bernstein.cc

   1 #include <assert.h>
   2 #include <vector>
   3 #include <bernstein/bernstein.h>
   4 #include <bernstein/piecewise_lst.h>
   5 #include <barvinok/barvinok.h>
   6 #include <barvinok/util.h>
   7 #include <barvinok/bernstein.h>
   8 #include <barvinok/options.h>
   9 #include "reduce_domain.h"
  10
  11 using namespace GiNaC;
  12 using namespace bernstein;
  13
  14 using std::pair;
  15 using std::vector;
  16 using std::cerr;
  17 using std::endl;
  18
  19 namespace barvinok {
  20
  21 ex evalue2ex(evalue *e, const exvector& vars)
  22 {
  23     if (value_pos_p(e->d))
  24         return value2numeric(e->x.n)/value2numeric(e->d);
  25     if (EVALUE_IS_NAN(*e))
  26         return fail();
  27     if (e->x.p->type != polynomial)
  28         return fail();
  29     ex poly = 0;
  30     for (int i = e->x.p->size-1; i >= 0; --i) {
  31         poly *= vars[e->x.p->pos-1];
  32         ex t = evalue2ex(&e->x.p->arr[i], vars);
  33         if (is_exactly_a<fail>(t))
  34             return t;
  35         poly += t;
  36     }
  37     return poly;
  38 }
  39
  40 static int type_offset(enode *p)
  41 {
  42    return p->type == fractional ? 1 :
  43           p->type == flooring ? 1 : 0;
  44 }
  45
  46 typedef pair<bool, const evalue *> typed_evalue;
  47
  48 static ex evalue2ex_add_var(evalue *e, exvector& extravar,
  49                             vector<typed_evalue>& expr, bool is_fract)
  50 {
  51     ex base_var = 0;
  52
  53     for (int i = 0; i < expr.size(); ++i) {
  54         if (is_fract == expr[i].first && eequal(e, expr[i].second)) {
  55             base_var = extravar[i];
  56             break;
  57         }
  58     }
  59     if (base_var != 0)
  60         return base_var;
  61
  62     char name[20];
  63     snprintf(name, sizeof(name), "f%c%d", is_fract ? 'r' : 'l', expr.size());
  64     extravar.push_back(base_var = symbol(name));
  65     expr.push_back(typed_evalue(is_fract, e));
  66
  67     return base_var;
  68 }
  69
  70 /* For the argument e=(f/d) of a fractional, return (d-1)/d times
  71  * a variable in [0,1] (see setup_constraints).
  72  */
  73 static ex evalue2ex_get_fract(evalue *e, exvector& extravar,
  74                                 vector<typed_evalue>& expr)
  75 {
  76     ex f;
  77     Value d;
  78     ex den;
  79     value_init(d);
  80     value_set_si(d, 1);
  81     evalue_denom(e, &d);
  82     den = value2numeric(d);
  83     value_clear(d);
  84     f = (den-1)/den;
  85
  86     ex base_var = evalue2ex_add_var(e, extravar, expr, true);
  87     base_var *= f;
  88     return base_var;
  89 }
  90
  91 static ex evalue2ex_r(const evalue *e, const exvector& vars,
  92                       exvector& extravar, vector<typed_evalue>& expr,
  93                       Vector *coset)
  94 {
  95     if (value_notzero_p(e->d))
  96         return value2numeric(e->x.n)/value2numeric(e->d);
  97     ex base_var = 0;
  98     ex poly = 0;
  99
 100     switch (e->x.p->type) {
 101     case polynomial:
 102         base_var = vars[e->x.p->pos-1];
 103         break;
 104     case flooring:
 105         base_var = evalue2ex_add_var(&e->x.p->arr[0], extravar, expr, false);
 106         break;
 107     case fractional:
 108         base_var = evalue2ex_get_fract(&e->x.p->arr[0], extravar, expr);
 109         break;
 110     case periodic:
 111         assert(coset);
 112         return evalue2ex_r(&e->x.p->arr[VALUE_TO_INT(coset->p[e->x.p->pos-1])],
 113                            vars, extravar, expr, coset);
 114     default:
 115         return fail();
 116     }
 117
 118     int offset = type_offset(e->x.p);
 119     for (int i = e->x.p->size-1; i >= offset; --i) {
 120         poly *= base_var;
 121         ex t = evalue2ex_r(&e->x.p->arr[i], vars, extravar, expr, coset);
 122         if (is_exactly_a<fail>(t))
 123             return t;
 124         poly += t;
 125     }
 126     return poly;
 127 }
 128
 129 /* For each t = floor(e/d), set up two constraints
 130  *
 131  *       e - d t       >= 0
 132  *      -e + d t + d-1 >= 0
 133  *
 134  * e is assumed to be an affine expression.
