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rename cdd2polylib.pl to latte2polylib.pl
[barvinok.git] / barvinok.cc
blob18fc50fadf1c5a30f8fd51c1c44827bc22cc177d
1 #include <assert.h>
2 #include <iostream>
3 #include <vector>
4 #include <deque>
5 #include <string>
6 #include <sstream>
7 #include <gmp.h>
8 #include <NTL/mat_ZZ.h>
9 #include <NTL/LLL.h>
10 #include <barvinok/util.h>
11 extern "C" {
12 #include <polylib/polylibgmp.h>
13 #include <barvinok/evalue.h>
14 #include "piputil.h"
15 }
16 #include "config.h"
17 #include <barvinok/barvinok.h>
18 #include <barvinok/genfun.h>
19 #include "conversion.h"
20 #include "decomposer.h"
21 #include "lattice_point.h"
22 #include "reduce_domain.h"
23
24 #ifdef NTL_STD_CXX
25 using namespace NTL;
26 #endif
27 using std::cerr;
28 using std::cout;
29 using std::endl;
30 using std::vector;
31 using std::deque;
32 using std::string;
33 using std::ostringstream;
34
35 #define ALLOC(t,p) p = (t*)malloc(sizeof(*p))
36
37 static void rays(mat_ZZ& r, Polyhedron *C)
38 {
39 unsigned dim = C->NbRays - 1; /* don't count zero vertex */
40 assert(C->NbRays - 1 == C->Dimension);
41 r.SetDims(dim, dim);
42 ZZ tmp;
43
44 int i, c;
45 for (i = 0, c = 0; i < dim; ++i)
46 if (value_zero_p(C->Ray[i][dim+1])) {
47 for (int j = 0; j < dim; ++j) {
48 value2zz(C->Ray[i][j+1], tmp);
49 r[j][c] = tmp;
50 }
51 ++c;
52 }
53 }
54
55 class dpoly {
56 public:
57 vec_ZZ coeff;
58 dpoly(int d, ZZ& degree, int offset = 0) {
59 coeff.SetLength(d+1);
60
61 int min = d + offset;
62 if (degree >= 0 && degree < ZZ(INIT_VAL, min))
63 min = to_int(degree);
64
65 ZZ c = ZZ(INIT_VAL, 1);
66 if (!offset)
67 coeff[0] = c;
68 for (int i = 1; i <= min; ++i) {
69 c *= (degree -i + 1);
70 c /= i;
71 coeff[i-offset] = c;
72 }
73 }
74 void operator *= (dpoly& f) {
75 assert(coeff.length() == f.coeff.length());
76 vec_ZZ old = coeff;
77 coeff = f.coeff[0] * coeff;
78 for (int i = 1; i < coeff.length(); ++i)
79 for (int j = 0; i+j < coeff.length(); ++j)
80 coeff[i+j] += f.coeff[i] * old[j];
81 }
82 void div(dpoly& d, mpq_t count, ZZ& sign) {
83 int len = coeff.length();
84 Value tmp;
85 value_init(tmp);
86 mpq_t* c = new mpq_t[coeff.length()];
87 mpq_t qtmp;
88 mpq_init(qtmp);
89 for (int i = 0; i < len; ++i) {
90 mpq_init(c[i]);
91 zz2value(coeff[i], tmp);
92 mpq_set_z(c[i], tmp);
93
94 for (int j = 1; j <= i; ++j) {
95 zz2value(d.coeff[j], tmp);
96 mpq_set_z(qtmp, tmp);
97 mpq_mul(qtmp, qtmp, c[i-j]);
98 mpq_sub(c[i], c[i], qtmp);
99 }
100
101 zz2value(d.coeff[0], tmp);
102 mpq_set_z(qtmp, tmp);
103 mpq_div(c[i], c[i], qtmp);
104 }
105 if (sign == -1)
106 mpq_sub(count, count, c[len-1]);
107 else
108 mpq_add(count, count, c[len-1]);
109
110 value_clear(tmp);
111 mpq_clear(qtmp);
112 for (int i = 0; i < len; ++i)
113 mpq_clear(c[i]);
114 delete [] c;
115 }
116 };
117
118 class dpoly_n {
119 public:
120 Matrix *coeff;
121 ~dpoly_n() {
122 Matrix_Free(coeff);
123 }
124 dpoly_n(int d, ZZ& degree_0, ZZ& degree_1, int offset = 0) {
125 Value d0, d1;
126 value_init(d0);
127 value_init(d1);
128 zz2value(degree_0, d0);
129 zz2value(degree_1, d1);
130 coeff = Matrix_Alloc(d+1, d+1+1);
131 value_set_si(coeff->p[0][0], 1);
132 value_set_si(coeff->p[0][d+1], 1);
133 for (int i = 1; i <= d; ++i) {
134 value_multiply(coeff->p[i][0], coeff->p[i-1][0], d0);
135 Vector_Combine(coeff->p[i-1], coeff->p[i-1]+1, coeff->p[i]+1,
136 d1, d0, i);
137 value_set_si(coeff->p[i][d+1], i);
138 value_multiply(coeff->p[i][d+1], coeff->p[i][d+1], coeff->p[i-1][d+1]);
139 value_decrement(d0, d0);
140 }
141 value_clear(d0);
142 value_clear(d1);
143 }
144 void div(dpoly& d, Vector *count, ZZ& sign) {
145 int len = coeff->NbRows;
146 Matrix * c = Matrix_Alloc(coeff->NbRows, coeff->NbColumns);
147 Value tmp;
148 value_init(tmp);
149 for (int i = 0; i < len; ++i) {
150 Vector_Copy(coeff->p[i], c->p[i], len+1);
151 for (int j = 1; j <= i; ++j) {
152 zz2value(d.coeff[j], tmp);
153 value_multiply(tmp, tmp, c->p[i][len]);
154 value_oppose(tmp, tmp);
155 Vector_Combine(c->p[i], c->p[i-j], c->p[i],
156 c->p[i-j][len], tmp, len);
157 value_multiply(c->p[i][len], c->p[i][len], c->p[i-j][len]);
158 }
159 zz2value(d.coeff[0], tmp);
160 value_multiply(c->p[i][len], c->p[i][len], tmp);
161 }
162 if (sign == -1) {
163 value_set_si(tmp, -1);
164 Vector_Scale(c->p[len-1], count->p, tmp, len);
165 value_assign(count->p[len], c->p[len-1][len]);
166 } else
167 Vector_Copy(c->p[len-1], count->p, len+1);
168 Vector_Normalize(count->p, len+1);
169 value_clear(tmp);
170 Matrix_Free(c);
171 }
172 };
173
174 struct dpoly_r_term {
175 int *powers;
176 ZZ coeff;
177 };
178
179 /* len: number of elements in c
180 * each element in c is the coefficient of a power of t
181 * in the MacLaurin expansion
182 */
183 struct dpoly_r {
184 vector< dpoly_r_term * > *c;
185 int len;
186 int dim;
187 ZZ denom;
188
189 void add_term(int i, int * powers, ZZ& coeff) {
190 if (coeff == 0)
191 return;
192 for (int k = 0; k < c[i].size(); ++k) {
193 if (memcmp(c[i][k]->powers, powers, dim * sizeof(int)) == 0) {
194 c[i][k]->coeff += coeff;
195 return;
196 }
197 }
198 dpoly_r_term *t = new dpoly_r_term;
199 t->powers = new int[dim];
200 memcpy(t->powers, powers, dim * sizeof(int));
201 t->coeff = coeff;
202 c[i].push_back(t);
203 }
204 dpoly_r(int len, int dim) {
205 denom = 1;
206 this->len = len;
207 this->dim = dim;
208 c = new vector< dpoly_r_term * > [len];
209 }
210 dpoly_r(dpoly& num, int dim) {
211 denom = 1;
212 len = num.coeff.length();
213 c = new vector< dpoly_r_term * > [len];
214 this->dim = dim;
215 int powers[dim];
216 memset(powers, 0, dim * sizeof(int));
217
218 for (int i = 0; i < len; ++i) {
219 ZZ coeff = num.coeff[i];
220 add_term(i, powers, coeff);
221 }
222 }
223 dpoly_r(dpoly& num, dpoly& den, int pos, int dim) {
224 denom = 1;
225 len = num.coeff.length();
226 c = new vector< dpoly_r_term * > [len];
227 this->dim = dim;
228 int powers[dim];
229
230 for (int i = 0; i < len; ++i) {
231 ZZ coeff = num.coeff[i];
232 memset(powers, 0, dim * sizeof(int));
233 powers[pos] = 1;
234
235 add_term(i, powers, coeff);
236
237 for (int j = 1; j <= i; ++j) {
238 for (int k = 0; k < c[i-j].size(); ++k) {
239 memcpy(powers, c[i-j][k]->powers, dim*sizeof(int));
240 powers[pos]++;
241 coeff = -den.coeff[j-1] * c[i-j][k]->coeff;
242 add_term(i, powers, coeff);
243 }
244 }
245 }
246 //dump();
247 }
248 dpoly_r(dpoly_r* num, dpoly& den, int pos, int dim) {
249 denom = num->denom;
250 len = num->len;
251 c = new vector< dpoly_r_term * > [len];
252 this->dim = dim;
253 int powers[dim];
254 ZZ coeff;
255
256 for (int i = 0 ; i < len; ++i) {
257 for (int k = 0; k < num->c[i].size(); ++k) {
258 memcpy(powers, num->c[i][k]->powers, dim*sizeof(int));
259 powers[pos]++;
260 add_term(i, powers, num->c[i][k]->coeff);
261 }
262
263 for (int j = 1; j <= i; ++j) {
264 for (int k = 0; k < c[i-j].size(); ++k) {
265 memcpy(powers, c[i-j][k]->powers, dim*sizeof(int));
266 powers[pos]++;
267 coeff = -den.coeff[j-1] * c[i-j][k]->coeff;
268 add_term(i, powers, coeff);
269 }
270 }
271 }
272 }
273 ~dpoly_r() {
274 for (int i = 0 ; i < len; ++i)
275 for (int k = 0; k < c[i].size(); ++k) {
276 delete [] c[i][k]->powers;
277 delete c[i][k];
278 }
279 delete [] c;
280 }
281 dpoly_r *div(dpoly& d) {
282 dpoly_r *rc = new dpoly_r(len, dim);
283 rc->denom = power(d.coeff[0], len);
284 ZZ inv_d = rc->denom / d.coeff[0];
285 ZZ coeff;
286
287 for (int i = 0; i < len; ++i) {
288 for (int k = 0; k < c[i].size(); ++k) {
289 coeff = c[i][k]->coeff * inv_d;
290 rc->add_term(i, c[i][k]->powers, coeff);
291 }
292
293 for (int j = 1; j <= i; ++j) {
294 for (int k = 0; k < rc->c[i-j].size(); ++k) {
295 coeff = - d.coeff[j] * rc->c[i-j][k]->coeff / d.coeff[0];
296 rc->add_term(i, rc->c[i-j][k]->powers, coeff);
297 }
298 }
299 }
300 return rc;
301 }
302 void dump(void) {
303 for (int i = 0; i < len; ++i) {
304 cerr << endl;
305 cerr << i << endl;
306 cerr << c[i].size() << endl;
307 for (int j = 0; j < c[i].size(); ++j) {
308 for (int k = 0; k < dim; ++k) {
309 cerr << c[i][j]->powers[k] << " ";
310 }
311 cerr << ": " << c[i][j]->coeff << "/" << denom << endl;
312 }
313 cerr << endl;
314 }
315 }
316 };
317
318 const int MAX_TRY=10;
319 /*
320 * Searches for a vector that is not orthogonal to any
321 * of the rays in rays.
322 */
323 static void nonorthog(mat_ZZ& rays, vec_ZZ& lambda)
324 {
325 int dim = rays.NumCols();
326 bool found = false;
327 lambda.SetLength(dim);
328 if (dim == 0)
329 return;
330
331 for (int i = 2; !found && i <= 50*dim; i+=4) {
332 for (int j = 0; j < MAX_TRY; ++j) {
333 for (int k = 0; k < dim; ++k) {
334 int r = random_int(i)+2;
335 int v = (2*(r%2)-1) * (r >> 1);
336 lambda[k] = v;
337 }
338 int k = 0;
339 for (; k < rays.NumRows(); ++k)
340 if (lambda * rays[k] == 0)
341 break;
342 if (k == rays.NumRows()) {
343 found = true;
344 break;
345 }
346 }
347 }
348 assert(found);
349 }
350
351 static void randomvector(Polyhedron *P, vec_ZZ& lambda, int nvar)
352 {
353 Value tmp;
354 int max = 10 * 16;
355 unsigned int dim = P->Dimension;
356 value_init(tmp);
357
358 for (int i = 0; i < P->NbRays; ++i) {
359 for (int j = 1; j <= dim; ++j) {
360 value_absolute(tmp, P->Ray[i][j]);
361 int t = VALUE_TO_LONG(tmp) * 16;
362 if (t > max)
363 max = t;
364 }
365 }
366 for (int i = 0; i < P->NbConstraints; ++i) {
367 for (int j = 1; j <= dim; ++j) {
368 value_absolute(tmp, P->Constraint[i][j]);
369 int t = VALUE_TO_LONG(tmp) * 16;
370 if (t > max)
371 max = t;
372 }
373 }
374 value_clear(tmp);
375
376 lambda.SetLength(nvar);
377 for (int k = 0; k < nvar; ++k) {
378 int r = random_int(max*dim)+2;
379 int v = (2*(r%2)-1) * (max/2*dim + (r >> 1));
380 lambda[k] = v;
381 }
382 }
383
384 static void add_rays(mat_ZZ& rays, Polyhedron *i, int *r, int nvar = -1,
385 bool all = false)
386 {
387 unsigned dim = i->Dimension;
388 if (nvar == -1)
389 nvar = dim;
390 for (int k = 0; k < i->NbRays; ++k) {
391 if (!value_zero_p(i->Ray[k][dim+1]))
392 continue;
393 if (!all && nvar != dim && First_Non_Zero(i->Ray[k]+1, nvar) == -1)
394 continue;
395 values2zz(i->Ray[k]+1, rays[(*r)++], nvar);
396 }
397 }
398
399 static void mask_r(Matrix *f, int nr, Vector *lcm, int p, Vector *val, evalue *ev)
400 {
401 unsigned nparam = lcm->Size;
402
403 if (p == nparam) {
404 Vector * prod = Vector_Alloc(f->NbRows);
405 Matrix_Vector_Product(f, val->p, prod->p);
406 int isint = 1;
407 for (int i = 0; i < nr; ++i) {
408 value_modulus(prod->p[i], prod->p[i], f->p[i][nparam+1]);
409 isint &= value_zero_p(prod->p[i]);
410 }
411 value_set_si(ev->d, 1);
412 value_init(ev->x.n);
413 value_set_si(ev->x.n, isint);
414 Vector_Free(prod);
415 return;
416 }
417
418 Value tmp;
419 value_init(tmp);
420 if (value_one_p(lcm->p[p]))
421 mask_r(f, nr, lcm, p+1, val, ev);
422 else {
423 value_assign(tmp, lcm->p[p]);
424 value_set_si(ev->d, 0);
425 ev->x.p = new_enode(periodic, VALUE_TO_INT(tmp), p+1);
426 do {
427 value_decrement(tmp, tmp);
428 value_assign(val->p[p], tmp);
429 mask_r(f, nr, lcm, p+1, val, &ev->x.p->arr[VALUE_TO_INT(tmp)]);
430 } while (value_pos_p(tmp));
431 }
432 value_clear(tmp);
433 }
434
435 #ifdef USE_MODULO
436 static void mask(Matrix *f, evalue *factor)
437 {
438 int nr = f->NbRows, nc = f->NbColumns;
439 int n;
440 bool found = false;
441 for (n = 0; n < nr && value_notzero_p(f->p[n][nc-1]); ++n)
442 if (value_notone_p(f->p[n][nc-1]) &&
443 value_notmone_p(f->p[n][nc-1]))
444 found = true;
445 if (!found)
446 return;
447
448 evalue EP;
449 nr = n;
450
451 Value m;
452 value_init(m);
453
454 evalue EV;
455 value_init(EV.d);
456 value_init(EV.x.n);
457 value_set_si(EV.x.n, 1);
458
459 for (n = 0; n < nr; ++n) {
460 value_assign(m, f->p[n][nc-1]);
461 if (value_one_p(m) || value_mone_p(m))
462 continue;
463
464 int j = normal_mod(f->p[n], nc-1, &m);
465 if (j == nc-1) {
466 free_evalue_refs(factor);
467 value_init(factor->d);
468 evalue_set_si(factor, 0, 1);
469 break;
470 }
471 vec_ZZ row;
472 values2zz(f->p[n], row, nc-1);
473 ZZ g;
474 value2zz(m, g);
475 if (j < (nc-1)-1 && row[j] > g/2) {
476 for (int k = j; k < (nc-1); ++k)
477 if (row[k] != 0)
478 row[k] = g - row[k];
479 }
480
481 value_init(EP.d);
482 value_set_si(EP.d, 0);
483 EP.x.p = new_enode(relation, 2, 0);
484 value_clear(EP.x.p->arr[1].d);
485 EP.x.p->arr[1] = *factor;
486 evalue *ev = &EP.x.p->arr[0];
487 value_set_si(ev->d, 0);
488 ev->x.p = new_enode(fractional, 3, -1);
489 evalue_set_si(&ev->x.p->arr[1], 0, 1);
490 evalue_set_si(&ev->x.p->arr[2], 1, 1);
491 evalue *E = multi_monom(row);
492 value_assign(EV.d, m);
493 emul(&EV, E);
494 value_clear(ev->x.p->arr[0].d);
495 ev->x.p->arr[0] = *E;
496 delete E;
497 *factor = EP;
498 }
499
500 value_clear(m);
501 free_evalue_refs(&EV);
502 }
503 #else
504 /*
505 *
506 */
507 static void mask(Matrix *f, evalue *factor)
508 {
509 int nr = f->NbRows, nc = f->NbColumns;
510 int n;
511 bool found = false;
512 for (n = 0; n < nr && value_notzero_p(f->p[n][nc-1]); ++n)
513 if (value_notone_p(f->p[n][nc-1]) &&
514 value_notmone_p(f->p[n][nc-1]))
515 found = true;
516 if (!found)
517 return;
518
519 Value tmp;
520 value_init(tmp);
521 nr = n;
522 unsigned np = nc - 2;
523 Vector *lcm = Vector_Alloc(np);
524 Vector *val = Vector_Alloc(nc);
525 Vector_Set(val->p, 0, nc);
526 value_set_si(val->p[np], 1);
527 Vector_Set(lcm->p, 1, np);
528 for (n = 0; n < nr; ++n) {
529 if (value_one_p(f->p[n][nc-1]) ||
530 value_mone_p(f->p[n][nc-1]))
531 continue;
532 for (int j = 0; j < np; ++j)
533 if (value_notzero_p(f->p[n][j])) {
534 Gcd(f->p[n][j], f->p[n][nc-1], &tmp);
535 value_division(tmp, f->p[n][nc-1], tmp);
536 value_lcm(tmp, lcm->p[j], &lcm->p[j]);
537 }
538 }
539 evalue EP;
540 value_init(EP.d);
541 mask_r(f, nr, lcm, 0, val, &EP);
542 value_clear(tmp);
543 Vector_Free(val);
544 Vector_Free(lcm);
545 emul(&EP,factor);
546 free_evalue_refs(&EP);
547 }
548 #endif
549
550 /* This structure encodes the power of the term in a rational generating function.
551 *
552 * Either E == NULL or constant = 0
553 * If E != NULL, then the power is E
554 * If E == NULL, then the power is coeff * param[pos] + constant
555 */
556 struct term_info {
557 evalue *E;
558 ZZ constant;
559 ZZ coeff;
560 int pos;
561 };
562
563 /* Returns the power of (t+1) in the term of a rational generating function,
564 * i.e., the scalar product of the actual lattice point and lambda.
565 * The lattice point is the unique lattice point in the fundamental parallelepiped
566 * of the unimodual cone i shifted to the parametric vertex V.
567 *
568 * PD is the parameter domain, which, if != NULL, may be used to simply the
569 * resulting expression.
570 *
571 * The result is returned in term.
