isl_fold.c

   1 /*
   2  * Copyright 2010      INRIA Saclay
   3  *
   4  * Use of this software is governed by the MIT license
   5  *
   6  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   7  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   8  * 91893 Orsay, France
   9  */
  10
  11 #define ISL_DIM_H
  12 #include <isl_map_private.h>
  13 #include <isl_union_map_private.h>
  14 #include <isl_polynomial_private.h>
  15 #include <isl_point_private.h>
  16 #include <isl_space_private.h>
  17 #include <isl/lp.h>
  18 #include <isl/seq.h>
  19 #include <isl_mat_private.h>
  20 #include <isl_config.h>
  21
  22 enum isl_fold isl_fold_type_negate(enum isl_fold type)
  23 {
  24         switch (type) {
  25         case isl_fold_min:
  26                 return isl_fold_max;
  27         case isl_fold_max:
  28                 return isl_fold_min;
  29         case isl_fold_list:
  30                 return isl_fold_list;
  31         }
  32
  33         isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
  34 }
  35
  36 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
  37         enum isl_fold type, __isl_take isl_space *dim, int n)
  38 {
  39         isl_qpolynomial_fold *fold;
  40
  41         if (!dim)
  42                 goto error;
  43
  44         isl_assert(dim->ctx, n >= 0, goto error);
  45         fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
  46                         sizeof(struct isl_qpolynomial_fold) +
  47                         (n - 1) * sizeof(struct isl_qpolynomial *));
  48         if (!fold)
  49                 goto error;
  50
  51         fold->ref = 1;
  52         fold->size = n;
  53         fold->n = 0;
  54         fold->type = type;
  55         fold->dim = dim;
  56
  57         return fold;
  58 error:
  59         isl_space_free(dim);
  60         return NULL;
  61 }
  62
  63 isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
  64 {
  65         return fold ? fold->dim->ctx : NULL;
  66 }
  67
  68 __isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
  69         __isl_keep isl_qpolynomial_fold *fold)
  70 {
  71         return fold ? isl_space_copy(fold->dim) : NULL;
  72 }
  73
  74 __isl_give isl_space *isl_qpolynomial_fold_get_space(
  75         __isl_keep isl_qpolynomial_fold *fold)
  76 {
  77         isl_space *space;
  78         if (!fold)
  79                 return NULL;
  80         space = isl_space_copy(fold->dim);
  81         space = isl_space_from_domain(space);
  82         space = isl_space_add_dims(space, isl_dim_out, 1);
  83         return space;
  84 }
  85
  86 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
  87         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
  88 {
  89         int i;
  90
  91         fold = isl_qpolynomial_fold_cow(fold);
  92         if (!fold || !dim)
  93                 goto error;
  94
  95         for (i = 0; i < fold->n; ++i) {
  96                 fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
  97                                                         isl_space_copy(dim));
  98                 if (!fold->qp[i])
  99                         goto error;
 100         }
 101
 102         isl_space_free(fold->dim);
 103         fold->dim = dim;
 104
 105         return fold;
 106 error:
 107         isl_qpolynomial_fold_free(fold);
 108         isl_space_free(dim);
 109         return NULL;
 110 }
 111
 112 /* Reset the space of "fold".  This function is called from isl_pw_templ.c
 113  * and doesn't know if the space of an element object is represented
 114  * directly or through its domain.  It therefore passes along both.
 115  */
 116 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
 117         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
 118         __isl_take isl_space *domain)
 119 {
 120         isl_space_free(space);
 121         return isl_qpolynomial_fold_reset_domain_space(fold, domain);
 122 }
 123
 124 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
 125         enum isl_dim_type type, unsigned first, unsigned n)
 126 {
 127         int i;
 128
 129         if (!fold)
 130                 return -1;
 131         if (fold->n == 0 || n == 0)
 132                 return 0;
 133
 134         for (i = 0; i < fold->n; ++i) {
 135                 int involves = isl_qpolynomial_involves_dims(fold->qp[i],
 136                                                             type, first, n);
 137                 if (involves < 0 || involves)
 138                         return involves;
 139         }
 140         return 0;
 141 }
 142
 143 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
 144         __isl_take isl_qpolynomial_fold *fold,
 145         enum isl_dim_type type, unsigned pos, const char *s)
 146 {
 147         int i;
 148
 149         fold = isl_qpolynomial_fold_cow(fold);
 150         if (!fold)
 151                 return NULL;
 152         fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
 153         if (!fold->dim)
 154                 goto error;
 155
 156         for (i = 0; i < fold->n; ++i) {
 157                 fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
 158                                                             type, pos, s);
 159                 if (!fold->qp[i])
 160                         goto error;
 161         }
 162
 163         return fold;
 164 error:
 165         isl_qpolynomial_fold_free(fold);
 166         return NULL;
 167 }
 168
 169 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
 170         __isl_take isl_qpolynomial_fold *fold,
 171         enum isl_dim_type type, unsigned first, unsigned n)
 172 {
 173         int i;
 174         enum isl_dim_type set_type;
 175
 176         if (!fold)
 177                 return NULL;
 178         if (n == 0)
 179                 return fold;
 180
 181         set_type = type == isl_dim_in ? isl_dim_set : type;
 182
 183         fold = isl_qpolynomial_fold_cow(fold);
 184         if (!fold)
 185                 return NULL;
 186         fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
 187         if (!fold->dim)
 188                 goto error;
 189
 190         for (i = 0; i < fold->n; ++i) {
 191                 fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
 192                                                             type, first, n);
 193                 if (!fold->qp[i])
 194                         goto error;
 195         }
