scale.c

   1 #include <assert.h>
   2 #include <barvinok/barvinok.h>
   3 #include <barvinok/util.h>
   4 #include <barvinok/options.h>
   5 #include "scale.h"
   6 #include "reduce_domain.h"
   7 #include "param_util.h"
   8
   9 #define ALLOC(type) (type*)malloc(sizeof(type))
  10 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
  11
  12 /* If a vertex is described by A x + B p + c = 0, then
  13  * M = [A B] and we want to compute a linear transformation L such
  14  * that H L = A and H \Z contains both A \Z and B \Z.
  15  * We compute
  16  *             [ A B ] = [ H 0 ] [ U_11  U_12 ]
  17  *                               [ U_21  U_22 ]
  18  *
  19  * U_11 is the required linear transformation.
  20  * Note that this also works if M has more rows than there are variables,
  21  * i.e., if some rows in M are linear combinations of other rows.
  22  * These extra rows only affect and H and not U.
  23  */
  24 static Lattice *extract_lattice(Matrix *M, unsigned nvar)
  25 {
  26     int row;
  27     Matrix *H, *Q, *U, *Li;
  28     Lattice *L;
  29     int ok;
  30
  31     left_hermite(M, &H, &Q, &U);
  32     Matrix_Free(U);
  33
  34     Li = Matrix_Alloc(nvar+1, nvar+1);
  35     L = Matrix_Alloc(nvar+1, nvar+1);
  36     value_set_si(Li->p[nvar][nvar], 1);
  37
  38     for (row = 0; row < nvar; ++row)
  39         Vector_Copy(Q->p[row], Li->p[row], nvar);
  40     Matrix_Free(H);
  41     Matrix_Free(Q);
  42
  43     ok = Matrix_Inverse(Li, L);
  44     assert(ok);
  45     Matrix_Free(Li);
  46
  47     return L;
  48 }
  49
  50 /* Returns the smallest (wrt inclusion) lattice that contains both X and Y */
  51 static Lattice *LatticeJoin(Lattice *X, Lattice *Y)
  52 {
  53     int i;
  54     int dim = X->NbRows-1;
  55     Value lcm;
  56     Value tmp;
  57     Lattice *L;
  58     Matrix *M, *H, *U, *Q;
  59
  60     assert(X->NbColumns-1 == dim);
  61     assert(Y->NbRows-1 == dim);
  62     assert(Y->NbColumns-1 == dim);
  63
  64     value_init(lcm);
  65     value_init(tmp);
  66
  67     M = Matrix_Alloc(dim, 2*dim);
  68     value_lcm(lcm, X->p[dim][dim], Y->p[dim][dim]);
  69
  70     value_division(tmp, lcm, X->p[dim][dim]);
  71     for (i = 0; i < dim; ++i)
  72         Vector_Scale(X->p[i], M->p[i], tmp, dim);
  73     value_division(tmp, lcm, Y->p[dim][dim]);
  74     for (i = 0; i < dim; ++i)
  75         Vector_Scale(Y->p[i], M->p[i]+dim, tmp, dim);
  76
  77     left_hermite(M, &H, &Q, &U);
  78     Matrix_Free(M);
  79     Matrix_Free(Q);
  80     Matrix_Free(U);
  81
  82     L = Matrix_Alloc(dim+1, dim+1);
  83     value_assign(L->p[dim][dim], lcm);
  84     for (i = 0; i < dim; ++i)
  85         Vector_Copy(H->p[i], L->p[i], dim);
  86     Matrix_Free(H);
  87
  88     value_clear(tmp);
  89     value_clear(lcm);
  90     return L;
  91 }
  92
  93 static void Param_Vertex_Image(Param_Vertices *V, Matrix *T)
  94 {
  95     unsigned nvar  = V->Vertex->NbRows;
  96     unsigned nparam = V->Vertex->NbColumns - 2;
  97     Matrix *Vertex;
  98     int i;
  99
 100     Param_Vertex_Common_Denominator(V);
 101     Vertex = Matrix_Alloc(V->Vertex->NbRows, V->Vertex->NbColumns);
 102     Matrix_Product(T, V->Vertex, Vertex);
 103     for (i = 0; i < nvar; ++i) {
 104         value_assign(Vertex->p[i][nparam+1], V->Vertex->p[i][nparam+1]);
