8 #include <NTL/mat_ZZ.h>
10 #include <barvinok/util.h>
12 #include <polylib/polylibgmp.h>
13 #include <barvinok/evalue.h>
17 #include <barvinok/barvinok.h>
18 #include <barvinok/genfun.h>
29 using std::ostringstream
;
31 #define ALLOC(p) (((long *) (p))[0])
32 #define SIZE(p) (((long *) (p))[1])
33 #define DATA(p) ((mp_limb_t *) (((long *) (p)) + 2))
35 static void value2zz(Value v
, ZZ
& z
)
37 int sa
= v
[0]._mp_size
;
38 int abs_sa
= sa
< 0 ? -sa
: sa
;
40 _ntl_gsetlength(&z
.rep
, abs_sa
);
41 mp_limb_t
* adata
= DATA(z
.rep
);
42 for (int i
= 0; i
< abs_sa
; ++i
)
43 adata
[i
] = v
[0]._mp_d
[i
];
47 void zz2value(ZZ
& z
, Value
& v
)
55 int abs_sa
= sa
< 0 ? -sa
: sa
;
57 mp_limb_t
* adata
= DATA(z
.rep
);
58 _mpz_realloc(v
, abs_sa
);
59 for (int i
= 0; i
< abs_sa
; ++i
)
60 v
[0]._mp_d
[i
] = adata
[i
];
65 #define ALLOC(t,p) p = (t*)malloc(sizeof(*p))
68 * We just ignore the last column and row
69 * If the final element is not equal to one
70 * then the result will actually be a multiple of the input
72 static void matrix2zz(Matrix
*M
, mat_ZZ
& m
, unsigned nr
, unsigned nc
)
76 for (int i
= 0; i
< nr
; ++i
) {
77 // assert(value_one_p(M->p[i][M->NbColumns - 1]));
78 for (int j
= 0; j
< nc
; ++j
) {
79 value2zz(M
->p
[i
][j
], m
[i
][j
]);
84 static void values2zz(Value
*p
, vec_ZZ
& v
, int len
)
88 for (int i
= 0; i
< len
; ++i
) {
95 static void zz2values(vec_ZZ
& v
, Value
*p
)
97 for (int i
= 0; i
< v
.length(); ++i
)
101 static void rays(mat_ZZ
& r
, Polyhedron
*C
)
103 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
104 assert(C
->NbRays
- 1 == C
->Dimension
);
109 for (i
= 0, c
= 0; i
< dim
; ++i
)
110 if (value_zero_p(C
->Ray
[i
][dim
+1])) {
111 for (int j
= 0; j
< dim
; ++j
) {
112 value2zz(C
->Ray
[i
][j
+1], tmp
);
119 static Matrix
* rays(Polyhedron
*C
)
121 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
122 assert(C
->NbRays
- 1 == C
->Dimension
);
124 Matrix
*M
= Matrix_Alloc(dim
+1, dim
+1);
128 for (i
= 0, c
= 0; i
<= dim
&& c
< dim
; ++i
)
129 if (value_zero_p(C
->Ray
[i
][dim
+1])) {
130 Vector_Copy(C
->Ray
[i
] + 1, M
->p
[c
], dim
);
131 value_set_si(M
->p
[c
++][dim
], 0);
134 value_set_si(M
->p
[dim
][dim
], 1);
139 static Matrix
* rays2(Polyhedron
*C
)
141 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
142 assert(C
->NbRays
- 1 == C
->Dimension
);
144 Matrix
*M
= Matrix_Alloc(dim
, dim
);
148 for (i
= 0, c
= 0; i
<= dim
&& c
< dim
; ++i
)
149 if (value_zero_p(C
->Ray
[i
][dim
+1]))
150 Vector_Copy(C
->Ray
[i
] + 1, M
->p
[c
++], dim
);
157 * Returns the largest absolute value in the vector
159 static ZZ
max(vec_ZZ
& v
)
162 for (int i
= 1; i
< v
.length(); ++i
)
172 Rays
= Matrix_Copy(M
);
175 cone(Polyhedron
*C
) {
176 Cone
= Polyhedron_Copy(C
);
182 matrix2zz(Rays
, A
, Rays
->NbRows
- 1, Rays
->NbColumns
- 1);
183 det
= determinant(A
);
186 Vector
* short_vector(vec_ZZ
& lambda
) {
187 Matrix
*M
= Matrix_Copy(Rays
);
188 Matrix
*inv
= Matrix_Alloc(M
