1);
 826         res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
 827                                                 pw1->type, n);
 828
 829         for (i = 0; i < pw1->n; ++i) {
 830                 set = isl_set_copy(pw1->p[i].set);
 831                 for (j = 0; j < pw2->n; ++j) {
 832                         struct isl_set *common;
 833                         isl_qpolynomial_fold *sum;
 834                         set = isl_set_subtract(set,
 835                                         isl_set_copy(pw2->p[j].set));
 836                         common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 837                                                 isl_set_copy(pw2->p[j].set));
 838                         if (isl_set_plain_is_empty(common)) {
 839                                 isl_set_free(common);
 840                                 continue;
 841                         }
 842
 843                         sum = isl_qpolynomial_fold_fold_on_domain(common,
 844                                isl_qpolynomial_fold_copy(pw1->p[i].fold),
 845                                isl_qpolynomial_fold_copy(pw2->p[j].fold));
 846
 847                         res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
 848                 }
 849                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 850                         isl_qpolynomial_fold_copy(pw1->p[i].fold));
 851         }
 852
 853         for (j = 0; j < pw2->n; ++j) {
 854                 set = isl_set_copy(pw2->p[j].set);
 855                 for (i = 0; i < pw1->n; ++i)
 856                         set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
 857                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 858                                     isl_qpolynomial_fold_copy(pw2->p[j].fold));
 859         }
 860
 861         isl_pw_qpolynomial_fold_free(pw1);
 862         isl_pw_qpolynomial_fold_free(pw2);
 863
 864         return res;
 865 error:
 866         isl_pw_qpolynomial_fold_free(pw1);
 867         isl_pw_qpolynomial_fold_free(pw2);
 868         return NULL;
 869 }
 870
 871 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
 872         __isl_take isl_union_pw_qpolynomial_fold *u,
 873         __isl_take isl_pw_qpolynomial_fold *part)
 874 {
 875         uint32_t hash;
 876         struct isl_hash_table_entry *entry;
 877
 878         u = isl_union_pw_qpolynomial_fold_cow(u);
 879
 880         if (!part || !u)
 881                 goto error;
 882
 883         isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
 884                                               isl_dim_param), goto error);
 885
 886         hash = isl_space_get_hash(part->dim);
 887         entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
 888                                     &has_dim, part->dim, 1);
 889         if (!entry)
 890                 goto error;
 891
 892         if (!entry->data)
 893                 entry->data = part;
 894         else {
 895                 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
 896                                             isl_pw_qpolynomial_fold_copy(part));
 897                 if (!entry->data)
 898                         goto error;
 899                 isl_pw_qpolynomial_fold_free(part);
 900         }
 901
 902         return u;
 903 error:
 904         isl_pw_qpolynomial_fold_free(part);
 905         isl_union_pw_qpolynomial_fold_free(u);
 906         return NULL;
 907 }
 908
 909 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
 910 {
 911         isl_union_pw_qpolynomial_fold **u;
 912         u = (isl_union_pw_qpolynomial_fold **)user;
 913
 914         *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 915
 916         return 0;
 917 }
 918
 919 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
 920         __isl_take isl_union_pw_qpolynomial_fold *u1,
 921         __isl_take isl_union_pw_qpolynomial_fold *u2)
 922 {
 923         u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 924
 925         if (!u1 || !u2)
 926                 goto error;
 927
 928         if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
 929                                                         &fold_part, &u1) < 0)
 930                 goto error;
 931
 932         isl_union_pw_qpolynomial_fold_free(u2);
 933
 934         return u1;
 935 error:
 936         isl_union_pw_qpolynomial_fold_free(u1);
 937         isl_union_pw_qpolynomial_fold_free(u2);
 938         return NULL;
 939 }
 940
 941 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
 942         enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 943 {
 944         int i;
 945         isl_pw_qpolynomial_fold *pwf;
 946
 947         if (!pwqp)
 948                 return NULL;
 949
 950         pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
 951                                                 type, pwqp->n);
 952
 953         for (i = 0; i < pwqp->n; ++i)
 954                 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
 955                         isl_set_copy(pwqp->p[i].set),
 956                         isl_qpolynomial_fold_alloc(type,
 957                                 isl_qpolynomial_copy(pwqp->p[i].qp)));
 958
 959         isl_pw_qpolynomial_free(pwqp);
 960
 961         return pwf;
 962 }
 963
 964 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
 965         __isl_take isl_pw_qpolynomial_fold *pwf1,