572 */
573 void lattice_point(
574 Param_Vertices* V, Polyhedron *i, vec_ZZ& lambda, term_info* term,
575 Polyhedron *PD)
576 {
577 unsigned nparam = V->Vertex->NbColumns - 2;
578 unsigned dim = i->Dimension;
579 mat_ZZ vertex;
580 vertex.SetDims(V->Vertex->NbRows, nparam+1);
581 Value lcm, tmp;
582 value_init(lcm);
583 value_init(tmp);
584 value_set_si(lcm, 1);
585 for (int j = 0; j < V->Vertex->NbRows; ++j) {
586 value_lcm(lcm, V->Vertex->p[j][nparam+1], &lcm);
587 }
588 if (value_notone_p(lcm)) {
589 Matrix * mv = Matrix_Alloc(dim, nparam+1);
590 for (int j = 0 ; j < dim; ++j) {
591 value_division(tmp, lcm, V->Vertex->p[j][nparam+1]);
592 Vector_Scale(V->Vertex->p[j], mv->p[j], tmp, nparam+1);
593 }
594
595 term->E = lattice_point(i, lambda, mv, lcm, PD);
596 term->constant = 0;
597
598 Matrix_Free(mv);
599 value_clear(lcm);
600 value_clear(tmp);
601 return;
602 }
603 for (int i = 0; i < V->Vertex->NbRows; ++i) {
604 assert(value_one_p(V->Vertex->p[i][nparam+1])); // for now
605 values2zz(V->Vertex->p[i], vertex[i], nparam+1);
606 }
607
608 vec_ZZ num;
609 num = lambda * vertex;
610
611 int p = -1;
612 int nn = 0;
613 for (int j = 0; j < nparam; ++j)
614 if (num[j] != 0) {
615 ++nn;
616 p = j;
617 }
618 if (nn >= 2) {
619 term->E = multi_monom(num);
620 term->constant = 0;
621 } else {
622 term->E = NULL;
623 term->constant = num[nparam];
624 term->pos = p;
625 if (p != -1)
626 term->coeff = num[p];
627 }
628
629 value_clear(lcm);
630 value_clear(tmp);
631 }
632
633 static void normalize(ZZ& sign, ZZ& num, vec_ZZ& den)
634 {
635 unsigned dim = den.length();
636
637 int change = 0;
638
639 for (int j = 0; j < den.length(); ++j) {
640 if (den[j] > 0)
641 change ^= 1;
642 else {
643 den[j] = abs(den[j]);
644 num += den[j];
645 }
646 }
647 if (change)
648 sign = -sign;
649 }
650
651 /* input:
652 * f: the powers in the denominator for the remaining vars
653 * each row refers to a factor
654 * den_s: for each factor, the power of (s+1)
655 * sign
656 * num_s: powers in the numerator corresponding to the summed vars
657 * num_p: powers in the numerator corresponding to the remaining vars
658 * number of rays in cone: "dim" = "k"
659 * length of each ray: "dim" = "d"
660 * for now, it is assumed: k == d
661 * output:
662 * den_p: for each factor
663 * 0: independent of remaining vars
664 * 1: power corresponds to corresponding row in f
665 *
666 * all inputs are subject to change
667 */
668 static void normalize(ZZ& sign,
669 ZZ& num_s, vec_ZZ& num_p, vec_ZZ& den_s, vec_ZZ& den_p,
670 mat_ZZ& f)
671 {
672 unsigned dim = f.NumRows();
673 unsigned nparam = num_p.length();
674 unsigned nvar = dim - nparam;
675
676 int change = 0;
677
678 for (int j = 0; j < den_s.length(); ++j) {
679 if (den_s[j] == 0) {
680 den_p[j] = 1;
681 continue;
682 }
683 int k;
684 for (k = 0; k < nparam; ++k)
685 if (f[j][k] != 0)
686 break;
687 if (k < nparam) {
688 den_p[j] = 1;
689 if (den_s[j] > 0) {
690 f[j] = -f[j];
691 num_p += f[j];
692 }
693 } else
694 den_p[j] = 0;
695 if (den_s[j] > 0)
696 change ^= 1;
697 else {
698 den_s[j] = abs(den_s[j]);
699 num_s += den_s[j];
700 }
701 }
702
703 if (change)
704 sign = -sign;
705 }
706
707 struct counter : public polar_decomposer {
708 vec_ZZ lambda;
709 mat_ZZ rays;
710 vec_ZZ vertex;
711 vec_ZZ den;
712 ZZ sign;
713 ZZ num;
714 int j;
715 Polyhedron *P;
716 unsigned dim;
717 mpq_t count;
718
719 counter(Polyhedron *P) {
720 this->P = P;
721 dim = P->Dimension;
722 rays.SetDims(dim, dim);
723 den.SetLength(dim);
724 mpq_init(count);
725 }
726
727 void start(unsigned MaxRays);
728
729 ~counter() {
730 mpq_clear(count);
731 }
732
733 virtual void handle_polar(Polyhedron *P, int sign);
734 };
735
736 struct OrthogonalException {} Orthogonal;
737
738 void counter::handle_polar(Polyhedron *C, int s)
739 {
740 int r = 0;
741 assert(C->NbRays-1 == dim);
742 add_rays(rays, C, &r);
743 for (int k = 0; k < dim; ++k) {
744 if (lambda * rays[k] == 0)
745 throw Orthogonal;
746 }
747
748 sign = s;
749
750 lattice_point(P->Ray[j]+1, C, vertex);
751 num = vertex * lambda;
752 den = rays * lambda;
753 normalize(sign, num, den);
754
755 dpoly d(dim, num);
756 dpoly n(dim, den[0], 1);
757 for (int k = 1; k < dim; ++k) {
758 dpoly fact(dim, den[k], 1);
759 n *= fact;
760 }
761 d.div(n, count, sign);
762 }
763
764 void counter::start(unsigned MaxRays)
765 {
766 for (;;) {
767 try {
768 randomvector(P, lambda, dim);
769 for (j = 0; j < P->NbRays; ++j) {
770 Polyhedron *C = supporting_cone(P, j);
771 decompose(C, MaxRays);
772 }
773 break;
774 } catch (OrthogonalException &e) {
775 mpq_set_si(count, 0, 0);
776 }
777 }
778 }
779
780 /* base for non-parametric counting */
781 struct np_base : public polar_decomposer {
782 int current_vertex;
783 Polyhedron *P;
784 unsigned dim;
785
786 np_base(Polyhedron *P, unsigned dim) {
787 this->P = P;
788 this->dim = dim;
789 }
790 };
791
792 struct reducer : public np_base {
793 vec_ZZ vertex;
794 //vec_ZZ den;
795 ZZ sgn;
796 ZZ num;
797 ZZ one;
798 mpq_t tcount;
799 mpz_t tn;
800 mpz_t td;
801 int lower; // call base when only this many variables is left
802
803 reducer(Polyhedron *P) : np_base(P, P->Dimension) {
804 //den.SetLength(dim);
805 mpq_init(tcount);
806 mpz_init(tn);
807 mpz_init(td);
808 one = 1;
809 }
810
811 void start(unsigned MaxRays);
812
813 ~reducer() {
814 mpq_clear(tcount);
815 mpz_clear(tn);
816 mpz_clear(td);
817 }
818
819 virtual void handle_polar(Polyhedron *P, int sign);
820 void reduce(ZZ c, ZZ cd, vec_ZZ& num, mat_ZZ& den_f);
821 virtual void base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f) = 0;
822 virtual void split(vec_ZZ& num, ZZ& num_s, vec_ZZ& num_p,
823 mat_ZZ& den_f, vec_ZZ& den_s, mat_ZZ& den_r) = 0;
824 };
825
826 void reducer::reduce(ZZ c, ZZ cd, vec_ZZ& num, mat_ZZ& den_f)
827 {
828 unsigned len = den_f.NumRows(); // number of factors in den
829
830 if (num.length() == lower) {
831 base(c, cd, num, den_f);
832 return;
833 }
834 assert(num.length() > 1);
835
836 vec_ZZ den_s;
837 mat_ZZ den_r;
838 ZZ num_s;
839 vec_ZZ num_p;
840
841 split(num, num_s, num_p, den_f, den_s, den_r);
842
843 vec_ZZ den_p;
844 den_p.SetLength(len);
845
846 normalize(c, num_s, num_p, den_s, den_p, den_r);
847
848 int only_param = 0; // k-r-s from text
849 int no_param = 0; // r from text
850 for (int k = 0; k < len; ++k) {
851 if (den_p[k] == 0)
852 ++no_param;
853 else if (den_s[k] == 0)
854 ++only_param;
855 }
856 if (no_param == 0) {
857 reduce(c, cd, num_p, den_r);
858 } else {
859 int k, l;
860 mat_ZZ pden;
861 pden.SetDims(only_param, den_r.NumCols());
862
863 for (k = 0, l = 0; k < len; ++k)
864 if (den_s[k] == 0)
865 pden[l++] = den_r[k];
866
867 for (k = 0; k < len; ++k)
868 if (den_p[k] == 0)
869 break;
870
871 dpoly n(no_param, num_s);
872 dpoly D(no_param, den_s[k], 1);
873 for ( ; ++k < len; )
874 if (den_p[k] == 0) {
875 dpoly fact(no_param, den_s[k], 1);
876 D *= fact;
877 }
878
879 if (no_param + only_param == len) {
880 mpq_set_si(tcount, 0, 1);
881 n.div(D, tcount, one);
882
883 ZZ qn, qd;
884 value2zz(mpq_numref(tcount), qn);
885 value2zz(mpq_denref(tcount), qd);
886
887 qn *= c;
888 qd *= cd;
889
890 if (qn != 0)
891 reduce(qn, qd, num_p, pden);
892 } else {
893 dpoly_r * r = 0;
894
895 for (k = 0; k < len; ++k) {
896 if (den_s[k] == 0 || den_p[k] == 0)
897 continue;
898
899 dpoly pd(no_param-1, den_s[k], 1);
900
901 int l;
902 for (l = 0; l < k; ++l)
903 if (den_r[l] == den_r[k])
904 break;
905
906 if (r == 0)
907 r = new dpoly_r(n, pd, l, len);
908 else {
909 dpoly_r *nr = new dpoly_r(r, pd, l, len);
910 delete r;
911 r = nr;
912 }
913 }
914
915 dpoly_r *rc = r->div(D);
916
917 rc->denom *= cd;
918
919 int common = pden.NumRows();
920 vector< dpoly_r_term * >& final = rc->c[rc->len-1];
921 int rows;
922 for (int j = 0; j < final.size(); ++j) {
923 if (final[j]->coeff == 0)
924 continue;
925 rows = common;
926 pden.SetDims(rows, pden.NumCols());
927 for (int k = 0; k < rc->dim; ++k) {
928 int n = final[j]->powers[k];
929 if (n == 0)
930 continue;
931 pden.SetDims(rows+n, pden.NumCols());
932 for (int l = 0; l < n; ++l)
933 pden[rows+l] = den_r[k];
934 rows += n;
935 }
936 final[j]->coeff *= c;
937 reduce(final[j]->coeff, rc->denom, num_p, pden);
938 }
939
940 delete rc;
941 delete r;
942 }
943 }
944 }
945
946 void reducer::handle_polar(Polyhedron *C, int s)
947 {
948 assert(C->NbRays-1 == dim);
949
950 sgn = s;
951
952 lattice_point(P->Ray[current_vertex]+1, C, vertex);
953
954 mat_ZZ den;
955 den.SetDims(dim, dim);
956
957 int r;
958 for (r = 0; r < dim; ++r)
959 values2zz(C->Ray[r]+1, den[r], dim);
960
961 reduce(sgn, one, vertex, den);
962 }
963
964 void reducer::start(unsigned MaxRays)
965 {
966 for (current_vertex = 0; current_vertex < P->NbRays; ++current_vertex) {
967 Polyhedron *C = supporting_cone(P, current_vertex);
968 decompose(C, MaxRays);
969 }
970 }
971
972 struct ireducer : public reducer {
973 ireducer(Polyhedron *P) : reducer(P) {}
974
975 virtual void split(vec_ZZ& num, ZZ& num_s, vec_ZZ& num_p,
976 mat_ZZ& den_f, vec_ZZ& den_s, mat_ZZ& den_r) {
977 unsigned len = den_f.NumRows(); // number of factors in den
978 unsigned d = num.length() - 1;
979
980 den_s.SetLength(len);
981 den_r.SetDims(len, d);
982
983 for (int r = 0; r < len; ++r) {
984 den_s[r] = den_f[r][0];
985 for (int k = 1; k <= d; ++k)
986 den_r[r][k-1] = den_f[r][k];
987 }
988
989 num_s = num[0];
990 num_p.SetLength(d);
991 for (int k = 1 ; k <= d; ++k)
992 num_p[k-1] = num[k];
993 }
994 };
995
996 // incremental counter
997 struct icounter : public ireducer {
998 mpq_t count;
999
1000 icounter(Polyhedron *P) : ireducer(P) {
1001 mpq_init(count);
1002 lower = 1;
1003 }
1004 ~icounter() {
1005 mpq_clear(count);
1006 }
1007 virtual void base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f);
1008 };
1009
1010 void icounter::base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f)
1011 {
1012 int r;
1013 unsigned len = den_f.NumRows(); // number of factors in den
1014 vec_ZZ den_s;
1015 den_s.SetLength(len);
1016 ZZ num_s = num[0];
1017 for (r = 0; r < len; ++r)
1018 den_s[r] = den_f[r][0];
1019 normalize(c, num_s, den_s);
1020
1021 dpoly n(len, num_s);
1022 dpoly D(len, den_s[0], 1);
1023 for (int k = 1; k < len; ++k) {
1024 dpoly fact(len, den_s[k], 1);
1025 D *= fact;
1026 }
1027 mpq_set_si(tcount, 0, 1);
1028 n.div(D, tcount, one);
1029 zz2value(c, tn);
1030 zz2value(cd, td);
1031 mpz_mul(mpq_numref(tcount), mpq_numref(tcount), tn);
1032 mpz_mul(mpq_denref(tcount), mpq_denref(tcount), td);
1033 mpq_canonicalize(tcount);
1034 mpq_add(count, count, tcount);
1035 }
1036
1037 /* base for generating function counting */
1038 struct gf_base {
1039 np_base *base;
1040 gen_fun *gf;
1041
1042 gf_base(np_base *npb, unsigned nparam) : base(npb) {
1043 gf = new gen_fun(Polyhedron_Project(base->P, nparam));
1044 }
1045 void start(unsigned MaxRays);
1046 };
1047
1048 void gf_base::start(unsigned MaxRays)
1049 {
1050 for (int i = 0; i < base->P->NbRays; ++i) {
1051 if (!value_pos_p(base->P->Ray[i][base->dim+1]))
1052 continue;
1053
1054 Polyhedron *C = supporting_cone(base->P, i);
1055 base->current_vertex = i;
1056 base->decompose(C, MaxRays);
1057 }
1058 }
1059
1060 struct partial_ireducer : public ireducer, public gf_base {
1061 partial_ireducer(Polyhedron *P, unsigned nparam) :
1062 ireducer(P), gf_base(this, nparam) {
1063 lower = nparam;
1064 }
1065 ~partial_ireducer() {
1066 }
1067 virtual void base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f);
1068 /* we want to override the start method from reducer with the one from gf_base */
1069 void start(unsigned MaxRays) {
1070 gf_base::start(MaxRays);
1071 }
1072 };
1073
1074 void partial_ireducer::base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f)
1075 {
1076 gf->add(c, cd, num, den_f);
1077 }
1078
1079 struct partial_reducer : public reducer, public gf_base {
1080 vec_ZZ lambda;
1081 vec_ZZ tmp;
1082
1083 partial_reducer(Polyhedron *P, unsigned nparam) :
1084 reducer(P), gf_base(this, nparam) {
1085 lower = nparam;
1086
1087 tmp.SetLength(dim - nparam);
1088 randomvector(P, lambda, dim - nparam);
1089 }
1090 ~partial_reducer() {
1091 }
1092 virtual void base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f);
1093 /* we want to override the start method from reducer with the one from gf_base */
1094 void start(unsigned MaxRays) {
1095 gf_base::start(MaxRays);
1096 }
1097
1098 virtual void split(vec_ZZ& num, ZZ& num_s, vec_ZZ& num_p,
1099 mat_ZZ& den_f, vec_ZZ& den_s, mat_ZZ& den_r) {
1100 unsigned len = den_f.NumRows(); // number of factors in den
1101 unsigned nvar = tmp.length();
1102
1103 den_s.SetLength(len);
1104 den_r.SetDims(len, lower);
1105
1106 for (int r = 0; r < len; ++r) {
1107 for (int k = 0; k < nvar; ++k)
1108 tmp[k] = den_f[r][k];
1109 den_s[r] = tmp * lambda;
1110
1111 for (int k = nvar; k < dim; ++k)
1112 den_r[r][k-nvar] = den_f[r][k];
1113 }
1114
1115 for (int k = 0; k < nvar; ++k)
1116 tmp[k] = num[k];
1117 num_s = tmp *lambda;
1118 num_p.SetLength(lower);
1119 for (int k = nvar ; k < dim; ++k)
1120 num_p[k-nvar] = num[k];
1121 }
1122 };
1123
1124 void partial_reducer::base(ZZ& c, ZZ& cd, vec_ZZ& num, mat_ZZ& den_f)
1125 {
1126 gf->add(c, cd, num, den_f);
1127 }
1128
1129 struct bfc_term_base {
1130 // the number of times a given factor appears in the denominator
1131 int *powers;
1132 mat_ZZ terms;
1133
1134 bfc_term_base(int len) {
1135 powers = new int[len];
1136 }
1137
1138 virtual ~bfc_term_base() {
1139 delete [] powers;
1140 }
1141 };
1142
1143 struct bfc_term : public bfc_term_base {
1144 vec_ZZ cn;
1145 vec_ZZ cd;
1146
1147 bfc_term(int len) : bfc_term_base(len) {}
1148 };
1149
1150 struct bfe_term : public bfc_term_base {
1151 vector<evalue *> factors;
1152
1153 bfe_term(int len) : bfc_term_base(len) {
1154 }
1155
1156 ~bfe_term() {
1157 for (int i = 0; i < factors.size(); ++i) {
1158 if (!factors[i])
1159 continue;
1160 free_evalue_refs(factors[i]);
1161 delete factors[i];
1162 }
1163 }
1164 };
1165
1166 typedef vector< bfc_term_base * > bfc_vec;
1167
1168 struct bf_reducer;
1169
1170 struct bf_base : public np_base {
1171 ZZ one;
1172 mpq_t tcount;
1173 mpz_t tn;
1174 mpz_t td;
1175 int lower; // call base when only this many variables is left
1176
1177 bf_base(Polyhedron *P, unsigned dim) : np_base(P, dim) {
1178 mpq_init(tcount);
1179 mpz_init(tn);
1180 mpz_init(td);
1181 one = 1;
1182 }
1183
1184 ~bf_base() {
1185 mpq_clear(tcount);
1186 mpz_clear(tn);
1187 mpz_clear(td);
1188 }
1189
1190 void start(unsigned MaxRays);
1191 virtual void handle_polar(Polyhedron *P, int sign);
1192 int setup_factors(Polyhedron *P, mat_ZZ& factors, bfc_term_base* t, int s);
1193
1194 bfc_term_base* find_bfc_term(bfc_vec& v, int *powers, int len);
1195 void add_term(bfc_term_base *t, vec_ZZ& num1, vec_ZZ& num);
1196 void add_term(bfc_term_base *t, vec_ZZ& num);
1197
1198 void reduce(mat_ZZ& factors, bfc_vec& v);
1199 virtual void base(mat_ZZ& factors, bfc_vec& v) = 0;
1200
1201 virtual bfc_term_base* new_bf_term(int len) = 0;
1202 virtual void set_factor(bfc_term_base *t, int k, int change) = 0;
1203 virtual void set_factor(bfc_term_base *t, int k, mpq_t &f, int change) = 0;
1204 virtual void set_factor(bfc_term_base *t, int k, ZZ& n, ZZ& d, int change) = 0;
1205 virtual void update_term(bfc_term_base *t, int i) = 0;
1206 virtual void insert_term(bfc_term_base *t, int i) = 0;
1207 virtual bool constant_vertex(int dim) = 0;
1208 virtual void cum(bf_reducer *bfr, bfc_term_base *t, int k,
1209 dpoly_r *r) = 0;
1210 };
1211
1212 static int lex_cmp(vec_ZZ& a, vec_ZZ& b)
1213 {
1214 assert(a.length() == b.length());
1215
1216 for (int j = 0; j < a.length(); ++j)
1217 if (a[j] != b[j])
1218 return a[j] < b[j] ? -1 : 1;
1219 return 0;
1220 }
1221
1222 void bf_base::add_term(bfc_term_base *t, vec_ZZ& num_orig, vec_ZZ& extra_num)
1223 {
1224 vec_ZZ num;
1225 int d = num_orig.length();
1226 num.SetLength(d-1);
1227 for (int l = 0; l < d-1; ++l)
1228 num[l] = num_orig[l+1] + extra_num[l];
1229
1230 add_term(t, num);
1231 }
1232
1233 void bf_base::add_term(bfc_term_base *t, vec_ZZ& num)
1234 {
1235 int len = t->terms.NumRows();
1236 int i, r;