 135  *
 136  * For each t = fract(e/d), set up two constraints
 137  *
 138  *          -d t + d-1 >= 0
 139  *             t       >= 0
 140  */
 141 static Matrix *setup_constraints(const vector<typed_evalue> expr, int nvar)
 142 {
 143     int extra = expr.size();
 144     if (!extra)
 145         return NULL;
 146     Matrix *M = Matrix_Alloc(2*extra, 1+extra+nvar+1);
 147     for (int i = 0; i < extra; ++i) {
 148         if (expr[i].first) {
 149             value_set_si(M->p[2*i][0], 1);
 150             value_set_si(M->p[2*i][1+i], -1);
 151             value_set_si(M->p[2*i][1+extra+nvar], 1);
 152             value_set_si(M->p[2*i+1][0], 1);
 153             value_set_si(M->p[2*i+1][1+i], 1);
 154         } else {
 155             Value *d = &M->p[2*i][1+i];
 156             evalue_extract_affine(expr[i].second, M->p[2*i]+1+extra,
 157                                   M->p[2*i]+1+extra+nvar, d);
 158             value_oppose(*d, *d);
 159             value_set_si(M->p[2*i][0], -1);
 160             Vector_Scale(M->p[2*i], M->p[2*i+1], M->p[2*i][0], 1+extra+nvar+1);
 161             value_set_si(M->p[2*i][0], 1);
 162             value_subtract(M->p[2*i+1][1+extra+nvar], M->p[2*i+1][1+extra+nvar], *d);
 163             value_decrement(M->p[2*i+1][1+extra+nvar], M->p[2*i+1][1+extra+nvar]);
 164         }
 165     }
 166     return M;
 167 }
 168
 169 static bool evalue_is_periodic(const evalue *e, Vector *periods)
 170 {
 171     int i, offset;
 172     bool is_periodic = false;
 173
 174     if (value_notzero_p(e->d))
 175         return false;
 176
 177     assert(e->x.p->type != partition);
 178     if (e->x.p->type == periodic) {
 179         Value size;
 180         value_init(size);
 181         value_set_si(size, e->x.p->size);
 182         value_lcm(periods->p[e->x.p->pos-1], periods->p[e->x.p->pos-1], size);
 183         value_clear(size);
 184         is_periodic = true;
 185     }
 186     offset = type_offset(e->x.p);
 187     for (i = e->x.p->size-1; i >= offset; --i)
 188         is_periodic = evalue_is_periodic(&e->x.p->arr[i], periods) || is_periodic;
 189     return is_periodic;
 190 }
 191
 192 static ex evalue2lst(const evalue *e, const exvector& vars,
 193                      exvector& extravar, vector<typed_evalue>& expr,
 194                      Vector *periods)
 195 {
 196     Vector *coset = Vector_Alloc(periods->Size);
 197     lst list;
 198     for (;;) {
 199         int i;
 200         list.append(evalue2ex_r(e, vars, extravar, expr, coset));
 201         for (i = coset->Size-1; i >= 0; --i) {
 202             value_increment(coset->p[i], coset->p[i]);
 203             if (value_lt(coset->p[i], periods->p[i]))
 204                 break;
 205             value_set_si(coset->p[i], 0);
 206         }
 207         if (i < 0)
 208             break;
 209     }
 210     Vector_Free(coset);
 211     return list;
 212 }
 213
 214 ex evalue2ex(const evalue *e, const exvector& vars, exvector& floorvar,
 215              Matrix **C, Vector **p)
 216 {
 217     vector<typed_evalue> expr;
 218     Vector *periods = Vector_Alloc(vars.size());
 219     assert(p);
 220     assert(C);
 221     for (int i = 0; i < periods->Size; ++i)
 222         value_set_si(periods->p[i], 1);
 223     if (evalue_is_periodic(e, periods)) {
 224         *p = periods;
