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lattice_point.h: make self-contained
[barvinok.git] / barvinok.cc
blob2aa25f3ec48fd4667785725b56f14bdad0b0ce3e
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 #include <barvinok/evalue.h>
12 extern "C" {
13 #include "piputil.h"
14 }
15 #include "config.h"
16 #include <barvinok/barvinok.h>
17 #include <barvinok/genfun.h>
18 #include <barvinok/options.h>
19 #include <barvinok/sample.h>
20 #include "conversion.h"
21 #include "decomposer.h"
22 #include "lattice_point.h"
23 #include "reduce_domain.h"
24 #include "genfun_constructor.h"
25 #include "remove_equalities.h"
26
27 #ifndef HAVE_PARAM_POLYHEDRON_SCALE_INTEGER
28 extern "C" void Param_Polyhedron_Scale_Integer(Param_Polyhedron *PP, Polyhedron **P,
29 Value *det, unsigned MaxRays);
30 #endif
31
32 #ifdef NTL_STD_CXX
33 using namespace NTL;
34 #endif
35 using std::cerr;
36 using std::cout;
37 using std::endl;
38 using std::vector;
39 using std::deque;
40 using std::string;
41 using std::ostringstream;
42
43 #define ALLOC(t,p) p = (t*)malloc(sizeof(*p))
44
45 class dpoly_n {
46 public:
47 Matrix *coeff;
48 ~dpoly_n() {
49 Matrix_Free(coeff);
50 }
51 dpoly_n(int d, ZZ& degree_0, ZZ& degree_1, int offset = 0) {
52 Value d0, d1;
53 value_init(d0);
54 value_init(d1);
55 zz2value(degree_0, d0);
56 zz2value(degree_1, d1);
57 coeff = Matrix_Alloc(d+1, d+1+1);
58 value_set_si(coeff->p[0][0], 1);
59 value_set_si(coeff->p[0][d+1], 1);
60 for (int i = 1; i <= d; ++i) {
61 value_multiply(coeff->p[i][0], coeff->p[i-1][0], d0);
62 Vector_Combine(coeff->p[i-1], coeff->p[i-1]+1, coeff->p[i]+1,
63 d1, d0, i);
64 value_set_si(coeff->p[i][d+1], i);
65 value_multiply(coeff->p[i][d+1], coeff->p[i][d+1], coeff->p[i-1][d+1]);
66 value_decrement(d0, d0);
67 }
68 value_clear(d0);
69 value_clear(d1);
70 }
71 void div(dpoly& d, Vector *count, ZZ& sign) {
72 int len = coeff->NbRows;
73 Matrix * c = Matrix_Alloc(coeff->NbRows, coeff->NbColumns);
74 Value tmp;
75 value_init(tmp);
76 for (int i = 0; i < len; ++i) {
77 Vector_Copy(coeff->p[i], c->p[i], len+1);
78 for (int j = 1; j <= i; ++j) {
79 zz2value(d.coeff[j], tmp);
80 value_multiply(tmp, tmp, c->p[i][len]);
81 value_oppose(tmp, tmp);
82 Vector_Combine(c->p[i], c->p[i-j], c->p[i],
83 c->p[i-j][len], tmp, len);
84 value_multiply(c->p[i][len], c->p[i][len], c->p[i-j][len]);
85 }
86 zz2value(d.coeff[0], tmp);
87 value_multiply(c->p[i][len], c->p[i][len], tmp);
88 }
89 if (sign == -1) {
90 value_set_si(tmp, -1);
91 Vector_Scale(c->p[len-1], count->p, tmp, len);
92 value_assign(count->p[len], c->p[len-1][len]);
93 } else
94 Vector_Copy(c->p[len-1], count->p, len+1);
95 Vector_Normalize(count->p, len+1);
96 value_clear(tmp);
97 Matrix_Free(c);
98 }
99 };
100
101 const int MAX_TRY=10;
102 /*
103 * Searches for a vector that is not orthogonal to any
104 * of the rays in rays.
105 */
106 static void nonorthog(mat_ZZ& rays, vec_ZZ& lambda)
107 {
108 int dim = rays.NumCols();
109 bool found = false;
110 lambda.SetLength(dim);
111 if (dim == 0)
112 return;
113
114 for (int i = 2; !found && i <= 50*dim; i+=4) {
115 for (int j = 0; j < MAX_TRY; ++j) {
116 for (int k = 0; k < dim; ++k) {
117 int r = random_int(i)+2;
118 int v = (2*(r%2)-1) * (r >> 1);
119 lambda[k] = v;
120 }
121 int k = 0;
122 for (; k < rays.NumRows(); ++k)
123 if (lambda * rays[k] == 0)
124 break;
125 if (k == rays.NumRows()) {
126 found = true;
127 break;
128 }
129 }
130 }
131 assert(found);
132 }
133
134 static void add_rays(mat_ZZ& rays, Polyhedron *i, int *r, int nvar = -1,
135 bool all = false)
136 {
137 unsigned dim = i->Dimension;
138 if (nvar == -1)
139 nvar = dim;
140 for (int k = 0; k < i->NbRays; ++k) {
141 if (!value_zero_p(i->Ray[k][dim+1]))
142 continue;
143 if (!all && nvar != dim && First_Non_Zero(i->Ray[k]+1, nvar) == -1)
144 continue;
145 values2zz(i->Ray[k]+1, rays[(*r)++], nvar);
146 }
147 }
148
149 static void mask_r(Matrix *f, int nr, Vector *lcm, int p, Vector *val, evalue *ev)
150 {
151 unsigned nparam = lcm->Size;
152
153 if (p == nparam) {
154 Vector * prod = Vector_Alloc(f->NbRows);
155 Matrix_Vector_Product(f, val->p, prod->p);
156 int isint = 1;
157 for (int i = 0; i < nr; ++i) {
158 value_modulus(prod->p[i], prod->p[i], f->p[i][nparam+1]);
159 isint &= value_zero_p(prod->p[i]);
160 }
161 value_set_si(ev->d, 1);
162 value_init(ev->x.n);
163 value_set_si(ev->x.n, isint);
164 Vector_Free(prod);
165 return;
166 }
167
168 Value tmp;
169 value_init(tmp);
170 if (value_one_p(lcm->p[p]))
171 mask_r(f, nr, lcm, p+1, val, ev);
172 else {
173 value_assign(tmp, lcm->p[p]);
174 value_set_si(ev->d, 0);
175 ev->x.p = new_enode(periodic, VALUE_TO_INT(tmp), p+1);
176 do {
177 value_decrement(tmp, tmp);
178 value_assign(val->p[p], tmp);
179 mask_r(f, nr, lcm, p+1, val, &ev->x.p->arr[VALUE_TO_INT(tmp)]);
180 } while (value_pos_p(tmp));
181 }
182 value_clear(tmp);
183 }
184
185 static void mask_fractional(Matrix *f, evalue *factor)
186 {
187 int nr = f->NbRows, nc = f->NbColumns;
188 int n;
189 bool found = false;
190 for (n = 0; n < nr && value_notzero_p(f->p[n][nc-1]); ++n)
191 if (value_notone_p(f->p[n][nc-1]) &&
192 value_notmone_p(f->p[n][nc-1]))
193 found = true;
194 if (!found)
195 return;
196
197 evalue EP;
198 nr = n;
199
200 Value m;
201 value_init(m);
202
203 evalue EV;
204 value_init(EV.d);
205 value_init(EV.x.n);
206 value_set_si(EV.x.n, 1);
207
208 for (n = 0; n < nr; ++n) {
209 value_assign(m, f->p[n][nc-1]);
210 if (value_one_p(m) || value_mone_p(m))
211 continue;
212
213 int j = normal_mod(f->p[n], nc-1, &m);
214 if (j == nc-1) {
215 free_evalue_refs(factor);
216 value_init(factor->d);
217 evalue_set_si(factor, 0, 1);
218 break;
219 }
220 vec_ZZ row;
221 values2zz(f->p[n], row, nc-1);
222 ZZ g;
223 value2zz(m, g);
224 if (j < (nc-1)-1 && row[j] > g/2) {
225 for (int k = j; k < (nc-1); ++k)
226 if (row[k] != 0)
227 row[k] = g - row[k];
228 }
229
230 value_init(EP.d);
231 value_set_si(EP.d, 0);
232 EP.x.p = new_enode(relation, 2, 0);
233 value_clear(EP.x.p->arr[1].d);
234 EP.x.p->arr[1] = *factor;
235 evalue *ev = &EP.x.p->arr[0];
236 value_set_si(ev->d, 0);
237 ev->x.p = new_enode(fractional, 3, -1);
238 evalue_set_si(&ev->x.p->arr[1], 0, 1);
239 evalue_set_si(&ev->x.p->arr[2], 1, 1);
240 evalue *E = multi_monom(row);
241 value_assign(EV.d, m);
242 emul(&EV, E);
243 value_clear(ev->x.p->arr[0].d);
244 ev->x.p->arr[0] = *E;
245 delete E;
246 *factor = EP;
247 }
248
249 value_clear(m);
250 free_evalue_refs(&EV);
251 }
252
253 /*
254 *
255 */
256 static void mask_table(Matrix *f, evalue *factor)
257 {
258 int nr = f->NbRows, nc = f->NbColumns;
259 int n;
260 bool found = false;
261 for (n = 0; n < nr && value_notzero_p(f->p[n][nc-1]); ++n)
262 if (value_notone_p(f->p[n][nc-1]) &&
263 value_notmone_p(f->p[n][nc-1]))
264 found = true;
265 if (!found)
266 return;
267
268 Value tmp;
269 value_init(tmp);
270 nr = n;
271 unsigned np = nc - 2;
272 Vector *lcm = Vector_Alloc(np);
273 Vector *val = Vector_Alloc(nc);
274 Vector_Set(val->p, 0, nc);
275 value_set_si(val->p[np], 1);
276 Vector_Set(lcm->p, 1, np);
277 for (n = 0; n < nr; ++n) {
278 if (value_one_p(f->p[n][nc-1]) ||
279 value_mone_p(f->p[n][nc-1]))
280 continue;
281 for (int j = 0; j < np; ++j)
282 if (value_notzero_p(f->p[n][j])) {
283 Gcd(f->p[n][j], f->p[n][nc-1], &tmp);
284 value_division(tmp, f->p[n][nc-1], tmp);
285 value_lcm(tmp, lcm->p[j], &lcm->p[j]);
286 }
287 }
288 evalue EP;
289 value_init(EP.d);
290 mask_r(f, nr, lcm, 0, val, &EP);
291 value_clear(tmp);
292 Vector_Free(val);
293 Vector_Free(lcm);
294 emul(&EP,factor);
295 free_evalue_refs(&EP);
296 }
297
298 static void mask(Matrix *f, evalue *factor, barvinok_options *options)
299 {
300 if (options->lookup_table)
301 mask_table(f, factor);
302 else
303 mask_fractional(f, factor);
304 }
305
306 /* This structure encodes the power of the term in a rational generating function.
307 *
308 * Either E == NULL or constant = 0
309 * If E != NULL, then the power is E
310 * If E == NULL, then the power is coeff * param[pos] + constant
311 */
312 struct term_info {
313 evalue *E;
314 ZZ constant;
315 ZZ coeff;
316 int pos;
317 };
318
319 /* Returns the power of (t+1) in the term of a rational generating function,
320 * i.e., the scalar product of the actual lattice point and lambda.
321 * The lattice point is the unique lattice point in the fundamental parallelepiped
322 * of the unimodual cone i shifted to the parametric vertex V.
323 *
324 * PD is the parameter domain, which, if != NULL, may be used to simply the
325 * resulting expression.
326 *
327 * The result is returned in term.
328 */
329 void lattice_point(Param_Vertices* V, const mat_ZZ& rays, vec_ZZ& lambda,
330 term_info* term, Polyhedron *PD, barvinok_options *options)
331 {
332 unsigned nparam = V->Vertex->NbColumns - 2;
333 unsigned dim = rays.NumCols();
334 mat_ZZ vertex;
335 vertex.SetDims(V->Vertex->NbRows, nparam+1);
336 Value lcm, tmp;
337 value_init(lcm);
338 value_init(tmp);
339 value_set_si(lcm, 1);
340 for (int j = 0; j < V->Vertex->NbRows; ++j) {
341 value_lcm(lcm, V->Vertex->p[j][nparam+1], &lcm);
342 }
343 if (value_notone_p(lcm)) {
344 Matrix * mv = Matrix_Alloc(dim, nparam+1);
345 for (int j = 0 ; j < dim; ++j) {
346 value_division(tmp, lcm, V->Vertex->p[j][nparam+1]);
347 Vector_Scale(V->Vertex->p[j], mv->p[j], tmp, nparam+1);
348 }
349
350 term->E = lattice_point(rays, lambda, mv, lcm, PD, options);
351 term->constant = 0;
352
353 Matrix_Free(mv);
354 value_clear(lcm);
355 value_clear(tmp);
356 return;
357 }
358 for (int i = 0; i < V->Vertex->NbRows; ++i) {
359 assert(value_one_p(V->Vertex->p[i][nparam+1])); // for now
360 values2zz(V->Vertex->p[i], vertex[i], nparam+1);
361 }
362
363 vec_ZZ num;
364 num = lambda * vertex;
365
366 int p = -1;
367 int nn = 0;
368 for (int j = 0; j < nparam; ++j)
369 if (num[j] != 0) {
370 ++nn;
371 p = j;
372 }
373 if (nn >= 2) {
374 term->E = multi_monom(num);
375 term->constant = 0;
376 } else {
377 term->E = NULL;
378 term->constant = num[nparam];
379 term->pos = p;
380 if (p != -1)
381 term->coeff = num[p];
382 }
383
384 value_clear(lcm);
385 value_clear(tmp);
386 }
387
388
389 struct counter : public np_base {
390 vec_ZZ lambda;
391 mat_ZZ vertex;
392 vec_ZZ den;
393 ZZ sign;
394 vec_ZZ num;
395 ZZ offset;
396 int j;
397 mpq_t count;
398
399 counter(unsigned dim) : np_base(dim) {
400 den.SetLength(dim);
401 mpq_init(count);
402 }
403
404 virtual void init(Polyhedron *P) {
405 randomvector(P, lambda, dim);
406 }
407
408 virtual void reset() {
409 mpq_set_si(count, 0, 0);
410 }
411
412 ~counter() {
413 mpq_clear(count);
414 }
415
416 virtual void handle(const mat_ZZ& rays, Value *vertex, const QQ& c,
417 unsigned long det, int *closed, barvinok_options *options);
418 virtual void get_count(Value *result) {
419 assert(value_one_p(&count[0]._mp_den));
420 value_assign(*result, &count[0]._mp_num);
421 }
422 };
423
424 void counter::handle(const mat_ZZ& rays, Value *V, const QQ& c, unsigned long det,
425 int *closed, barvinok_options *options)
426 {
427 for (int k = 0; k < dim; ++k) {
428 if (lambda * rays[k] == 0)
429 throw Orthogonal;
430 }
431
432 assert(c.d == 1);
433 assert(c.n == 1 || c.n == -1);
434 sign = c.n;
435
436 lattice_point(V, rays, vertex, det, closed);
437 num = vertex * lambda;
438 den = rays * lambda;
439 offset = 0;
440 normalize(sign, offset, den);
441
442 num[0] += offset;
443 dpoly d(dim, num[0]);
444 for (int k = 1; k < num.length(); ++k) {
445 num[k] += offset;
446 dpoly term(dim, num[k]);
447 d += term;
448 }
449 dpoly n(dim, den[0], 1);
450 for (int k = 1; k < dim; ++k) {
451 dpoly fact(dim, den[k], 1);
452 n *= fact;
453 }
454 d.div(n, count, sign);
455 }
456
457 struct bfe_term : public bfc_term_base {
458 vector<evalue *> factors;
459
460 bfe_term(int len) : bfc_term_base(len) {
461 }
462
463 ~bfe_term() {
464 for (int i = 0; i < factors.size(); ++i) {
465 if (!factors[i])
466 continue;
467 free_evalue_refs(factors[i]);
468 delete factors[i];
469 }
470 }
471 };
472
473 static void print_int_vector(int *v, int len, char *name)
474 {
475 cerr << name << endl;
476 for (int j = 0; j < len; ++j) {
477 cerr << v[j] << " ";
478 }
479 cerr << endl;
480 }
481
482 static void print_bfc_terms(mat_ZZ& factors, bfc_vec& v)
483 {
484 cerr << endl;
485 cerr << "factors" << endl;
486 cerr << factors << endl;
487 for (int i = 0; i < v.size(); ++i) {
488 cerr << "term: " << i << endl;
489 print_int_vector(v[i]->powers, factors.NumRows(), "powers");
490 cerr << "terms" << endl;
491 cerr << v[i]->terms << endl;
492 bfc_term* bfct = static_cast<bfc_term *>(v[i]);
493 cerr << bfct->c << endl;
494 }
495 }
496
497 static void print_bfe_terms(mat_ZZ& factors, bfc_vec& v)
498 {
499 cerr << endl;
500 cerr << "factors" << endl;
501 cerr << factors << endl;
502 for (int i = 0; i < v.size(); ++i) {
503 cerr << "term: " << i << endl;
504 print_int_vector(v[i]->powers, factors.NumRows(), "powers");
505 cerr << "terms" << endl;
506 cerr << v[i]->terms << endl;
507 bfe_term* bfet = static_cast<bfe_term *>(v[i]);
508 for (int j = 0; j < v[i]->terms.NumRows(); ++j) {
509 char * test[] = {"a", "b"};
510 print_evalue(stderr, bfet->factors[j], test);
511 fprintf(stderr, "\n");
512 }
513 }
514 }
515
516 struct bfcounter : public bfcounter_base {
517 mpq_t count;
518
519 bfcounter(unsigned dim) : bfcounter_base(dim) {
520 mpq_init(count);
521 lower = 1;
522 }
523 ~bfcounter() {
524 mpq_clear(count);
525 }
526 virtual void base(mat_ZZ& factors, bfc_vec& v);
527 virtual void get_count(Value *result) {
528 assert(value_one_p(&count[0]._mp_den));
529 value_assign(*result, &count[0]._mp_num);
530 }
531 };
532
533 void bfcounter::base(mat_ZZ& factors, bfc_vec& v)
534 {
535 unsigned nf = factors.NumRows();
536
537 for (int i = 0; i < v.size(); ++i) {
538 bfc_term* bfct = static_cast<bfc_term *>(v[i]);
539 int total_power = 0;
540 // factor is always positive, so we always
541 // change signs
542 for (int k = 0; k < nf; ++k)
543 total_power += v[i]->powers[k];
544
545 int j;
546 for (j = 0; j < nf; ++j)
547 if (v[i]->powers[j] > 0)
548 break;
549
550 dpoly D(total_power, factors[j][0], 1);
551 for (int k = 1; k < v[i]->powers[j]; ++k) {
552 dpoly fact(total_power, factors[j][0], 1);
553 D *= fact;
554 }
555 for ( ; ++j < nf; )
556 for (int k = 0; k < v[i]->powers[j]; ++k) {
557 dpoly fact(total_power, factors[j][0], 1);
558 D *= fact;
559 }
560
561 for (int k = 0; k < v[i]->terms.NumRows(); ++k) {
562 dpoly n(total_power, v[i]->terms[k][0]);
563 mpq_set_si(tcount, 0, 1);
564 n.div(D, tcount, one);
565 if (total_power % 2)
566 bfct->c[k].n = -bfct->c[k].n;
567 zz2value(bfct->c[k].n, tn);
568 zz2value(bfct->c[k].d, td);
569
570 mpz_mul(mpq_numref(tcount), mpq_numref(tcount), tn);
571 mpz_mul(mpq_denref(tcount), mpq_denref(tcount), td);
572 mpq_canonicalize(tcount);
573 mpq_add(count, count, tcount);
574 }
575 delete v[i];
576 }
577 }
578
579
580 /* Check whether the polyhedron is unbounded and if so,
581 * check whether it has any (and therefore an infinite number of)
582 * integer points.
