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lattice_point.cc: rename ceil_mod to fractional_part
[barvinok.git] / util.c
blobdab71210ff7a624c18e46582974a2b9d16cad0e4
1 #include <stdlib.h>
2 #include <assert.h>
3 #include <barvinok/util.h>
4 #include <barvinok/options.h>
5 #include "config.h"
6
7 #ifndef HAVE_ENUMERATE4
8 #define Polyhedron_Enumerate(a,b,c,d) Polyhedron_Enumerate(a,b,c)
9 #endif
10
11 #define ALLOC(type) (type*)malloc(sizeof(type))
12 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
13
14 #ifdef __GNUC__
15 #define NALLOC(p,n) p = (typeof(p))malloc((n) * sizeof(*p))
16 #else
17 #define NALLOC(p,n) p = (void *)malloc((n) * sizeof(*p))
18 #endif
19
20 #ifndef HAVE_ENUMERATION_FREE
21 #define Enumeration_Free(en) /* just leak some memory */
22 #endif
23
24 void manual_count(Polyhedron *P, Value* result)
25 {
26 Polyhedron *U = Universe_Polyhedron(0);
27 Enumeration *en = Polyhedron_Enumerate(P,U,1024,NULL);
28 Value *v = compute_poly(en,NULL);
29 value_assign(*result, *v);
30 value_clear(*v);
31 free(v);
32 Enumeration_Free(en);
33 Polyhedron_Free(U);
34 }
35
36 #ifndef HAVE_ENUMERATION_FREE
37 #undef Enumeration_Free
38 #endif
39
40 #include <barvinok/evalue.h>
41 #include <barvinok/util.h>
42 #include <barvinok/barvinok.h>
43
44 /* Return random value between 0 and max-1 inclusive
45 */
46 int random_int(int max) {
47 return (int) (((double)(max))*rand()/(RAND_MAX+1.0));
48 }
49
50 Polyhedron *Polyhedron_Read(unsigned MaxRays)
51 {
52 int vertices = 0;
53 unsigned NbRows, NbColumns;
54 Matrix *M;
55 Polyhedron *P;
56 char s[128];
57
58 while (fgets(s, sizeof(s), stdin)) {
59 if (*s == '#')
60 continue;
61 if (strncasecmp(s, "vertices", sizeof("vertices")-1) == 0)
62 vertices = 1;
63 if (sscanf(s, "%u %u", &NbRows, &NbColumns) == 2)
64 break;
65 }
66 if (feof(stdin))
67 return NULL;
68 M = Matrix_Alloc(NbRows,NbColumns);
69 Matrix_Read_Input(M);
70 if (vertices)
71 P = Rays2Polyhedron(M, MaxRays);
72 else
73 P = Constraints2Polyhedron(M, MaxRays);
74 Matrix_Free(M);
75 return P;
76 }
77
78 /* Inplace polarization
79 */
80 void Polyhedron_Polarize(Polyhedron *P)
81 {
82 unsigned NbRows = P->NbConstraints + P->NbRays;
83 int i;
84 Value **q;
85
86 q = (Value **)malloc(NbRows * sizeof(Value *));
87 assert(q);
88 for (i = 0; i < P->NbRays; ++i)
89 q[i] = P->Ray[i];
90 for (; i < NbRows; ++i)
91 q[i] = P->Constraint[i-P->NbRays];
92 P->NbConstraints = NbRows - P->NbConstraints;
93 P->NbRays = NbRows - P->NbRays;
94 free(P->Constraint);
95 P->Constraint = q;
96 P->Ray = q + P->NbConstraints;
97 }
98
99 /*
100 * Rather general polar
101 * We can optimize it significantly if we assume that
102 * P includes zero
103 *
104 * Also, we calculate the polar as defined in Schrijver
105 * The opposite should probably work as well and would
106 * eliminate the need for multiplying by -1
107 */
108 Polyhedron* Polyhedron_Polar(Polyhedron *P, unsigned NbMaxRays)
109 {
110 int i;
111 Value mone;
112 unsigned dim = P->Dimension + 2;
113 Matrix *M = Matrix_Alloc(P->NbRays, dim);
114
115 assert(M);
116 value_init(mone);
117 value_set_si(mone, -1);
118 for (i = 0; i < P->NbRays; ++i) {
119 Vector_Scale(P->Ray[i], M->p[i], mone, dim);
120 value_multiply(M->p[i][0], M->p[i][0], mone);
121 value_multiply(M->p[i][dim-1], M->p[i][dim-1], mone);
122 }
123 P = Constraints2Polyhedron(M, NbMaxRays);
124 assert(P);
125 Matrix_Free(M);
126 value_clear(mone);
127 return P;
128 }
129
130 /*
131 * Returns the supporting cone of P at the vertex with index v
132 */
133 Polyhedron* supporting_cone(Polyhedron *P, int v)
134 {
135 Matrix *M;
136 Value tmp;
137 int i, n, j;
138 unsigned char *supporting = (unsigned char *)malloc(P->NbConstraints);
139 unsigned dim = P->Dimension + 2;
140
141 assert(v >=0 && v < P->NbRays);
142 assert(value_pos_p(P->Ray[v][dim-1]));
143 assert(supporting);
144
145 value_init(tmp);
146 for (i = 0, n = 0; i < P->NbConstraints; ++i) {
147 Inner_Product(P->Constraint[i] + 1, P->Ray[v] + 1, dim - 1, &tmp);
148 if ((supporting[i] = value_zero_p(tmp)))
149 ++n;
150 }
151 assert(n >= dim - 2);
152 value_clear(tmp);
153 M = Matrix_Alloc(n, dim);
154 assert(M);
155 for (i = 0, j = 0; i < P->NbConstraints; ++i)
156 if (supporting[i]) {
157 value_set_si(M->p[j][dim-1], 0);
158 Vector_Copy(P->Constraint[i], M->p[j++], dim-1);
159 }
160 free(supporting);
161 P = Constraints2Polyhedron(M, P->NbRays+1);
162 assert(P);
163 Matrix_Free(M);
164 return P;
165 }
166
167 void value_lcm(const Value i, const Value j, Value* lcm)
168 {
169 Value aux;
170 value_init(aux);
171 value_multiply(aux,i,j);
172 Gcd(i,j,lcm);
173 value_division(*lcm,aux,*lcm);
174 value_clear(aux);
175 }
176
177 unsigned char *supporting_constraints(Polyhedron *P, Param_Vertices *v, int *n)
178 {
179 Value lcm, tmp, tmp2;
180 unsigned dim = P->Dimension + 2;
181 unsigned nparam = v->Vertex->NbColumns - 2;
182 unsigned nvar = dim - nparam - 2;
183 unsigned char *supporting = (unsigned char *)malloc(P->NbConstraints);
184 int i, j;
185 Vector *row;
186
187 assert(supporting);
188 row = Vector_Alloc(nparam+1);
189 assert(row);
190 value_init(lcm);
191 value_init(tmp);
192 value_init(tmp2);
193 value_set_si(lcm, 1);
194 for (i = 0, *n = 0; i < P->NbConstraints; ++i) {
195 Vector_Set(row->p, 0, nparam+1);
196 for (j = 0 ; j < nvar; ++j) {
197 value_set_si(tmp, 1);
198 value_assign(tmp2, P->Constraint[i][j+1]);
199 if (value_ne(lcm, v->Vertex->p[j][nparam+1])) {
200 value_assign(tmp, lcm);
201 value_lcm(lcm, v->Vertex->p[j][nparam+1], &lcm);
202 value_division(tmp, lcm, tmp);
203 value_multiply(tmp2, tmp2, lcm);
204 value_division(tmp2, tmp2, v->Vertex->p[j][nparam+1]);
205 }
206 Vector_Combine(row->p, v->Vertex->p[j], row->p,
