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util.c: internalize ugly bv_ceil3
[barvinok.git] / util.c
blob3a97f9f9f6d32e19d234a9fb62cbf09ce0ba517f
1 #include <stdlib.h>
2 #include <assert.h>
3 #include <barvinok/util.h>
4 #include <barvinok/options.h>
5 #include <polylib/ranking.h>
6 #include "config.h"
7 #include "lattice_point.h"
8
9 #define ALLOC(type) (type*)malloc(sizeof(type))
10 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
11
12 #ifdef __GNUC__
13 #define NALLOC(p,n) p = (typeof(p))malloc((n) * sizeof(*p))
14 #else
15 #define NALLOC(p,n) p = (void *)malloc((n) * sizeof(*p))
16 #endif
17
18 void manual_count(Polyhedron *P, Value* result)
19 {
20 Polyhedron *U = Universe_Polyhedron(0);
21 Enumeration *en = Polyhedron_Enumerate(P,U,1024,NULL);
22 Value *v = compute_poly(en,NULL);
23 value_assign(*result, *v);
24 value_clear(*v);
25 free(v);
26 Enumeration_Free(en);
27 Polyhedron_Free(U);
28 }
29
30 #include <barvinok/evalue.h>
31 #include <barvinok/util.h>
32 #include <barvinok/barvinok.h>
33
34 /* Return random value between 0 and max-1 inclusive
35 */
36 int random_int(int max) {
37 return (int) (((double)(max))*rand()/(RAND_MAX+1.0));
38 }
39
40 Polyhedron *Polyhedron_Read(unsigned MaxRays)
41 {
42 int vertices = 0;
43 unsigned NbRows, NbColumns;
44 Matrix *M;
45 Polyhedron *P;
46 char s[128];
47
48 while (fgets(s, sizeof(s), stdin)) {
49 if (*s == '#')
50 continue;
51 if (strncasecmp(s, "vertices", sizeof("vertices")-1) == 0)
52 vertices = 1;
53 if (sscanf(s, "%u %u", &NbRows, &NbColumns) == 2)
54 break;
55 }
56 if (feof(stdin))
57 return NULL;
58 M = Matrix_Alloc(NbRows,NbColumns);
59 Matrix_Read_Input(M);
60 if (vertices)
61 P = Rays2Polyhedron(M, MaxRays);
62 else
63 P = Constraints2Polyhedron(M, MaxRays);
64 Matrix_Free(M);
65 return P;
66 }
67
68 /* Inplace polarization
69 */
70 void Polyhedron_Polarize(Polyhedron *P)
71 {
72 unsigned NbRows = P->NbConstraints + P->NbRays;
73 int i;
74 Value **q;
75
76 q = (Value **)malloc(NbRows * sizeof(Value *));
77 assert(q);
78 for (i = 0; i < P->NbRays; ++i)
79 q[i] = P->Ray[i];
80 for (; i < NbRows; ++i)
81 q[i] = P->Constraint[i-P->NbRays];
82 P->NbConstraints = NbRows - P->NbConstraints;
83 P->NbRays = NbRows - P->NbRays;
84 free(P->Constraint);
85 P->Constraint = q;
86 P->Ray = q + P->NbConstraints;
87 }
88
89 /*
90 * Rather general polar
91 * We can optimize it significantly if we assume that
92 * P includes zero
93 *
94 * Also, we calculate the polar as defined in Schrijver
95 * The opposite should probably work as well and would
96 * eliminate the need for multiplying by -1
97 */
98 Polyhedron* Polyhedron_Polar(Polyhedron *P, unsigned NbMaxRays)
99 {
100 int i;
101 Value mone;
102 unsigned dim = P->Dimension + 2;
103 Matrix *M = Matrix_Alloc(P->NbRays, dim);
104
105 assert(M);
106 value_init(mone);
107 value_set_si(mone, -1);
108 for (i = 0; i < P->NbRays; ++i) {
109 Vector_Scale(P->Ray[i], M->p[i], mone, dim);
110 value_multiply(M->p[i][0], M->p[i][0], mone);
111 value_multiply(M->p[i][dim-1], M->p[i][dim-1], mone);
112 }
113 P = Constraints2Polyhedron(M, NbMaxRays);
114 assert(P);
115 Matrix_Free(M);
116 value_clear(mone);
117 return P;
118 }
119
120 /*
121 * Returns the supporting cone of P at the vertex with index v
122 */
123 Polyhedron* supporting_cone(Polyhedron *P, int v)
124 {
125 Matrix *M;
126 Value tmp;
127 int i, n, j;
128 unsigned char *supporting = (unsigned char *)malloc(P->NbConstraints);
129 unsigned dim = P->Dimension + 2;
130
131 assert(v >=0 && v < P->NbRays);
132 assert(value_pos_p(P->Ray[v][dim-1]));
133 assert(supporting);
134
135 value_init(tmp);
136 for (i = 0, n = 0; i < P->NbConstraints; ++i) {
137 Inner_Product(P->Constraint[i] + 1, P->Ray[v] + 1, dim - 1, &tmp);
138 if ((supporting[i] = value_zero_p(tmp)))
139 ++n;
140 }
141 assert(n >= dim - 2);
142 value_clear(tmp);
143 M = Matrix_Alloc(n, dim);
144 assert(M);
145 for (i = 0, j = 0; i < P->NbConstraints; ++i)
146 if (supporting[i]) {
147 value_set_si(M->p[j][dim-1], 0);
148 Vector_Copy(P->Constraint[i], M->p[j++], dim-1);
149 }
150 free(supporting);
151 P = Constraints2Polyhedron(M, P->NbRays+1);
152 assert(P);
153 Matrix_Free(M);
154 return P;
155 }
156
157 #define INT_BITS (sizeof(unsigned) * 8)
158
159 unsigned *supporting_constraints(Matrix *Constraints, Param_Vertices *v, int *n)
160 {
161 Value lcm, tmp, tmp2;
162 unsigned dim = Constraints->NbColumns;
163 unsigned nparam = v->Vertex->NbColumns - 2;
164 unsigned nvar = dim - nparam - 2;
165 int len = (Constraints->NbRows+INT_BITS-1)/INT_BITS;
166 unsigned *supporting = (unsigned *)calloc(len, sizeof(unsigned));
167 int i, j;
168 Vector *row;
169 int ix;
170 unsigned bx;
171
172 assert(supporting);
173 row = Vector_Alloc(nparam+1);
174 assert(row);
175 value_init(lcm);
176 value_init(tmp);
177 value_init(tmp2);
178 value_set_si(lcm, 1);
179 for (i = 0, *n = 0, ix = 0, bx = MSB; i < Constraints->NbRows; ++i) {
180 Vector_Set(row->p, 0, nparam+1);
181 for (j = 0 ; j < nvar; ++j) {
182 value_set_si(tmp, 1);
183 value_assign(tmp2, Constraints->p[i][j+1]);
184 if (value_ne(lcm, v->Vertex->p[j][nparam+1])) {
185 value_assign(tmp, lcm);
186 value_lcm(lcm, lcm, v->Vertex->p[j][nparam+1]);
187 value_division(tmp, lcm, tmp);
188 value_multiply(tmp2, tmp2, lcm);
189 value_division(tmp2, tmp2, v->Vertex->p[j][nparam+1]);
190 }
191 Vector_Combine(row->p, v->Vertex->p[j], row->p,
192 tmp, tmp2, nparam+1);
193 }
194 value_set_si(tmp, 1);
195 Vector_Combine(row->p, Constraints->p[i]+1+nvar, row->p, tmp, lcm, nparam+1);
196 for (j = 0; j < nparam+1; ++j)
197 if (value_notzero_p(row->p[j]))
198 break;
199 if (j == nparam + 1) {
200 supporting[ix] |= bx;
201 ++*n;
202 }
203 NEXT(ix, bx);
204 }
205 assert(*n >= nvar);
206 value_clear(tmp);
207 value_clear(tmp2);
208 value_clear(lcm);
209 Vector_Free(row);
210
211 return supporting;
212 }
213
214 Polyhedron* supporting_cone_p(Polyhedron *P, Param_Vertices *v)
215 {
216 Matrix *M;
217 unsigned dim = P->Dimension + 2;
218 unsigned nparam = v->Vertex->NbColumns - 2;
219 unsigned nvar = dim - nparam - 2;
220 int i, n, j;
221 int ix;
222 unsigned bx;
223 unsigned *supporting;
224 Matrix View;
225
226 Polyhedron_Matrix_View(P, &View, P->NbConstraints);
227 supporting = supporting_constraints(&View, v, &n);
228 M = Matrix_Alloc(n, nvar+2);
229 assert(M);
230 for (i = 0, j = 0, ix = 0, bx = MSB; i < P->NbConstraints; ++i) {