583 * If one of the vertices is integer, then we are done.
584 * Otherwise, transform the polyhedron such that one of the rays
585 * is the first unit vector and cut it off at a height that ensures
586 * that if the whole polyhedron has any points, then the remaining part
587 * has integer points. In particular we add the largest coefficient
588 * of a ray to the highest vertex (rounded up).
589 */
590 static bool Polyhedron_is_infinite(Polyhedron *P, Value* result,
591 barvinok_options *options)
592 {
593 int r = 0;
594 Matrix *M, *M2;
595 Value c, tmp;
596 Value g;
597 bool first;
598 Vector *v;
599 Value offset, size;
600 Polyhedron *R;
601
602 if (P->NbBid == 0)
603 for (; r < P->NbRays; ++r)
604 if (value_zero_p(P->Ray[r][P->Dimension+1]))
605 break;
606 if (P->NbBid == 0 && r == P->NbRays)
607 return false;
608
609 if (options->count_sample_infinite) {
610 Vector *sample;
611
612 sample = Polyhedron_Sample(P, options);
613 if (!sample)
614 value_set_si(*result, 0);
615 else {
616 value_set_si(*result, -1);
617 Vector_Free(sample);
618 }
619 return true;
620 }
621
622 for (int i = 0; i < P->NbRays; ++i)
623 if (value_one_p(P->Ray[i][1+P->Dimension])) {
624 value_set_si(*result, -1);
625 return true;
626 }
627
628 value_init(g);
629 v = Vector_Alloc(P->Dimension+1);
630 Vector_Gcd(P->Ray[r]+1, P->Dimension, &g);
631 Vector_AntiScale(P->Ray[r]+1, v->p, g, P->Dimension+1);
632 M = unimodular_complete(v);
633 value_set_si(M->p[P->Dimension][P->Dimension], 1);
634 M2 = Transpose(M);
635 Matrix_Free(M);
636 P = Polyhedron_Preimage(P, M2, 0);
637 Matrix_Free(M2);
638 value_clear(g);
639 Vector_Free(v);
640
641 first = true;
642 value_init(offset);
643 value_init(size);
644 value_init(tmp);
645 value_set_si(size, 0);
646
647 for (int i = 0; i < P->NbBid; ++i) {
648 value_absolute(tmp, P->Ray[i][1]);
649 if (value_gt(tmp, size))
650 value_assign(size, tmp);
651 }
652 for (int i = P->NbBid; i < P->NbRays; ++i) {
653 if (value_zero_p(P->Ray[i][P->Dimension+1])) {
654 if (value_gt(P->Ray[i][1], size))
655 value_assign(size, P->Ray[i][1]);
656 continue;
657 }
658 mpz_cdiv_q(tmp, P->Ray[i][1], P->Ray[i][P->Dimension+1]);
659 if (first || value_gt(tmp, offset)) {
660 value_assign(offset, tmp);
661 first = false;
662 }
663 }
664 value_addto(offset, offset, size);
665 value_clear(size);
666 value_clear(tmp);
667
668 v = Vector_Alloc(P->Dimension+2);
669 value_set_si(v->p[0], 1);
670 value_set_si(v->p[1], -1);
671 value_assign(v->p[1+P->Dimension], offset);
672 R = AddConstraints(v->p, 1, P, options->MaxRays);
673 Polyhedron_Free(P);
674 P = R;
675
676 value_clear(offset);
677 Vector_Free(v);
678
679 value_init(c);
680 barvinok_count_with_options(P, &c, options);
681 Polyhedron_Free(P);
682 if (value_zero_p(c))
683 value_set_si(*result, 0);
684 else
685 value_set_si(*result, -1);
686 value_clear(c);
687
688 return true;
689 }
690
691 typedef Polyhedron * Polyhedron_p;
692
693 static void barvinok_count_f(Polyhedron *P, Value* result,
694 barvinok_options *options);
695
696 void barvinok_count_with_options(Polyhedron *P, Value* result,
697 struct barvinok_options *options)
698 {
699 unsigned dim;
700 int allocated = 0;
701 Polyhedron *Q;
702 bool infinite = false;
703
704 if (P->next)
705 fprintf(stderr,
706 "barvinok_count: input is a union; only first polyhedron is counted\n");
707
708 if (emptyQ2(P)) {
709 value_set_si(*result, 0);
710 return;
711 }
712 if (P->NbEq != 0) {
713 Q = NULL;
714 do {
715 P = remove_equalities(P);
716 P = DomainConstraintSimplify(P, options->MaxRays);
717 if (Q)
718 Polyhedron_Free(Q);
719 Q = P;
720 } while (!emptyQ(P) && P->NbEq != 0);
721 if (emptyQ(P)) {
722 Polyhedron_Free(P);
723 value_set_si(*result, 0);
724 return;
725 }
726 allocated = 1;
727 }
728 if (Polyhedron_is_infinite(P, result, options)) {
729 if (allocated)
730 Polyhedron_Free(P);
731 return;
732 }
733 if (P->Dimension == 0) {
734 /* Test whether the constraints are satisfied */
735 POL_ENSURE_VERTICES(P);
736 value_set_si(*result, !emptyQ(P));
737 if (allocated)
738 Polyhedron_Free(P);
739 return;
740 }
741 Q = Polyhedron_Factor(P, 0, NULL, options->MaxRays);
742 if (Q) {
743 if (allocated)
744 Polyhedron_Free(P);
745 P = Q;
746 allocated = 1;
747 }
748
749 barvinok_count_f(P, result, options);
750 if (value_neg_p(*result))
751 infinite = true;
752 if (Q && P->next && value_notzero_p(*result)) {
753 Value factor;
754 value_init(factor);
755
756 for (Q = P->next; Q; Q = Q->next) {
757 barvinok_count_f(Q, &factor, options);
758 if (value_neg_p(factor)) {
759 infinite = true;
760 continue;
761 } else if (Q->next && value_zero_p(factor)) {
762 value_set_si(*result, 0);
763 break;
764 }
765 value_multiply(*result, *result, factor);
766 }
767
768 value_clear(factor);
769 }
770
771 if (allocated)
772 Domain_Free(P);
773 if (infinite)
774 value_set_si(*result, -1);
775 }
776
777 void barvinok_count(Polyhedron *P, Value* result, unsigned NbMaxCons)
778 {
779 barvinok_options *options = barvinok_options_new_with_defaults();
780 options->MaxRays = NbMaxCons;
781 barvinok_count_with_options(P, result, options);
782 barvinok_options_free(options);
783 }
784
785 static void barvinok_count_f(Polyhedron *P, Value* result,
786 barvinok_options *options)
787 {
788 if (emptyQ2(P)) {
789 value_set_si(*result, 0);
790 return;
791 }
792
793 if (P->Dimension == 1)
794 return Line_Length(P, result);
795
796 int c = P->NbConstraints;
797 POL_ENSURE_FACETS(P);
798 if (c != P->NbConstraints || P->NbEq != 0)
799 return barvinok_count_with_options(P, result, options);
800
801 POL_ENSURE_VERTICES(P);
802
803 if (Polyhedron_is_infinite(P, result, options))
804 return;
805
806 np_base *cnt;
807 if (options->incremental_specialization == 2)
808 cnt = new bfcounter(P->Dimension);
809 else if (options->incremental_specialization == 1)
810 cnt = new icounter(P->Dimension);
811 else
812 cnt = new counter(P->Dimension);
813 cnt->start(P, options);
814
815 cnt->get_count(result);
816 delete cnt;
817 }
818
819 static void uni_polynom(int param, Vector *c, evalue *EP)
820 {
821 unsigned dim = c->Size-2;
822 value_init(EP->d);
823 value_set_si(EP->d,0);
824 EP->x.p = new_enode(polynomial, dim+1, param+1);
825 for (int j = 0; j <= dim; ++j)
826 evalue_set(&EP->x.p->arr[j], c->p[j], c->p[dim+1]);
827 }
828
829 static void multi_polynom(Vector *c, evalue* X, evalue *EP)
830 {
831 unsigned dim = c->Size-2;
832 evalue EC;
833
834 value_init(EC.d);
835 evalue_set(&EC, c->p[dim], c->p[dim+1]);
836
837 value_init(EP->d);
838 evalue_set(EP, c->p[dim], c->p[dim+1]);
839
840 for (int i = dim-1; i >= 0; --i) {
841 emul(X, EP);
842 value_assign(EC.x.n, c->p[i]);
843 eadd(&EC, EP);
844 }
845 free_evalue_refs(&EC);
846 }
847
848 Polyhedron *unfringe (Polyhedron *P, unsigned MaxRays)
849 {
850 int len = P->Dimension+2;
851 Polyhedron *T, *R = P;
852 Value g;
853 value_init(g);
854 Vector *row = Vector_Alloc(len);
855 value_set_si(row->p[0], 1);
856
857 R = DomainConstraintSimplify(Polyhedron_Copy(P), MaxRays);
858
859 Matrix *M = Matrix_Alloc(2, len-1);
860 value_set_si(M->p[1][len-2], 1);
861 for (int v = 0; v < P->Dimension; ++v) {
862 value_set_si(M->p[0][v], 1);
863 Polyhedron *I = Polyhedron_Image(R, M, 2+1);
864 value_set_si(M->p[0][v], 0);
865 for (int r = 0; r < I->NbConstraints; ++r) {
866 if (value_zero_p(I->Constraint[r][0]))
867 continue;
868 if (value_zero_p(I->Constraint[r][1]))
869 continue;
870 if (value_one_p(I->Constraint[r][1]))
871 continue;
872 if (value_mone_p(I->Constraint[r][1]))
873 continue;
874 value_absolute(g, I->Constraint[r][1]);
875 Vector_Set(row->p+1, 0, len-2);
876 value_division(row->p[1+v], I->Constraint[r][1], g);
877 mpz_fdiv_q(row->p[len-1], I->Constraint[r][2], g);
878 T = R;
879 R = AddConstraints(row->p, 1, R, MaxRays);
880 if (T != P)
881 Polyhedron_Free(T);
882 }
883 Polyhedron_Free(I);
884 }
885 Matrix_Free(M);
886 Vector_Free(row);
887 value_clear(g);
888 return R;
889 }
890
891 /* Check whether all rays point in the positive directions
892 * for the parameters
893 */
894 static bool Polyhedron_has_positive_rays(Polyhedron *P, unsigned nparam)
895 {
896 int r;
897 for (r = 0; r < P->NbRays; ++r)
898 if (value_zero_p(P->Ray[r][P->Dimension+1])) {
899 int i;
900 for (i = P->Dimension - nparam; i < P->Dimension; ++i)
901 if (value_neg_p(P->Ray[r][i+1]))
902 return false;
903 }
904 return true;
905 }
906
907 typedef evalue * evalue_p;
908
909 struct enumerator_base {
910 unsigned dim;
911 evalue ** vE;
912 evalue mone;
913 vertex_decomposer *vpd;
914
915 enumerator_base(unsigned dim, vertex_decomposer *vpd)
916 {
917 this->dim = dim;
918 this->vpd = vpd;
919
920 vE = new evalue_p[vpd->nbV];
921 for (int j = 0; j < vpd->nbV; ++j)
922 vE[j] = 0;
923
924 value_init(mone.d);
925 evalue_set_si(&mone, -1, 1);
926 }
927
928 void decompose_at(Param_Vertices *V, int _i, barvinok_options *options) {
929 //this->pVD = pVD;
930
931 vE[_i] = new evalue;
932 value_init(vE[_i]->d);
933 evalue_set_si(vE[_i], 0, 1);
934
935 vpd->decompose_at_vertex(V, _i, options);
936 }
937
938 virtual ~enumerator_base() {
939 for (int j = 0; j < vpd->nbV; ++j)
940 if (vE[j]) {
941 free_evalue_refs(vE[j]);
942 delete vE[j];
943 }
944 delete [] vE;
945
946 free_evalue_refs(&mone);
947 }
948
949 static enumerator_base *create(Polyhedron *P, unsigned dim, unsigned nbV,
950 barvinok_options *options);
951 };
952
953 struct enumerator : public signed_cone_consumer, public vertex_decomposer,
954 public enumerator_base {
955 vec_ZZ lambda;
956 vec_ZZ den;
957 ZZ sign;
958 term_info num;
959 Vector *c;
960 mpq_t count;
961
962 enumerator(Polyhedron *P, unsigned dim, unsigned nbV) :
963 vertex_decomposer(P, nbV, *this), enumerator_base(dim, this) {
964 this->P = P;
965 this->nbV = nbV;
966 randomvector(P, lambda, dim);
967 den.SetLength(dim);
968 c = Vector_Alloc(dim+2);
969
970 mpq_init(count);
971 }
972
973 ~enumerator() {
974 mpq_clear(count);
975 Vector_Free(c);
976 }
977
978 virtual void handle(const signed_cone& sc, barvinok_options *options);
979 };
980
981 void enumerator::handle(const signed_cone& sc, barvinok_options *options)
982 {
983 assert(sc.det == 1);
984 assert(!sc.closed);
985 int r = 0;
986 assert(sc.rays.NumRows() == dim);
987 for (int k = 0; k < dim; ++k) {
988 if (lambda * sc.rays[k] == 0)
989 throw Orthogonal;
990 }
991
992 sign = sc.sign;
993
994 lattice_point(V, sc.rays, lambda, &num, 0, options);
995 den = sc.rays * lambda;
996 normalize(sign, num.constant, den);
997
998 dpoly n(dim, den[0], 1);
999 for (int k = 1; k < dim; ++k) {
1000 dpoly fact(dim, den[k], 1);
1001 n *= fact;
1002 }
1003 if (num.E != NULL) {
1004 ZZ one(INIT_VAL, 1);
1005 dpoly_n d(dim, num.constant, one);
1006 d.div(n, c, sign);
1007 evalue EV;
1008 multi_polynom(c, num.E, &EV);
1009 eadd(&EV , vE[vert]);
1010 free_evalue_refs(&EV);
1011 free_evalue_refs(num.E);
1012 delete num.E;
1013 } else if (num.pos != -1) {
1014 dpoly_n d(dim, num.constant, num.coeff);
1015 d.div(n, c, sign);
1016 evalue EV;
1017 uni_polynom(num.pos, c, &EV);
1018 eadd(&EV , vE[vert]);
1019 free_evalue_refs(&EV);
1020 } else {
1021 mpq_set_si(count, 0, 1);
1022 dpoly d(dim, num.constant);
1023 d.div(n, count, sign);
1024 evalue EV;
1025 value_init(EV.d);
1026 evalue_set(&EV, &count[0]._mp_num, &count[0]._mp_den);
1027 eadd(&EV , vE[vert]);
1028 free_evalue_refs(&EV);
1029 }
1030 }
1031
1032 struct ienumerator_base : enumerator_base {
1033 evalue ** E_vertex;
1034
1035 ienumerator_base(unsigned dim, vertex_decomposer *vpd) :
1036 enumerator_base(dim,vpd) {
1037 E_vertex = new evalue_p[dim];
1038 }
1039
1040 virtual ~ienumerator_base() {
1041 delete [] E_vertex;
1042 }
1043
1044 evalue *E_num(int i, int d) {
1045 return E_vertex[i + (dim-d)];
1046 }
1047 };
1048
1049 struct cumulator {
1050 evalue *factor;
1051 evalue *v;
1052 dpoly_r *r;
1053
1054 cumulator(evalue *factor, evalue *v, dpoly_r *r) :
1055 factor(factor), v(v), r(r) {}
1056
1057 void cumulate(barvinok_options *options);
1058
1059 virtual void add_term(const vector<int>& powers, evalue *f2) = 0;
1060 virtual ~cumulator() {}
1061 };
1062
1063 void cumulator::cumulate(barvinok_options *options)
1064 {
1065 evalue cum; // factor * 1 * E_num[0]/1 * (E_num[0]-1)/2 *...