1237 for (i = 0; i < len; ++i) {
1238 r = lex_cmp(t->terms[i], num);
1239 if (r >= 0)
1240 break;
1241 }
1242 if (i == len || r > 0) {
1243 t->terms.SetDims(len+1, num.length());
1244 insert_term(t, i);
1245 t->terms[i] = num;
1246 } else {
1247 // i < len && r == 0
1248 update_term(t, i);
1249 }
1250 }
1251
1252 static void print_int_vector(int *v, int len, char *name)
1253 {
1254 cerr << name << endl;
1255 for (int j = 0; j < len; ++j) {
1256 cerr << v[j] << " ";
1257 }
1258 cerr << endl;
1259 }
1260
1261 static void print_bfc_terms(mat_ZZ& factors, bfc_vec& v)
1262 {
1263 cerr << endl;
1264 cerr << "factors" << endl;
1265 cerr << factors << endl;
1266 for (int i = 0; i < v.size(); ++i) {
1267 cerr << "term: " << i << endl;
1268 print_int_vector(v[i]->powers, factors.NumRows(), "powers");
1269 cerr << "terms" << endl;
1270 cerr << v[i]->terms << endl;
1271 bfc_term* bfct = static_cast<bfc_term *>(v[i]);
1272 cerr << bfct->cn << endl;
1273 cerr << bfct->cd << endl;
1274 }
1275 }
1276
1277 static void print_bfe_terms(mat_ZZ& factors, bfc_vec& v)
1278 {
1279 cerr << endl;
1280 cerr << "factors" << endl;
1281 cerr << factors << endl;
1282 for (int i = 0; i < v.size(); ++i) {
1283 cerr << "term: " << i << endl;
1284 print_int_vector(v[i]->powers, factors.NumRows(), "powers");
1285 cerr << "terms" << endl;
1286 cerr << v[i]->terms << endl;
1287 bfe_term* bfet = static_cast<bfe_term *>(v[i]);
1288 for (int j = 0; j < v[i]->terms.NumRows(); ++j) {
1289 char * test[] = {"a", "b"};
1290 print_evalue(stderr, bfet->factors[j], test);
1291 fprintf(stderr, "\n");
1292 }
1293 }
1294 }
1295
1296 bfc_term_base* bf_base::find_bfc_term(bfc_vec& v, int *powers, int len)
1297 {
1298 bfc_vec::iterator i;
1299 for (i = v.begin(); i != v.end(); ++i) {
1300 int j;
1301 for (j = 0; j < len; ++j)
1302 if ((*i)->powers[j] != powers[j])
1303 break;
1304 if (j == len)
1305 return (*i);
1306 if ((*i)->powers[j] > powers[j])
1307 break;
1308 }
1309
1310 bfc_term_base* t = new_bf_term(len);
1311 v.insert(i, t);
1312 memcpy(t->powers, powers, len * sizeof(int));
1313
1314 return t;
1315 }
1316
1317 struct bf_reducer {
1318 mat_ZZ& factors;
1319 bfc_vec& v;
1320 bf_base *bf;
1321
1322 unsigned nf;
1323 unsigned d;
1324
1325 mat_ZZ nfactors;
1326 int *old2new;
1327 int *sign;
1328 unsigned int nnf;
1329 bfc_vec vn;
1330
1331 vec_ZZ extra_num;
1332 int changes;
1333 int no_param; // r from text
1334 int only_param; // k-r-s from text
1335 int total_power; // k from text
1336
1337 // created in compute_reduced_factors
1338 int *bpowers;
1339 // set in update_powers
1340 int *npowers;
1341 vec_ZZ l_extra_num;
1342 int l_changes;
1343
1344 bf_reducer(mat_ZZ& factors, bfc_vec& v, bf_base *bf)
1345 : factors(factors), v(v), bf(bf) {
1346 nf = factors.NumRows();
1347 d = factors.NumCols();
1348 old2new = new int[nf];
1349 sign = new int[nf];
1350
1351 extra_num.SetLength(d-1);
1352 }
1353 ~bf_reducer() {
1354 delete [] old2new;
1355 delete [] sign;
1356 delete [] npowers;
1357 delete [] bpowers;
1358 }
1359
1360 void compute_reduced_factors();
1361 void compute_extra_num(int i);
1362
1363 void reduce();
1364
1365 void update_powers(int *powers, int len);
1366 };
1367
1368 void bf_reducer::compute_extra_num(int i)
1369 {
1370 clear(extra_num);
1371 changes = 0;
1372 no_param = 0; // r from text
1373 only_param = 0; // k-r-s from text
1374 total_power = 0; // k from text
1375
1376 for (int j = 0; j < nf; ++j) {
1377 if (v[i]->powers[j] == 0)
1378 continue;
1379
1380 total_power += v[i]->powers[j];
1381 if (factors[j][0] == 0) {
1382 only_param += v[i]->powers[j];
1383 continue;
1384 }
1385
1386 if (old2new[j] == -1)
1387 no_param += v[i]->powers[j];
1388 else
1389 extra_num += -sign[j] * v[i]->powers[j] * nfactors[old2new[j]];
1390 changes += v[i]->powers[j];
1391 }
1392 }
1393
1394 void bf_reducer::update_powers(int *powers, int len)
1395 {
1396 for (int l = 0; l < nnf; ++l)
1397 npowers[l] = bpowers[l];
1398
1399 l_extra_num = extra_num;
1400 l_changes = changes;
1401
1402 for (int l = 0; l < len; ++l) {
1403 int n = powers[l];
1404 if (n == 0)
1405 continue;
1406 assert(old2new[l] != -1);
1407
1408 npowers[old2new[l]] += n;
1409 // interpretation of sign has been inverted
1410 // since we inverted the power for specialization
1411 if (sign[l] == 1) {
1412 l_extra_num += n * nfactors[old2new[l]];
1413 l_changes += n;
1414 }
1415 }
1416 }
1417
1418
1419 void bf_reducer::compute_reduced_factors()
1420 {
1421 unsigned nf = factors.NumRows();
1422 unsigned d = factors.NumCols();
1423 nnf = 0;
1424 nfactors.SetDims(nnf, d-1);
1425
1426 for (int i = 0; i < nf; ++i) {
1427 int j;
1428 int s = 1;
1429 for (j = 0; j < nnf; ++j) {
1430 int k;
1431 for (k = 1; k < d; ++k)
1432 if (factors[i][k] != 0 || nfactors[j][k-1] != 0)
1433 break;
1434 if (k < d && factors[i][k] == -nfactors[j][k-1])
1435 s = -1;
1436 for (; k < d; ++k)
1437 if (factors[i][k] != s * nfactors[j][k-1])
1438 break;
1439 if (k == d)
1440 break;
1441 }
1442 old2new[i] = j;
1443 if (j == nnf) {
1444 int k;
1445 for (k = 1; k < d; ++k)
1446 if (factors[i][k] != 0)
1447 break;
1448 if (k < d) {
1449 if (factors[i][k] < 0)
1450 s = -1;
1451 nfactors.SetDims(++nnf, d-1);
1452 for (int k = 1; k < d; ++k)
1453 nfactors[j][k-1] = s * factors[i][k];
1454 } else
1455 old2new[i] = -1;
1456 }
1457 sign[i] = s;
1458 }
1459 npowers = new int[nnf];
1460 bpowers = new int[nnf];
1461 }
1462
1463 void bf_reducer::reduce()
1464 {
1465 compute_reduced_factors();
1466
1467 for (int i = 0; i < v.size(); ++i) {
1468 compute_extra_num(i);
1469
1470 if (no_param == 0) {
1471 vec_ZZ extra_num;
1472 extra_num.SetLength(d-1);
1473 int changes = 0;
1474 int npowers[nnf];
1475 for (int k = 0; k < nnf; ++k)
1476 npowers[k] = 0;
1477 for (int k = 0; k < nf; ++k) {
1478 assert(old2new[k] != -1);
1479 npowers[old2new[k]] += v[i]->powers[k];
1480 if (sign[k] == -1) {
1481 extra_num += v[i]->powers[k] * nfactors[old2new[k]];
1482 changes += v[i]->powers[k];
1483 }
1484 }
1485
1486 bfc_term_base * t = bf->find_bfc_term(vn, npowers, nnf);
1487 for (int k = 0; k < v[i]->terms.NumRows(); ++k) {
1488 bf->set_factor(v[i], k, changes % 2);
1489 bf->add_term(t, v[i]->terms[k], extra_num);
1490 }
1491 } else {
1492 // powers of "constant" part
1493 for (int k = 0; k < nnf; ++k)
1494 bpowers[k] = 0;
1495 for (int k = 0; k < nf; ++k) {
1496 if (factors[k][0] != 0)
1497 continue;
1498 assert(old2new[k] != -1);
1499 bpowers[old2new[k]] += v[i]->powers[k];
1500 if (sign[k] == -1) {
1501 extra_num += v[i]->powers[k] * nfactors[old2new[k]];
1502 changes += v[i]->powers[k];
1503 }
1504 }
1505
1506 int j;
1507 for (j = 0; j < nf; ++j)
1508 if (old2new[j] == -1 && v[i]->powers[j] > 0)
1509 break;
1510
1511 dpoly D(no_param, factors[j][0], 1);
1512 for (int k = 1; k < v[i]->powers[j]; ++k) {
1513 dpoly fact(no_param, factors[j][0], 1);
1514 D *= fact;
1515 }
1516 for ( ; ++j < nf; )
1517 if (old2new[j] == -1)
1518 for (int k = 0; k < v[i]->powers[j]; ++k) {
1519 dpoly fact(no_param, factors[j][0], 1);
1520 D *= fact;
1521 }
1522
1523 if (no_param + only_param == total_power &&
1524 bf->constant_vertex(d)) {
1525 bfc_term_base * t = NULL;
1526 vec_ZZ num;
1527 num.SetLength(d-1);
1528 ZZ cn;
1529 ZZ cd;
1530 for (int k = 0; k < v[i]->terms.NumRows(); ++k) {
1531 dpoly n(no_param, v[i]->terms[k][0]);
1532 mpq_set_si(bf->tcount, 0, 1);
1533 n.div(D, bf->tcount, bf->one);
1534
1535 if (value_zero_p(mpq_numref(bf->tcount)))
1536 continue;
1537
1538 if (!t)
1539 t = bf->find_bfc_term(vn, bpowers, nnf);
1540 bf->set_factor(v[i], k, bf->tcount, changes % 2);
1541 bf->add_term(t, v[i]->terms[k], extra_num);
1542 }
1543 } else {
1544 for (int j = 0; j < v[i]->terms.NumRows(); ++j) {
1545 dpoly n(no_param, v[i]->terms[j][0]);
1546
1547 dpoly_r * r = 0;
1548 if (no_param + only_param == total_power)
1549 r = new dpoly_r(n, nf);
1550 else
1551 for (int k = 0; k < nf; ++k) {
1552 if (v[i]->powers[k] == 0)
1553 continue;
1554 if (factors[k][0] == 0 || old2new[k] == -1)
1555 continue;
1556
1557 dpoly pd(no_param-1, factors[k][0], 1);
1558
1559 for (int l = 0; l < v[i]->powers[k]; ++l) {
1560 int q;
1561 for (q = 0; q < k; ++q)
1562 if (old2new[q] == old2new[k] &&
1563 sign[q] == sign[k])
1564 break;
1565
1566 if (r == 0)
1567 r = new dpoly_r(n, pd, q, nf);
1568 else {
1569 dpoly_r *nr = new dpoly_r(r, pd, q, nf);
1570 delete r;
1571 r = nr;
1572 }
1573 }
1574 }
1575
1576 dpoly_r *rc = r->div(D);
1577 delete r;
1578
1579 if (bf->constant_vertex(d)) {
1580 vector< dpoly_r_term * >& final = rc->c[rc->len-1];
1581
1582 for (int k = 0; k < final.size(); ++k) {
1583 if (final[k]->coeff == 0)
1584 continue;
1585
1586 update_powers(final[k]->powers, rc->dim);
1587
1588 bfc_term_base * t = bf->find_bfc_term(vn, npowers, nnf);
1589 bf->set_factor(v[i], j, final[k]->coeff, rc->denom, l_changes % 2);
1590 bf->add_term(t, v[i]->terms[j], l_extra_num);
1591 }
1592 } else
1593 bf->cum(this, v[i], j, rc);
1594
1595 delete rc;
1596 }
1597 }
1598 }
1599 delete v[i];
1600 }
1601
1602 }
1603
1604 void bf_base::reduce(mat_ZZ& factors, bfc_vec& v)
1605 {
1606 assert(v.size() > 0);
1607 unsigned nf = factors.NumRows();
1608 unsigned d = factors.NumCols();
1609
1610 if (d == lower)
1611 return base(factors, v);
1612
1613 bf_reducer bfr(factors, v, this);
1614
1615 bfr.reduce();
1616
1617 if (bfr.vn.size() > 0)
1618 reduce(bfr.nfactors, bfr.vn);
1619 }
1620
1621 int bf_base::setup_factors(Polyhedron *C, mat_ZZ& factors,
1622 bfc_term_base* t, int s)
1623 {
1624 factors.SetDims(dim, dim);
1625
1626 int r;
1627
1628 for (r = 0; r < dim; ++r)
1629 t->powers[r] = 1;
1630
1631 for (r = 0; r < dim; ++r) {
1632 values2zz(C->Ray[r]+1, factors[r], dim);
1633 int k;
1634 for (k = 0; k < dim; ++k)
1635 if (factors[r][k] != 0)
1636 break;
1637 if (factors[r][k] < 0) {
1638 factors[r] = -factors[r];
1639 t->terms[0] += factors[r];
1640 s = -s;
1641 }
1642 }
1643
1644 return s;
1645 }
1646
1647 void bf_base::handle_polar(Polyhedron *C, int s)
1648 {
1649 bfc_term* t = new bfc_term(dim);
1650 vector< bfc_term_base * > v;
1651 v.push_back(t);
1652
1653 assert(C->NbRays-1 == dim);
1654
1655 t->cn.SetLength(1);
1656 t->cd.SetLength(1);
1657
1658 t->terms.SetDims(1, dim);
1659 lattice_point(P->Ray[current_vertex]+1, C, t->terms[0]);
1660
1661 // the elements of factors are always lexpositive
1662 mat_ZZ factors;
1663 s = setup_factors(C, factors, t, s);
1664
1665 t->cn[0] = s;
1666 t->cd[0] = 1;
1667
1668 reduce(factors, v);
1669 }
1670
1671 void bf_base::start(unsigned MaxRays)
1672 {
1673 for (current_vertex = 0; current_vertex < P->NbRays; ++current_vertex) {
1674 Polyhedron *C = supporting_cone(P, current_vertex);
1675 decompose(C, MaxRays);
1676 }
1677 }
1678
1679 struct bfcounter_base : public bf_base {
1680 ZZ cn;
1681 ZZ cd;
1682
1683 bfcounter_base(Polyhedron *P) : bf_base(P, P->Dimension) {
1684 }
1685
1686 bfc_term_base* new_bf_term(int len) {
1687 bfc_term* t = new bfc_term(len);
1688 t->cn.SetLength(0);
1689 t->cd.SetLength(0);
1690 return t;
1691 }
1692
1693 virtual void set_factor(bfc_term_base *t, int k, int change) {
1694 bfc_term* bfct = static_cast<bfc_term *>(t);
1695 cn = bfct->cn[k];
1696 if (change)
1697 cn = -cn;
1698 cd = bfct->cd[k];
1699 }
1700
1701 virtual void set_factor(bfc_term_base *t, int k, mpq_t &f, int change) {
1702 bfc_term* bfct = static_cast<bfc_term *>(t);
1703 value2zz(mpq_numref(f), cn);
1704 value2zz(mpq_denref(f), cd);
1705 cn *= bfct->cn[k];
1706 if (change)
1707 cn = -cn;
1708 cd *= bfct->cd[k];
1709 }
1710
1711 virtual void set_factor(bfc_term_base *t, int k, ZZ& n, ZZ& d, int change) {
1712 bfc_term* bfct = static_cast<bfc_term *>(t);
1713 cn = bfct->cn[k] * n;
1714 if (change)
1715 cn = -cn;
1716 cd = bfct->cd[k] * d;
1717 }
1718
1719 virtual void insert_term(bfc_term_base *t, int i) {
1720 bfc_term* bfct = static_cast<bfc_term *>(t);
1721 int len = t->terms.NumRows()-1; // already increased by one
1722
1723 bfct->cn.SetLength(len+1);
1724 bfct->cd.SetLength(len+1);
1725 for (int j = len; j > i; --j) {
1726 bfct->cn[j] = bfct->cn[j-1];
1727 bfct->cd[j] = bfct->cd[j-1];
1728 t->terms[j] = t->terms[j-1];
1729 }
1730 bfct->cn[i] = cn;
1731 bfct->cd[i] = cd;
1732 }
1733
1734 virtual void update_term(bfc_term_base *t, int i) {
1735 bfc_term* bfct = static_cast<bfc_term *>(t);
1736
1737 ZZ g = GCD(bfct->cd[i], cd);
1738 ZZ n = cn * bfct->cd[i]/g + bfct->cn[i] * cd/g;
1739 ZZ d = bfct->cd[i] * cd / g;
1740 bfct->cn[i] = n;
1741 bfct->cd[i] = d;
1742 }
1743
1744 virtual bool constant_vertex(int dim) { return true; }
1745 virtual void cum(bf_reducer *bfr, bfc_term_base *t, int k, dpoly_r *r) {
1746 assert(0);
1747 }
1748 };
1749
1750 struct bfcounter : public bfcounter_base {
1751 mpq_t count;
1752
1753 bfcounter(Polyhedron *P) : bfcounter_base(P) {
1754 mpq_init(count);
1755 lower = 1;
1756 }
1757 ~bfcounter() {
1758 mpq_clear(count);
1759 }
1760 virtual void base(mat_ZZ& factors, bfc_vec& v);
1761 };
1762
1763 void bfcounter::base(mat_ZZ& factors, bfc_vec& v)
1764 {
1765 unsigned nf = factors.NumRows();
1766
1767 for (int i = 0; i < v.size(); ++i) {
1768 bfc_term* bfct = static_cast<bfc_term *>(v[i]);
1769 int total_power = 0;
1770 // factor is always positive, so we always
1771 // change signs
1772 for (int k = 0; k < nf; ++k)
1773 total_power += v[i]->powers[k];
1774
1775 int j;
1776 for (j = 0; j < nf; ++j)
1777 if (v[i]->powers[j] > 0)
1778 break;
1779
1780 dpoly D(total_power, factors[j][0], 1);
1781 for (int k = 1; k < v[i]->powers[j]; ++k) {
1782 dpoly fact(total_power, factors[j][0], 1);
1783 D *= fact;
1784 }
1785 for ( ; ++j < nf; )
1786 for (int k = 0; k < v[i]->powers[j]; ++k) {
1787 dpoly fact(total_power, factors[j][0], 1);
1788 D *= fact;
1789 }
1790
1791 for (int k = 0; k < v[i]->terms.NumRows(); ++k) {
1792 dpoly n(total_power, v[i]->terms[k][0]);
1793 mpq_set_si(tcount, 0, 1);
1794 n.div(D, tcount, one);
1795 if (total_power % 2)
1796 bfct->cn[k] = -bfct->cn[k];
1797 zz2value(bfct->cn[k], tn);
1798 zz2value(bfct->cd[k], td);
1799
1800 mpz_mul(mpq_numref(tcount), mpq_numref(tcount), tn);
1801 mpz_mul(mpq_denref(tcount), mpq_denref(tcount), td);
1802 mpq_canonicalize(tcount);
1803 mpq_add(count, count, tcount);
1804 }
1805 delete v[i];
1806 }
1807 }
1808
1809 struct partial_bfcounter : public bfcounter_base, public gf_base {
1810 partial_bfcounter(Polyhedron *P, unsigned nparam) :
1811 bfcounter_base(P), gf_base(this, nparam) {
1812 lower = nparam;
1813 }
1814 ~partial_bfcounter() {
1815 }
1816 virtual void base(mat_ZZ& factors, bfc_vec& v);
1817 /* we want to override the start method from bf_base with the one from gf_base */
1818 void start(unsigned MaxRays) {
1819 gf_base::start(MaxRays);
1820 }
1821 };
1822
1823 void partial_bfcounter::base(mat_ZZ& factors, bfc_vec& v)
1824 {
1825 mat_ZZ den;
1826 unsigned nf = factors.NumRows();
1827
1828 for (int i = 0; i < v.size(); ++i) {
1829 bfc_term* bfct = static_cast<bfc_term *>(v[i]);
1830 den.SetDims(0, lower);
1831 int total_power = 0;
1832 int p = 0;
1833 for (int j = 0; j < nf; ++j) {
1834 total_power += v[i]->powers[j];
1835 den.SetDims(total_power, lower);
1836 for (int k = 0; k < v[i]->powers[j]; ++k)
1837 den[p++] = factors[j];
1838 }
1839 for (int j = 0; j < v[i]->terms.NumRows(); ++j)
1840 gf->add(bfct->cn[j], bfct->cd[j], v[i]->terms[j], den);
1841 delete v[i];
1842 }
1843 }
1844
1845
1846 typedef Polyhedron * Polyhedron_p;
1847
1848 static void barvinok_count_f(Polyhedron *P, Value* result, unsigned NbMaxCons);
1849
1850 void barvinok_count(Polyhedron *P, Value* result, unsigned NbMaxCons)
1851 {
1852 unsigned dim;
1853 int allocated = 0;
1854 Polyhedron *Q;
1855 int r = 0;
1856 bool infinite = false;
1857
1858 if (emptyQ2(P)) {
1859 value_set_si(*result, 0);
1860 return;
1861 }
1862 if (P->NbEq != 0) {
1863 P = remove_equalities(P);
1864 if (emptyQ(P)) {
1865 Polyhedron_Free(P);
1866 value_set_si(*result, 0);
1867 return;
1868 }
1869 allocated = 1;
1870 }
1871 if (P->NbBid == 0)
1872 for (; r < P->NbRays; ++r)
1873 if (value_zero_p(P->Ray[r][P->Dimension+1]))
1874 break;
1875 if (P->NbBid != 0 || r < P->NbRays) {
1876 value_set_si(*result, -1);
1877 if (allocated)