231 if (supporting[ix] & bx) {
232 value_set_si(M->p[j][nvar+1], 0);
233 Vector_Copy(P->Constraint[i], M->p[j++], nvar+1);
234 }
235 NEXT(ix, bx);
236 }
237 free(supporting);
238 P = Constraints2Polyhedron(M, P->NbRays+1);
239 assert(P);
240 Matrix_Free(M);
241 return P;
242 }
243
244 Polyhedron* triangulate_cone(Polyhedron *P, unsigned NbMaxCons)
245 {
246 struct barvinok_options *options = barvinok_options_new_with_defaults();
247 options->MaxRays = NbMaxCons;
248 P = triangulate_cone_with_options(P, options);
249 barvinok_options_free(options);
250 return P;
251 }
252
253 Polyhedron* triangulate_cone_with_options(Polyhedron *P,
254 struct barvinok_options *options)
255 {
256 const static int MAX_TRY=10;
257 int i, j, r, n, t;
258 Value tmp;
259 unsigned dim = P->Dimension;
260 Matrix *M = Matrix_Alloc(P->NbRays+1, dim+3);
261 Matrix *M2, *M3;
262 Polyhedron *L, *R, *T;
263 assert(P->NbEq == 0);
264
265 L = NULL;
266 R = NULL;
267 value_init(tmp);
268
269 Vector_Set(M->p[0]+1, 0, dim+1);
270 value_set_si(M->p[0][0], 1);
271 value_set_si(M->p[0][dim+2], 1);
272 Vector_Set(M->p[P->NbRays]+1, 0, dim+2);
273 value_set_si(M->p[P->NbRays][0], 1);
274 value_set_si(M->p[P->NbRays][dim+1], 1);
275
276 for (i = 0, r = 1; i < P->NbRays; ++i) {
277 if (value_notzero_p(P->Ray[i][dim+1]))
278 continue;
279 Vector_Copy(P->Ray[i], M->p[r], dim+1);
280 value_set_si(M->p[r][dim+2], 0);
281 ++r;
282 }
283
284 M2 = Matrix_Alloc(dim+1, dim+2);
285
286 t = 0;
287 if (options->try_Delaunay_triangulation) {
288 /* Delaunay triangulation */
289 for (r = 1; r < P->NbRays; ++r) {
290 Inner_Product(M->p[r]+1, M->p[r]+1, dim, &tmp);
291 value_assign(M->p[r][dim+1], tmp);
292 }
293 M3 = Matrix_Copy(M);
294 L = Rays2Polyhedron(M3, options->MaxRays);
295 Matrix_Free(M3);
296 ++t;
297 } else {
298 try_again:
299 /* Usually R should still be 0 */
300 Domain_Free(R);
301 Polyhedron_Free(L);
302 for (r = 1; r < P->NbRays; ++r) {
303 value_set_si(M->p[r][dim+1], random_int((t+1)*dim*P->NbRays)+1);
304 }
305 M3 = Matrix_Copy(M);
306 L = Rays2Polyhedron(M3, options->MaxRays);
307 Matrix_Free(M3);
308 ++t;
309 }
310 assert(t <= MAX_TRY);
311
312 R = NULL;
313 n = 0;
314
315 POL_ENSURE_FACETS(L);
316 for (i = 0; i < L->NbConstraints; ++i) {
317 /* Ignore perpendicular facets, i.e., facets with 0 z-coordinate */
318 if (value_negz_p(L->Constraint[i][dim+1]))
319 continue;
320 if (value_notzero_p(L->Constraint[i][dim+2]))
321 continue;
322 for (j = 1, r = 1; j < M->NbRows; ++j) {
323 Inner_Product(M->p[j]+1, L->Constraint[i]+1, dim+1, &tmp);
324 if (value_notzero_p(tmp))
325 continue;
326 if (r > dim)
327 goto try_again;
328 Vector_Copy(M->p[j]+1, M2->p[r]+1, dim);
329 value_set_si(M2->p[r][0], 1);
330 value_set_si(M2->p[r][dim+1], 0);
331 ++r;
332 }
333 assert(r == dim+1);
334 Vector_Set(M2->p[0]+1, 0, dim);
335 value_set_si(M2->p[0][0], 1);
336 value_set_si(M2->p[0][dim+1], 1);
337 T = Rays2Polyhedron(M2, P->NbConstraints+1);
338 T->next = R;
339 R = T;
340 ++n;
341 }
342 Matrix_Free(M2);
343
344 Polyhedron_Free(L);
345 value_clear(tmp);
346 Matrix_Free(M);
347
348 return R;
349 }
350
351 void check_triangulization(Polyhedron *P, Polyhedron *T)
352 {
353 Polyhedron *C, *D, *E, *F, *G, *U;
354 for (C = T; C; C = C->next) {
355 if (C == T)
356 U = C;
357 else
358 U = DomainConvex(DomainUnion(U, C, 100), 100);
359 for (D = C->next; D; D = D->next) {
360 F = C->next;
361 G = D->next;
362 C->next = NULL;
363 D->next = NULL;
364 E = DomainIntersection(C, D, 600);
365 assert(E->NbRays == 0 || E->NbEq >= 1);
366 Polyhedron_Free(E);
367 C->next = F;
368 D->next = G;
369 }
370 }
371 assert(PolyhedronIncludes(U, P));
372 assert(PolyhedronIncludes(P, U));
373 }
374
375 /* Computes x, y and g such that g = gcd(a,b) and a*x+b*y = g */
376 void Extended_Euclid(Value a, Value b, Value *x, Value *y, Value *g)
377 {
378 Value c, d, e, f, tmp;
379
380 value_init(c);
381 value_init(d);
382 value_init(e);
383 value_init(f);
384 value_init(tmp);
385 value_absolute(c, a);
386 value_absolute(d, b);
387 value_set_si(e, 1);
388 value_set_si(f, 0);
389 while(value_pos_p(d)) {
390 value_division(tmp, c, d);
391 value_multiply(tmp, tmp, f);
392 value_subtract(e, e, tmp);
393 value_division(tmp, c, d);
394 value_multiply(tmp, tmp, d);
395 value_subtract(c, c, tmp);
396 value_swap(c, d);
397 value_swap(e, f);
398 }
399 value_assign(*g, c);
400 if (value_zero_p(a))
401 value_set_si(*x, 0);
402 else if (value_pos_p(a))
403 value_assign(*x, e);
404 else value_oppose(*x, e);
405 if (value_zero_p(b))
406 value_set_si(*y, 0);
407 else {
408 value_multiply(tmp, a, *x);
409 value_subtract(tmp, c, tmp);
410 value_division(*y, tmp, b);
411 }
412 value_clear(c);
413 value_clear(d);
414 value_clear(e);
415 value_clear(f);
416 value_clear(tmp);
417 }
418
419 static int unimodular_complete_1(Matrix *m)
420 {
421 Value g, b, c, old, tmp;
422 unsigned i, j;
423 int ok;
424
425 value_init(b);
426 value_init(c);
427 value_init(g);
428 value_init(old);
429 value_init(tmp);
430 value_assign(g, m->p[0][0]);
431 for (i = 1; value_zero_p(g) && i < m->NbColumns; ++i) {
432 for (j = 0; j < m->NbColumns; ++j) {
433 if (j == i-1)
434 value_set_si(m->p[i][j], 1);
435 else
436 value_set_si(m->p[i][j], 0);
437 }
438 value_assign(g, m->p[0][i]);
439 }
440 for (; i < m->NbColumns; ++i) {
441 value_assign(old, g);
442 Extended_Euclid(old, m->p[0][i], &c, &b, &g);
443 value_oppose(b, b);
444 for (j = 0; j < m->NbColumns; ++j) {
445 if (j < i) {
446 value_multiply(tmp, m->p[0][j], b);
447 value_division(m->p[i][j], tmp, old);
448 } else if (j == i)
449 value_assign(m->p[i][j], c);
450 else
451 value_set_si(m->p[i][j], 0);
452 }
453 }
454 ok = value_one_p(g);
455 value_clear(b);
456 value_clear(c);
457 value_clear(g);
458 value_clear(old);
459 value_clear(tmp);
460 return ok;
461 }
462
463 int unimodular_complete(Matrix *M, int row)
464 {
465 int r;
466 int ok = 1;
467 Matrix *H, *Q, *U;
468
469 if (row == 1)
470 return unimodular_complete_1(M);
471
472 left_hermite(M, &H, &Q, &U);
473 Matrix_Free(U);
474 for (r = 0; ok && r < row; ++r)
475 if (value_notone_p(H->p[r][r]))
476 ok = 0;
477 Matrix_Free(H);
478 for (r = row; r < M->NbRows; ++r)
479 Vector_Copy(Q->p[r], M->p[r], M->NbColumns);
480 Matrix_Free(Q);
481 return ok;
482 }
483
484 /*
485 * left_hermite may leave positive entries below the main diagonal in H.