1066 evalue f;
1067 evalue t; // E_num[0] - (m-1)
1068 evalue *cst;
1069 evalue mone;
1070
1071 if (options->lookup_table) {
1072 value_init(mone.d);
1073 evalue_set_si(&mone, -1, 1);
1074 }
1075
1076 value_init(cum.d);
1077 evalue_copy(&cum, factor);
1078 value_init(f.d);
1079 value_init(f.x.n);
1080 value_set_si(f.d, 1);
1081 value_set_si(f.x.n, 1);
1082 value_init(t.d);
1083 evalue_copy(&t, v);
1084
1085 if (!options->lookup_table) {
1086 for (cst = &t; value_zero_p(cst->d); ) {
1087 if (cst->x.p->type == fractional)
1088 cst = &cst->x.p->arr[1];
1089 else
1090 cst = &cst->x.p->arr[0];
1091 }
1092 }
1093
1094 for (int m = 0; m < r->len; ++m) {
1095 if (m > 0) {
1096 if (m > 1) {
1097 value_set_si(f.d, m);
1098 emul(&f, &cum);
1099 if (!options->lookup_table)
1100 value_subtract(cst->x.n, cst->x.n, cst->d);
1101 else
1102 eadd(&mone, &t);
1103 }
1104 emul(&t, &cum);
1105 }
1106 dpoly_r_term_list& current = r->c[r->len-1-m];
1107 dpoly_r_term_list::iterator j;
1108 for (j = current.begin(); j != current.end(); ++j) {
1109 if ((*j)->coeff == 0)
1110 continue;
1111 evalue *f2 = new evalue;
1112 value_init(f2->d);
1113 value_init(f2->x.n);
1114 zz2value((*j)->coeff, f2->x.n);
1115 zz2value(r->denom, f2->d);
1116 emul(&cum, f2);
1117
1118 add_term((*j)->powers, f2);
1119 }
1120 }
1121 free_evalue_refs(&f);
1122 free_evalue_refs(&t);
1123 free_evalue_refs(&cum);
1124 if (options->lookup_table)
1125 free_evalue_refs(&mone);
1126 }
1127
1128 struct E_poly_term {
1129 vector<int> powers;
1130 evalue *E;
1131 };
1132
1133 struct ie_cum : public cumulator {
1134 vector<E_poly_term *> terms;
1135
1136 ie_cum(evalue *factor, evalue *v, dpoly_r *r) : cumulator(factor, v, r) {}
1137
1138 virtual void add_term(const vector<int>& powers, evalue *f2);
1139 };
1140
1141 void ie_cum::add_term(const vector<int>& powers, evalue *f2)
1142 {
1143 int k;
1144 for (k = 0; k < terms.size(); ++k) {
1145 if (terms[k]->powers == powers) {
1146 eadd(f2, terms[k]->E);
1147 free_evalue_refs(f2);
1148 delete f2;
1149 break;
1150 }
1151 }
1152 if (k >= terms.size()) {
1153 E_poly_term *ET = new E_poly_term;
1154 ET->powers = powers;
1155 ET->E = f2;
1156 terms.push_back(ET);
1157 }
1158 }
1159
1160 struct ienumerator : public signed_cone_consumer, public vertex_decomposer,
1161 public ienumerator_base {
1162 //Polyhedron *pVD;
1163 mat_ZZ den;
1164 mat_ZZ vertex;
1165 mpq_t tcount;
1166
1167 ienumerator(Polyhedron *P, unsigned dim, unsigned nbV) :
1168 vertex_decomposer(P, nbV, *this), ienumerator_base(dim, this) {
1169 vertex.SetDims(1, dim);
1170
1171 den.SetDims(dim, dim);
1172 mpq_init(tcount);
1173 }
1174
1175 ~ienumerator() {
1176 mpq_clear(tcount);
1177 }
1178
1179 virtual void handle(const signed_cone& sc, barvinok_options *options);
1180 void reduce(evalue *factor, const mat_ZZ& num, const mat_ZZ& den_f,
1181 barvinok_options *options);
1182 };
1183
1184 void ienumerator::reduce(evalue *factor, const mat_ZZ& num, const mat_ZZ& den_f,
1185 barvinok_options *options)
1186 {
1187 unsigned len = den_f.NumRows(); // number of factors in den
1188 unsigned dim = num.NumCols();
1189 assert(num.NumRows() == 1);
1190
1191 if (dim == 0) {
1192 eadd(factor, vE[vert]);
1193 return;
1194 }
1195
1196 vec_ZZ den_s;
1197 mat_ZZ den_r;
1198 vec_ZZ num_s;
1199 mat_ZZ num_p;
1200
1201 split_one(num, num_s, num_p, den_f, den_s, den_r);
1202
1203 vec_ZZ den_p;
1204 den_p.SetLength(len);
1205
1206 ZZ one;
1207 one = 1;
1208 normalize(one, num_s, num_p, den_s, den_p, den_r);
1209 if (one != 1)
1210 emul(&mone, factor);
1211
1212 int only_param = 0;
1213 int no_param = 0;
1214 for (int k = 0; k < len; ++k) {
1215 if (den_p[k] == 0)
1216 ++no_param;
1217 else if (den_s[k] == 0)
1218 ++only_param;
1219 }
1220 if (no_param == 0) {
1221 reduce(factor, num_p, den_r, options);
1222 } else {
1223 int k, l;
1224 mat_ZZ pden;
1225 pden.SetDims(only_param, dim-1);
1226
1227 for (k = 0, l = 0; k < len; ++k)
1228 if (den_s[k] == 0)
1229 pden[l++] = den_r[k];
1230
1231 for (k = 0; k < len; ++k)
1232 if (den_p[k] == 0)
1233 break;
1234
1235 dpoly n(no_param, num_s[0]);
1236 dpoly D(no_param, den_s[k], 1);
1237 for ( ; ++k < len; )
1238 if (den_p[k] == 0) {
1239 dpoly fact(no_param, den_s[k], 1);
1240 D *= fact;
1241 }
1242
1243 dpoly_r * r = 0;
1244 // if no_param + only_param == len then all powers
1245 // below will be all zero
1246 if (no_param + only_param == len) {
1247 if (E_num(0, dim) != 0)
1248 r = new dpoly_r(n, len);
1249 else {
1250 mpq_set_si(tcount, 0, 1);
1251 one = 1;
1252 n.div(D, tcount, one);
1253
1254 if (value_notzero_p(mpq_numref(tcount))) {
1255 evalue f;
1256 value_init(f.d);
1257 value_init(f.x.n);
1258 value_assign(f.x.n, mpq_numref(tcount));
1259 value_assign(f.d, mpq_denref(tcount));
1260 emul(&f, factor);
1261 reduce(factor, num_p, pden, options);
1262 free_evalue_refs(&f);
1263 }
1264 return;
1265 }
1266 } else {
1267 for (k = 0; k < len; ++k) {
1268 if (den_s[k] == 0 || den_p[k] == 0)
1269 continue;
1270
1271 dpoly pd(no_param-1, den_s[k], 1);
1272
1273 int l;
1274 for (l = 0; l < k; ++l)
1275 if (den_r[l] == den_r[k])
1276 break;
1277
1278 if (r == 0)
1279 r = new dpoly_r(n, pd, l, len);
1280 else {
1281 dpoly_r *nr = new dpoly_r(r, pd, l, len);
1282 delete r;
1283 r = nr;
1284 }
1285 }
1286 }
1287 dpoly_r *rc = r->div(D);
1288 delete r;
1289 r = rc;
1290 if (E_num(0, dim) == 0) {
1291 int common = pden.NumRows();
1292 dpoly_r_term_list& final = r->c[r->len-1];
1293 int rows;
1294 evalue t;
1295 evalue f;
1296 value_init(f.d);
1297 value_init(f.x.n);
1298 zz2value(r->denom, f.d);
1299 dpoly_r_term_list::iterator j;
1300 for (j = final.begin(); j != final.end(); ++j) {
1301 if ((*j)->coeff == 0)
1302 continue;
1303 rows = common;
1304 for (int k = 0; k < r->dim; ++k) {
1305 int n = (*j)->powers[k];
1306 if (n == 0)
1307 continue;
1308 pden.SetDims(rows+n, pden.NumCols());
1309 for (int l = 0; l < n; ++l)
1310 pden[rows+l] = den_r[k];
1311 rows += n;
1312 }
1313 value_init(t.d);
1314 evalue_copy(&t, factor);
1315 zz2value((*j)->coeff, f.x.n);
1316 emul(&f, &t);
1317 reduce(&t, num_p, pden, options);
1318 free_evalue_refs(&t);
1319 }
1320 free_evalue_refs(&f);
1321 } else {
1322 ie_cum cum(factor, E_num(0, dim), r);
1323 cum.cumulate(options);
1324
1325 int common = pden.NumRows();
1326 int rows;
1327 for (int j = 0; j < cum.terms.size(); ++j) {
1328 rows = common;
1329 pden.SetDims(rows, pden.NumCols());
1330 for (int k = 0; k < r->dim; ++k) {
1331 int n = cum.terms[j]->powers[k];
1332 if (n == 0)
1333 continue;
1334 pden.SetDims(rows+n, pden.NumCols());
1335 for (int l = 0; l < n; ++l)
1336 pden[rows+l] = den_r[k];
1337 rows += n;
1338 }
1339 reduce(cum.terms[j]->E, num_p, pden, options);
1340 free_evalue_refs(cum.terms[j]->E);
1341 delete cum.terms[j]->E;
1342 delete cum.terms[j];
1343 }
1344 }
1345 delete r;
1346 }
1347 }
1348
1349 static int type_offset(enode *p)
1350 {
1351 return p->type == fractional ? 1 :
1352 p->type == flooring ? 1 : 0;
1353 }
1354
1355 static int edegree(evalue *e)
1356 {
1357 int d = 0;
1358 enode *p;
1359
1360 if (value_notzero_p(e->d))
1361 return 0;
1362
1363 p = e->x.p;
1364 int i = type_offset(p);
1365 if (p->size-i-1 > d)
1366 d = p->size - i - 1;
1367 for (; i < p->size; i++) {
1368 int d2 = edegree(&p->arr[i]);
1369 if (d2 > d)
1370 d = d2;
1371 }
1372 return d;
1373 }
1374
1375 void ienumerator::handle(const signed_cone& sc, barvinok_options *options)
1376 {
1377 assert(sc.det == 1);
1378 assert(!sc.closed);
1379 assert(sc.rays.NumRows() == dim);
1380
1381 lattice_point(V, sc.rays, vertex[0], E_vertex, options);
1382
1383 den = sc.rays;
1384
1385 evalue one;
1386 value_init(one.d);
1387 evalue_set_si(&one, sc.sign, 1);
1388 reduce(&one, vertex, den, options);
1389 free_evalue_refs(&one);
1390
1391 for (int i = 0; i < dim; ++i)
1392 if (E_vertex[i]) {
1393 free_evalue_refs(E_vertex[i]);
1394 delete E_vertex[i];
1395 }
1396 }
1397
1398 struct bfenumerator : public vertex_decomposer, public bf_base,
1399 public ienumerator_base {
1400 evalue *factor;
1401
1402 bfenumerator(Polyhedron *P, unsigned dim, unsigned nbV) :
1403 vertex_decomposer(P, nbV, *this),
1404 bf_base(dim), ienumerator_base(dim, this) {
1405 lower = 0;
1406 factor = NULL;
1407 }
1408
1409 ~bfenumerator() {
1410 }
1411
1412 virtual void handle(const signed_cone& sc, barvinok_options *options);
1413 virtual void base(mat_ZZ& factors, bfc_vec& v);
1414
1415 bfc_term_base* new_bf_term(int len) {
1416 bfe_term* t = new bfe_term(len);
1417 return t;
1418 }
1419
1420 virtual void set_factor(bfc_term_base *t, int k, int change) {
1421 bfe_term* bfet = static_cast<bfe_term *>(t);
1422 factor = bfet->factors[k];
1423 assert(factor != NULL);
1424 bfet->factors[k] = NULL;
1425 if (change)
1426 emul(&mone, factor);
1427 }
1428
1429 virtual void set_factor(bfc_term_base *t, int k, mpq_t &q, int change) {
1430 bfe_term* bfet = static_cast<bfe_term *>(t);
1431 factor = bfet->factors[k];
1432 assert(factor != NULL);
1433 bfet->factors[k] = NULL;
1434
1435 evalue f;
1436 value_init(f.d);
1437 value_init(f.x.n);
1438 if (change)
1439 value_oppose(f.x.n, mpq_numref(q));
1440 else
1441 value_assign(f.x.n, mpq_numref(q));
1442 value_assign(f.d, mpq_denref(q));
1443 emul(&f, factor);
1444 free_evalue_refs(&f);
1445 }
1446
1447 virtual void set_factor(bfc_term_base *t, int k, const QQ& c, int change) {
1448 bfe_term* bfet = static_cast<bfe_term *>(t);
1449
1450 factor = new evalue;
1451
1452 evalue f;
1453 value_init(f.d);
1454 value_init(f.x.n);
1455 zz2value(c.n, f.x.n);
1456 if (change)
1457 value_oppose(f.x.n, f.x.n);
1458 zz2value(c.d, f.d);
1459
1460 value_init(factor->d);
1461 evalue_copy(factor, bfet->factors[k]);
1462 emul(&f, factor);
1463 free_evalue_refs(&f);
1464 }
1465
1466 void set_factor(evalue *f, int change) {
1467 if (change)
1468 emul(&mone, f);
1469 factor = f;
1470 }
1471
1472 virtual void insert_term(bfc_term_base *t, int i) {
1473 bfe_term* bfet = static_cast<bfe_term *>(t);
1474 int len = t->terms.NumRows()-1; // already increased by one
1475
1476 bfet->factors.resize(len+1);
1477 for (int j = len; j > i; --j) {
1478 bfet->factors[j] = bfet->factors[j-1];
1479 t->terms[j] = t->terms[j-1];
1480 }
1481 bfet->factors[i] = factor;
1482 factor = NULL;
1483 }
1484
1485 virtual void update_term(bfc_term_base *t, int i) {
1486 bfe_term* bfet = static_cast<bfe_term *>(t);
1487
1488 eadd(factor, bfet->factors[i]);
1489 free_evalue_refs(factor);
1490 delete factor;
1491 }
1492
1493 virtual bool constant_vertex(int dim) { return E_num(0, dim) == 0; }
1494
1495 virtual void cum(bf_reducer *bfr, bfc_term_base *t, int k, dpoly_r *r,
1496 barvinok_options *options);
1497 };
1498
1499 enumerator_base *enumerator_base::create(Polyhedron *P, unsigned dim, unsigned nbV,
1500 barvinok_options *options)
1501 {
1502 enumerator_base *eb;
1503
1504 if (options->incremental_specialization == BV_SPECIALIZATION_BF)
1505 eb = new bfenumerator(P, dim, nbV);
1506 else if (options->incremental_specialization == BV_SPECIALIZATION_DF)
1507 eb = new ienumerator(P, dim, nbV);
1508 else
1509 eb = new enumerator(P, dim, nbV);
1510
1511 return eb;
1512 }
1513
1514 struct bfe_cum : public cumulator {
1515 bfenumerator *bfe;
1516 bfc_term_base *told;
1517 int k;
1518 bf_reducer *bfr;
1519
1520 bfe_cum(evalue *factor, evalue *v, dpoly_r *r, bf_reducer *bfr,
1521 bfc_term_base *t, int k, bfenumerator *e) :
1522 cumulator(factor, v, r), told(t), k(k),
1523 bfr(bfr), bfe(e) {
1524 }
1525
1526 virtual void add_term(const vector<int>& powers, evalue *f2);
1527 };
1528
1529 void bfe_cum::add_term(const vector<int>& powers, evalue *f2)
1530 {
1531 bfr->update_powers(powers);
1532
1533 bfc_term_base * t = bfe->find_bfc_term(bfr->vn, bfr->npowers, bfr->nnf);
1534 bfe->set_factor(f2, bfr->l_changes % 2);
1535 bfe->add_term(t, told->terms[k], bfr->l_extra_num);
1536 }
1537
1538 void bfenumerator::cum(bf_reducer *bfr, bfc_term_base *t, int k,
1539 dpoly_r *r, barvinok_options *options)
1540 {
1541 bfe_term* bfet = static_cast<bfe_term *>(t);
1542 bfe_cum cum(bfet->factors[k], E_num(0, bfr->d), r, bfr, t, k, this);
1543 cum.cumulate(options);
1544 }
1545
1546 void bfenumerator::base(mat_ZZ& factors, bfc_vec& v)
1547 {
1548 for (int i = 0; i < v.size(); ++i) {
1549 assert(v[i]->terms.NumRows() == 1);
1550 evalue *factor = static_cast<bfe_term *>(v[i])->factors[0];
1551 eadd(factor, vE[vert]);
1552 delete v[i];
1553 }
1554 }
1555
1556 void bfenumerator::handle(const signed_cone& sc, barvinok_options *options)
1557 {
1558 assert(sc.det == 1);
1559 assert(!sc.closed);
1560 assert(sc.rays.NumRows() == enumerator_base::dim);
1561
1562 bfe_term* t = new bfe_term(enumerator_base::dim);