1878 Polyhedron_Free(P);
1879 return;
1880 }
1881 if (P->Dimension == 0) {
1882 /* Test whether the constraints are satisfied */
1883 POL_ENSURE_VERTICES(P);
1884 value_set_si(*result, !emptyQ(P));
1885 if (allocated)
1886 Polyhedron_Free(P);
1887 return;
1888 }
1889 Q = Polyhedron_Factor(P, 0, NbMaxCons);
1890 if (Q) {
1891 if (allocated)
1892 Polyhedron_Free(P);
1893 P = Q;
1894 allocated = 1;
1895 }
1896
1897 barvinok_count_f(P, result, NbMaxCons);
1898 if (Q && P->next) {
1899 Value factor;
1900 value_init(factor);
1901
1902 for (Q = P->next; Q; Q = Q->next) {
1903 barvinok_count_f(Q, &factor, NbMaxCons);
1904 if (value_neg_p(factor)) {
1905 infinite = true;
1906 continue;
1907 } else if (Q->next && value_zero_p(factor)) {
1908 value_set_si(*result, 0);
1909 break;
1910 }
1911 value_multiply(*result, *result, factor);
1912 }
1913
1914 value_clear(factor);
1915 }
1916
1917 if (allocated)
1918 Domain_Free(P);
1919 if (infinite)
1920 value_set_si(*result, -1);
1921 }
1922
1923 static void barvinok_count_f(Polyhedron *P, Value* result, unsigned NbMaxCons)
1924 {
1925 if (P->Dimension == 1)
1926 return Line_Length(P, result);
1927
1928 int c = P->NbConstraints;
1929 POL_ENSURE_FACETS(P);
1930 if (c != P->NbConstraints || P->NbEq != 0)
1931 return barvinok_count(P, result, NbMaxCons);
1932
1933 POL_ENSURE_VERTICES(P);
1934
1935 #ifdef USE_INCREMENTAL_BF
1936 bfcounter cnt(P);
1937 #elif defined USE_INCREMENTAL_DF
1938 icounter cnt(P);
1939 #else
1940 counter cnt(P);
1941 #endif
1942 cnt.start(NbMaxCons);
1943
1944 assert(value_one_p(&cnt.count[0]._mp_den));
1945 value_assign(*result, &cnt.count[0]._mp_num);
1946 }
1947
1948 static void uni_polynom(int param, Vector *c, evalue *EP)
1949 {
1950 unsigned dim = c->Size-2;
1951 value_init(EP->d);
1952 value_set_si(EP->d,0);
1953 EP->x.p = new_enode(polynomial, dim+1, param+1);
1954 for (int j = 0; j <= dim; ++j)
1955 evalue_set(&EP->x.p->arr[j], c->p[j], c->p[dim+1]);
1956 }
1957
1958 static void multi_polynom(Vector *c, evalue* X, evalue *EP)
1959 {
1960 unsigned dim = c->Size-2;
1961 evalue EC;
1962
1963 value_init(EC.d);
1964 evalue_set(&EC, c->p[dim], c->p[dim+1]);
1965
1966 value_init(EP->d);
1967 evalue_set(EP, c->p[dim], c->p[dim+1]);
1968
1969 for (int i = dim-1; i >= 0; --i) {
1970 emul(X, EP);
1971 value_assign(EC.x.n, c->p[i]);
1972 eadd(&EC, EP);
1973 }
1974 free_evalue_refs(&EC);
1975 }
1976
1977 Polyhedron *unfringe (Polyhedron *P, unsigned MaxRays)
1978 {
1979 int len = P->Dimension+2;
1980 Polyhedron *T, *R = P;
1981 Value g;
1982 value_init(g);
1983 Vector *row = Vector_Alloc(len);
1984 value_set_si(row->p[0], 1);
1985
1986 R = DomainConstraintSimplify(Polyhedron_Copy(P), MaxRays);
1987
1988 Matrix *M = Matrix_Alloc(2, len-1);
1989 value_set_si(M->p[1][len-2], 1);
1990 for (int v = 0; v < P->Dimension; ++v) {
1991 value_set_si(M->p[0][v], 1);
1992 Polyhedron *I = Polyhedron_Image(P, M, 2+1);
1993 value_set_si(M->p[0][v], 0);
1994 for (int r = 0; r < I->NbConstraints; ++r) {
1995 if (value_zero_p(I->Constraint[r][0]))
1996 continue;
1997 if (value_zero_p(I->Constraint[r][1]))
1998 continue;
1999 if (value_one_p(I->Constraint[r][1]))
2000 continue;
2001 if (value_mone_p(I->Constraint[r][1]))
2002 continue;
2003 value_absolute(g, I->Constraint[r][1]);
2004 Vector_Set(row->p+1, 0, len-2);
2005 value_division(row->p[1+v], I->Constraint[r][1], g);
2006 mpz_fdiv_q(row->p[len-1], I->Constraint[r][2], g);
2007 T = R;
2008 R = AddConstraints(row->p, 1, R, MaxRays);
2009 if (T != P)
2010 Polyhedron_Free(T);
2011 }
2012 Polyhedron_Free(I);
2013 }
2014 Matrix_Free(M);
2015 Vector_Free(row);
2016 value_clear(g);
2017 return R;
2018 }
2019
2020 /* this procedure may have false negatives */
2021 static bool Polyhedron_is_infinite(Polyhedron *P, unsigned nparam)
2022 {
2023 int r;
2024 for (r = 0; r < P->NbRays; ++r) {
2025 if (!value_zero_p(P->Ray[r][0]) &&
2026 !value_zero_p(P->Ray[r][P->Dimension+1]))
2027 continue;
2028 if (First_Non_Zero(P->Ray[r]+1+P->Dimension-nparam, nparam) == -1)
2029 return true;
2030 }
2031 return false;
2032 }
2033
2034 /* Check whether all rays point in the positive directions
2035 * for the parameters
2036 */
2037 static bool Polyhedron_has_positive_rays(Polyhedron *P, unsigned nparam)
2038 {
2039 int r;
2040 for (r = 0; r < P->NbRays; ++r)
2041 if (value_zero_p(P->Ray[r][P->Dimension+1])) {
2042 int i;
2043 for (i = P->Dimension - nparam; i < P->Dimension; ++i)
2044 if (value_neg_p(P->Ray[r][i+1]))
2045 return false;
2046 }
2047 return true;
2048 }
2049
2050 typedef evalue * evalue_p;
2051
2052 struct enumerator : public polar_decomposer {
2053 vec_ZZ lambda;
2054 unsigned dim, nbV;
2055 evalue ** vE;
2056 int _i;
2057 mat_ZZ rays;
2058 vec_ZZ den;
2059 ZZ sign;
2060 Polyhedron *P;
2061 Param_Vertices *V;
2062 term_info num;
2063 Vector *c;
2064 mpq_t count;
2065
2066 enumerator(Polyhedron *P, unsigned dim, unsigned nbV) {
2067 this->P = P;
2068 this->dim = dim;
2069 this->nbV = nbV;
2070 randomvector(P, lambda, dim);
2071 rays.SetDims(dim, dim);
2072 den.SetLength(dim);
2073 c = Vector_Alloc(dim+2);
2074
2075 vE = new evalue_p[nbV];
2076 for (int j = 0; j < nbV; ++j)
2077 vE[j] = 0;
2078
2079 mpq_init(count);
2080 }
2081
2082 void decompose_at(Param_Vertices *V, int _i, unsigned MaxRays) {
2083 Polyhedron *C = supporting_cone_p(P, V);
2084 this->_i = _i;
2085 this->V = V;
2086
2087 vE[_i] = new evalue;
2088 value_init(vE[_i]->d);
2089 evalue_set_si(vE[_i], 0, 1);
2090
2091 decompose(C, MaxRays);
2092 }
2093
2094 ~enumerator() {
2095 mpq_clear(count);
2096 Vector_Free(c);
2097
2098 for (int j = 0; j < nbV; ++j)
2099 if (vE[j]) {
2100 free_evalue_refs(vE[j]);
2101 delete vE[j];
2102 }
2103 delete [] vE;
2104 }
2105
2106 virtual void handle_polar(Polyhedron *P, int sign);
2107 };
2108
2109 void enumerator::handle_polar(Polyhedron *C, int s)
2110 {
2111 int r = 0;
2112 assert(C->NbRays-1 == dim);
2113 add_rays(rays, C, &r);
2114 for (int k = 0; k < dim; ++k) {
2115 if (lambda * rays[k] == 0)
2116 throw Orthogonal;
2117 }
2118
2119 sign = s;
2120
2121 lattice_point(V, C, lambda, &num, 0);
2122 den = rays * lambda;
2123 normalize(sign, num.constant, den);
2124
2125 dpoly n(dim, den[0], 1);
2126 for (int k = 1; k < dim; ++k) {
2127 dpoly fact(dim, den[k], 1);
2128 n *= fact;
2129 }
2130 if (num.E != NULL) {
2131 ZZ one(INIT_VAL, 1);
2132 dpoly_n d(dim, num.constant, one);
2133 d.div(n, c, sign);
2134 evalue EV;
2135 multi_polynom(c, num.E, &EV);
2136 eadd(&EV , vE[_i]);
2137 free_evalue_refs(&EV);
2138 free_evalue_refs(num.E);
2139 delete num.E;
2140 } else if (num.pos != -1) {
2141 dpoly_n d(dim, num.constant, num.coeff);
2142 d.div(n, c, sign);
2143 evalue EV;
2144 uni_polynom(num.pos, c, &EV);
2145 eadd(&EV , vE[_i]);
2146 free_evalue_refs(&EV);
2147 } else {
2148 mpq_set_si(count, 0, 1);
2149 dpoly d(dim, num.constant);
2150 d.div(n, count, sign);
2151 evalue EV;
2152 value_init(EV.d);
2153 evalue_set(&EV, &count[0]._mp_num, &count[0]._mp_den);
2154 eadd(&EV , vE[_i]);
2155 free_evalue_refs(&EV);
2156 }
2157 }
2158
2159 struct enumerator_base {
2160 unsigned dim;
2161 evalue ** vE;
2162 evalue ** E_vertex;
2163 evalue mone;
2164 vertex_decomposer *vpd;
2165
2166 enumerator_base(unsigned dim, vertex_decomposer *vpd)
2167 {
2168 this->dim = dim;
2169 this->vpd = vpd;
2170
2171 vE = new evalue_p[vpd->nbV];
2172 for (int j = 0; j < vpd->nbV; ++j)
2173 vE[j] = 0;
2174
2175 E_vertex = new evalue_p[dim];
2176
2177 value_init(mone.d);
2178 evalue_set_si(&mone, -1, 1);
2179 }
2180
2181 void decompose_at(Param_Vertices *V, int _i, unsigned MaxRays/*, Polyhedron *pVD*/) {
2182 //this->pVD = pVD;
2183
2184 vE[_i] = new evalue;
2185 value_init(vE[_i]->d);
2186 evalue_set_si(vE[_i], 0, 1);
2187
2188 vpd->decompose_at_vertex(V, _i, MaxRays);
2189 }
2190
2191 ~enumerator_base() {
2192 for (int j = 0; j < vpd->nbV; ++j)
2193 if (vE[j]) {
2194 free_evalue_refs(vE[j]);
2195 delete vE[j];
2196 }
2197 delete [] vE;
2198
2199 delete [] E_vertex;
2200
2201 free_evalue_refs(&mone);
2202 }
2203
2204 evalue *E_num(int i, int d) {
2205 return E_vertex[i + (dim-d)];
2206 }
2207 };
2208
2209 struct cumulator {
2210 evalue *factor;
2211 evalue *v;
2212 dpoly_r *r;
2213
2214 cumulator(evalue *factor, evalue *v, dpoly_r *r) :
2215 factor(factor), v(v), r(r) {}
2216
2217 void cumulate();
2218
2219 virtual void add_term(int *powers, int len, evalue *f2) = 0;
2220 };
2221
2222 void cumulator::cumulate()
2223 {
2224 evalue cum; // factor * 1 * E_num[0]/1 * (E_num[0]-1)/2 *...
2225 evalue f;
2226 evalue t; // E_num[0] - (m-1)
2227 #ifdef USE_MODULO
2228 evalue *cst;
2229 #else
2230 evalue mone;
2231 value_init(mone.d);
2232 evalue_set_si(&mone, -1, 1);
2233 #endif
2234
2235 value_init(cum.d);
2236 evalue_copy(&cum, factor);
2237 value_init(f.d);
2238 value_init(f.x.n);
2239 value_set_si(f.d, 1);
2240 value_set_si(f.x.n, 1);
2241 value_init(t.d);
2242 evalue_copy(&t, v);
2243
2244 #ifdef USE_MODULO
2245 for (cst = &t; value_zero_p(cst->d); ) {
2246 if (cst->x.p->type == fractional)
2247 cst = &cst->x.p->arr[1];
2248 else
2249 cst = &cst->x.p->arr[0];
2250 }
2251 #endif
2252
2253 for (int m = 0; m < r->len; ++m) {
2254 if (m > 0) {
2255 if (m > 1) {
2256 value_set_si(f.d, m);
2257 emul(&f, &cum);
2258 #ifdef USE_MODULO
2259 value_subtract(cst->x.n, cst->x.n, cst->d);
2260 #else
2261 eadd(&mone, &t);
2262 #endif
2263 }
2264 emul(&t, &cum);
2265 }
2266 vector< dpoly_r_term * >& current = r->c[r->len-1-m];
2267 for (int j = 0; j < current.size(); ++j) {
2268 if (current[j]->coeff == 0)
2269 continue;
2270 evalue *f2 = new evalue;
2271 value_init(f2->d);
2272 value_init(f2->x.n);
2273 zz2value(current[j]->coeff, f2->x.n);
2274 zz2value(r->denom, f2->d);
2275 emul(&cum, f2);
2276
2277 add_term(current[j]->powers, r->dim, f2);
2278 }
2279 }
2280 free_evalue_refs(&f);
2281 free_evalue_refs(&t);
2282 free_evalue_refs(&cum);
2283 #ifndef USE_MODULO
2284 free_evalue_refs(&mone);
2285 #endif
2286 }
2287
2288 struct E_poly_term {
2289 int *powers;
2290 evalue *E;
2291 };
2292
2293 struct ie_cum : public cumulator {
2294 vector<E_poly_term *> terms;
2295
2296 ie_cum(evalue *factor, evalue *v, dpoly_r *r) : cumulator(factor, v, r) {}
2297
2298 virtual void add_term(int *powers, int len, evalue *f2);
2299 };
2300
2301 void ie_cum::add_term(int *powers, int len, evalue *f2)
2302 {
2303 int k;
2304 for (k = 0; k < terms.size(); ++k) {
2305 if (memcmp(terms[k]->powers, powers, len * sizeof(int)) == 0) {
2306 eadd(f2, terms[k]->E);
2307 free_evalue_refs(f2);
2308 delete f2;
2309 break;
2310 }
2311 }
2312 if (k >= terms.size()) {
2313 E_poly_term *ET = new E_poly_term;
2314 ET->powers = new int[len];
2315 memcpy(ET->powers, powers, len * sizeof(int));
2316 ET->E = f2;
2317 terms.push_back(ET);
2318 }
2319 }
2320
2321 struct ienumerator : public polar_decomposer, public vertex_decomposer,
2322 public enumerator_base {
2323 //Polyhedron *pVD;
2324 mat_ZZ den;
2325 vec_ZZ vertex;
2326 mpq_t tcount;
2327
2328 ienumerator(Polyhedron *P, unsigned dim, unsigned nbV) :
2329 vertex_decomposer(P, nbV, this), enumerator_base(dim, this) {
2330 vertex.SetLength(dim);
2331
2332 den.SetDims(dim, dim);
2333 mpq_init(tcount);
2334 }
2335
2336 ~ienumerator() {
2337 mpq_clear(tcount);
2338 }
2339
2340 virtual void handle_polar(Polyhedron *P, int sign);
2341 void reduce(evalue *factor, vec_ZZ& num, mat_ZZ& den_f);
2342 };
2343
2344 void ienumerator::reduce(
2345 evalue *factor, vec_ZZ& num, mat_ZZ& den_f)
2346 {
2347 unsigned len = den_f.NumRows(); // number of factors in den
2348 unsigned dim = num.length();
2349
2350 if (dim == 0) {
2351 eadd(factor, vE[vert]);
2352 return;
2353 }
2354
2355 vec_ZZ den_s;
2356 den_s.SetLength(len);
2357 mat_ZZ den_r;
2358 den_r.SetDims(len, dim-1);
2359
2360 int r, k;
2361
2362 for (r = 0; r < len; ++r) {
2363 den_s[r] = den_f[r][0];
2364 for (k = 0; k <= dim-1; ++k)
2365 if (k != 0)
2366 den_r[r][k-(k>0)] = den_f[r][k];
2367 }
2368
2369 ZZ num_s = num[0];
2370 vec_ZZ num_p;
2371 num_p.SetLength(dim-1);
2372 for (k = 0 ; k <= dim-1; ++k)
2373 if (k != 0)
2374 num_p[k-(k>0)] = num[k];
2375
2376 vec_ZZ den_p;
2377 den_p.SetLength(len);
2378
2379 ZZ one;
2380 one = 1;
2381 normalize(one, num_s, num_p, den_s, den_p, den_r);
2382 if (one != 1)
2383 emul(&mone, factor);
2384
2385 int only_param = 0;
2386 int no_param = 0;
2387 for (int k = 0; k < len; ++k) {
2388 if (den_p[k] == 0)
2389 ++no_param;
2390 else if (den_s[k] == 0)
2391 ++only_param;
2392 }
2393 if (no_param == 0) {
2394 reduce(factor, num_p, den_r);
2395 } else {
2396 int k, l;
2397 mat_ZZ pden;
2398 pden.SetDims(only_param, dim-1);
2399
2400 for (k = 0, l = 0; k < len; ++k)
2401 if (den_s[k] == 0)
2402 pden[l++] = den_r[k];
2403
2404 for (k = 0; k < len; ++k)
2405 if (den_p[k] == 0)
2406 break;
2407
2408 dpoly n(no_param, num_s);
2409 dpoly D(no_param, den_s[k], 1);
2410 for ( ; ++k < len; )
2411 if (den_p[k] == 0) {
2412 dpoly fact(no_param, den_s[k], 1);
2413 D *= fact;
2414 }
2415
2416 dpoly_r * r = 0;
2417 // if no_param + only_param == len then all powers
2418 // below will be all zero
2419 if (no_param + only_param == len) {
2420 if (E_num(0, dim) != 0)
2421 r = new dpoly_r(n, len);
2422 else {
2423 mpq_set_si(tcount, 0, 1);
2424 one = 1;
2425 n.div(D, tcount, one);
2426
2427 if (value_notzero_p(mpq_numref(tcount))) {
2428 evalue f;
2429 value_init(f.d);
2430 value_init(f.x.n);
2431 value_assign(f.x.n, mpq_numref(tcount));
2432 value_assign(f.d, mpq_denref(tcount));
2433 emul(&f, factor);
2434 reduce(factor, num_p, pden);
2435 free_evalue_refs(&f);
2436 }
2437 return;
2438 }
2439 } else {
2440 for (k = 0; k < len; ++k) {
2441 if (den_s[k] == 0 || den_p[k] == 0)
2442 continue;
2443
2444 dpoly pd(no_param-1, den_s[k], 1);
2445
2446 int l;
2447 for (l = 0; l < k; ++l)
2448 if (den_r[l] == den_r[k])
2449 break;
2450
2451 if (r == 0)
2452 r = new dpoly_r(n, pd, l, len);
2453 else {
2454 dpoly_r *nr = new dpoly_r(r, pd, l, len);
2455 delete r;
2456 r = nr;
2457 }
2458 }
2459 }
2460 dpoly_r *rc = r->div(D);
2461 delete r;
2462 r = rc;
2463 if (E_num(0, dim) == 0) {
2464 int common = pden.NumRows();
2465 vector< dpoly_r_term * >& final = r->c[r->len-1];
2466 int rows;
2467 evalue t;
2468 evalue f;
2469 value_init(f.d);
2470 value_init(f.x.n);
2471 zz2value(r->denom, f.d);
2472 for (int j = 0; j < final.size(); ++j) {
2473 if (final[j]->coeff == 0)
2474 continue;
2475 rows = common;
2476 for (int k = 0; k < r->dim; ++k) {
2477 int n = final[j]->powers[k];
2478 if (n == 0)
2479 continue;
2480 pden.SetDims(rows+n, pden.NumCols());
2481 for (int l = 0; l < n; ++l)
2482 pden[rows+l] = den_r[k];
2483 rows += n;
2484 }
2485 value_init(t.d);
2486 evalue_copy(&t, factor);
2487 zz2value(final[j]->coeff, f.x.n);
2488 emul(&f, &t);
2489 reduce(&t, num_p, pden);
2490 free_evalue_refs(&t);
2491 }
2492 free_evalue_refs(&f);
2493 } else {
2494 ie_cum cum(factor, E_num(0, dim), r);
2495 cum.cumulate();
2496
2497 int common = pden.NumRows();
2498 int rows;
2499 for (int j = 0; j < cum.terms.size(); ++j) {
2500 rows = common;
2501 pden.SetDims(rows, pden.NumCols());
2502 for (int k = 0; k < r->dim; ++k) {
2503 int n = cum.terms[j]->powers[k];
2504 if (n == 0)
2505 continue;
2506 pden.SetDims(rows+n, pden.NumCols());
2507 for (int l = 0; l < n; ++l)
2508 pden[rows+l] = den_r[k];
2509 rows += n;
2510 }
2511 reduce(cum.terms[j]->E, num_p, pden);
2512 free_evalue_refs(cum.terms[j]->E);
2513 delete cum.terms[j]->E;
2514 delete [] cum.terms[j]->powers;
2515 delete cum.terms[j];
2516 }
2517 }
2518 delete r;
2519 }
2520 }
2521
2522 static int type_offset(enode *p)
2523 {
2524 return p->type == fractional ? 1 :
2525 p->type == flooring ? 1 : 0;
2526 }
2527
2528 static int edegree(evalue *e)
2529 {
2530 int d = 0;
2531 enode *p;
2532
2533 if (value_notzero_p(e->d))
2534 return 0;
2535
2536 p = e->x.p;
2537 int i = type_offset(p);
2538 if (p->size-i-1 > d)
2539 d = p->size - i - 1;
2540 for (; i < p->size; i++) {
2541 int d2 = edegree(&p->arr[i]);
2542 if (d2 > d)
2543 d = d2;
2544 }
2545 return d;
2546 }
2547
2548 void ienumerator::handle_polar(Polyhedron *C, int s)
2549 {
2550 assert(C->NbRays-1 == dim);
2551
2552 lattice_point(V, C, vertex, E_vertex);