->NbRows
, M
->NbColumns
);
189 int ok
= Matrix_Inverse(M
, inv
);
196 matrix2zz(inv
, B
, inv
->NbRows
- 1, inv
->NbColumns
- 1);
197 long r
= LLL(det2
, B
, U
);
201 for (int i
= 1; i
< B
.NumRows(); ++i
) {
213 Vector
*z
= Vector_Alloc(U
[index
].length()+1);
215 zz2values(U
[index
], z
->p
);
216 value_set_si(z
->p
[U
[index
].length()], 0);
218 Polyhedron
*C
= poly();
220 for (i
= 0; i
< lambda
.length(); ++i
)
223 if (i
== lambda
.length()) {
226 value_set_si(tmp
, -1);
227 Vector_Scale(z
->p
, z
->p
, tmp
, z
->Size
-1);
234 Polyhedron_Free(Cone
);
240 Matrix
*M
= Matrix_Alloc(Rays
->NbRows
+1, Rays
->NbColumns
+1);
241 for (int i
= 0; i
< Rays
->NbRows
; ++i
) {
242 Vector_Copy(Rays
->p
[i
], M
->p
[i
]+1, Rays
->NbColumns
);
243 value_set_si(M
->p
[i
][0], 1);
245 Vector_Set(M
->p
[Rays
->NbRows
]+1, 0, Rays
->NbColumns
-1);
246 value_set_si(M
->p
[Rays
->NbRows
][0], 1);
247 value_set_si(M
->p
[Rays
->NbRows
][Rays
->NbColumns
], 1);
248 Cone
= Rays2Polyhedron(M
, M
->NbRows
+1);
249 assert(Cone
->NbConstraints
== Cone
->NbRays
);
263 dpoly(int d
, ZZ
& degree
, int offset
= 0) {
264 coeff
.SetLength(d
+1);
266 int min
= d
+ offset
;
267 if (degree
>= 0 && degree
< ZZ(INIT_VAL
, min
))
268 min
= to_int(degree
);
270 ZZ c
= ZZ(INIT_VAL
, 1);
273 for (int i
= 1; i
<= min
; ++i
) {
274 c
*= (degree
-i
+ 1);
279 void operator *= (dpoly
& f
) {
280 assert(coeff
.length() == f
.coeff
.length());
282 coeff
= f
.coeff
[0] * coeff
;
283 for (int i
= 1; i
< coeff
.length(); ++i
)
284 for (int j
= 0; i
+j
< coeff
.length(); ++j
)
285 coeff
[i
+j
] += f
.coeff
[i
] * old
[j
];
287 void div(dpoly
& d
, mpq_t count
, ZZ
& sign
) {
288 int len
= coeff
.length();
291 mpq_t
* c
= new mpq_t
[coeff
.length()];
294 for (int i
= 0; i
< len
; ++i
) {
296 zz2value(coeff
[i
], tmp
);
297 mpq_set_z(c
[i
], tmp
);
299 for (int j
= 1; j
<= i
; ++j
) {
300 zz2value(d
.coeff
[j
], tmp
);
301 mpq_set_z(qtmp
, tmp
);
302 mpq_mul(qtmp
, qtmp
, c
[i
-j
]);
303 mpq_sub(c
[i
], c
[i
], qtmp
);
306 zz2value(d
.coeff
[0], tmp
);
307 mpq_set_z(qtmp
, tmp
);
308 mpq_div(c
[i
], c
[i
], qtmp
);
311 mpq_sub(count
, count
, c
[len
-1]);
313 mpq_add(count
, count
, c
[len
-1]);
317 for (int i
= 0; i
< len
; ++i
)
329 dpoly_n(int d
, ZZ
& degree_0
, ZZ
& degree_1
, int offset
= 0) {
333 zz2value(degree_0
, d0
);
334 zz2value(degree_1
, d1
);
335 coeff
= Matrix_Alloc(d
+1, d
+1+1);
336 value_set_si(coeff
->p
[0][0], 1);
337 value_set_si(coeff
->p
[0][d
+1], 1);
338 for (int i
= 1; i
<= d
; ++i
) {
339 value_multiply(coeff
->p
[i
][0], coeff
->p
[i
-1][0], d0
);
340 Vector_Combine(coeff
->p
[i
-1], coeff
->p
[i
-1]+1, coeff
->p
[i
]+1,
342 value_set_si(coeff
->p
[i
][d
+1], i
);
343 value_multiply(coeff
->p
[i
][d
+1], coeff
->p
[i
][d
+1], coeff
->p
[i
-1][d
+1]);
344 value_decrement(d0
, d0
);
349 void div(dpoly
& d
, Vector
*count
, ZZ
& sign
) {
350 int len
= coeff
->NbRows
;
351 Matrix
* c
= Matrix_Alloc(coeff
->NbRows
, coeff
->NbColumns
);
