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, Polyhedron **P,
 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     if (P)
 127         *P = Polyhedron_Preimage(*P, expansion, MaxRays);
 128 }
 129
 130 /* Scales the parametric polyhedron with constraints *P and vertices PP
 131  * such that the number of integer points can be represented by a polynomial.
 132  * Both *P and P->Vertex are adapted according to the scaling.
 133  * The scaling factor is returned in *det.
 134  * The transformation that maps the new coordinates to the original
 135  * coordinates is returned in *Lat (if Lat != NULL).
 136  * The enumerator of the scaled parametric polyhedron should be divided
 137  * by this number to obtain an approximation of the enumerator of the
 138  * original parametric polyhedron.
 139  *
 140  * The algorithm is described in "Approximating Ehrhart Polynomials using
 141  * affine transformations" by B. Meister.
 142  */
 143 void Param_Polyhedron_Scale_Integer_Slow(Param_Polyhedron *PP, Polyhedron **P,
 144                                          Lattice **Lat,
 145                                          Value *det, unsigned MaxRays)
 146 {
 147     Param_Vertices *V;
 148     unsigned dim = (*P)->Dimension;
 149     unsigned nparam;
 150     unsigned nvar;
 151     Lattice *L = NULL, *Li;
 152     Matrix *T;
 153     Matrix *expansion;
 154     int i;
 155     int ok;
 156
 157     if (!PP->nbV)
 158         return;
 159
 160     nparam = PP->V->Vertex->NbColumns - 2;
 161     nvar = dim - nparam;
 162
 163     for (V = PP->V; V; V = V->next) {
 164         Lattice *L2;
 165         Matrix *M;
 166         int i, j, n;
 167         unsigned *supporting;
 168         int ix;
 169         unsigned bx;
 170
 171         supporting = supporting_constraints(PP->Constraints, V, &n);
 172         M = Matrix_Alloc(n, PP->Constraints->NbColumns-2);
 173         for (i = 0, j = 0, ix = 0, bx = MSB; i < PP->Constraints->NbRows; ++i) {
 174             if (supporting[ix] & bx)
 175                 Vector_Copy(PP->Constraints->p[i]+1, M->p[j++],
 176                             PP->Constraints->NbColumns-2);
 177             NEXT(ix, bx);
 178         }
 179         free(supporting);
 180         L2 = extract_lattice(M, nvar);
 181         Matrix_Free(M);
 182
 183         if (!L)
 184             L = L2;
 185         else {
 186             Lattice *L3 = LatticeJoin(L, L2);
 187             Matrix_Free(L);
 188             Matrix_Free(L2);
 189             L = L3;
 190         }
 191     }
 192
 193     if (Lat)
 194         *Lat = Matrix_Copy(L);
 195
 196     /* apply the variable expansion to the polyhedron (constraints) */
 197     expansion = Matrix_Alloc(nvar + nparam + 1,  nvar + nparam + 1);
 198     for (i = 0; i < nvar; ++i)
 199         Vector_Copy(L->p[i], expansion->p[i], nvar);
 200     for (i = nvar; i < nvar+nparam+1; ++i)
 201         value_assign(expansion->p[i][i], L->p[nvar][nvar]);
 202
 203     apply_expansion(PP, P, expansion, MaxRays);
 204     Matrix_Free(expansion);
 205
 206     /* apply the variable expansion to the parametric vertices */
 207     Li = Matrix_Alloc(nvar+1, nvar+1);
 208     ok = Matrix_Inverse(L, Li);
 209     assert(ok);
 210     Matrix_Free(L);
 211     assert(value_one_p(Li->p[nvar][nvar]));
 212     T = Matrix_Alloc(nvar, nvar);
 213     value_set_si(*det, 1);
 214     for (i = 0; i < nvar; ++i) {
 215         value_multiply(*det, *det, Li->p[i][i]);
 216         Vector_Copy(Li->p[i], T->p[i], nvar);
 217     }
 218     Matrix_Free(Li);
 219     for (V = PP->V; V; V = V->next)
 220         Param_Vertex_Image(V, T);
 221     Matrix_Free(T);
 222 }
 223
 224 /* Scales the parametric polyhedron with constraints *P and vertices PP
 225  * such that the number of integer points can be represented by a polynomial.
 226  * Both *P and P->Vertex are adapted according to the scaling.
 227  * The scaling factor is returned in *det.
 228  * The transformation that maps the new coordinates to the original
 229  * coordinates is returned in *Lat (if Lat != NULL).