207 tmp, tmp2, nparam+1);
208 }
209 value_set_si(tmp, 1);
210 Vector_Combine(row->p, P->Constraint[i]+1+nvar, row->p, tmp, lcm, nparam+1);
211 for (j = 0; j < nparam+1; ++j)
212 if (value_notzero_p(row->p[j]))
213 break;
214 if ((supporting[i] = (j == nparam + 1)))
215 ++*n;
216 }
217 assert(*n >= nvar);
218 value_clear(tmp);
219 value_clear(tmp2);
220 value_clear(lcm);
221 Vector_Free(row);
222
223 return supporting;
224 }
225
226 Polyhedron* supporting_cone_p(Polyhedron *P, Param_Vertices *v)
227 {
228 Matrix *M;
229 unsigned dim = P->Dimension + 2;
230 unsigned nparam = v->Vertex->NbColumns - 2;
231 unsigned nvar = dim - nparam - 2;
232 int i, n, j;
233 unsigned char *supporting;
234
235 supporting = supporting_constraints(P, v, &n);
236 M = Matrix_Alloc(n, nvar+2);
237 assert(M);
238 for (i = 0, j = 0; i < P->NbConstraints; ++i)
239 if (supporting[i]) {
240 value_set_si(M->p[j][nvar+1], 0);
241 Vector_Copy(P->Constraint[i], M->p[j++], nvar+1);
242 }
243 free(supporting);
244 P = Constraints2Polyhedron(M, P->NbRays+1);
245 assert(P);
246 Matrix_Free(M);
247 return P;
248 }
249
250 Polyhedron* triangulate_cone(Polyhedron *P, unsigned NbMaxCons)
251 {
252 struct barvinok_options *options = barvinok_options_new_with_defaults();
253 options->MaxRays = NbMaxCons;
254 P = triangulate_cone_with_options(P, options);
255 barvinok_options_free(options);
256 return P;
257 }
258
259 Polyhedron* triangulate_cone_with_options(Polyhedron *P,
260 struct barvinok_options *options)
261 {
262 const static int MAX_TRY=10;
263 int i, j, r, n, t;
264 Value tmp;
265 unsigned dim = P->Dimension;
266 Matrix *M = Matrix_Alloc(P->NbRays+1, dim+3);
267 Matrix *M2, *M3;
268 Polyhedron *L, *R, *T;
269 assert(P->NbEq == 0);
270
271 L = NULL;
272 R = NULL;
273 value_init(tmp);
274
275 Vector_Set(M->p[0]+1, 0, dim+1);
276 value_set_si(M->p[0][0], 1);
277 value_set_si(M->p[0][dim+2], 1);
278 Vector_Set(M->p[P->NbRays]+1, 0, dim+2);
279 value_set_si(M->p[P->NbRays][0], 1);
280 value_set_si(M->p[P->NbRays][dim+1], 1);
281
282 for (i = 0, r = 1; i < P->NbRays; ++i) {
283 if (value_notzero_p(P->Ray[i][dim+1]))
284 continue;
285 Vector_Copy(P->Ray[i], M->p[r], dim+1);
286 value_set_si(M->p[r][dim+2], 0);
287 ++r;
288 }
289
290 M2 = Matrix_Alloc(dim+1, dim+2);
291
292 t = 0;
293 if (options->try_Delaunay_triangulation) {
294 /* Delaunay triangulation */
295 for (r = 1; r < P->NbRays; ++r) {
296 Inner_Product(M->p[r]+1, M->p[r]+1, dim, &tmp);
297 value_assign(M->p[r][dim+1], tmp);
298 }
299 M3 = Matrix_Copy(M);
300 L = Rays2Polyhedron(M3, options->MaxRays);
301 Matrix_Free(M3);
302 ++t;
303 } else {
304 try_again:
305 /* Usually R should still be 0 */
306 Domain_Free(R);
307 Polyhedron_Free(L);
308 for (r = 1; r < P->NbRays; ++r) {
309 value_set_si(M->p[r][dim+1], random_int((t+1)*dim*P->NbRays)+1);
310 }
311 M3 = Matrix_Copy(M);
312 L = Rays2Polyhedron(M3, options->MaxRays);
313 Matrix_Free(M3);
314 ++t;
315 }
316 assert(t <= MAX_TRY);
317
318 R = NULL;
319 n = 0;
320
321 POL_ENSURE_FACETS(L);
322 for (i = 0; i < L->NbConstraints; ++i) {
323 /* Ignore perpendicular facets, i.e., facets with 0 z-coordinate */
324 if (value_negz_p(L->Constraint[i][dim+1]))
325 continue;
326 if (value_notzero_p(L->Constraint[i][dim+2]))
327 continue;
328 for (j = 1, r = 1; j < M->NbRows; ++j) {
329 Inner_Product(M->p[j]+1, L->Constraint[i]+1, dim+1, &tmp);
330 if (value_notzero_p(tmp))
331 continue;
332 if (r > dim)
333 goto try_again;
334 Vector_Copy(M->p[j]+1, M2->p[r]+1, dim);
335 value_set_si(M2->p[r][0], 1);
336 value_set_si(M2->p[r][dim+1], 0);
337 ++r;
338 }
339 assert(r == dim+1);
340 Vector_Set(M2->p[0]+1, 0, dim);
341 value_set_si(M2->p[0][0], 1);
342 value_set_si(M2->p[0][dim+1], 1);
343 T = Rays2Polyhedron(M2, P->NbConstraints+1);
344 T->next = R;
345 R = T;
346 ++n;
347 }
348 Matrix_Free(M2);
349
350 Polyhedron_Free(L);
351 value_clear(tmp);
352 Matrix_Free(M);
353
354 return R;
355 }
356
357 void check_triangulization(Polyhedron *P, Polyhedron *T)
358 {
359 Polyhedron *C, *D, *E, *F, *G, *U;
360 for (C = T; C; C = C->next) {
361 if (C == T)
362 U = C;
363 else
364 U = DomainConvex(DomainUnion(U, C, 100), 100);
365 for (D = C->next; D; D = D->next) {
366 F = C->next;
367 G = D->next;
368 C->next = NULL;
369 D->next = NULL;
370 E = DomainIntersection(C, D, 600);
371 assert(E->NbRays == 0 || E->NbEq >= 1);
372 Polyhedron_Free(E);
373 C->next = F;
374 D->next = G;
375 }
376 }
377 assert(PolyhedronIncludes(U, P));
378 assert(PolyhedronIncludes(P, U));
379 }
380
381 /* Computes x, y and g such that g = gcd(a,b) and a*x+b*y = g */
382 void Extended_Euclid(Value a, Value b, Value *x, Value *y, Value *g)
383 {
384 Value c, d, e, f, tmp;
385
386 value_init(c);
387 value_init(d);
388 value_init(e);
389 value_init(f);
390 value_init(tmp);
391 value_absolute(c, a);
392 value_absolute(d, b);
393 value_set_si(e, 1);
394 value_set_si(f, 0);
395 while(value_pos_p(d)) {
396 value_division(tmp, c, d);
397 value_multiply(tmp, tmp, f);
398 value_subtract(e, e, tmp);
399 value_division(tmp, c, d);
400 value_multiply(tmp, tmp, d);
401 value_subtract(c, c, tmp);
402 value_swap(c, d);
403 value_swap(e, f);
404 }
405 value_assign(*g, c);
406 if (value_zero_p(a))
407 value_set_si(*x, 0);
408 else if (value_pos_p(a))
409 value_assign(*x, e);
410 else value_oppose(*x, e);
411 if (value_zero_p(b))
412 value_set_si(*y, 0);
413 else {
414 value_multiply(tmp, a, *x);
415 value_subtract(tmp, c, tmp);
416 value_division(*y, tmp, b);
417 }
418 value_clear(c);
419 value_clear(d);
420 value_clear(e);
421 value_clear(f);
422 value_clear(tmp);
423 }
424
425 static int unimodular_complete_1(Matrix *m)
426 {
427 Value g, b, c, old, tmp;
428 unsigned i, j;
429 int ok;
430
