bernstein.cc

   1 #include <vector>
   2 #include <bernstein/bernstein.h>
   3 #include <bernstein/piecewise_lst.h>
   4 #include <barvinok/barvinok.h>
   5 #include <barvinok/util.h>
   6 #include <barvinok/bernstein.h>
   7 #include <barvinok/options.h>
   8
   9 using namespace GiNaC;
  10 using namespace bernstein;
  11
  12 using std::pair;
  13 using std::vector;
  14 using std::cerr;
  15 using std::endl;
  16
  17 namespace barvinok {
  18
  19 ex evalue2ex(evalue *e, const exvector& vars)
  20 {
  21     if (value_notzero_p(e->d))
  22         return value2numeric(e->x.n)/value2numeric(e->d);
  23     if (e->x.p->type != polynomial)
  24         return fail();
  25     ex poly = 0;
  26     for (int i = e->x.p->size-1; i >= 0; --i) {
  27         poly *= vars[e->x.p->pos-1];
  28         ex t = evalue2ex(&e->x.p->arr[i], vars);
  29         if (is_exactly_a<fail>(t))
  30             return t;
  31         poly += t;
  32     }
  33     return poly;
  34 }
  35
  36 static int type_offset(enode *p)
  37 {
  38    return p->type == fractional ? 1 :
  39           p->type == flooring ? 1 : 0;
  40 }
  41
  42 typedef pair<bool, const evalue *> typed_evalue;
  43
  44 static ex evalue2ex_add_var(evalue *e, exvector& extravar,
  45                             vector<typed_evalue>& expr, bool is_fract)
  46 {
  47     ex base_var = 0;
  48
  49     for (int i = 0; i < expr.size(); ++i) {
  50         if (is_fract == expr[i].first && eequal(e, expr[i].second)) {
  51             base_var = extravar[i];
  52             break;
  53         }
  54     }
  55     if (base_var != 0)
  56         return base_var;
  57
  58     char name[20];
  59     snprintf(name, sizeof(name), "f%c%d", is_fract ? 'r' : 'l', expr.size());
  60     extravar.push_back(base_var = symbol(name));
  61     expr.push_back(typed_evalue(is_fract, e));
  62
  63     return base_var;
  64 }
  65
  66 /* For the argument e=(f/d) of a fractional, return (d-1)/d times
  67  * a variable in [0,1] (see setup_constraints).
  68  */
  69 static ex evalue2ex_get_fract(evalue *e, exvector& extravar,
  70                                 vector<typed_evalue>& expr)
  71 {
  72     ex f;
  73     Value d;
  74     ex den;
  75     value_init(d);
  76     value_set_si(d, 1);
  77     evalue_denom(e, &d);
  78     den = value2numeric(d);
  79     value_clear(d);
  80     f = (den-1)/den;
  81
  82     ex base_var = evalue2ex_add_var(e, extravar, expr, true);
  83     base_var *= f;
  84     return base_var;
  85 }
  86
  87 static ex evalue2ex_r(const evalue *e, const exvector& vars,
  88                       exvector& extravar, vector<typed_evalue>& expr,
  89                       Vector *coset)
  90 {
  91     if (value_notzero_p(e->d))
  92         return value2numeric(e->x.n)/value2numeric(e->d);
  93     ex base_var = 0;
  94     ex poly = 0;
  95
  96     switch (e->x.p->type) {
  97     case polynomial:
  98         base_var = vars[e->x.p->pos-1];
  99         break;
 100     case flooring:
 101         base_var = evalue2ex_add_var(&e->x.p->arr[0], extravar, expr, false);
 102         break;
 103     case fractional:
 104         base_var = evalue2ex_get_fract(&e->x.p->arr[0], extravar, expr);
 105         break;
 106     case periodic:
 107         assert(coset);
 108         return evalue2ex_r(&e->x.p->arr[VALUE_TO_INT(coset->p[e->x.p->pos-1])],
 109                            vars, extravar, expr, coset);
 110     default:
 111         return fail();
 112     }
 113
 114     int offset = type_offset(e->x.p);
 115     for (int i = e->x.p->size-1; i >= offset; --i) {
 116         poly *= base_var;
 117         ex t = evalue2ex_r(&e->x.p->arr[i], vars, extravar, expr, coset);
 118         if (is_exactly_a<fail>(t))
 119             return t;
 120         poly += t;
 121     }
 122     return poly;
 123 }
 124
 125 /* For each t = floor(e/d), set up two constraints
 126  *
 127  *       e - d t       >= 0
 128  *      -e + d t + d-1 >= 0
 129  *
 130  * e is assumed to be an affine expression.