354 for (int i
= 0; i
< len
; ++i
) {
355 Vector_Copy(coeff
->p
[i
], c
->p
[i
], len
+1);
356 for (int j
= 1; j
<= i
; ++j
) {
357 zz2value(d
.coeff
[j
], tmp
);
358 value_multiply(tmp
, tmp
, c
->p
[i
][len
]);
359 value_oppose(tmp
, tmp
);
360 Vector_Combine(c
->p
[i
], c
->p
[i
-j
], c
->p
[i
],
361 c
->p
[i
-j
][len
], tmp
, len
);
362 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], c
->p
[i
-j
][len
]);
364 zz2value(d
.coeff
[0], tmp
);
365 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], tmp
);
368 value_set_si(tmp
, -1);
369 Vector_Scale(c
->p
[len
-1], count
->p
, tmp
, len
);
370 value_assign(count
->p
[len
], c
->p
[len
-1][len
]);
372 Vector_Copy(c
->p
[len
-1], count
->p
, len
+1);
373 Vector_Normalize(count
->p
, len
+1);
379 struct dpoly_r_term
{
384 /* len: number of elements in c
385 * each element in c is the coefficient of a power of t
386 * in the MacLaurin expansion
389 vector
< dpoly_r_term
* > *c
;
394 void add_term(int i
, int * powers
, ZZ
& coeff
) {
397 for (int k
= 0; k
< c
[i
].size(); ++k
) {
398 if (memcmp(c
[i
][k
]->powers
, powers
, dim
* sizeof(int)) == 0) {
399 c
[i
][k
]->coeff
+= coeff
;
403 dpoly_r_term
*t
= new dpoly_r_term
;
404 t
->powers
= new int[dim
];
405 memcpy(t
->powers
, powers
, dim
* sizeof(int));
409 dpoly_r(int len
, int dim
) {
413 c
= new vector
< dpoly_r_term
* > [len
];
415 dpoly_r(dpoly
& num
, int dim
) {
417 len
= num
.coeff
.length();
418 c
= new vector
< dpoly_r_term
* > [len
];
421 memset(powers
, 0, dim
* sizeof(int));
423 for (int i
= 0; i
< len
; ++i
) {
424 ZZ coeff
= num
.coeff
[i
];
425 add_term(i
, powers
, coeff
);
428 dpoly_r(dpoly
& num
, dpoly
& den
, int pos
, int dim
) {
430 len
= num
.coeff
.length();
431 c
= new vector
< dpoly_r_term
* > [len
];
435 for (int i
= 0; i
< len
; ++i
) {
436 ZZ coeff
= num
.coeff
[i
];
437 memset(powers
, 0, dim
* sizeof(int));
440 add_term(i
, powers
, coeff
);
442 for (int j
= 1; j
<= i
; ++j
) {
443 for (int k
= 0; k
< c
[i
-j
].size(); ++k
) {
444 memcpy(powers
, c
[i
-j
][k
]->powers
, dim
*sizeof(int));
446 coeff
= -den
.coeff
[j
-1] * c
[i
-j
][k
]->coeff
;
447 add_term(i
, powers
, coeff
);
453 dpoly_r(dpoly_r
* num
, dpoly
& den
, int pos
, int dim
) {
456 c
= new vector
< dpoly_r_term
* > [len
];
461 for (int i
= 0 ; i
< len
; ++i
) {
462 for (int k
= 0; k
< num
->c
[i
].size(); ++k
) {
463 memcpy(powers
, num
->c
[i
][k
]->powers
, dim
*sizeof(int));
465 add_term(i
, powers
, num
->c
[i
][k
]->coeff
);
468 for (int j
= 1; j
<= i
; ++j
) {
469 for (int k
= 0; k
< c
[i
-j
].size(); ++k
) {
470 memcpy(powers
, c
[i
-j
][k
]->powers
, dim
*sizeof(int));
472 coeff
= -den
.coeff
[j
-1] * c
[i
-j
][k
]->coeff
;
473 add_term(i
, powers
, coeff
);
479 for (int i
= 0 ; i
< len
; ++i
)
480 for (int k
= 0; k
< c
[i
].size(); ++k
) {
481 delete [] c
[i
][k
]->powers
;
486 dpoly_r
*div(dpoly
& d
) {
487 dpoly_r
*rc
= new dpoly_r(len
, dim
);
488 rc
->denom
= power(d
.coeff
[0], len
);
489 ZZ inv_d