 196
 197         return fold;
 198 error:
 199         isl_qpolynomial_fold_free(fold);
 200         return NULL;
 201 }
 202
 203 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
 204         __isl_take isl_qpolynomial_fold *fold,
 205         enum isl_dim_type type, unsigned first, unsigned n)
 206 {
 207         int i;
 208
 209         if (!fold)
 210                 return NULL;
 211         if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
 212                 return fold;
 213
 214         fold = isl_qpolynomial_fold_cow(fold);
 215         if (!fold)
 216                 return NULL;
 217         fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
 218         if (!fold->dim)
 219                 goto error;
 220
 221         for (i = 0; i < fold->n; ++i) {
 222                 fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
 223                                                             type, first, n);
 224                 if (!fold->qp[i])
 225                         goto error;
 226         }
 227
 228         return fold;
 229 error:
 230         isl_qpolynomial_fold_free(fold);
 231         return NULL;
 232 }
 233
 234 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
 235 {
 236         struct isl_upoly_cst *cst;
 237
 238         cst = isl_upoly_as_cst(qp->upoly);
 239         if (!cst)
 240                 return 0;
 241
 242         return isl_int_sgn(cst->n) < 0 ? -1 : 1;
 243 }
 244
 245 static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
 246         __isl_keep isl_qpolynomial *qp)
 247 {
 248         enum isl_lp_result res;
 249         isl_vec *aff;
 250         isl_int opt;
 251         int sgn = 0;
 252
 253         aff = isl_qpolynomial_extract_affine(qp);
 254         if (!aff)
 255                 return 0;
 256
 257         isl_int_init(opt);
 258
 259         res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
 260                                 &opt, NULL, NULL);
 261         if (res == isl_lp_error)
 262                 goto done;
 263         if (res == isl_lp_empty ||
 264             (res == isl_lp_ok && !isl_int_is_neg(opt))) {
 265                 sgn = 1;
 266                 goto done;
 267         }
 268
 269         res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
 270                                 &opt, NULL, NULL);
 271         if (res == isl_lp_ok && !isl_int_is_pos(opt))
 272                 sgn = -1;
 273
 274 done:
 275         isl_int_clear(opt);
 276         isl_vec_free(aff);
 277         return sgn;
 278 }
 279
 280 /* Determine, if possible, the sign of the quasipolynomial "qp" on
 281  * the domain "set".
 282  *
 283  * If qp is a constant, then the problem is trivial.
 284  * If qp is linear, then we check if the minimum of the corresponding
 285  * affine constraint is non-negative or if the maximum is non-positive.
 286  *
 287  * Otherwise, we check if the outermost variable "v" has a lower bound "l"
 288  * in "set".  If so, we write qp(v,v') as
 289  *
 290  *      q(v,v') * (v - l) + r(v')
 291  *
 292  * if q(v,v') and r(v') have the same known sign, then the original
 293  * quasipolynomial has the same sign as well.
 294  *
 295  * Return
 296  *      -1 if qp <= 0
 297  *       1 if qp >= 0
 298  *       0 if unknown
 299  */
 300 static int isl_qpolynomial_sign(__isl_keep isl_set *set,
 301         __isl_keep isl_qpolynomial *qp)
 302 {
 303         int d;
 304         int i;
 305         int is;
 306         struct isl_upoly_rec *rec;
 307         isl_vec *v;
 308         isl_int l;
 309         enum isl_lp_result res;
 310         int sgn = 0;
 311
 312         is = isl_qpolynomial_is_cst(qp, NULL, NULL);
 313         if (is < 0)
 314                 return 0;
 315         if (is)
 316                 return isl_qpolynomial_cst_sign(qp);
 317
 318         is = isl_qpolynomial_is_affine(qp);
 319         if (is < 0)
 320                 return 0;
 321         if (is)
 322                 return isl_qpolynomial_aff_sign(set, qp);
 323
 324         if (qp->div->n_row > 0)
 325                 return 0;
 326
 327         rec = isl_upoly_as_rec(qp->upoly);
 328         if (!rec)
 329                 return 0;
 330
 331         d = isl_space_dim(qp->dim, isl_dim_all);
 332         v = isl_vec_alloc(set->ctx, 2 + d);
 333         if (!v)
 334                 return 0;
 335
 336         isl_seq_clr(v->el + 1, 1 + d);
 337         isl_int_set_si(v->el[0], 1);
 338         isl_int_set_si(v->el[2 + qp->upoly->var], 1);
 339
 340         isl_int_init(l);
 341
 342         res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
 343         if (res == isl_lp_ok) {
 344                 isl_qpolynomial *min;
 345                 isl_qpolynomial *base;
 346                 isl_qpolynomial *r, *q;
 347                 isl_qpolynomial *t;
 348
 349                 min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
 350                 base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
 351                                                 qp->upoly->var, 1);
 352
 353                 r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
 354                                           isl_upoly_copy(rec->p[rec->n - 1]));
 355                 q = isl_qpolynomial_copy(r);
 356
 357                 for (i = rec->n - 2; i >= 0; --i) {
 358                         r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
 359                         t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
 360                                                   isl_upoly_copy(rec->p[i]));
 361                         r = isl_qpolynomial_add(r, t);
 362                         if (i == 0)
 363                                 break;
 364                         q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
 365                         q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
 366                 }
 367
 368                 if (isl_qpolynomial_is_zero(q))
 369                         sgn = isl_qpolynomial_sign(set, r);
 370                 else if (isl_qpolynomial_is_zero(r))
 371                         sgn = isl_qpolynomial_sign(set, q);
 372                 else {
 373                         int sgn_q, sgn_r;
 374                         sgn_r = isl_qpolynomial_sign(set, r);
 375                         sgn_q = isl_qpolynomial_sign(set, q);
 376                         if (sgn_r == sgn_q)