 131  *
 132  * For each t = fract(e/d), set up two constraints
 133  *
 134  *          -d t + d-1 >= 0
 135  *             t       >= 0
 136  */
 137 static Matrix *setup_constraints(const vector<typed_evalue> expr, int nvar)
 138 {
 139     int extra = expr.size();
 140     if (!extra)
 141         return NULL;
 142     Matrix *M = Matrix_Alloc(2*extra, 1+extra+nvar+1);
 143     for (int i = 0; i < extra; ++i) {
 144         if (expr[i].first) {
 145             value_set_si(M->p[2*i][0], 1);
 146             value_set_si(M->p[2*i][1+i], -1);
 147             value_set_si(M->p[2*i][1+extra+nvar], 1);
 148             value_set_si(M->p[2*i+1][0], 1);
 149             value_set_si(M->p[2*i+1][1+i], 1);
 150         } else {
 151             Value *d = &M->p[2*i][1+i];
 152             evalue_extract_affine(expr[i].second, M->p[2*i]+1+extra,
 153                                   M->p[2*i]+1+extra+nvar, d);
 154             value_oppose(*d, *d);
 155             value_set_si(M->p[2*i][0], -1);
 156             Vector_Scale(M->p[2*i], M->p[2*i+1], M->p[2*i][0], 1+extra+nvar+1);
 157             value_set_si(M->p[2*i][0], 1);
 158             value_subtract(M->p[2*i+1][1+extra+nvar], M->p[2*i+1][1+extra+nvar], *d);
 159             value_decrement(M->p[2*i+1][1+extra+nvar], M->p[2*i+1][1+extra+nvar]);
 160         }
 161     }
 162     return M;
 163 }
 164
 165 static bool evalue_is_periodic(const evalue *e, Vector *periods)
 166 {
 167     int i, offset;
 168     bool is_periodic = false;
 169
 170     if (value_notzero_p(e->d))
 171         return false;
 172
 173     assert(e->x.p->type != partition);
 174     if (e->x.p->type == periodic) {
 175         Value size;
 176         value_init(size);
 177         value_set_si(size, e->x.p->size);
 178         value_lcm(periods->p[e->x.p->pos-1], size, &periods->p[e->x.p->pos-1]);
 179         value_clear(size);
 180         is_periodic = true;
 181     }
 182     offset = type_offset(e->x.p);
 183     for (i = e->x.p->size-1; i >= offset; --i)
 184         is_periodic = evalue_is_periodic(&e->x.p->arr[i], periods) || is_periodic;
 185     return is_periodic;
 186 }
 187
 188 static ex evalue2lst(const evalue *e, const exvector& vars,
 189                      exvector& extravar, vector<typed_evalue>& expr,
 190                      Vector *periods)
 191 {
 192     Vector *coset = Vector_Alloc(periods->Size);
 193     lst list;
 194     for (;;) {
 195         int i;
 196         list.append(evalue2ex_r(e, vars, extravar, expr, coset));
 197         for (i = coset->Size-1; i >= 0; --i) {
 198             value_increment(coset->p[i], coset->p[i]);
 199             if (value_lt(coset->p[i], periods->p[i]))
 200                 break;
 201             value_set_si(coset->p[i], 0);
 202         }
 203         if (i < 0)
 204             break;
 205     }
 206     Vector_Free(coset);
 207     return list;
 208 }
 209
 210 ex evalue2ex(const evalue *e, const exvector& vars, exvector& floorvar,
 211              Matrix **C, Vector **p)
 212 {
 213     vector<typed_evalue> expr;
 214     Vector *periods = Vector_Alloc(vars.size());
 215     assert(p);
 216     assert(C);
 217     for (int i = 0; i < periods->Size; ++i)
 218         value_set_si(periods->p[i], 1);
 219     if (evalue_is_periodic(e, periods)) {
 220         *p = periods;
 221         *C = NULL;