= rc
->denom
/ d
.coeff
[0];
492 for (int i
= 0; i
< len
; ++i
) {
493 for (int k
= 0; k
< c
[i
].size(); ++k
) {
494 coeff
= c
[i
][k
]->coeff
* inv_d
;
495 rc
->add_term(i
, c
[i
][k
]->powers
, coeff
);
498 for (int j
= 1; j
<= i
; ++j
) {
499 for (int k
= 0; k
< rc
->c
[i
-j
].size(); ++k
) {
500 coeff
= - d
.coeff
[j
] * rc
->c
[i
-j
][k
]->coeff
/ d
.coeff
[0];
501 rc
->add_term(i
, rc
->c
[i
-j
][k
]->powers
, coeff
);
508 for (int i
= 0; i
< len
; ++i
) {
511 cerr
<< c
[i
].size() << endl
;
512 for (int j
= 0; j
< c
[i
].size(); ++j
) {
513 for (int k
= 0; k
< dim
; ++k
) {
514 cerr
<< c
[i
][j
]->powers
[k
] << " ";
516 cerr
<< ": " << c
[i
][j
]->coeff
<< "/" << denom
<< endl
;
524 void decompose(Polyhedron
*C
);
525 virtual void handle(Polyhedron
*P
, int sign
) = 0;
528 struct polar_decomposer
: public decomposer
{
529 void decompose(Polyhedron
*C
, unsigned MaxRays
);
530 virtual void handle(Polyhedron
*P
, int sign
);
531 virtual void handle_polar(Polyhedron
*P
, int sign
) = 0;
534 void decomposer::decompose(Polyhedron
*C
)
536 vector
<cone
*> nonuni
;
537 cone
* c
= new cone(C
);
553 while (!nonuni
.empty()) {
556 Vector
* v
= c
->short_vector(lambda
);
557 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
560 Matrix
* M
= Matrix_Copy(c
->Rays
);
561 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
562 cone
* pc
= new cone(M
);
563 assert (pc
->det
!= 0);
564 if (abs(pc
->det
) > 1) {
565 assert(abs(pc
->det
) < abs(c
->det
));
566 nonuni
.push_back(pc
);
569 handle(pc
->poly(), sign(pc
->det
) * s
);
574 while (!nonuni
.empty()) {
591 void polar_decomposer::decompose(Polyhedron
*cone
, unsigned MaxRays
)
593 Polyhedron_Polarize(cone
);
594 if (cone
->NbRays
- 1 != cone
->Dimension
) {
595 Polyhedron
*tmp
= cone
;
596 cone
= triangulate_cone(cone
, MaxRays
);
597 Polyhedron_Free(tmp
);
600 for (Polyhedron
*Polar
= cone
; Polar
; Polar
= Polar
->next
)
601 decomposer::decompose(Polar
);
609 void polar_decomposer::handle(Polyhedron
*P
, int sign
)
611 Polyhedron_Polarize(P
);
612 handle_polar(P
, sign
);
616 * Barvinok's Decomposition of a simplicial cone
618 * Returns two lists of polyhedra
620 void barvinok_decompose(Polyhedron
*C
, Polyhedron
**ppos
, Polyhedron
**pneg
)
622 Polyhedron
*pos
= *ppos
, *neg
= *pneg
;
623 vector
<cone
*> nonuni
;
624 cone
* c
= new cone(C
);
631 Polyhedron
*p
= Polyhedron_Copy(c
->Cone
);
637 while (!nonuni
.empty()) {
640 Vector
* v
= c
->short_vector(lambda
);
641 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
644 Matrix
* M
= Matrix_Copy(c
->Rays
);
645 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
646 cone
* pc
= new cone(M
);
647 assert (pc
->det
!= 0);
648 if (abs(pc
->det
) > 1) {
649 assert(abs(pc
->det
) < abs(c
->det
));
650 nonuni
.push_back(pc
);
652 Polyhedron
*p
= pc
->poly();
654 if (sign(pc
->det
) == s
) {
672 const int MAX_TRY
=10;
674 * Searches for a vector that is not orthogonal to any
675 * of the rays in rays.