 105         Vector_Normalize(Vertex->p[i], nparam+2);
 106     }
 107     Matrix_Free(V->Vertex);
 108     V->Vertex = Vertex;
 109 }
 110
 111 static void apply_expansion(Param_Polyhedron *PP,
 112                             Matrix *expansion, unsigned MaxRays)
 113 {
 114     int i;
 115     unsigned nparam = PP->V->Vertex->NbColumns - 2;
 116     unsigned nvar = PP->V->Vertex->NbRows;
 117     Vector *constraint;
 118
 119     constraint = Vector_Alloc(nvar+nparam+1);
 120     for (i = 0; i < PP->Constraints->NbRows; ++i) {
 121         Vector_Matrix_Product(PP->Constraints->p[i]+1, expansion, constraint->p);
 122         Vector_Copy(constraint->p, PP->Constraints->p[i]+1, nvar+nparam+1);
 123         Vector_Normalize(PP->Constraints->p[i]+1, nvar+nparam+1);
 124     }
 125     Vector_Free(constraint);
 126 }
 127
 128 /* Scales the parametric polyhedron with constraints vertices PP
 129  * such that the number of integer points can be represented by a polynomial.
 130  * The vertices of "PP" are adapted according to the scaling.
 131  * The scaling factor is returned in *det.
 132  * The transformation that maps the new coordinates to the original
 133  * coordinates is returned in *Lat (if Lat != NULL).
 134  * The enumerator of the scaled parametric polyhedron should be divided
 135  * by this number to obtain an approximation of the enumerator of the
 136  * original parametric polyhedron.
 137  *
 138  * The algorithm is described in "Approximating Ehrhart Polynomials using
 139  * affine transformations" by B. Meister.
 140  */
 141 static void Param_Polyhedron_Scale_Integer_Slow(Param_Polyhedron *PP,
 142                                          Lattice **Lat,
 143                                          Value *det, unsigned MaxRays)
 144 {
 145     Param_Vertices *V;
 146     unsigned nparam;
 147     unsigned nvar;
 148     Lattice *L = NULL, *Li;
 149     Matrix *T;
 150     Matrix *expansion;
 151     int i;
 152     int ok;
 153
 154     if (!PP->nbV)
 155         return;
 156
 157     nparam = PP->V->Vertex->NbColumns - 2;
 158     nvar = PP->V->Vertex->NbRows;
 159
 160     for (V = PP->V; V; V = V->next) {
 161         Lattice *L2;
 162         Matrix *M;
 163         int i, j, n;
 164         unsigned *supporting;
 165         int ix;
 166         unsigned bx;
 167
 168         supporting = supporting_constraints(PP->Constraints, V, &n);
 169         M = Matrix_Alloc(n, PP->Constraints->NbColumns-2);
 170         for (i = 0, j = 0, ix = 0, bx = MSB; i < PP->Constraints->NbRows; ++i) {
 171             if (supporting[ix] & bx)
 172                 Vector_Copy(PP->Constraints->p[i]+1, M->p[j++],
 173                             PP->Constraints->NbColumns-2);
 174             NEXT(ix, bx);
 175         }
 176         free(supporting);
 177         L2 = extract_lattice(M, nvar);
 178         Matrix_Free(M);
 179
 180         if (!L)
 181             L = L2;
 182         else {
 183             Lattice *L3 = LatticeJoin(L, L2);
 184             Matrix_Free(L);
 185             Matrix_Free(L2);
 186             L = L3;
 187         }
 188     }
 189
 190     if (Lat)
 191         *Lat = Matrix_Copy(L);
 192
 193     /* apply the variable expansion to the polyhedron (constraints) */
 194     expansion = Matrix_Alloc(nvar + nparam + 1,  nvar + nparam + 1);
 195     for (i = 0; i < nvar; ++i)
