isl_map_piplib.c

   1 #include "isl_set.h"
   2 #include "isl_map.h"
   3 #include "isl_seq.h"
   4 #include "isl_piplib.h"
   5 #include "isl_map_piplib.h"
   6 #include "isl_map_private.h"
   7
   8 static void copy_values_from(isl_int *dst, Entier *src, unsigned n)
   9 {
  10         int i;
  11
  12         for (i = 0; i < n; ++i)
  13                 entier_assign(dst[i], src[i]);
  14 }
  15
  16 static void add_value(isl_int *dst, Entier *src)
  17 {
  18         mpz_add(*dst, *dst, *src);
  19 }
  20
  21 static void copy_constraint_from(isl_int *dst, PipVector *src,
  22                 unsigned nparam, unsigned n_in, unsigned n_out,
  23                 unsigned extra, int *pos)
  24 {
  25         int i;
  26
  27         copy_values_from(dst, src->the_vector+src->nb_elements-1, 1);
  28         copy_values_from(dst+1, src->the_vector, nparam+n_in);
  29         isl_seq_clr(dst+1+nparam+n_in, n_out);
  30         isl_seq_clr(dst+1+nparam+n_in+n_out, extra);
  31         for (i = 0; i + n_in + nparam < src->nb_elements-1; ++i) {
  32                 int p = pos[i];
  33                 add_value(&dst[1+nparam+n_in+n_out+p],
  34                           &src->the_vector[n_in+nparam+i]);
  35         }
  36 }
  37
  38 static int add_inequality(struct isl_ctx *ctx,
  39                    struct isl_basic_map *bmap, int *pos, PipVector *vec)
  40 {
  41         unsigned nparam = isl_basic_map_n_param(bmap);
  42         unsigned n_in = isl_basic_map_n_in(bmap);
  43         unsigned n_out = isl_basic_map_n_out(bmap);
  44         unsigned n_div = isl_basic_map_n_div(bmap);
  45         int i = isl_basic_map_alloc_inequality(bmap);
  46         if (i < 0)
  47                 return -1;
  48         copy_constraint_from(bmap->ineq[i], vec,
  49             nparam, n_in, n_out, n_div, pos);
  50
  51         return i;
  52 }
  53
  54 /* For a div d = floor(f/m), add the constraints
  55  *
  56  *              f - m d >= 0
  57  *              -(f-(n-1)) + m d >= 0
  58  *
  59  * Note that the second constraint is the negation of
  60  *
  61  *              f - m d >= n
  62  */
  63 static int add_div_constraints(struct isl_ctx *ctx,
  64         struct isl_basic_map *bmap, int *pos, PipNewparm *p, unsigned div)
  65 {
  66         int i, j;
  67         unsigned total = isl_basic_map_total_dim(bmap);
  68         unsigned div_pos = 1 + total - bmap->n_div + div;
  69
  70         i = add_inequality(ctx, bmap, pos, p->vector);
  71         if (i < 0)
  72                 return -1;
  73         copy_values_from(&bmap->ineq[i][div_pos], &p->deno, 1);
  74         isl_int_neg(bmap->ineq[i][div_pos], bmap->ineq[i][div_pos]);
  75
  76         j = isl_basic_map_alloc_inequality(bmap);
  77         if (j < 0)
  78                 return -1;
  79         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
  80         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
  81         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
  82         return j;
  83 }
  84
  85 static int add_equality(struct isl_ctx *ctx,
  86                    struct isl_basic_map *bmap, int *pos,
  87                    unsigned var, PipVector *vec)
  88 {
  89         int i;