 966         __isl_take isl_pw_qpolynomial_fold *pwf2)
 967 {
 968         return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
 969 }
 970
 971 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 972         __isl_keep isl_qpolynomial_fold *fold2)
 973 {
 974         int i;
 975
 976         if (!fold1 || !fold2)
 977                 return -1;
 978
 979         if (fold1->n != fold2->n)
 980                 return 0;
 981
 982         /* We probably want to sort the qps first... */
 983         for (i = 0; i < fold1->n; ++i) {
 984                 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
 985                 if (eq < 0 || !eq)
 986                         return eq;
 987         }
 988
 989         return 1;
 990 }
 991
 992 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
 993         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
 994 {
 995         isl_qpolynomial *qp;
 996
 997         if (!fold || !pnt)
 998                 goto error;
 999         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
1000         isl_assert(pnt->dim->ctx,
1001                 fold->type == isl_fold_max || fold->type == isl_fold_min,
1002                 goto error);
1003
1004         if (fold->n == 0)
1005                 qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
1006         else {
1007                 int i;
1008                 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
1009                                                 isl_point_copy(pnt));
1010                 for (i = 1; i < fold->n; ++i) {
1011                         isl_qpolynomial *qp_i;
1012                         qp_i = isl_qpolynomial_eval(
1013                                             isl_qpolynomial_copy(fold->qp[i]),
1014                                             isl_point_copy(pnt));
1015                         if (fold->type == isl_fold_max)
1016                                 qp = isl_qpolynomial_max_cst(qp, qp_i);
1017                         else
1018                                 qp = isl_qpolynomial_min_cst(qp, qp_i);
1019                 }
1020         }
1021         isl_qpolynomial_fold_free(fold);
1022         isl_point_free(pnt);
1023
1024         return qp;
1025 error:
1026         isl_qpolynomial_fold_free(fold);
1027         isl_point_free(pnt);
1028         return NULL;
1029 }
1030
1031 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
1032 {
1033         int i;
1034         size_t n = 0;
1035
1036         for (i = 0; i < pwf->n; ++i)
1037                 n += pwf->p[i].fold->n;
1038
1039         return n;
1040 }
1041
1042 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1043         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1044 {
1045         int i;
1046         isl_qpolynomial *opt;
1047
1048         if (!set || !fold)
1049                 goto error;
1050
1051         if (fold->n == 0) {
1052                 isl_space *dim = isl_space_copy(fold->dim);
1053                 isl_set_free(set);
1054                 isl_qpolynomial_fold_free(fold);
1055                 return isl_qpolynomial_zero_on_domain(dim);
1056         }
1057
1058         opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1059                                                 isl_set_copy(set), max);
1060         for (i = 1; i < fold->n; ++i) {
1061                 isl_qpolynomial *opt_i;
1062                 opt_i = isl_qpolynomial_opt_on_domain(
1063                                 isl_qpolynomial_copy(fold->qp[i]),
1064                                 isl_set_copy(set), max);
1065                 if (max)
1066                         opt = isl_qpolynomial_max_cst(opt, opt_i);
1067                 else
1068                         opt = isl_qpolynomial_min_cst(opt, opt_i);
1069         }
1070
1071         isl_set_free(set);
1072         isl_qpolynomial_fold_free(fold);
1073
1074         return opt;
1075 error:
1076         isl_set_free(set);
1077         isl_qpolynomial_fold_free(fold);
1078         return NULL;
1079 }
1080
1081 /* Check whether for each quasi-polynomial in "fold2" there is
1082  * a quasi-polynomial in "fold1" that dominates it on "set".
1083  */
1084 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1085         __isl_keep isl_qpolynomial_fold *fold1,
1086         __isl_keep isl_qpolynomial_fold *fold2)
1087 {
1088         int i, j;
1089         int covers;
1090
1091         if (!set || !fold1 || !fold2)
1092                 return -1;
1093
1094         covers = fold1->type == isl_fold_max ? 1 : -1;
1095
1096         for (i = 0; i < fold2->n; ++i) {
1097                 for (j = 0; j < fold1->n; ++j) {
1098                         isl_qpolynomial *d;
1099                         int sgn;
1100
1101                         d = isl_qpolynomial_sub(
1102                                 isl_qpolynomial_copy(fold1->qp[j]),
1103                                 isl_qpolynomial_copy(fold2->qp[i]));
1104                         sgn = isl_qpolynomial_sign(set, d);
1105                         isl_qpolynomial_free(d);
1106                         if (sgn == covers)
1107                                 break;
1108                 }
1109                 if (j >= fold1->n)
1110                         return 0;
1111         }
1112
1113         return 1;
1114 }
1115
1116 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1117  * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1118  * that of pwf2.