486 * This function postprocesses the output of left_hermite to make
487 * the non-zero entries below the main diagonal negative.
488 */
489 void neg_left_hermite(Matrix *A, Matrix **H_p, Matrix **Q_p, Matrix **U_p)
490 {
491 int row, col, i, j;
492 Matrix *H, *U, *Q;
493
494 left_hermite(A, &H, &Q, &U);
495 *H_p = H;
496 *Q_p = Q;
497 *U_p = U;
498
499 for (row = 0, col = 0; col < H->NbColumns; ++col, ++row) {
500 while (value_zero_p(H->p[row][col]))
501 ++row;
502 for (i = 0; i < col; ++i) {
503 if (value_negz_p(H->p[row][i]))
504 continue;
505
506 /* subtract column col from column i in H and U */
507 for (j = 0; j < H->NbRows; ++j)
508 value_subtract(H->p[j][i], H->p[j][i], H->p[j][col]);
509 for (j = 0; j < U->NbRows; ++j)
510 value_subtract(U->p[j][i], U->p[j][i], U->p[j][col]);
511
512 /* add row i to row col in Q */
513 for (j = 0; j < Q->NbColumns; ++j)
514 value_addto(Q->p[col][j], Q->p[col][j], Q->p[i][j]);
515 }
516 }
517 }
518
519 /*
520 * Returns a full-dimensional polyhedron with the same number
521 * of integer points as P
522 */
523 Polyhedron *remove_equalities(Polyhedron *P, unsigned MaxRays)
524 {
525 Polyhedron *Q = Polyhedron_Copy(P);
526 unsigned dim = P->Dimension;
527 Matrix *m1, *m2;
528 int i;
529
530 if (Q->NbEq == 0)
531 return Q;
532
533 Q = DomainConstraintSimplify(Q, MaxRays);
534 if (emptyQ2(Q))
535 return Q;
536
537 m1 = Matrix_Alloc(dim, dim);
538 for (i = 0; i < Q->NbEq; ++i)
539 Vector_Copy(Q->Constraint[i]+1, m1->p[i], dim);
540
541 /* m1 may not be unimodular, but we won't be throwing anything away */
542 unimodular_complete(m1, Q->NbEq);
543
544 m2 = Matrix_Alloc(dim+1-Q->NbEq, dim+1);
545 for (i = Q->NbEq; i < dim; ++i)
546 Vector_Copy(m1->p[i], m2->p[i-Q->NbEq], dim);
547 value_set_si(m2->p[dim-Q->NbEq][dim], 1);
548 Matrix_Free(m1);
549
550 P = Polyhedron_Image(Q, m2, MaxRays);
551 Matrix_Free(m2);
552 Polyhedron_Free(Q);
553
554 return P;
555 }
556
557 /*
558 * Returns a full-dimensional polyhedron with the same number
559 * of integer points as P
560 * nvar specifies the number of variables
561 * The remaining dimensions are assumed to be parameters
562 * Destroys P
563 * factor is NbEq x (nparam+2) matrix, containing stride constraints
564 * on the parameters; column nparam is the constant;
565 * column nparam+1 is the stride
566 *
567 * if factor is NULL, only remove equalities that don't affect
568 * the number of points
569 */
570 Polyhedron *remove_equalities_p(Polyhedron *P, unsigned nvar, Matrix **factor,
571 unsigned MaxRays)
572 {
573 Value g;
574 Polyhedron *Q;
575 unsigned dim = P->Dimension;
576 Matrix *m1, *m2, *f;
577 int i, j;
578
579 if (P->NbEq == 0)
580 return P;
581
582 m1 = Matrix_Alloc(nvar, nvar);
583 P = DomainConstraintSimplify(P, MaxRays);
584 if (factor) {
585 f = Matrix_Alloc(P->NbEq, dim-nvar+2);
586 *factor = f;
587 }
588 value_init(g);
589 for (i = 0, j = 0; i < P->NbEq; ++i) {
590 if (First_Non_Zero(P->Constraint[i]+1, nvar) == -1)
591 continue;
592
593 Vector_Gcd(P->Constraint[i]+1, nvar, &g);
594 if (!factor && value_notone_p(g))
595 continue;
596
597 if (factor) {
598 Vector_Copy(P->Constraint[i]+1+nvar, f->p[j], dim-nvar+1);
599 value_assign(f->p[j][dim-nvar+1], g);
600 }
601
602 Vector_Copy(P->Constraint[i]+1, m1->p[j], nvar);
603
604 ++j;
605 }
606 value_clear(g);
607
608 unimodular_complete(m1, j);
609
610 m2 = Matrix_Alloc(dim+1-j, dim+1);
611 for (i = 0; i < nvar-j ; ++i)
612 Vector_Copy(m1->p[i+j], m2->p[i], nvar);
613 Matrix_Free(m1);
614 for (i = nvar-j; i <= dim-j; ++i)
615 value_set_si(m2->p[i][i+j], 1);
616
617 Q = Polyhedron_Image(P, m2, MaxRays);
618 Matrix_Free(m2);
619 Polyhedron_Free(P);
620
621 return Q;
622 }
623
624 void Line_Length(Polyhedron *P, Value *len)
625 {
626 Value tmp, pos, neg;
627 int p = 0, n = 0;
628 int i;
629
630 assert(P->Dimension == 1);
631
632 value_init(tmp);
633 value_init(pos);
634 value_init(neg);
635
636 for (i = 0; i < P->NbConstraints; ++i) {
637 value_oppose(tmp, P->Constraint[i][2]);
638 if (value_pos_p(P->Constraint[i][1])) {
639 mpz_cdiv_q(tmp, tmp, P->Constraint[i][1]);
640 if (!p || value_gt(tmp, pos))
641 value_assign(pos, tmp);
642 p = 1;
643 } else if (value_neg_p(P->Constraint[i][1])) {
644 mpz_fdiv_q(tmp, tmp, P->Constraint[i][1]);
645 if (!n || value_lt(tmp, neg))
646 value_assign(neg, tmp);
647 n = 1;
648 }
649 if (n && p) {
650 value_subtract(tmp, neg, pos);
651 value_increment(*len, tmp);
652 } else
653 value_set_si(*len, -1);
654 }
655
656 value_clear(tmp);
657 value_clear(pos);
658 value_clear(neg);
659 }
660
661 /*
662 * Factors the polyhedron P into polyhedra Q_i such that
663 * the number of integer points in P is equal to the product
664 * of the number of integer points in the individual Q_i
665 *
666 * If no factors can be found, NULL is returned.
667 * Otherwise, a linked list of the factors is returned.
668 *
669 * If there are factors and if T is not NULL, then a matrix will be
670 * returned through T expressing the old variables in terms of the
671 * new variables as they appear in the sequence of factors.
672 *
673 * The algorithm works by first computing the Hermite normal form
674 * and then grouping columns linked by one or more constraints together,
675 * where a constraints "links" two or more columns if the constraint
676 * has nonzero coefficients in the columns.