  90         unsigned nparam = isl_basic_map_n_param(bmap);
  91         unsigned n_in = isl_basic_map_n_in(bmap);
  92         unsigned n_out = isl_basic_map_n_out(bmap);
  93
  94         isl_assert(ctx, var < n_out, return -1);
  95
  96         i = isl_basic_map_alloc_equality(bmap);
  97         if (i < 0)
  98                 return -1;
  99         copy_constraint_from(bmap->eq[i], vec,
 100             nparam, n_in, n_out, bmap->extra, pos);
 101         isl_int_set_si(bmap->eq[i][1+nparam+n_in+var], -1);
 102
 103         return i;
 104 }
 105
 106 static int find_div(struct isl_ctx *ctx,
 107                    struct isl_basic_map *bmap, int *pos, PipNewparm *p)
 108 {
 109         int i, j;
 110         unsigned nparam = isl_basic_map_n_param(bmap);
 111         unsigned n_in = isl_basic_map_n_in(bmap);
 112         unsigned n_out = isl_basic_map_n_out(bmap);
 113
 114         i = isl_basic_map_alloc_div(bmap);
 115         if (i < 0)
 116                 return -1;
 117
 118         copy_constraint_from(bmap->div[i]+1, p->vector,
 119             nparam, n_in, n_out, bmap->extra, pos);
 120
 121         copy_values_from(bmap->div[i], &p->deno, 1);
 122         for (j = 0; j < i; ++j)
 123                 if (isl_seq_eq(bmap->div[i], bmap->div[j],
 124                                 1+1+isl_basic_map_total_dim(bmap)+j)) {
 125                         isl_basic_map_free_div(bmap, 1);
 126                         return j;
 127                 }
 128
 129         if (add_div_constraints(ctx, bmap, pos, p, i) < 0)
 130                 return -1;
 131
 132         return i;
 133 }
 134
 135 /* Count some properties of a quast
 136  * - maximal number of new parameters
 137  * - maximal depth
 138  * - total number of solutions
 139  * - total number of empty branches
 140  */
 141 static void quast_count(PipQuast *q, int *maxnew, int depth, int *maxdepth,
 142                         int *sol, int *nosol)
 143 {
 144         PipNewparm *p;
 145
 146         for (p = q->newparm; p; p = p->next)
 147                 if (p->rank > *maxnew)
 148                         *maxnew = p->rank;
 149         if (q->condition) {
 150                 if (++depth > *maxdepth)
 151                         *maxdepth = depth;
 152                 quast_count(q->next_else, maxnew, depth, maxdepth, sol, nosol);
 153                 quast_count(q->next_then, maxnew, depth, maxdepth, sol, nosol);
 154         } else {
 155                 if (q->list)
 156                         ++(*sol);
 157                 else
 158                         ++(*nosol);
 159         }
 160 }
 161
 162 /*
 163  * pos: array of length bmap->set.extra, mapping each of the existential
 164  *              variables PIP proposes to an existential variable in bmap
 165  * bmap: collects the currently active constraints
 166  * rest: collects the empty leaves of the quast (if not NULL)
 167  */
 168 struct scan_data {
 169         struct isl_ctx                  *ctx;
 170         struct isl_basic_map            *bmap;
 171         struct isl_set                  **rest;
 172         int        *pos;
 173 };
 174
 175 /*
 176  * New existentially quantified variables are places after the existing ones.