 196         Vector_Copy(L->p[i], expansion->p[i], nvar);
 197     for (i = nvar; i < nvar+nparam+1; ++i)
 198         value_assign(expansion->p[i][i], L->p[nvar][nvar]);
 199
 200     apply_expansion(PP, expansion, MaxRays);
 201     Matrix_Free(expansion);
 202
 203     /* apply the variable expansion to the parametric vertices */
 204     Li = Matrix_Alloc(nvar+1, nvar+1);
 205     ok = Matrix_Inverse(L, Li);
 206     assert(ok);
 207     Matrix_Free(L);
 208     assert(value_one_p(Li->p[nvar][nvar]));
 209     T = Matrix_Alloc(nvar, nvar);
 210     value_set_si(*det, 1);
 211     for (i = 0; i < nvar; ++i) {
 212         value_multiply(*det, *det, Li->p[i][i]);
 213         Vector_Copy(Li->p[i], T->p[i], nvar);
 214     }
 215     Matrix_Free(Li);
 216     for (V = PP->V; V; V = V->next)
 217         Param_Vertex_Image(V, T);
 218     Matrix_Free(T);
 219 }
 220
 221 /* Scales the parametric polyhedron with constraints vertices PP
 222  * such that the number of integer points can be represented by a polynomial.
 223  * The vertices of "PP" are adapted according to the scaling.
 224  * The scaling factor is returned in *det.
 225  * The transformation that maps the new coordinates to the original
 226  * coordinates is returned in *Lat (if Lat != NULL).
 227  * The enumerator of the scaled parametric polyhedron should be divided
 228  * by this number to obtain an approximation of the enumerator of the
 229  * original parametric polyhedron.
 230  *
 231  * The algorithm is described in "Approximating Ehrhart Polynomials using
 232  * affine transformations" by B. Meister.
 233  */
 234 static void Param_Polyhedron_Scale_Integer_Fast(Param_Polyhedron *PP,
 235                                          Lattice **Lat,
 236                                          Value *det, unsigned MaxRays)
 237 {
 238   int i;
 239   int nb_param, nb_vars;
 240   Vector *denoms;
 241   Param_Vertices *V;
 242   Value global_var_lcm;
 243   Value tmp;
 244   Matrix *expansion;
 245
 246   value_set_si(*det, 1);
 247   if (!PP->nbV)
 248     return;
 249
 250   nb_param = PP->D->Domain->Dimension;
 251   nb_vars = PP->V->Vertex->NbRows;
 252
 253   /* Scan the vertices and make an orthogonal expansion of the variable
 254      space */
 255   /* a- prepare the array of common denominators */
 256   denoms = Vector_Alloc(nb_vars);
 257   value_init(global_var_lcm);
 258
 259   value_init(tmp);
 260   /* b- scan the vertices and compute the variables' global lcms */
 261   for (V = PP->V; V; V = V->next) {
 262     for (i = 0; i < nb_vars; i++) {
 263       Vector_Gcd(V->Vertex->p[i], nb_param, &tmp);
 264       value_gcd(tmp, tmp, V->Vertex->p[i][nb_param+1]);
 265       value_division(tmp, V->Vertex->p[i][nb_param+1], tmp);
 266       Lcm3(denoms->p[i], tmp, &denoms->p[i]);
 267     }
 268   }
 269   value_clear(tmp);
 270
 271   value_set_si(global_var_lcm, 1);
 272   for (i = 0; i < nb_vars; i++) {
 273     value_multiply(*det, *det, denoms->p[i]);
 274     Lcm3(global_var_lcm, denoms->p[i], &global_var_lcm);
 275   }
 276
 277   /* scale vertices */
 278   for (V = PP->V; V; V = V->next)
 279     for (i = 0; i < nb_vars; i++) {
 280       Vector_Scale(V->Vertex->p[i], V->Vertex->p[i], denoms->p[i], nb_param+1);
 281       Vector_Normalize(V->Vertex->p[i], nb_param+2);
 282     }