2553
2554 int r;
2555 for (r = 0; r < dim; ++r)
2556 values2zz(C->Ray[r]+1, den[r], dim);
2557
2558 evalue one;
2559 value_init(one.d);
2560 evalue_set_si(&one, s, 1);
2561 reduce(&one, vertex, den);
2562 free_evalue_refs(&one);
2563
2564 for (int i = 0; i < dim; ++i)
2565 if (E_vertex[i]) {
2566 free_evalue_refs(E_vertex[i]);
2567 delete E_vertex[i];
2568 }
2569 }
2570
2571 struct bfenumerator : public vertex_decomposer, public bf_base,
2572 public enumerator_base {
2573 evalue *factor;
2574
2575 bfenumerator(Polyhedron *P, unsigned dim, unsigned nbV) :
2576 vertex_decomposer(P, nbV, this),
2577 bf_base(P, dim), enumerator_base(dim, this) {
2578 lower = 0;
2579 factor = NULL;
2580 }
2581
2582 ~bfenumerator() {
2583 }
2584
2585 virtual void handle_polar(Polyhedron *P, int sign);
2586 virtual void base(mat_ZZ& factors, bfc_vec& v);
2587
2588 bfc_term_base* new_bf_term(int len) {
2589 bfe_term* t = new bfe_term(len);
2590 return t;
2591 }
2592
2593 virtual void set_factor(bfc_term_base *t, int k, int change) {
2594 bfe_term* bfet = static_cast<bfe_term *>(t);
2595 factor = bfet->factors[k];
2596 assert(factor != NULL);
2597 bfet->factors[k] = NULL;
2598 if (change)
2599 emul(&mone, factor);
2600 }
2601
2602 virtual void set_factor(bfc_term_base *t, int k, mpq_t &q, int change) {
2603 bfe_term* bfet = static_cast<bfe_term *>(t);
2604 factor = bfet->factors[k];
2605 assert(factor != NULL);
2606 bfet->factors[k] = NULL;
2607
2608 evalue f;
2609 value_init(f.d);
2610 value_init(f.x.n);
2611 if (change)
2612 value_oppose(f.x.n, mpq_numref(q));
2613 else
2614 value_assign(f.x.n, mpq_numref(q));
2615 value_assign(f.d, mpq_denref(q));
2616 emul(&f, factor);
2617 }
2618
2619 virtual void set_factor(bfc_term_base *t, int k, ZZ& n, ZZ& d, int change) {
2620 bfe_term* bfet = static_cast<bfe_term *>(t);
2621
2622 factor = new evalue;
2623
2624 evalue f;
2625 value_init(f.d);
2626 value_init(f.x.n);
2627 zz2value(n, f.x.n);
2628 if (change)
2629 value_oppose(f.x.n, f.x.n);
2630 zz2value(d, f.d);
2631
2632 value_init(factor->d);
2633 evalue_copy(factor, bfet->factors[k]);
2634 emul(&f, factor);
2635 }
2636
2637 void set_factor(evalue *f, int change) {
2638 if (change)
2639 emul(&mone, f);
2640 factor = f;
2641 }
2642
2643 virtual void insert_term(bfc_term_base *t, int i) {
2644 bfe_term* bfet = static_cast<bfe_term *>(t);
2645 int len = t->terms.NumRows()-1; // already increased by one
2646
2647 bfet->factors.resize(len+1);
2648 for (int j = len; j > i; --j) {
2649 bfet->factors[j] = bfet->factors[j-1];
2650 t->terms[j] = t->terms[j-1];
2651 }
2652 bfet->factors[i] = factor;
2653 factor = NULL;
2654 }
2655
2656 virtual void update_term(bfc_term_base *t, int i) {
2657 bfe_term* bfet = static_cast<bfe_term *>(t);
2658
2659 eadd(factor, bfet->factors[i]);
2660 free_evalue_refs(factor);
2661 delete factor;
2662 }
2663
2664 virtual bool constant_vertex(int dim) { return E_num(0, dim) == 0; }
2665
2666 virtual void cum(bf_reducer *bfr, bfc_term_base *t, int k, dpoly_r *r);
2667 };
2668
2669 struct bfe_cum : public cumulator {
2670 bfenumerator *bfe;
2671 bfc_term_base *told;
2672 int k;
2673 bf_reducer *bfr;
2674
2675 bfe_cum(evalue *factor, evalue *v, dpoly_r *r, bf_reducer *bfr,
2676 bfc_term_base *t, int k, bfenumerator *e) :
2677 cumulator(factor, v, r), told(t), k(k),
2678 bfr(bfr), bfe(e) {
2679 }
2680
2681 virtual void add_term(int *powers, int len, evalue *f2);
2682 };
2683
2684 void bfe_cum::add_term(int *powers, int len, evalue *f2)
2685 {
2686 bfr->update_powers(powers, len);
2687
2688 bfc_term_base * t = bfe->find_bfc_term(bfr->vn, bfr->npowers, bfr->nnf);
2689 bfe->set_factor(f2, bfr->l_changes % 2);
2690 bfe->add_term(t, told->terms[k], bfr->l_extra_num);
2691 }
2692
2693 void bfenumerator::cum(bf_reducer *bfr, bfc_term_base *t, int k,
2694 dpoly_r *r)
2695 {
2696 bfe_term* bfet = static_cast<bfe_term *>(t);
2697 bfe_cum cum(bfet->factors[k], E_num(0, bfr->d), r, bfr, t, k, this);
2698 cum.cumulate();
2699 }
2700
2701 void bfenumerator::base(mat_ZZ& factors, bfc_vec& v)
2702 {
2703 for (int i = 0; i < v.size(); ++i) {
2704 assert(v[i]->terms.NumRows() == 1);
2705 evalue *factor = static_cast<bfe_term *>(v[i])->factors[0];
2706 eadd(factor, vE[vert]);
2707 delete v[i];
2708 }
2709 }
2710
2711 void bfenumerator::handle_polar(Polyhedron *C, int s)
2712 {
2713 assert(C->NbRays-1 == enumerator_base::dim);
2714
2715 bfe_term* t = new bfe_term(enumerator_base::dim);
2716 vector< bfc_term_base * > v;
2717 v.push_back(t);
2718
2719 t->factors.resize(1);
2720
2721 t->terms.SetDims(1, enumerator_base::dim);
2722 lattice_point(V, C, t->terms[0], E_vertex);
2723
2724 // the elements of factors are always lexpositive
2725 mat_ZZ factors;
2726 s = setup_factors(C, factors, t, s);
2727
2728 t->factors[0] = new evalue;
2729 value_init(t->factors[0]->d);
2730 evalue_set_si(t->factors[0], s, 1);
2731 reduce(factors, v);
2732
2733 for (int i = 0; i < enumerator_base::dim; ++i)
2734 if (E_vertex[i]) {
2735 free_evalue_refs(E_vertex[i]);
2736 delete E_vertex[i];
2737 }
2738 }
2739
2740 #ifdef HAVE_CORRECT_VERTICES
2741 static inline Param_Polyhedron *Polyhedron2Param_SD(Polyhedron **Din,
2742 Polyhedron *Cin,int WS,Polyhedron **CEq,Matrix **CT)
2743 {
2744 if (WS & POL_NO_DUAL)
2745 WS = 0;
2746 return Polyhedron2Param_SimplifiedDomain(Din, Cin, WS, CEq, CT);
2747 }
2748 #else
2749 static Param_Polyhedron *Polyhedron2Param_SD(Polyhedron **Din,
2750 Polyhedron *Cin,int WS,Polyhedron **CEq,Matrix **CT)
2751 {
2752 static char data[] = " 1 0 0 0 0 1 -18 "
2753 " 1 0 0 -20 0 19 1 "
2754 " 1 0 1 20 0 -20 16 "
2755 " 1 0 0 0 0 -1 19 "
2756 " 1 0 -1 0 0 0 4 "
2757 " 1 4 -20 0 0 -1 23 "
2758 " 1 -4 20 0 0 1 -22 "
2759 " 1 0 1 0 20 -20 16 "
2760 " 1 0 0 0 -20 19 1 ";
2761 static int checked = 0;
2762 if (!checked) {
2763 checked = 1;
2764 char *p = data;
2765 int n, v, i;
2766 Matrix *M = Matrix_Alloc(9, 7);
2767 for (i = 0; i < 9; ++i)
2768 for (int j = 0; j < 7; ++j) {
2769 sscanf(p, "%d%n", &v, &n);
2770 p += n;
2771 value_set_si(M->p[i][j], v);
2772 }
2773 Polyhedron *P = Constraints2Polyhedron(M, 1024);
2774 Matrix_Free(M);
2775 Polyhedron *U = Universe_Polyhedron(1);
2776 Param_Polyhedron *PP = Polyhedron2Param_Domain(P, U, 1024);
2777 Polyhedron_Free(P);
2778 Polyhedron_Free(U);
2779 Param_Vertices *V;
2780 for (i = 0, V = PP->V; V; ++i, V = V->next)
2781 ;
2782 if (PP)
2783 Param_Polyhedron_Free(PP);
2784 if (i != 10) {
2785 fprintf(stderr, "WARNING: results may be incorrect\n");
2786 fprintf(stderr,
2787 "WARNING: use latest version of PolyLib to remove this warning\n");
2788 }
2789 }
2790
2791 return Polyhedron2Param_SimplifiedDomain(Din, Cin, WS, CEq, CT);
2792 }
2793 #endif
2794
2795 static evalue* barvinok_enumerate_ev_f(Polyhedron *P, Polyhedron* C,
2796 unsigned MaxRays);
2797
2798 /* Destroys C */
2799 static evalue* barvinok_enumerate_cst(Polyhedron *P, Polyhedron* C,
2800 unsigned MaxRays)
2801 {
2802 evalue *eres;
2803
2804 ALLOC(evalue, eres);
2805 value_init(eres->d);
2806 value_set_si(eres->d, 0);
2807 eres->x.p = new_enode(partition, 2, C->Dimension);
2808 EVALUE_SET_DOMAIN(eres->x.p->arr[0], DomainConstraintSimplify(C, MaxRays));
2809 value_set_si(eres->x.p->arr[1].d, 1);
2810 value_init(eres->x.p->arr[1].x.n);
2811 if (emptyQ(P))
2812 value_set_si(eres->x.p->arr[1].x.n, 0);
2813 else
2814 barvinok_count(P, &eres->x.p->arr[1].x.n, MaxRays);
2815
2816 return eres;
2817 }
2818
2819 evalue* barvinok_enumerate_ev(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
2820 {
2821 //P = unfringe(P, MaxRays);
2822 Polyhedron *Corig = C;
2823 Polyhedron *CEq = NULL, *rVD, *CA;
2824 int r = 0;
2825 unsigned nparam = C->Dimension;
2826 evalue *eres;
2827
2828 evalue factor;
2829 value_init(factor.d);
2830 evalue_set_si(&factor, 1, 1);
2831
2832 CA = align_context(C, P->Dimension, MaxRays);
2833 P = DomainIntersection(P, CA, MaxRays);
2834 Polyhedron_Free(CA);
2835
2836 /* for now */
2837 POL_ENSURE_FACETS(P);
2838 POL_ENSURE_VERTICES(P);
2839 POL_ENSURE_FACETS(C);
2840 POL_ENSURE_VERTICES(C);
2841
2842 if (C->Dimension == 0 || emptyQ(P)) {
2843 constant:
2844 eres = barvinok_enumerate_cst(P, CEq ? CEq : Polyhedron_Copy(C),
2845 MaxRays);
2846 out:
2847 emul(&factor, eres);
2848 reduce_evalue(eres);
2849 free_evalue_refs(&factor);
2850 Domain_Free(P);
2851 if (C != Corig)
2852 Polyhedron_Free(C);
2853
2854 return eres;
2855 }
2856 if (Polyhedron_is_infinite(P, nparam))
2857 goto constant;
2858
2859 if (P->NbEq != 0) {
2860 Matrix *f;
2861 P = remove_equalities_p(P, P->Dimension-nparam, &f);
2862 mask(f, &factor);
2863 Matrix_Free(f);
2864 }
2865 if (P->Dimension == nparam) {
2866 CEq = P;
2867 P = Universe_Polyhedron(0);
2868 goto constant;
2869 }
2870
2871 Polyhedron *T = Polyhedron_Factor(P, nparam, MaxRays);
2872 if (T || (P->Dimension == nparam+1)) {
2873 Polyhedron *Q;
2874 Polyhedron *C2;
2875 for (Q = T ? T : P; Q; Q = Q->next) {
2876 Polyhedron *next = Q->next;
2877 Q->next = NULL;
2878
2879 Polyhedron *QC = Q;
2880 if (Q->Dimension != C->Dimension)
2881 QC = Polyhedron_Project(Q, nparam);
2882
2883 C2 = C;
2884 C = DomainIntersection(C, QC, MaxRays);
2885 if (C2 != Corig)
2886 Polyhedron_Free(C2);
2887 if (QC != Q)
2888 Polyhedron_Free(QC);
2889
2890 Q->next = next;
2891 }
2892 }
2893 if (T) {
2894 Polyhedron_Free(P);
2895 P = T;
2896 if (T->Dimension == C->Dimension) {
2897 P = T->next;
2898 T->next = NULL;
2899 Polyhedron_Free(T);
2900 }
2901 }
2902
2903 Polyhedron *next = P->next;
2904 P->next = NULL;
2905 eres = barvinok_enumerate_ev_f(P, C, MaxRays);
2906 P->next = next;
2907
2908 if (P->next) {
2909 Polyhedron *Q;
2910 evalue *f;
2911
2912 for (Q = P->next; Q; Q = Q->next) {
2913 Polyhedron *next = Q->next;
2914 Q->next = NULL;
2915
2916 f = barvinok_enumerate_ev_f(Q, C, MaxRays);
2917 emul(f, eres);
2918 free_evalue_refs(f);
2919 free(f);
2920
2921 Q->next = next;
2922 }
2923 }
2924
2925 goto out;
2926 }
2927
2928 static evalue* barvinok_enumerate_ev_f(Polyhedron *P, Polyhedron* C,
2929 unsigned MaxRays)
2930 {
2931 unsigned nparam = C->Dimension;
2932
2933 if (P->Dimension - nparam == 1)
2934 return ParamLine_Length(P, C, MaxRays);
2935
2936 Param_Polyhedron *PP = NULL;
2937 Polyhedron *CEq = NULL, *pVD;
2938 Matrix *CT = NULL;
2939 Param_Domain *D, *next;
2940 Param_Vertices *V;
2941 evalue *eres;
2942 Polyhedron *Porig = P;
2943
2944 PP = Polyhedron2Param_SD(&P,C,MaxRays,&CEq,&CT);
2945
2946 if (isIdentity(CT)) {
2947 Matrix_Free(CT);
2948 CT = NULL;
2949 } else {
2950 assert(CT->NbRows != CT->NbColumns);
2951 if (CT->NbRows == 1) { // no more parameters
2952 eres = barvinok_enumerate_cst(P, CEq, MaxRays);
2953 out:
2954 if (CT)
2955 Matrix_Free(CT);
2956 if (PP)
2957 Param_Polyhedron_Free(PP);
2958 if (P != Porig)
2959 Polyhedron_Free(P);
2960
2961 return eres;
2962 }
2963 nparam = CT->NbRows - 1;
2964 }
2965
2966 unsigned dim = P->Dimension - nparam;
2967
2968 ALLOC(evalue, eres);
2969 value_init(eres->d);
2970 value_set_si(eres->d, 0);
2971
2972 int nd;
2973 for (nd = 0, D=PP->D; D; ++nd, D=D->next);
2974 struct section { Polyhedron *D; evalue E; };
2975 section *s = new section[nd];
2976 Polyhedron **fVD = new Polyhedron_p[nd];
2977
2978 try_again:
2979 #ifdef USE_INCREMENTAL_BF
2980 bfenumerator et(P, dim, PP->nbV);
2981 #elif defined USE_INCREMENTAL_DF
2982 ienumerator et(P, dim, PP->nbV);
2983 #else
2984 enumerator et(P, dim, PP->nbV);
2985 #endif
2986
2987 for(nd = 0, D=PP->D; D; D=next) {
2988 next = D->next;
2989
2990 Polyhedron *rVD = reduce_domain(D->Domain, CT, CEq,
2991 fVD, nd, MaxRays);
2992 if (!rVD)
2993 continue;
2994
2995 pVD = CT ? DomainImage(rVD,CT,MaxRays) : rVD;
2996
2997 value_init(s[nd].E.d);
2998 evalue_set_si(&s[nd].E, 0, 1);
2999 s[nd].D = rVD;
3000
3001 FORALL_PVertex_in_ParamPolyhedron(V,D,PP) // _i is internal counter
3002 if (!et.vE[_i])
3003 try {
3004 et.decompose_at(V, _i, MaxRays);
3005 } catch (OrthogonalException &e) {
3006 if (rVD != pVD)
3007 Domain_Free(pVD);
3008 for (; nd >= 0; --nd) {
3009 free_evalue_refs(&s[nd].E);
3010 Domain_Free(s[nd].D);
3011 Domain_Free(fVD[nd]);
3012 }
3013 goto try_again;
3014 }
3015 eadd(et.vE[_i] , &s[nd].E);
3016 END_FORALL_PVertex_in_ParamPolyhedron;
3017 evalue_range_reduction_in_domain(&s[nd].E, pVD);
3018
3019 if (CT)
3020 addeliminatedparams_evalue(&s[nd].E, CT);
3021 ++nd;
3022 if (rVD != pVD)
3023 Domain_Free(pVD);
3024 }
3025
3026 if (nd == 0)
3027 evalue_set_si(eres, 0, 1);
3028 else {
3029 eres->x.p = new_enode(partition, 2*nd, C->Dimension);
3030 for (int j = 0; j < nd; ++j) {
3031 EVALUE_SET_DOMAIN(eres->x.p->arr[2*j], s[j].D);
3032 value_clear(eres->x.p->arr[2*j+1].d);
3033 eres->x.p->arr[2*j+1] = s[j].E;
3034 Domain_Free(fVD[j]);
3035 }
3036 }
3037 delete [] s;
3038 delete [] fVD;
3039
3040 if (CEq)
3041 Polyhedron_Free(CEq);
3042 goto out;
3043 }
3044
3045 Enumeration* barvinok_enumerate(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
3046 {
3047 evalue *EP = barvinok_enumerate_ev(P, C, MaxRays);
3048
3049 return partition2enumeration(EP);
3050 }
3051
3052 static void SwapColumns(Value **V, int n, int i, int j)
3053 {
3054 for (int r = 0; r < n; ++r)
3055 value_swap(V[r][i], V[r][j]);
3056 }
3057
3058 static void SwapColumns(Polyhedron *P, int i, int j)
3059 {
3060 SwapColumns(P->Constraint, P->NbConstraints, i, j);
3061 SwapColumns(P->Ray, P->NbRays, i, j);
3062 }
3063
3064 /* Construct a constraint c from constraints l and u such that if
3065 * if constraint c holds then for each value of the other variables
3066 * there is at most one value of variable pos (position pos+1 in the constraints).
3067 *
3068 * Given a lower and an upper bound
3069 * n_l v_i + <c_l,x> + c_l >= 0
3070 * -n_u v_i + <c_u,x> + c_u >= 0
3071 * the constructed constraint is
3072 *
3073 * -(n_l<c_u,x> + n_u<c_l,x>) + (-n_l c_u - n_u c_l + n_l n_u - 1)
3074 *
3075 * which is then simplified to remove the content of the non-constant coefficients
3076 *
3077 * len is the total length of the constraints.
3078 * v is a temporary variable that can be used by this procedure
3079 */
3080 static void negative_test_constraint(Value *l, Value *u, Value *c, int pos,
3081 int len, Value *v)
3082 {
3083 value_oppose(*v, u[pos+1]);
3084 Vector_Combine(l+1, u+1, c+1, *v, l[pos+1], len-1);
3085 value_multiply(*v, *v, l[pos+1]);
3086 value_subtract(c[len-1], c[len-1], *v);
3087 value_set_si(*v, -1);
3088 Vector_Scale(c+1, c+1, *v, len-1);
3089 value_decrement(c[len-1], c[len-1]);
3090 ConstraintSimplify(c, c, len, v);
3091 }
3092
3093 static bool parallel_constraints(Value *l, Value *u, Value *c, int pos,
3094 int len)
3095 {
3096 bool parallel;
3097 Value g1;
3098 Value g2;
3099 value_init(g1);
3100 value_init(g2);
3101
3102 Vector_Gcd(&l[1+pos], len, &g1);
3103 Vector_Gcd(&u[1+pos], len, &g2);
3104 Vector_Combine(l+1+pos, u+1+pos, c+1, g2, g1, len);
3105 parallel = First_Non_Zero(c+1, len) == -1;
3106
3107 value_clear(g1);
3108 value_clear(g2);
3109
3110 return parallel;
3111 }
3112
3113 static void negative_test_constraint7(Value *l, Value *u, Value *c, int pos,
3114 int exist, int len, Value *v)
3115 {
3116 Value g;
3117 value_init(g);
3118
3119 Vector_Gcd(&u[1+pos], exist, v);
3120 Vector_Gcd(&l[1+pos], exist, &g);
3121 Vector_Combine(l+1, u+1, c+1, *v, g, len-1);
3122 value_multiply(*v, *v, g);
3123 value_subtract(c[len-1], c[len-1], *v);
3124 value_set_si(*v, -1);
3125 Vector_Scale(c+1, c+1, *v, len-1);
3126 value_decrement(c[len-1], c[len-1]);
3127 ConstraintSimplify(c, c, len, v);
3128
3129 value_clear(g);
3130 }
3131
3132 /* Turns a x + b >= 0 into a x + b <= -1
3133 *
3134 * len is the total length of the constraint.
3135 * v is a temporary variable that can be used by this procedure
3136 */
3137 static void oppose_constraint(Value *c, int len, Value *v)
3138 {
3139 value_set_si(*v, -1);
3140 Vector_Scale(c+1, c+1, *v, len-1);
3141 value_decrement(c[len-1], c[len-1]);
3142 }
3143
3144 /* Split polyhedron P into two polyhedra *pos and *neg, where
3145 * existential variable i has at most one solution for each
3146 * value of the other variables in *neg.
3147 *
3148 * The splitting is performed using constraints l and u.