431 value_init(b);
432 value_init(c);
433 value_init(g);
434 value_init(old);
435 value_init(tmp);
436 value_assign(g, m->p[0][0]);
437 for (i = 1; value_zero_p(g) && i < m->NbColumns; ++i) {
438 for (j = 0; j < m->NbColumns; ++j) {
439 if (j == i-1)
440 value_set_si(m->p[i][j], 1);
441 else
442 value_set_si(m->p[i][j], 0);
443 }
444 value_assign(g, m->p[0][i]);
445 }
446 for (; i < m->NbColumns; ++i) {
447 value_assign(old, g);
448 Extended_Euclid(old, m->p[0][i], &c, &b, &g);
449 value_oppose(b, b);
450 for (j = 0; j < m->NbColumns; ++j) {
451 if (j < i) {
452 value_multiply(tmp, m->p[0][j], b);
453 value_division(m->p[i][j], tmp, old);
454 } else if (j == i)
455 value_assign(m->p[i][j], c);
456 else
457 value_set_si(m->p[i][j], 0);
458 }
459 }
460 ok = value_one_p(g);
461 value_clear(b);
462 value_clear(c);
463 value_clear(g);
464 value_clear(old);
465 value_clear(tmp);
466 return ok;
467 }
468
469 int unimodular_complete(Matrix *M, int row)
470 {
471 int r;
472 int ok = 1;
473 Matrix *H, *Q, *U;
474
475 if (row == 1)
476 return unimodular_complete_1(M);
477
478 left_hermite(M, &H, &Q, &U);
479 Matrix_Free(U);
480 for (r = 0; ok && r < row; ++r)
481 if (value_notone_p(H->p[r][r]))
482 ok = 0;
483 Matrix_Free(H);
484 for (r = row; r < M->NbRows; ++r)
485 Vector_Copy(Q->p[r], M->p[r], M->NbColumns);
486 Matrix_Free(Q);
487 return ok;
488 }
489
490 /*
491 * Returns a full-dimensional polyhedron with the same number
492 * of integer points as P
493 */
494 Polyhedron *remove_equalities(Polyhedron *P, unsigned MaxRays)
495 {
496 Polyhedron *Q = Polyhedron_Copy(P);
497 unsigned dim = P->Dimension;
498 Matrix *m1, *m2;
499 int i;
500
501 if (Q->NbEq == 0)
502 return Q;
503
504 Q = DomainConstraintSimplify(Q, MaxRays);
505 if (emptyQ2(Q))
506 return Q;
507
508 m1 = Matrix_Alloc(dim, dim);
509 for (i = 0; i < Q->NbEq; ++i)
510 Vector_Copy(P->Constraint[i]+1, m1->p[i], dim);
511
512 /* m1 may not be unimodular, but we won't be throwing anything away */
513 unimodular_complete(m1, Q->NbEq);
514
515 m2 = Matrix_Alloc(dim+1-Q->NbEq, dim+1);
516 for (i = Q->NbEq; i < dim; ++i)
517 Vector_Copy(m1->p[i], m2->p[i-Q->NbEq], dim);
518 value_set_si(m2->p[dim-Q->NbEq][dim], 1);
519 Matrix_Free(m1);
520
521 P = Polyhedron_Image(Q, m2, MaxRays);
522 Matrix_Free(m2);
523 Polyhedron_Free(Q);
524
525 return P;
526 }
527
528 /*
529 * Returns a full-dimensional polyhedron with the same number
530 * of integer points as P
531 * nvar specifies the number of variables
532 * The remaining dimensions are assumed to be parameters
533 * Destroys P
534 * factor is NbEq x (nparam+2) matrix, containing stride constraints
535 * on the parameters; column nparam is the constant;
536 * column nparam+1 is the stride
537 *
538 * if factor is NULL, only remove equalities that don't affect
539 * the number of points
540 */
541 Polyhedron *remove_equalities_p(Polyhedron *P, unsigned nvar, Matrix **factor,
542 unsigned MaxRays)
543 {
544 Value g;
545 Polyhedron *Q;
546 unsigned dim = P->Dimension;
547 Matrix *m1, *m2, *f;
548 int i, j;
549
550 if (P->NbEq == 0)
551 return P;
552
553 m1 = Matrix_Alloc(nvar, nvar);
554 P = DomainConstraintSimplify(P, MaxRays);
555 if (factor) {
556 f = Matrix_Alloc(P->NbEq, dim-nvar+2);
557 *factor = f;
558 }
559 value_init(g);
560 for (i = 0, j = 0; i < P->NbEq; ++i) {
561 if (First_Non_Zero(P->Constraint[i]+1, nvar) == -1)
562 continue;
563
564 Vector_Gcd(P->Constraint[i]+1, nvar, &g);
565 if (!factor && value_notone_p(g))
566 continue;
567
568 if (factor) {
569 Vector_Copy(P->Constraint[i]+1+nvar, f->p[j], dim-nvar+1);
570 value_assign(f->p[j][dim-nvar+1], g);
571 }
572
573 Vector_Copy(P->Constraint[i]+1, m1->p[j], nvar);
574
575 ++j;
576 }
577 value_clear(g);
578
579 unimodular_complete(m1, j);
580
581 m2 = Matrix_Alloc(dim+1-j, dim+1);
582 for (i = 0; i < nvar-j ; ++i)
583 Vector_Copy(m1->p[i+j], m2->p[i], nvar);
584 Matrix_Free(m1);
585 for (i = nvar-j; i <= dim-j; ++i)
586 value_set_si(m2->p[i][i+j], 1);
587
588 Q = Polyhedron_Image(P, m2, MaxRays);
589 Matrix_Free(m2);
590 Polyhedron_Free(P);
591
592 return Q;
593 }
594
595 void Line_Length(Polyhedron *P, Value *len)
596 {
597 Value tmp, pos, neg;
598 int p = 0, n = 0;
599 int i;
600
601 assert(P->Dimension == 1);
602
603 value_init(tmp);
604 value_init(pos);
605 value_init(neg);
606
607 for (i = 0; i < P->NbConstraints; ++i) {
608 value_oppose(tmp, P->Constraint[i][2]);
609 if (value_pos_p(P->Constraint[i][1])) {
610 mpz_cdiv_q(tmp, tmp, P->Constraint[i][1]);
611 if (!p || value_gt(tmp, pos))
612 value_assign(pos, tmp);
613 p = 1;
614 } else {
615 mpz_fdiv_q(tmp, tmp, P->Constraint[i][1]);
616 if (!n || value_lt(tmp, neg))
617 value_assign(neg, tmp);
618 n = 1;
619 }
620 if (n && p) {
621 value_subtract(tmp, neg, pos);
622 value_increment(*len, tmp);
623 } else
624 value_set_si(*len, -1);
625 }
626
627 value_clear(tmp);
628 value_clear(pos);
629 value_clear(neg);
630 }
631
632 /*
633 * Factors the polyhedron P into polyhedra Q_i such that
634 * the number of integer points in P is equal to the product
635 * of the number of integer points in the individual Q_i
636 *
637 * If no factors can be found, NULL is returned.
638 * Otherwise, a linked list of the factors is returned.
639 *
640 * If there are factors and if T is not NULL, then a matrix will be
641 * returned through T expressing the old variables in terms of the
642 * new variables as they appear in the sequence of factors.
643 *
644 * The algorithm works by first computing the Hermite normal form
645 * and then grouping columns linked by one or more constraints together,
646 * where a constraints "links" two or more columns if the constraint
647 * has nonzero coefficients in the columns.