1563 vector< bfc_term_base * > v;
1564 v.push_back(t);
1565
1566 t->factors.resize(1);
1567
1568 t->terms.SetDims(1, enumerator_base::dim);
1569 lattice_point(V, sc.rays, t->terms[0], E_vertex, options);
1570
1571 // the elements of factors are always lexpositive
1572 mat_ZZ factors;
1573 int s = setup_factors(sc.rays, factors, t, sc.sign);
1574
1575 t->factors[0] = new evalue;
1576 value_init(t->factors[0]->d);
1577 evalue_set_si(t->factors[0], s, 1);
1578 reduce(factors, v, options);
1579
1580 for (int i = 0; i < enumerator_base::dim; ++i)
1581 if (E_vertex[i]) {
1582 free_evalue_refs(E_vertex[i]);
1583 delete E_vertex[i];
1584 }
1585 }
1586
1587 #ifdef HAVE_CORRECT_VERTICES
1588 static inline Param_Polyhedron *Polyhedron2Param_SD(Polyhedron **Din,
1589 Polyhedron *Cin,int WS,Polyhedron **CEq,Matrix **CT)
1590 {
1591 if (WS & POL_NO_DUAL)
1592 WS = 0;
1593 return Polyhedron2Param_SimplifiedDomain(Din, Cin, WS, CEq, CT);
1594 }
1595 #else
1596 static Param_Polyhedron *Polyhedron2Param_SD(Polyhedron **Din,
1597 Polyhedron *Cin,int WS,Polyhedron **CEq,Matrix **CT)
1598 {
1599 static char data[] = " 1 0 0 0 0 1 -18 "
1600 " 1 0 0 -20 0 19 1 "
1601 " 1 0 1 20 0 -20 16 "
1602 " 1 0 0 0 0 -1 19 "
1603 " 1 0 -1 0 0 0 4 "
1604 " 1 4 -20 0 0 -1 23 "
1605 " 1 -4 20 0 0 1 -22 "
1606 " 1 0 1 0 20 -20 16 "
1607 " 1 0 0 0 -20 19 1 ";
1608 static int checked = 0;
1609 if (!checked) {
1610 checked = 1;
1611 char *p = data;
1612 int n, v, i;
1613 Matrix *M = Matrix_Alloc(9, 7);
1614 for (i = 0; i < 9; ++i)
1615 for (int j = 0; j < 7; ++j) {
1616 sscanf(p, "%d%n", &v, &n);
1617 p += n;
1618 value_set_si(M->p[i][j], v);
1619 }
1620 Polyhedron *P = Constraints2Polyhedron(M, 1024);
1621 Matrix_Free(M);
1622 Polyhedron *U = Universe_Polyhedron(1);
1623 Param_Polyhedron *PP = Polyhedron2Param_Domain(P, U, 1024);
1624 Polyhedron_Free(P);
1625 Polyhedron_Free(U);
1626 Param_Vertices *V;
1627 for (i = 0, V = PP->V; V; ++i, V = V->next)
1628 ;
1629 if (PP)
1630 Param_Polyhedron_Free(PP);
1631 if (i != 10) {
1632 fprintf(stderr, "WARNING: results may be incorrect\n");
1633 fprintf(stderr,
1634 "WARNING: use latest version of PolyLib to remove this warning\n");
1635 }
1636 }
1637
1638 return Polyhedron2Param_SimplifiedDomain(Din, Cin, WS, CEq, CT);
1639 }
1640 #endif
1641
1642 static evalue* barvinok_enumerate_ev_f(Polyhedron *P, Polyhedron* C,
1643 barvinok_options *options);
1644
1645 /* Destroys C */
1646 static evalue* barvinok_enumerate_cst(Polyhedron *P, Polyhedron* C,
1647 struct barvinok_options *options)
1648 {
1649 evalue *eres;
1650
1651 ALLOC(evalue, eres);
1652 value_init(eres->d);
1653 value_set_si(eres->d, 0);
1654 eres->x.p = new_enode(partition, 2, C->Dimension);
1655 EVALUE_SET_DOMAIN(eres->x.p->arr[0],
1656 DomainConstraintSimplify(C, options->MaxRays));
1657 value_set_si(eres->x.p->arr[1].d, 1);
1658 value_init(eres->x.p->arr[1].x.n);
1659 if (emptyQ(P))
1660 value_set_si(eres->x.p->arr[1].x.n, 0);
1661 else
1662 barvinok_count_with_options(P, &eres->x.p->arr[1].x.n, options);
1663
1664 return eres;
1665 }
1666
1667 evalue* barvinok_enumerate_with_options(Polyhedron *P, Polyhedron* C,
1668 struct barvinok_options *options)
1669 {
1670 //P = unfringe(P, MaxRays);
1671 Polyhedron *next, *Cnext;
1672 Polyhedron *Corig = C;
1673 Polyhedron *Porig = P;
1674 Polyhedron *CEq = NULL, *rVD, *CA;
1675 int r = 0;
1676 unsigned nparam = C->Dimension;
1677 evalue *eres;
1678
1679 if (P->next)
1680 fprintf(stderr,
1681 "barvinok_enumerate: input is a union; only first polyhedron is enumerated\n");
1682
1683 if (C->next)
1684 fprintf(stderr,
1685 "barvinok_enumerate: context is a union; only first polyhedron is considered\n");
1686
1687 evalue factor;
1688 value_init(factor.d);
1689 evalue_set_si(&factor, 1, 1);
1690
1691 Cnext = C->next;
1692 C->next = NULL;
1693 CA = align_context(C, P->Dimension, options->MaxRays);
1694 next = P->next;
1695 P->next = NULL;
1696 P = DomainIntersection(P, CA, options->MaxRays);
1697 Porig->next = next;
1698 Polyhedron_Free(CA);
1699
1700 /* for now */
1701 POL_ENSURE_FACETS(P);
1702 POL_ENSURE_VERTICES(P);
1703 POL_ENSURE_FACETS(C);
1704 POL_ENSURE_VERTICES(C);
1705
1706 if (C->Dimension == 0 || emptyQ(P)) {
1707 constant:
1708 eres = barvinok_enumerate_cst(P, CEq ? CEq : Polyhedron_Copy(C), options);
1709 out:
1710 emul(&factor, eres);
1711 if (options->polynomial_approximation == BV_POLAPPROX_UPPER)
1712 evalue_frac2polynomial(eres, 1, options->MaxRays);
1713 if (options->polynomial_approximation == BV_POLAPPROX_LOWER)
1714 evalue_frac2polynomial(eres, 0, options->MaxRays);
1715 reduce_evalue(eres);
1716 free_evalue_refs(&factor);
1717 Domain_Free(P);
1718 if (C != Corig)
1719 Polyhedron_Free(C);
1720
1721 Corig->next = Cnext;
1722 return eres;
1723 }
1724 if (Polyhedron_is_unbounded(P, nparam, options->MaxRays))
1725 goto constant;
1726
1727 if (P->NbEq != 0) {
1728 Matrix *f;
1729 P = remove_equalities_p(P, P->Dimension-nparam, &f);
1730 mask(f, &factor, options);
1731 Matrix_Free(f);
1732 }
1733 if (P->Dimension == nparam) {
1734 CEq = P;
1735 P = Universe_Polyhedron(0);
1736 goto constant;
1737 }
1738
1739 Polyhedron *T = Polyhedron_Factor(P, nparam, NULL, options->MaxRays);
1740 if (T || (P->Dimension == nparam+1)) {
1741 Polyhedron *Q;
1742 Polyhedron *C2;
1743 for (Q = T ? T : P; Q; Q = Q->next) {
1744 Polyhedron *next = Q->next;
1745 Q->next = NULL;
1746
1747 Polyhedron *QC = Q;
1748 if (Q->Dimension != C->Dimension)
1749 QC = Polyhedron_Project(Q, nparam);
1750
1751 C2 = C;
1752 C = DomainIntersection(C, QC, options->MaxRays);
1753 if (C2 != Corig)
1754 Polyhedron_Free(C2);
1755 if (QC != Q)
1756 Polyhedron_Free(QC);
1757
1758 Q->next = next;
1759 }
1760 }
1761 if (T) {
1762 Polyhedron_Free(P);
1763 P = T;
1764 if (T->Dimension == C->Dimension) {
1765 P = T->next;
1766 T->next = NULL;
1767 Polyhedron_Free(T);
1768 }
1769 }
1770
1771 next = P->next;
1772 P->next = NULL;
1773 eres = barvinok_enumerate_ev_f(P, C, options);
1774 P->next = next;
1775
1776 if (P->next) {
1777 Polyhedron *Q;
1778 evalue *f;
1779
1780 for (Q = P->next; Q; Q = Q->next) {
1781 Polyhedron *next = Q->next;
1782 Q->next = NULL;
1783
1784 f = barvinok_enumerate_ev_f(Q, C, options);
1785 emul(f, eres);
1786 free_evalue_refs(f);
1787 free(f);
1788
1789 Q->next = next;
1790 }
1791 }
1792
1793 goto out;
1794 }
1795
1796 evalue* barvinok_enumerate_ev(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
1797 {
1798 evalue *E;
1799 barvinok_options *options = barvinok_options_new_with_defaults();
1800 options->MaxRays = MaxRays;
1801 E = barvinok_enumerate_with_options(P, C, options);
1802 barvinok_options_free(options);
1803 return E;
1804 }
1805
1806 /* adapted from mpolyhedron_inflate in PolyLib */
1807 static Polyhedron *Polyhedron_Inflate(Polyhedron *P, unsigned nparam,
1808 unsigned MaxRays)
1809 {
1810 Value sum;
1811 int nvar = P->Dimension - nparam;
1812 Matrix *C = Polyhedron2Constraints(P);
1813 Polyhedron *P2;
1814
1815 value_init(sum);
1816 /* subtract the sum of the negative coefficients of each inequality */
1817 for (int i = 0; i < C->NbRows; ++i) {
1818 value_set_si(sum, 0);
1819 for (int j = 0; j < nvar; ++j)
1820 if (value_neg_p(C->p[i][1+j]))
1821 value_addto(sum, sum, C->p[i][1+j]);
1822 value_subtract(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], sum);
1823 }
1824 value_clear(sum);
1825 P2 = Constraints2Polyhedron(C, MaxRays);
1826 Matrix_Free(C);
1827 return P2;
1828 }
1829
1830 /* adapted from mpolyhedron_deflate in PolyLib */
1831 static Polyhedron *Polyhedron_Deflate(Polyhedron *P, unsigned nparam,
1832 unsigned MaxRays)
1833 {
1834 Value sum;
1835 int nvar = P->Dimension - nparam;
1836 Matrix *C = Polyhedron2Constraints(P);
1837 Polyhedron *P2;
1838
1839 value_init(sum);
1840 /* subtract the sum of the positive coefficients of each inequality */
1841 for (int i = 0; i < C->NbRows; ++i) {
1842 value_set_si(sum, 0);
1843 for (int j = 0; j < nvar; ++j)
1844 if (value_pos_p(C->p[i][1+j]))
1845 value_addto(sum, sum, C->p[i][1+j]);
1846 value_subtract(C->p[i][1+P->Dimension], C->p[i][1+P->Dimension], sum);
1847 }
1848 value_clear(sum);
1849 P2 = Constraints2Polyhedron(C, MaxRays);
1850 Matrix_Free(C);
1851 return P2;
1852 }
1853
1854 static evalue* barvinok_enumerate_ev_f(Polyhedron *P, Polyhedron* C,
1855 barvinok_options *options)
1856 {
1857 unsigned nparam = C->Dimension;
1858 bool pre_approx = options->polynomial_approximation >= BV_POLAPPROX_PRE_LOWER &&
1859 options->polynomial_approximation <= BV_POLAPPROX_PRE_APPROX;
1860
1861 if (P->Dimension - nparam == 1 && !pre_approx)
1862 return ParamLine_Length(P, C, options);
1863
1864 Param_Polyhedron *PP = NULL;
1865 Polyhedron *CEq = NULL, *pVD;
1866 Matrix *CT = NULL;
1867 Param_Domain *D, *next;
1868 Param_Vertices *V;
1869 evalue *eres;
1870 Polyhedron *Porig = P;
1871 Value det;
1872 Polyhedron *T;
1873
1874 if (options->polynomial_approximation == BV_POLAPPROX_PRE_UPPER)
1875 P = Polyhedron_Inflate(P, nparam, options->MaxRays);
1876 if (options->polynomial_approximation == BV_POLAPPROX_PRE_LOWER)
1877 P = Polyhedron_Deflate(P, nparam, options->MaxRays);
1878
1879 T = P;
1880 PP = Polyhedron2Param_SD(&T, C, options->MaxRays, &CEq, &CT);
1881 if (T != P && P != Porig)
1882 Polyhedron_Free(P);
1883 P = T;
1884
1885 if (isIdentity(CT)) {
1886 Matrix_Free(CT);
1887 CT = NULL;
1888 } else {
1889 assert(CT->NbRows != CT->NbColumns);
1890 if (CT->NbRows == 1) { // no more parameters
1891 eres = barvinok_enumerate_cst(P, CEq, options);
1892 out:
1893 if (CT)
1894 Matrix_Free(CT);
1895 if (PP)
1896 Param_Polyhedron_Free(PP);
1897 if (P != Porig)
1898 Polyhedron_Free(P);
1899
1900 return eres;
1901 }
1902 nparam = CT->NbRows - 1;
1903 }
1904
1905 if (pre_approx) {
1906 value_init(det);
1907 Polyhedron *T = P;
1908 Param_Polyhedron_Scale_Integer(PP, &T, &det, options->MaxRays);
1909 if (P != Porig)
1910 Polyhedron_Free(P);
1911 P = T;
1912 }
1913
1914 unsigned dim = P->Dimension - nparam;
1915
1916 ALLOC(evalue, eres);
1917 value_init(eres->d);
1918 value_set_si(eres->d, 0);
1919
1920 int nd;
1921 for (nd = 0, D=PP->D; D; ++nd, D=D->next);
1922 struct section { Polyhedron *D; evalue E; };
1923 section *s = new section[nd];
1924 Polyhedron **fVD = new Polyhedron_p[nd];
1925
1926 enumerator_base *et = NULL;
1927 try_again:
1928 if (et)
1929 delete et;
1930
1931 et = enumerator_base::create(P, dim, PP->nbV, options);
1932
1933 for(nd = 0, D=PP->D; D; D=next) {
1934 next = D->next;
1935
1936 Polyhedron *rVD = reduce_domain(D->Domain, CT, CEq, fVD, nd, options);
1937 if (!rVD)
1938 continue;
1939
1940 pVD = CT ? DomainImage(rVD,CT,options->MaxRays) : rVD;
1941
1942 value_init(s[nd].E.d);
1943 evalue_set_si(&s[nd].E, 0, 1);
1944 s[nd].D = rVD;
1945
1946 FORALL_PVertex_in_ParamPolyhedron(V,D,PP) // _i is internal counter
1947 if (!et->vE[_i])
1948 try {
1949 et->decompose_at(V, _i, options);
1950 } catch (OrthogonalException &e) {
1951 if (rVD != pVD)
1952 Domain_Free(pVD);
1953 for (; nd >= 0; --nd) {
1954 free_evalue_refs(&s[nd].E);
1955 Domain_Free(s[nd].D);
1956 Domain_Free(fVD[nd]);
1957 }
1958 goto try_again;
1959 }
1960 eadd(et->vE[_i] , &s[nd].E);
1961 END_FORALL_PVertex_in_ParamPolyhedron;
1962 evalue_range_reduction_in_domain(&s[nd].E, pVD);
1963
1964 if (CT)
1965 addeliminatedparams_evalue(&s[nd].E, CT);
1966 ++nd;
1967 if (rVD != pVD)
1968 Domain_Free(pVD);
1969 }
1970
1971 delete et;
1972 if (nd == 0)
1973 evalue_set_si(eres, 0, 1);
1974 else {
1975 eres->x.p = new_enode(partition, 2*nd, C->Dimension);
1976 for (int j = 0; j < nd; ++j) {
1977 EVALUE_SET_DOMAIN(eres->x.p->arr[2*j], s[j].D);
1978 value_clear(eres->x.p->arr[2*j+1].d);
1979 eres->x.p->arr[2*j+1] = s[j].E;
1980 Domain_Free(fVD[j]);
1981 }
1982 }
1983 delete [] s;
1984 delete [] fVD;
1985
1986 if (pre_approx) {
1987 evalue_div(eres, det);
1988 value_clear(det);
1989 }
1990
1991 if (CEq)
1992 Polyhedron_Free(CEq);
1993 goto out;
1994 }
1995
1996 Enumeration* barvinok_enumerate(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
1997 {
1998 evalue *EP = barvinok_enumerate_ev(P, C, MaxRays);
1999
2000 return partition2enumeration(EP);
2001 }
2002
2003 static void SwapColumns(Value **V, int n, int i, int j)
2004 {
2005 for (int r = 0; r < n; ++r)
2006 value_swap(V[r][i], V[r][j]);
2007 }
2008
2009 static void SwapColumns(Polyhedron *P, int i, int j)
2010 {
2011 SwapColumns(P->Constraint, P->NbConstraints, i, j);
2012 SwapColumns(P->Ray, P->NbRays, i, j);
2013 }
2014
2015 /* Construct a constraint c from constraints l and u such that if
2016 * if constraint c holds then for each value of the other variables
2017 * there is at most one value of variable pos (position pos+1 in the constraints).