3149 *
3150 * nvar: number of set variables
3151 * row: temporary vector that can be used by this procedure
3152 * f: temporary value that can be used by this procedure
3153 */
3154 static bool SplitOnConstraint(Polyhedron *P, int i, int l, int u,
3155 int nvar, int MaxRays, Vector *row, Value& f,
3156 Polyhedron **pos, Polyhedron **neg)
3157 {
3158 negative_test_constraint(P->Constraint[l], P->Constraint[u],
3159 row->p, nvar+i, P->Dimension+2, &f);
3160 *neg = AddConstraints(row->p, 1, P, MaxRays);
3161
3162 /* We found an independent, but useless constraint
3163 * Maybe we should detect this earlier and not
3164 * mark the variable as INDEPENDENT
3165 */
3166 if (emptyQ((*neg))) {
3167 Polyhedron_Free(*neg);
3168 return false;
3169 }
3170
3171 oppose_constraint(row->p, P->Dimension+2, &f);
3172 *pos = AddConstraints(row->p, 1, P, MaxRays);
3173
3174 if (emptyQ((*pos))) {
3175 Polyhedron_Free(*neg);
3176 Polyhedron_Free(*pos);
3177 return false;
3178 }
3179
3180 return true;
3181 }
3182
3183 /*
3184 * unimodularly transform P such that constraint r is transformed
3185 * into a constraint that involves only a single (the first)
3186 * existential variable
3187 *
3188 */
3189 static Polyhedron *rotate_along(Polyhedron *P, int r, int nvar, int exist,
3190 unsigned MaxRays)
3191 {
3192 Value g;
3193 value_init(g);
3194
3195 Vector *row = Vector_Alloc(exist);
3196 Vector_Copy(P->Constraint[r]+1+nvar, row->p, exist);
3197 Vector_Gcd(row->p, exist, &g);
3198 if (value_notone_p(g))
3199 Vector_AntiScale(row->p, row->p, g, exist);
3200 value_clear(g);
3201
3202 Matrix *M = unimodular_complete(row);
3203 Matrix *M2 = Matrix_Alloc(P->Dimension+1, P->Dimension+1);
3204 for (r = 0; r < nvar; ++r)
3205 value_set_si(M2->p[r][r], 1);
3206 for ( ; r < nvar+exist; ++r)
3207 Vector_Copy(M->p[r-nvar], M2->p[r]+nvar, exist);
3208 for ( ; r < P->Dimension+1; ++r)
3209 value_set_si(M2->p[r][r], 1);
3210 Polyhedron *T = Polyhedron_Image(P, M2, MaxRays);
3211
3212 Matrix_Free(M2);
3213 Matrix_Free(M);
3214 Vector_Free(row);
3215
3216 return T;
3217 }
3218
3219 /* Split polyhedron P into two polyhedra *pos and *neg, where
3220 * existential variable i has at most one solution for each
3221 * value of the other variables in *neg.
3222 *
3223 * If independent is set, then the two constraints on which the
3224 * split will be performed need to be independent of the other
3225 * existential variables.
3226 *
3227 * Return true if an appropriate split could be performed.
3228 *
3229 * nvar: number of set variables
3230 * exist: number of existential variables
3231 * row: temporary vector that can be used by this procedure
3232 * f: temporary value that can be used by this procedure
3233 */
3234 static bool SplitOnVar(Polyhedron *P, int i,
3235 int nvar, int exist, int MaxRays,
3236 Vector *row, Value& f, bool independent,
3237 Polyhedron **pos, Polyhedron **neg)
3238 {
3239 int j;
3240
3241 for (int l = P->NbEq; l < P->NbConstraints; ++l) {
3242 if (value_negz_p(P->Constraint[l][nvar+i+1]))
3243 continue;
3244
3245 if (independent) {
3246 for (j = 0; j < exist; ++j)
3247 if (j != i && value_notzero_p(P->Constraint[l][nvar+j+1]))
3248 break;
3249 if (j < exist)
3250 continue;
3251 }
3252
3253 for (int u = P->NbEq; u < P->NbConstraints; ++u) {
3254 if (value_posz_p(P->Constraint[u][nvar+i+1]))
3255 continue;
3256
3257 if (independent) {
3258 for (j = 0; j < exist; ++j)
3259 if (j != i && value_notzero_p(P->Constraint[u][nvar+j+1]))
3260 break;
3261 if (j < exist)
3262 continue;
3263 }
3264
3265 if (SplitOnConstraint(P, i, l, u, nvar, MaxRays, row, f, pos, neg)) {
3266 if (independent) {
3267 if (i != 0)
3268 SwapColumns(*neg, nvar+1, nvar+1+i);
3269 }
3270 return true;
3271 }
3272 }
3273 }
3274
3275 return false;
3276 }
3277
3278 static bool double_bound_pair(Polyhedron *P, int nvar, int exist,
3279 int i, int l1, int l2,
3280 Polyhedron **pos, Polyhedron **neg)
3281 {
3282 Value f;
3283 value_init(f);
3284 Vector *row = Vector_Alloc(P->Dimension+2);
3285 value_set_si(row->p[0], 1);
3286 value_oppose(f, P->Constraint[l1][nvar+i+1]);
3287 Vector_Combine(P->Constraint[l1]+1, P->Constraint[l2]+1,
3288 row->p+1,
3289 P->Constraint[l2][nvar+i+1], f,
3290 P->Dimension+1);
3291 ConstraintSimplify(row->p, row->p, P->Dimension+2, &f);
3292 *pos = AddConstraints(row->p, 1, P, 0);
3293 value_set_si(f, -1);
3294 Vector_Scale(row->p+1, row->p+1, f, P->Dimension+1);
3295 value_decrement(row->p[P->Dimension+1], row->p[P->Dimension+1]);
3296 *neg = AddConstraints(row->p, 1, P, 0);
3297 Vector_Free(row);
3298 value_clear(f);
3299
3300 return !emptyQ((*pos)) && !emptyQ((*neg));
3301 }
3302
3303 static bool double_bound(Polyhedron *P, int nvar, int exist,
3304 Polyhedron **pos, Polyhedron **neg)
3305 {
3306 for (int i = 0; i < exist; ++i) {
3307 int l1, l2;
3308 for (l1 = P->NbEq; l1 < P->NbConstraints; ++l1) {
3309 if (value_negz_p(P->Constraint[l1][nvar+i+1]))
3310 continue;
3311 for (l2 = l1 + 1; l2 < P->NbConstraints; ++l2) {
3312 if (value_negz_p(P->Constraint[l2][nvar+i+1]))
3313 continue;
3314 if (double_bound_pair(P, nvar, exist, i, l1, l2, pos, neg))
3315 return true;
3316 }
3317 }
3318 for (l1 = P->NbEq; l1 < P->NbConstraints; ++l1) {
3319 if (value_posz_p(P->Constraint[l1][nvar+i+1]))
3320 continue;
3321 if (l1 < P->NbConstraints)
3322 for (l2 = l1 + 1; l2 < P->NbConstraints; ++l2) {
3323 if (value_posz_p(P->Constraint[l2][nvar+i+1]))
3324 continue;
3325 if (double_bound_pair(P, nvar, exist, i, l1, l2, pos, neg))
3326 return true;
3327 }
3328 }
3329 return false;
3330 }
3331 return false;
3332 }
3333
3334 enum constraint {
3335 ALL_POS = 1 << 0,
3336 ONE_NEG = 1 << 1,
3337 INDEPENDENT = 1 << 2,
3338 ROT_NEG = 1 << 3
3339 };
3340
3341 static evalue* enumerate_or(Polyhedron *D,
3342 unsigned exist, unsigned nparam, unsigned MaxRays)
3343 {
3344 #ifdef DEBUG_ER
3345 fprintf(stderr, "\nER: Or\n");
3346 #endif /* DEBUG_ER */
3347
3348 Polyhedron *N = D->next;
3349 D->next = 0;
3350 evalue *EP =
3351 barvinok_enumerate_e(D, exist, nparam, MaxRays);
3352 Polyhedron_Free(D);
3353
3354 for (D = N; D; D = N) {
3355 N = D->next;
3356 D->next = 0;
3357
3358 evalue *EN =
3359 barvinok_enumerate_e(D, exist, nparam, MaxRays);
3360
3361 eor(EN, EP);
3362 free_evalue_refs(EN);
3363 free(EN);
3364 Polyhedron_Free(D);
3365 }
3366
3367 reduce_evalue(EP);
3368
3369 return EP;
3370 }
3371
3372 static evalue* enumerate_sum(Polyhedron *P,
3373 unsigned exist, unsigned nparam, unsigned MaxRays)
3374 {
3375 int nvar = P->Dimension - exist - nparam;
3376 int toswap = nvar < exist ? nvar : exist;
3377 for (int i = 0; i < toswap; ++i)
3378 SwapColumns(P, 1 + i, nvar+exist - i);
3379 nparam += nvar;
3380
3381 #ifdef DEBUG_ER
3382 fprintf(stderr, "\nER: Sum\n");
3383 #endif /* DEBUG_ER */
3384
3385 evalue *EP = barvinok_enumerate_e(P, exist, nparam, MaxRays);
3386
3387 for (int i = 0; i < /* nvar */ nparam; ++i) {
3388 Matrix *C = Matrix_Alloc(1, 1 + nparam + 1);
3389 value_set_si(C->p[0][0], 1);
3390 evalue split;
3391 value_init(split.d);
3392 value_set_si(split.d, 0);
3393 split.x.p = new_enode(partition, 4, nparam);
3394 value_set_si(C->p[0][1+i], 1);
3395 Matrix *C2 = Matrix_Copy(C);
3396 EVALUE_SET_DOMAIN(split.x.p->arr[0],
3397 Constraints2Polyhedron(C2, MaxRays));
3398 Matrix_Free(C2);
3399 evalue_set_si(&split.x.p->arr[1], 1, 1);
3400 value_set_si(C->p[0][1+i], -1);
3401 value_set_si(C->p[0][1+nparam], -1);
3402 EVALUE_SET_DOMAIN(split.x.p->arr[2],
3403 Constraints2Polyhedron(C, MaxRays));
3404 evalue_set_si(&split.x.p->arr[3], 1, 1);
3405 emul(&split, EP);
3406 free_evalue_refs(&split);
3407 Matrix_Free(C);
3408 }
3409 reduce_evalue(EP);
3410 evalue_range_reduction(EP);
3411
3412 evalue_frac2floor(EP);
3413
3414 evalue *sum = esum(EP, nvar);
3415
3416 free_evalue_refs(EP);
3417 free(EP);
3418 EP = sum;
3419
3420 evalue_range_reduction(EP);
3421
3422 return EP;
3423 }
3424
3425 static evalue* split_sure(Polyhedron *P, Polyhedron *S,
3426 unsigned exist, unsigned nparam, unsigned MaxRays)
3427 {
3428 int nvar = P->Dimension - exist - nparam;
3429
3430 Matrix *M = Matrix_Alloc(exist, S->Dimension+2);
3431 for (int i = 0; i < exist; ++i)
3432 value_set_si(M->p[i][nvar+i+1], 1);
3433 Polyhedron *O = S;
3434 S = DomainAddRays(S, M, MaxRays);
3435 Polyhedron_Free(O);
3436 Polyhedron *F = DomainAddRays(P, M, MaxRays);
3437 Polyhedron *D = DomainDifference(F, S, MaxRays);
3438 O = D;
3439 D = Disjoint_Domain(D, 0, MaxRays);
3440 Polyhedron_Free(F);
3441 Domain_Free(O);
3442 Matrix_Free(M);
3443
3444 M = Matrix_Alloc(P->Dimension+1-exist, P->Dimension+1);
3445 for (int j = 0; j < nvar; ++j)
3446 value_set_si(M->p[j][j], 1);
3447 for (int j = 0; j < nparam+1; ++j)
3448 value_set_si(M->p[nvar+j][nvar+exist+j], 1);
3449 Polyhedron *T = Polyhedron_Image(S, M, MaxRays);
3450 evalue *EP = barvinok_enumerate_e(T, 0, nparam, MaxRays);
3451 Polyhedron_Free(S);
3452 Polyhedron_Free(T);
3453 Matrix_Free(M);
3454
3455 for (Polyhedron *Q = D; Q; Q = Q->next) {
3456 Polyhedron *N = Q->next;
3457 Q->next = 0;
3458 T = DomainIntersection(P, Q, MaxRays);
3459 evalue *E = barvinok_enumerate_e(T, exist, nparam, MaxRays);
3460 eadd(E, EP);
3461 free_evalue_refs(E);
3462 free(E);
3463 Polyhedron_Free(T);
3464 Q->next = N;
3465 }
3466 Domain_Free(D);
3467 return EP;
3468 }
3469
3470 static evalue* enumerate_sure(Polyhedron *P,
3471 unsigned exist, unsigned nparam, unsigned MaxRays)
3472 {
3473 int i;
3474 Polyhedron *S = P;
3475 int nvar = P->Dimension - exist - nparam;
3476 Value lcm;
3477 Value f;
3478 value_init(lcm);
3479 value_init(f);
3480
3481 for (i = 0; i < exist; ++i) {
3482 Matrix *M = Matrix_Alloc(S->NbConstraints, S->Dimension+2);
3483 int c = 0;
3484 value_set_si(lcm, 1);
3485 for (int j = 0; j < S->NbConstraints; ++j) {
3486 if (value_negz_p(S->Constraint[j][1+nvar+i]))
3487 continue;
3488 if (value_one_p(S->Constraint[j][1+nvar+i]))
3489 continue;
3490 value_lcm(lcm, S->Constraint[j][1+nvar+i], &lcm);
3491 }
3492
3493 for (int j = 0; j < S->NbConstraints; ++j) {
3494 if (value_negz_p(S->Constraint[j][1+nvar+i]))
3495 continue;
3496 if (value_one_p(S->Constraint[j][1+nvar+i]))
3497 continue;
3498 value_division(f, lcm, S->Constraint[j][1+nvar+i]);
3499 Vector_Scale(S->Constraint[j], M->p[c], f, S->Dimension+2);
3500 value_subtract(M->p[c][S->Dimension+1],
3501 M->p[c][S->Dimension+1],
3502 lcm);
3503 value_increment(M->p[c][S->Dimension+1],
3504 M->p[c][S->Dimension+1]);
3505 ++c;
3506 }
3507 Polyhedron *O = S;
3508 S = AddConstraints(M->p[0], c, S, MaxRays);
3509 if (O != P)
3510 Polyhedron_Free(O);
3511 Matrix_Free(M);
3512 if (emptyQ(S)) {
3513 Polyhedron_Free(S);
3514 value_clear(lcm);
3515 value_clear(f);
3516 return 0;
3517 }
3518 }
3519 value_clear(lcm);
3520 value_clear(f);
3521
3522 #ifdef DEBUG_ER
3523 fprintf(stderr, "\nER: Sure\n");
3524 #endif /* DEBUG_ER */
3525
3526 return split_sure(P, S, exist, nparam, MaxRays);
3527 }
3528
3529 static evalue* enumerate_sure2(Polyhedron *P,
3530 unsigned exist, unsigned nparam, unsigned MaxRays)
3531 {
3532 int nvar = P->Dimension - exist - nparam;
3533 int r;
3534 for (r = 0; r < P->NbRays; ++r)
3535 if (value_one_p(P->Ray[r][0]) &&
3536 value_one_p(P->Ray[r][P->Dimension+1]))
3537 break;
3538
3539 if (r >= P->NbRays)
3540 return 0;
3541
3542 Matrix *M = Matrix_Alloc(nvar + 1 + nparam, P->Dimension+2);
3543 for (int i = 0; i < nvar; ++i)
3544 value_set_si(M->p[i][1+i], 1);
3545 for (int i = 0; i < nparam; ++i)
3546 value_set_si(M->p[i+nvar][1+nvar+exist+i], 1);
3547 Vector_Copy(P->Ray[r]+1+nvar, M->p[nvar+nparam]+1+nvar, exist);
3548 value_set_si(M->p[nvar+nparam][0], 1);
3549 value_set_si(M->p[nvar+nparam][P->Dimension+1], 1);
3550 Polyhedron * F = Rays2Polyhedron(M, MaxRays);
3551 Matrix_Free(M);
3552
3553 Polyhedron *I = DomainIntersection(F, P, MaxRays);
3554 Polyhedron_Free(F);
3555
3556 #ifdef DEBUG_ER
3557 fprintf(stderr, "\nER: Sure2\n");
3558 #endif /* DEBUG_ER */
3559
3560 return split_sure(P, I, exist, nparam, MaxRays);
3561 }
3562
3563 static evalue* enumerate_cyclic(Polyhedron *P,
3564 unsigned exist, unsigned nparam,
3565 evalue * EP, int r, int p, unsigned MaxRays)
3566 {
3567 int nvar = P->Dimension - exist - nparam;
3568
3569 /* If EP in its fractional maps only contains references
3570 * to the remainder parameter with appropriate coefficients
3571 * then we could in principle avoid adding existentially
3572 * quantified variables to the validity domains.
3573 * We'd have to replace the remainder by m { p/m }
3574 * and multiply with an appropriate factor that is one
3575 * only in the appropriate range.