648 */
649 Polyhedron* Polyhedron_Factor(Polyhedron *P, unsigned nparam, Matrix **T,
650 unsigned NbMaxRays)
651 {
652 int i, j, k;
653 Matrix *M, *H, *Q, *U;
654 int *pos; /* for each column: row position of pivot */
655 int *group; /* group to which a column belongs */
656 int *cnt; /* number of columns in the group */
657 int *rowgroup; /* group to which a constraint belongs */
658 int nvar = P->Dimension - nparam;
659 Polyhedron *F = NULL;
660
661 if (nvar <= 1)
662 return NULL;
663
664 NALLOC(pos, nvar);
665 NALLOC(group, nvar);
666 NALLOC(cnt, nvar);
667 NALLOC(rowgroup, P->NbConstraints);
668
669 M = Matrix_Alloc(P->NbConstraints, nvar);
670 for (i = 0; i < P->NbConstraints; ++i)
671 Vector_Copy(P->Constraint[i]+1, M->p[i], nvar);
672 left_hermite(M, &H, &Q, &U);
673 Matrix_Free(M);
674 Matrix_Free(Q);
675
676 for (i = 0; i < P->NbConstraints; ++i)
677 rowgroup[i] = -1;
678 for (i = 0, j = 0; i < H->NbColumns; ++i) {
679 for ( ; j < H->NbRows; ++j)
680 if (value_notzero_p(H->p[j][i]))
681 break;
682 assert (j < H->NbRows);
683 pos[i] = j;
684 }
685 for (i = 0; i < nvar; ++i) {
686 group[i] = i;
687 cnt[i] = 1;
688 }
689 for (i = 0; i < H->NbColumns && cnt[0] < nvar; ++i) {
690 if (rowgroup[pos[i]] == -1)
691 rowgroup[pos[i]] = i;
692 for (j = pos[i]+1; j < H->NbRows; ++j) {
693 if (value_zero_p(H->p[j][i]))
694 continue;
695 if (rowgroup[j] != -1)
696 continue;
697 rowgroup[j] = group[i];
698 for (k = i+1; k < H->NbColumns && j >= pos[k]; ++k) {
699 int g = group[k];
700 while (cnt[g] == 0)
701 g = group[g];
702 group[k] = g;
703 if (group[k] != group[i] && value_notzero_p(H->p[j][k])) {
704 assert(cnt[group[k]] != 0);
705 assert(cnt[group[i]] != 0);
706 if (group[i] < group[k]) {
707 cnt[group[i]] += cnt[group[k]];
708 cnt[group[k]] = 0;
709 group[k] = group[i];
710 } else {
711 cnt[group[k]] += cnt[group[i]];
712 cnt[group[i]] = 0;
713 group[i] = group[k];
714 }
715 }
716 }
717 }
718 }
719
720 if (cnt[0] != nvar) {
721 /* Extract out pure context constraints separately */
722 Polyhedron **next = &F;
723 int tot_d = 0;
724 if (T)
725 *T = Matrix_Alloc(nvar, nvar);
726 for (i = nparam ? -1 : 0; i < nvar; ++i) {
727 int d;
728
729 if (i == -1) {
730 for (j = 0, k = 0; j < P->NbConstraints; ++j)
731 if (rowgroup[j] == -1) {
732 if (First_Non_Zero(P->Constraint[j]+1+nvar,
733 nparam) == -1)
734 rowgroup[j] = -2;
735 else
736 ++k;
737 }
738 if (k == 0)
739 continue;
740 d = 0;
741 } else {
742 if (cnt[i] == 0)
743 continue;
744 d = cnt[i];
745 for (j = 0, k = 0; j < P->NbConstraints; ++j)
746 if (rowgroup[j] >= 0 && group[rowgroup[j]] == i) {
747 rowgroup[j] = i;
748 ++k;
749 }
750 }
751
752 if (T)
753 for (j = 0; j < nvar; ++j) {
754 int l, m;
755 for (l = 0, m = 0; m < d; ++l) {
756 if (group[l] != i)
757 continue;
758 value_assign((*T)->p[j][tot_d+m++], U->p[j][l]);
759 }
760 }
761
762 M = Matrix_Alloc(k, d+nparam+2);
763 for (j = 0, k = 0; j < P->NbConstraints; ++j) {
764 int l, m;
765 if (rowgroup[j] != i)
766 continue;
767 value_assign(M->p[k][0], P->Constraint[j][0]);
768 for (l = 0, m = 0; m < d; ++l) {
769 if (group[l] != i)
770 continue;
771 value_assign(M->p[k][1+m++], H->p[j][l]);
772 }
773 Vector_Copy(P->Constraint[j]+1+nvar, M->p[k]+1+m, nparam+1);
774 ++k;
775 }
776 *next = Constraints2Polyhedron(M, NbMaxRays);
777 next = &(*next)->next;
778 Matrix_Free(M);
779 tot_d += d;
780 }
781 }
782 Matrix_Free(U);
783 Matrix_Free(H);
784 free(pos);
785 free(group);
786 free(cnt);
787 free(rowgroup);
788 return F;
789 }
790
791 /*
792 * Project on final dim dimensions
793 */
794 Polyhedron* Polyhedron_Project(Polyhedron *P, int dim)
795 {
796 int i;
797 int remove = P->Dimension - dim;
798 Matrix *T;
799 Polyhedron *I;
800
801 if (P->Dimension == dim)
802 return Polyhedron_Copy(P);
803
804 T = Matrix_Alloc(dim+1, P->Dimension+1);
805 for (i = 0; i < dim+1; ++i)
806 value_set_si(T->p[i][i+remove], 1);
807 I = Polyhedron_Image(P, T, P->NbConstraints);
808 Matrix_Free(T);
809 return I;
810 }
811
812 /* Constructs a new constraint that ensures that
813 * the first constraint is (strictly) smaller than
814 * the second.
815 */
816 static void smaller_constraint(Value *a, Value *b, Value *c, int pos, int shift,
817 int len, int strict, Value *tmp)
818 {
819 value_oppose(*tmp, b[pos+1]);
820 value_set_si(c[0], 1);
821 Vector_Combine(a+1+shift, b+1+shift, c+1, *tmp, a[pos+1], len-shift-1);
822 if (strict)
823 value_decrement(c[len-shift-1], c[len-shift-1]);
824 ConstraintSimplify(c, c, len-shift, tmp);
825 }
826
827 struct section { Polyhedron * D; evalue E; };
828
829 evalue * ParamLine_Length_mod(Polyhedron *P, Polyhedron *C, int MaxRays)
830 {
831 unsigned dim = P->Dimension;
832 unsigned nvar = dim - C->Dimension;
833 int *pos;
834 int i, j, p, n, z;
835 struct section *s;
836 Matrix *M, *M2;
837 int nd = 0;
838 int k, l, k2, l2, q;
839 evalue *L, *U;
840 evalue *F;
841 Value g;
842 Polyhedron *T;
843 evalue mone;
844
845 assert(nvar == 1);
846
847 NALLOC(pos, P->NbConstraints);
848 value_init(g);
849 value_init(mone.d);
850 evalue_set_si(&mone, -1, 1);
851
852 for (i = 0, z = 0; i < P->NbConstraints; ++i)
853 if (value_zero_p(P->Constraint[i][1]))
854 ++z;
855 /* put those with positive coefficients first; number: p */
856 for (i = 0, p = 0, n = P->NbConstraints-z-1; i < P->NbConstraints; ++i)
857 if (value_pos_p(P->Constraint[i][1]))
858 pos[p++] = i;
859 else if (value_neg_p(P->Constraint[i][1]))
860 pos[n--] = i;
861 n = P->NbConstraints-z-p;
862 assert (p >= 1 && n >= 1);
863 s = (struct section *) malloc(p * n * sizeof(struct section));
864 M = Matrix_Alloc((p-1) + (n-1), dim-nvar+2);
865 for (k = 0; k < p; ++k) {
866 for (k2 = 0; k2 < p; ++k2) {
867 if (k2 == k)
868 continue;
869 q = k2 - (k2 > k);
870 smaller_constraint(
871 P->Constraint[pos[k]],
872 P->Constraint[pos[k2]],
873 M->p[q], 0, nvar, dim+2, k2 > k, &g);
874 }
875 for (l = p; l < p+n; ++l) {
876 for (l2 = p; l2 < p+n; ++l2) {
877 if (l2 == l)
878 continue;
879 q = l2-1 - (l2 > l);
880 smaller_constraint(
881 P->Constraint[pos[l2]],
882 P->Constraint[pos[l]],
883 M->p[q], 0, nvar, dim+2, l2 > l, &g);
884 }
885 M2 = Matrix_Copy(M);