 222         lst list;
 223         return list;
 224     } else {
 225         Vector_Free(periods);
 226         *p = NULL;
 227         ex poly = evalue2ex_r(e, vars, floorvar, expr, NULL);
 228         Matrix *M = setup_constraints(expr, vars.size());
 229         *C = M;
 230         return poly;
 231     }
 232 }
 233
 234 /* if the evalue is a relation, we use the relation to cut off the
 235  * the edges of the domain
 236  */
 237 static void evalue_extract_poly(evalue *e, int i, Polyhedron **D, evalue **poly,
 238                                 unsigned MaxRays)
 239 {
 240     *D = EVALUE_DOMAIN(e->x.p->arr[2*i]);
 241     *poly = e = &e->x.p->arr[2*i+1];
 242     if (value_notzero_p(e->d))
 243         return;
 244     if (e->x.p->type != relation)
 245         return;
 246     if (e->x.p->size > 2)
 247         return;
 248     evalue *fr = &e->x.p->arr[0];
 249     assert(value_zero_p(fr->d));
 250     assert(fr->x.p->type == fractional);
 251     assert(fr->x.p->size == 3);
 252     Matrix *T = Matrix_Alloc(2, (*D)->Dimension+1);
 253     value_set_si(T->p[1][(*D)->Dimension], 1);
 254
 255     /* convert argument of fractional to polylib */
 256     /* the argument is assumed to be linear */
 257     evalue *p = &fr->x.p->arr[0];
 258     evalue_denom(p, &T->p[1][(*D)->Dimension]);
 259     for (;value_zero_p(p->d); p = &p->x.p->arr[0]) {
 260         assert(p->x.p->type == polynomial);
 261         assert(p->x.p->size == 2);
 262         assert(value_notzero_p(p->x.p->arr[1].d));
 263         int pos = p->x.p->pos - 1;
 264         value_assign(T->p[0][pos], p->x.p->arr[1].x.n);
 265         value_multiply(T->p[0][pos], T->p[0][pos], T->p[1][(*D)->Dimension]);
 266         value_division(T->p[0][pos], T->p[0][pos], p->x.p->arr[1].d);
 267     }
 268     int pos = (*D)->Dimension;
 269     value_assign(T->p[0][pos], p->x.n);
 270     value_multiply(T->p[0][pos], T->p[0][pos], T->p[1][(*D)->Dimension]);
 271     value_division(T->p[0][pos], T->p[0][pos], p->d);
 272
 273     Polyhedron *E = NULL;
 274     for (Polyhedron *P = *D; P; P = P->next) {
 275         Polyhedron *I = Polyhedron_Image(P, T, MaxRays);
 276         I = DomainConstraintSimplify(I, MaxRays);
 277         Polyhedron *R = Polyhedron_Preimage(I, T, MaxRays);
 278         Polyhedron_Free(I);
 279         Polyhedron *next = P->next;
 280         P->next = NULL;
 281         Polyhedron *S = DomainIntersection(P, R, MaxRays);
 282         Polyhedron_Free(R);
 283         P->next = next;
 284         if (emptyQ2(S))
 285             Polyhedron_Free(S);
 286         else
 287             E = DomainConcat(S, E);
 288     }
 289     Matrix_Free(T);
 290
 291     *D = E;
 292     *poly = &e->x.p->arr[1];
 293 }
 294
 295 piecewise_lst *evalue_bernstein_coefficients(piecewise_lst *pl_all, evalue *e,
 296                                       Polyhedron *ctx, const exvector& params)
 297 {
 298     piecewise_lst *pl;
 299     barvinok_options *options = barvinok_options_new_with_defaults();
 300     pl = evalue_bernstein_coefficients(pl_all, e, ctx, params, options);
 301     barvinok_options_free(options);
 302     return pl;
 303 }
 304
 305 static piecewise_lst *bernstein_coefficients(piecewise_lst *pl_all,
 306                             Polyhedron *D, const ex& poly,
 307                             Polyhedron *ctx,