677 */
678 Polyhedron* Polyhedron_Factor(Polyhedron *P, unsigned nparam, Matrix **T,
679 unsigned NbMaxRays)
680 {
681 int i, j, k;
682 Matrix *M, *H, *Q, *U;
683 int *pos; /* for each column: row position of pivot */
684 int *group; /* group to which a column belongs */
685 int *cnt; /* number of columns in the group */
686 int *rowgroup; /* group to which a constraint belongs */
687 int nvar = P->Dimension - nparam;
688 Polyhedron *F = NULL;
689
690 if (nvar <= 1)
691 return NULL;
692
693 NALLOC(pos, nvar);
694 NALLOC(group, nvar);
695 NALLOC(cnt, nvar);
696 NALLOC(rowgroup, P->NbConstraints);
697
698 M = Matrix_Alloc(P->NbConstraints, nvar);
699 for (i = 0; i < P->NbConstraints; ++i)
700 Vector_Copy(P->Constraint[i]+1, M->p[i], nvar);
701 left_hermite(M, &H, &Q, &U);
702 Matrix_Free(M);
703 Matrix_Free(Q);
704
705 for (i = 0; i < P->NbConstraints; ++i)
706 rowgroup[i] = -1;
707 for (i = 0, j = 0; i < H->NbColumns; ++i) {
708 for ( ; j < H->NbRows; ++j)
709 if (value_notzero_p(H->p[j][i]))
710 break;
711 assert (j < H->NbRows);
712 pos[i] = j;
713 }
714 for (i = 0; i < nvar; ++i) {
715 group[i] = i;
716 cnt[i] = 1;
717 }
718 for (i = 0; i < H->NbColumns && cnt[0] < nvar; ++i) {
719 if (rowgroup[pos[i]] == -1)
720 rowgroup[pos[i]] = i;
721 for (j = pos[i]+1; j < H->NbRows; ++j) {
722 if (value_zero_p(H->p[j][i]))
723 continue;
724 if (rowgroup[j] != -1)
725 continue;
726 rowgroup[j] = group[i];
727 for (k = i+1; k < H->NbColumns && j >= pos[k]; ++k) {
728 int g = group[k];
729 while (cnt[g] == 0)
730 g = group[g];
731 group[k] = g;
732 if (group[k] != group[i] && value_notzero_p(H->p[j][k])) {
733 assert(cnt[group[k]] != 0);
734 assert(cnt[group[i]] != 0);
735 if (group[i] < group[k]) {
736 cnt[group[i]] += cnt[group[k]];
737 cnt[group[k]] = 0;
738 group[k] = group[i];
739 } else {
740 cnt[group[k]] += cnt[group[i]];
741 cnt[group[i]] = 0;
742 group[i] = group[k];
743 }
744 }
745 }
746 }
747 }
748
749 if (cnt[0] != nvar) {
750 /* Extract out pure context constraints separately */
751 Polyhedron **next = &F;
752 int tot_d = 0;
753 if (T)
754 *T = Matrix_Alloc(nvar, nvar);
755 for (i = nparam ? -1 : 0; i < nvar; ++i) {
756 int d;
757
758 if (i == -1) {
759 for (j = 0, k = 0; j < P->NbConstraints; ++j)
760 if (rowgroup[j] == -1) {
761 if (First_Non_Zero(P->Constraint[j]+1+nvar,
762 nparam) == -1)
763 rowgroup[j] = -2;
764 else
765 ++k;
766 }
767 if (k == 0)
768 continue;
769 d = 0;
770 } else {
771 if (cnt[i] == 0)
772 continue;
773 d = cnt[i];
774 for (j = 0, k = 0; j < P->NbConstraints; ++j)
775 if (rowgroup[j] >= 0 && group[rowgroup[j]] == i) {
776 rowgroup[j] = i;
777 ++k;
778 }
779 }
780
781 if (T)
782 for (j = 0; j < nvar; ++j) {
783 int l, m;
784 for (l = 0, m = 0; m < d; ++l) {
785 if (group[l] != i)
786 continue;
787 value_assign((*T)->p[j][tot_d+m++], U->p[j][l]);
788 }
789 }
790
791 M = Matrix_Alloc(k, d+nparam+2);
792 for (j = 0, k = 0; j < P->NbConstraints; ++j) {
793 int l, m;
794 if (rowgroup[j] != i)
795 continue;
796 value_assign(M->p[k][0], P->Constraint[j][0]);
797 for (l = 0, m = 0; m < d; ++l) {
798 if (group[l] != i)
799 continue;
800 value_assign(M->p[k][1+m++], H->p[j][l]);
801 }
802 Vector_Copy(P->Constraint[j]+1+nvar, M->p[k]+1+m, nparam+1);
803 ++k;
804 }
805 *next = Constraints2Polyhedron(M, NbMaxRays);
806 next = &(*next)->next;
807 Matrix_Free(M);
808 tot_d += d;
809 }
810 }
811 Matrix_Free(U);
812 Matrix_Free(H);
813 free(pos);
814 free(group);
815 free(cnt);
816 free(rowgroup);
817 return F;
818 }
819
820 /*
821 * Project on final dim dimensions
822 */
823 Polyhedron* Polyhedron_Project(Polyhedron *P, int dim)
824 {
825 int i;
826 int remove = P->Dimension - dim;
827 Matrix *T;
828 Polyhedron *I;
829
830 if (P->Dimension == dim)
831 return Polyhedron_Copy(P);
832
833 T = Matrix_Alloc(dim+1, P->Dimension+1);
834 for (i = 0; i < dim+1; ++i)
835 value_set_si(T->p[i][i+remove], 1);
836 I = Polyhedron_Image(P, T, P->NbConstraints);
837 Matrix_Free(T);
838 return I;
839 }
840
841 /* Constructs a new constraint that ensures that
842 * the first constraint is (strictly) smaller than
843 * the second.
844 */
845 static void smaller_constraint(Value *a, Value *b, Value *c, int pos, int shift,
846 int len, int strict, Value *tmp)
847 {
848 value_oppose(*tmp, b[pos+1]);
849 value_set_si(c[0], 1);
850 Vector_Combine(a+1+shift, b+1+shift, c+1, *tmp, a[pos+1], len-shift-1);
851 if (strict)
852 value_decrement(c[len-shift-1], c[len-shift-1]);
853 ConstraintSimplify(c, c, len-shift, tmp);
854 }
855
856
857 /* For each pair of lower and upper bounds on the first variable,
858 * calls fn with the set of constraints on the remaining variables
859 * where these bounds are active, i.e., (stricly) larger/smaller than
860 * the other lower/upper bounds, the lower and upper bound and the
861 * call back data.
862 *
863 * If the first variable is equal to an affine combination of the
864 * other variables then fn is called with both lower and upper
865 * pointing to the corresponding equality.
866 *
867 * If there is no lower (or upper) bound, then NULL is passed
868 * as the corresponding bound.
869 */
870 void for_each_lower_upper_bound(Polyhedron *P,
871 for_each_lower_upper_bound_init init,
872 for_each_lower_upper_bound_fn fn,
873 void *cb_data)
874 {
875 unsigned dim = P->Dimension;
876 Matrix *M;
877 int *pos;
878 int i, j, p, n, z;
879 int k, l, k2, l2, q;
880 Value g;
881
882 if (value_zero_p(P->Constraint[0][0]) &&
883 value_notzero_p(P->Constraint[0][1])) {
884 M = Matrix_Alloc(P->NbConstraints-1, dim-1+2);
885 for (i = 1; i < P->NbConstraints; ++i) {
886 value_assign(M->p[i-1][0], P->Constraint[i][0]);
887 Vector_Copy(P->Constraint[i]+2, M->p[i-1]+1, dim);
888 }
889 if (init)
890 init(1, cb_data);
891 fn(M, P->Constraint[0], P->Constraint[0], cb_data);
892 Matrix_Free(M);
893 return;
894 }
895
896 value_init(g);
897 pos = ALLOCN(int, P->NbConstraints);
898
899 for (i = 0, z = 0; i < P->NbConstraints; ++i)
900 if (value_zero_p(P->Constraint[i][1]))
901 pos[P->NbConstraints-1 - z++] = i;
902 /* put those with positive coefficients first; number: p */
903 for (i = 0, p = 0, n = P->NbConstraints-z-1; i < P->NbConstraints; ++i)
904 if (value_pos_p(P->Constraint[i][1]))
905 pos[p++] = i;
906 else if (value_neg_p(P->Constraint[i][1]))
907 pos[n--] = i;
908 n = P->NbConstraints-z-p;
909
910 if (init)
911 init(p*n, cb_data);
912
913 M = Matrix_Alloc((p ? p-1 : 0) + (n ? n-1 : 0) + z + 1, dim-1+2);
914 for (i = 0; i < z; ++i) {
915 value_assign(M->p[i][0], P->Constraint[pos[P->NbConstraints-1 - i]][0]);
916 Vector_Copy(P->Constraint[pos[P->NbConstraints-1 - i]]+2,
917 M->p[i]+1, dim);
918 }
919 for (k = p ? 0 : -1; k < p; ++k) {
920 for (k2 = 0; k2 < p; ++k2) {
921 if (k2 == k)
922 continue;
923 q = 1 + z + k2 - (k2 > k);
924 smaller_constraint(
925 P->Constraint[pos[k]],
926 P->Constraint[pos[k2]],
927 M->p[q], 0, 1, dim+2, k2 > k, &g);
928 }