677 static void nonorthog(mat_ZZ
& rays
, vec_ZZ
& lambda
)
679 int dim
= rays
.NumCols();
681 lambda
.SetLength(dim
);
685 for (int i
= 2; !found
&& i
<= 50*dim
; i
+=4) {
686 for (int j
= 0; j
< MAX_TRY
; ++j
) {
687 for (int k
= 0; k
< dim
; ++k
) {
688 int r
= random_int(i
)+2;
689 int v
= (2*(r
%2)-1) * (r
>> 1);
693 for (; k
< rays
.NumRows(); ++k
)
694 if (lambda
* rays
[k
] == 0)
696 if (k
== rays
.NumRows()) {
705 static void randomvector(Polyhedron
*P
, vec_ZZ
& lambda
, int nvar
)
709 unsigned int dim
= P
->Dimension
;
712 for (int i
= 0; i
< P
->NbRays
; ++i
) {
713 for (int j
= 1; j
<= dim
; ++j
) {
714 value_absolute(tmp
, P
->Ray
[i
][j
]);
715 int t
= VALUE_TO_LONG(tmp
) * 16;
720 for (int i
= 0; i
< P
->NbConstraints
; ++i
) {
721 for (int j
= 1; j
<= dim
; ++j
) {
722 value_absolute(tmp
, P
->Constraint
[i
][j
]);
723 int t
= VALUE_TO_LONG(tmp
) * 16;
730 lambda
.SetLength(nvar
);
731 for (int k
= 0; k
< nvar
; ++k
) {
732 int r
= random_int(max
*dim
)+2;
733 int v
= (2*(r
%2)-1) * (max
/2*dim
+ (r
>> 1));
738 static void add_rays(mat_ZZ
& rays
, Polyhedron
*i
, int *r
, int nvar
= -1,
741 unsigned dim
= i
->Dimension
;
744 for (int k
= 0; k
< i
->NbRays
; ++k
) {
745 if (!value_zero_p(i
->Ray
[k
][dim
+1]))
747 if (!all
&& nvar
!= dim
&& First_Non_Zero(i
->Ray
[k
]+1, nvar
) == -1)
749 values2zz(i
->Ray
[k
]+1, rays
[(*r
)++], nvar
);
753 void lattice_point(Value
* values
, Polyhedron
*i
, vec_ZZ
& vertex
)
755 unsigned dim
= i
->Dimension
;
756 if(!value_one_p(values
[dim
])) {
757 Matrix
* Rays
= rays(i
);
758 Matrix
*inv
= Matrix_Alloc(Rays
->NbRows
, Rays
->NbColumns
);
759 int ok
= Matrix_Inverse(Rays
, inv
);
763 Vector
*lambda
= Vector_Alloc(dim
+1);
764 Vector_Matrix_Product(values
, inv
, lambda
->p
);
766 for (int j
= 0; j
< dim
; ++j
)
767 mpz_cdiv_q(lambda
->p
[j
], lambda
->p
[j
], lambda
->p
[dim
]);
768 value_set_si(lambda
->p
[dim
], 1);
769 Vector
*A
= Vector_Alloc(dim
+1);
770 Vector_Matrix_Product(lambda
->p
, Rays
, A
->p
);
773 values2zz(A
->p
, vertex
, dim
);
776 values2zz(values
, vertex
, dim
);
779 static evalue
*term(int param
, ZZ
& c
, Value
*den
= NULL
)
781 evalue
*EP
= new evalue();
783 value_set_si(EP
->d
,0);
784 EP
->x
.p
= new_enode(polynomial
, 2, param
+ 1);
785 evalue_set_si(&EP
->x
.p
->arr
[0], 0, 1);
786 value_init(EP
->x
.p
->arr
[1].x
.n
);
788 value_set_si(EP
->x
.p
->arr
[1].d
, 1);
790 value_assign(EP
->x
.p
->arr
[1].d
, *den
);
791 zz2value(c
, EP
->x
.p
->arr
[1].x
.n
);
795 static void vertex_period(
796 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*T
,
797 Value lcm
, int p
, Vector
*val
,
798 evalue
*E
, evalue
* ev
,
801 unsigned nparam
= T
->NbRows
- 1;
802 unsigned dim
= i
->Dimension
;
809 Vector
* values
= Vector_Alloc(dim
+ 1);
810 Vector_Matrix_Product(val
->p
, T
, values
->p
);
811 value_assign(values
->p
[dim
], lcm
);
812 lattice_point(values
->p
, i
, vertex
);
813 num
= vertex
* lambda
;
818 zz2value(num
, ev
->x
.n
);
819 value_assign(ev
->d
, lcm
);
826 values2zz(T
->p
[p
], vertex
, dim
);
827 nump
= vertex
* lambda
;
828 if (First_Non_Zero(val
->p
, p
) == -1) {