1119  */
1120 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1121         __isl_keep isl_pw_qpolynomial_fold *pwf2)
1122 {
1123         int i, j;
1124         isl_set *dom1, *dom2;
1125         int is_subset;
1126
1127         if (!pwf1 || !pwf2)
1128                 return -1;
1129
1130         if (pwf2->n == 0)
1131                 return 1;
1132         if (pwf1->n == 0)
1133                 return 0;
1134
1135         dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1136         dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1137         is_subset = isl_set_is_subset(dom2, dom1);
1138         isl_set_free(dom1);
1139         isl_set_free(dom2);
1140
1141         if (is_subset < 0 || !is_subset)
1142                 return is_subset;
1143
1144         for (i = 0; i < pwf2->n; ++i) {
1145                 for (j = 0; j < pwf1->n; ++j) {
1146                         int is_empty;
1147                         isl_set *common;
1148                         int covers;
1149
1150                         common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1151                                                    isl_set_copy(pwf2->p[i].set));
1152                         is_empty = isl_set_is_empty(common);
1153                         if (is_empty < 0 || is_empty) {
1154                                 isl_set_free(common);
1155                                 if (is_empty < 0)
1156                                         return -1;
1157                                 continue;
1158                         }
1159                         covers = qpolynomial_fold_covers_on_domain(common,
1160                                         pwf1->p[j].fold, pwf2->p[i].fold);
1161                         isl_set_free(common);
1162                         if (covers < 0 || !covers)
1163                                 return covers;
1164                 }
1165         }
1166
1167         return 1;
1168 }
1169
1170 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
1171         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1172 {
1173         int i;
1174         isl_ctx *ctx;
1175
1176         if (!fold || !morph)
1177                 goto error;
1178
1179         ctx = fold->dim->ctx;
1180         isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
1181
1182         fold = isl_qpolynomial_fold_cow(fold);
1183         if (!fold)
1184                 goto error;
1185
1186         isl_space_free(fold->dim);
1187         fold->dim = isl_space_copy(morph->ran->dim);
1188         if (!fold->dim)
1189                 goto error;
1190
1191         for (i = 0; i < fold->n; ++i) {
1192                 fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
1193                                                 isl_morph_copy(morph));
1194                 if (!fold->qp[i])
1195                         goto error;
1196         }
1197
1198         isl_morph_free(morph);
1199
1200         return fold;
1201 error:
1202         isl_qpolynomial_fold_free(fold);
1203         isl_morph_free(morph);
1204         return NULL;
1205 }
1206
1207 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1208 {
1209         if (!fold)
1210                 return isl_fold_list;
1211         return fold->type;
1212 }
1213
1214 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1215         __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1216 {
1217         if (!upwf)
1218                 return isl_fold_list;
1219         return upwf->type;
1220 }
1221
1222 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1223         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
1224 {
1225         int i;
1226
1227         if (!fold || !dim)
1228                 goto error;
1229
1230         if (isl_space_is_equal(fold->dim, dim)) {
1231                 isl_space_free(dim);
1232                 return fold;
1233         }
1234
1235         fold = isl_qpolynomial_fold_cow(fold);
1236         if (!fold)
1237                 goto error;
1238
1239         isl_space_free(fold->dim);
1240         fold->dim = isl_space_copy(dim);
1241         if (!fold->dim)
1242                 goto error;
1243
1244         for (i = 0; i < fold->n; ++i) {
1245                 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1246                                                 isl_space_copy(dim));
1247                 if (!fold->qp[i])
1248                         goto error;
1249         }
1250
1251         isl_space_free(dim);
1252
1253         return fold;
1254 error:
1255         isl_qpolynomial_fold_free(fold);
1256         isl_space_free(dim);
1257         return NULL;
1258 }
1259
1260 int isl_qpolynomial_fold_foreach_qpolynomial(
1261         __isl_keep isl_qpolynomial_fold *fold,
1262         int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1263 {
1264         int i;
1265
1266         if (!fold)
1267                 return -1;
1268
1269         for (i = 0; i < fold->n; ++i)
1270                 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1271                         return -1;
1272
1273         return 0;
1274 }
1275
1276 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1277         __isl_take isl_qpolynomial_fold *fold,
1278         enum isl_dim_type dst_type, unsigned dst_pos,
1279         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1280 {
1281         int i;
1282
1283         if (n == 0)
1284                 return fold;
1285
1286         fold = isl_qpolynomial_fold_cow(fold);
1287         if (!fold)
1288                 return NULL;
1289
1290         fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
1291                                                 src_type, src_pos, n);
1292         if (!fold->dim)
1293                 goto error;
1294
1295         for (i = 0; i < fold->n; ++i) {
1296                 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1297                                 dst_type, dst_pos, src_type, src_pos, n);
1298                 if (!fold->qp[i])
1299                         goto error;
1300         }
1301
1302         return fold;
1303 error:
1304         isl_qpolynomial_fold_free(fold);
1305         return NULL;
1306 }
1307
1308 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1309  * in fold->qp[k] by subs[i].