 377                                 sgn = sgn_r;
 378                 }
 379
 380                 isl_qpolynomial_free(min);
 381                 isl_qpolynomial_free(base);
 382                 isl_qpolynomial_free(q);
 383                 isl_qpolynomial_free(r);
 384         }
 385
 386         isl_int_clear(l);
 387
 388         isl_vec_free(v);
 389
 390         return sgn;
 391 }
 392
 393 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
 394         __isl_keep isl_set *set,
 395         __isl_take isl_qpolynomial_fold *fold1,
 396         __isl_take isl_qpolynomial_fold *fold2)
 397 {
 398         int i, j;
 399         int n1;
 400         struct isl_qpolynomial_fold *res = NULL;
 401         int better;
 402
 403         if (!fold1 || !fold2)
 404                 goto error;
 405
 406         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 407         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 408                         goto error);
 409
 410         better = fold1->type == isl_fold_max ? -1 : 1;
 411
 412         if (isl_qpolynomial_fold_is_empty(fold1)) {
 413                 isl_qpolynomial_fold_free(fold1);
 414                 return fold2;
 415         }
 416
 417         if (isl_qpolynomial_fold_is_empty(fold2)) {
 418                 isl_qpolynomial_fold_free(fold2);
 419                 return fold1;
 420         }
 421
 422         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 423                                         fold1->n + fold2->n);
 424         if (!res)
 425                 goto error;
 426
 427         for (i = 0; i < fold1->n; ++i) {
 428                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 429                 if (!res->qp[res->n])
 430                         goto error;
 431                 res->n++;
 432         }
 433         n1 = res->n;
 434
 435         for (i = 0; i < fold2->n; ++i) {
 436                 for (j = n1 - 1; j >= 0; --j) {
 437                         isl_qpolynomial *d;
 438                         int sgn;
 439                         d = isl_qpolynomial_sub(
 440                                 isl_qpolynomial_copy(res->qp[j]),
 441                                 isl_qpolynomial_copy(fold2->qp[i]));
 442                         sgn = isl_qpolynomial_sign(set, d);
 443                         isl_qpolynomial_free(d);
 444                         if (sgn == 0)
 445                                 continue;
 446                         if (sgn != better)
 447                                 break;
 448                         isl_qpolynomial_free(res->qp[j]);
 449                         if (j != n1 - 1)
 450                                 res->qp[j] = res->qp[n1 - 1];
 451                         n1--;
 452                         if (n1 != res->n - 1)
 453                                 res->qp[n1] = res->qp[res->n - 1];
 454                         res->n--;
 455                 }
 456                 if (j >= 0)
 457                         continue;
 458                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 459                 if (!res->qp[res->n])
 460                         goto error;
 461                 res->n++;
 462         }
 463
 464         isl_qpolynomial_fold_free(fold1);
 465         isl_qpolynomial_fold_free(fold2);
 466
 467         return res;
 468 error:
 469         isl_qpolynomial_fold_free(res);
 470         isl_qpolynomial_fold_free(fold1);
 471         isl_qpolynomial_fold_free(fold2);
 472         return NULL;
 473 }
 474
 475 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
 476         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
 477 {
 478         int i;
 479
 480         if (!fold || !qp)
 481                 goto error;
 482
 483         if (isl_qpolynomial_is_zero(qp)) {
 484                 isl_qpolynomial_free(qp);
 485                 return fold;
 486         }
 487
 488         fold = isl_qpolynomial_fold_cow(fold);
 489         if (!fold)
 490                 goto error;
 491
 492         for (i = 0; i < fold->n; ++i) {
 493                 fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
 494                                                 isl_qpolynomial_copy(qp));
 495                 if (!fold->qp[i])
 496                         goto error;
 497         }
 498
 499         isl_qpolynomial_free(qp);
 500         return fold;
 501 error:
 502         isl_qpolynomial_fold_free(fold);
 503         isl_qpolynomial_free(qp);
 504         return NULL;
 505 }
 506
 507 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
 508         __isl_keep isl_set *dom,
 509         __isl_take isl_qpolynomial_fold *fold1,
 510         __isl_take isl_qpolynomial_fold *fold2)
 511 {
 512         int i;
 513         isl_qpolynomial_fold *res = NULL;
 514
 515         if (!fold1 || !fold2)
 516                 goto error;
 517
 518         if (isl_qpolynomial_fold_is_empty(fold1)) {
 519                 isl_qpolynomial_fold_free(fold1);
 520                 return fold2;
 521         }
 522
 523         if (isl_qpolynomial_fold_is_empty(fold2)) {
 524                 isl_qpolynomial_fold_free(fold2);
 525                 return fold1;
 526         }
 527
 528         if (fold1->n == 1 && fold2->n != 1)
 529                 return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
 530
 531         if (fold2->n == 1) {
 532                 res = isl_qpolynomial_fold_add_qpolynomial(fold1,
 533                                         isl_qpolynomial_copy(fold2->qp[0]));
 534                 isl_qpolynomial_fold_free(fold2);
 535                 return res;
 536         }
 537
 538         res = isl_qpolynomial_fold_add_qpolynomial(
 539                                 isl_qpolynomial_fold_copy(fold1),
 540                                 isl_qpolynomial_copy(fold2->qp[0]));
 541
 542         for (i = 1; i < fold2->n; ++i) {
 543                 isl_qpolynomial_fold *res_i;
 544                 res_i = isl_qpolynomial_fold_add_qpolynomial(
 545                                         isl_qpolynomial_fold_copy(fold1),
 546                                         isl_qpolynomial_copy(fold2->qp[i]));
 547                 res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
 548         }
 549
 550         isl_qpolynomial_fold_free(fold1);
 551         isl_qpolynomial_fold_free(fold2);
 552         return res;
 553 error:
 554         isl_qpolynomial_fold_free(res);
 555         isl_qpolynomial_fold_free(fold1);