 283
 284   /* the expansion can be actually writen as global_var_lcm.L^{-1} */
 285   /* this is equivalent to multiply the rows of P by denoms_det */
 286   for (i = 0; i < nb_vars; i++)
 287     value_division(denoms->p[i], global_var_lcm, denoms->p[i]);
 288
 289   /* OPT : we could use a vector instead of a diagonal matrix here (c- and d-).*/
 290   /* c- make the quick expansion matrix */
 291   expansion = Matrix_Alloc(nb_vars+nb_param+1, nb_vars+nb_param+1);
 292   for (i = 0; i < nb_vars; i++)
 293     value_assign(expansion->p[i][i], denoms->p[i]);
 294   for (i = nb_vars; i < nb_vars+nb_param+1; i++)
 295     value_assign(expansion->p[i][i], global_var_lcm);
 296
 297   /* d- apply the variable expansion to the polyhedron */
 298   apply_expansion(PP, expansion, MaxRays);
 299
 300   if (Lat) {
 301     Lattice *L = Matrix_Alloc(nb_vars+1, nb_vars+1);
 302     for (i = 0; i < nb_vars; ++i)
 303         value_assign(L->p[i][i], denoms->p[i]);
 304     value_assign(L->p[nb_vars][nb_vars], global_var_lcm);
 305     *Lat = L;
 306   }
 307
 308   Matrix_Free(expansion);
 309   value_clear(global_var_lcm);
 310   Vector_Free(denoms);
 311 }
 312
 313 /* Compute negated sum of all positive or negative coefficients in a row */
 314 static void negated_sum(Value *v, int len, int negative, Value *sum)
 315 {
 316     int j;
 317
 318     value_set_si(*sum, 0);
 319     for (j = 0; j < len; ++j)
 320         if (negative ? value_neg_p(v[j]) : value_pos_p(v[j]))
 321             value_subtract(*sum, *sum, v[j]);
 322 }
 323
 324 /* adapted from mpolyhedron_inflate in PolyLib */
 325 Polyhedron *Polyhedron_Flate(Polyhedron *P, unsigned nparam, int inflate,
 326                              unsigned MaxRays)
 327 {
 328     Value sum;
 329     int nvar = P->Dimension - nparam;
 330     Matrix *C = Polyhedron2Constraints(P);
 331     Polyhedron *P2;
 332     int i;
 333
 334     value_init(sum);
 335     /* subtract the sum of the negative coefficients of each inequality */
 336     for (i = 0; i < C->NbRows; ++i) {
 337         negated_sum(C->p[i]+1, nvar, inflate, &sum);
 338         value_addto(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], sum);
 339     }
 340     value_clear(sum);
 341     P2 = Constraints2Polyhedron(C, MaxRays);
 342     Matrix_Free(C);
 343
 344     if (inflate) {
 345         Polyhedron *C, *CA;
 346         C = Polyhedron_Project(P, nparam);
 347         CA = align_context(C, P->Dimension, MaxRays);
 348         P = P2;
 349         P2 = DomainIntersection(P, CA, MaxRays);
 350         Polyhedron_Free(C);
 351         Polyhedron_Free(CA);
 352         Polyhedron_Free(P);
 353     }
 354
 355     return P2;
 356 }
 357
 358 static Polyhedron *flate_narrow2(Polyhedron *P, Lattice *L,
 359                                  unsigned nparam, int inflate,
 360                                  unsigned MaxRays)
 361 {
 362     Value sum;
 363     unsigned nvar = P->Dimension - nparam;
 364     Matrix *expansion;
 365     Matrix *C;
 366     int i;
 367     Polyhedron *P2;
 368
 369     expansion = Matrix_Alloc(nvar + nparam + 1,  nvar + nparam + 1);
 370     for (i = 0; i < nvar; ++i)
 371         Vector_Copy(L->p[i], expansion->p[i], nvar);
 372     for (i = nvar; i < nvar+nparam+1; ++i)
 373         value_assign(expansion->p[i][i], L->p[nvar][nvar]);
 374