1310  */
1311 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1312         __isl_take isl_qpolynomial_fold *fold,
1313         enum isl_dim_type type, unsigned first, unsigned n,
1314         __isl_keep isl_qpolynomial **subs)
1315 {
1316         int i;
1317
1318         if (n == 0)
1319                 return fold;
1320
1321         fold = isl_qpolynomial_fold_cow(fold);
1322         if (!fold)
1323                 return NULL;
1324
1325         for (i = 0; i < fold->n; ++i) {
1326                 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1327                                 type, first, n, subs);
1328                 if (!fold->qp[i])
1329                         goto error;
1330         }
1331
1332         return fold;
1333 error:
1334         isl_qpolynomial_fold_free(fold);
1335         return NULL;
1336 }
1337
1338 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1339 {
1340         isl_ctx *ctx;
1341         isl_pw_qpolynomial_fold *pwf;
1342         isl_union_pw_qpolynomial_fold **upwf;
1343         uint32_t hash;
1344         struct isl_hash_table_entry *entry;
1345
1346         upwf = (isl_union_pw_qpolynomial_fold **)user;
1347
1348         ctx = pwqp->dim->ctx;
1349         hash = isl_space_get_hash(pwqp->dim);
1350         entry = isl_hash_table_find(ctx, &(*upwf)->table,
1351                                      hash, &has_dim, pwqp->dim, 1);
1352         if (!entry)
1353                 goto error;
1354
1355         pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1356         if (!entry->data)
1357                 entry->data = pwf;
1358         else {
1359                 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1360                 if (!entry->data)
1361                         return -1;
1362                 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1363                         isl_pw_qpolynomial_fold_free(entry->data);
1364                         isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1365                 }
1366         }
1367
1368         return 0;
1369 error:
1370         isl_pw_qpolynomial_free(pwqp);
1371         return -1;
1372 }
1373
1374 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1375         __isl_take isl_union_pw_qpolynomial_fold *upwf,
1376         __isl_take isl_union_pw_qpolynomial *upwqp)
1377 {
1378         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1379                                 isl_union_pw_qpolynomial_get_space(upwqp));
1380         upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1381                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1382
1383         upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1384         if (!upwf || !upwqp)
1385                 goto error;
1386
1387         if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1388                                                          &upwf) < 0)
1389                 goto error;
1390
1391         isl_union_pw_qpolynomial_free(upwqp);
1392
1393         return upwf;
1394 error:
1395         isl_union_pw_qpolynomial_fold_free(upwf);
1396         isl_union_pw_qpolynomial_free(upwqp);
1397         return NULL;
1398 }
1399
1400 static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
1401 {
1402         int m;
1403         m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
1404         if (m < 0 || !m)
1405                 return m;
1406         return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
1407 }
1408
1409 /* Compute the intersection of the range of the map and the domain
1410  * of the piecewise quasipolynomial reduction and then compute a bound
1411  * on the associated quasipolynomial reduction over all elements
1412  * in this intersection.
1413  *
1414  * We first introduce some unconstrained dimensions in the
1415  * piecewise quasipolynomial, intersect the resulting domain
1416  * with the wrapped map and the compute the sum.