 225         *C = NULL;
 226         lst list;
 227         return list;
 228     } else {
 229         Vector_Free(periods);
 230         *p = NULL;
 231         ex poly = evalue2ex_r(e, vars, floorvar, expr, NULL);
 232         Matrix *M = setup_constraints(expr, vars.size());
 233         *C = M;
 234         return poly;
 235     }
 236 }
 237
 238 /* if the evalue is a relation, we use the relation to cut off the
 239  * the edges of the domain
 240  */
 241 static Polyhedron *relation_domain(Polyhedron *D, evalue *fr, unsigned MaxRays)
 242 {
 243     assert(value_zero_p(fr->d));
 244     assert(fr->x.p->type == fractional);
 245     assert(fr->x.p->size == 3);
 246     Matrix *T = Matrix_Alloc(2, D->Dimension+1);
 247     value_set_si(T->p[1][D->Dimension], 1);
 248
 249     /* convert argument of fractional to polylib */
 250     /* the argument is assumed to be linear */
 251     evalue *p = &fr->x.p->arr[0];
 252     evalue_denom(p, &T->p[1][D->Dimension]);
 253     for (;value_zero_p(p->d); p = &p->x.p->arr[0]) {
 254         assert(p->x.p->type == polynomial);
 255         assert(p->x.p->size == 2);
 256         assert(value_notzero_p(p->x.p->arr[1].d));
 257         int pos = p->x.p->pos - 1;
 258         value_assign(T->p[0][pos], p->x.p->arr[1].x.n);
 259         value_multiply(T->p[0][pos], T->p[0][pos], T->p[1][D->Dimension]);
 260         value_division(T->p[0][pos], T->p[0][pos], p->x.p->arr[1].d);
 261     }
 262     int pos = D->Dimension;
 263     value_assign(T->p[0][pos], p->x.n);
 264     value_multiply(T->p[0][pos], T->p[0][pos], T->p[1][D->Dimension]);
 265     value_division(T->p[0][pos], T->p[0][pos], p->d);
 266
 267     Polyhedron *E = NULL;
 268     for (Polyhedron *P = D; P; P = P->next) {
 269         Polyhedron *I = Polyhedron_Image(P, T, MaxRays);
 270         I = DomainConstraintSimplify(I, MaxRays);
 271         Polyhedron *R = Polyhedron_Preimage(I, T, MaxRays);
 272         Polyhedron_Free(I);
 273         Polyhedron *next = P->next;
 274         P->next = NULL;
 275         Polyhedron *S = DomainIntersection(P, R, MaxRays);
 276         Polyhedron_Free(R);
 277         P->next = next;
 278         if (emptyQ2(S))
 279             Polyhedron_Free(S);
 280         else
 281             E = DomainConcat(S, E);
 282     }
 283     Matrix_Free(T);
 284
 285     return E;
 286 }
 287
 288 piecewise_lst *evalue_bernstein_coefficients(piecewise_lst *pl_all, evalue *e,
 289                                       Polyhedron *ctx, const exvector& params)
 290 {
 291     piecewise_lst *pl;
 292     barvinok_options *options = barvinok_options_new_with_defaults();
 293     pl = evalue_bernstein_coefficients(pl_all, e, ctx, params, options);
 294     barvinok_options_free(options);
 295     return pl;
 296 }
 297
 298 static piecewise_lst *bernstein_coefficients(piecewise_lst *pl_all,
 299                             Polyhedron *D, const ex& poly,
 300                             Polyhedron *ctx,
 301                             const exvector& params, const exvector& floorvar,
 302                             barvinok_options *options);
 303
 304 /* Recursively apply Bernstein expansion on P, optimizing over dims[i]
 305  * variables in each level.  The context ctx is assumed to have been adapted
 306  * to the first level in the recursion.