929 for (l = n ? p : p-1; l < p+n; ++l) {
930 Value *lower;
931 Value *upper;
932 for (l2 = p; l2 < p+n; ++l2) {
933 if (l2 == l)
934 continue;
935 q = 1 + z + l2-1 - (l2 > l);
936 smaller_constraint(
937 P->Constraint[pos[l2]],
938 P->Constraint[pos[l]],
939 M->p[q], 0, 1, dim+2, l2 > l, &g);
940 }
941 if (p && n)
942 smaller_constraint(P->Constraint[pos[k]],
943 P->Constraint[pos[l]],
944 M->p[z], 0, 1, dim+2, 0, &g);
945 lower = p ? P->Constraint[pos[k]] : NULL;
946 upper = n ? P->Constraint[pos[l]] : NULL;
947 fn(M, lower, upper, cb_data);
948 }
949 }
950 Matrix_Free(M);
951
952 free(pos);
953 value_clear(g);
954 }
955
956 struct section { Polyhedron * D; evalue E; };
957
958 struct PLL_data {
959 int nd;
960 unsigned MaxRays;
961 Polyhedron *C;
962 evalue mone;
963 struct section *s;
964 };
965
966 static void PLL_init(unsigned n, void *cb_data)
967 {
968 struct PLL_data *data = (struct PLL_data *)cb_data;
969
970 data->s = ALLOCN(struct section, n);
971 }
972
973 /* Computes ceil(-coef/abs(d)) */
974 static evalue* bv_ceil3(Value *coef, int len, Value d, Polyhedron *P)
975 {
976 Value t;
977 evalue *EP, *f;
978 Vector *val = Vector_Alloc(len);
979
980 value_init(t);
981 Vector_Oppose(coef, val->p, len);
982 value_absolute(t, d);
983
984 EP = affine2evalue(val->p, t, len-1);
985
986 Vector_Oppose(val->p, val->p, len);
987 f = fractional_part(val->p, t, len-1, P);
988 value_clear(t);
989
990 eadd(f, EP);
991 evalue_free(f);
992
993 Vector_Free(val);
994
995 return EP;
996 }
997
998 static void PLL_cb(Matrix *M, Value *lower, Value *upper, void *cb_data)
999 {
1000 struct PLL_data *data = (struct PLL_data *)cb_data;
1001 unsigned dim = M->NbColumns-1;
1002 Matrix *M2;
1003 Polyhedron *T;
1004 evalue *L, *U;
1005
1006 assert(lower);
1007 assert(upper);
1008
1009 M2 = Matrix_Copy(M);
1010 T = Constraints2Polyhedron(M2, data->MaxRays);
1011 Matrix_Free(M2);
1012 data->s[data->nd].D = DomainIntersection(T, data->C, data->MaxRays);
1013 Domain_Free(T);
1014
1015 POL_ENSURE_VERTICES(data->s[data->nd].D);
1016 if (emptyQ(data->s[data->nd].D)) {
1017 Polyhedron_Free(data->s[data->nd].D);
1018 return;
1019 }
1020 L = bv_ceil3(lower+1+1, dim-1+1, lower[0+1], data->s[data->nd].D);
1021 U = bv_ceil3(upper+1+1, dim-1+1, upper[0+1], data->s[data->nd].D);
1022 eadd(L, U);
1023 eadd(&data->mone, U);
1024 emul(&data->mone, U);
1025 data->s[data->nd].E = *U;
1026 evalue_free(L);
1027 free(U);
1028 ++data->nd;
1029 }
1030
1031 static evalue *ParamLine_Length_mod(Polyhedron *P, Polyhedron *C, unsigned MaxRays)
1032 {
1033 unsigned dim = P->Dimension;
1034 unsigned nvar = dim - C->Dimension;
1035 struct PLL_data data;
1036 evalue *F;
1037 int k;
1038
1039 assert(nvar == 1);
1040
1041 value_init(data.mone.d);
1042 evalue_set_si(&data.mone, -1, 1);
1043
1044 data.nd = 0;
1045 data.MaxRays = MaxRays;
1046 data.C = C;
1047 for_each_lower_upper_bound(P, PLL_init, PLL_cb, &data);
1048
1049 F = ALLOC(evalue);
1050 value_init(F->d);
1051 value_set_si(F->d, 0);
1052 F->x.p = new_enode(partition, 2*data.nd, dim-nvar);
1053 for (k = 0; k < data.nd; ++k) {
1054 EVALUE_SET_DOMAIN(F->x.p->arr[2*k], data.s[k].D);
1055 value_clear(F->x.p->arr[2*k+1].d);
1056 F->x.p->arr[2*k+1] = data.s[k].E;
1057 }
1058 free(data.s);
1059
1060 free_evalue_refs(&data.mone);
1061
1062 return F;
1063 }
1064
1065 evalue* ParamLine_Length(Polyhedron *P, Polyhedron *C,
1066 struct barvinok_options *options)
1067 {
1068 evalue* tmp;
1069 tmp = ParamLine_Length_mod(P, C, options->MaxRays);
1070 if (options->lookup_table) {
1071 evalue_mod2table(tmp, C->Dimension);
1072 reduce_evalue(tmp);
1073 }
1074 return tmp;
1075 }
1076
1077 Bool isIdentity(Matrix *M)
1078 {
1079 unsigned i, j;
1080 if (M->NbRows != M->NbColumns)
1081 return False;
1082
1083 for (i = 0;i < M->NbRows; i ++)
1084 for (j = 0; j < M->NbColumns; j ++)
1085 if (i == j) {
1086 if(value_notone_p(M->p[i][j]))
1087 return False;
1088 } else {
1089 if(value_notzero_p(M->p[i][j]))
1090 return False;
1091 }
1092 return True;
1093 }
1094
1095 void Param_Polyhedron_Print(FILE* DST, Param_Polyhedron *PP, char **param_names)
1096 {
1097 Param_Domain *P;
1098 Param_Vertices *V;
1099
1100 for(P=PP->D;P;P=P->next) {
1101
1102 /* prints current val. dom. */
1103 fprintf(DST, "---------------------------------------\n");
1104 fprintf(DST, "Domain :\n");
1105 Print_Domain(DST, P->Domain, param_names);
1106
1107 /* scan the vertices */
1108 fprintf(DST, "Vertices :\n");
1109 FORALL_PVertex_in_ParamPolyhedron(V,P,PP) {
1110
1111 /* prints each vertex */
1112 Print_Vertex(DST, V->Vertex, param_names);
1113 fprintf(DST, "\n");
1114 }
1115 END_FORALL_PVertex_in_ParamPolyhedron;
1116 }
1117 }
1118
1119 void Enumeration_Print(FILE *Dst, Enumeration *en, const char * const *params)
1120 {
1121 for (; en; en = en->next) {
1122 Print_Domain(Dst, en->ValidityDomain, params);
1123 print_evalue(Dst, &en->EP, params);
1124 }
1125 }
1126
1127 void Enumeration_Free(Enumeration *en)
1128 {
1129 Enumeration *ee;
1130
1131 while( en )
1132 {
1133 free_evalue_refs( &(en->EP) );
1134 Domain_Free( en->ValidityDomain );
1135 ee = en ->next;
1136 free( en );
1137 en = ee;
1138 }
1139 }
1140
1141 void Enumeration_mod2table(Enumeration *en, unsigned nparam)
1142 {
1143 for (; en; en = en->next) {
1144 evalue_mod2table(&en->EP, nparam);
1145 reduce_evalue(&en->EP);
1146 }
1147 }
1148
1149 size_t Enumeration_size(Enumeration *en)
1150 {
1151 size_t s = 0;
1152
1153 for (; en; en = en->next) {
1154 s += domain_size(en->ValidityDomain);
1155 s += evalue_size(&en->EP);
1156 }
1157 return s;
1158 }
1159
1160 void Free_ParamNames(char **params, int m)
1161 {
1162 while (--m >= 0)
1163 free(params[m]);
1164 free(params);
1165 }
1166
1167 /* Check whether every set in D2 is included in some set of D1 */
1168 int DomainIncludes(Polyhedron *D1, Polyhedron *D2)
1169 {
1170 for ( ; D2; D2 = D2->next) {
1171 Polyhedron *P1;
1172 for (P1 = D1; P1; P1 = P1->next)
1173 if (PolyhedronIncludes(P1, D2))
1174 break;
1175 if (!P1)
1176 return 0;
1177 }
1178 return 1;
1179 }
1180
1181 int line_minmax(Polyhedron *I, Value *min, Value *max)
1182 {
1183 int i;
1184
1185 if (I->NbEq >= 1) {
1186 value_oppose(I->Constraint[0][2], I->Constraint[0][2]);
1187 /* There should never be a remainder here */
1188 if (value_pos_p(I->Constraint[0][1]))
1189 mpz_fdiv_q(*min, I->Constraint[0][2], I->Constraint[0][1]);
1190 else
1191 mpz_fdiv_q(*min, I->Constraint[0][2], I->Constraint[0][1]);
1192 value_assign(*max, *min);
1193 } else for (i = 0; i < I->NbConstraints; ++i) {
1194 if (value_zero_p(I->Constraint[i][1])) {
1195 Polyhedron_Free(I);
1196 return 0;
1197 }
1198
1199 value_oppose(I->Constraint[i][2], I->Constraint[i][2]);
1200 if (value_pos_p(I->Constraint[i][1]))
1201 mpz_cdiv_q(*min, I->Constraint[i][2], I->Constraint[i][1]);
1202 else
1203 mpz_fdiv_q(*max, I->Constraint[i][2], I->Constraint[i][1]);
1204 }