 308                             const exvector& params, const exvector& floorvar,
 309                             barvinok_options *options);
 310
 311 static piecewise_lst *bernstein_coefficients_product(piecewise_lst *pl_all,
 312                             Polyhedron *F, Matrix *T, const ex& poly,
 313                             Polyhedron *ctx,
 314                             const exvector& params, const exvector& vars,
 315                             barvinok_options *options)
 316 {
 317     if (emptyQ2(ctx))
 318         return pl_all;
 319     for (Polyhedron *G = F; G; G = G->next)
 320         if (emptyQ2(G))
 321             return pl_all;
 322
 323     unsigned nparam = params.size();
 324     unsigned nvar = vars.size();
 325     unsigned constraints;
 326     Polyhedron *C = NULL;
 327
 328     /* More context constraints */
 329     if (F->Dimension == ctx->Dimension) {
 330         C = F;
 331         F = F->next;
 332     }
 333     assert(F);
 334     assert(F->next);
 335
 336     Matrix *M;
 337     Polyhedron *P;
 338     Polyhedron *PC;
 339     M = Matrix_Alloc(F->NbConstraints, 1+nvar+nparam+1);
 340     for (int i = 0; i < F->NbConstraints; ++i) {
 341         Vector_Copy(F->Constraint[i], M->p[i], 1+F->Dimension-nparam);
 342         Vector_Copy(F->Constraint[i]+1+F->Dimension-nparam,
 343                     M->p[i]+1+nvar, nparam+1);
 344     }
 345     P = Constraints2Polyhedron(M, options->MaxRays);
 346     Matrix_Free(M);
 347
 348     constraints = C ? C->NbConstraints : 0;
 349     constraints += ctx->NbConstraints;
 350     for (Polyhedron *G = F->next; G; G = G->next)
 351         constraints += G->NbConstraints;
 352
 353     unsigned total_var = nvar-(F->Dimension-nparam);
 354     unsigned skip = 0;
 355     unsigned c = 0;
 356     M = Matrix_Alloc(constraints, 1+total_var+nparam+1);
 357     for (Polyhedron *G = F->next; G; G = G->next) {
 358         unsigned this_var = G->Dimension - nparam;
 359         for (int i = 0; i < G->NbConstraints; ++i) {
 360             value_assign(M->p[c+i][0], G->Constraint[i][0]);
 361             Vector_Copy(G->Constraint[i]+1, M->p[c+i]+1+skip, this_var);
 362             Vector_Copy(G->Constraint[i]+1+this_var, M->p[c+i]+1+total_var,
 363                         nparam+1);
 364         }
 365         c += G->NbConstraints;
 366         skip += this_var;
 367     }
 368     assert(skip == total_var);
 369     if (C) {
 370         for (int i = 0; i < C->NbConstraints; ++i) {
 371             value_assign(M->p[c+i][0], C->Constraint[i][0]);
 372             Vector_Copy(C->Constraint[i]+1, M->p[c+i]+1+total_var,
 373                         nparam+1);
 374         }
 375         c += C->NbConstraints;
 376     }
 377     for (int i = 0; i < ctx->NbConstraints; ++i) {
 378         value_assign(M->p[c+i][0], ctx->Constraint[i][0]);
 379         Vector_Copy(ctx->Constraint[i]+1, M->p[c+i]+1+total_var, nparam+1);
 380     }
 381     PC = Constraints2Polyhedron(M, options->MaxRays);
 382     Matrix_Free(M);
 383
 384     exvector newvars = constructVariableVector(nvar, "t");
 385     matrix subs(1, nvar);
 386     for (int i = 0; i < nvar; ++i)
 387         for (int j = 0; j < nvar; ++j)
 388             subs(0,i) += value2numeric(T->p[i][j]) * newvars[j];
 389
 390     ex newpoly = replaceVariablesInPolynomial(poly, vars, subs);
 391
 392     exvector P_vars;