 307  */
 308 static piecewise_lst *bernstein_coefficients_recursive(piecewise_lst *pl_all,
 309                             Polyhedron *P, const vector<int>& dims, const ex& poly,
 310                             Polyhedron *ctx,
 311                             const exvector& params, const exvector& vars,
 312                             barvinok_options *options)
 313 {
 314     assert(dims.size() > 0);
 315     assert(ctx->Dimension == P->Dimension - dims[0]);
 316     piecewise_lst *pl;
 317     unsigned done = 0;
 318     for (int j = 0; j < dims.size(); ++j) {
 319         exvector pl_vars;
 320         pl_vars.insert(pl_vars.end(), vars.begin()+done, vars.begin()+done+dims[j]);
 321         exvector pl_params;
 322         pl_params.insert(pl_params.end(), vars.begin()+done+dims[j], vars.end());
 323         pl_params.insert(pl_params.end(), params.begin(), params.end());
 324
 325         if (!j)
 326             pl = bernstein_coefficients(NULL, P, poly, ctx,
 327                                         pl_params, pl_vars, options);
 328         else {
 329             piecewise_lst *new_pl = NULL;
 330             Polyhedron *U = Universe_Polyhedron(pl_params.size());
 331
 332             for (int i = 0; i < pl->list.size(); ++i) {
 333                 Polyhedron *D = pl->list[i].first;
 334                 lst polys = pl->list[i].second;
 335                 new_pl = bernstein_coefficients(new_pl, D, polys, U, pl_params,
 336                                                 pl_vars, options);
 337             }
 338
 339             Polyhedron_Free(U);
 340
 341             delete pl;
 342             pl = new_pl;
 343         }
 344
 345         done += dims[j];
 346
 347         if (!pl)
 348             return pl_all;
 349     }
 350
 351     if (!pl_all)
 352         pl_all = pl;
 353     else {
 354         pl_all->combine(*pl);
 355         delete pl;
 356     }
 357
 358     return pl_all;
 359 }
 360
 361 static piecewise_lst *bernstein_coefficients_full_recurse(piecewise_lst *pl_all,
 362                             Polyhedron *P, const ex& poly,
 363                             Polyhedron *ctx,
 364                             const exvector& params, const exvector& vars,
 365                             barvinok_options *options)
 366 {
 367     Polyhedron *CR = align_context(ctx, P->Dimension-1, options->MaxRays);
 368     vector<int> dims(vars.size());
 369     for (int i = 0; i < dims.size(); ++i)
 370         dims[i] = 1;
 371     pl_all = bernstein_coefficients_recursive(pl_all, P, dims, poly, CR,
 372                                               params, vars, options);
 373     Polyhedron_Free(CR);
 374
 375     return pl_all;
 376 }
 377
 378 static piecewise_lst *bernstein_coefficients_product(piecewise_lst *pl_all,
 379                             Polyhedron *F, Matrix *T, const ex& poly,
 380                             Polyhedron *ctx,
 381                             const exvector& params, const exvector& vars,
 382                             barvinok_options *options)
 383 {
 384     if (emptyQ2(ctx))
 385         return pl_all;
 386     for (Polyhedron *G = F; G; G = G->next)
 387         if (emptyQ2(G))
 388             return pl_all;
 389
 390     unsigned nparam = params.size();
 391     unsigned nvar = vars.size();
 392     unsigned constraints;
 393     unsigned factors;
 394     Polyhedron *C = NULL;
 395
 396     /* More context constraints */
 397     if (F->Dimension == ctx->Dimension) {
 398         C = F;
 399         F = F->next;
 400     }
 401     assert(F);
 402     assert(F->next);
 403
 404     Matrix *M;
 405     Polyhedron *P;
 406     Polyhedron *PC;
 407     M = Matrix_Alloc(F->NbConstraints, 1+nvar+nparam+1);
 408     for (int i = 0; i < F->NbConstraints; ++i) {
 409         Vector_Copy(F->Constraint[i], M->p[i], 1+F->Dimension-nparam);
 410         Vector_Copy(F->Constraint[i]+1+F->Dimension-nparam,
 411                     M->p[i]+1+nvar, nparam+1);