 230  * The enumerator of the scaled parametric polyhedron should be divided
 231  * by this number to obtain an approximation of the enumerator of the
 232  * original parametric polyhedron.
 233  *
 234  * The algorithm is described in "Approximating Ehrhart Polynomials using
 235  * affine transformations" by B. Meister.
 236  */
 237 void Param_Polyhedron_Scale_Integer_Fast(Param_Polyhedron *PP, Polyhedron **P,
 238                                          Lattice **Lat,
 239                                          Value *det, unsigned MaxRays)
 240 {
 241   int i;
 242   int nb_param, nb_vars;
 243   Vector *denoms;
 244   Param_Vertices *V;
 245   Value global_var_lcm;
 246   Value tmp;
 247   Matrix *expansion;
 248
 249   value_set_si(*det, 1);
 250   if (!PP->nbV)
 251     return;
 252
 253   nb_param = PP->D->Domain->Dimension;
 254   nb_vars = PP->V->Vertex->NbRows;
 255
 256   /* Scan the vertices and make an orthogonal expansion of the variable
 257      space */
 258   /* a- prepare the array of common denominators */
 259   denoms = Vector_Alloc(nb_vars);
 260   value_init(global_var_lcm);
 261
 262   value_init(tmp);
 263   /* b- scan the vertices and compute the variables' global lcms */
 264   for (V = PP->V; V; V = V->next) {
 265     for (i = 0; i < nb_vars; i++) {
 266       Vector_Gcd(V->Vertex->p[i], nb_param, &tmp);
 267       value_gcd(tmp, tmp, V->Vertex->p[i][nb_param+1]);
 268       value_division(tmp, V->Vertex->p[i][nb_param+1], tmp);
 269       Lcm3(denoms->p[i], tmp, &denoms->p[i]);
 270     }
 271   }
 272   value_clear(tmp);
 273
 274   value_set_si(global_var_lcm, 1);
 275   for (i = 0; i < nb_vars; i++) {
 276     value_multiply(*det, *det, denoms->p[i]);
 277     Lcm3(global_var_lcm, denoms->p[i], &global_var_lcm);
 278   }
 279
 280   /* scale vertices */
 281   for (V = PP->V; V; V = V->next)
 282     for (i = 0; i < nb_vars; i++) {
 283       Vector_Scale(V->Vertex->p[i], V->Vertex->p[i], denoms->p[i], nb_param+1);
 284       Vector_Normalize(V->Vertex->p[i], nb_param+2);
 285     }
 286
 287   /* the expansion can be actually writen as global_var_lcm.L^{-1} */
 288   /* this is equivalent to multiply the rows of P by denoms_det */
 289   for (i = 0; i < nb_vars; i++)
 290     value_division(denoms->p[i], global_var_lcm, denoms->p[i]);
 291
 292   /* OPT : we could use a vector instead of a diagonal matrix here (c- and d-).*/
 293   /* c- make the quick expansion matrix */
 294   expansion = Matrix_Alloc(nb_vars+nb_param+1, nb_vars+nb_param+1);
 295   for (i = 0; i < nb_vars; i++)
 296     value_assign(expansion->p[i][i], denoms->p[i]);
 297   for (i = nb_vars; i < nb_vars+nb_param+1; i++)
 298     value_assign(expansion->p[i][i], global_var_lcm);
 299
 300   /* d- apply the variable expansion to the polyhedron */
 301   apply_expansion(PP, P, expansion, MaxRays);
 302
 303   if (Lat) {
 304     Lattice *L = Matrix_Alloc(nb_vars+1, nb_vars+1);
 305     for (i = 0; i < nb_vars; ++i)
 306         value_assign(L->p[i][i], denoms->p[i]);
 307     value_assign(L->p[nb_vars][nb_vars], global_var_lcm);
 308     *Lat = L;
 309   }
 310
 311   Matrix_Free(expansion);
 312   value_clear(global_var_lcm);
 313   Vector_Free(denoms);
 314 }
 315
 316 /* Compute negated sum of all positive or negative coefficients in a row */
 317 static void negated_sum(Value *v, int len, int negative, Value *sum)
 318 {
 319     int j;
 320
 321     value_set_si(*sum, 0);
 322     for (j = 0; j < len; ++j)
 323         if (negative ? value_neg_p(v[j]) : value_pos_p(v[j]))
 324             value_subtract(*sum, *sum, v[j]);
 325 }
 326
 327 /* adapted from mpolyhedron_inflate in PolyLib */
 328 Polyhedron *Polyhedron_Flate(Polyhedron *P, unsigned nparam, int inflate,
 329                              unsigned MaxRays)
 330 {
 331     Value sum;
 332     int nvar = P->Dimension - nparam;