886 T = Constraints2Polyhedron(M2, P->NbRays);
887 Matrix_Free(M2);
888 s[nd].D = DomainIntersection(T, C, MaxRays);
889 Domain_Free(T);
890 POL_ENSURE_VERTICES(s[nd].D);
891 if (emptyQ(s[nd].D)) {
892 Polyhedron_Free(s[nd].D);
893 continue;
894 }
895 L = bv_ceil3(P->Constraint[pos[k]]+1+nvar,
896 dim-nvar+1,
897 P->Constraint[pos[k]][0+1], s[nd].D);
898 U = bv_ceil3(P->Constraint[pos[l]]+1+nvar,
899 dim-nvar+1,
900 P->Constraint[pos[l]][0+1], s[nd].D);
901 eadd(L, U);
902 eadd(&mone, U);
903 emul(&mone, U);
904 s[nd].E = *U;
905 free_evalue_refs(L);
906 free(L);
907 free(U);
908 ++nd;
909 }
910 }
911
912 Matrix_Free(M);
913
914 F = ALLOC(evalue);
915 value_init(F->d);
916 value_set_si(F->d, 0);
917 F->x.p = new_enode(partition, 2*nd, dim-nvar);
918 for (k = 0; k < nd; ++k) {
919 EVALUE_SET_DOMAIN(F->x.p->arr[2*k], s[k].D);
920 value_clear(F->x.p->arr[2*k+1].d);
921 F->x.p->arr[2*k+1] = s[k].E;
922 }
923 free(s);
924
925 free_evalue_refs(&mone);
926 value_clear(g);
927 free(pos);
928
929 return F;
930 }
931
932 evalue* ParamLine_Length(Polyhedron *P, Polyhedron *C,
933 struct barvinok_options *options)
934 {
935 evalue* tmp;
936 tmp = ParamLine_Length_mod(P, C, options->MaxRays);
937 if (options->lookup_table) {
938 evalue_mod2table(tmp, C->Dimension);
939 reduce_evalue(tmp);
940 }
941 return tmp;
942 }
943
944 Bool isIdentity(Matrix *M)
945 {
946 unsigned i, j;
947 if (M->NbRows != M->NbColumns)
948 return False;
949
950 for (i = 0;i < M->NbRows; i ++)
951 for (j = 0; j < M->NbColumns; j ++)
952 if (i == j) {
953 if(value_notone_p(M->p[i][j]))
954 return False;
955 } else {
956 if(value_notzero_p(M->p[i][j]))
957 return False;
958 }
959 return True;
960 }
961
962 void Param_Polyhedron_Print(FILE* DST, Param_Polyhedron *PP, char **param_names)
963 {
964 Param_Domain *P;
965 Param_Vertices *V;
966
967 for(P=PP->D;P;P=P->next) {
968
969 /* prints current val. dom. */
970 fprintf(DST, "---------------------------------------\n");
971 fprintf(DST, "Domain :\n");
972 Print_Domain(DST, P->Domain, param_names);
973
974 /* scan the vertices */
975 fprintf(DST, "Vertices :\n");
976 FORALL_PVertex_in_ParamPolyhedron(V,P,PP) {
977
978 /* prints each vertex */
979 Print_Vertex(DST, V->Vertex, param_names);
980 printf( "\n" );
981 }
982 END_FORALL_PVertex_in_ParamPolyhedron;
983 }
984 }
985
986 void Enumeration_Print(FILE *Dst, Enumeration *en, char **params)
987 {
988 for (; en; en = en->next) {
989 Print_Domain(Dst, en->ValidityDomain, params);
990 print_evalue(Dst, &en->EP, params);
991 }
992 }
993
994 void Enumeration_Free(Enumeration *en)
995 {
996 Enumeration *ee;
997
998 while( en )
999 {
1000 free_evalue_refs( &(en->EP) );
1001 Domain_Free( en->ValidityDomain );
1002 ee = en ->next;
1003 free( en );
1004 en = ee;
1005 }
1006 }
1007
1008 void Enumeration_mod2table(Enumeration *en, unsigned nparam)
1009 {
1010 for (; en; en = en->next) {
1011 evalue_mod2table(&en->EP, nparam);
1012 reduce_evalue(&en->EP);
1013 }
1014 }
1015
1016 size_t Enumeration_size(Enumeration *en)
1017 {
1018 size_t s = 0;
1019
1020 for (; en; en = en->next) {
1021 s += domain_size(en->ValidityDomain);
1022 s += evalue_size(&en->EP);
1023 }
1024 return s;
1025 }
1026
1027 void Free_ParamNames(char **params, int m)
1028 {
1029 while (--m >= 0)
1030 free(params[m]);
1031 free(params);
1032 }
1033
1034 /* Check whether every set in D2 is included in some set of D1 */
1035 int DomainIncludes(Polyhedron *D1, Polyhedron *D2)
1036 {
1037 for ( ; D2; D2 = D2->next) {
1038 Polyhedron *P1;
1039 for (P1 = D1; P1; P1 = P1->next)
1040 if (PolyhedronIncludes(P1, D2))
1041 break;
1042 if (!P1)
1043 return 0;
1044 }
1045 return 1;
1046 }
1047
1048 int line_minmax(Polyhedron *I, Value *min, Value *max)
1049 {
1050 int i;
1051
1052 if (I->NbEq >= 1) {
1053 value_oppose(I->Constraint[0][2], I->Constraint[0][2]);
1054 /* There should never be a remainder here */
1055 if (value_pos_p(I->Constraint[0][1]))
1056 mpz_fdiv_q(*min, I->Constraint[0][2], I->Constraint[0][1]);
1057 else
1058 mpz_fdiv_q(*min, I->Constraint[0][2], I->Constraint[0][1]);
1059 value_assign(*max, *min);
1060 } else for (i = 0; i < I->NbConstraints; ++i) {
1061 if (value_zero_p(I->Constraint[i][1])) {
1062 Polyhedron_Free(I);
1063 return 0;
1064 }
1065
1066 value_oppose(I->Constraint[i][2], I->Constraint[i][2]);
1067 if (value_pos_p(I->Constraint[i][1]))
1068 mpz_cdiv_q(*min, I->Constraint[i][2], I->Constraint[i][1]);
1069 else
1070 mpz_fdiv_q(*max, I->Constraint[i][2], I->Constraint[i][1]);
1071 }
1072 Polyhedron_Free(I);
1073 return 1;
1074 }
1075
1076 /**
1077
1078 PROCEDURES TO COMPUTE ENUMERATION. recursive procedure, recurse for
1079 each imbriquation
1080
1081 @param pos index position of current loop index (1..hdim-1)
1082 @param P loop domain
1083 @param context context values for fixed indices
1084 @param exist number of existential variables
1085 @return the number of integer points in this
1086 polyhedron
1087
1088 */
1089 void count_points_e (int pos, Polyhedron *P, int exist, int nparam,
1090 Value *context, Value *res)
1091 {
1092 Value LB, UB, k, c;
1093
1094 if (emptyQ(P)) {
1095 value_set_si(*res, 0);
1096 return;
1097 }
1098
1099 value_init(LB); value_init(UB); value_init(k);
1100 value_set_si(LB,0);
1101 value_set_si(UB,0);
1102
1103 if (lower_upper_bounds(pos,P,context,&LB,&UB) !=0) {
1104 /* Problem if UB or LB is INFINITY */
1105 value_clear(LB); value_clear(UB); value_clear(k);
1106 if (pos > P->Dimension - nparam - exist)
1107 value_set_si(*res, 1);
1108 else
1109 value_set_si(*res, -1);
1110 return;
1111 }
1112
1113 #ifdef EDEBUG1
1114 if (!P->next) {
1115 int i;
1116 for (value_assign(k,LB); value_le(k,UB); value_increment(k,k)) {
1117 fprintf(stderr, "(");
1118 for (i=1; i<pos; i++) {
1119 value_print(stderr,P_VALUE_FMT,context[i]);
1120 fprintf(stderr,",");
1121 }
1122 value_print(stderr,P_VALUE_FMT,k);
1123 fprintf(stderr,")\n");
1124 }
1125 }
1126 #endif
1127
1128 value_set_si(context[pos],0);
1129 if (value_lt(UB,LB)) {
1130 value_clear(LB); value_clear(UB); value_clear(k);
1131 value_set_si(*res, 0);
1132 return;
1133 }
1134 if (!P->next) {
1135 if (exist)
1136 value_set_si(*res, 1);
1137 else {