 177  */
 178 static struct isl_map *scan_quast_r(struct scan_data *data, PipQuast *q,
 179                                     struct isl_map *map)
 180 {
 181         PipNewparm *p;
 182         struct isl_basic_map *bmap = data->bmap;
 183         unsigned old_n_div = bmap->n_div;
 184         unsigned nparam = isl_basic_map_n_param(bmap);
 185         unsigned n_in = isl_basic_map_n_in(bmap);
 186         unsigned n_out = isl_basic_map_n_out(bmap);
 187
 188         if (!map)
 189                 goto error;
 190
 191         for (p = q->newparm; p; p = p->next) {
 192                 int pos;
 193                 unsigned pip_param = nparam + n_in;
 194
 195                 pos = find_div(data->ctx, bmap, data->pos, p);
 196                 if (pos < 0)
 197                         goto error;
 198                 data->pos[p->rank - pip_param] = pos;
 199         }
 200
 201         if (q->condition) {
 202                 int pos = add_inequality(data->ctx, bmap, data->pos,
 203                                          q->condition);
 204                 if (pos < 0)
 205                         goto error;
 206                 map = scan_quast_r(data, q->next_then, map);
 207
 208                 if (isl_inequality_negate(bmap, pos))
 209                         goto error;
 210                 map = scan_quast_r(data, q->next_else, map);
 211
 212                 if (isl_basic_map_free_inequality(bmap, 1))
 213                         goto error;
 214         } else if (q->list) {
 215                 PipList *l;
 216                 int j;
 217                 /* if bmap->n_out is zero, we are only interested in the domains
 218                  * where a solution exists and not in the actual solution
 219                  */
 220                 for (j = 0, l = q->list; j < n_out && l; ++j, l = l->next)
 221                         if (add_equality(data->ctx, bmap, data->pos, j,
 222                                                 l->vector) < 0)
 223                                 goto error;
 224                 map = isl_map_add(map, isl_basic_map_copy(bmap));
 225                 if (isl_basic_map_free_equality(bmap, n_out))
 226                         goto error;
 227         } else if (data->rest) {
 228                 struct isl_basic_set *bset;
 229                 bset = isl_basic_set_from_basic_map(isl_basic_map_copy(bmap));
 230                 bset = isl_basic_set_drop_dims(bset, n_in, n_out);
 231                 if (!bset)
 232                         goto error;
 233                 *data->rest = isl_set_add(*data->rest, bset);
 234         }
 235
 236         if (isl_basic_map_free_inequality(bmap, 2*(bmap->n_div - old_n_div)))
 237                 goto error;
 238         if (isl_basic_map_free_div(bmap, bmap->n_div - old_n_div))
 239                 goto error;
 240         return map;
 241 error:
 242         isl_map_free(map);
 243         return NULL;
 244 }
 245
 246 /*
 247  * Returns a map with "context" as domain and as range the first
 248  * "keep" variables in the quast lists.
 249  */
 250 static struct isl_map *isl_map_from_quast(struct isl_ctx *ctx, PipQuast *q,
 251                 unsigned keep,
 252                 struct isl_basic_set *context,
 253                 struct isl_set **rest)
 254 {
 255         int             pip_param;
 256         int             nexist;
 257         int             max_depth;
 258         int             n_sol, n_nosol;
 259         struct scan_data        data;
 260         struct isl_map          *map;
 261         struct isl_dim          *dims;
 262         unsigned                nparam;
 263         unsigned                dim;
 264
 265         data.ctx = ctx;
 266         data.rest = rest;
 267         data.bmap = NULL;
 268         data.pos = NULL;
 269
 270         if (!context)
 271                 goto error;
 272
 273         dim = isl_basic_set_n_dim(context);
 274         nparam = isl_basic_set_n_param(context);
 275         pip_param = nparam + dim;
 276
 277         max_depth = 0;
 278         n_sol = 0;
 279         n_nosol = 0;
 280         nexist = pip_param-1;
 281         quast_count(q, &nexist, 0, &max_depth, &n_sol, &n_nosol);
 282         nexist -= pip_param-1;
 283
 284         if (rest) {
 285                 *rest = isl_set_alloc(data.ctx, nparam, dim, n_nosol,