 556         isl_qpolynomial_fold_free(fold2);
 557         return NULL;
 558 }
 559
 560 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
 561         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
 562 {
 563         int i;
 564
 565         if (!fold || !eq)
 566                 goto error;
 567
 568         fold = isl_qpolynomial_fold_cow(fold);
 569         if (!fold)
 570                 return NULL;
 571
 572         for (i = 0; i < fold->n; ++i) {
 573                 fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
 574                                                         isl_basic_set_copy(eq));
 575                 if (!fold->qp[i])
 576                         goto error;
 577         }
 578
 579         isl_basic_set_free(eq);
 580         return fold;
 581 error:
 582         isl_basic_set_free(eq);
 583         isl_qpolynomial_fold_free(fold);
 584         return NULL;
 585 }
 586
 587 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
 588         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 589 {
 590         int i;
 591
 592         if (!fold || !context)
 593                 goto error;
 594
 595         fold = isl_qpolynomial_fold_cow(fold);
 596         if (!fold)
 597                 return NULL;
 598
 599         for (i = 0; i < fold->n; ++i) {
 600                 fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
 601                                                         isl_set_copy(context));
 602                 if (!fold->qp[i])
 603                         goto error;
 604         }
 605
 606         isl_set_free(context);
 607         return fold;
 608 error:
 609         isl_set_free(context);
 610         isl_qpolynomial_fold_free(fold);
 611         return NULL;
 612 }
 613
 614 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
 615         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 616 {
 617         isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
 618         isl_set *dom_context = isl_set_universe(space);
 619         dom_context = isl_set_intersect_params(dom_context, context);
 620         return isl_qpolynomial_fold_gist(fold, dom_context);
 621 }
 622
 623 #define HAS_TYPE
 624
 625 #undef PW
 626 #define PW isl_pw_qpolynomial_fold
 627 #undef EL
 628 #define EL isl_qpolynomial_fold
 629 #undef EL_IS_ZERO
 630 #define EL_IS_ZERO is_empty
 631 #undef ZERO
 632 #define ZERO zero
 633 #undef IS_ZERO
 634 #define IS_ZERO is_zero
 635 #undef FIELD
 636 #define FIELD fold
 637 #undef DEFAULT_IS_ZERO
 638 #define DEFAULT_IS_ZERO 1
 639
 640 #define NO_NEG
 641
 642 #include <isl_pw_templ.c>
 643
 644 #undef UNION
 645 #define UNION isl_union_pw_qpolynomial_fold
 646 #undef PART
 647 #define PART isl_pw_qpolynomial_fold
 648 #undef PARTS
 649 #define PARTS pw_qpolynomial_fold
 650 #define ALIGN_DOMAIN
 651
 652 #include <isl_union_templ.c>
 653
 654 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
 655         __isl_take isl_space *dim)
 656 {
 657         return qpolynomial_fold_alloc(type, dim, 0);
 658 }
 659
 660 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
 661         enum isl_fold type, __isl_take isl_qpolynomial *qp)
 662 {
 663         isl_qpolynomial_fold *fold;
 664
 665         if (!qp)
 666                 return NULL;
 667
 668         fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
 669         if (!fold)
 670                 goto error;
 671
 672         fold->qp[0] = qp;
 673         fold->n++;
 674
 675         return fold;
 676 error:
 677         isl_qpolynomial_fold_free(fold);
 678         isl_qpolynomial_free(qp);
 679         return NULL;
 680 }
 681
 682 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
 683         __isl_keep isl_qpolynomial_fold *fold)
 684 {
 685         if (!fold)
 686                 return NULL;
 687
 688         fold->ref++;
 689         return fold;
 690 }
 691
 692 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
 693         __isl_keep isl_qpolynomial_fold *fold)
 694 {
 695         int i;
 696         isl_qpolynomial_fold *dup;
 697
 698         if (!fold)
 699                 return NULL;
 700         dup = qpolynomial_fold_alloc(fold->type,
 701                                         isl_space_copy(fold->dim), fold->n);
 702         if (!dup)
 703                 return NULL;
 704
 705         dup->n = fold->n;
 706         for (i = 0; i < fold->n; ++i) {
 707                 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
 708                 if (!dup->qp[i])
 709                         goto error;
 710         }
 711
 712         return dup;
 713 error:
 714         isl_qpolynomial_fold_free(dup);
 715         return NULL;
 716 }
 717
 718 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
 719         __isl_take isl_qpolynomial_fold *fold)
 720 {
 721         if (!fold)
 722                 return NULL;
 723
 724         if (fold->ref == 1)
 725                 return fold;
 726         fold->ref--;
 727         return isl_qpolynomial_fold_dup(fold);
 728 }
 729
 730 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 731 {
 732         int i;
 733
 734         if (!fold)
 735                 return;
 736         if (--fold->ref > 0)
 737                 return;
 738
 739         for (i = 0; i < fold->n; ++i)
 740                 isl_qpolynomial_free(fold->qp[i]);
 741         isl_space_free(fold->dim);
 742         free(fold);
 743 }
 744
 745 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
 746 {
 747         if (!fold)
 748                 return -1;
 749
 750         return fold->n == 0;
 751 }
 752
 753 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
 754         __isl_take isl_qpolynomial_fold *fold1,
 755         __isl_take isl_qpolynomial_fold *fold2)
 756 {
 757         int i;
 758         struct isl_qpolynomial_fold *res = NULL;
 759
 760         if (!fold1 || !fold2)
 761                 goto error;
 762
 763         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 764         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 765                         goto error);
 766
 767         if (isl_qpolynomial_fold_is_empty(fold1)) {
 768                 isl_qpolynomial_fold_free(fold1);
 769                 return fold2;
 770         }
 771
 772         if (isl_qpolynomial_fold_is_empty(fold2)) {
 773                 isl_qpolynomial_fold_free(fold2);
 774                 return fold1;
 775         }
 776