1138 value_subtract(k,UB,LB);
1139 value_add_int(k,k,1);
1140 value_assign(*res, k);
1141 }
1142 value_clear(LB); value_clear(UB); value_clear(k);
1143 return;
1144 }
1145
1146 /*-----------------------------------------------------------------*/
1147 /* Optimization idea */
1148 /* If inner loops are not a function of k (the current index) */
1149 /* i.e. if P->Constraint[i][pos]==0 for all P following this and */
1150 /* for all i, */
1151 /* Then CNT = (UB-LB+1)*count_points(pos+1, P->next, context) */
1152 /* (skip the for loop) */
1153 /*-----------------------------------------------------------------*/
1154
1155 value_init(c);
1156 value_set_si(*res, 0);
1157 for (value_assign(k,LB);value_le(k,UB);value_increment(k,k)) {
1158 /* Insert k in context */
1159 value_assign(context[pos],k);
1160 count_points_e(pos+1, P->next, exist, nparam, context, &c);
1161 if(value_notmone_p(c))
1162 value_addto(*res, *res, c);
1163 else {
1164 value_set_si(*res, -1);
1165 break;
1166 }
1167 if (pos > P->Dimension - nparam - exist &&
1168 value_pos_p(*res))
1169 break;
1170 }
1171 value_clear(c);
1172
1173 #ifdef EDEBUG11
1174 fprintf(stderr,"%d\n",CNT);
1175 #endif
1176
1177 /* Reset context */
1178 value_set_si(context[pos],0);
1179 value_clear(LB); value_clear(UB); value_clear(k);
1180 return;
1181 } /* count_points_e */
1182
1183 int DomainContains(Polyhedron *P, Value *list_args, int len,
1184 unsigned MaxRays, int set)
1185 {
1186 int i;
1187 Value m;
1188
1189 if (P->Dimension == len)
1190 return in_domain(P, list_args);
1191
1192 assert(set); // assume list_args is large enough
1193 assert((P->Dimension - len) % 2 == 0);
1194 value_init(m);
1195 for (i = 0; i < P->Dimension - len; i += 2) {
1196 int j, k;
1197 for (j = 0 ; j < P->NbEq; ++j)
1198 if (value_notzero_p(P->Constraint[j][1+len+i]))
1199 break;
1200 assert(j < P->NbEq);
1201 value_absolute(m, P->Constraint[j][1+len+i]);
1202 k = First_Non_Zero(P->Constraint[j]+1, len);
1203 assert(k != -1);
1204 assert(First_Non_Zero(P->Constraint[j]+1+k+1, len - k - 1) == -1);
1205 mpz_fdiv_q(list_args[len+i], list_args[k], m);
1206 mpz_fdiv_r(list_args[len+i+1], list_args[k], m);
1207 }
1208 value_clear(m);
1209
1210 return in_domain(P, list_args);
1211 }
1212
1213 Polyhedron *DomainConcat(Polyhedron *head, Polyhedron *tail)
1214 {
1215 Polyhedron *S;
1216 if (!head)
1217 return tail;
1218 for (S = head; S->next; S = S->next)
1219 ;
1220 S->next = tail;
1221 return head;
1222 }
1223
1224 #ifndef HAVE_LEXSMALLER
1225
1226 evalue *barvinok_lexsmaller_ev(Polyhedron *P, Polyhedron *D, unsigned dim,
1227 Polyhedron *C, unsigned MaxRays)
1228 {
1229 assert(0);
1230 }
1231
1232 #else
1233 #include <polylib/ranking.h>
1234
1235 evalue *barvinok_lexsmaller_ev(Polyhedron *P, Polyhedron *D, unsigned dim,
1236 Polyhedron *C, unsigned MaxRays)
1237 {
1238 evalue *ranking;
1239 Polyhedron *RC, *RD, *Q;
1240 unsigned nparam = dim + C->Dimension;
1241 unsigned exist;
1242 Polyhedron *CA;
1243
1244 RC = LexSmaller(P, D, dim, C, MaxRays);
1245 RD = RC->next;
1246 RC->next = NULL;
1247
1248 exist = RD->Dimension - nparam - dim;
1249 CA = align_context(RC, RD->Dimension, MaxRays);
1250 Q = DomainIntersection(RD, CA, MaxRays);
1251 Polyhedron_Free(CA);
1252 Domain_Free(RD);
1253 Polyhedron_Free(RC);
1254 RD = Q;
1255
1256 for (Q = RD; Q; Q = Q->next) {
1257 evalue *t;
1258 Polyhedron *next = Q->next;
1259 Q->next = 0;
1260
1261 t = barvinok_enumerate_e(Q, exist, nparam, MaxRays);
1262
1263 if (Q == RD)
1264 ranking = t;
1265 else {
1266 eadd(t, ranking);
1267 free_evalue_refs(t);
1268 free(t);
1269 }
1270
1271 Q->next = next;
1272 }
1273
1274 Domain_Free(RD);
1275
1276 return ranking;
1277 }
1278
1279 Enumeration *barvinok_lexsmaller(Polyhedron *P, Polyhedron *D, unsigned dim,
1280 Polyhedron *C, unsigned MaxRays)
1281 {
1282 evalue *EP = barvinok_lexsmaller_ev(P, D, dim, C, MaxRays);
1283
1284 return partition2enumeration(EP);
1285 }
1286 #endif
1287
1288 /* "align" matrix to have nrows by inserting
1289 * the necessary number of rows and an equal number of columns in front
1290 */
1291 Matrix *align_matrix(Matrix *M, int nrows)
1292 {
1293 int i;
1294 int newrows = nrows - M->NbRows;
1295 Matrix *M2 = Matrix_Alloc(nrows, newrows + M->NbColumns);
1296 for (i = 0; i < newrows; ++i)
1297 value_set_si(M2->p[i][i], 1);
1298 for (i = 0; i < M->NbRows; ++i)
1299 Vector_Copy(M->p[i], M2->p[newrows+i]+newrows, M->NbColumns);
1300 return M2;
1301 }
1302
1303 static void print_varlist(FILE *out, int n, char **names)
1304 {
1305 int i;
1306 fprintf(out, "[");
1307 for (i = 0; i < n; ++i) {
1308 if (i)
1309 fprintf(out, ",");
1310 fprintf(out, "%s", names[i]);
1311 }
1312 fprintf(out, "]");
1313 }
1314
1315 static void print_term(FILE *out, Value v, int pos, int dim, int nparam,
1316 char **iter_names, char **param_names, int *first)
1317 {
1318 if (value_zero_p(v)) {
1319 if (first && *first && pos >= dim + nparam)
1320 fprintf(out, "0");
1321 return;
1322 }
1323
1324 if (first) {
1325 if (!*first && value_pos_p(v))
1326 fprintf(out, "+");
1327 *first = 0;
1328 }
1329 if (pos < dim + nparam) {
1330 if (value_mone_p(v))
1331 fprintf(out, "-");
1332 else if (!value_one_p(v))
1333 value_print(out, VALUE_FMT, v);
1334 if (pos < dim)
1335 fprintf(out, "%s", iter_names[pos]);
1336 else
1337 fprintf(out, "%s", param_names[pos-dim]);
1338 } else
1339 value_print(out, VALUE_FMT, v);
1340 }
1341
1342 char **util_generate_names(int n, char *prefix)
1343 {
1344 int i;
1345 int len = (prefix ? strlen(prefix) : 0) + 10;
1346 char **names = ALLOCN(char*, n);
1347 if (!names) {
1348 fprintf(stderr, "ERROR: memory overflow.\n");
1349 exit(1);
1350 }
1351 for (i = 0; i < n; ++i) {
1352 names[i] = ALLOCN(char, len);
1353 if (!names[i]) {
1354 fprintf(stderr, "ERROR: memory overflow.\n");
1355 exit(1);
1356 }
1357 if (!prefix)
1358 snprintf(names[i], len, "%d", i);
1359 else
1360 snprintf(names[i], len, "%s%d", prefix, i);
1361 }
1362
1363 return names;
1364 }
1365
1366 void util_free_names(int n, char **names)
1367 {
1368 int i;
1369 for (i = 0; i < n; ++i)
1370 free(names[i]);
1371 free(names);
1372 }
1373