 375     C = Matrix_Alloc(P->NbConstraints+1, 1+P->Dimension+1);
 376     value_init(sum);
 377     for (i = 0; i < P->NbConstraints; ++i) {
 378         negated_sum(P->Constraint[i]+1, nvar, inflate, &sum);
 379         value_assign(C->p[i][0], P->Constraint[i][0]);
 380         Vector_Matrix_Product(P->Constraint[i]+1, expansion, C->p[i]+1);
 381         if (value_zero_p(sum))
 382             continue;
 383         Vector_Copy(C->p[i]+1, C->p[i+1]+1, P->Dimension+1);
 384         value_addmul(C->p[i][1+P->Dimension], sum, L->p[nvar][nvar]);
 385         ConstraintSimplify(C->p[i], C->p[i], P->Dimension+2, &sum);
 386         ConstraintSimplify(C->p[i+1], C->p[i+1], P->Dimension+2, &sum);
 387         if (value_ne(C->p[i][1+P->Dimension], C->p[i+1][1+P->Dimension])) {
 388             if (inflate)
 389                 value_decrement(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension]);
 390             else
 391                 value_increment(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension]);
 392         }
 393     }
 394     value_clear(sum);
 395     C->NbRows--;
 396     P2 = Constraints2Polyhedron(C, MaxRays);
 397     Matrix_Free(C);
 398
 399     Matrix_Free(expansion);
 400
 401     if (inflate) {
 402         Polyhedron *C, *CA;
 403         C = Polyhedron_Project(P, nparam);
 404         CA = align_context(C, P->Dimension, MaxRays);
 405         P = P2;
 406         P2 = DomainIntersection(P, CA, MaxRays);
 407         Polyhedron_Free(C);
 408         Polyhedron_Free(CA);
 409         Polyhedron_Free(P);
 410     }
 411
 412     return P2;
 413 }
 414
 415 static void linear_min(Polyhedron *D, Value *obj, Value *min)
 416 {
 417     int i;
 418     Value tmp;
 419     value_init(tmp);
 420     POL_ENSURE_VERTICES(D);
 421     for (i = 0; i < D->NbRays; ++i) {
 422         Inner_Product(obj, D->Ray[i]+1, D->Dimension, &tmp);
 423         mpz_cdiv_q(tmp, tmp, D->Ray[i][1+D->Dimension]);
 424         if (!i || value_lt(tmp, *min))
 425             value_assign(*min, tmp);
 426     }
 427     value_clear(tmp);
 428 }
 429
 430 static Polyhedron *inflate_deflate_domain(Lattice *L, unsigned MaxRays)
 431 {
 432     unsigned nvar = L->NbRows-1;
 433     int i;
 434     Matrix *M;
 435     Polyhedron *D;
 436
 437     M = Matrix_Alloc(2*nvar, 1+nvar+1);
 438     for (i = 0; i < nvar; ++i) {
 439         value_set_si(M->p[2*i][0], 1);
 440         Vector_Copy(L->p[i], M->p[2*i]+1, nvar);
 441         Vector_Normalize(M->p[2*i]+1, nvar);
 442
 443         value_set_si(M->p[2*i+1][0], 1);
 444         Vector_Oppose(L->p[i], M->p[2*i+1]+1, nvar);
 445         value_assign(M->p[2*i+1][1+nvar], L->p[nvar][nvar]);
 446         Vector_Normalize(M->p[2*i+1]+1, nvar+1);
 447         value_decrement(M->p[2*i+1][1+nvar], M->p[2*i+1][1+nvar]);
 448     }
 449     D = Constraints2Polyhedron(M, MaxRays);
 450     Matrix_Free(M);
 451
 452     return D;
 453 }
 454
 455 static Polyhedron *flate_narrow(Polyhedron *P, Lattice *L,
 456                                 unsigned nparam, int inflate, unsigned MaxRays)
 457 {
 458     int i;
 459     unsigned nvar = P->Dimension - nparam;
 460     Vector *obj;
 461     Value min;
 462     Matrix *C;
 463     Polyhedron *D;
 464     Polyhedron *P2;
 465
 466     D = inflate_deflate_domain(L, MaxRays);
 467     value_init(min);