 412     }
 413     P = Constraints2Polyhedron(M, options->MaxRays);
 414     Matrix_Free(M);
 415
 416     factors = 1;
 417     constraints = C ? C->NbConstraints : 0;
 418     constraints += ctx->NbConstraints;
 419     for (Polyhedron *G = F->next; G; G = G->next) {
 420         constraints += G->NbConstraints;
 421         ++factors;
 422     }
 423
 424     unsigned total_var = nvar-(F->Dimension-nparam);
 425     unsigned skip = 0;
 426     unsigned c = 0;
 427     M = Matrix_Alloc(constraints, 1+total_var+nparam+1);
 428     for (Polyhedron *G = F->next; G; G = G->next) {
 429         unsigned this_var = G->Dimension - nparam;
 430         for (int i = 0; i < G->NbConstraints; ++i) {
 431             value_assign(M->p[c+i][0], G->Constraint[i][0]);
 432             Vector_Copy(G->Constraint[i]+1, M->p[c+i]+1+skip, this_var);
 433             Vector_Copy(G->Constraint[i]+1+this_var, M->p[c+i]+1+total_var,
 434                         nparam+1);
 435         }
 436         c += G->NbConstraints;
 437         skip += this_var;
 438     }
 439     assert(skip == total_var);
 440     if (C) {
 441         for (int i = 0; i < C->NbConstraints; ++i) {
 442             value_assign(M->p[c+i][0], C->Constraint[i][0]);
 443             Vector_Copy(C->Constraint[i]+1, M->p[c+i]+1+total_var,
 444                         nparam+1);
 445         }
 446         c += C->NbConstraints;
 447     }
 448     for (int i = 0; i < ctx->NbConstraints; ++i) {
 449         value_assign(M->p[c+i][0], ctx->Constraint[i][0]);
 450         Vector_Copy(ctx->Constraint[i]+1, M->p[c+i]+1+total_var, nparam+1);
 451     }
 452     PC = Constraints2Polyhedron(M, options->MaxRays);
 453     Matrix_Free(M);
 454
 455     exvector newvars = constructVariableVector(nvar, "t");
 456     matrix subs(1, nvar);
 457     for (int i = 0; i < nvar; ++i)
 458         for (int j = 0; j < nvar; ++j)
 459             subs(0,i) += value2numeric(T->p[i][j]) * newvars[j];
 460
 461     ex newpoly = replaceVariablesInPolynomial(poly, vars, subs);
 462
 463     vector<int> dims(factors);
 464     for (int i = 0; F; ++i, F = F->next)
 465         dims[i] = F->Dimension-nparam;
 466
 467     pl_all = bernstein_coefficients_recursive(pl_all, P, dims, newpoly, PC,
 468                                               params, newvars, options);
 469
 470     Polyhedron_Free(P);
 471     Polyhedron_Free(PC);
 472
 473     return pl_all;
 474 }
 475
 476 static piecewise_lst *bernstein_coefficients_polyhedron(piecewise_lst *pl_all,
 477                             Polyhedron *P, const ex& poly,
 478                             Polyhedron *ctx,
 479                             const exvector& params, const exvector& floorvar,
 480                             barvinok_options *options)
 481 {
 482     if (Polyhedron_is_unbounded(P, ctx->Dimension, options->MaxRays)) {
 483         fprintf(stderr, "warning: unbounded domain skipped\n");
 484         Polyhedron_Print(stderr, P_VALUE_FMT, P);
 485         return pl_all;
 486     }
 487
 488     if (options->bernstein_recurse & BV_BERNSTEIN_FACTORS) {
 489         Matrix *T = NULL;
 490         Polyhedron *F = Polyhedron_Factor(P, ctx->Dimension, &T, options->MaxRays);
 491         if (F) {
 492             pl_all = bernstein_coefficients_product(pl_all, F, T, poly, ctx, params,
 493                                                     floorvar, options);
 494             Domain_Free(F);
 495             Matrix_Free(T);
 496             return pl_all;
 497         }
 498     }
 499     if (floorvar.size() > 1 &&
 500                 options->bernstein_recurse & BV_BERNSTEIN_INTERVALS)
 501         return bernstein_coefficients_full_recurse(pl_all, P, poly, ctx,
 502                                                    params, floorvar, options);
 503
 504     unsigned PP_MaxRays = options->MaxRays;
 505     if (PP_MaxRays & POL_NO_DUAL)
 506         PP_MaxRays = 0;
 507