829 value_assign(tmp
, lcm
);
830 evalue
*ET
= term(p
, nump
, &tmp
);
832 free_evalue_refs(ET
);
836 value_assign(tmp
, lcm
);
837 if (First_Non_Zero(T
->p
[p
], dim
) != -1)
838 Vector_Gcd(T
->p
[p
], dim
, &tmp
);
840 if (value_lt(tmp
, lcm
)) {
843 value_division(tmp
, lcm
, tmp
);
844 value_set_si(ev
->d
, 0);
845 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
846 value2zz(tmp
, count
);
848 value_decrement(tmp
, tmp
);
850 ZZ new_offset
= offset
- count
* nump
;
851 value_assign(val
->p
[p
], tmp
);
852 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
,
853 &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)], new_offset
);
854 } while (value_pos_p(tmp
));
856 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
, ev
, offset
);
860 static void mask_r(Matrix
*f
, int nr
, Vector
*lcm
, int p
, Vector
*val
, evalue
*ev
)
862 unsigned nparam
= lcm
->Size
;
865 Vector
* prod
= Vector_Alloc(f
->NbRows
);
866 Matrix_Vector_Product(f
, val
->p
, prod
->p
);
868 for (int i
= 0; i
< nr
; ++i
) {
869 value_modulus(prod
->p
[i
], prod
->p
[i
], f
->p
[i
][nparam
+1]);
870 isint
&= value_zero_p(prod
->p
[i
]);
872 value_set_si(ev
->d
, 1);
874 value_set_si(ev
->x
.n
, isint
);
881 if (value_one_p(lcm
->p
[p
]))
882 mask_r(f
, nr
, lcm
, p
+1, val
, ev
);
884 value_assign(tmp
, lcm
->p
[p
]);
885 value_set_si(ev
->d
, 0);
886 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
888 value_decrement(tmp
, tmp
);
889 value_assign(val
->p
[p
], tmp
);
890 mask_r(f
, nr
, lcm
, p
+1, val
, &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)]);
891 } while (value_pos_p(tmp
));
896 static evalue
*multi_monom(vec_ZZ
& p
)
898 evalue
*X
= new evalue();
901 unsigned nparam
= p
.length()-1;
902 zz2value(p
[nparam
], X
->x
.n
);
903 value_set_si(X
->d
, 1);
904 for (int i
= 0; i
< nparam
; ++i
) {
907 evalue
*T
= term(i
, p
[i
]);
916 * Check whether mapping polyhedron P on the affine combination
917 * num yields a range that has a fixed quotient on integer
919 * If zero is true, then we are only interested in the quotient
920 * for the cases where the remainder is zero.
921 * Returns NULL if false and a newly allocated value if true.
923 static Value
*fixed_quotient(Polyhedron
*P
, vec_ZZ
& num
, Value d
, bool zero
)
926 int len
= num
.length();
927 Matrix
*T
= Matrix_Alloc(2, len
);
928 zz2values(num
, T
->p
[0]);
929 value_set_si(T
->p
[1][len
-1], 1);
930 Polyhedron
*I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
934 for (i
= 0; i
< I
->NbRays
; ++i
)
935 if (value_zero_p(I
->Ray
[i
][2])) {
943 int bounded
= line_minmax(I
, &min
, &max
);
947 mpz_cdiv_q(min
, min
, d
);
949 mpz_fdiv_q(min
, min
, d
);
950 mpz_fdiv_q(max
, max
, d
);
952 if (value_eq(min
, max
)) {
955 value_assign(*ret
, min
);
963 * Normalize linear expression coef modulo m
964 * Removes common factor and reduces coefficients
965 * Returns index of first non-zero coefficient or len
967 static int normal_mod(Value
*coef
, int len
, Value
*m
)
972 Vector_Gcd(coef
, len
, &gcd
);
974 Vector_AntiScale(coef
, coef
, gcd
, len
);
976 value_division(*m
, *m
, gcd
);
983 for (j