 468     obj = Vector_Alloc(nvar);
 469     C = Polyhedron2Constraints(P);
 470
 471     for (i = 0; i < C->NbRows; ++i) {
 472         if (inflate)
 473             Vector_Copy(C->p[i]+1, obj->p, nvar);
 474         else
 475             Vector_Oppose(C->p[i]+1, obj->p, nvar);
 476         linear_min(D, obj->p, &min);
 477         if (inflate)
 478             value_subtract(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], min);
 479         else
 480             value_addto(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], min);
 481     }
 482
 483     Polyhedron_Free(D);
 484     P2 = Constraints2Polyhedron(C, MaxRays);
 485     Matrix_Free(C);
 486     Vector_Free(obj);
 487     value_clear(min);
 488
 489     if (inflate) {
 490         Polyhedron *C, *CA;
 491         C = Polyhedron_Project(P, nparam);
 492         CA = align_context(C, P->Dimension, MaxRays);
 493         P = P2;
 494         P2 = DomainIntersection(P, CA, MaxRays);
 495         Polyhedron_Free(C);
 496         Polyhedron_Free(CA);
 497         Polyhedron_Free(P);
 498     }
 499
 500     return P2;
 501 }
 502
 503 static Polyhedron *flate(Polyhedron *P, Lattice *L,
 504                          unsigned nparam, int inflate,
 505                          struct barvinok_options *options)
 506 {
 507     if (options->approx->scale_flags & BV_APPROX_SCALE_NARROW2)
 508         return flate_narrow2(P, L, nparam, inflate, options->MaxRays);
 509     else if (options->approx->scale_flags & BV_APPROX_SCALE_NARROW)
 510         return flate_narrow(P, L, nparam, inflate, options->MaxRays);
 511     else
 512         return Polyhedron_Flate(P, nparam, inflate, options->MaxRays);
 513 }
 514
 515 static void Param_Polyhedron_Scale(Param_Polyhedron *PP, Lattice **L,
 516                                    Value *det, struct barvinok_options *options)
 517 {
 518     if (options->approx->scale_flags & BV_APPROX_SCALE_FAST)
 519         Param_Polyhedron_Scale_Integer_Fast(PP, L, det, options->MaxRays);
 520     else
 521         Param_Polyhedron_Scale_Integer_Slow(PP, L, det, options->MaxRays);
 522 }
 523
 524 static evalue *enumerate_flated(Polyhedron *P, Polyhedron *C, Lattice *L,
 525                                 struct barvinok_options *options)
 526 {
 527     unsigned nparam = C->Dimension;
 528     evalue *eres;
 529     int save_approximation = options->approx->approximation;
 530
 531     if (options->approx->approximation == BV_APPROX_SIGN_UPPER)
 532         P = flate(P, L, nparam, 1, options);
 533     if (options->approx->approximation == BV_APPROX_SIGN_LOWER)
 534         P = flate(P, L, nparam, 0, options);
 535
 536     /* Don't deflate/inflate again (on this polytope) */
 537     options->approx->approximation = BV_APPROX_SIGN_NONE;
 538     eres = barvinok_enumerate_with_options(P, C, options);
 539     options->approx->approximation = save_approximation;
 540     Polyhedron_Free(P);
 541
 542     return eres;
 543 }
 544
 545 static evalue *PP_enumerate_narrow_flated(Param_Polyhedron *PP,
 546                                           Polyhedron *P, Polyhedron *C,
 547                                           struct barvinok_options *options)
 548 {
 549     Polyhedron *Porig = P;
 550     int scale_narrow2 = options->approx->scale_flags & BV_APPROX_SCALE_NARROW2;
 551     Lattice *L = NULL;