 777         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 778                                         fold1->n + fold2->n);
 779         if (!res)
 780                 goto error;
 781
 782         for (i = 0; i < fold1->n; ++i) {
 783                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 784                 if (!res->qp[res->n])
 785                         goto error;
 786                 res->n++;
 787         }
 788
 789         for (i = 0; i < fold2->n; ++i) {
 790                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 791                 if (!res->qp[res->n])
 792                         goto error;
 793                 res->n++;
 794         }
 795
 796         isl_qpolynomial_fold_free(fold1);
 797         isl_qpolynomial_fold_free(fold2);
 798
 799         return res;
 800 error:
 801         isl_qpolynomial_fold_free(res);
 802         isl_qpolynomial_fold_free(fold1);
 803         isl_qpolynomial_fold_free(fold2);
 804         return NULL;
 805 }
 806
 807 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
 808         __isl_take isl_pw_qpolynomial_fold *pw1,
 809         __isl_take isl_pw_qpolynomial_fold *pw2)
 810 {
 811         int i, j, n;
 812         struct isl_pw_qpolynomial_fold *res;
 813         isl_set *set;
 814
 815         if (!pw1 || !pw2)
 816                 goto error;
 817
 818         isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 819
 820         if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
 821                 isl_pw_qpolynomial_fold_free(pw1);
 822                 return pw2;
 823         }
 824
 825         if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
 826                 isl_pw_qpolynomial_fold_free(pw2);
 827                 return pw1;
 828         }
 829
 830         if (pw1->type != pw2->type)
 831                 isl_die(pw1->dim->ctx, isl_error_invalid,
 832                         "fold types don't match", goto error);
 833
 834         n = (pw1->n + 1) * (pw2->n + 1);
 835         res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
 836                                                 pw1->type, n);
 837
 838         for (i = 0; i < pw1->n; ++i) {
 839                 set = isl_set_copy(pw1->p[i].set);
 840                 for (j = 0; j < pw2->n; ++j) {
 841                         struct isl_set *common;
 842                         isl_qpolynomial_fold *sum;
 843                         set = isl_set_subtract(set,
 844                                         isl_set_copy(pw2->p[j].set));
 845                         common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 846                                                 isl_set_copy(pw2->p[j].set));
 847                         if (isl_set_plain_is_empty(common)) {
 848                                 isl_set_free(common);
 849                                 continue;
 850                         }
 851
 852                         sum = isl_qpolynomial_fold_fold_on_domain(common,
 853                                isl_qpolynomial_fold_copy(pw1->p[i].fold),
 854                                isl_qpolynomial_fold_copy(pw2->p[j].fold));
 855
 856                         res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
 857                 }
 858                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 859                         isl_qpolynomial_fold_copy(pw1->p[i].fold));
 860         }
 861
 862         for (j = 0; j < pw2->n; ++j) {
 863                 set = isl_set_copy(pw2->p[j].set);
 864                 for (i = 0; i < pw1->n; ++i)
 865                         set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
 866                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 867                                     isl_qpolynomial_fold_copy(pw2->p[j].fold));
 868         }
 869
 870         isl_pw_qpolynomial_fold_free(pw1);
 871         isl_pw_qpolynomial_fold_free(pw2);
 872
 873         return res;
 874 error:
 875         isl_pw_qpolynomial_fold_free(pw1);
 876         isl_pw_qpolynomial_fold_free(pw2);
 877         return NULL;
 878 }
 879
 880 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
 881         __isl_take isl_union_pw_qpolynomial_fold *u,
 882         __isl_take isl_pw_qpolynomial_fold *part)
 883 {
 884         uint32_t hash;
 885         struct isl_hash_table_entry *entry;
 886
 887         u = isl_union_pw_qpolynomial_fold_cow(u);
 888
 889         if (!part || !u)
 890                 goto error;
 891
 892         isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
 893                                               isl_dim_param), goto error);
 894
 895         hash = isl_space_get_hash(part->dim);
 896         entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
 897                                     &has_dim, part->dim, 1);
 898         if (!entry)
 899                 goto error;
 900
 901         if (!entry->data)
 902                 entry->data = part;
 903         else {
 904                 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
 905                                             isl_pw_qpolynomial_fold_copy(part));
 906                 if (!entry->data)
 907                         goto error;
 908                 isl_pw_qpolynomial_fold_free(part);
 909         }
 910
 911         return u;
 912 error:
 913         isl_pw_qpolynomial_fold_free(part);
 914         isl_union_pw_qpolynomial_fold_free(u);
 915         return NULL;
 916 }
 917
 918 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
 919 {
 920         isl_union_pw_qpolynomial_fold **u;
 921         u = (isl_union_pw_qpolynomial_fold **)user;
 922
 923         *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 924
 925         return 0;
 926 }
 927
 928 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
 929         __isl_take isl_union_pw_qpolynomial_fold *u1,
 930         __isl_take isl_union_pw_qpolynomial_fold *u2)
 931 {
 932         u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 933
 934         if (!u1 || !u2)
 935                 goto error;
 936
 937         if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
 938                                                         &fold_part, &u1) < 0)
 939                 goto error;
 940
 941         isl_union_pw_qpolynomial_fold_free(u2);
 942
 943         return u1;
 944 error:
 945         isl_union_pw_qpolynomial_fold_free(u1);