 333     Matrix *C = Polyhedron2Constraints(P);
 334     Polyhedron *P2;
 335     int i;
 336
 337     value_init(sum);
 338     /* subtract the sum of the negative coefficients of each inequality */
 339     for (i = 0; i < C->NbRows; ++i) {
 340         negated_sum(C->p[i]+1, nvar, inflate, &sum);
 341         value_addto(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], sum);
 342     }
 343     value_clear(sum);
 344     P2 = Constraints2Polyhedron(C, MaxRays);
 345     Matrix_Free(C);
 346
 347     if (inflate) {
 348         Polyhedron *C, *CA;
 349         C = Polyhedron_Project(P, nparam);
 350         CA = align_context(C, P->Dimension, MaxRays);
 351         P = P2;
 352         P2 = DomainIntersection(P, CA, MaxRays);
 353         Polyhedron_Free(C);
 354         Polyhedron_Free(CA);
 355         Polyhedron_Free(P);
 356     }
 357
 358     return P2;
 359 }
 360
 361 static Polyhedron *flate_narrow2(Polyhedron *P, Lattice *L,
 362                                  unsigned nparam, int inflate,
 363                                  unsigned MaxRays)
 364 {
 365     Value sum;
 366     unsigned nvar = P->Dimension - nparam;
 367     Matrix *expansion;
 368     Matrix *C;
 369     int i, j;
 370     Polyhedron *P2;
 371
 372     expansion = Matrix_Alloc(nvar + nparam + 1,  nvar + nparam + 1);
 373     for (i = 0; i < nvar; ++i)
 374         Vector_Copy(L->p[i], expansion->p[i], nvar);
 375     for (i = nvar; i < nvar+nparam+1; ++i)
 376         value_assign(expansion->p[i][i], L->p[nvar][nvar]);
 377
 378     C = Matrix_Alloc(P->NbConstraints+1, 1+P->Dimension+1);
 379     value_init(sum);
 380     for (i = 0; i < P->NbConstraints; ++i) {
 381         negated_sum(P->Constraint[i]+1, nvar, inflate, &sum);
 382         value_assign(C->p[i][0], P->Constraint[i][0]);
 383         Vector_Matrix_Product(P->Constraint[i]+1, expansion, C->p[i]+1);
 384         if (value_zero_p(sum))
 385             continue;
 386         Vector_Copy(C->p[i]+1, C->p[i+1]+1, P->Dimension+1);
 387         value_addmul(C->p[i][1+P->Dimension], sum, L->p[nvar][nvar]);
 388         ConstraintSimplify(C->p[i], C->p[i], P->Dimension+2, &sum);
 389         ConstraintSimplify(C->p[i+1], C->p[i+1], P->Dimension+2, &sum);
 390         if (value_ne(C->p[i][1+P->Dimension], C->p[i+1][1+P->Dimension])) {
 391             if (inflate)
 392                 value_decrement(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension]);
 393             else
 394                 value_increment(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension]);
 395         }
 396     }
 397     value_clear(sum);
 398     C->NbRows--;
 399     P2 = Constraints2Polyhedron(C, MaxRays);
 400     Matrix_Free(C);
 401
 402     Matrix_Free(expansion);
 403
 404     if (inflate) {
 405         Polyhedron *C, *CA;
 406         C = Polyhedron_Project(P, nparam);
 407         CA = align_context(C, P->Dimension, MaxRays);
 408         P = P2;
 409         P2 = DomainIntersection(P, CA, MaxRays);
 410         Polyhedron_Free(C);
 411         Polyhedron_Free(CA);
 412         Polyhedron_Free(P);
 413     }
 414
 415     return P2;
 416 }
 417
 418 static void linear_min(Polyhedron *D, Value *obj, Value *min)
 419 {
 420     int i;
 421     Value tmp;
 422     value_init(tmp);
 423     POL_ENSURE_VERTICES(D);
 424     for (i = 0; i < D->NbRays; ++i) {
 425         Inner_Product(obj, D->Ray[i]+1, D->Dimension, &tmp);
 426         mpz_cdiv_q(tmp, tmp, D->Ray[i][1+D->Dimension]);
 427         if (!i || value_lt(tmp, *min))
 428             value_assign(*min, tmp);
 429     }
 430     value_clear(tmp);
 431 }
 432
 433 static Polyhedron *inflate_deflate_domain(Lattice *L, unsigned MaxRays)
 434 {
 435     unsigned nvar = L->NbRows-1;
 436     int i;
 437     Matrix *M;
 438     Polyhedron *D;
 439
 440     M = Matrix_Alloc(2*nvar, 1+nvar+1);