3576 * This last multiplication can be avoided if EP
3577 * has a single validity domain with no (further)
3578 * constraints on the remainder parameter
3579 */
3580
3581 Matrix *CT = Matrix_Alloc(nparam+1, nparam+3);
3582 Matrix *M = Matrix_Alloc(1, 1+nparam+3);
3583 for (int j = 0; j < nparam; ++j)
3584 if (j != p)
3585 value_set_si(CT->p[j][j], 1);
3586 value_set_si(CT->p[p][nparam+1], 1);
3587 value_set_si(CT->p[nparam][nparam+2], 1);
3588 value_set_si(M->p[0][1+p], -1);
3589 value_absolute(M->p[0][1+nparam], P->Ray[0][1+nvar+exist+p]);
3590 value_set_si(M->p[0][1+nparam+1], 1);
3591 Polyhedron *CEq = Constraints2Polyhedron(M, 1);
3592 Matrix_Free(M);
3593 addeliminatedparams_enum(EP, CT, CEq, MaxRays, nparam);
3594 Polyhedron_Free(CEq);
3595 Matrix_Free(CT);
3596
3597 return EP;
3598 }
3599
3600 static void enumerate_vd_add_ray(evalue *EP, Matrix *Rays, unsigned MaxRays)
3601 {
3602 if (value_notzero_p(EP->d))
3603 return;
3604
3605 assert(EP->x.p->type == partition);
3606 assert(EP->x.p->pos == EVALUE_DOMAIN(EP->x.p->arr[0])->Dimension);
3607 for (int i = 0; i < EP->x.p->size/2; ++i) {
3608 Polyhedron *D = EVALUE_DOMAIN(EP->x.p->arr[2*i]);
3609 Polyhedron *N = DomainAddRays(D, Rays, MaxRays);
3610 EVALUE_SET_DOMAIN(EP->x.p->arr[2*i], N);
3611 Domain_Free(D);
3612 }
3613 }
3614
3615 static evalue* enumerate_line(Polyhedron *P,
3616 unsigned exist, unsigned nparam, unsigned MaxRays)
3617 {
3618 if (P->NbBid == 0)
3619 return 0;
3620
3621 #ifdef DEBUG_ER
3622 fprintf(stderr, "\nER: Line\n");
3623 #endif /* DEBUG_ER */
3624
3625 int nvar = P->Dimension - exist - nparam;
3626 int i, j;
3627 for (i = 0; i < nparam; ++i)
3628 if (value_notzero_p(P->Ray[0][1+nvar+exist+i]))
3629 break;
3630 assert(i < nparam);
3631 for (j = i+1; j < nparam; ++j)
3632 if (value_notzero_p(P->Ray[0][1+nvar+exist+i]))
3633 break;
3634 assert(j >= nparam); // for now
3635
3636 Matrix *M = Matrix_Alloc(2, P->Dimension+2);
3637 value_set_si(M->p[0][0], 1);
3638 value_set_si(M->p[0][1+nvar+exist+i], 1);
3639 value_set_si(M->p[1][0], 1);
3640 value_set_si(M->p[1][1+nvar+exist+i], -1);
3641 value_absolute(M->p[1][1+P->Dimension], P->Ray[0][1+nvar+exist+i]);
3642 value_decrement(M->p[1][1+P->Dimension], M->p[1][1+P->Dimension]);
3643 Polyhedron *S = AddConstraints(M->p[0], 2, P, MaxRays);
3644 evalue *EP = barvinok_enumerate_e(S, exist, nparam, MaxRays);
3645 Polyhedron_Free(S);
3646 Matrix_Free(M);
3647
3648 return enumerate_cyclic(P, exist, nparam, EP, 0, i, MaxRays);
3649 }
3650
3651 static int single_param_pos(Polyhedron*P, unsigned exist, unsigned nparam,
3652 int r)
3653 {
3654 int nvar = P->Dimension - exist - nparam;
3655 if (First_Non_Zero(P->Ray[r]+1, nvar) != -1)
3656 return -1;
3657 int i = First_Non_Zero(P->Ray[r]+1+nvar+exist, nparam);
3658 if (i == -1)
3659 return -1;
3660 if (First_Non_Zero(P->Ray[r]+1+nvar+exist+1, nparam-i-1) != -1)
3661 return -1;
3662 return i;
3663 }
3664
3665 static evalue* enumerate_remove_ray(Polyhedron *P, int r,
3666 unsigned exist, unsigned nparam, unsigned MaxRays)
3667 {
3668 #ifdef DEBUG_ER
3669 fprintf(stderr, "\nER: RedundantRay\n");
3670 #endif /* DEBUG_ER */
3671
3672 Value one;
3673 value_init(one);
3674 value_set_si(one, 1);
3675 int len = P->NbRays-1;
3676 Matrix *M = Matrix_Alloc(2 * len, P->Dimension+2);
3677 Vector_Copy(P->Ray[0], M->p[0], r * (P->Dimension+2));
3678 Vector_Copy(P->Ray[r+1], M->p[r], (len-r) * (P->Dimension+2));
3679 for (int j = 0; j < P->NbRays; ++j) {
3680 if (j == r)
3681 continue;
3682 Vector_Combine(P->Ray[j], P->Ray[r], M->p[len+j-(j>r)],
3683 one, P->Ray[j][P->Dimension+1], P->Dimension+2);
3684 }
3685
3686 P = Rays2Polyhedron(M, MaxRays);
3687 Matrix_Free(M);
3688 evalue *EP = barvinok_enumerate_e(P, exist, nparam, MaxRays);
3689 Polyhedron_Free(P);
3690 value_clear(one);
3691
3692 return EP;
3693 }
3694
3695 static evalue* enumerate_redundant_ray(Polyhedron *P,
3696 unsigned exist, unsigned nparam, unsigned MaxRays)
3697 {
3698 assert(P->NbBid == 0);
3699 int nvar = P->Dimension - exist - nparam;
3700 Value m;
3701 value_init(m);
3702
3703 for (int r = 0; r < P->NbRays; ++r) {
3704 if (value_notzero_p(P->Ray[r][P->Dimension+1]))
3705 continue;
3706 int i1 = single_param_pos(P, exist, nparam, r);
3707 if (i1 == -1)
3708 continue;
3709 for (int r2 = r+1; r2 < P->NbRays; ++r2) {
3710 if (value_notzero_p(P->Ray[r2][P->Dimension+1]))
3711 continue;
3712 int i2 = single_param_pos(P, exist, nparam, r2);
3713 if (i2 == -1)
3714 continue;
3715 if (i1 != i2)
3716 continue;
3717
3718 value_division(m, P->Ray[r][1+nvar+exist+i1],
3719 P->Ray[r2][1+nvar+exist+i1]);
3720 value_multiply(m, m, P->Ray[r2][1+nvar+exist+i1]);
3721 /* r2 divides r => r redundant */
3722 if (value_eq(m, P->Ray[r][1+nvar+exist+i1])) {
3723 value_clear(m);
3724 return enumerate_remove_ray(P, r, exist, nparam, MaxRays);
3725 }
3726
3727 value_division(m, P->Ray[r2][1+nvar+exist+i1],
3728 P->Ray[r][1+nvar+exist+i1]);
3729 value_multiply(m, m, P->Ray[r][1+nvar+exist+i1]);
3730 /* r divides r2 => r2 redundant */
3731 if (value_eq(m, P->Ray[r2][1+nvar+exist+i1])) {
3732 value_clear(m);
3733 return enumerate_remove_ray(P, r2, exist, nparam, MaxRays);
3734 }
3735 }
3736 }
3737 value_clear(m);
3738 return 0;
3739 }
3740
3741 static Polyhedron *upper_bound(Polyhedron *P,
3742 int pos, Value *max, Polyhedron **R)
3743 {
3744 Value v;
3745 int r;
3746 value_init(v);
3747
3748 *R = 0;
3749 Polyhedron *N;
3750 Polyhedron *B = 0;
3751 for (Polyhedron *Q = P; Q; Q = N) {
3752 N = Q->next;
3753 for (r = 0; r < P->NbRays; ++r) {
3754 if (value_zero_p(P->Ray[r][P->Dimension+1]) &&
3755 value_pos_p(P->Ray[r][1+pos]))
3756 break;
3757 }
3758 if (r < P->NbRays) {
3759 Q->next = *R;
3760 *R = Q;
3761 continue;
3762 } else {
3763 Q->next = B;
3764 B = Q;
3765 }
3766 for (r = 0; r < P->NbRays; ++r) {
3767 if (value_zero_p(P->Ray[r][P->Dimension+1]))
3768 continue;
3769 mpz_fdiv_q(v, P->Ray[r][1+pos], P->Ray[r][1+P->Dimension]);
3770 if ((!Q->next && r == 0) || value_gt(v, *max))
3771 value_assign(*max, v);
3772 }
3773 }
3774 value_clear(v);
3775 return B;
3776 }
3777
3778 static evalue* enumerate_ray(Polyhedron *P,
3779 unsigned exist, unsigned nparam, unsigned MaxRays)
3780 {
3781 assert(P->NbBid == 0);
3782 int nvar = P->Dimension - exist - nparam;
3783
3784 int r;
3785 for (r = 0; r < P->NbRays; ++r)
3786 if (value_zero_p(P->Ray[r][P->Dimension+1]))
3787 break;
3788 if (r >= P->NbRays)
3789 return 0;
3790
3791 int r2;
3792 for (r2 = r+1; r2 < P->NbRays; ++r2)
3793 if (value_zero_p(P->Ray[r2][P->Dimension+1]))
3794 break;
3795 if (r2 < P->NbRays) {
3796 if (nvar > 0)
3797 return enumerate_sum(P, exist, nparam, MaxRays);
3798 }
3799
3800 #ifdef DEBUG_ER
3801 fprintf(stderr, "\nER: Ray\n");
3802 #endif /* DEBUG_ER */
3803
3804 Value m;
3805 Value one;
3806 value_init(m);
3807 value_init(one);
3808 value_set_si(one, 1);
3809 int i = single_param_pos(P, exist, nparam, r);
3810 assert(i != -1); // for now;
3811
3812 Matrix *M = Matrix_Alloc(P->NbRays, P->Dimension+2);
3813 for (int j = 0; j < P->NbRays; ++j) {
3814 Vector_Combine(P->Ray[j], P->Ray[r], M->p[j],
3815 one, P->Ray[j][P->Dimension+1], P->Dimension+2);
3816 }
3817 Polyhedron *S = Rays2Polyhedron(M, MaxRays);
3818 Matrix_Free(M);
3819 Polyhedron *D = DomainDifference(P, S, MaxRays);
3820 Polyhedron_Free(S);
3821 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
3822 assert(value_pos_p(P->Ray[r][1+nvar+exist+i])); // for now
3823 Polyhedron *R;
3824 D = upper_bound(D, nvar+exist+i, &m, &R);
3825 assert(D);
3826 Domain_Free(D);
3827
3828 M = Matrix_Alloc(2, P->Dimension+2);
3829 value_set_si(M->p[0][0], 1);
3830 value_set_si(M->p[1][0], 1);
3831 value_set_si(M->p[0][1+nvar+exist+i], -1);
3832 value_set_si(M->p[1][1+nvar+exist+i], 1);
3833 value_assign(M->p[0][1+P->Dimension], m);
3834 value_oppose(M->p[1][1+P->Dimension], m);
3835 value_addto(M->p[1][1+P->Dimension], M->p[1][1+P->Dimension],
3836 P->Ray[r][1+nvar+exist+i]);
3837 value_decrement(M->p[1][1+P->Dimension], M->p[1][1+P->Dimension]);
3838 // Matrix_Print(stderr, P_VALUE_FMT, M);
3839 D = AddConstraints(M->p[0], 2, P, MaxRays);
3840 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
3841 value_subtract(M->p[0][1+P->Dimension], M->p[0][1+P->Dimension],
3842 P->Ray[r][1+nvar+exist+i]);
3843 // Matrix_Print(stderr, P_VALUE_FMT, M);
3844 S = AddConstraints(M->p[0], 1, P, MaxRays);
3845 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
3846 Matrix_Free(M);
3847
3848 evalue *EP = barvinok_enumerate_e(D, exist, nparam, MaxRays);
3849 Polyhedron_Free(D);
3850 value_clear(one);
3851 value_clear(m);
3852
3853 if (value_notone_p(P->Ray[r][1+nvar+exist+i]))
3854 EP = enumerate_cyclic(P, exist, nparam, EP, r, i, MaxRays);
3855 else {
3856 M = Matrix_Alloc(1, nparam+2);
3857 value_set_si(M->p[0][0], 1);
3858 value_set_si(M->p[0][1+i], 1);
3859 enumerate_vd_add_ray(EP, M, MaxRays);
3860 Matrix_Free(M);
3861 }
3862
3863 if (!emptyQ(S)) {
3864 evalue *E = barvinok_enumerate_e(S, exist, nparam, MaxRays);
3865 eadd(E, EP);
3866 free_evalue_refs(E);
3867 free(E);
3868 }
3869 Polyhedron_Free(S);
3870
3871 if (R) {
3872 assert(nvar == 0);
3873 evalue *ER = enumerate_or(R, exist, nparam, MaxRays);
3874 eor(ER, EP);
3875 free_evalue_refs(ER);
3876 free(ER);
3877 }
3878
3879 return EP;
3880 }
3881
3882 static evalue* enumerate_vd(Polyhedron **PA,
3883 unsigned exist, unsigned nparam, unsigned MaxRays)
3884 {
3885 Polyhedron *P = *PA;
3886 int nvar = P->Dimension - exist - nparam;
3887 Param_Polyhedron *PP = NULL;
3888 Polyhedron *C = Universe_Polyhedron(nparam);
3889 Polyhedron *CEq;
3890 Matrix *CT;
3891 Polyhedron *PR = P;
3892 PP = Polyhedron2Param_SimplifiedDomain(&PR,C,MaxRays,&CEq,&CT);
3893 Polyhedron_Free(C);
3894
3895 int nd;
3896 Param_Domain *D, *last;
3897 Value c;
3898 value_init(c);
3899 for (nd = 0, D=PP->D; D; D=D->next, ++nd)
3900 ;
3901
3902 Polyhedron **VD = new Polyhedron_p[nd];
3903 Polyhedron **fVD = new Polyhedron_p[nd];
3904 for(nd = 0, D=PP->D; D; D=D->next) {
3905 Polyhedron *rVD = reduce_domain(D->Domain, CT, CEq,
3906 fVD, nd, MaxRays);
3907 if (!rVD)
3908 continue;
3909
3910 VD[nd++] = rVD;
3911 last = D;
3912 }
3913
3914 evalue *EP = 0;
3915
3916 if (nd == 0)
3917 EP = evalue_zero();
3918
3919 /* This doesn't seem to have any effect */
3920 if (nd == 1) {
3921 Polyhedron *CA = align_context(VD[0], P->Dimension, MaxRays);
3922 Polyhedron *O = P;
3923 P = DomainIntersection(P, CA, MaxRays);
3924 if (O != *PA)
3925 Polyhedron_Free(O);
3926 Polyhedron_Free(CA);
3927 if (emptyQ(P))
3928 EP = evalue_zero();
3929 }
3930
3931 if (!EP && CT->NbColumns != CT->NbRows) {
3932 Polyhedron *CEqr = DomainImage(CEq, CT, MaxRays);
3933 Polyhedron *CA = align_context(CEqr, PR->Dimension, MaxRays);
3934 Polyhedron *I = DomainIntersection(PR, CA, MaxRays);
3935 Polyhedron_Free(CEqr);
3936 Polyhedron_Free(CA);
3937 #ifdef DEBUG_ER
3938 fprintf(stderr, "\nER: Eliminate\n");
3939 #endif /* DEBUG_ER */
3940 nparam -= CT->NbColumns - CT->NbRows;
3941 EP = barvinok_enumerate_e(I, exist, nparam, MaxRays);
3942 nparam += CT->NbColumns - CT->NbRows;
3943 addeliminatedparams_enum(EP, CT, CEq, MaxRays, nparam);
3944 Polyhedron_Free(I);
3945 }
3946 if (PR != *PA)
3947 Polyhedron_Free(PR);
3948 PR = 0;
3949
3950 if (!EP && nd > 1) {
3951 #ifdef DEBUG_ER
3952 fprintf(stderr, "\nER: VD\n");
3953 #endif /* DEBUG_ER */
3954 for (int i = 0; i < nd; ++i) {
3955 Polyhedron *CA = align_context(VD[i], P->Dimension, MaxRays);
3956 Polyhedron *I = DomainIntersection(P, CA, MaxRays);
3957
3958 if (i == 0)
3959 EP = barvinok_enumerate_e(I, exist, nparam, MaxRays);
3960 else {
3961 evalue *E = barvinok_enumerate_e(I, exist, nparam, MaxRays);
3962 eadd(E, EP);
3963 free_evalue_refs(E);
3964 free(E);
3965 }
3966 Polyhedron_Free(I);
3967 Polyhedron_Free(CA);
3968 }
3969 }
3970
3971 for (int i = 0; i < nd; ++i) {
3972 Polyhedron_Free(VD[i]);
3973 Polyhedron_Free(fVD[i]);
3974 }
3975 delete [] VD;
3976 delete [] fVD;
3977 value_clear(c);
3978
3979 if (!EP && nvar == 0) {
3980 Value f;
3981 value_init(f);
3982 Param_Vertices *V, *V2;
3983 Matrix* M = Matrix_Alloc(1, P->Dimension+2);
3984
3985 FORALL_PVertex_in_ParamPolyhedron(V, last, PP) {
3986 bool found = false;
3987 FORALL_PVertex_in_ParamPolyhedron(V2, last, PP) {
3988 if (V == V2) {
3989 found = true;
3990 continue;
3991 }
3992 if (!found)
3993 continue;
3994 for (int i = 0; i < exist; ++i) {
3995 value_oppose(f, V->Vertex->p[i][nparam+1]);
3996 Vector_Combine(V->Vertex->p[i],
3997 V2->Vertex->p[i],
3998 M->p[0] + 1 + nvar + exist,
3999 V2->Vertex->p[i][nparam+1],
4000 f,
4001 nparam+1);
4002 int j;
4003 for (j = 0; j < nparam; ++j)
4004 if (value_notzero_p(M->p[0][1+nvar+exist+j]))
4005 break;
4006 if (j >= nparam)
4007 continue;
4008 ConstraintSimplify(M->p[0], M->p[0],
4009 P->Dimension+2, &f);
4010 value_set_si(M->p[0][0], 0);
4011 Polyhedron *para = AddConstraints(M->p[0], 1, P,
4012 MaxRays);
4013 if (emptyQ(para)) {
4014 Polyhedron_Free(para);
4015 continue;
4016 }
4017 Polyhedron *pos, *neg;
4018 value_set_si(M->p[0][0], 1);
4019 value_decrement(M->p[0][P->Dimension+1],
4020 M->p[0][P->Dimension+1]);
4021 neg = AddConstraints(M->p[0], 1, P, MaxRays);
4022 value_set_si(f, -1);
4023 Vector_Scale(M->p[0]+1, M->p[0]+1, f,
4024 P->Dimension+1);
4025 value_decrement(M->p[0][P->Dimension+1],
4026 M->p[0][P->Dimension+1]);
4027 value_decrement(M->p[0][P->Dimension+1],
4028 M->p[0][P->Dimension+1]);
4029 pos = AddConstraints(M->p[0], 1, P, MaxRays);
4030 if (emptyQ(neg) && emptyQ(pos)) {
4031 Polyhedron_Free(para);
4032 Polyhedron_Free(pos);
4033 Polyhedron_Free(neg);
4034 continue;
4035 }
4036 #ifdef DEBUG_ER
4037 fprintf(stderr, "\nER: Order\n");
4038 #endif /* DEBUG_ER */
4039 EP = barvinok_enumerate_e(para, exist, nparam, MaxRays);
4040 evalue *E;
4041 if (!emptyQ(pos)) {
4042 E = barvinok_enumerate_e(pos, exist, nparam, MaxRays);
4043 eadd(E, EP);
4044 free_evalue_refs(E);
4045 free(E);
4046 }
4047 if (!emptyQ(neg)) {
4048 E = barvinok_enumerate_e(neg, exist, nparam, MaxRays);
4049 eadd(E, EP);
4050 free_evalue_refs(E);
4051 free(E);
4052 }
4053 Polyhedron_Free(para);
4054 Polyhedron_Free(pos);
4055 Polyhedron_Free(neg);
4056 break;
4057 }
4058 if (EP)
4059 break;
4060 } END_FORALL_PVertex_in_ParamPolyhedron;
4061 if (EP)
4062 break;
4063 } END_FORALL_PVertex_in_ParamPolyhedron;
4064
4065 if (!EP) {
4066 /* Search for vertex coordinate to split on */
4067 /* First look for one independent of the parameters */
4068 FORALL_PVertex_in_ParamPolyhedron(V, last, PP) {
4069 for (int i = 0; i < exist; ++i) {
4070 int j;
4071 for (j = 0; j < nparam; ++j)
4072 if (value_notzero_p(V->Vertex->p[i][j]))
4073 break;
4074 if (j < nparam)
4075 continue;
4076 value_set_si(M->p[0][0], 1);
4077 Vector_Set(M->p[0]+1, 0, nvar+exist);
4078 Vector_Copy(V->Vertex->p[i],
4079 M->p[0] + 1 + nvar + exist, nparam+1);
4080 value_oppose(M->p[0][1+nvar+i],
4081 V->Vertex->p[i][nparam+1]);
4082
4083 Polyhedron *pos, *neg;
4084 value_set_si(M->p[0][0], 1);
4085 value_decrement(M->p[0][P->Dimension+1],
4086 M->p[0][P->Dimension+1]);
4087 neg = AddConstraints(M->p[0], 1, P, MaxRays);
4088 value_set_si(f, -1);
4089 Vector_Scale(M->p[0]+1, M->p[0]+1, f,
4090 P->Dimension+1);
4091 value_decrement(M->p[0][P->Dimension+1],
4092 M->p[0][P->Dimension+1]);
4093 value_decrement(M->p[0][P->Dimension+1],
4094 M->p[0][P->Dimension+1]);
4095 pos = AddConstraints(M->p[0], 1, P, MaxRays);
4096 if (emptyQ(neg) || emptyQ(pos)) {
4097 Polyhedron_Free(pos);
4098 Polyhedron_Free(neg);
4099 continue;
4100 }
4101 Polyhedron_Free(pos);
4102 value_increment(M->p[0][P->Dimension+1],
4103 M->p[0][P->Dimension+1]);
4104 pos = AddConstraints(M->p[0], 1, P, MaxRays);
4105 #ifdef DEBUG_ER
4106 fprintf(stderr, "\nER: Vertex\n");
4107 #endif /* DEBUG_ER */
4108 pos->next = neg;
4109 EP = enumerate_or(pos, exist, nparam, MaxRays);
4110 break;
4111 }
4112 if (EP)
4113 break;
4114 } END_FORALL_PVertex_in_ParamPolyhedron;
4115 }
4116
4117 if (!EP) {
4118 /* Search for vertex coordinate to split on */
4119 /* Now look for one that depends on the parameters */
4120 FORALL_PVertex_in_ParamPolyhedron(V, last, PP) {
4121 for (int i = 0; i < exist; ++i) {
4122 value_set_si(M->p[0][0], 1);
4123 Vector_Set(M->p[0]+1, 0, nvar+exist);
4124 Vector_Copy(V->Vertex->p[i],
4125 M->p[0] + 1 + nvar + exist, nparam+1);
4126 value_oppose(M->p[0][1+nvar+i],
4127 V->Vertex->p[i][nparam+1]);
4128
4129 Polyhedron *pos, *neg;
4130 value_set_si(M->p[0][0], 1);
4131 value_decrement(M->p[0][P->Dimension+1],
4132 M->p[0][P->Dimension+1]);
4133 neg = AddConstraints(M->p[0], 1, P, MaxRays);
4134 value_set_si(f, -1);
4135 Vector_Scale(M->p[0]+1, M->p[0]+1, f,
4136 P->Dimension+1);
4137 value_decrement(M->p[0][P->Dimension+1],
4138 M->p[0][P->Dimension+1]);
4139 value_decrement(M->p[0][P->Dimension+1],
4140 M->p[0][P->Dimension+1]);
4141 pos = AddConstraints(M->p[0], 1, P, MaxRays);
4142 if (emptyQ(neg) || emptyQ(pos)) {
4143 Polyhedron_Free(pos);
4144 Polyhedron_Free(neg);
4145 continue;
4146 }
4147 Polyhedron_Free(pos);
4148 value_increment(M->p[0][P->Dimension+1],
4149 M->p[0][P->Dimension+1]);
4150 pos = AddConstraints(M->p[0], 1, P, MaxRays);
4151 #ifdef DEBUG_ER
4152 fprintf(stderr, "\nER: ParamVertex\n");
4153 #endif /* DEBUG_ER */
4154 pos->next = neg;
4155 EP = enumerate_or(pos, exist, nparam, MaxRays);
4156 break;