1374 void Polyhedron_pprint(FILE *out, Polyhedron *P, int dim, int nparam,
1375 char **iter_names, char **param_names)
1376 {
1377 int i, j;
1378 Value tmp;
1379
1380 assert(dim + nparam == P->Dimension);
1381
1382 value_init(tmp);
1383
1384 fprintf(out, "{ ");
1385 if (nparam) {
1386 print_varlist(out, nparam, param_names);
1387 fprintf(out, " -> ");
1388 }
1389 print_varlist(out, dim, iter_names);
1390 fprintf(out, " : ");
1391
1392 if (emptyQ2(P))
1393 fprintf(out, "FALSE");
1394 else for (i = 0; i < P->NbConstraints; ++i) {
1395 int first = 1;
1396 int v = First_Non_Zero(P->Constraint[i]+1, P->Dimension);
1397 if (v == -1 && value_pos_p(P->Constraint[i][0]))
1398 continue;
1399 if (i)
1400 fprintf(out, " && ");
1401 if (v == -1 && value_notzero_p(P->Constraint[i][1+P->Dimension]))
1402 fprintf(out, "FALSE");
1403 else if (value_pos_p(P->Constraint[i][v+1])) {
1404 print_term(out, P->Constraint[i][v+1], v, dim, nparam,
1405 iter_names, param_names, NULL);
1406 if (value_zero_p(P->Constraint[i][0]))
1407 fprintf(out, " = ");
1408 else
1409 fprintf(out, " >= ");
1410 for (j = v+1; j <= dim+nparam; ++j) {
1411 value_oppose(tmp, P->Constraint[i][1+j]);
1412 print_term(out, tmp, j, dim, nparam,
1413 iter_names, param_names, &first);
1414 }
1415 } else {
1416 value_oppose(tmp, P->Constraint[i][1+v]);
1417 print_term(out, tmp, v, dim, nparam,
1418 iter_names, param_names, NULL);
1419 fprintf(out, " <= ");
1420 for (j = v+1; j <= dim+nparam; ++j)
1421 print_term(out, P->Constraint[i][1+j], j, dim, nparam,
1422 iter_names, param_names, &first);
1423 }
1424 }
1425
1426 fprintf(out, " }\n");
1427
1428 value_clear(tmp);
1429 }
1430
1431 /* Construct a cone over P with P placed at x_d = 1, with
1432 * x_d the coordinate of an extra dimension
1433 *
1434 * It's probably a mistake to depend so much on the internal
1435 * representation. We should probably simply compute the
1436 * vertices/facets first.
1437 */
1438 Polyhedron *Cone_over_Polyhedron(Polyhedron *P)
1439 {
1440 unsigned NbConstraints = 0;
1441 unsigned NbRays = 0;
1442 Polyhedron *C;
1443 int i;
1444
1445 if (POL_HAS(P, POL_INEQUALITIES))
1446 NbConstraints = P->NbConstraints + 1;
1447 if (POL_HAS(P, POL_POINTS))
1448 NbRays = P->NbRays + 1;
1449
1450 C = Polyhedron_Alloc(P->Dimension+1, NbConstraints, NbRays);
1451 if (POL_HAS(P, POL_INEQUALITIES)) {
1452 C->NbEq = P->NbEq;
1453 for (i = 0; i < P->NbConstraints; ++i)
1454 Vector_Copy(P->Constraint[i], C->Constraint[i], P->Dimension+2);
1455 /* n >= 0 */
1456 value_set_si(C->Constraint[P->NbConstraints][0], 1);
1457 value_set_si(C->Constraint[P->NbConstraints][1+P->Dimension], 1);
1458 }
1459 if (POL_HAS(P, POL_POINTS)) {
1460 C->NbBid = P->NbBid;
1461 for (i = 0; i < P->NbRays; ++i)
1462 Vector_Copy(P->Ray[i], C->Ray[i], P->Dimension+2);
1463 /* vertex 0 */
1464 value_set_si(C->Ray[P->NbRays][0], 1);
1465 value_set_si(C->Ray[P->NbRays][1+C->Dimension], 1);
1466 }
1467 POL_SET(C, POL_VALID);
1468 if (POL_HAS(P, POL_INEQUALITIES))
1469 POL_SET(C, POL_INEQUALITIES);
1470 if (POL_HAS(P, POL_POINTS))
1471 POL_SET(C, POL_POINTS);
1472 if (POL_HAS(P, POL_VERTICES))
1473 POL_SET(C, POL_VERTICES);
1474 return C;
1475 }
1476
1477 /* Returns a (dim+nparam+1)x((dim-n)+nparam+1) matrix
1478 * mapping the transformed subspace back to the original space.
1479 * n is the number of equalities involving the variables
1480 * (i.e., not purely the parameters).
1481 * The remaining n coordinates in the transformed space would
1482 * have constant (parametric) values and are therefore not
1483 * included in the variables of the new space.
1484 */
1485 Matrix *compress_variables(Matrix *Equalities, unsigned nparam)
1486 {
1487 unsigned dim = (Equalities->NbColumns-2) - nparam;
1488 Matrix *M, *H, *Q, *U, *C, *ratH, *invH, *Ul, *T1, *T2, *T;
1489 Value mone;
1490 int n, i, j;
1491 int ok;
1492
1493 for (n = 0; n < Equalities->NbRows; ++n)
1494 if (First_Non_Zero(Equalities->p[n]+1, dim) == -1)
1495 break;
1496 if (n == 0)
1497 return Identity(dim+nparam+1);
1498 value_init(mone);
1499 value_set_si(mone, -1);
1500 M = Matrix_Alloc(n, dim);
1501 C = Matrix_Alloc(n+1, nparam+1);
1502 for (i = 0; i < n; ++i) {
1503 Vector_Copy(Equalities->p[i]+1, M->p[i], dim);
1504 Vector_Scale(Equalities->p[i]+1+dim, C->p[i], mone, nparam+1);
1505 }
1506 value_set_si(C->p[n][nparam], 1);
1507 left_hermite(M, &H, &Q, &U);
1508 Matrix_Free(M);
1509 Matrix_Free(Q);
1510 value_clear(mone);
1511
1512 ratH = Matrix_Alloc(n+1, n+1);
1513 invH = Matrix_Alloc(n+1, n+1);
1514 for (i = 0; i < n; ++i)
1515 Vector_Copy(H->p[i], ratH->p[i], n);
1516 value_set_si(ratH->p[n][n], 1);
1517 ok = Matrix_Inverse(ratH, invH);
1518 assert(ok);
1519 Matrix_Free(H);
1520 Matrix_Free(ratH);
1521 T1 = Matrix_Alloc(n+1, nparam+1);
1522 Matrix_Product(invH, C, T1);
1523 Matrix_Free(C);
1524 Matrix_Free(invH);
1525 if (value_notone_p(T1->p[n][nparam])) {
1526 for (i = 0; i < n; ++i) {
1527 if (!mpz_divisible_p(T1->p[i][nparam], T1->p[n][nparam])) {
1528 Matrix_Free(T1);
1529 Matrix_Free(U);
1530 return NULL;
1531 }
1532 /* compress_params should have taken care of this */
1533 for (j = 0; j < nparam; ++j)
1534 assert(mpz_divisible_p(T1->p[i][j], T1->p[n][nparam]));
1535 Vector_AntiScale(T1->p[i], T1->p[i], T1->p[n][nparam], nparam+1);
1536 }
1537 value_set_si(T1->p[n][nparam], 1);
1538 }
1539 Ul = Matrix_Alloc(dim+1, n+1);
1540 for (i = 0; i < dim; ++i)
1541 Vector_Copy(U->p[i], Ul->p[i], n);
1542 value_set_si(Ul->p[dim][n], 1);
1543 T2 = Matrix_Alloc(dim+1, nparam+1);
1544 Matrix_Product(Ul, T1, T2);
1545 Matrix_Free(Ul);
1546 Matrix_Free(T1);
1547
1548 T = Matrix_Alloc(dim+nparam+1, (dim-n)+nparam+1);
1549 for (i = 0; i < dim; ++i) {
1550 Vector_Copy(U->p[i]+n, T->p[i], dim-n);
1551 Vector_Copy(T2->p[i], T->p[i]+dim-n, nparam+1);
1552 }
1553 for (i = 0; i < nparam+1; ++i)
1554 value_set_si(T->p[dim+i][(dim-n)+i], 1);
1555 assert(value_one_p(T2->p[dim][nparam]));
1556 Matrix_Free(U);
1557 Matrix_Free(T2);
1558
1559 return T;
1560 }
1561
1562 /* Computes the left inverse of an affine embedding M and, if Eq is not NULL,
1563 * the equalities that define the affine subspace onto which M maps
1564 * its argument.