 441     for (i = 0; i < nvar; ++i) {
 442         value_set_si(M->p[2*i][0], 1);
 443         Vector_Copy(L->p[i], M->p[2*i]+1, nvar);
 444         Vector_Normalize(M->p[2*i]+1, nvar);
 445
 446         value_set_si(M->p[2*i+1][0], 1);
 447         Vector_Oppose(L->p[i], M->p[2*i+1]+1, nvar);
 448         value_assign(M->p[2*i+1][1+nvar], L->p[nvar][nvar]);
 449         Vector_Normalize(M->p[2*i+1]+1, nvar+1);
 450         value_decrement(M->p[2*i+1][1+nvar], M->p[2*i+1][1+nvar]);
 451     }
 452     D = Constraints2Polyhedron(M, MaxRays);
 453     Matrix_Free(M);
 454
 455     return D;
 456 }
 457
 458 static Polyhedron *flate_narrow(Polyhedron *P, Lattice *L,
 459                                 unsigned nparam, int inflate, unsigned MaxRays)
 460 {
 461     int i;
 462     unsigned nvar = P->Dimension - nparam;
 463     Vector *obj;
 464     Value min;
 465     Matrix *C;
 466     Polyhedron *D;
 467     Polyhedron *P2;
 468
 469     D = inflate_deflate_domain(L, MaxRays);
 470     value_init(min);
 471     obj = Vector_Alloc(nvar);
 472     C = Polyhedron2Constraints(P);
 473
 474     for (i = 0; i < C->NbRows; ++i) {
 475         if (inflate)
 476             Vector_Copy(C->p[i]+1, obj->p, nvar);
 477         else
 478             Vector_Oppose(C->p[i]+1, obj->p, nvar);
 479         linear_min(D, obj->p, &min);
 480         if (inflate)
 481             value_subtract(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], min);
 482         else
 483             value_addto(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], min);
 484     }
 485
 486     Polyhedron_Free(D);
 487     P2 = Constraints2Polyhedron(C, MaxRays);
 488     Matrix_Free(C);
 489     Vector_Free(obj);
 490     value_clear(min);
 491
 492     if (inflate) {
 493         Polyhedron *C, *CA;
 494         C = Polyhedron_Project(P, nparam);
 495         CA = align_context(C, P->Dimension, MaxRays);
 496         P = P2;
 497         P2 = DomainIntersection(P, CA, MaxRays);
 498         Polyhedron_Free(C);
 499         Polyhedron_Free(CA);
 500         Polyhedron_Free(P);
 501     }
 502
 503     return P2;
 504 }
 505
 506 static Polyhedron *flate(Polyhedron *P, Lattice *L,
 507                          unsigned nparam, int inflate,
 508                          struct barvinok_options *options)
 509 {
 510     if (options->scale_flags & BV_APPROX_SCALE_NARROW2)
 511         return flate_narrow2(P, L, nparam, inflate, options->MaxRays);
 512     else if (options->scale_flags & BV_APPROX_SCALE_NARROW)
 513         return flate_narrow(P, L, nparam, inflate, options->MaxRays);
 514     else
 515         return Polyhedron_Flate(P, nparam, inflate, options->MaxRays);
 516 }
 517
 518 static void Param_Polyhedron_Scale(Param_Polyhedron *PP, Polyhedron **P,
 519                                    Lattice **L,
 520                                    Value *det, struct barvinok_options *options)
 521 {
 522     if (options->scale_flags & BV_APPROX_SCALE_FAST)
 523         Param_Polyhedron_Scale_Integer_Fast(PP, P, L, det, options->MaxRays);
 524     else
 525         Param_Polyhedron_Scale_Integer_Slow(PP, P, L, det, options->MaxRays);
 526 }
 527
 528 static evalue *enumerate_flated(Polyhedron *P, Polyhedron *C, Lattice *L,
 529                                 struct barvinok_options *options)
 530 {
 531     unsigned nparam = C->Dimension;
 532     evalue *eres;
 533     int save_approximation = options->polynomial_approximation;
 534
 535     if (options->polynomial_approximation == BV_APPROX_SIGN_UPPER)
 536         P = flate(P, L, nparam, 1, options);
 537     if (options->polynomial_approximation == BV_APPROX_SIGN_LOWER)
 538         P = flate(P, L, nparam, 0, options);
 539
 540     /* Don't deflate/inflate again (on this polytope) */
 541     options->polynomial_approximation = BV_APPROX_SIGN_NONE;