4157 }
4158 if (EP)
4159 break;
4160 } END_FORALL_PVertex_in_ParamPolyhedron;
4161 }
4162
4163 Matrix_Free(M);
4164 value_clear(f);
4165 }
4166
4167 if (CEq)
4168 Polyhedron_Free(CEq);
4169 if (CT)
4170 Matrix_Free(CT);
4171 if (PP)
4172 Param_Polyhedron_Free(PP);
4173 *PA = P;
4174
4175 return EP;
4176 }
4177
4178 #ifndef HAVE_PIPLIB
4179 evalue *barvinok_enumerate_pip(Polyhedron *P,
4180 unsigned exist, unsigned nparam, unsigned MaxRays)
4181 {
4182 return 0;
4183 }
4184 #else
4185 evalue *barvinok_enumerate_pip(Polyhedron *P,
4186 unsigned exist, unsigned nparam, unsigned MaxRays)
4187 {
4188 int nvar = P->Dimension - exist - nparam;
4189 evalue *EP = evalue_zero();
4190 Polyhedron *Q, *N;
4191
4192 #ifdef DEBUG_ER
4193 fprintf(stderr, "\nER: PIP\n");
4194 #endif /* DEBUG_ER */
4195
4196 Polyhedron *D = pip_projectout(P, nvar, exist, nparam);
4197 for (Q = D; Q; Q = N) {
4198 N = Q->next;
4199 Q->next = 0;
4200 evalue *E;
4201 exist = Q->Dimension - nvar - nparam;
4202 E = barvinok_enumerate_e(Q, exist, nparam, MaxRays);
4203 Polyhedron_Free(Q);
4204 eadd(E, EP);
4205 free_evalue_refs(E);
4206 free(E);
4207 }
4208
4209 return EP;
4210 }
4211 #endif
4212
4213
4214 static bool is_single(Value *row, int pos, int len)
4215 {
4216 return First_Non_Zero(row, pos) == -1 &&
4217 First_Non_Zero(row+pos+1, len-pos-1) == -1;
4218 }
4219
4220 static evalue* barvinok_enumerate_e_r(Polyhedron *P,
4221 unsigned exist, unsigned nparam, unsigned MaxRays);
4222
4223 #ifdef DEBUG_ER
4224 static int er_level = 0;
4225
4226 evalue* barvinok_enumerate_e(Polyhedron *P,
4227 unsigned exist, unsigned nparam, unsigned MaxRays)
4228 {
4229 fprintf(stderr, "\nER: level %i\n", er_level);
4230
4231 Polyhedron_PrintConstraints(stderr, P_VALUE_FMT, P);
4232 fprintf(stderr, "\nE %d\nP %d\n", exist, nparam);
4233 ++er_level;
4234 P = DomainConstraintSimplify(Polyhedron_Copy(P), MaxRays);
4235 evalue *EP = barvinok_enumerate_e_r(P, exist, nparam, MaxRays);
4236 Polyhedron_Free(P);
4237 --er_level;
4238 return EP;
4239 }
4240 #else
4241 evalue* barvinok_enumerate_e(Polyhedron *P,
4242 unsigned exist, unsigned nparam, unsigned MaxRays)
4243 {
4244 P = DomainConstraintSimplify(Polyhedron_Copy(P), MaxRays);
4245 evalue *EP = barvinok_enumerate_e_r(P, exist, nparam, MaxRays);
4246 Polyhedron_Free(P);
4247 return EP;
4248 }
4249 #endif
4250
4251 static evalue* barvinok_enumerate_e_r(Polyhedron *P,
4252 unsigned exist, unsigned nparam, unsigned MaxRays)
4253 {
4254 if (exist == 0) {
4255 Polyhedron *U = Universe_Polyhedron(nparam);
4256 evalue *EP = barvinok_enumerate_ev(P, U, MaxRays);
4257 //char *param_name[] = {"P", "Q", "R", "S", "T" };
4258 //print_evalue(stdout, EP, param_name);
4259 Polyhedron_Free(U);
4260 return EP;
4261 }
4262
4263 int nvar = P->Dimension - exist - nparam;
4264 int len = P->Dimension + 2;
4265
4266 /* for now */
4267 POL_ENSURE_FACETS(P);
4268 POL_ENSURE_VERTICES(P);
4269
4270 if (emptyQ(P))
4271 return evalue_zero();
4272
4273 if (nvar == 0 && nparam == 0) {
4274 evalue *EP = evalue_zero();
4275 barvinok_count(P, &EP->x.n, MaxRays);
4276 if (value_pos_p(EP->x.n))
4277 value_set_si(EP->x.n, 1);
4278 return EP;
4279 }
4280
4281 int r;
4282 for (r = 0; r < P->NbRays; ++r)
4283 if (value_zero_p(P->Ray[r][0]) ||
4284 value_zero_p(P->Ray[r][P->Dimension+1])) {
4285 int i;
4286 for (i = 0; i < nvar; ++i)
4287 if (value_notzero_p(P->Ray[r][i+1]))
4288 break;
4289 if (i >= nvar)
4290 continue;
4291 for (i = nvar + exist; i < nvar + exist + nparam; ++i)
4292 if (value_notzero_p(P->Ray[r][i+1]))
4293 break;
4294 if (i >= nvar + exist + nparam)
4295 break;
4296 }
4297 if (r < P->NbRays) {
4298 evalue *EP = evalue_zero();
4299 value_set_si(EP->x.n, -1);
4300 return EP;
4301 }
4302
4303 int first;
4304 for (r = 0; r < P->NbEq; ++r)
4305 if ((first = First_Non_Zero(P->Constraint[r]+1+nvar, exist)) != -1)
4306 break;
4307 if (r < P->NbEq) {
4308 if (First_Non_Zero(P->Constraint[r]+1+nvar+first+1,
4309 exist-first-1) != -1) {
4310 Polyhedron *T = rotate_along(P, r, nvar, exist, MaxRays);
4311 #ifdef DEBUG_ER
4312 fprintf(stderr, "\nER: Equality\n");
4313 #endif /* DEBUG_ER */
4314 evalue *EP = barvinok_enumerate_e(T, exist-1, nparam, MaxRays);
4315 Polyhedron_Free(T);
4316 return EP;
4317 } else {
4318 #ifdef DEBUG_ER
4319 fprintf(stderr, "\nER: Fixed\n");
4320 #endif /* DEBUG_ER */
4321 if (first == 0)
4322 return barvinok_enumerate_e(P, exist-1, nparam, MaxRays);
4323 else {
4324 Polyhedron *T = Polyhedron_Copy(P);
4325 SwapColumns(T, nvar+1, nvar+1+first);
4326 evalue *EP = barvinok_enumerate_e(T, exist-1, nparam, MaxRays);
4327 Polyhedron_Free(T);
4328 return EP;
4329 }
4330 }
4331 }
4332
4333 Vector *row = Vector_Alloc(len);
4334 value_set_si(row->p[0], 1);
4335
4336 Value f;
4337 value_init(f);
4338
4339 enum constraint* info = new constraint[exist];
4340 for (int i = 0; i < exist; ++i) {
4341 info[i] = ALL_POS;
4342 for (int l = P->NbEq; l < P->NbConstraints; ++l) {
4343 if (value_negz_p(P->Constraint[l][nvar+i+1]))
4344 continue;
4345 bool l_parallel = is_single(P->Constraint[l]+nvar+1, i, exist);
4346 for (int u = P->NbEq; u < P->NbConstraints; ++u) {
4347 if (value_posz_p(P->Constraint[u][nvar+i+1]))
4348 continue;
4349 bool lu_parallel = l_parallel ||
4350 is_single(P->Constraint[u]+nvar+1, i, exist);
4351 value_oppose(f, P->Constraint[u][nvar+i+1]);
4352 Vector_Combine(P->Constraint[l]+1, P->Constraint[u]+1, row->p+1,
4353 f, P->Constraint[l][nvar+i+1], len-1);
4354 if (!(info[i] & INDEPENDENT)) {
4355 int j;
4356 for (j = 0; j < exist; ++j)
4357 if (j != i && value_notzero_p(row->p[nvar+j+1]))
4358 break;
4359 if (j == exist) {
4360 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
4361 info[i] = (constraint)(info[i] | INDEPENDENT);
4362 }
4363 }
4364 if (info[i] & ALL_POS) {
4365 value_addto(row->p[len-1], row->p[len-1],
4366 P->Constraint[l][nvar+i+1]);
4367 value_addto(row->p[len-1], row->p[len-1], f);
4368 value_multiply(f, f, P->Constraint[l][nvar+i+1]);
4369 value_subtract(row->p[len-1], row->p[len-1], f);
4370 value_decrement(row->p[len-1], row->p[len-1]);
4371 ConstraintSimplify(row->p, row->p, len, &f);
4372 value_set_si(f, -1);
4373 Vector_Scale(row->p+1, row->p+1, f, len-1);
4374 value_decrement(row->p[len-1], row->p[len-1]);
4375 Polyhedron *T = AddConstraints(row->p, 1, P, MaxRays);
4376 if (!emptyQ(T)) {
4377 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
4378 info[i] = (constraint)(info[i] ^ ALL_POS);
4379 }
4380 //puts("pos remainder");
4381 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
4382 Polyhedron_Free(T);
4383 }
4384 if (!(info[i] & ONE_NEG)) {
4385 if (lu_parallel) {
4386 negative_test_constraint(P->Constraint[l],
4387 P->Constraint[u],
4388 row->p, nvar+i, len, &f);
4389 oppose_constraint(row->p, len, &f);
4390 Polyhedron *T = AddConstraints(row->p, 1, P, MaxRays);
4391 if (emptyQ(T)) {
4392 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
4393 info[i] = (constraint)(info[i] | ONE_NEG);
4394 }
4395 //puts("neg remainder");
4396 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
4397 Polyhedron_Free(T);
4398 } else if (!(info[i] & ROT_NEG)) {
4399 if (parallel_constraints(P->Constraint[l],
4400 P->Constraint[u],
4401 row->p, nvar, exist)) {
4402 negative_test_constraint7(P->Constraint[l],
4403 P->Constraint[u],
4404 row->p, nvar, exist,
4405 len, &f);
4406 oppose_constraint(row->p, len, &f);
4407 Polyhedron *T = AddConstraints(row->p, 1, P, MaxRays);
4408 if (emptyQ(T)) {
4409 // printf("rot_neg i: %d, l: %d, u: %d\n", i, l, u);
4410 info[i] = (constraint)(info[i] | ROT_NEG);
4411 r = l;
4412 }
4413 //puts("neg remainder");
4414 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
4415 Polyhedron_Free(T);
4416 }
4417 }
4418 }
4419 if (!(info[i] & ALL_POS) && (info[i] & (ONE_NEG | ROT_NEG)))
4420 goto next;
4421 }
4422 }
4423 if (info[i] & ALL_POS)
4424 break;
4425 next:
4426 ;
4427 }
4428
4429 /*
4430 for (int i = 0; i < exist; ++i)
4431 printf("%i: %i\n", i, info[i]);
4432 */
4433 for (int i = 0; i < exist; ++i)
4434 if (info[i] & ALL_POS) {
4435 #ifdef DEBUG_ER
4436 fprintf(stderr, "\nER: Positive\n");
4437 #endif /* DEBUG_ER */
4438 // Eliminate
4439 // Maybe we should chew off some of the fat here
4440 Matrix *M = Matrix_Alloc(P->Dimension, P->Dimension+1);
4441 for (int j = 0; j < P->Dimension; ++j)
4442 value_set_si(M->p[j][j + (j >= i+nvar)], 1);
4443 Polyhedron *T = Polyhedron_Image(P, M, MaxRays);
4444 Matrix_Free(M);
4445 evalue *EP = barvinok_enumerate_e(T, exist-1, nparam, MaxRays);
4446 Polyhedron_Free(T);
4447 value_clear(f);
4448 Vector_Free(row);
4449 delete [] info;
4450 return EP;
4451 }
4452 for (int i = 0; i < exist; ++i)
4453 if (info[i] & ONE_NEG) {
4454 #ifdef DEBUG_ER
4455 fprintf(stderr, "\nER: Negative\n");
4456 #endif /* DEBUG_ER */
4457 Vector_Free(row);
4458 value_clear(f);
4459 delete [] info;
4460 if (i == 0)
4461 return barvinok_enumerate_e(P, exist-1, nparam, MaxRays);
4462 else {
4463 Polyhedron *T = Polyhedron_Copy(P);
4464 SwapColumns(T, nvar+1, nvar+1+i);
4465 evalue *EP = barvinok_enumerate_e(T, exist-1, nparam, MaxRays);
4466 Polyhedron_Free(T);
4467 return EP;
4468 }
4469 }
4470 for (int i = 0; i < exist; ++i)
4471 if (info[i] & ROT_NEG) {
4472 #ifdef DEBUG_ER
4473 fprintf(stderr, "\nER: Rotate\n");
4474 #endif /* DEBUG_ER */
4475 Vector_Free(row);
4476 value_clear(f);
4477 delete [] info;
4478 Polyhedron *T = rotate_along(P, r, nvar, exist, MaxRays);
4479 evalue *EP = barvinok_enumerate_e(T, exist-1, nparam, MaxRays);
4480 Polyhedron_Free(T);
4481 return EP;
4482 }
4483 for (int i = 0; i < exist; ++i)
4484 if (info[i] & INDEPENDENT) {
4485 Polyhedron *pos, *neg;
4486
4487 /* Find constraint again and split off negative part */
4488
4489 if (SplitOnVar(P, i, nvar, exist, MaxRays,
4490 row, f, true, &pos, &neg)) {
4491 #ifdef DEBUG_ER
4492 fprintf(stderr, "\nER: Split\n");
4493 #endif /* DEBUG_ER */
4494
4495 evalue *EP =
4496 barvinok_enumerate_e(neg, exist-1, nparam, MaxRays);
4497 evalue *E =
4498 barvinok_enumerate_e(pos, exist, nparam, MaxRays);
4499 eadd(E, EP);
4500 free_evalue_refs(E);
4501 free(E);
4502 Polyhedron_Free(neg);
4503 Polyhedron_Free(pos);
4504 value_clear(f);
4505 Vector_Free(row);
4506 delete [] info;
4507 return EP;
4508 }
4509 }
4510 delete [] info;
4511
4512 Polyhedron *O = P;
4513 Polyhedron *F;
4514
4515 evalue *EP;
4516
4517 EP = enumerate_line(P, exist, nparam, MaxRays);
4518 if (EP)
4519 goto out;
4520
4521 EP = barvinok_enumerate_pip(P, exist, nparam, MaxRays);
4522 if (EP)
4523 goto out;
4524
4525 EP = enumerate_redundant_ray(P, exist, nparam, MaxRays);
4526 if (EP)
4527 goto out;
4528
4529 EP = enumerate_sure(P, exist, nparam, MaxRays);
4530 if (EP)
4531 goto out;
4532
4533 EP = enumerate_ray(P, exist, nparam, MaxRays);
4534 if (EP)
4535 goto out;
4536
4537 EP = enumerate_sure2(P, exist, nparam, MaxRays);
4538 if (EP)
4539 goto out;
4540
4541 F = unfringe(P, MaxRays);
4542 if (!PolyhedronIncludes(F, P)) {
4543 #ifdef DEBUG_ER
4544 fprintf(stderr, "\nER: Fringed\n");
4545 #endif /* DEBUG_ER */
4546 EP = barvinok_enumerate_e(F, exist, nparam, MaxRays);
4547 Polyhedron_Free(F);
4548 goto out;
4549 }
4550 Polyhedron_Free(F);
4551
4552 if (nparam)
4553 EP = enumerate_vd(&P, exist, nparam, MaxRays);
4554 if (EP)
4555 goto out2;
4556
4557 if (nvar != 0) {
4558 EP = enumerate_sum(P, exist, nparam, MaxRays);
4559 goto out2;
4560 }
4561
4562 assert(nvar == 0);
4563
4564 int i;
4565 Polyhedron *pos, *neg;
4566 for (i = 0; i < exist; ++i)
4567 if (SplitOnVar(P, i, nvar, exist, MaxRays,
4568 row, f, false, &pos, &neg))
4569 break;
4570
4571 assert (i < exist);
4572
4573 pos->next = neg;
4574 EP = enumerate_or(pos, exist, nparam, MaxRays);
4575
4576 out2:
4577 if (O != P)
4578 Polyhedron_Free(P);
4579
4580 out:
4581 value_clear(f);
4582 Vector_Free(row);
4583 return EP;
4584 }
4585
4586 static void split_param_compression(Matrix *CP, mat_ZZ& map, vec_ZZ& offset)
4587 {
4588 Matrix *T = Transpose(CP);
4589 matrix2zz(T, map, T->NbRows-1, T->NbColumns-1);
4590 values2zz(T->p[T->NbRows-1], offset, T->NbColumns-1);
4591 Matrix_Free(T);
4592 }
4593
4594 /*
4595 * remove equalities that require a "compression" of the parameters
4596 */
4597 #ifndef HAVE_COMPRESS_PARMS
4598 static Polyhedron *remove_more_equalities(Polyhedron *P, unsigned nparam,
4599 Matrix **CP, unsigned MaxRays)
4600 {
4601 return P;
4602 }
4603 #else
4604 static Polyhedron *remove_more_equalities(Polyhedron *P, unsigned nparam,
4605 Matrix **CP, unsigned MaxRays)
4606 {
4607 Matrix *M, *T;
4608 Polyhedron *Q;
4609
4610 /* compress_parms doesn't like equalities that only involve parameters */
4611 for (int i = 0; i < P->NbEq; ++i)
4612 assert(First_Non_Zero(P->Constraint[i]+1, P->Dimension-nparam) != -1);
4613
4614 M = Matrix_Alloc(P->NbEq, P->Dimension+2);
4615 Vector_Copy(P->Constraint[0], M->p[0], P->NbEq * (P->Dimension+2));
4616 *CP = compress_parms(M, nparam);
4617 T = align_matrix(*CP, P->Dimension+1);
4618 Q = Polyhedron_Preimage(P, T, MaxRays);
4619 Polyhedron_Free(P);
4620 P = Q;
4621 P = remove_equalities_p(P, P->Dimension-nparam, NULL);
4622 Matrix_Free(T);
4623 Matrix_Free(M);
4624 return P;
4625 }
4626 #endif
4627
4628 gen_fun * barvinok_series(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
4629 {
4630 Matrix *CP = NULL;
4631 Polyhedron *CA;
4632 unsigned nparam = C->Dimension;
4633
4634 CA = align_context(C, P->Dimension, MaxRays);
4635 P = DomainIntersection(P, CA, MaxRays);
4636 Polyhedron_Free(CA);
4637
4638 if (emptyQ2(P)) {
4639 Polyhedron_Free(P);
4640 return new gen_fun;
4641 }
4642
4643 assert(!Polyhedron_is_infinite(P, nparam));
4644 assert(P->NbBid == 0);
4645 assert(Polyhedron_has_positive_rays(P, nparam));
4646 if (P->NbEq != 0)
4647 P = remove_equalities_p(P, P->Dimension-nparam, NULL);
4648 if (P->NbEq != 0)
4649 P = remove_more_equalities(P, nparam, &CP, MaxRays);
4650 assert(P->NbEq == 0);
4651
4652 #ifdef USE_INCREMENTAL_BF
4653 partial_bfcounter red(P, nparam);
4654 #elif defined USE_INCREMENTAL_DF
4655 partial_ireducer red(P, nparam);
4656 #else
4657 partial_reducer red(P, nparam);
4658 #endif
4659 red.start(MaxRays);
4660 Polyhedron_Free(P);
4661 if (CP) {
4662 mat_ZZ map;
4663 vec_ZZ offset;
4664 split_param_compression(CP, map, offset);
4665 red.gf->substitute(CP, map, offset);
4666 Matrix_Free(CP);
4667 }
4668 return red.gf;
4669 }
4670
4671 static Polyhedron *skew_into_positive_orthant(Polyhedron *D, unsigned nparam,
4672 unsigned MaxRays)
4673 {
4674 Matrix *M = NULL;
4675 Value tmp;
4676 value_init(tmp);
4677 for (Polyhedron *P = D; P; P = P->next) {
4678 POL_ENSURE_VERTICES(P);
4679 assert(!Polyhedron_is_infinite(P, nparam));
4680 assert(P->NbBid == 0);
4681 assert(Polyhedron_has_positive_rays(P, nparam));
4682
4683 for (int r = 0; r < P->NbRays; ++r) {
4684 if (value_notzero_p(P->Ray[r][P->Dimension+1]))
4685 continue;
4686 for (int i = 0; i < nparam; ++i) {
4687 int j;
4688 if (value_posz_p(P->Ray[r][i+1]))
4689 continue;
4690 if (!M) {
4691 M = Matrix_Alloc(D->Dimension+1, D->Dimension+1);
4692 for (int i = 0; i < D->Dimension+1; ++i)
4693 value_set_si(M->p[i][i], 1);
4694 } else {
4695 Inner_Product(P->Ray[r]+1, M->p[i], D->Dimension+1, &tmp);
4696 if (value_posz_p(tmp))
4697 continue;
4698 }
4699 for (j = P->Dimension - nparam; j < P->Dimension; ++j)
4700 if (value_pos_p(P->Ray[r][j+1]))
4701 break;
4702 assert(j < P->Dimension);
4703 value_pdivision(tmp, P->Ray[r][j+1], P->Ray[r][i+1]);
4704 value_subtract(M->p[i][j], M->p[i][j], tmp);
4705 }
4706 }
4707 }
4708 value_clear(tmp);
4709 if (M) {
4710 D = DomainImage(D, M, MaxRays);
4711 Matrix_Free(M);
4712 }
4713 return D;
4714 }
4715
4716 gen_fun* barvinok_enumerate_union_series(Polyhedron *D, Polyhedron* C,
4717 unsigned MaxRays)
4718 {
4719 Polyhedron *conv, *D2;
4720 gen_fun *gf = NULL;
4721 unsigned nparam = C->Dimension;
4722 ZZ one, mone;
4723 one = 1;
4724 mone = -1;
4725 D2 = skew_into_positive_orthant(D, nparam, MaxRays);
4726 for (Polyhedron *P = D2; P; P = P->next) {
4727 assert(P->Dimension == D2->Dimension);
4728 POL_ENSURE_VERTICES(P);
4729 /* it doesn't matter which reducer we use, since we don't actually
4730 * reduce anything here
4731 */
4732 partial_reducer red(P, P->Dimension);
4733 red.start(MaxRays);
4734 if (!gf)
4735 gf = red.gf;
4736 else {
4737 gf->add_union(red.gf, MaxRays);
4738 delete red.gf;
4739 }
4740 }
4741 /* we actually only need the convex union of the parameter space
4742 * but the reducer classes currently expect a polyhedron in
4743 * the combined space
4744 */
4745 conv = DomainConvex(D2, MaxRays);
4746 #ifdef USE_INCREMENTAL_DF
4747 partial_ireducer red(conv, nparam);
4748 #else
4749 partial_reducer red(conv, nparam);
4750 #endif
4751 for (int i = 0; i < gf->term.size(); ++i) {
4752 for (int j = 0; j < gf->term[i]->n.power.NumRows(); ++j) {
4753 red.reduce(gf->term[i]->n.coeff[j][0], gf->term[i]->n.coeff[j][1],
4754 gf->term[i]->n.power[j], gf->term[i]->d.power);
4755 }
4756 }
4757 delete gf;
4758 if (D != D2)
4759 Domain_Free(D2);
4760 Polyhedron_Free(conv);
4761 return red.gf;
4762 }
4763
4764 evalue* barvinok_enumerate_union(Polyhedron *D, Polyhedron* C, unsigned MaxRays)
4765 {
4766 evalue *EP;
4767 gen_fun *gf = barvinok_enumerate_union_series(D, C, MaxRays);
4768 EP = *gf;
4769 delete gf;
4770 return EP;
4771 }
lattice point enumeration library