 286                                         ISL_MAP_DISJOINT);
 287                 if (!*rest)
 288                         goto error;
 289         }
 290         map = isl_map_alloc(data.ctx, nparam, dim, keep, n_sol,
 291                                 ISL_MAP_DISJOINT);
 292         if (!map)
 293                 goto error;
 294
 295         dims = isl_dim_reverse(isl_dim_copy(context->dim));
 296         data.bmap = isl_basic_map_from_basic_set(context, dims);
 297         data.bmap = isl_basic_map_extend(data.bmap,
 298             nparam, dim, keep, nexist, keep, max_depth+2*nexist);
 299         if (!data.bmap)
 300                 goto error;
 301
 302         if (data.bmap->extra) {
 303                 int i;
 304                 data.pos = isl_alloc_array(ctx, int, data.bmap->extra);
 305                 if (!data.pos)
 306                         goto error;
 307                 for (i = 0; i < data.bmap->n_div; ++i)
 308                         data.pos[i] = i;
 309         }
 310
 311         map = scan_quast_r(&data, q, map);
 312         map = isl_map_finalize(map);
 313         if (!map)
 314                 goto error;
 315         if (rest) {
 316                 *rest = isl_set_finalize(*rest);
 317                 if (!*rest)
 318                         goto error;
 319         }
 320         isl_basic_map_free(data.bmap);
 321         if (data.pos)
 322                 free(data.pos);
 323         return map;
 324 error:
 325         if (data.pos)
 326                 free(data.pos);
 327         isl_basic_map_free(data.bmap);
 328         isl_map_free(map);
 329         if (rest) {
 330                 isl_set_free(*rest);
 331                 *rest = NULL;
 332         }
 333         return NULL;
 334 }
 335
 336 static void copy_values_to(Entier *dst, isl_int *src, unsigned n)
 337 {
 338         int i;
 339
 340         for (i = 0; i < n; ++i)
 341                 entier_assign(dst[i], src[i]);
 342 }
 343
 344 static void copy_constraint_to(Entier *dst, isl_int *src,
 345                 unsigned pip_param, unsigned pip_var,
 346                 unsigned extra_front, unsigned extra_back)
 347 {
 348         copy_values_to(dst+1+extra_front+pip_var+pip_param+extra_back, src, 1);
 349         copy_values_to(dst+1+extra_front+pip_var, src+1, pip_param);
 350         copy_values_to(dst+1+extra_front, src+1+pip_param, pip_var);
 351 }
 352
 353 PipMatrix *isl_basic_map_to_pip(struct isl_basic_map *bmap, unsigned pip_param,
 354                          unsigned extra_front, unsigned extra_back)
 355 {
 356         int i;
 357         unsigned nrow;
 358         unsigned ncol;
 359         PipMatrix *M;
 360         unsigned off;
 361         unsigned pip_var = isl_basic_map_total_dim(bmap) - pip_param;
 362
 363         nrow = extra_front + bmap->n_eq + bmap->n_ineq;
 364         ncol = 1 + extra_front + pip_var + pip_param + extra_back + 1;
 365         M = pip_matrix_alloc(nrow, ncol);
 366         if (!M)
 367                 return NULL;
 368
 369         off = extra_front;
 370         for (i = 0; i < bmap->n_eq; ++i) {
 371                 entier_set_si(M->p[off+i][0], 0);
 372                 copy_constraint_to(M->p[off+i], bmap->eq[i],
 373                                    pip_param, pip_var, extra_front, extra_back);
 374         }
 375         off += bmap->n_eq;
 376         for (i = 0; i < bmap->n_ineq; ++i) {
 377                 entier_set_si(M->p[off+i][0], 1);
 378                 copy_constraint_to(M->p[off+i], bmap->ineq[i],
 379                                    pip_param, pip_var, extra_front, extra_back);
 380         }
 381         return M;
 382 }
 383
 384 static struct isl_map *extremum_on(
 385                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 386                 struct isl_set **empty, int max)
 387 {
 388         PipOptions      *options;
 389         PipQuast        *sol;
 390         struct isl_map  *map;
 391         struct isl_ctx  *ctx;
 392         PipMatrix *domain = NULL, *context = NULL;
 393         unsigned         nparam, n_in, n_out;
 394
 395         if (!bmap || !dom)
 396                 goto error;
 397
 398         ctx = bmap->ctx;
 399         isl_assert(ctx, isl_basic_map_compatible_domain(bmap, dom), goto error);