= 0; j
< len
; ++j
)
984 mpz_fdiv_r(coef
[j
], coef
[j
], *m
);
985 for (j
= 0; j
< len
; ++j
)
986 if (value_notzero_p(coef
[j
]))
993 static void mask(Matrix
*f
, evalue
*factor
)
995 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
998 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
999 if (value_notone_p(f
->p
[n
][nc
-1]) &&
1000 value_notmone_p(f
->p
[n
][nc
-1]))
1014 value_set_si(EV
.x
.n
, 1);
1016 for (n
= 0; n
< nr
; ++n
) {
1017 value_assign(m
, f
->p
[n
][nc
-1]);
1018 if (value_one_p(m
) || value_mone_p(m
))
1021 int j
= normal_mod(f
->p
[n
], nc
-1, &m
);
1023 free_evalue_refs(factor
);
1024 value_init(factor
->d
);
1025 evalue_set_si(factor
, 0, 1);
1029 values2zz(f
->p
[n
], row
, nc
-1);
1032 if (j
< (nc
-1)-1 && row
[j
] > g
/2) {
1033 for (int k
= j
; k
< (nc
-1); ++k
)
1035 row
[k
] = g
- row
[k
];
1039 value_set_si(EP
.d
, 0);
1040 EP
.x
.p
= new_enode(relation
, 2, 0);
1041 value_clear(EP
.x
.p
->arr
[1].d
);
1042 EP
.x
.p
->arr
[1] = *factor
;
1043 evalue
*ev
= &EP
.x
.p
->arr
[0];
1044 value_set_si(ev
->d
, 0);
1045 ev
->x
.p
= new_enode(fractional
, 3, -1);
1046 evalue_set_si(&ev
->x
.p
->arr
[1], 0, 1);
1047 evalue_set_si(&ev
->x
.p
->arr
[2], 1, 1);
1048 evalue
*E
= multi_monom(row
);
1049 value_assign(EV
.d
, m
);
1051 value_clear(ev
->x
.p
->arr
[0].d
);
1052 ev
->x
.p
->arr
[0] = *E
;
1058 free_evalue_refs(&EV
);
1064 static void mask(Matrix
*f
, evalue
*factor
)
1066 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
1069 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
1070 if (value_notone_p(f
->p
[n
][nc
-1]) &&
1071 value_notmone_p(f
->p
[n
][nc
-1]))
1079 unsigned np
= nc
- 2;
1080 Vector
*lcm
= Vector_Alloc(np
);
1081 Vector
*val
= Vector_Alloc(nc
);
1082 Vector_Set(val
->p
, 0, nc
);
1083 value_set_si(val
->p
[np
], 1);
1084 Vector_Set(lcm
->p
, 1, np
);
1085 for (n
= 0; n
< nr
; ++n
) {
1086 if (value_one_p(f
->p
[n
][nc
-1]) ||
1087 value_mone_p(f
->p
[n
][nc
-1]))
1089 for (int j
= 0; j
< np
; ++j
)
1090 if (value_notzero_p(f
->p
[n
][j
])) {
1091 Gcd(f
->p
[n
][j
], f
->p
[n
][nc
-1], &tmp
);
1092 value_division(tmp
, f
->p
[n
][nc
-1], tmp
);
1093 value_lcm(tmp
, lcm
->p
[j
], &lcm
->p
[j
]);
1098 mask_r(f
, nr
, lcm
, 0, val
, &EP
);
1103 free_evalue_refs(&EP
);
1114 static bool mod_needed(Polyhedron
*PD
, vec_ZZ
& num
, Value d
, evalue
*E
)
1116 Value
*q
= fixed_quotient(PD
, num
, d
, false);
1121 value_oppose(*q
, *q
);
1124 value_set_si(EV
.d
, 1);
1126 value_multiply(EV
.x
.n
, *q
, d
);
1128 free_evalue_refs(&EV
);
1134 /* modifies f argument ! */
1135 static void ceil_mod(Value
*coef
, int len
, Value d
, ZZ
& f
, evalue
*EP
, Polyhedron
*PD
)
1139 value_set_si(m
, -1);
1141 Vector_Scale(coef
, coef
, m
, len
);
1144 int j
= normal_mod(coef
, len
, &m
);
1152 values2zz(coef
, num
, len
);
1159 evalue_set_si(&tmp
, 0, 1);
1163 while (j
< len
-1 && (num
[j
] == g
/2 || num
[j
] == 0))
1165 if ((j
< len
-1 && num
[j
] > g
/2) || (j
== len
-1 && num
[j
] >= (g
+1)/2)) {
1166 for (int k
= j
; k
< len
-1; ++k
)
1168 num
[k
] = g
- num
[k
];
1169 num
[len
-1] = g
- 1 - num
[len
-1];