1205 Polyhedron_Free(I);
1206 return 1;
1207 }
1208
1209 /**
1210
1211 PROCEDURES TO COMPUTE ENUMERATION. recursive procedure, recurse for
1212 each imbriquation
1213
1214 @param pos index position of current loop index (1..hdim-1)
1215 @param P loop domain
1216 @param context context values for fixed indices
1217 @param exist number of existential variables
1218 @return the number of integer points in this
1219 polyhedron
1220
1221 */
1222 void count_points_e (int pos, Polyhedron *P, int exist, int nparam,
1223 Value *context, Value *res)
1224 {
1225 Value LB, UB, k, c;
1226
1227 if (emptyQ(P)) {
1228 value_set_si(*res, 0);
1229 return;
1230 }
1231
1232 if (!exist) {
1233 count_points(pos, P, context, res);
1234 return;
1235 }
1236
1237 value_init(LB); value_init(UB); value_init(k);
1238 value_set_si(LB,0);
1239 value_set_si(UB,0);
1240
1241 if (lower_upper_bounds(pos,P,context,&LB,&UB) !=0) {
1242 /* Problem if UB or LB is INFINITY */
1243 value_clear(LB); value_clear(UB); value_clear(k);
1244 if (pos > P->Dimension - nparam - exist)
1245 value_set_si(*res, 1);
1246 else
1247 value_set_si(*res, -1);
1248 return;
1249 }
1250
1251 #ifdef EDEBUG1
1252 if (!P->next) {
1253 int i;
1254 for (value_assign(k,LB); value_le(k,UB); value_increment(k,k)) {
1255 fprintf(stderr, "(");
1256 for (i=1; i<pos; i++) {
1257 value_print(stderr,P_VALUE_FMT,context[i]);
1258 fprintf(stderr,",");
1259 }
1260 value_print(stderr,P_VALUE_FMT,k);
1261 fprintf(stderr,")\n");
1262 }
1263 }
1264 #endif
1265
1266 value_set_si(context[pos],0);
1267 if (value_lt(UB,LB)) {
1268 value_clear(LB); value_clear(UB); value_clear(k);
1269 value_set_si(*res, 0);
1270 return;
1271 }
1272 if (!P->next) {
1273 if (exist)
1274 value_set_si(*res, 1);
1275 else {
1276 value_subtract(k,UB,LB);
1277 value_add_int(k,k,1);
1278 value_assign(*res, k);
1279 }
1280 value_clear(LB); value_clear(UB); value_clear(k);
1281 return;
1282 }
1283
1284 /*-----------------------------------------------------------------*/
1285 /* Optimization idea */
1286 /* If inner loops are not a function of k (the current index) */
1287 /* i.e. if P->Constraint[i][pos]==0 for all P following this and */
1288 /* for all i, */
1289 /* Then CNT = (UB-LB+1)*count_points(pos+1, P->next, context) */
1290 /* (skip the for loop) */
1291 /*-----------------------------------------------------------------*/
1292
1293 value_init(c);
1294 value_set_si(*res, 0);
1295 for (value_assign(k,LB);value_le(k,UB);value_increment(k,k)) {
1296 /* Insert k in context */
1297 value_assign(context[pos],k);
1298 count_points_e(pos+1, P->next, exist, nparam, context, &c);
1299 if(value_notmone_p(c))
1300 value_addto(*res, *res, c);
1301 else {
1302 value_set_si(*res, -1);
1303 break;
1304 }
1305 if (pos > P->Dimension - nparam - exist &&
1306 value_pos_p(*res))
1307 break;
1308 }
1309 value_clear(c);
1310
1311 #ifdef EDEBUG11
1312 fprintf(stderr,"%d\n",CNT);
1313 #endif
1314
1315 /* Reset context */
1316 value_set_si(context[pos],0);
1317 value_clear(LB); value_clear(UB); value_clear(k);
1318 return;
1319 } /* count_points_e */
1320
1321 int DomainContains(Polyhedron *P, Value *list_args, int len,
1322 unsigned MaxRays, int set)
1323 {
1324 int i;
1325 Value m;
1326
1327 if (P->Dimension == len)
1328 return in_domain(P, list_args);
1329
1330 assert(set); // assume list_args is large enough
1331 assert((P->Dimension - len) % 2 == 0);
1332 value_init(m);
1333 for (i = 0; i < P->Dimension - len; i += 2) {
1334 int j, k;
1335 for (j = 0 ; j < P->NbEq; ++j)
1336 if (value_notzero_p(P->Constraint[j][1+len+i]))
1337 break;
1338 assert(j < P->NbEq);
1339 value_absolute(m, P->Constraint[j][1+len+i]);
1340 k = First_Non_Zero(P->Constraint[j]+1, len);
1341 assert(k != -1);
1342 assert(First_Non_Zero(P->Constraint[j]+1+k+1, len - k - 1) == -1);
1343 mpz_fdiv_q(list_args[len+i], list_args[k], m);
1344 mpz_fdiv_r(list_args[len+i+1], list_args[k], m);
1345 }
1346 value_clear(m);
1347
1348 return in_domain(P, list_args);
1349 }
1350
1351 Polyhedron *DomainConcat(Polyhedron *head, Polyhedron *tail)
1352 {
1353 Polyhedron *S;
1354 if (!head)
1355 return tail;
1356 for (S = head; S->next; S = S->next)
1357 ;
1358 S->next = tail;
1359 return head;
1360 }
1361
1362 evalue *barvinok_lexsmaller_ev(Polyhedron *P, Polyhedron *D, unsigned dim,
1363 Polyhedron *C, unsigned MaxRays)
1364 {
1365 evalue *ranking;
1366 Polyhedron *RC, *RD, *Q;
1367 unsigned nparam = dim + C->Dimension;
1368 unsigned exist;
1369 Polyhedron *CA;
1370
1371 RC = LexSmaller(P, D, dim, C, MaxRays);
1372 RD = RC->next;
1373 RC->next = NULL;
1374
1375 exist = RD->Dimension - nparam - dim;
1376 CA = align_context(RC, RD->Dimension, MaxRays);
1377 Q = DomainIntersection(RD, CA, MaxRays);
1378 Polyhedron_Free(CA);
1379 Domain_Free(RD);
1380 Polyhedron_Free(RC);
1381 RD = Q;
1382
1383 for (Q = RD; Q; Q = Q->next) {
1384 evalue *t;
1385 Polyhedron *next = Q->next;
1386 Q->next = 0;
1387
1388 t = barvinok_enumerate_e(Q, exist, nparam, MaxRays);
1389
1390 if (Q == RD)
1391 ranking = t;
1392 else {
1393 eadd(t, ranking);
1394 evalue_free(t);
1395 }
1396
1397 Q->next = next;
1398 }
1399
1400 Domain_Free(RD);
1401
1402 return ranking;
1403 }
1404
1405 Enumeration *barvinok_lexsmaller(Polyhedron *P, Polyhedron *D, unsigned dim,
1406 Polyhedron *C, unsigned MaxRays)
1407 {
1408 evalue *EP = barvinok_lexsmaller_ev(P, D, dim, C, MaxRays);
1409
1410 return partition2enumeration(EP);
1411 }
1412
1413 /* "align" matrix to have nrows by inserting
1414 * the necessary number of rows and an equal number of columns in front
1415 */
1416 Matrix *align_matrix(Matrix *M, int nrows)
1417 {
1418 int i;
1419 int newrows = nrows - M->NbRows;
1420 Matrix *M2 = Matrix_Alloc(nrows, newrows + M->NbColumns);
1421 for (i = 0; i < newrows; ++i)
1422 value_set_si(M2->p[i][i], 1);
1423 for (i = 0; i < M->NbRows; ++i)
1424 Vector_Copy(M->p[i], M2->p[newrows+i]+newrows, M->NbColumns);
1425 return M2;
1426 }
1427
1428 static void print_varlist(FILE *out, int n, char **names)
1429 {
1430 int i;
1431 fprintf(out, "[");
1432 for (i = 0; i < n; ++i) {
1433 if (i)
1434 fprintf(out, ",");
1435 fprintf(out, "%s", names[i]);
1436 }
1437 fprintf(out, "]");
1438 }
1439
1440 static void print_term(FILE *out, Value v, int pos, int dim, int nparam,
1441 char **iter_names, char **param_names, int *first)
1442 {
1443 if (value_zero_p(v)) {
1444 if (first && *first && pos >= dim + nparam)
1445 fprintf(out, "0");
1446 return;
1447 }
1448
1449 if (first) {
1450 if (!*first && value_pos_p(v))
1451 fprintf(out, "+");
1452 *first = 0;
1453 }
1454 if (pos < dim + nparam) {
1455 if (value_mone_p(v))
1456 fprintf(out, "-");
1457 else if (!value_one_p(v))
1458 value_print(out, VALUE_FMT, v);
1459 if (pos < dim)
1460 fprintf(out, "%s", iter_names[pos]);
1461 else
1462 fprintf(out, "%s", param_names[pos-dim]);
1463 } else
1464 value_print(out, VALUE_FMT, v);
1465 }
1466