 946         isl_union_pw_qpolynomial_fold_free(u2);
 947         return NULL;
 948 }
 949
 950 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
 951         enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 952 {
 953         int i;
 954         isl_pw_qpolynomial_fold *pwf;
 955
 956         if (!pwqp)
 957                 return NULL;
 958
 959         pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
 960                                                 type, pwqp->n);
 961
 962         for (i = 0; i < pwqp->n; ++i)
 963                 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
 964                         isl_set_copy(pwqp->p[i].set),
 965                         isl_qpolynomial_fold_alloc(type,
 966                                 isl_qpolynomial_copy(pwqp->p[i].qp)));
 967
 968         isl_pw_qpolynomial_free(pwqp);
 969
 970         return pwf;
 971 }
 972
 973 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
 974         __isl_take isl_pw_qpolynomial_fold *pwf1,
 975         __isl_take isl_pw_qpolynomial_fold *pwf2)
 976 {
 977         return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
 978 }
 979
 980 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 981         __isl_keep isl_qpolynomial_fold *fold2)
 982 {
 983         int i;
 984
 985         if (!fold1 || !fold2)
 986                 return -1;
 987
 988         if (fold1->n != fold2->n)
 989                 return 0;
 990
 991         /* We probably want to sort the qps first... */
 992         for (i = 0; i < fold1->n; ++i) {
 993                 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
 994                 if (eq < 0 || !eq)
 995                         return eq;
 996         }
 997
 998         return 1;
 999 }
1000
1001 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
1002         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
1003 {
1004         isl_qpolynomial *qp;
1005
1006         if (!fold || !pnt)
1007                 goto error;
1008         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
1009         isl_assert(pnt->dim->ctx,
1010                 fold->type == isl_fold_max || fold->type == isl_fold_min,
1011                 goto error);
1012
1013         if (fold->n == 0)
1014                 qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
1015         else {
1016                 int i;
1017                 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
1018                                                 isl_point_copy(pnt));
1019                 for (i = 1; i < fold->n; ++i) {
1020                         isl_qpolynomial *qp_i;
1021                         qp_i = isl_qpolynomial_eval(
1022                                             isl_qpolynomial_copy(fold->qp[i]),
1023                                             isl_point_copy(pnt));
1024                         if (fold->type == isl_fold_max)
1025                                 qp = isl_qpolynomial_max_cst(qp, qp_i);
1026                         else
1027                                 qp = isl_qpolynomial_min_cst(qp, qp_i);
1028                 }
1029         }
1030         isl_qpolynomial_fold_free(fold);
1031         isl_point_free(pnt);
1032
1033         return qp;
1034 error:
1035         isl_qpolynomial_fold_free(fold);
1036         isl_point_free(pnt);
1037         return NULL;
1038 }
1039
1040 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
1041 {
1042         int i;
1043         size_t n = 0;
1044
1045         for (i = 0; i < pwf->n; ++i)
1046                 n += pwf->p[i].fold->n;
1047
1048         return n;
1049 }
1050
1051 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1052         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1053 {
1054         int i;
1055         isl_qpolynomial *opt;
1056
1057         if (!set || !fold)
1058                 goto error;
1059
1060         if (fold->n == 0) {
1061                 isl_space *dim = isl_space_copy(fold->dim);
1062                 isl_set_free(set);
1063                 isl_qpolynomial_fold_free(fold);
1064                 return isl_qpolynomial_zero_on_domain(dim);
1065         }
1066
1067         opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1068                                                 isl_set_copy(set), max);
1069         for (i = 1; i < fold->n; ++i) {
1070                 isl_qpolynomial *opt_i;
1071                 opt_i = isl_qpolynomial_opt_on_domain(
1072                                 isl_qpolynomial_copy(fold->qp[i]),
1073                                 isl_set_copy(set), max);
1074                 if (max)
1075                         opt = isl_qpolynomial_max_cst(opt, opt_i);
1076                 else
1077                         opt = isl_qpolynomial_min_cst(opt, opt_i);
1078         }
1079
1080         isl_set_free(set);
1081         isl_qpolynomial_fold_free(fold);
1082
1083         return opt;
1084 error:
1085         isl_set_free(set);
1086         isl_qpolynomial_fold_free(fold);
1087         return NULL;
1088 }
1089
1090 /* Check whether for each quasi-polynomial in "fold2" there is
1091  * a quasi-polynomial in "fold1" that dominates it on "set".
1092  */
1093 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1094         __isl_keep isl_qpolynomial_fold *fold1,
1095         __isl_keep isl_qpolynomial_fold *fold2)
1096 {
1097         int i, j;
1098         int covers;
1099
1100         if (!set || !fold1 || !fold2)
1101                 return -1;
1102
1103         covers = fold1->type == isl_fold_max ? 1 : -1;
1104
1105         for (i = 0; i < fold2->n; ++i) {
1106                 for (j = 0; j < fold1->n; ++j) {
1107                         isl_qpolynomial *d;
1108                         int sgn;
1109
1110                         d = isl_qpolynomial_sub(
1111                                 isl_qpolynomial_copy(fold1->qp[j]),
1112                                 isl_qpolynomial_copy(fold2->qp[i]));
1113                         sgn = isl_qpolynomial_sign(set, d);
1114                         isl_qpolynomial_free(d);
1115                         if (sgn == covers)
1116                                 break;
1117                 }
1118                 if (j >= fold1->n)
1119                         return 0;
1120         }
1121
1122         return 1;
1123 }
1124
1125 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1126  * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1127  * that of pwf2.