 508     Param_Polyhedron *PP = Polyhedron2Param_Domain(P, ctx, PP_MaxRays);
 509     if (!PP)
 510         return pl_all;
 511     piecewise_lst *pl = new piecewise_lst(params, options->bernstein_optimize);
 512
 513     int nd = -1;
 514     Polyhedron *TC = true_context(P, ctx, options->MaxRays);
 515     FORALL_REDUCED_DOMAIN(PP, TC, nd, options, i, PD, rVD)
 516         matrix VM = domainVertices(PP, PD, params);
 517         lst coeffs = bernsteinExpansion(VM, poly, floorvar, params);
 518         pl->add_guarded_lst(rVD, coeffs);
 519     END_FORALL_REDUCED_DOMAIN
 520     Polyhedron_Free(TC);
 521
 522     Param_Polyhedron_Free(PP);
 523     if (!pl_all)
 524         pl_all = pl;
 525     else {
 526         pl_all->combine(*pl);
 527         delete pl;
 528     }
 529
 530     return pl_all;
 531 }
 532
 533 static piecewise_lst *bernstein_coefficients(piecewise_lst *pl_all,
 534                             Polyhedron *D, const ex& poly,
 535                             Polyhedron *ctx,
 536                             const exvector& params, const exvector& floorvar,
 537                             barvinok_options *options)
 538 {
 539     if (!D->next && emptyQ2(D))
 540         return pl_all;
 541
 542     for (Polyhedron *P = D; P; P = P->next) {
 543         /* This shouldn't happen */
 544         if (emptyQ2(P))
 545             continue;
 546         Polyhedron *next = P->next;
 547         P->next = NULL;
 548         pl_all = bernstein_coefficients_polyhedron(pl_all, P, poly, ctx,
 549                                                    params, floorvar, options);
 550         P->next = next;
 551     }
 552     return pl_all;
 553 }
 554
 555 /* Compute the coefficients of the polynomial corresponding to each coset
 556  * on its own domain.  This allows us to cut the domain on multiples of
 557  * the period.
 558  * To perform the cutting for a coset "i mod n = c" we map the domain
 559  * to the quotient space trough "i = i' n + c", simplify the constraints
 560  * (implicitly) and then map back to the original space.
 561  */
 562 static piecewise_lst *bernstein_coefficients_periodic(piecewise_lst *pl_all,
 563                             Polyhedron *D, const evalue *e,
 564                             Polyhedron *ctx, const exvector& vars,
 565                             const exvector& params, Vector *periods,
 566                             barvinok_options *options)
 567 {
 568     assert(D->Dimension == periods->Size);
 569     Matrix *T = Matrix_Alloc(D->Dimension+1, D->Dimension+1);
 570     Matrix *T2 = Matrix_Alloc(D->Dimension+1, D->Dimension+1);
 571     Vector *coset = Vector_Alloc(periods->Size);
 572     exvector extravar;
 573     vector<typed_evalue> expr;
 574     exvector allvars = vars;
 575     allvars.insert(allvars.end(), params.begin(), params.end());
 576
 577     value_set_si(T2->p[D->Dimension][D->Dimension], 1);
 578     for (int i = 0; i < D->Dimension; ++i) {
 579         value_assign(T->p[i][i], periods->p[i]);
 580         value_lcm(T2->p[D->Dimension][D->Dimension],
 581                   T2->p[D->Dimension][D->Dimension], periods->p[i]);
 582     }
 583     value_set_si(T->p[D->Dimension][D->Dimension], 1);
 584     for (int i = 0; i < D->Dimension; ++i)
 585         value_division(T2->p[i][i], T2->p[D->Dimension][D->Dimension],
 586                        periods->p[i]);
 587     for (;;) {
 588         int i;
 589         ex poly = evalue2ex_r(e, allvars, extravar, expr, coset);
 590         assert(extravar.size() == 0);
 591         assert(expr.size() == 0);
 592         Polyhedron *E = DomainPreimage(D, T, options->MaxRays);
 593         Polyhedron *F = DomainPreimage(E, T2, options->MaxRays);
 594         Polyhedron_Free(E);
 595         if (!emptyQ(F))
 596             pl_all = bernstein_coefficients(pl_all, F, poly, ctx, params,
 597                                             vars, options);
 598         Polyhedron_Free(F);
 599         for (i = D->Dimension-1; i >= 0; --i) {