1467 char **util_generate_names(int n, const char *prefix)
1468 {
1469 int i;
1470 int len = (prefix ? strlen(prefix) : 0) + 10;
1471 char **names = ALLOCN(char*, n);
1472 if (!names) {
1473 fprintf(stderr, "ERROR: memory overflow.\n");
1474 exit(1);
1475 }
1476 for (i = 0; i < n; ++i) {
1477 names[i] = ALLOCN(char, len);
1478 if (!names[i]) {
1479 fprintf(stderr, "ERROR: memory overflow.\n");
1480 exit(1);
1481 }
1482 if (!prefix)
1483 snprintf(names[i], len, "%d", i);
1484 else
1485 snprintf(names[i], len, "%s%d", prefix, i);
1486 }
1487
1488 return names;
1489 }
1490
1491 void util_free_names(int n, char **names)
1492 {
1493 int i;
1494 for (i = 0; i < n; ++i)
1495 free(names[i]);
1496 free(names);
1497 }
1498
1499 void Polyhedron_pprint(FILE *out, Polyhedron *P, int dim, int nparam,
1500 char **iter_names, char **param_names)
1501 {
1502 int i, j;
1503 Value tmp;
1504
1505 assert(dim + nparam == P->Dimension);
1506
1507 value_init(tmp);
1508
1509 fprintf(out, "{ ");
1510 if (nparam) {
1511 print_varlist(out, nparam, param_names);
1512 fprintf(out, " -> ");
1513 }
1514 print_varlist(out, dim, iter_names);
1515 fprintf(out, " : ");
1516
1517 if (emptyQ2(P))
1518 fprintf(out, "FALSE");
1519 else for (i = 0; i < P->NbConstraints; ++i) {
1520 int first = 1;
1521 int v = First_Non_Zero(P->Constraint[i]+1, P->Dimension);
1522 if (v == -1 && value_pos_p(P->Constraint[i][0]))
1523 continue;
1524 if (i)
1525 fprintf(out, " && ");
1526 if (v == -1 && value_notzero_p(P->Constraint[i][1+P->Dimension]))
1527 fprintf(out, "FALSE");
1528 else if (value_pos_p(P->Constraint[i][v+1])) {
1529 print_term(out, P->Constraint[i][v+1], v, dim, nparam,
1530 iter_names, param_names, NULL);
1531 if (value_zero_p(P->Constraint[i][0]))
1532 fprintf(out, " = ");
1533 else
1534 fprintf(out, " >= ");
1535 for (j = v+1; j <= dim+nparam; ++j) {
1536 value_oppose(tmp, P->Constraint[i][1+j]);
1537 print_term(out, tmp, j, dim, nparam,
1538 iter_names, param_names, &first);
1539 }
1540 } else {
1541 value_oppose(tmp, P->Constraint[i][1+v]);
1542 print_term(out, tmp, v, dim, nparam,
1543 iter_names, param_names, NULL);
1544 fprintf(out, " <= ");
1545 for (j = v+1; j <= dim+nparam; ++j)
1546 print_term(out, P->Constraint[i][1+j], j, dim, nparam,
1547 iter_names, param_names, &first);
1548 }
1549 }
1550
1551 fprintf(out, " }\n");
1552
1553 value_clear(tmp);
1554 }
1555
1556 /* Construct a cone over P with P placed at x_d = 1, with
1557 * x_d the coordinate of an extra dimension
1558 *
1559 * It's probably a mistake to depend so much on the internal
1560 * representation. We should probably simply compute the
1561 * vertices/facets first.
1562 */
1563 Polyhedron *Cone_over_Polyhedron(Polyhedron *P)
1564 {
1565 unsigned NbConstraints = 0;
1566 unsigned NbRays = 0;
1567 Polyhedron *C;
1568 int i;
1569
1570 if (POL_HAS(P, POL_INEQUALITIES))
1571 NbConstraints = P->NbConstraints + 1;
1572 if (POL_HAS(P, POL_POINTS))
1573 NbRays = P->NbRays + 1;
1574
1575 C = Polyhedron_Alloc(P->Dimension+1, NbConstraints, NbRays);
1576 if (POL_HAS(P, POL_INEQUALITIES)) {
1577 C->NbEq = P->NbEq;
1578 for (i = 0; i < P->NbConstraints; ++i)
1579 Vector_Copy(P->Constraint[i], C->Constraint[i], P->Dimension+2);
1580 /* n >= 0 */
1581 value_set_si(C->Constraint[P->NbConstraints][0], 1);
1582 value_set_si(C->Constraint[P->NbConstraints][1+P->Dimension], 1);
1583 }
1584 if (POL_HAS(P, POL_POINTS)) {
1585 C->NbBid = P->NbBid;
1586 for (i = 0; i < P->NbRays; ++i)
1587 Vector_Copy(P->Ray[i], C->Ray[i], P->Dimension+2);
1588 /* vertex 0 */
1589 value_set_si(C->Ray[P->NbRays][0], 1);
1590 value_set_si(C->Ray[P->NbRays][1+C->Dimension], 1);
1591 }
1592 POL_SET(C, POL_VALID);
1593 if (POL_HAS(P, POL_INEQUALITIES))
1594 POL_SET(C, POL_INEQUALITIES);
1595 if (POL_HAS(P, POL_POINTS))
1596 POL_SET(C, POL_POINTS);
1597 if (POL_HAS(P, POL_VERTICES))
1598 POL_SET(C, POL_VERTICES);
1599 return C;
1600 }
1601
1602 /* Returns a (dim+nparam+1)x((dim-n)+nparam+1) matrix
1603 * mapping the transformed subspace back to the original space.
1604 * n is the number of equalities involving the variables
1605 * (i.e., not purely the parameters).
1606 * The remaining n coordinates in the transformed space would
1607 * have constant (parametric) values and are therefore not
1608 * included in the variables of the new space.
1609 */
1610 Matrix *compress_variables(Matrix *Equalities, unsigned nparam)
1611 {
1612 unsigned dim = (Equalities->NbColumns-2) - nparam;
1613 Matrix *M, *H, *Q, *U, *C, *ratH, *invH, *Ul, *T1, *T2, *T;
1614 Value mone;
1615 int n, i, j;
1616 int ok;
1617
1618 for (n = 0; n < Equalities->NbRows; ++n)
1619 if (First_Non_Zero(Equalities->p[n]+1, dim) == -1)
1620 break;
1621 if (n == 0)
1622 return Identity(dim+nparam+1);
1623 value_init(mone);
1624 value_set_si(mone, -1);
1625 M = Matrix_Alloc(n, dim);
1626 C = Matrix_Alloc(n+1, nparam+1);
1627 for (i = 0; i < n; ++i) {
1628 Vector_Copy(Equalities->p[i]+1, M->p[i], dim);
1629 Vector_Scale(Equalities->p[i]+1+dim, C->p[i], mone, nparam+1);
1630 }
1631 value_set_si(C->p[n][nparam], 1);
1632 left_hermite(M, &H, &Q, &U);
1633 Matrix_Free(M);
1634 Matrix_Free(Q);
1635 value_clear(mone);
1636
1637 ratH = Matrix_Alloc(n+1, n+1);
1638 invH = Matrix_Alloc(n+1, n+1);
1639 for (i = 0; i < n; ++i)
1640 Vector_Copy(H->p[i], ratH->p[i], n);
1641 value_set_si(ratH->p[n][n], 1);
1642 ok = Matrix_Inverse(ratH, invH);
1643 assert(ok);
1644 Matrix_Free(H);
1645 Matrix_Free(ratH);
1646 T1 = Matrix_Alloc(n+1, nparam+1);
1647 Matrix_Product(invH, C, T1);
1648 Matrix_Free(C);
1649 Matrix_Free(invH);
1650 if (value_notone_p(T1->p[n][nparam])) {
1651 for (i = 0; i < n; ++i) {
1652 if (!mpz_divisible_p(T1->p[i][nparam], T1->p[n][nparam])) {
1653 Matrix_Free(T1);
1654 Matrix_Free(U);
1655 return NULL;
1656 }
1657 /* compress_params should have taken care of this */
1658 for (j = 0; j < nparam; ++j)
1659 assert(mpz_divisible_p(T1->p[i][j], T1->p[n][nparam]));
1660 Vector_AntiScale(T1->p[i], T1->p[i], T1->p[n][nparam], nparam+1);
1661 }
1662 value_set_si(T1->p[n][nparam], 1);
1663 }
1664 Ul = Matrix_Alloc(dim+1, n+1);
1665 for (i = 0; i < dim; ++i)
1666 Vector_Copy(U->p[i], Ul->p[i], n);
1667 value_set_si(Ul->p[dim][n], 1);
1668 T2 = Matrix_Alloc(dim+1, nparam+1);
1669 Matrix_Product(Ul, T1, T2);
1670 Matrix_Free(Ul);
1671 Matrix_Free(T1);
1672
1673 T = Matrix_Alloc(dim+nparam+1, (dim-n)+nparam+1);
1674 for (i = 0; i < dim; ++i) {
1675 Vector_Copy(U->p[i]+n, T->p[i], dim-n);
1676 Vector_Copy(T2->p[i], T->p[i]+dim-n, nparam+1);
1677 }
1678 for (i = 0; i < nparam+1; ++i)
1679 value_set_si(T->p[dim+i][(dim-n)+i], 1);
1680 assert(value_one_p(T2->p[dim][nparam]));
1681 Matrix_Free(U);
1682 Matrix_Free(T2);
1683
1684 return T;
1685 }
1686
1687 /* Computes the left inverse of an affine embedding M and, if Eq is not NULL,
1688 * the equalities that define the affine subspace onto which M maps
1689 * its argument.