 542     eres = barvinok_enumerate_with_options(P, C, options);
 543     options->polynomial_approximation = save_approximation;
 544     Polyhedron_Free(P);
 545
 546     return eres;
 547 }
 548
 549 static evalue *PP_enumerate_narrow_flated(Param_Polyhedron *PP,
 550                                           Polyhedron *P, Polyhedron *C,
 551                                           struct barvinok_options *options)
 552 {
 553     Polyhedron *Porig = P;
 554     int scale_narrow2 = options->scale_flags & BV_APPROX_SCALE_NARROW2;
 555     Lattice *L = NULL;
 556     Value det;
 557     evalue *eres;
 558
 559     value_init(det);
 560     value_set_si(det, 1);
 561
 562     Param_Polyhedron_Scale(PP, &P, &L, &det, options);
 563     Param_Polyhedron_Free(PP);
 564     if (scale_narrow2) {
 565         Polyhedron_Free(P);
 566         P = Porig;
 567     }
 568     /* Don't scale again (on this polytope) */
 569     options->approximation_method = BV_APPROX_NONE;
 570     eres = enumerate_flated(P, C, L, options);
 571     options->approximation_method = BV_APPROX_SCALE;
 572     Matrix_Free(L);
 573     if (P != Porig)
 574         Polyhedron_Free(P);
 575     if (value_notone_p(det))
 576         evalue_div(eres, det);
 577     value_clear(det);
 578     return eres;
 579 }
 580
 581 #define INT_BITS (sizeof(unsigned) * 8)
 582
 583 static Param_Polyhedron *Param_Polyhedron_Domain(Param_Polyhedron *PP,
 584                                                  Param_Domain *D,
 585                                                  Polyhedron *rVD)
 586 {
 587     int nv;
 588     Param_Polyhedron *PP_D;
 589     int i, ix;
 590     unsigned bx;
 591     Param_Vertices **next, *V;
 592     int facet_len = (PP->Constraints->NbRows+INT_BITS-1)/INT_BITS;
 593
 594     PP_D = ALLOC(Param_Polyhedron);
 595     PP_D->D = ALLOC(Param_Domain);
 596     PP_D->D->next = NULL;
 597     PP_D->D->Domain = Domain_Copy(rVD);
 598     PP_D->V = NULL;
 599     PP_D->Constraints = Matrix_Copy(PP->Constraints);
 600     PP_D->Rays = NULL;
 601
 602     nv = (PP->nbV - 1)/(8*sizeof(int)) + 1;
 603     PP_D->D->F = ALLOCN(unsigned, nv);
 604     memset(PP_D->D->F, 0, nv * sizeof(unsigned));
 605
 606     next = &PP_D->V;
 607     i = 0;
 608     ix = 0;
 609     bx = MSB;
 610     FORALL_PVertex_in_ParamPolyhedron(V, D, PP)
 611         Param_Vertices *V2 = ALLOC(Param_Vertices);
 612         V2->Vertex = Matrix_Copy(V->Vertex);
 613         V2->Domain = NULL;
 614         V2->next = NULL;
 615         V2->Facets = ALLOCN(unsigned, facet_len);
 616         memcpy(V2->Facets, V->Facets, facet_len * sizeof(unsigned));
 617         *next = V2;
 618         next = &V2->next;
 619         PP_D->D->F[ix] |= bx;
 620         NEXT(ix, bx);
 621         ++i;
 622     END_FORALL_PVertex_in_ParamPolyhedron;
 623     PP_D->nbV = i;
 624
 625     return PP_D;
 626 }
 627
 628 static evalue *enumerate_narrow_flated(Polyhedron *P, Polyhedron *C,
 629                                         struct barvinok_options *options)
 630 {
 631     unsigned Rat_MaxRays = options->MaxRays;
 632     Param_Polyhedron *PP;
 633     PP = Polyhedron2Param_Polyhedron(P, C, options);
 634     POL_UNSET(Rat_MaxRays, POL_INTEGER);
 635
 636     if ((options->scale_flags & BV_APPROX_SCALE_CHAMBER) && PP->D->next) {
 637         int nd = -1;
 638         evalue *tmp, *eres = NULL;
 639         Polyhedron *TC = true_context(P, C, options->MaxRays);
 640
 641         FORALL_REDUCED_DOMAIN(PP, TC, nd, options, i, D, rVD)
 642             Polyhedron *P2, *CA;
 643             Param_Polyhedron *PP_D;
 644             /* Intersect with D->Domain, so we only have the relevant constraints
 645              * left.  Don't use rVD, though, since we still want to recognize
 646              * the defining constraints of the parametric vertices.