 600             value_increment(coset->p[i], coset->p[i]);
 601             value_increment(T->p[i][D->Dimension], T->p[i][D->Dimension]);
 602             value_subtract(T2->p[i][D->Dimension], T2->p[i][D->Dimension],
 603                            T2->p[i][i]);
 604             if (value_lt(coset->p[i], periods->p[i]))
 605                 break;
 606             value_set_si(coset->p[i], 0);
 607             value_set_si(T->p[i][D->Dimension], 0);
 608             value_set_si(T2->p[i][D->Dimension], 0);
 609         }
 610         if (i < 0)
 611             break;
 612     }
 613     Vector_Free(coset);
 614     Matrix_Free(T);
 615     Matrix_Free(T2);
 616     return pl_all;
 617 }
 618
 619 piecewise_lst *bernstein_coefficients_relation(piecewise_lst *pl_all,
 620                     Polyhedron *D, evalue *EP, Polyhedron *ctx,
 621                     const exvector& allvars, const exvector& vars,
 622                     const exvector& params, barvinok_options *options)
 623 {
 624     if (value_zero_p(EP->d) && EP->x.p->type == relation) {
 625         Polyhedron *E = relation_domain(D, &EP->x.p->arr[0], options->MaxRays);
 626         if (E) {
 627             pl_all = bernstein_coefficients_relation(pl_all, E, &EP->x.p->arr[1],
 628                                                      ctx, allvars, vars, params,
 629                                                      options);
 630             Domain_Free(E);
 631         }
 632         /* In principle, we could cut off the edges of this domain too */
 633         if (EP->x.p->size > 2)
 634             pl_all = bernstein_coefficients_relation(pl_all, D, &EP->x.p->arr[2],
 635                                                      ctx, allvars, vars, params,
 636                                                      options);
 637         return pl_all;
 638     }
 639
 640     Matrix *M;
 641     exvector floorvar;
 642     Vector *periods;
 643     ex poly = evalue2ex(EP, allvars, floorvar, &M, &periods);
 644     floorvar.insert(floorvar.end(), vars.begin(), vars.end());
 645     Polyhedron *E = D;
 646     if (M) {
 647         Polyhedron *AE = align_context(D, M->NbColumns-2, options->MaxRays);
 648         E = DomainAddConstraints(AE, M, options->MaxRays);
 649         Matrix_Free(M);
 650         Domain_Free(AE);
 651     }
 652     if (is_exactly_a<fail>(poly)) {
 653         delete pl_all;
 654         return NULL;
 655     }
 656     if (periods)
 657         pl_all = bernstein_coefficients_periodic(pl_all, E, EP, ctx, vars,
 658                                                  params, periods, options);
 659     else
 660         pl_all = bernstein_coefficients(pl_all, E, poly, ctx, params,
 661                                         floorvar, options);
 662     if (periods)
 663         Vector_Free(periods);
 664     if (D != E)
 665         Domain_Free(E);
 666
 667     return pl_all;
 668 }
 669
 670 piecewise_lst *evalue_bernstein_coefficients(piecewise_lst *pl_all, evalue *e,
 671                                       Polyhedron *ctx, const exvector& params,
 672                                       barvinok_options *options)
 673 {
 674     unsigned nparam = ctx->Dimension;
 675     if (EVALUE_IS_ZERO(*e))
 676         return pl_all;
 677     assert(value_zero_p(e->d));
 678     assert(e->x.p->type == partition);
 679     assert(e->x.p->size >= 2);
 680     unsigned nvars = EVALUE_DOMAIN(e->x.p->arr[0])->Dimension - nparam;
 681
 682     exvector vars = constructVariableVector(nvars, "v");
 683     exvector allvars = vars;
 684     allvars.insert(allvars.end(), params.begin(), params.end());
 685
 686     for (int i = 0; i < e->x.p->size/2; ++i) {
 687         pl_all = bernstein_coefficients_relation(pl_all,
 688                         EVALUE_DOMAIN(e->x.p->arr[2*i]), &e->x.p->arr[2*i+1],
 689                         ctx, allvars, vars, params, options);
 690     }
 691     return pl_all;
 692 }
 693
 694 }