1128  */
1129 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1130         __isl_keep isl_pw_qpolynomial_fold *pwf2)
1131 {
1132         int i, j;
1133         isl_set *dom1, *dom2;
1134         int is_subset;
1135
1136         if (!pwf1 || !pwf2)
1137                 return -1;
1138
1139         if (pwf2->n == 0)
1140                 return 1;
1141         if (pwf1->n == 0)
1142                 return 0;
1143
1144         dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1145         dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1146         is_subset = isl_set_is_subset(dom2, dom1);
1147         isl_set_free(dom1);
1148         isl_set_free(dom2);
1149
1150         if (is_subset < 0 || !is_subset)
1151                 return is_subset;
1152
1153         for (i = 0; i < pwf2->n; ++i) {
1154                 for (j = 0; j < pwf1->n; ++j) {
1155                         int is_empty;
1156                         isl_set *common;
1157                         int covers;
1158
1159                         common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1160                                                    isl_set_copy(pwf2->p[i].set));
1161                         is_empty = isl_set_is_empty(common);
1162                         if (is_empty < 0 || is_empty) {
1163                                 isl_set_free(common);
1164                                 if (is_empty < 0)
1165                                         return -1;
1166                                 continue;
1167                         }
1168                         covers = qpolynomial_fold_covers_on_domain(common,
1169                                         pwf1->p[j].fold, pwf2->p[i].fold);
1170                         isl_set_free(common);
1171                         if (covers < 0 || !covers)
1172                                 return covers;
1173                 }
1174         }
1175
1176         return 1;
1177 }
1178
1179 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
1180         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1181 {
1182         int i;
1183         isl_ctx *ctx;
1184
1185         if (!fold || !morph)
1186                 goto error;
1187
1188         ctx = fold->dim->ctx;
1189         isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
1190
1191         fold = isl_qpolynomial_fold_cow(fold);
1192         if (!fold)
1193                 goto error;
1194
1195         isl_space_free(fold->dim);
1196         fold->dim = isl_space_copy(morph->ran->dim);
1197         if (!fold->dim)
1198                 goto error;
1199
1200         for (i = 0; i < fold->n; ++i) {
1201                 fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
1202                                                 isl_morph_copy(morph));
1203                 if (!fold->qp[i])
1204                         goto error;
1205         }
1206
1207         isl_morph_free(morph);
1208
1209         return fold;
1210 error:
1211         isl_qpolynomial_fold_free(fold);
1212         isl_morph_free(morph);
1213         return NULL;
1214 }
1215
1216 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1217 {
1218         if (!fold)
1219                 return isl_fold_list;
1220         return fold->type;
1221 }
1222
1223 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1224         __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1225 {
1226         if (!upwf)
1227                 return isl_fold_list;
1228         return upwf->type;
1229 }
1230
1231 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1232         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
1233 {
1234         int i;
1235
1236         if (!fold || !dim)
1237                 goto error;
1238
1239         if (isl_space_is_equal(fold->dim, dim)) {
1240                 isl_space_free(dim);
1241                 return fold;
1242         }
1243
1244         fold = isl_qpolynomial_fold_cow(fold);
1245         if (!fold)
1246                 goto error;
1247
1248         isl_space_free(fold->dim);
1249         fold->dim = isl_space_copy(dim);
1250         if (!fold->dim)
1251                 goto error;
1252
1253         for (i = 0; i < fold->n; ++i) {
1254                 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1255                                                 isl_space_copy(dim));
1256                 if (!fold->qp[i])
1257                         goto error;
1258         }
1259
1260         isl_space_free(dim);
1261
1262         return fold;
1263 error:
1264         isl_qpolynomial_fold_free(fold);
1265         isl_space_free(dim);
1266         return NULL;
1267 }
1268
1269 int isl_qpolynomial_fold_foreach_qpolynomial(
1270         __isl_keep isl_qpolynomial_fold *fold,
1271         int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1272 {
1273         int i;
1274
1275         if (!fold)
1276                 return -1;
1277
1278         for (i = 0; i < fold->n; ++i)
1279                 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1280                         return -1;
1281
1282         return 0;
1283 }
1284
1285 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1286         __isl_take isl_qpolynomial_fold *fold,
1287         enum isl_dim_type dst_type, unsigned dst_pos,
1288         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1289 {
1290         int i;
1291
1292         if (n == 0)
1293                 return fold;
1294
1295         fold = isl_qpolynomial_fold_cow(fold);
1296         if (!fold)
1297                 return NULL;
1298
1299         fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
1300                                                 src_type, src_pos, n);
1301         if (!fold->dim)
1302                 goto error;
1303
1304         for (i = 0; i < fold->n; ++i) {
1305                 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1306                                 dst_type, dst_pos, src_type, src_pos, n);
1307                 if (!fold->qp[i])
1308                         goto error;
1309         }
1310
1311         return fold;
1312 error:
1313         isl_qpolynomial_fold_free(fold);
1314         return NULL;
1315 }
1316
1317 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1318  * in fold->qp[k] by subs[i].
1319  */
1320 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1321         __isl_take isl_qpolynomial_fold *fold,
1322         enum isl_dim_type type, unsigned first, unsigned n,
1323         __isl_keep isl_qpolynomial **subs)
1324 {
1325         int i;
1326
1327         if (n == 0)
1328                 return fold;
1329
1330         fold = isl_qpolynomial_fold_cow(fold);
1331         if (!fold)
1332                 return NULL;
1333
1334         for (i = 0; i < fold->n; ++i) {
1335                 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1336                                 type, first, n, subs);
1337                 if (!fold->qp[i])
1338                         goto error;
1339         }
1340
1341         return fold;
1342 error:
1343         isl_qpolynomial_fold_free(fold);
1344         return NULL;
1345 }
1346
1347 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1348 {
1349         isl_ctx *ctx;
1350         isl_pw_qpolynomial_fold *pwf;
1351         isl_union_pw_qpolynomial_fold **upwf;
1352         uint32_t hash;
1353         struct isl_hash_table_entry *entry;
1354
1355         upwf = (isl_union_pw_qpolynomial_fold **)user;
1356
1357         ctx = pwqp->dim->ctx;
1358         hash = isl_space_get_hash(pwqp->dim);
1359         entry = isl_hash_table_find(ctx, &(*upwf)->table,
1360                                      hash, &has_dim, pwqp->dim, 1);
1361         if (!entry)
1362                 goto error;
1363
1364         pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1365         if (!entry->data)
1366                 entry->data = pwf;
1367         else {
1368                 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1369                 if (!entry->data)
1370                         return -1;
1371                 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1372                         isl_pw_qpolynomial_fold_free(entry->data);
1373                         isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1374                 }
1375         }
1376
1377         return 0;
1378 error:
1379         isl_pw_qpolynomial_free(pwqp);
1380         return -1;
1381 }
1382
1383 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1384         __isl_take isl_union_pw_qpolynomial_fold *upwf,
1385         __isl_take isl_union_pw_qpolynomial *upwqp)
1386 {
1387         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1388                                 isl_union_pw_qpolynomial_get_space(upwqp));
1389         upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1390                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1391
1392         upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1393         if (!upwf || !upwqp)
1394                 goto error;
1395
1396         if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1397                                                          &upwf) < 0)
1398                 goto error;
1399
1400         isl_union_pw_qpolynomial_free(upwqp);
1401
1402         return upwf;
1403 error:
1404         isl_union_pw_qpolynomial_fold_free(upwf);
1405         isl_union_pw_qpolynomial_free(upwqp);
1406         return NULL;
1407 }
1408
1409 static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
1410 {
1411         int m;
1412         m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
1413         if (m < 0 || !m)
1414                 return m;
1415         return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
1416 }
1417
1418 /* Compute the intersection of the range of the map and the domain
1419  * of the piecewise quasipolynomial reduction and then compute a bound
1420  * on the associated quasipolynomial reduction over all elements
1421  * in this intersection.