 647              */
 648             CA = align_context(D->Domain, P->Dimension, options->MaxRays);
 649             P2 = DomainIntersection(P, CA, Rat_MaxRays);
 650             POL_ENSURE_VERTICES(P2);
 651             Polyhedron_Free(CA);
 652             /* Use rVD for context, to avoid overlapping domains in
 653              * results of computations in different chambers.
 654              */
 655             PP_D = Param_Polyhedron_Domain(PP, D, rVD);
 656             tmp = PP_enumerate_narrow_flated(PP_D, P2, rVD, options);
 657             Polyhedron_Free(P2);
 658             if (!eres)
 659                 eres = tmp;
 660             else {
 661                 eadd(tmp, eres);
 662                 free_evalue_refs(tmp);
 663                 free(tmp);
 664             }
 665             Polyhedron_Free(rVD);
 666         END_FORALL_REDUCED_DOMAIN
 667         Param_Polyhedron_Free(PP);
 668         if (!eres)
 669             eres = evalue_zero();
 670         Polyhedron_Free(TC);
 671         return eres;
 672     } else
 673         return PP_enumerate_narrow_flated(PP, P, C, options);
 674 }
 675
 676 /* If scaling is to be performed in combination with deflation/inflation,
 677  * do both and return the result.
 678  * Otherwise return NULL.
 679  */
 680 evalue *scale_bound(Polyhedron *P, Polyhedron *C,
 681                     struct barvinok_options *options)
 682 {
 683     int scale_narrow = options->scale_flags & BV_APPROX_SCALE_NARROW;
 684     int scale_narrow2 = options->scale_flags & BV_APPROX_SCALE_NARROW2;
 685
 686     if (options->polynomial_approximation == BV_APPROX_SIGN_NONE ||
 687         options->polynomial_approximation == BV_APPROX_SIGN_APPROX)
 688         return NULL;
 689
 690     if (scale_narrow || scale_narrow2)
 691         return enumerate_narrow_flated(P, C, options);
 692     else
 693         return enumerate_flated(P, C, NULL, options);
 694 }
 695
 696 evalue *scale(Param_Polyhedron *PP, Polyhedron *P, Polyhedron *C,
 697               struct barvinok_options *options)
 698 {
 699     Polyhedron *T = P;
 700     unsigned MaxRays;
 701     evalue *eres = NULL;
 702     Value det;
 703
 704     if ((options->scale_flags & BV_APPROX_SCALE_CHAMBER) && PP->D->next) {
 705         int nd = -1;
 706         evalue *tmp;
 707         Polyhedron *TC = true_context(P, C, options->MaxRays);
 708
 709         FORALL_REDUCED_DOMAIN(PP, TC, nd, options, i, D, rVD)
 710             Param_Polyhedron *PP_D = Param_Polyhedron_Domain(PP, D, rVD);
 711             tmp = scale(PP_D, P, rVD, options);
 712             if (!eres)
 713                 eres = tmp;
 714             else {
 715                 eadd(tmp, eres);
 716                 free_evalue_refs(tmp);
 717                 free(tmp);
 718             }
 719             Param_Polyhedron_Free(PP_D);
 720             Polyhedron_Free(rVD);
 721         END_FORALL_REDUCED_DOMAIN
 722         if (!eres)
 723             eres = evalue_zero();
 724         Polyhedron_Free(TC);
 725         return eres;
 726     }
 727
 728     value_init(det);
 729     value_set_si(det, 1);
 730
 731     MaxRays = options->MaxRays;
 732     POL_UNSET(options->MaxRays, POL_INTEGER);
 733     Param_Polyhedron_Scale(PP, &T, NULL, &det, options);
 734     options->MaxRays = MaxRays;
 735
 736     eres = Param_Polyhedron_Enumerate(PP, T, C, options);
 737     if (P != T)
 738         Polyhedron_Free(T);
 739
 740     if (value_notone_p(det))
 741         evalue_div(eres, det);
 742     value_clear(det);
 743
 744     return eres;
 745 }