1417  */
1418 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1419         __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1420         int *tight)
1421 {
1422         isl_ctx *ctx;
1423         isl_set *dom;
1424         isl_space *map_dim;
1425         isl_space *pwf_dim;
1426         unsigned n_in;
1427         int ok;
1428
1429         ctx = isl_map_get_ctx(map);
1430         if (!ctx)
1431                 goto error;
1432
1433         map_dim = isl_map_get_space(map);
1434         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1435         ok = join_compatible(map_dim, pwf_dim);
1436         isl_space_free(map_dim);
1437         isl_space_free(pwf_dim);
1438         if (!ok)
1439                 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1440                         goto error);
1441
1442         n_in = isl_map_dim(map, isl_dim_in);
1443         pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
1444
1445         dom = isl_map_wrap(map);
1446         pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
1447                                                 isl_set_get_space(dom));
1448
1449         pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1450         pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1451
1452         return pwf;
1453 error:
1454         isl_map_free(map);
1455         isl_pw_qpolynomial_fold_free(pwf);
1456         return NULL;
1457 }
1458
1459 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1460         __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1461         int *tight)
1462 {
1463         return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
1464 }
1465
1466 struct isl_apply_fold_data {
1467         isl_union_pw_qpolynomial_fold *upwf;
1468         isl_union_pw_qpolynomial_fold *res;
1469         isl_map *map;
1470         int tight;
1471 };
1472
1473 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1474         void *user)
1475 {
1476         isl_space *map_dim;
1477         isl_space *pwf_dim;
1478         struct isl_apply_fold_data *data = user;
1479         int ok;
1480
1481         map_dim = isl_map_get_space(data->map);
1482         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1483         ok = join_compatible(map_dim, pwf_dim);
1484         isl_space_free(map_dim);
1485         isl_space_free(pwf_dim);
1486
1487         if (ok) {
1488                 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1489                                     pwf, data->tight ? &data->tight : NULL);
1490                 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1491                                                         data->res, pwf);
1492         } else
1493                 isl_pw_qpolynomial_fold_free(pwf);
1494
1495         return 0;
1496 }
1497
1498 static int map_apply(__isl_take isl_map *map, void *user)
1499 {
1500         struct isl_apply_fold_data *data = user;
1501         int r;
1502
1503         data->map = map;
1504         r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1505                                 data->upwf, &pw_qpolynomial_fold_apply, data);
1506
1507         isl_map_free(map);
1508         return r;
1509 }
1510
1511 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1512         __isl_take isl_union_map *umap,
1513         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1514 {
1515         isl_space *dim;
1516         enum isl_fold type;
1517         struct isl_apply_fold_data data;
1518
1519         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1520                                 isl_union_map_get_space(umap));
1521         umap = isl_union_map_align_params(umap,
1522                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1523
1524         data.upwf = upwf;
1525         data.tight = tight ? 1 : 0;
1526         dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
1527         type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1528         data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1529         if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1530                 goto error;
1531
1532         isl_union_map_free(umap);
1533         isl_union_pw_qpolynomial_fold_free(upwf);
1534
1535         if (tight)
1536                 *tight = data.tight;
1537
1538         return data.res;
1539 error:
1540         isl_union_map_free(umap);
1541         isl_union_pw_qpolynomial_fold_free(upwf);
1542         isl_union_pw_qpolynomial_fold_free(data.res);
1543         return NULL;
1544 }
1545
1546 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1547         __isl_take isl_union_set *uset,
1548         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1549 {
1550         return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1551 }
1552
1553 /* Reorder the dimension of "fold" according to the given reordering.
1554  */
1555 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
1556         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1557 {
1558         int i;
1559
1560         fold = isl_qpolynomial_fold_cow(fold);
1561         if (!fold || !r)
1562                 goto error;
1563
1564         for (i = 0; i < fold->n; ++i) {
1565                 fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
1566                                                     isl_reordering_copy(r));
1567                 if (!fold->qp[i])
1568                         goto error;
1569         }
1570
1571         fold = isl_qpolynomial_fold_reset_domain_space(fold,
1572                                                     isl_space_copy(r->dim));
1573
1574         isl_reordering_free(r);
1575
1576         return fold;
1577 error:
1578         isl_qpolynomial_fold_free(fold);
1579         isl_reordering_free(r);
1580         return NULL;
1581 }
1582
1583 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1584         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1585 {
1586         int i;
1587
1588         if (isl_int_is_one(v))
1589                 return fold;
1590         if (fold && isl_int_is_zero(v)) {
1591                 isl_qpolynomial_fold *zero;
1592                 isl_space *dim = isl_space_copy(fold->dim);
1593                 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1594                 isl_qpolynomial_fold_free(fold);
1595                 return zero;
1596         }
1597
1598         fold = isl_qpolynomial_fold_cow(fold);
1599         if (!fold)
1600                 return NULL;
1601
1602         if (isl_int_is_neg(v))
1603                 fold->type = isl_fold_type_negate(fold->type);
1604         for (i = 0; i < fold->n; ++i) {
1605                 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1606                 if (!fold->qp[i])
1607                         goto error;
1608         }
1609
1610         return fold;
1611 error:
1612         isl_qpolynomial_fold_free(fold);
1613         return NULL;
1614 }
1615
1616 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1617         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1618 {
1619         return isl_qpolynomial_fold_mul_isl_int(fold, v);
1620 }