 393     P_vars.insert(P_vars.end(), newvars.begin(),
 394                   newvars.begin()+(F->Dimension-nparam));
 395     exvector P_params;
 396     P_params.insert(P_params.end(), newvars.begin()+(F->Dimension-nparam),
 397                     newvars.end());
 398     P_params.insert(P_params.end(), params.begin(), params.end());
 399     piecewise_lst *pl;
 400     pl = bernstein_coefficients(NULL, P, newpoly, PC, P_params, P_vars, options);
 401     Polyhedron_Free(P);
 402     Polyhedron_Free(PC);
 403
 404     if (options->bernstein_optimize == BV_BERNSTEIN_MIN)
 405         pl->minimize();
 406     else if (options->bernstein_optimize == BV_BERNSTEIN_MAX)
 407         pl->maximize();
 408
 409     unsigned done = F->Dimension-nparam;
 410     for (F = F->next ; F; F = F->next) {
 411         exvector pl_vars;
 412         pl_vars.insert(pl_vars.end(), newvars.begin()+done,
 413                        newvars.begin()+done+(F->Dimension-nparam));
 414         exvector pl_params;
 415         pl_params.insert(pl_params.end(), newvars.begin()+done+(F->Dimension-nparam),
 416                          newvars.end());
 417         pl_params.insert(pl_params.end(), params.begin(), params.end());
 418         piecewise_lst *new_pl = NULL;
 419         Polyhedron *U = Universe_Polyhedron(pl_params.size());
 420
 421         for (int i = 0; i < pl->list.size(); ++i) {
 422             Polyhedron *D = pl->list[i].first;
 423             lst polys = pl->list[i].second;
 424             new_pl = bernstein_coefficients(new_pl, D, polys, U, pl_params,
 425                                             pl_vars, options);
 426         }
 427
 428         delete pl;
 429         pl = new_pl;
 430
 431         if (options->bernstein_optimize == BV_BERNSTEIN_MIN)
 432             pl->minimize();
 433         else if (options->bernstein_optimize == BV_BERNSTEIN_MAX)
 434             pl->maximize();
 435
 436         Polyhedron_Free(U);
 437         done += F->Dimension-nparam;
 438     }
 439
 440     if (!pl_all)
 441         pl_all = pl;
 442     else {
 443         pl_all->combine(*pl);
 444         delete pl;
 445     }
 446
 447     return pl_all;
 448 }
 449
 450 static piecewise_lst *bernstein_coefficients_polyhedron(piecewise_lst *pl_all,
 451                             Polyhedron *P, const ex& poly,
 452                             Polyhedron *ctx,
 453                             const exvector& params, const exvector& floorvar,
 454                             barvinok_options *options)
 455 {
 456     if (Polyhedron_is_unbounded(P, ctx->Dimension, options->MaxRays)) {
 457         fprintf(stderr, "warning: unbounded domain skipped\n");
 458         Polyhedron_Print(stderr, P_VALUE_FMT, P);
 459         return pl_all;
 460     }
 461
 462     Matrix *T = NULL;
 463     Polyhedron *F = Polyhedron_Factor(P, ctx->Dimension, &T, options->MaxRays);
 464     if (F) {
 465         pl_all = bernstein_coefficients_product(pl_all, F, T, poly, ctx, params,
 466                                                 floorvar, options);
 467         Domain_Free(F);
 468         Matrix_Free(T);
 469         return pl_all;
 470     }
 471
 472     unsigned PP_MaxRays = options->MaxRays;
 473     if (PP_MaxRays & POL_NO_DUAL)
 474         PP_MaxRays = 0;
 475
 476     Param_Polyhedron *PP = Polyhedron2Param_Domain(P, ctx, PP_MaxRays);