2018 *
2019 * Given a lower and an upper bound
2020 * n_l v_i + <c_l,x> + c_l >= 0
2021 * -n_u v_i + <c_u,x> + c_u >= 0
2022 * the constructed constraint is
2023 *
2024 * -(n_l<c_u,x> + n_u<c_l,x>) + (-n_l c_u - n_u c_l + n_l n_u - 1)
2025 *
2026 * which is then simplified to remove the content of the non-constant coefficients
2027 *
2028 * len is the total length of the constraints.
2029 * v is a temporary variable that can be used by this procedure
2030 */
2031 static void negative_test_constraint(Value *l, Value *u, Value *c, int pos,
2032 int len, Value *v)
2033 {
2034 value_oppose(*v, u[pos+1]);
2035 Vector_Combine(l+1, u+1, c+1, *v, l[pos+1], len-1);
2036 value_multiply(*v, *v, l[pos+1]);
2037 value_subtract(c[len-1], c[len-1], *v);
2038 value_set_si(*v, -1);
2039 Vector_Scale(c+1, c+1, *v, len-1);
2040 value_decrement(c[len-1], c[len-1]);
2041 ConstraintSimplify(c, c, len, v);
2042 }
2043
2044 static bool parallel_constraints(Value *l, Value *u, Value *c, int pos,
2045 int len)
2046 {
2047 bool parallel;
2048 Value g1;
2049 Value g2;
2050 value_init(g1);
2051 value_init(g2);
2052
2053 Vector_Gcd(&l[1+pos], len, &g1);
2054 Vector_Gcd(&u[1+pos], len, &g2);
2055 Vector_Combine(l+1+pos, u+1+pos, c+1, g2, g1, len);
2056 parallel = First_Non_Zero(c+1, len) == -1;
2057
2058 value_clear(g1);
2059 value_clear(g2);
2060
2061 return parallel;
2062 }
2063
2064 static void negative_test_constraint7(Value *l, Value *u, Value *c, int pos,
2065 int exist, int len, Value *v)
2066 {
2067 Value g;
2068 value_init(g);
2069
2070 Vector_Gcd(&u[1+pos], exist, v);
2071 Vector_Gcd(&l[1+pos], exist, &g);
2072 Vector_Combine(l+1, u+1, c+1, *v, g, len-1);
2073 value_multiply(*v, *v, g);
2074 value_subtract(c[len-1], c[len-1], *v);
2075 value_set_si(*v, -1);
2076 Vector_Scale(c+1, c+1, *v, len-1);
2077 value_decrement(c[len-1], c[len-1]);
2078 ConstraintSimplify(c, c, len, v);
2079
2080 value_clear(g);
2081 }
2082
2083 /* Turns a x + b >= 0 into a x + b <= -1
2084 *
2085 * len is the total length of the constraint.
2086 * v is a temporary variable that can be used by this procedure
2087 */
2088 static void oppose_constraint(Value *c, int len, Value *v)
2089 {
2090 value_set_si(*v, -1);
2091 Vector_Scale(c+1, c+1, *v, len-1);
2092 value_decrement(c[len-1], c[len-1]);
2093 }
2094
2095 /* Split polyhedron P into two polyhedra *pos and *neg, where
2096 * existential variable i has at most one solution for each
2097 * value of the other variables in *neg.
2098 *
2099 * The splitting is performed using constraints l and u.
2100 *
2101 * nvar: number of set variables
2102 * row: temporary vector that can be used by this procedure
2103 * f: temporary value that can be used by this procedure
2104 */
2105 static bool SplitOnConstraint(Polyhedron *P, int i, int l, int u,
2106 int nvar, int MaxRays, Vector *row, Value& f,
2107 Polyhedron **pos, Polyhedron **neg)
2108 {
2109 negative_test_constraint(P->Constraint[l], P->Constraint[u],
2110 row->p, nvar+i, P->Dimension+2, &f);
2111 *neg = AddConstraints(row->p, 1, P, MaxRays);
2112
2113 /* We found an independent, but useless constraint
2114 * Maybe we should detect this earlier and not
2115 * mark the variable as INDEPENDENT
2116 */
2117 if (emptyQ((*neg))) {
2118 Polyhedron_Free(*neg);
2119 return false;
2120 }
2121
2122 oppose_constraint(row->p, P->Dimension+2, &f);
2123 *pos = AddConstraints(row->p, 1, P, MaxRays);
2124
2125 if (emptyQ((*pos))) {
2126 Polyhedron_Free(*neg);
2127 Polyhedron_Free(*pos);
2128 return false;
2129 }
2130
2131 return true;
2132 }
2133
2134 /*
2135 * unimodularly transform P such that constraint r is transformed
2136 * into a constraint that involves only a single (the first)
2137 * existential variable
2138 *
2139 */
2140 static Polyhedron *rotate_along(Polyhedron *P, int r, int nvar, int exist,
2141 unsigned MaxRays)
2142 {
2143 Value g;
2144 value_init(g);
2145
2146 Vector *row = Vector_Alloc(exist);
2147 Vector_Copy(P->Constraint[r]+1+nvar, row->p, exist);
2148 Vector_Gcd(row->p, exist, &g);
2149 if (value_notone_p(g))
2150 Vector_AntiScale(row->p, row->p, g, exist);
2151 value_clear(g);
2152
2153 Matrix *M = unimodular_complete(row);
2154 Matrix *M2 = Matrix_Alloc(P->Dimension+1, P->Dimension+1);
2155 for (r = 0; r < nvar; ++r)
2156 value_set_si(M2->p[r][r], 1);
2157 for ( ; r < nvar+exist; ++r)
2158 Vector_Copy(M->p[r-nvar], M2->p[r]+nvar, exist);
2159 for ( ; r < P->Dimension+1; ++r)
2160 value_set_si(M2->p[r][r], 1);
2161 Polyhedron *T = Polyhedron_Image(P, M2, MaxRays);
2162
2163 Matrix_Free(M2);
2164 Matrix_Free(M);
2165 Vector_Free(row);
2166
2167 return T;
2168 }
2169
2170 /* Split polyhedron P into two polyhedra *pos and *neg, where
2171 * existential variable i has at most one solution for each
2172 * value of the other variables in *neg.
2173 *
2174 * If independent is set, then the two constraints on which the
2175 * split will be performed need to be independent of the other
2176 * existential variables.
2177 *
2178 * Return true if an appropriate split could be performed.
2179 *
2180 * nvar: number of set variables
2181 * exist: number of existential variables
2182 * row: temporary vector that can be used by this procedure
2183 * f: temporary value that can be used by this procedure
2184 */
2185 static bool SplitOnVar(Polyhedron *P, int i,
2186 int nvar, int exist, int MaxRays,
2187 Vector *row, Value& f, bool independent,
2188 Polyhedron **pos, Polyhedron **neg)
2189 {
2190 int j;
2191
2192 for (int l = P->NbEq; l < P->NbConstraints; ++l) {
2193 if (value_negz_p(P->Constraint[l][nvar+i+1]))
2194 continue;
2195
2196 if (independent) {
2197 for (j = 0; j < exist; ++j)
2198 if (j != i && value_notzero_p(P->Constraint[l][nvar+j+1]))
2199 break;
2200 if (j < exist)
2201 continue;
2202 }
2203
2204 for (int u = P->NbEq; u < P->NbConstraints; ++u) {
2205 if (value_posz_p(P->Constraint[u][nvar+i+1]))
2206 continue;
2207
2208 if (independent) {
2209 for (j = 0; j < exist; ++j)
2210 if (j != i && value_notzero_p(P->Constraint[u][nvar+j+1]))
2211 break;
2212 if (j < exist)
2213 continue;
2214 }
2215
2216 if (SplitOnConstraint(P, i, l, u, nvar, MaxRays, row, f, pos, neg)) {
2217 if (independent) {
2218 if (i != 0)
2219 SwapColumns(*neg, nvar+1, nvar+1+i);
2220 }
2221 return true;
2222 }
2223 }
2224 }
2225
2226 return false;
2227 }
2228
2229 static bool double_bound_pair(Polyhedron *P, int nvar, int exist,
2230 int i, int l1, int l2,
2231 Polyhedron **pos, Polyhedron **neg)
2232 {
2233 Value f;
2234 value_init(f);
2235 Vector *row = Vector_Alloc(P->Dimension+2);
2236 value_set_si(row->p[0], 1);
2237 value_oppose(f, P->Constraint[l1][nvar+i+1]);
2238 Vector_Combine(P->Constraint[l1]+1, P->Constraint[l2]+1,
2239 row->p+1,
2240 P->Constraint[l2][nvar+i+1], f,
2241 P->Dimension+1);
2242 ConstraintSimplify(row->p, row->p, P->Dimension+2, &f);
2243 *pos = AddConstraints(row->p, 1, P, 0);
2244 value_set_si(f, -1);
2245 Vector_Scale(row->p+1, row->p+1, f, P->Dimension+1);
2246 value_decrement(row->p[P->Dimension+1], row->p[P->Dimension+1]);
2247 *neg = AddConstraints(row->p, 1, P, 0);
2248 Vector_Free(row);
2249 value_clear(f);
2250
2251 return !emptyQ((*pos)) && !emptyQ((*neg));
2252 }
2253
2254 static bool double_bound(Polyhedron *P, int nvar, int exist,
2255 Polyhedron **pos, Polyhedron **neg)
2256 {
2257 for (int i = 0; i < exist; ++i) {
2258 int l1, l2;
2259 for (l1 = P->NbEq; l1 < P->NbConstraints; ++l1) {
2260 if (value_negz_p(P->Constraint[l1][nvar+i+1]))
2261 continue;
2262 for (l2 = l1 + 1; l2 < P->NbConstraints; ++l2) {
2263 if (value_negz_p(P->Constraint[l2][nvar+i+1]))
2264 continue;
2265 if (double_bound_pair(P, nvar, exist, i, l1, l2, pos, neg))
2266 return true;
2267 }
2268 }
2269 for (l1 = P->NbEq; l1 < P->NbConstraints; ++l1) {
2270 if (value_posz_p(P->Constraint[l1][nvar+i+1]))
2271 continue;
2272 if (l1 < P->NbConstraints)
2273 for (l2 = l1 + 1; l2 < P->NbConstraints; ++l2) {
2274 if (value_posz_p(P->Constraint[l2][nvar+i+1]))
2275 continue;
2276 if (double_bound_pair(P, nvar, exist, i, l1, l2, pos, neg))
2277 return true;
2278 }
2279 }
2280 return false;
2281 }
2282 return false;
2283 }
2284
2285 enum constraint {
2286 ALL_POS = 1 << 0,
2287 ONE_NEG = 1 << 1,
2288 INDEPENDENT = 1 << 2,
2289 ROT_NEG = 1 << 3
2290 };
2291
2292 static evalue* enumerate_or(Polyhedron *D,
2293 unsigned exist, unsigned nparam, barvinok_options *options)
2294 {
2295 #ifdef DEBUG_ER
2296 fprintf(stderr, "\nER: Or\n");
2297 #endif /* DEBUG_ER */
2298
2299 Polyhedron *N = D->next;
2300 D->next = 0;
2301 evalue *EP =
2302 barvinok_enumerate_e_with_options(D, exist, nparam, options);
2303 Polyhedron_Free(D);
2304
2305 for (D = N; D; D = N) {
2306 N = D->next;
2307 D->next = 0;
2308
2309 evalue *EN =
2310 barvinok_enumerate_e_with_options(D, exist, nparam, options);
2311
2312 eor(EN, EP);
2313 free_evalue_refs(EN);
2314 free(EN);
2315 Polyhedron_Free(D);
2316 }
2317
2318 reduce_evalue(EP);
2319
2320 return EP;
2321 }
2322
2323 static evalue* enumerate_sum(Polyhedron *P,
2324 unsigned exist, unsigned nparam, barvinok_options *options)
2325 {
2326 int nvar = P->Dimension - exist - nparam;
2327 int toswap = nvar < exist ? nvar : exist;
2328 for (int i = 0; i < toswap; ++i)
2329 SwapColumns(P, 1 + i, nvar+exist - i);
2330 nparam += nvar;
2331
2332 #ifdef DEBUG_ER
2333 fprintf(stderr, "\nER: Sum\n");
2334 #endif /* DEBUG_ER */
2335
2336 evalue *EP = barvinok_enumerate_e_with_options(P, exist, nparam, options);
2337
2338 evalue_split_domains_into_orthants(EP, options->MaxRays);
2339 reduce_evalue(EP);
2340 evalue_range_reduction(EP);
2341
2342 evalue_frac2floor2(EP, 1);
2343
2344 evalue *sum = esum(EP, nvar);
2345
2346 free_evalue_refs(EP);
2347 free(EP);
2348 EP = sum;
2349
2350 evalue_range_reduction(EP);
2351
2352 return EP;
2353 }
2354
2355 static evalue* split_sure(Polyhedron *P, Polyhedron *S,
2356 unsigned exist, unsigned nparam, barvinok_options *options)
2357 {
2358 int nvar = P->Dimension - exist - nparam;
2359
2360 Matrix *M = Matrix_Alloc(exist, S->Dimension+2);
2361 for (int i = 0; i < exist; ++i)
2362 value_set_si(M->p[i][nvar+i+1], 1);
2363 Polyhedron *O = S;
2364 S = DomainAddRays(S, M, options->MaxRays);
2365 Polyhedron_Free(O);
2366 Polyhedron *F = DomainAddRays(P, M, options->MaxRays);
2367 Polyhedron *D = DomainDifference(F, S, options->MaxRays);
2368 O = D;
2369 D = Disjoint_Domain(D, 0, options->MaxRays);
2370 Polyhedron_Free(F);
2371 Domain_Free(O);
2372 Matrix_Free(M);
2373
2374 M = Matrix_Alloc(P->Dimension+1-exist, P->Dimension+1);
2375 for (int j = 0; j < nvar; ++j)
2376 value_set_si(M->p[j][j], 1);
2377 for (int j = 0; j < nparam+1; ++j)
2378 value_set_si(M->p[nvar+j][nvar+exist+j], 1);
2379 Polyhedron *T = Polyhedron_Image(S, M, options->MaxRays);
2380 evalue *EP = barvinok_enumerate_e_with_options(T, 0, nparam, options);
2381 Polyhedron_Free(S);
2382 Polyhedron_Free(T);
2383 Matrix_Free(M);
2384
2385 for (Polyhedron *Q = D; Q; Q = Q->next) {
2386 Polyhedron *N = Q->next;
2387 Q->next = 0;
2388 T = DomainIntersection(P, Q, options->MaxRays);
2389 evalue *E = barvinok_enumerate_e_with_options(T, exist, nparam, options);
2390 eadd(E, EP);
2391 free_evalue_refs(E);
2392 free(E);
2393 Polyhedron_Free(T);
2394 Q->next = N;
2395 }
2396 Domain_Free(D);
2397 return EP;
2398 }
2399
2400 static evalue* enumerate_sure(Polyhedron *P,
2401 unsigned exist, unsigned nparam, barvinok_options *options)
2402 {
2403 int i;
2404 Polyhedron *S = P;
2405 int nvar = P->Dimension - exist - nparam;
2406 Value lcm;
2407 Value f;
2408 value_init(lcm);
2409 value_init(f);
2410
2411 for (i = 0; i < exist; ++i) {
2412 Matrix *M = Matrix_Alloc(S->NbConstraints, S->Dimension+2);
2413 int c = 0;
2414 value_set_si(lcm, 1);
2415 for (int j = 0; j < S->NbConstraints; ++j) {
2416 if (value_negz_p(S->Constraint[j][1+nvar+i]))
2417 continue;
2418 if (value_one_p(S->Constraint[j][1+nvar+i]))
2419 continue;
2420 value_lcm(lcm, S->Constraint[j][1+nvar+i], &lcm);
2421 }
2422
2423 for (int j = 0; j < S->NbConstraints; ++j) {
2424 if (value_negz_p(S->Constraint[j][1+nvar+i]))
2425 continue;
2426 if (value_one_p(S->Constraint[j][1+nvar+i]))
2427 continue;
2428 value_division(f, lcm, S->Constraint[j][1+nvar+i]);
2429 Vector_Scale(S->Constraint[j], M->p[c], f, S->Dimension+2);
2430 value_subtract(M->p[c][S->Dimension+1],
2431 M->p[c][S->Dimension+1],
2432 lcm);
2433 value_increment(M->p[c][S->Dimension+1],
2434 M->p[c][S->Dimension+1]);
2435 ++c;
2436 }
2437 Polyhedron *O = S;
2438 S = AddConstraints(M->p[0], c, S, options->MaxRays);
2439 if (O != P)
2440 Polyhedron_Free(O);
2441 Matrix_Free(M);
2442 if (emptyQ(S)) {
2443 Polyhedron_Free(S);
2444 value_clear(lcm);
2445 value_clear(f);
2446 return 0;
2447 }
2448 }
2449 value_clear(lcm);
2450 value_clear(f);
2451
2452 #ifdef DEBUG_ER
2453 fprintf(stderr, "\nER: Sure\n");
2454 #endif /* DEBUG_ER */
2455
2456 return split_sure(P, S, exist, nparam, options);
2457 }
2458
2459 static evalue* enumerate_sure2(Polyhedron *P,
2460 unsigned exist, unsigned nparam, barvinok_options *options)
2461 {
2462 int nvar = P->Dimension - exist - nparam;
2463 int r;
2464 for (r = 0; r < P->NbRays; ++r)
2465 if (value_one_p(P->Ray[r][0]) &&
2466 value_one_p(P->Ray[r][P->Dimension+1]))
2467 break;
2468
2469 if (r >= P->NbRays)
2470 return 0;
2471
2472 Matrix *M = Matrix_Alloc(nvar + 1 + nparam, P->Dimension+2);
2473 for (int i = 0; i < nvar; ++i)
2474 value_set_si(M->p[i][1+i], 1);
2475 for (int i = 0; i < nparam; ++i)
2476 value_set_si(M->p[i+nvar][1+nvar+exist+i], 1);
2477 Vector_Copy(P->Ray[r]+1+nvar, M->p[nvar+nparam]+1+nvar, exist);
2478 value_set_si(M->p[nvar+nparam][0], 1);
2479 value_set_si(M->p[nvar+nparam][P->Dimension+1], 1);
2480 Polyhedron * F = Rays2Polyhedron(M, options->MaxRays);
2481 Matrix_Free(M);
2482
2483 Polyhedron *I = DomainIntersection(F, P, options->MaxRays);
2484 Polyhedron_Free(F);
2485
2486 #ifdef DEBUG_ER
2487 fprintf(stderr, "\nER: Sure2\n");
2488 #endif /* DEBUG_ER */
2489
2490 return split_sure(P, I, exist, nparam, options);
2491 }
2492
2493 static evalue* enumerate_cyclic(Polyhedron *P,
2494 unsigned exist, unsigned nparam,
2495 evalue * EP, int r, int p, unsigned MaxRays)
2496 {
2497 int nvar = P->Dimension - exist - nparam;
2498
2499 /* If EP in its fractional maps only contains references
2500 * to the remainder parameter with appropriate coefficients
2501 * then we could in principle avoid adding existentially
2502 * quantified variables to the validity domains.