 552     Value det;
 553     evalue *eres;
 554
 555     value_init(det);
 556     value_set_si(det, 1);
 557
 558     Param_Polyhedron_Scale(PP, &L, &det, options);
 559     if (!scale_narrow2)
 560         P = Param_Polyhedron2Polyhedron(PP, options);
 561     Param_Polyhedron_Free(PP);
 562     /* Don't scale again (on this polytope) */
 563     options->approx->method = BV_APPROX_NONE;
 564     eres = enumerate_flated(P, C, L, options);
 565     options->approx->method = BV_APPROX_SCALE;
 566     Matrix_Free(L);
 567     if (P != Porig)
 568         Polyhedron_Free(P);
 569     if (value_notone_p(det))
 570         evalue_div(eres, det);
 571     value_clear(det);
 572     return eres;
 573 }
 574
 575 #define INT_BITS (sizeof(unsigned) * 8)
 576
 577 static Param_Polyhedron *Param_Polyhedron_Domain(Param_Polyhedron *PP,
 578                                                  Param_Domain *D,
 579                                                  Polyhedron *rVD)
 580 {
 581     int nv;
 582     Param_Polyhedron *PP_D;
 583     int i, ix;
 584     unsigned bx;
 585     Param_Vertices **next, *V;
 586     int facet_len = (PP->Constraints->NbRows+INT_BITS-1)/INT_BITS;
 587
 588     PP_D = ALLOC(Param_Polyhedron);
 589     PP_D->D = ALLOC(Param_Domain);
 590     PP_D->D->next = NULL;
 591     PP_D->D->Domain = Domain_Copy(rVD);
 592     PP_D->V = NULL;
 593     PP_D->Constraints = Matrix_Copy(PP->Constraints);
 594     PP_D->Rays = NULL;
 595
 596     nv = (PP->nbV - 1)/(8*sizeof(int)) + 1;
 597     PP_D->D->F = ALLOCN(unsigned, nv);
 598     memset(PP_D->D->F, 0, nv * sizeof(unsigned));
 599
 600     next = &PP_D->V;
 601     i = 0;
 602     ix = 0;
 603     bx = MSB;
 604     FORALL_PVertex_in_ParamPolyhedron(V, D, PP)
 605         Param_Vertices *V2 = ALLOC(Param_Vertices);
 606         V2->Vertex = Matrix_Copy(V->Vertex);
 607         V2->Domain = NULL;
 608         V2->next = NULL;
 609         V2->Facets = NULL;
 610         if (V->Facets) {
 611             V2->Facets = ALLOCN(unsigned, facet_len);
 612             memcpy(V2->Facets, V->Facets, facet_len * sizeof(unsigned));
 613         }
 614         *next = V2;
 615         next = &V2->next;
 616         PP_D->D->F[ix] |= bx;
 617         NEXT(ix, bx);
 618         ++i;
 619     END_FORALL_PVertex_in_ParamPolyhedron;
 620     PP_D->nbV = i;
 621
 622     return PP_D;
 623 }
 624
 625 static evalue *enumerate_narrow_flated(Polyhedron *P, Polyhedron *C,
 626                                         struct barvinok_options *options)
 627 {
 628     unsigned Rat_MaxRays = options->MaxRays;
 629     Param_Polyhedron *PP;
 630     PP = Polyhedron2Param_Polyhedron(P, C, options);
 631     POL_UNSET(Rat_MaxRays, POL_INTEGER);
 632
 633     if ((options->approx->scale_flags & BV_APPROX_SCALE_CHAMBER) && PP->D->next) {
 634         int nd = -1;
 635         evalue *tmp, *eres = NULL;
 636         Polyhedron *TC = true_context(P, C, options->MaxRays);
 637
 638         FORALL_REDUCED_DOMAIN(PP, TC, nd, options, i, D, rVD)
 639             Polyhedron *P2, *CA;
 640             Param_Polyhedron *PP_D;
 641             /* Intersect with D->Domain, so we only have the relevant constraints
 642              * left.  Don't use rVD, though, since we still want to recognize
 643              * the defining constraints of the parametric vertices.