 400         nparam = isl_basic_map_n_param(bmap);
 401         n_in = isl_basic_map_n_in(bmap);
 402         n_out = isl_basic_map_n_out(bmap);
 403
 404         domain = isl_basic_map_to_pip(bmap, nparam + n_in, 0, dom->n_div);
 405         if (!domain)
 406                 goto error;
 407         context = isl_basic_map_to_pip((struct isl_basic_map *)dom, 0, 0, 0);
 408         if (!context)
 409                 goto error;
 410
 411         options = pip_options_init();
 412         options->Simplify = 1;
 413         options->Maximize = max;
 414         options->Urs_unknowns = -1;
 415         options->Urs_parms = -1;
 416         sol = pip_solve(domain, context, -1, options);
 417
 418         if (sol) {
 419                 struct isl_basic_set *copy;
 420                 copy = isl_basic_set_copy(dom);
 421                 map = isl_map_from_quast(ctx, sol, n_out, copy, empty);
 422         } else {
 423                 map = isl_map_empty_like_basic_map(bmap);
 424                 if (empty)
 425                         *empty = NULL;
 426         }
 427         if (!map)
 428                 goto error;
 429         if (map->n == 0 && empty) {
 430                 isl_set_free(*empty);
 431                 *empty = isl_set_from_basic_set(dom);
 432         } else
 433                 isl_basic_set_free(dom);
 434         isl_basic_map_free(bmap);
 435
 436         pip_quast_free(sol);
 437         pip_options_free(options);
 438         pip_matrix_free(domain);
 439         pip_matrix_free(context);
 440
 441         return map;
 442 error:
 443         if (domain)
 444                 pip_matrix_free(domain);
 445         if (context)
 446                 pip_matrix_free(context);
 447         isl_basic_map_free(bmap);
 448         isl_basic_set_free(dom);
 449         return NULL;
 450 }
 451
 452 struct isl_map *isl_pip_basic_map_lexmax(
 453                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 454                 struct isl_set **empty)
 455 {
 456         return extremum_on(bmap, dom, empty, 1);
 457 }
 458
 459 struct isl_map *isl_pip_basic_map_lexmin(
 460                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 461                 struct isl_set **empty)
 462 {
 463         return extremum_on(bmap, dom, empty, 0);
 464 }
 465
 466 struct isl_map *isl_pip_basic_map_compute_divs(struct isl_basic_map *bmap)
 467 {
 468         PipMatrix *domain = NULL, *context = NULL;
 469         PipOptions      *options;
 470         PipQuast        *sol;
 471         struct isl_ctx  *ctx;
 472         struct isl_dim  *dim;
 473         struct isl_map  *map;
 474         struct isl_set  *set;
 475         struct isl_basic_set    *dom;
 476         unsigned         nparam;
 477         unsigned         n_in;
 478         unsigned         n_out;
 479
 480         if (!bmap)
 481                 goto error;
 482
 483         ctx = bmap->ctx;
 484         nparam = isl_basic_map_n_param(bmap);
 485         n_in = isl_basic_map_n_in(bmap);
 486         n_out = isl_basic_map_n_out(bmap);
 487
 488         domain = isl_basic_map_to_pip(bmap, nparam + n_in + n_out, 0, 0);
 489         if (!domain)
 490                 goto error;
 491         context = pip_matrix_alloc(0, nparam + n_in + n_out + 2);
 492         if (!context)
 493                 goto error;
 494
 495         options = pip_options_init();
 496         options->Simplify = 1;
 497         options->Urs_unknowns = -1;
 498         options->Urs_parms = -1;
 499         sol = pip_solve(domain, context, -1, options);
 500
 501         dom = isl_basic_set_alloc(ctx, nparam, n_in + n_out, 0, 0, 0);
 502         map = isl_map_from_quast(ctx, sol, 0, dom, NULL);
 503
 504         pip_quast_free(sol);
 505         pip_options_free(options);
 506         pip_matrix_free(domain);
 507         pip_matrix_free(context);
 508
 509         dim = isl_dim_copy(bmap->dim);
 510         isl_basic_map_free(bmap);
 511
 512         set = isl_map_domain(map);
 513
 514         return isl_map_from_set(set, dim);
 515 error:
 516         if (domain)
 517                 pip_matrix_free(domain);
 518         if (context)
 519                 pip_matrix_free(context);
 520         isl_basic_set_free(dom);
 521         isl_basic_map_free(bmap);
 522         return NULL;
 523 }