 477     assert(PP);
 478     piecewise_lst *pl = new piecewise_lst(params);
 479     for (Param_Domain *Q = PP->D; Q; Q = Q->next) {
 480         matrix VM = domainVertices(PP, Q, params);
 481         lst coeffs = bernsteinExpansion(VM, poly, floorvar, params);
 482         pl->list.push_back(guarded_lst(Polyhedron_Copy(Q->Domain), coeffs));
 483     }
 484     Param_Polyhedron_Free(PP);
 485     if (!pl_all)
 486         pl_all = pl;
 487     else {
 488         pl_all->combine(*pl);
 489         delete pl;
 490     }
 491
 492     return pl_all;
 493 }
 494
 495 static piecewise_lst *bernstein_coefficients(piecewise_lst *pl_all,
 496                             Polyhedron *D, const ex& poly,
 497                             Polyhedron *ctx,
 498                             const exvector& params, const exvector& floorvar,
 499                             barvinok_options *options)
 500 {
 501     if (!D->next && emptyQ2(D))
 502         return pl_all;
 503
 504     for (Polyhedron *P = D; P; P = P->next) {
 505         /* This shouldn't happen */
 506         if (emptyQ2(P))
 507             continue;
 508         Polyhedron *next = P->next;
 509         P->next = NULL;
 510         pl_all = bernstein_coefficients_polyhedron(pl_all, P, poly, ctx,
 511                                                    params, floorvar, options);
 512         P->next = next;
 513     }
 514     return pl_all;
 515 }
 516
 517 /* Compute the coefficients of the polynomial corresponding to each coset
 518  * on its own domain.  This allows us to cut the domain on multiples of
 519  * the period.
 520  * To perform the cutting for a coset "i mod n = c" we map the domain
 521  * to the quotient space trough "i = i' n + c", simplify the constraints
 522  * (implicitly) and then map back to the original space.
 523  */
 524 static piecewise_lst *bernstein_coefficients_periodic(piecewise_lst *pl_all,
 525                             Polyhedron *D, const evalue *e,
 526                             Polyhedron *ctx, const exvector& vars,
 527                             const exvector& params, Vector *periods,
 528                             barvinok_options *options)
 529 {
 530     assert(D->Dimension == periods->Size);
 531     Matrix *T = Matrix_Alloc(D->Dimension+1, D->Dimension+1);
 532     Matrix *T2 = Matrix_Alloc(D->Dimension+1, D->Dimension+1);
 533     Vector *coset = Vector_Alloc(periods->Size);
 534     exvector extravar;
 535     vector<typed_evalue> expr;
 536     exvector allvars = vars;
 537     allvars.insert(allvars.end(), params.begin(), params.end());
 538
 539     value_set_si(T2->p[D->Dimension][D->Dimension], 1);
 540     for (int i = 0; i < D->Dimension; ++i) {
 541         value_assign(T->p[i][i], periods->p[i]);
 542         value_lcm(T2->p[D->Dimension][D->Dimension], periods->p[i],
 543                   &T2->p[D->Dimension][D->Dimension]);
 544     }
 545     value_set_si(T->p[D->Dimension][D->Dimension], 1);
 546     for (int i = 0; i < D->Dimension; ++i)
 547         value_division(T2->p[i][i], T2->p[D->Dimension][D->Dimension],
 548                        periods->p[i]);
 549     for (;;) {
 550         int i;
 551         ex poly = evalue2ex_r(e, allvars, extravar, expr, coset);
 552         assert(extravar.size() == 0);
 553         assert(expr.size() == 0);