 644              */
 645             CA = align_context(D->Domain, P->Dimension, options->MaxRays);
 646             P2 = DomainIntersection(P, CA, Rat_MaxRays);
 647             POL_ENSURE_VERTICES(P2);
 648             Polyhedron_Free(CA);
 649             /* Use rVD for context, to avoid overlapping domains in
 650              * results of computations in different chambers.
 651              */
 652             PP_D = Param_Polyhedron_Domain(PP, D, rVD);
 653             tmp = PP_enumerate_narrow_flated(PP_D, P2, rVD, options);
 654             Polyhedron_Free(P2);
 655             if (!eres)
 656                 eres = tmp;
 657             else {
 658                 eadd(tmp, eres);
 659                 free_evalue_refs(tmp);
 660                 free(tmp);
 661             }
 662             Polyhedron_Free(rVD);
 663         END_FORALL_REDUCED_DOMAIN
 664         Param_Polyhedron_Free(PP);
 665         if (!eres)
 666             eres = evalue_zero();
 667         Polyhedron_Free(TC);
 668         return eres;
 669     } else
 670         return PP_enumerate_narrow_flated(PP, P, C, options);
 671 }
 672
 673 /* If scaling is to be performed in combination with deflation/inflation,
 674  * do both and return the result.
 675  * Otherwise return NULL.
 676  */
 677 evalue *scale_bound(Polyhedron *P, Polyhedron *C,
 678                     struct barvinok_options *options)
 679 {
 680     int scale_narrow = options->approx->scale_flags & BV_APPROX_SCALE_NARROW;
 681     int scale_narrow2 = options->approx->scale_flags & BV_APPROX_SCALE_NARROW2;
 682
 683     if (options->approx->approximation == BV_APPROX_SIGN_NONE ||
 684         options->approx->approximation == BV_APPROX_SIGN_APPROX)
 685         return NULL;
 686
 687     if (scale_narrow || scale_narrow2)
 688         return enumerate_narrow_flated(P, C, options);
 689     else
 690         return enumerate_flated(P, C, NULL, options);
 691 }
 692
 693 evalue *scale(Param_Polyhedron *PP, Polyhedron *P, Polyhedron *C,
 694               struct barvinok_options *options)
 695 {
 696     Polyhedron *T;
 697     unsigned MaxRays;
 698     evalue *eres = NULL;
 699     Value det;
 700
 701     if ((options->approx->scale_flags & BV_APPROX_SCALE_CHAMBER) && PP->D->next) {
 702         int nd = -1;
 703         evalue *tmp;
 704         Polyhedron *TC = true_context(P, C, options->MaxRays);
 705
 706         FORALL_REDUCED_DOMAIN(PP, TC, nd, options, i, D, rVD)
 707             Param_Polyhedron *PP_D = Param_Polyhedron_Domain(PP, D, rVD);
 708             tmp = scale(PP_D, P, rVD, options);
 709             if (!eres)
 710                 eres = tmp;
 711             else {
 712                 eadd(tmp, eres);
 713                 free_evalue_refs(tmp);
 714                 free(tmp);
 715             }
 716             Param_Polyhedron_Free(PP_D);
 717             Polyhedron_Free(rVD);
 718         END_FORALL_REDUCED_DOMAIN
 719         if (!eres)
 720             eres = evalue_zero();
 721         Polyhedron_Free(TC);
 722         return eres;
 723     }
 724
 725     value_init(det);
 726     value_set_si(det, 1);
 727
 728     MaxRays = options->MaxRays;
 729     POL_UNSET(options->MaxRays, POL_INTEGER);
 730     Param_Polyhedron_Scale(PP, NULL, &det, options);
 731     options->MaxRays = MaxRays;
 732
 733     T = Param_Polyhedron2Polyhedron(PP, options);
 734     eres = Param_Polyhedron_Enumerate(PP, T, C, options);
 735     Polyhedron_Free(T);
 736
 737     if (value_notone_p(det))
 738         evalue_div(eres, det);
 739     value_clear(det);
 740
 741     return eres;
 742 }