2503 * We'd have to replace the remainder by m { p/m }
2504 * and multiply with an appropriate factor that is one
2505 * only in the appropriate range.
2506 * This last multiplication can be avoided if EP
2507 * has a single validity domain with no (further)
2508 * constraints on the remainder parameter
2509 */
2510
2511 Matrix *CT = Matrix_Alloc(nparam+1, nparam+3);
2512 Matrix *M = Matrix_Alloc(1, 1+nparam+3);
2513 for (int j = 0; j < nparam; ++j)
2514 if (j != p)
2515 value_set_si(CT->p[j][j], 1);
2516 value_set_si(CT->p[p][nparam+1], 1);
2517 value_set_si(CT->p[nparam][nparam+2], 1);
2518 value_set_si(M->p[0][1+p], -1);
2519 value_absolute(M->p[0][1+nparam], P->Ray[0][1+nvar+exist+p]);
2520 value_set_si(M->p[0][1+nparam+1], 1);
2521 Polyhedron *CEq = Constraints2Polyhedron(M, 1);
2522 Matrix_Free(M);
2523 addeliminatedparams_enum(EP, CT, CEq, MaxRays, nparam);
2524 Polyhedron_Free(CEq);
2525 Matrix_Free(CT);
2526
2527 return EP;
2528 }
2529
2530 static void enumerate_vd_add_ray(evalue *EP, Matrix *Rays, unsigned MaxRays)
2531 {
2532 if (value_notzero_p(EP->d))
2533 return;
2534
2535 assert(EP->x.p->type == partition);
2536 assert(EP->x.p->pos == EVALUE_DOMAIN(EP->x.p->arr[0])->Dimension);
2537 for (int i = 0; i < EP->x.p->size/2; ++i) {
2538 Polyhedron *D = EVALUE_DOMAIN(EP->x.p->arr[2*i]);
2539 Polyhedron *N = DomainAddRays(D, Rays, MaxRays);
2540 EVALUE_SET_DOMAIN(EP->x.p->arr[2*i], N);
2541 Domain_Free(D);
2542 }
2543 }
2544
2545 static evalue* enumerate_line(Polyhedron *P,
2546 unsigned exist, unsigned nparam, barvinok_options *options)
2547 {
2548 if (P->NbBid == 0)
2549 return 0;
2550
2551 #ifdef DEBUG_ER
2552 fprintf(stderr, "\nER: Line\n");
2553 #endif /* DEBUG_ER */
2554
2555 int nvar = P->Dimension - exist - nparam;
2556 int i, j;
2557 for (i = 0; i < nparam; ++i)
2558 if (value_notzero_p(P->Ray[0][1+nvar+exist+i]))
2559 break;
2560 assert(i < nparam);
2561 for (j = i+1; j < nparam; ++j)
2562 if (value_notzero_p(P->Ray[0][1+nvar+exist+i]))
2563 break;
2564 assert(j >= nparam); // for now
2565
2566 Matrix *M = Matrix_Alloc(2, P->Dimension+2);
2567 value_set_si(M->p[0][0], 1);
2568 value_set_si(M->p[0][1+nvar+exist+i], 1);
2569 value_set_si(M->p[1][0], 1);
2570 value_set_si(M->p[1][1+nvar+exist+i], -1);
2571 value_absolute(M->p[1][1+P->Dimension], P->Ray[0][1+nvar+exist+i]);
2572 value_decrement(M->p[1][1+P->Dimension], M->p[1][1+P->Dimension]);
2573 Polyhedron *S = AddConstraints(M->p[0], 2, P, options->MaxRays);
2574 evalue *EP = barvinok_enumerate_e_with_options(S, exist, nparam, options);
2575 Polyhedron_Free(S);
2576 Matrix_Free(M);
2577
2578 return enumerate_cyclic(P, exist, nparam, EP, 0, i, options->MaxRays);
2579 }
2580
2581 static int single_param_pos(Polyhedron*P, unsigned exist, unsigned nparam,
2582 int r)
2583 {
2584 int nvar = P->Dimension - exist - nparam;
2585 if (First_Non_Zero(P->Ray[r]+1, nvar) != -1)
2586 return -1;
2587 int i = First_Non_Zero(P->Ray[r]+1+nvar+exist, nparam);
2588 if (i == -1)
2589 return -1;
2590 if (First_Non_Zero(P->Ray[r]+1+nvar+exist+1, nparam-i-1) != -1)
2591 return -1;
2592 return i;
2593 }
2594
2595 static evalue* enumerate_remove_ray(Polyhedron *P, int r,
2596 unsigned exist, unsigned nparam, barvinok_options *options)
2597 {
2598 #ifdef DEBUG_ER
2599 fprintf(stderr, "\nER: RedundantRay\n");
2600 #endif /* DEBUG_ER */
2601
2602 Value one;
2603 value_init(one);
2604 value_set_si(one, 1);
2605 int len = P->NbRays-1;
2606 Matrix *M = Matrix_Alloc(2 * len, P->Dimension+2);
2607 Vector_Copy(P->Ray[0], M->p[0], r * (P->Dimension+2));
2608 Vector_Copy(P->Ray[r+1], M->p[r], (len-r) * (P->Dimension+2));
2609 for (int j = 0; j < P->NbRays; ++j) {
2610 if (j == r)
2611 continue;
2612 Vector_Combine(P->Ray[j], P->Ray[r], M->p[len+j-(j>r)],
2613 one, P->Ray[j][P->Dimension+1], P->Dimension+2);
2614 }
2615
2616 P = Rays2Polyhedron(M, options->MaxRays);
2617 Matrix_Free(M);
2618 evalue *EP = barvinok_enumerate_e_with_options(P, exist, nparam, options);
2619 Polyhedron_Free(P);
2620 value_clear(one);
2621
2622 return EP;
2623 }
2624
2625 static evalue* enumerate_redundant_ray(Polyhedron *P,
2626 unsigned exist, unsigned nparam, barvinok_options *options)
2627 {
2628 assert(P->NbBid == 0);
2629 int nvar = P->Dimension - exist - nparam;
2630 Value m;
2631 value_init(m);
2632
2633 for (int r = 0; r < P->NbRays; ++r) {
2634 if (value_notzero_p(P->Ray[r][P->Dimension+1]))
2635 continue;
2636 int i1 = single_param_pos(P, exist, nparam, r);
2637 if (i1 == -1)
2638 continue;
2639 for (int r2 = r+1; r2 < P->NbRays; ++r2) {
2640 if (value_notzero_p(P->Ray[r2][P->Dimension+1]))
2641 continue;
2642 int i2 = single_param_pos(P, exist, nparam, r2);
2643 if (i2 == -1)
2644 continue;
2645 if (i1 != i2)
2646 continue;
2647
2648 value_division(m, P->Ray[r][1+nvar+exist+i1],
2649 P->Ray[r2][1+nvar+exist+i1]);
2650 value_multiply(m, m, P->Ray[r2][1+nvar+exist+i1]);
2651 /* r2 divides r => r redundant */
2652 if (value_eq(m, P->Ray[r][1+nvar+exist+i1])) {
2653 value_clear(m);
2654 return enumerate_remove_ray(P, r, exist, nparam, options);
2655 }
2656
2657 value_division(m, P->Ray[r2][1+nvar+exist+i1],
2658 P->Ray[r][1+nvar+exist+i1]);
2659 value_multiply(m, m, P->Ray[r][1+nvar+exist+i1]);
2660 /* r divides r2 => r2 redundant */
2661 if (value_eq(m, P->Ray[r2][1+nvar+exist+i1])) {
2662 value_clear(m);
2663 return enumerate_remove_ray(P, r2, exist, nparam, options);
2664 }
2665 }
2666 }
2667 value_clear(m);
2668 return 0;
2669 }
2670
2671 static Polyhedron *upper_bound(Polyhedron *P,
2672 int pos, Value *max, Polyhedron **R)
2673 {
2674 Value v;
2675 int r;
2676 value_init(v);
2677
2678 *R = 0;
2679 Polyhedron *N;
2680 Polyhedron *B = 0;
2681 for (Polyhedron *Q = P; Q; Q = N) {
2682 N = Q->next;
2683 for (r = 0; r < P->NbRays; ++r) {
2684 if (value_zero_p(P->Ray[r][P->Dimension+1]) &&
2685 value_pos_p(P->Ray[r][1+pos]))
2686 break;
2687 }
2688 if (r < P->NbRays) {
2689 Q->next = *R;
2690 *R = Q;
2691 continue;
2692 } else {
2693 Q->next = B;
2694 B = Q;
2695 }
2696 for (r = 0; r < P->NbRays; ++r) {
2697 if (value_zero_p(P->Ray[r][P->Dimension+1]))
2698 continue;
2699 mpz_fdiv_q(v, P->Ray[r][1+pos], P->Ray[r][1+P->Dimension]);
2700 if ((!Q->next && r == 0) || value_gt(v, *max))
2701 value_assign(*max, v);
2702 }
2703 }
2704 value_clear(v);
2705 return B;
2706 }
2707
2708 static evalue* enumerate_ray(Polyhedron *P,
2709 unsigned exist, unsigned nparam, barvinok_options *options)
2710 {
2711 assert(P->NbBid == 0);
2712 int nvar = P->Dimension - exist - nparam;
2713
2714 int r;
2715 for (r = 0; r < P->NbRays; ++r)
2716 if (value_zero_p(P->Ray[r][P->Dimension+1]))
2717 break;
2718 if (r >= P->NbRays)
2719 return 0;
2720
2721 int r2;
2722 for (r2 = r+1; r2 < P->NbRays; ++r2)
2723 if (value_zero_p(P->Ray[r2][P->Dimension+1]))
2724 break;
2725 if (r2 < P->NbRays) {
2726 if (nvar > 0)
2727 return enumerate_sum(P, exist, nparam, options);
2728 }
2729
2730 #ifdef DEBUG_ER
2731 fprintf(stderr, "\nER: Ray\n");
2732 #endif /* DEBUG_ER */
2733
2734 Value m;
2735 Value one;
2736 value_init(m);
2737 value_init(one);
2738 value_set_si(one, 1);
2739 int i = single_param_pos(P, exist, nparam, r);
2740 assert(i != -1); // for now;
2741
2742 Matrix *M = Matrix_Alloc(P->NbRays, P->Dimension+2);
2743 for (int j = 0; j < P->NbRays; ++j) {
2744 Vector_Combine(P->Ray[j], P->Ray[r], M->p[j],
2745 one, P->Ray[j][P->Dimension+1], P->Dimension+2);
2746 }
2747 Polyhedron *S = Rays2Polyhedron(M, options->MaxRays);
2748 Matrix_Free(M);
2749 Polyhedron *D = DomainDifference(P, S, options->MaxRays);
2750 Polyhedron_Free(S);
2751 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
2752 assert(value_pos_p(P->Ray[r][1+nvar+exist+i])); // for now
2753 Polyhedron *R;
2754 D = upper_bound(D, nvar+exist+i, &m, &R);
2755 assert(D);
2756 Domain_Free(D);
2757
2758 M = Matrix_Alloc(2, P->Dimension+2);
2759 value_set_si(M->p[0][0], 1);
2760 value_set_si(M->p[1][0], 1);
2761 value_set_si(M->p[0][1+nvar+exist+i], -1);
2762 value_set_si(M->p[1][1+nvar+exist+i], 1);
2763 value_assign(M->p[0][1+P->Dimension], m);
2764 value_oppose(M->p[1][1+P->Dimension], m);
2765 value_addto(M->p[1][1+P->Dimension], M->p[1][1+P->Dimension],
2766 P->Ray[r][1+nvar+exist+i]);
2767 value_decrement(M->p[1][1+P->Dimension], M->p[1][1+P->Dimension]);
2768 // Matrix_Print(stderr, P_VALUE_FMT, M);
2769 D = AddConstraints(M->p[0], 2, P, options->MaxRays);
2770 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
2771 value_subtract(M->p[0][1+P->Dimension], M->p[0][1+P->Dimension],
2772 P->Ray[r][1+nvar+exist+i]);
2773 // Matrix_Print(stderr, P_VALUE_FMT, M);
2774 S = AddConstraints(M->p[0], 1, P, options->MaxRays);
2775 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
2776 Matrix_Free(M);
2777
2778 evalue *EP = barvinok_enumerate_e_with_options(D, exist, nparam, options);
2779 Polyhedron_Free(D);
2780 value_clear(one);
2781 value_clear(m);
2782
2783 if (value_notone_p(P->Ray[r][1+nvar+exist+i]))
2784 EP = enumerate_cyclic(P, exist, nparam, EP, r, i, options->MaxRays);
2785 else {
2786 M = Matrix_Alloc(1, nparam+2);
2787 value_set_si(M->p[0][0], 1);
2788 value_set_si(M->p[0][1+i], 1);
2789 enumerate_vd_add_ray(EP, M, options->MaxRays);
2790 Matrix_Free(M);
2791 }
2792
2793 if (!emptyQ(S)) {
2794 evalue *E = barvinok_enumerate_e_with_options(S, exist, nparam, options);
2795 eadd(E, EP);
2796 free_evalue_refs(E);
2797 free(E);
2798 }
2799 Polyhedron_Free(S);
2800
2801 if (R) {
2802 assert(nvar == 0);
2803 evalue *ER = enumerate_or(R, exist, nparam, options);
2804 eor(ER, EP);
2805 free_evalue_refs(ER);
2806 free(ER);
2807 }
2808
2809 return EP;
2810 }
2811
2812 static evalue* enumerate_vd(Polyhedron **PA,
2813 unsigned exist, unsigned nparam, barvinok_options *options)
2814 {
2815 Polyhedron *P = *PA;
2816 int nvar = P->Dimension - exist - nparam;
2817 Param_Polyhedron *PP = NULL;
2818 Polyhedron *C = Universe_Polyhedron(nparam);
2819 Polyhedron *CEq;
2820 Matrix *CT;
2821 Polyhedron *PR = P;
2822 PP = Polyhedron2Param_SimplifiedDomain(&PR,C, options->MaxRays,&CEq,&CT);
2823 Polyhedron_Free(C);
2824
2825 int nd;
2826 Param_Domain *D, *last;
2827 Value c;
2828 value_init(c);
2829 for (nd = 0, D=PP->D; D; D=D->next, ++nd)
2830 ;
2831
2832 Polyhedron **VD = new Polyhedron_p[nd];
2833 Polyhedron **fVD = new Polyhedron_p[nd];
2834 for(nd = 0, D=PP->D; D; D=D->next) {
2835 Polyhedron *rVD = reduce_domain(D->Domain, CT, CEq, fVD, nd, options);
2836 if (!rVD)
2837 continue;
2838
2839 VD[nd++] = rVD;
2840 last = D;
2841 }
2842
2843 evalue *EP = 0;
2844
2845 if (nd == 0)
2846 EP = evalue_zero();
2847
2848 /* This doesn't seem to have any effect */
2849 if (nd == 1) {
2850 Polyhedron *CA = align_context(VD[0], P->Dimension, options->MaxRays);
2851 Polyhedron *O = P;
2852 P = DomainIntersection(P, CA, options->MaxRays);
2853 if (O != *PA)
2854 Polyhedron_Free(O);
2855 Polyhedron_Free(CA);
2856 if (emptyQ(P))
2857 EP = evalue_zero();
2858 }
2859
2860 if (!EP && CT->NbColumns != CT->NbRows) {
2861 Polyhedron *CEqr = DomainImage(CEq, CT, options->MaxRays);
2862 Polyhedron *CA = align_context(CEqr, PR->Dimension, options->MaxRays);
2863 Polyhedron *I = DomainIntersection(PR, CA, options->MaxRays);
2864 Polyhedron_Free(CEqr);
2865 Polyhedron_Free(CA);
2866 #ifdef DEBUG_ER
2867 fprintf(stderr, "\nER: Eliminate\n");
2868 #endif /* DEBUG_ER */
2869 nparam -= CT->NbColumns - CT->NbRows;
2870 EP = barvinok_enumerate_e_with_options(I, exist, nparam, options);
2871 nparam += CT->NbColumns - CT->NbRows;
2872 addeliminatedparams_enum(EP, CT, CEq, options->MaxRays, nparam);
2873 Polyhedron_Free(I);
2874 }
2875 if (PR != *PA)
2876 Polyhedron_Free(PR);
2877 PR = 0;
2878
2879 if (!EP && nd > 1) {
2880 #ifdef DEBUG_ER
2881 fprintf(stderr, "\nER: VD\n");
2882 #endif /* DEBUG_ER */
2883 for (int i = 0; i < nd; ++i) {
2884 Polyhedron *CA = align_context(VD[i], P->Dimension, options->MaxRays);
2885 Polyhedron *I = DomainIntersection(P, CA, options->MaxRays);
2886
2887 if (i == 0)
2888 EP = barvinok_enumerate_e_with_options(I, exist, nparam, options);
2889 else {
2890 evalue *E = barvinok_enumerate_e_with_options(I, exist, nparam,