1690 */
1691 Matrix *left_inverse(Matrix *M, Matrix **Eq)
1692 {
1693 int i, ok;
1694 Matrix *L, *H, *Q, *U, *ratH, *invH, *Ut, *inv;
1695 Vector *t;
1696
1697 if (M->NbColumns == 1) {
1698 inv = Matrix_Alloc(1, M->NbRows);
1699 value_set_si(inv->p[0][M->NbRows-1], 1);
1700 if (Eq) {
1701 *Eq = Matrix_Alloc(M->NbRows-1, 1+(M->NbRows-1)+1);
1702 for (i = 0; i < M->NbRows-1; ++i) {
1703 value_oppose((*Eq)->p[i][1+i], M->p[M->NbRows-1][0]);
1704 value_assign((*Eq)->p[i][1+(M->NbRows-1)], M->p[i][0]);
1705 }
1706 }
1707 return inv;
1708 }
1709 if (Eq)
1710 *Eq = NULL;
1711 L = Matrix_Alloc(M->NbRows-1, M->NbColumns-1);
1712 for (i = 0; i < L->NbRows; ++i)
1713 Vector_Copy(M->p[i], L->p[i], L->NbColumns);
1714 right_hermite(L, &H, &U, &Q);
1715 Matrix_Free(L);
1716 Matrix_Free(Q);
1717 t = Vector_Alloc(U->NbColumns);
1718 for (i = 0; i < U->NbColumns; ++i)
1719 value_oppose(t->p[i], M->p[i][M->NbColumns-1]);
1720 if (Eq) {
1721 *Eq = Matrix_Alloc(H->NbRows - H->NbColumns, 2 + U->NbColumns);
1722 for (i = 0; i < H->NbRows - H->NbColumns; ++i) {
1723 Vector_Copy(U->p[H->NbColumns+i], (*Eq)->p[i]+1, U->NbColumns);
1724 Inner_Product(U->p[H->NbColumns+i], t->p, U->NbColumns,
1725 (*Eq)->p[i]+1+U->NbColumns);
1726 }
1727 }
1728 ratH = Matrix_Alloc(H->NbColumns+1, H->NbColumns+1);
1729 invH = Matrix_Alloc(H->NbColumns+1, H->NbColumns+1);
1730 for (i = 0; i < H->NbColumns; ++i)
1731 Vector_Copy(H->p[i], ratH->p[i], H->NbColumns);
1732 value_set_si(ratH->p[ratH->NbRows-1][ratH->NbColumns-1], 1);
1733 Matrix_Free(H);
1734 ok = Matrix_Inverse(ratH, invH);
1735 assert(ok);
1736 Matrix_Free(ratH);
1737 Ut = Matrix_Alloc(invH->NbRows, U->NbColumns+1);
1738 for (i = 0; i < Ut->NbRows-1; ++i) {
1739 Vector_Copy(U->p[i], Ut->p[i], U->NbColumns);
1740 Inner_Product(U->p[i], t->p, U->NbColumns, &Ut->p[i][Ut->NbColumns-1]);
1741 }
1742 Matrix_Free(U);
1743 Vector_Free(t);
1744 value_set_si(Ut->p[Ut->NbRows-1][Ut->NbColumns-1], 1);
1745 inv = Matrix_Alloc(invH->NbRows, Ut->NbColumns);
1746 Matrix_Product(invH, Ut, inv);
1747 Matrix_Free(Ut);
1748 Matrix_Free(invH);
1749 return inv;
1750 }
1751
1752 /* Check whether all rays are revlex positive in the parameters
1753 */
1754 int Polyhedron_has_revlex_positive_rays(Polyhedron *P, unsigned nparam)
1755 {
1756 int r;
1757 for (r = 0; r < P->NbRays; ++r) {
1758 int i;
1759 if (value_notzero_p(P->Ray[r][P->Dimension+1]))
1760 continue;
1761 for (i = P->Dimension-1; i >= P->Dimension-nparam; --i) {
1762 if (value_neg_p(P->Ray[r][i+1]))
1763 return 0;
1764 if (value_pos_p(P->Ray[r][i+1]))
1765 break;
1766 }
1767 /* A ray independent of the parameters */
1768 if (i < P->Dimension-nparam)
1769 return 0;
1770 }
1771 return 1;
1772 }
1773
1774 static Polyhedron *Recession_Cone(Polyhedron *P, unsigned nparam, unsigned MaxRays)
1775 {
1776 int i;
1777 unsigned nvar = P->Dimension - nparam;
1778 Matrix *M = Matrix_Alloc(P->NbConstraints, 1 + nvar + 1);
1779 Polyhedron *R;
1780 for (i = 0; i < P->NbConstraints; ++i)
1781 Vector_Copy(P->Constraint[i], M->p[i], 1+nvar);
1782 R = Constraints2Polyhedron(M, MaxRays);
1783 Matrix_Free(M);
1784 return R;
1785 }
1786
1787 int Polyhedron_is_unbounded(Polyhedron *P, unsigned nparam, unsigned MaxRays)
1788 {
1789 int i;
1790 int is_unbounded;
1791 Polyhedron *R = Recession_Cone(P, nparam, MaxRays);
1792 POL_ENSURE_VERTICES(R);
1793 if (R->NbBid == 0)
1794 for (i = 0; i < R->NbRays; ++i)
1795 if (value_zero_p(R->Ray[i][1+R->Dimension]))
1796 break;
1797 is_unbounded = R->NbBid > 0 || i < R->NbRays;
1798 Polyhedron_Free(R);
1799 return is_unbounded;
1800 }
1801
1802 static void SwapColumns(Value **V, int n, int i, int j)
1803 {
1804 int r;
1805
1806 for (r = 0; r < n; ++r)
1807 value_swap(V[r][i], V[r][j]);
1808 }
1809
1810 void Polyhedron_ExchangeColumns(Polyhedron *P, int Column1, int Column2)
1811 {
1812 SwapColumns(P->Constraint, P->NbConstraints, Column1, Column2);
1813 SwapColumns(P->Ray, P->NbRays, Column1, Column2);
1814 if (P->NbEq) {
1815 Matrix M;
1816 Polyhedron_Matrix_View(P, &M, P->NbConstraints);
1817 Gauss(&M, P->NbEq, P->Dimension+1);
1818 }
1819 }
1820
1821 /* perform transposition inline; assumes M is a square matrix */
1822 void Matrix_Transposition(Matrix *M)
1823 {
1824 int i, j;
1825
1826 assert(M->NbRows == M->NbColumns);
1827 for (i = 0; i < M->NbRows; ++i)
1828 for (j = i+1; j < M->NbColumns; ++j)
1829 value_swap(M->p[i][j], M->p[j][i]);
1830 }
1831
1832 /* Matrix "view" of first rows rows */
1833 void Polyhedron_Matrix_View(Polyhedron *P, Matrix *M, unsigned rows)
1834 {
1835 M->NbRows = rows;
1836 M->NbColumns = P->Dimension+2;
1837 M->p_Init = P->p_Init;
1838 M->p = P->Constraint;
1839 }
lattice point enumeration library