1565 */
1566 Matrix *left_inverse(Matrix *M, Matrix **Eq)
1567 {
1568 int i, ok;
1569 Matrix *L, *H, *Q, *U, *ratH, *invH, *Ut, *inv;
1570 Vector *t;
1571
1572 if (M->NbColumns == 1) {
1573 inv = Matrix_Alloc(1, M->NbRows);
1574 value_set_si(inv->p[0][M->NbRows-1], 1);
1575 if (Eq) {
1576 *Eq = Matrix_Alloc(M->NbRows-1, 1+(M->NbRows-1)+1);
1577 for (i = 0; i < M->NbRows-1; ++i) {
1578 value_oppose((*Eq)->p[i][1+i], M->p[M->NbRows-1][0]);
1579 value_assign((*Eq)->p[i][1+(M->NbRows-1)], M->p[i][0]);
1580 }
1581 }
1582 return inv;
1583 }
1584 if (Eq)
1585 *Eq = NULL;
1586 L = Matrix_Alloc(M->NbRows-1, M->NbColumns-1);
1587 for (i = 0; i < L->NbRows; ++i)
1588 Vector_Copy(M->p[i], L->p[i], L->NbColumns);
1589 right_hermite(L, &H, &U, &Q);
1590 Matrix_Free(L);
1591 Matrix_Free(Q);
1592 t = Vector_Alloc(U->NbColumns);
1593 for (i = 0; i < U->NbColumns; ++i)
1594 value_oppose(t->p[i], M->p[i][M->NbColumns-1]);
1595 if (Eq) {
1596 *Eq = Matrix_Alloc(H->NbRows - H->NbColumns, 2 + U->NbColumns);
1597 for (i = 0; i < H->NbRows - H->NbColumns; ++i) {
1598 Vector_Copy(U->p[H->NbColumns+i], (*Eq)->p[i]+1, U->NbColumns);
1599 Inner_Product(U->p[H->NbColumns+i], t->p, U->NbColumns,
1600 (*Eq)->p[i]+1+U->NbColumns);
1601 }
1602 }
1603 ratH = Matrix_Alloc(H->NbColumns+1, H->NbColumns+1);
1604 invH = Matrix_Alloc(H->NbColumns+1, H->NbColumns+1);
1605 for (i = 0; i < H->NbColumns; ++i)
1606 Vector_Copy(H->p[i], ratH->p[i], H->NbColumns);
1607 value_set_si(ratH->p[ratH->NbRows-1][ratH->NbColumns-1], 1);
1608 Matrix_Free(H);
1609 ok = Matrix_Inverse(ratH, invH);
1610 assert(ok);
1611 Matrix_Free(ratH);
1612 Ut = Matrix_Alloc(invH->NbRows, U->NbColumns+1);
1613 for (i = 0; i < Ut->NbRows-1; ++i) {
1614 Vector_Copy(U->p[i], Ut->p[i], U->NbColumns);
1615 Inner_Product(U->p[i], t->p, U->NbColumns, &Ut->p[i][Ut->NbColumns-1]);
1616 }
1617 Matrix_Free(U);
1618 Vector_Free(t);
1619 value_set_si(Ut->p[Ut->NbRows-1][Ut->NbColumns-1], 1);
1620 inv = Matrix_Alloc(invH->NbRows, Ut->NbColumns);
1621 Matrix_Product(invH, Ut, inv);
1622 Matrix_Free(Ut);
1623 Matrix_Free(invH);
1624 return inv;
1625 }
1626
1627 /* Check whether all rays are revlex positive in the parameters
1628 */
1629 int Polyhedron_has_revlex_positive_rays(Polyhedron *P, unsigned nparam)
1630 {
1631 int r;
1632 for (r = 0; r < P->NbRays; ++r) {
1633 int i;
1634 if (value_notzero_p(P->Ray[r][P->Dimension+1]))
1635 continue;
1636 for (i = P->Dimension-1; i >= P->Dimension-nparam; --i) {
1637 if (value_neg_p(P->Ray[r][i+1]))
1638 return 0;
1639 if (value_pos_p(P->Ray[r][i+1]))
1640 break;
1641 }
1642 /* A ray independent of the parameters */
1643 if (i < P->Dimension-nparam)
1644 return 0;
1645 }
1646 return 1;
1647 }
1648
1649 static Polyhedron *Recession_Cone(Polyhedron *P, unsigned nparam, unsigned MaxRays)
1650 {
1651 int i;
1652 unsigned nvar = P->Dimension - nparam;
1653 Matrix *M = Matrix_Alloc(P->NbConstraints, 1 + nvar + 1);
1654 Polyhedron *R;
1655 for (i = 0; i < P->NbConstraints; ++i)
1656 Vector_Copy(P->Constraint[i], M->p[i], 1+nvar);
1657 R = Constraints2Polyhedron(M, MaxRays);
1658 Matrix_Free(M);
1659 return R;
1660 }
1661
1662 int Polyhedron_is_unbounded(Polyhedron *P, unsigned nparam, unsigned MaxRays)
1663 {
1664 int i;
1665 int is_unbounded;
1666 Polyhedron *R = Recession_Cone(P, nparam, MaxRays);
1667 POL_ENSURE_VERTICES(R);
1668 if (R->NbBid == 0)
1669 for (i = 0; i < R->NbRays; ++i)
1670 if (value_zero_p(R->Ray[i][1+R->Dimension]))
1671 break;
1672 is_unbounded = R->NbBid > 0 || i < R->NbRays;
1673 Polyhedron_Free(R);
1674 return is_unbounded;
1675 }
1676
1677 void Vector_Oppose(Value *p1, Value *p2, unsigned len)
1678 {
1679 unsigned i;
1680
1681 for (i = 0; i < len; ++i)
1682 value_oppose(p2[i], p1[i]);
1683 }
1684
1685 /* perform transposition inline; assumes M is a square matrix */
1686 void Matrix_Transposition(Matrix *M)
1687 {
1688 int i, j;
1689
1690 assert(M->NbRows == M->NbColumns);
1691 for (i = 0; i < M->NbRows; ++i)
1692 for (j = i+1; j < M->NbColumns; ++j)
1693 value_swap(M->p[i][j], M->p[j][i]);
1694 }
lattice point enumeration library