 554         Polyhedron *E = DomainPreimage(D, T, options->MaxRays);
 555         Polyhedron *F = DomainPreimage(E, T2, options->MaxRays);
 556         Polyhedron_Free(E);
 557         if (!emptyQ2(F))
 558             pl_all = bernstein_coefficients(pl_all, F, poly, ctx, params,
 559                                             vars, options);
 560         Polyhedron_Free(F);
 561         for (i = D->Dimension-1; i >= 0; --i) {
 562             value_increment(coset->p[i], coset->p[i]);
 563             value_increment(T->p[i][D->Dimension], T->p[i][D->Dimension]);
 564             value_subtract(T2->p[i][D->Dimension], T2->p[i][D->Dimension],
 565                            T2->p[i][i]);
 566             if (value_lt(coset->p[i], periods->p[i]))
 567                 break;
 568             value_set_si(coset->p[i], 0);
 569             value_set_si(T->p[i][D->Dimension], 0);
 570             value_set_si(T2->p[i][D->Dimension], 0);
 571         }
 572         if (i < 0)
 573             break;
 574     }
 575     Vector_Free(coset);
 576     Matrix_Free(T);
 577     Matrix_Free(T2);
 578     return pl_all;
 579 }
 580
 581 piecewise_lst *evalue_bernstein_coefficients(piecewise_lst *pl_all, evalue *e,
 582                                       Polyhedron *ctx, const exvector& params,
 583                                       barvinok_options *options)
 584 {
 585     unsigned nparam = ctx->Dimension;
 586     if (EVALUE_IS_ZERO(*e))
 587         return pl_all;
 588     assert(value_zero_p(e->d));
 589     assert(e->x.p->type == partition);
 590     assert(e->x.p->size >= 2);
 591     unsigned nvars = EVALUE_DOMAIN(e->x.p->arr[0])->Dimension - nparam;
 592
 593     exvector vars = constructVariableVector(nvars, "v");
 594     exvector allvars = vars;
 595     allvars.insert(allvars.end(), params.begin(), params.end());
 596
 597     for (int i = 0; i < e->x.p->size/2; ++i) {
 598         Polyhedron *E;
 599         evalue *EP;
 600         Matrix *M;
 601         Vector *periods;
 602         exvector floorvar;
 603
 604         evalue_extract_poly(e, i, &E, &EP, options->MaxRays);
 605         ex poly = evalue2ex(EP, allvars, floorvar, &M, &periods);
 606         floorvar.insert(floorvar.end(), vars.begin(), vars.end());
 607         if (M) {
 608             Polyhedron *AE = align_context(E, M->NbColumns-2, options->MaxRays);
 609             if (E != EVALUE_DOMAIN(e->x.p->arr[2*i]))
 610                 Domain_Free(E);
 611             E = DomainAddConstraints(AE, M, options->MaxRays);
 612             Matrix_Free(M);
 613             Domain_Free(AE);
 614         }
 615         if (is_exactly_a<fail>(poly)) {
 616             if (E != EVALUE_DOMAIN(e->x.p->arr[2*i]))
 617                 Domain_Free(E);
 618             delete pl_all;
 619             return NULL;
 620         }
 621         if (periods)
 622             pl_all = bernstein_coefficients_periodic(pl_all, E, EP, ctx, vars,
 623                                                      params, periods, options);
 624         else
 625             pl_all = bernstein_coefficients(pl_all, E, poly, ctx, params,
 626                                             floorvar, options);
 627         if (periods)
 628             Vector_Free(periods);
 629         if (E != EVALUE_DOMAIN(e->x.p->arr[2*i]))
 630             Domain_Free(E);
 631     }
 632     return pl_all;
 633 }
 634
 635 }