1422  *
1423  * We first introduce some unconstrained dimensions in the
1424  * piecewise quasipolynomial, intersect the resulting domain
1425  * with the wrapped map and the compute the sum.
1426  */
1427 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1428         __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1429         int *tight)
1430 {
1431         isl_ctx *ctx;
1432         isl_set *dom;
1433         isl_space *map_dim;
1434         isl_space *pwf_dim;
1435         unsigned n_in;
1436         int ok;
1437
1438         ctx = isl_map_get_ctx(map);
1439         if (!ctx)
1440                 goto error;
1441
1442         map_dim = isl_map_get_space(map);
1443         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1444         ok = join_compatible(map_dim, pwf_dim);
1445         isl_space_free(map_dim);
1446         isl_space_free(pwf_dim);
1447         if (!ok)
1448                 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1449                         goto error);
1450
1451         n_in = isl_map_dim(map, isl_dim_in);
1452         pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
1453
1454         dom = isl_map_wrap(map);
1455         pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
1456                                                 isl_set_get_space(dom));
1457
1458         pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1459         pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1460
1461         return pwf;
1462 error:
1463         isl_map_free(map);
1464         isl_pw_qpolynomial_fold_free(pwf);
1465         return NULL;
1466 }
1467
1468 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1469         __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1470         int *tight)
1471 {
1472         return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
1473 }
1474
1475 struct isl_apply_fold_data {
1476         isl_union_pw_qpolynomial_fold *upwf;
1477         isl_union_pw_qpolynomial_fold *res;
1478         isl_map *map;
1479         int tight;
1480 };
1481
1482 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1483         void *user)
1484 {
1485         isl_space *map_dim;
1486         isl_space *pwf_dim;
1487         struct isl_apply_fold_data *data = user;
1488         int ok;
1489
1490         map_dim = isl_map_get_space(data->map);
1491         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1492         ok = join_compatible(map_dim, pwf_dim);
1493         isl_space_free(map_dim);
1494         isl_space_free(pwf_dim);
1495
1496         if (ok) {
1497                 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1498                                     pwf, data->tight ? &data->tight : NULL);
1499                 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1500                                                         data->res, pwf);
1501         } else
1502                 isl_pw_qpolynomial_fold_free(pwf);
1503
1504         return 0;
1505 }
1506
1507 static int map_apply(__isl_take isl_map *map, void *user)
1508 {
1509         struct isl_apply_fold_data *data = user;
1510         int r;
1511
1512         data->map = map;
1513         r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1514                                 data->upwf, &pw_qpolynomial_fold_apply, data);
1515
1516         isl_map_free(map);
1517         return r;
1518 }
1519
1520 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1521         __isl_take isl_union_map *umap,
1522         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1523 {
1524         isl_space *dim;
1525         enum isl_fold type;
1526         struct isl_apply_fold_data data;
1527
1528         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1529                                 isl_union_map_get_space(umap));
1530         umap = isl_union_map_align_params(umap,
1531                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1532
1533         data.upwf = upwf;
1534         data.tight = tight ? 1 : 0;
1535         dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
1536         type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1537         data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1538         if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1539                 goto error;
1540
1541         isl_union_map_free(umap);
1542         isl_union_pw_qpolynomial_fold_free(upwf);
1543
1544         if (tight)
1545                 *tight = data.tight;
1546
1547         return data.res;
1548 error:
1549         isl_union_map_free(umap);
1550         isl_union_pw_qpolynomial_fold_free(upwf);
1551         isl_union_pw_qpolynomial_fold_free(data.res);
1552         return NULL;
1553 }
1554
1555 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1556         __isl_take isl_union_set *uset,
1557         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1558 {
1559         return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1560 }
1561
1562 /* Reorder the dimension of "fold" according to the given reordering.
1563  */
1564 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
1565         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1566 {
1567         int i;
1568
1569         fold = isl_qpolynomial_fold_cow(fold);
1570         if (!fold || !r)
1571                 goto error;
1572
1573         for (i = 0; i < fold->n; ++i) {
1574                 fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
1575                                                     isl_reordering_copy(r));
1576                 if (!fold->qp[i])
1577                         goto error;
1578         }
1579
1580         fold = isl_qpolynomial_fold_reset_domain_space(fold,
1581                                                     isl_space_copy(r->dim));
1582
1583         isl_reordering_free(r);
1584
1585         return fold;
1586 error:
1587         isl_qpolynomial_fold_free(fold);
1588         isl_reordering_free(r);
1589         return NULL;
1590 }
1591
1592 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1593         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1594 {
1595         int i;
1596
1597         if (isl_int_is_one(v))
1598                 return fold;
1599         if (fold && isl_int_is_zero(v)) {
1600                 isl_qpolynomial_fold *zero;
1601                 isl_space *dim = isl_space_copy(fold->dim);
1602                 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1603                 isl_qpolynomial_fold_free(fold);
1604                 return zero;
1605         }
1606
1607         fold = isl_qpolynomial_fold_cow(fold);
1608         if (!fold)
1609                 return NULL;
1610
1611         if (isl_int_is_neg(v))
1612                 fold->type = isl_fold_type_negate(fold->type);
1613         for (i = 0; i < fold->n; ++i) {
1614                 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1615                 if (!fold->qp[i])
1616                         goto error;
1617         }
1618
1619         return fold;
1620 error:
1621         isl_qpolynomial_fold_free(fold);
1622         return NULL;
1623 }
1624
1625 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1626         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1627 {
1628         return isl_qpolynomial_fold_mul_isl_int(fold, v);
1629 }