2891 options);
2892 eadd(E, EP);
2893 free_evalue_refs(E);
2894 free(E);
2895 }
2896 Polyhedron_Free(I);
2897 Polyhedron_Free(CA);
2898 }
2899 }
2900
2901 for (int i = 0; i < nd; ++i) {
2902 Polyhedron_Free(VD[i]);
2903 Polyhedron_Free(fVD[i]);
2904 }
2905 delete [] VD;
2906 delete [] fVD;
2907 value_clear(c);
2908
2909 if (!EP && nvar == 0) {
2910 Value f;
2911 value_init(f);
2912 Param_Vertices *V, *V2;
2913 Matrix* M = Matrix_Alloc(1, P->Dimension+2);
2914
2915 FORALL_PVertex_in_ParamPolyhedron(V, last, PP) {
2916 bool found = false;
2917 FORALL_PVertex_in_ParamPolyhedron(V2, last, PP) {
2918 if (V == V2) {
2919 found = true;
2920 continue;
2921 }
2922 if (!found)
2923 continue;
2924 for (int i = 0; i < exist; ++i) {
2925 value_oppose(f, V->Vertex->p[i][nparam+1]);
2926 Vector_Combine(V->Vertex->p[i],
2927 V2->Vertex->p[i],
2928 M->p[0] + 1 + nvar + exist,
2929 V2->Vertex->p[i][nparam+1],
2930 f,
2931 nparam+1);
2932 int j;
2933 for (j = 0; j < nparam; ++j)
2934 if (value_notzero_p(M->p[0][1+nvar+exist+j]))
2935 break;
2936 if (j >= nparam)
2937 continue;
2938 ConstraintSimplify(M->p[0], M->p[0],
2939 P->Dimension+2, &f);
2940 value_set_si(M->p[0][0], 0);
2941 Polyhedron *para = AddConstraints(M->p[0], 1, P,
2942 options->MaxRays);
2943 if (emptyQ(para)) {
2944 Polyhedron_Free(para);
2945 continue;
2946 }
2947 Polyhedron *pos, *neg;
2948 value_set_si(M->p[0][0], 1);
2949 value_decrement(M->p[0][P->Dimension+1],
2950 M->p[0][P->Dimension+1]);
2951 neg = AddConstraints(M->p[0], 1, P, options->MaxRays);
2952 value_set_si(f, -1);
2953 Vector_Scale(M->p[0]+1, M->p[0]+1, f,
2954 P->Dimension+1);
2955 value_decrement(M->p[0][P->Dimension+1],
2956 M->p[0][P->Dimension+1]);
2957 value_decrement(M->p[0][P->Dimension+1],
2958 M->p[0][P->Dimension+1]);
2959 pos = AddConstraints(M->p[0], 1, P, options->MaxRays);
2960 if (emptyQ(neg) && emptyQ(pos)) {
2961 Polyhedron_Free(para);
2962 Polyhedron_Free(pos);
2963 Polyhedron_Free(neg);
2964 continue;
2965 }
2966 #ifdef DEBUG_ER
2967 fprintf(stderr, "\nER: Order\n");
2968 #endif /* DEBUG_ER */
2969 EP = barvinok_enumerate_e_with_options(para, exist, nparam,
2970 options);
2971 evalue *E;
2972 if (!emptyQ(pos)) {
2973 E = barvinok_enumerate_e_with_options(pos, exist, nparam,
2974 options);
2975 eadd(E, EP);
2976 free_evalue_refs(E);
2977 free(E);
2978 }
2979 if (!emptyQ(neg)) {
2980 E = barvinok_enumerate_e_with_options(neg, exist, nparam,
2981 options);
2982 eadd(E, EP);
2983 free_evalue_refs(E);
2984 free(E);
2985 }
2986 Polyhedron_Free(para);
2987 Polyhedron_Free(pos);
2988 Polyhedron_Free(neg);
2989 break;
2990 }
2991 if (EP)
2992 break;
2993 } END_FORALL_PVertex_in_ParamPolyhedron;
2994 if (EP)
2995 break;
2996 } END_FORALL_PVertex_in_ParamPolyhedron;
2997
2998 if (!EP) {
2999 /* Search for vertex coordinate to split on */
3000 /* First look for one independent of the parameters */
3001 FORALL_PVertex_in_ParamPolyhedron(V, last, PP) {
3002 for (int i = 0; i < exist; ++i) {
3003 int j;
3004 for (j = 0; j < nparam; ++j)
3005 if (value_notzero_p(V->Vertex->p[i][j]))
3006 break;
3007 if (j < nparam)
3008 continue;
3009 value_set_si(M->p[0][0], 1);
3010 Vector_Set(M->p[0]+1, 0, nvar+exist);
3011 Vector_Copy(V->Vertex->p[i],
3012 M->p[0] + 1 + nvar + exist, nparam+1);
3013 value_oppose(M->p[0][1+nvar+i],
3014 V->Vertex->p[i][nparam+1]);
3015
3016 Polyhedron *pos, *neg;
3017 value_set_si(M->p[0][0], 1);
3018 value_decrement(M->p[0][P->Dimension+1],
3019 M->p[0][P->Dimension+1]);
3020 neg = AddConstraints(M->p[0], 1, P, options->MaxRays);
3021 value_set_si(f, -1);
3022 Vector_Scale(M->p[0]+1, M->p[0]+1, f,
3023 P->Dimension+1);
3024 value_decrement(M->p[0][P->Dimension+1],
3025 M->p[0][P->Dimension+1]);
3026 value_decrement(M->p[0][P->Dimension+1],
3027 M->p[0][P->Dimension+1]);
3028 pos = AddConstraints(M->p[0], 1, P, options->MaxRays);
3029 if (emptyQ(neg) || emptyQ(pos)) {
3030 Polyhedron_Free(pos);
3031 Polyhedron_Free(neg);
3032 continue;
3033 }
3034 Polyhedron_Free(pos);
3035 value_increment(M->p[0][P->Dimension+1],
3036 M->p[0][P->Dimension+1]);
3037 pos = AddConstraints(M->p[0], 1, P, options->MaxRays);
3038 #ifdef DEBUG_ER
3039 fprintf(stderr, "\nER: Vertex\n");
3040 #endif /* DEBUG_ER */
3041 pos->next = neg;
3042 EP = enumerate_or(pos, exist, nparam, options);
3043 break;
3044 }
3045 if (EP)
3046 break;
3047 } END_FORALL_PVertex_in_ParamPolyhedron;
3048 }
3049
3050 if (!EP) {
3051 /* Search for vertex coordinate to split on */
3052 /* Now look for one that depends on the parameters */
3053 FORALL_PVertex_in_ParamPolyhedron(V, last, PP) {
3054 for (int i = 0; i < exist; ++i) {
3055 value_set_si(M->p[0][0], 1);
3056 Vector_Set(M->p[0]+1, 0, nvar+exist);
3057 Vector_Copy(V->Vertex->p[i],
3058 M->p[0] + 1 + nvar + exist, nparam+1);
3059 value_oppose(M->p[0][1+nvar+i],
3060 V->Vertex->p[i][nparam+1]);
3061
3062 Polyhedron *pos, *neg;
3063 value_set_si(M->p[0][0], 1);
3064 value_decrement(M->p[0][P->Dimension+1],
3065 M->p[0][P->Dimension+1]);
3066 neg = AddConstraints(M->p[0], 1, P, options->MaxRays);
3067 value_set_si(f, -1);
3068 Vector_Scale(M->p[0]+1, M->p[0]+1, f,
3069 P->Dimension+1);
3070 value_decrement(M->p[0][P->Dimension+1],
3071 M->p[0][P->Dimension+1]);
3072 value_decrement(M->p[0][P->Dimension+1],
3073 M->p[0][P->Dimension+1]);
3074 pos = AddConstraints(M->p[0], 1, P, options->MaxRays);
3075 if (emptyQ(neg) || emptyQ(pos)) {
3076 Polyhedron_Free(pos);
3077 Polyhedron_Free(neg);
3078 continue;
3079 }
3080 Polyhedron_Free(pos);
3081 value_increment(M->p[0][P->Dimension+1],
3082 M->p[0][P->Dimension+1]);
3083 pos = AddConstraints(M->p[0], 1, P, options->MaxRays);
3084 #ifdef DEBUG_ER
3085 fprintf(stderr, "\nER: ParamVertex\n");
3086 #endif /* DEBUG_ER */
3087 pos->next = neg;
3088 EP = enumerate_or(pos, exist, nparam, options);
3089 break;
3090 }
3091 if (EP)
3092 break;
3093 } END_FORALL_PVertex_in_ParamPolyhedron;
3094 }
3095
3096 Matrix_Free(M);
3097 value_clear(f);
3098 }
3099
3100 if (CEq)
3101 Polyhedron_Free(CEq);
3102 if (CT)
3103 Matrix_Free(CT);
3104 if (PP)
3105 Param_Polyhedron_Free(PP);
3106 *PA = P;
3107
3108 return EP;
3109 }
3110
3111 evalue* barvinok_enumerate_pip(Polyhedron *P, unsigned exist, unsigned nparam,
3112 unsigned MaxRays)
3113 {
3114 evalue *E;
3115 barvinok_options *options = barvinok_options_new_with_defaults();
3116 options->MaxRays = MaxRays;
3117 E = barvinok_enumerate_pip_with_options(P, exist, nparam, options);
3118 barvinok_options_free(options);
3119 return E;
3120 }
3121
3122 #ifndef HAVE_PIPLIB
3123 evalue *barvinok_enumerate_pip_with_options(Polyhedron *P,
3124 unsigned exist, unsigned nparam, struct barvinok_options *options)
3125 {
3126 return 0;
3127 }
3128 #else
3129 evalue *barvinok_enumerate_pip_with_options(Polyhedron *P,
3130 unsigned exist, unsigned nparam, struct barvinok_options *options)
3131 {
3132 int nvar = P->Dimension - exist - nparam;
3133 evalue *EP = evalue_zero();
3134 Polyhedron *Q, *N;
3135
3136 #ifdef DEBUG_ER
3137 fprintf(stderr, "\nER: PIP\n");
3138 #endif /* DEBUG_ER */
3139
3140 Polyhedron *D = pip_projectout(P, nvar, exist, nparam);
3141 for (Q = D; Q; Q = N) {
3142 N = Q->next;
3143 Q->next = 0;
3144 evalue *E;
3145 exist = Q->Dimension - nvar - nparam;
3146 E = barvinok_enumerate_e_with_options(Q, exist, nparam, options);
3147 Polyhedron_Free(Q);
3148 eadd(E, EP);
3149 free_evalue_refs(E);
3150 free(E);
3151 }
3152
3153 return EP;
3154 }
3155 #endif
3156
3157
3158 static bool is_single(Value *row, int pos, int len)
3159 {
3160 return First_Non_Zero(row, pos) == -1 &&
3161 First_Non_Zero(row+pos+1, len-pos-1) == -1;
3162 }
3163
3164 static evalue* barvinok_enumerate_e_r(Polyhedron *P,
3165 unsigned exist, unsigned nparam, barvinok_options *options);
3166
3167 #ifdef DEBUG_ER
3168 static int er_level = 0;
3169
3170 evalue* barvinok_enumerate_e_with_options(Polyhedron *P,
3171 unsigned exist, unsigned nparam, barvinok_options *options)
3172 {
3173 fprintf(stderr, "\nER: level %i\n", er_level);
3174
3175 Polyhedron_PrintConstraints(stderr, P_VALUE_FMT, P);
3176 fprintf(stderr, "\nE %d\nP %d\n", exist, nparam);
3177 ++er_level;
3178 P = DomainConstraintSimplify(Polyhedron_Copy(P), options->MaxRays);
3179 evalue *EP = barvinok_enumerate_e_r(P, exist, nparam, options);
3180 Polyhedron_Free(P);
3181 --er_level;
3182 return EP;
3183 }
3184 #else
3185 evalue* barvinok_enumerate_e_with_options(Polyhedron *P,
3186 unsigned exist, unsigned nparam, barvinok_options *options)
3187 {
3188 P = DomainConstraintSimplify(Polyhedron_Copy(P), options->MaxRays);
3189 evalue *EP = barvinok_enumerate_e_r(P, exist, nparam, options);
3190 Polyhedron_Free(P);
3191 return EP;
3192 }
3193 #endif
3194
3195 evalue* barvinok_enumerate_e(Polyhedron *P, unsigned exist, unsigned nparam,
3196 unsigned MaxRays)
3197 {
3198 evalue *E;
3199 barvinok_options *options = barvinok_options_new_with_defaults();
3200 options->MaxRays = MaxRays;
3201 E = barvinok_enumerate_e_with_options(P, exist, nparam, options);
3202 barvinok_options_free(options);
3203 return E;
3204 }
3205
3206 static evalue* barvinok_enumerate_e_r(Polyhedron *P,
3207 unsigned exist, unsigned nparam, barvinok_options *options)
3208 {
3209 if (exist == 0) {
3210 Polyhedron *U = Universe_Polyhedron(nparam);
3211 evalue *EP = barvinok_enumerate_with_options(P, U, options);
3212 //char *param_name[] = {"P", "Q", "R", "S", "T" };
3213 //print_evalue(stdout, EP, param_name);
3214 Polyhedron_Free(U);
3215 return EP;
3216 }
3217
3218 int nvar = P->Dimension - exist - nparam;
3219 int len = P->Dimension + 2;
3220
3221 /* for now */
3222 POL_ENSURE_FACETS(P);
3223 POL_ENSURE_VERTICES(P);
3224
3225 if (emptyQ(P))
3226 return evalue_zero();
3227
3228 if (nvar == 0 && nparam == 0) {
3229 evalue *EP = evalue_zero();
3230 barvinok_count_with_options(P, &EP->x.n, options);
3231 if (value_pos_p(EP->x.n))
3232 value_set_si(EP->x.n, 1);
3233 return EP;
3234 }
3235
3236 int r;
3237 for (r = 0; r < P->NbRays; ++r)
3238 if (value_zero_p(P->Ray[r][0]) ||
3239 value_zero_p(P->Ray[r][P->Dimension+1])) {
3240 int i;
3241 for (i = 0; i < nvar; ++i)
3242 if (value_notzero_p(P->Ray[r][i+1]))
3243 break;
3244 if (i >= nvar)
3245 continue;
3246 for (i = nvar + exist; i < nvar + exist + nparam; ++i)
3247 if (value_notzero_p(P->Ray[r][i+1]))
3248 break;
3249 if (i >= nvar + exist + nparam)
3250 break;
3251 }
3252 if (r < P->NbRays) {
3253 evalue *EP = evalue_zero();
3254 value_set_si(EP->x.n, -1);
3255 return EP;
3256 }
3257
3258 int first;
3259 for (r = 0; r < P->NbEq; ++r)
3260 if ((first = First_Non_Zero(P->Constraint[r]+1+nvar, exist)) != -1)
3261 break;
3262 if (r < P->NbEq) {
3263 if (First_Non_Zero(P->Constraint[r]+1+nvar+first+1,
3264 exist-first-1) != -1) {
3265 Polyhedron *T = rotate_along(P, r, nvar, exist, options->MaxRays);
3266 #ifdef DEBUG_ER
3267 fprintf(stderr, "\nER: Equality\n");
3268 #endif /* DEBUG_ER */
3269 evalue *EP = barvinok_enumerate_e_with_options(T, exist-1, nparam,
3270 options);
3271 Polyhedron_Free(T);
3272 return EP;
3273 } else {
3274 #ifdef DEBUG_ER
3275 fprintf(stderr, "\nER: Fixed\n");
3276 #endif /* DEBUG_ER */
3277 if (first == 0)
3278 return barvinok_enumerate_e_with_options(P, exist-1, nparam,
3279 options);
3280 else {
3281 Polyhedron *T = Polyhedron_Copy(P);
3282 SwapColumns(T, nvar+1, nvar+1+first);
3283 evalue *EP = barvinok_enumerate_e_with_options(T, exist-1, nparam,
3284 options);
3285 Polyhedron_Free(T);
3286 return EP;
3287 }
3288 }
3289 }
3290
3291 Vector *row = Vector_Alloc(len);
3292 value_set_si(row->p[0], 1);
3293
3294 Value f;
3295 value_init(f);
3296
3297 enum constraint* info = new constraint[exist];
3298 for (int i = 0; i < exist; ++i) {
3299 info[i] = ALL_POS;
3300 for (int l = P->NbEq; l < P->NbConstraints; ++l) {
3301 if (value_negz_p(P->Constraint[l][nvar+i+1]))
3302 continue;
3303 bool l_parallel = is_single(P->Constraint[l]+nvar+1, i, exist);
3304 for (int u = P->NbEq; u < P->NbConstraints; ++u) {
3305 if (value_posz_p(P->Constraint[u][nvar+i+1]))
3306 continue;
3307 bool lu_parallel = l_parallel ||
3308 is_single(P->Constraint[u]+nvar+1, i, exist);
3309 value_oppose(f, P->Constraint[u][nvar+i+1]);
3310 Vector_Combine(P->Constraint[l]+1, P->Constraint[u]+1, row->p+1,
3311 f, P->Constraint[l][nvar+i+1], len-1);
3312 if (!(info[i] & INDEPENDENT)) {
3313 int j;
3314 for (j = 0; j < exist; ++j)
3315 if (j != i && value_notzero_p(row->p[nvar+j+1]))
3316 break;
3317 if (j == exist) {
3318 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
3319 info[i] = (constraint)(info[i] | INDEPENDENT);
3320 }
3321 }
3322 if (info[i] & ALL_POS) {
3323 value_addto(row->p[len-1], row->p[len-1],
3324 P->Constraint[l][nvar+i+1]);
3325 value_addto(row->p[len-1], row->p[len-1], f);
3326 value_multiply(f, f, P->Constraint[l][nvar+i+1]);
3327 value_subtract(row->p[len-1], row->p[len-1], f);
3328 value_decrement(row->p[len-1], row->p[len-1]);
3329 ConstraintSimplify(row->p, row->p, len, &f);
3330 value_set_si(f, -1);
3331 Vector_Scale(row->p+1, row->p+1, f, len-1);
3332 value_decrement(row->p[len-1], row->p[len-1]);
3333 Polyhedron *T = AddConstraints(row->p, 1, P, options->MaxRays);
3334 if (!emptyQ(T)) {
3335 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
3336 info[i] = (constraint)(info[i] ^ ALL_POS);
3337 }
3338 //puts("pos remainder");
3339 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3340 Polyhedron_Free(T);
3341 }
3342 if (!(info[i] & ONE_NEG)) {
3343 if (lu_parallel) {
3344 negative_test_constraint(P->Constraint[l],
3345 P->Constraint[u],
3346 row->p, nvar+i, len, &f);
3347 oppose_constraint(row->p, len, &f);
3348 Polyhedron *T = AddConstraints(row->p, 1, P,
3349 options->MaxRays);
3350 if (emptyQ(T)) {
3351 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
3352 info[i] = (constraint)(info[i] | ONE_NEG);
3353 }
3354 //puts("neg remainder");
3355 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3356 Polyhedron_Free(T);
3357 } else if (!(info[i] & ROT_NEG)) {
3358 if (parallel_constraints(P->Constraint[l],
3359 P->Constraint[u],
3360 row->p, nvar, exist)) {
3361 negative_test_constraint7(P->Constraint[l],
3362 P->Constraint[u],
3363 row->p, nvar, exist,
3364 len, &f);
3365 oppose_constraint(row->p, len, &f);
3366 Polyhedron *T = AddConstraints(row->p, 1, P,
3367 options->MaxRays);
3368 if (emptyQ(T)) {
3369 // printf("rot_neg i: %d, l: %d, u: %d\n", i, l, u);
3370 info[i] = (constraint)(info[i] | ROT_NEG);
3371 r = l;
3372 }
3373 //puts("neg remainder");
3374 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
3375 Polyhedron_Free(T);
3376 }
3377 }
3378 }
3379 if (!(info[i] & ALL_POS) && (info[i] & (ONE_NEG | ROT_NEG)))
3380 goto next;
3381 }
3382 }
3383 if (info[i] & ALL_POS)
3384 break;
3385 next:
3386 ;
3387 }
3388
3389 /*
3390 for (int i = 0; i < exist; ++i)
3391 printf("%i: %i\n", i, info[i]);
3392 */
3393 for (int i = 0; i < exist; ++i)
3394 if (info[i] & ALL_POS) {
3395 #ifdef DEBUG_ER
3396 fprintf(stderr, "\nER: Positive\n");
3397 #endif /* DEBUG_ER */
3398 // Eliminate
3399 // Maybe we should chew off some of the fat here
3400 Matrix *M = Matrix_Alloc(P->Dimension, P->Dimension+1);
3401 for (int j = 0; j < P->Dimension; ++j)
3402 value_set_si(M->p[j][j + (j >= i+nvar)], 1);
3403 Polyhedron *T = Polyhedron_Image(P, M, options->MaxRays);
3404 Matrix_Free(M);
3405 evalue *EP = barvinok_enumerate_e_with_options(T, exist-1, nparam,
3406 options);
3407 Polyhedron_Free(T);
3408 value_clear(f);
3409 Vector_Free(row);
3410 delete [] info;
3411 return EP;
3412 }
3413 for (int i = 0; i < exist; ++i)
3414 if (info[i] & ONE_NEG) {
3415 #ifdef DEBUG_ER
3416 fprintf(stderr, "\nER: Negative\n");
3417 #endif /* DEBUG_ER */
3418 Vector_Free(row);
3419 value_clear(f);
3420 delete [] info;
3421 if (i == 0)
3422 return barvinok_enumerate_e_with_options(P, exist-1, nparam,
3423 options);
3424 else {
3425 Polyhedron *T = Polyhedron_Copy(P);
3426 SwapColumns(T, nvar+1, nvar+1+i);
3427 evalue *EP = barvinok_enumerate_e_with_options(T, exist-1, nparam,
3428 options);
3429 Polyhedron_Free(T);
3430 return EP;
3431 }
3432 }
3433 for (int i = 0; i < exist; ++i)
3434 if (info[i] & ROT_NEG) {
3435 #ifdef DEBUG_ER
3436 fprintf(stderr, "\nER: Rotate\n");
3437 #endif /* DEBUG_ER */
3438 Vector_Free(row);
3439 value_clear(f);
3440 delete [] info;
3441 Polyhedron *T = rotate_along(P, r, nvar, exist, options->MaxRays);
3442 evalue *EP = barvinok_enumerate_e_with_options(T, exist-1, nparam,
3443 options);
3444 Polyhedron_Free(T);
3445 return EP;
3446 }
3447 for (int i = 0; i < exist; ++i)
3448 if (info[i] & INDEPENDENT) {
3449 Polyhedron *pos, *neg;
3450
3451 /* Find constraint again and split off negative part */
3452
3453 if (SplitOnVar(P, i, nvar, exist, options->MaxRays,
3454 row, f, true, &pos, &neg)) {
3455 #ifdef DEBUG_ER
3456 fprintf(stderr, "\nER: Split\n");
3457 #endif /* DEBUG_ER */
3458
3459 evalue *EP =
3460 barvinok_enumerate_e_with_options(neg, exist-1, nparam, options);
3461 evalue *E =
3462 barvinok_enumerate_e_with_options(pos, exist, nparam, options);
3463 eadd(E, EP);
3464 free_evalue_refs(E);
3465 free(E);
3466 Polyhedron_Free(neg);
3467 Polyhedron_Free(pos);
3468 value_clear(f);
3469 Vector_Free(row);
3470 delete [] info;
3471 return EP;
3472 }
3473 }
3474 delete [] info;
3475
3476 Polyhedron *O = P;
3477 Polyhedron *F;
3478
3479 evalue *EP;
3480
3481 EP = enumerate_line(P, exist, nparam, options);
3482 if (EP)
3483 goto out;
3484
3485 EP = barvinok_enumerate_pip_with_options(P, exist, nparam, options);
3486 if (EP)
3487 goto out;
3488
3489 EP = enumerate_redundant_ray(P, exist, nparam, options);
3490 if (EP)
3491 goto out;
3492
3493 EP = enumerate_sure(P, exist, nparam, options);
3494 if (EP)
3495 goto out;
3496
3497 EP = enumerate_ray(P, exist, nparam, options);
3498 if (EP)
3499 goto out;
3500
3501 EP = enumerate_sure2(P, exist, nparam, options);
3502 if (EP)
3503 goto out;
3504
3505 F = unfringe(P, options->MaxRays);
3506 if (!PolyhedronIncludes(F, P)) {
3507 #ifdef DEBUG_ER
3508 fprintf(stderr, "\nER: Fringed\n");
3509 #endif /* DEBUG_ER */
3510 EP = barvinok_enumerate_e_with_options(F, exist, nparam, options);
3511 Polyhedron_Free(F);
3512 goto out;
3513 }
3514 Polyhedron_Free(F);
3515
3516 if (nparam)
3517 EP = enumerate_vd(&P, exist, nparam, options);
3518 if (EP)
3519 goto out2;
3520
3521 if (nvar != 0) {
3522 EP = enumerate_sum(P, exist, nparam, options);
3523 goto out2;
3524 }
3525
3526 assert(nvar == 0);
3527
3528 int i;
3529 Polyhedron *pos, *neg;
3530 for (i = 0; i < exist; ++i)
3531 if (SplitOnVar(P, i, nvar, exist, options->MaxRays,
3532 row, f, false, &pos, &neg))
3533 break;
3534
3535 assert (i < exist);
3536
3537 pos->next = neg;
3538 EP = enumerate_or(pos, exist, nparam, options);
3539
3540 out2:
3541 if (O != P)
3542 Polyhedron_Free(P);
3543
3544 out:
3545 value_clear(f);
3546 Vector_Free(row);
3547 return EP;
3548 }
3549
3550 /*
3551 * remove equalities that require a "compression" of the parameters
3552 */
3553 static Polyhedron *remove_more_equalities(Polyhedron *P, unsigned nparam,
3554 Matrix **CP, unsigned MaxRays)
3555 {
3556 Polyhedron *Q = P;
3557 remove_all_equalities(&P, NULL, CP, NULL, nparam, MaxRays);
3558 if (P != Q)
3559 Polyhedron_Free(Q);
3560 return P;
3561 }
3562
3563 /* frees P */
3564 static gen_fun *series(Polyhedron *P, unsigned nparam, barvinok_options *options)
3565 {
3566 Matrix *CP = NULL;
3567 gen_fun *gf;
3568
3569 if (emptyQ2(P)) {
3570 Polyhedron_Free(P);
3571 return new gen_fun;
3572 }
3573
3574 assert(!Polyhedron_is_unbounded(P, nparam, options->MaxRays));
3575 assert(P->NbBid == 0);
3576 assert(Polyhedron_has_revlex_positive_rays(P, nparam));
3577 if (P->NbEq != 0)
3578 P = remove_more_equalities(P, nparam, &CP, options->MaxRays);
3579 assert(P->NbEq == 0);
3580 if (CP)
3581 nparam = CP->NbColumns-1;
3582
3583 if (nparam == 0) {
3584 Value c;
3585 value_init(c);
3586 barvinok_count_with_options(P, &c, options);
3587 gf = new gen_fun(c);
3588 value_clear(c);
3589 } else {
3590 gf_base *red;
3591 red = gf_base::create(Polyhedron_Project(P, nparam),
3592 P->Dimension, nparam, options);
3593 POL_ENSURE_VERTICES(P);
3594 red->start_gf(P, options);
3595 gf = red->gf;
3596 delete red;
3597 }
3598 if (CP) {
3599 gf->substitute(CP);
3600 Matrix_Free(CP);
3601 }
3602 Polyhedron_Free(P);
3603 return gf;
3604 }
3605
3606 gen_fun * barvinok_series_with_options(Polyhedron *P, Polyhedron* C,
3607 barvinok_options *options)
3608 {
3609 Polyhedron *CA;
3610 unsigned nparam = C->Dimension;
3611 gen_fun *gf;
3612
3613 CA = align_context(C, P->Dimension, options->MaxRays);
3614 P = DomainIntersection(P, CA, options->MaxRays);
3615 Polyhedron_Free(CA);
3616
3617 gf = series(P, nparam, options);
3618
3619 return gf;
3620 }
3621
3622 gen_fun * barvinok_series(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
3623 {
3624 gen_fun *gf;
3625 barvinok_options *options = barvinok_options_new_with_defaults();
3626 options->MaxRays = MaxRays;
3627 gf = barvinok_series_with_options(P, C, options);
3628 barvinok_options_free(options);
3629 return gf;
3630 }
3631
3632 static Polyhedron *skew_into_positive_orthant(Polyhedron *D, unsigned nparam,
3633 unsigned MaxRays)
3634 {
3635 Matrix *M = NULL;
3636 Value tmp;
3637 value_init(tmp);
3638 for (Polyhedron *P = D; P; P = P->next) {
3639 POL_ENSURE_VERTICES(P);
3640 assert(!Polyhedron_is_unbounded(P, nparam, MaxRays));
3641 assert(P->NbBid == 0);
3642 assert(Polyhedron_has_positive_rays(P, nparam));
3643
3644 for (int r = 0; r < P->NbRays; ++r) {
3645 if (value_notzero_p(P->Ray[r][P->Dimension+1]))
3646 continue;
3647 for (int i = 0; i < nparam; ++i) {
3648 int j;
3649 if (value_posz_p(P->Ray[r][i+1]))
3650 continue;
3651 if (!M) {
3652 M = Matrix_Alloc(D->Dimension+1, D->Dimension+1);
3653 for (int i = 0; i < D->Dimension+1; ++i)
3654 value_set_si(M->p[i][i], 1);
3655 } else {
3656 Inner_Product(P->Ray[r]+1, M->p[i], D->Dimension+1, &tmp);
3657 if (value_posz_p(tmp))
3658 continue;
3659 }
3660 for (j = P->Dimension - nparam; j < P->Dimension; ++j)
3661 if (value_pos_p(P->Ray[r][j+1]))
3662 break;
3663 assert(j < P->Dimension);
3664 value_pdivision(tmp, P->Ray[r][j+1], P->Ray[r][i+1]);
3665 value_subtract(M->p[i][j], M->p[i][j], tmp);
3666 }
3667 }
3668 }
3669 value_clear(tmp);
3670 if (M) {
3671 D = DomainImage(D, M, MaxRays);
3672 Matrix_Free(M);
3673 }
3674 return D;
3675 }
3676
3677 gen_fun* barvinok_enumerate_union_series_with_options(Polyhedron *D, Polyhedron* C,
3678 barvinok_options *options)
3679 {
3680 Polyhedron *conv, *D2;
3681 Polyhedron *CA;
3682 gen_fun *gf = NULL, *gf2;
3683 unsigned nparam = C->Dimension;
3684 ZZ one, mone;
3685 one = 1;
3686 mone = -1;
3687
3688 CA = align_context(C, D->Dimension, options->MaxRays);
3689 D = DomainIntersection(D, CA, options->MaxRays);
3690 Polyhedron_Free(CA);
3691
3692 D2 = skew_into_positive_orthant(D, nparam, options->MaxRays);
3693 for (Polyhedron *P = D2; P; P = P->next) {
3694 assert(P->Dimension == D2->Dimension);
3695 gen_fun *P_gf;
3696
3697 P_gf = series(Polyhedron_Copy(P), nparam, options);
3698 if (!gf)
3699 gf = P_gf;
3700 else {
3701 gf->add_union(P_gf, options);
3702 delete P_gf;
3703 }
3704 }
3705 /* we actually only need the convex union of the parameter space
3706 * but the reducer classes currently expect a polyhedron in
3707 * the combined space
3708 */
3709 Polyhedron_Free(gf->context);
3710 gf->context = DomainConvex(D2, options->MaxRays);
3711
3712 gf2 = gf->summate(D2->Dimension - nparam, options);
3713
3714 delete gf;
3715 if (D != D2)
3716 Domain_Free(D2);
3717 Domain_Free(D);
3718 return gf2;
3719 }
3720
3721 gen_fun* barvinok_enumerate_union_series(Polyhedron *D, Polyhedron* C,
3722 unsigned MaxRays)
3723 {
3724 gen_fun *gf;
3725 barvinok_options *options = barvinok_options_new_with_defaults();
3726 options->MaxRays = MaxRays;
3727 gf = barvinok_enumerate_union_series_with_options(D, C, options);
3728 barvinok_options_free(options);
3729 return gf;
3730 }
3731
3732 evalue* barvinok_enumerate_union(Polyhedron *D, Polyhedron* C, unsigned MaxRays)
3733 {
3734 evalue *EP;
3735 gen_fun *gf = barvinok_enumerate_union_series(D, C, MaxRays);
3736 EP = *gf;
3737 delete gf;
3738 return EP;
3739 }
lattice point enumeration library