1170 value_assign(tmp
.d
, m
);
1172 zz2value(t
, tmp
.x
.n
);
1178 ZZ t
= num
[len
-1] * f
;
1179 zz2value(t
, tmp
.x
.n
);
1180 value_assign(tmp
.d
, m
);
1183 evalue
*E
= multi_monom(num
);
1187 if (PD
&& !mod_needed(PD
, num
, m
, E
)) {
1189 zz2value(f
, EV
.x
.n
);
1190 value_assign(EV
.d
, m
);
1195 value_set_si(EV
.x
.n
, 1);
1196 value_assign(EV
.d
, m
);
1198 value_clear(EV
.x
.n
);
1199 value_set_si(EV
.d
, 0);
1200 EV
.x
.p
= new_enode(fractional
, 3, -1);
1201 evalue_copy(&EV
.x
.p
->arr
[0], E
);
1202 evalue_set_si(&EV
.x
.p
->arr
[1], 0, 1);
1203 value_init(EV
.x
.p
->arr
[2].x
.n
);
1204 zz2value(f
, EV
.x
.p
->arr
[2].x
.n
);
1205 value_set_si(EV
.x
.p
->arr
[2].d
, 1);
1210 free_evalue_refs(&EV
);
1211 free_evalue_refs(E
);
1215 free_evalue_refs(&tmp
);
1222 static void ceil(Value
*coef
, int len
, Value d
, ZZ
& f
,
1223 evalue
*EP
, Polyhedron
*PD
) {
1224 ceil_mod(coef
, len
, d
, f
, EP
, PD
);
1227 static void ceil(Value
*coef
, int len
, Value d
, ZZ
& f
,
1228 evalue
*EP
, Polyhedron
*PD
) {
1229 ceil_mod(coef
, len
, d
, f
, EP
, PD
);
1230 evalue_mod2table(EP
, len
-1);
1234 evalue
* bv_ceil3(Value
*coef
, int len
, Value d
, Polyhedron
*P
)
1236 Vector
*val
= Vector_Alloc(len
);
1240 value_set_si(t
, -1);
1241 Vector_Scale(coef
, val
->p
, t
, len
);
1242 value_absolute(t
, d
);
1245 values2zz(val
->p
, num
, len
);
1246 evalue
*EP
= multi_monom(num
);
1250 value_init(tmp
.x
.n
);
1251 value_set_si(tmp
.x
.n
, 1);
1252 value_assign(tmp
.d
, t
);
1258 ceil_mod(val
->p
, len
, t
, one
, EP
, P
);
1261 /* copy EP to malloc'ed evalue */
1267 free_evalue_refs(&tmp
);
1274 evalue
* lattice_point(
1275 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1277 unsigned nparam
= W
->NbColumns
- 1;
1279 Matrix
* Rays
= rays2(i
);
1280 Matrix
*T
= Transpose(Rays
);
1281 Matrix
*T2
= Matrix_Copy(T
);
1282 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
1283 int ok
= Matrix_Inverse(T2
, inv
);
1288 matrix2zz(W
, vertex
, W
->NbRows
, W
->NbColumns
);
1291 num
= lambda
* vertex
;
1293 evalue
*EP
= multi_monom(num
);
1297 value_init(tmp
.x
.n
);
1298 value_set_si(tmp
.x
.n
, 1);
1299 value_assign(tmp
.d
, lcm
);
1303 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, W
->NbColumns
);
1304 Matrix_Product(inv
, W
, L
);
1307 matrix2zz(T
, RT
, T
->NbRows
, T
->NbColumns
);
1310 vec_ZZ p
= lambda
* RT
;
1312 for (int i
= 0; i
< L
->NbRows
; ++i
) {
1313 ceil_mod(L
->p
[i
], nparam
+1, lcm
, p
[i
], EP
, PD
);
1319 free_evalue_refs(&tmp
);
1323 evalue
* lattice_point(
1324 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1326 Matrix
*T
= Transpose(W
);
1327 unsigned nparam
= T
->NbRows
- 1;
1329 evalue
*EP
= new evalue();
1331 evalue_set_si(EP
, 0, 1);
1334 Vector
*val
= Vector_Alloc(nparam
+1);
1335 value_set_si(val
->p
[nparam
], 1);
1336 ZZ
offset(INIT_VAL
, 0);
1338 vertex_period(i
, lambda
, T
, lcm
, 0, val
, EP
, &ev
, offset
);
1341 free_evalue_refs(&ev
);
1352 Param_Vertices
* V
, Polyhedron
*i
, vec_ZZ
& lambda
, term_info
* term
,
1355 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
1356 unsigned dim
= i
->Dimension
;
1358 vertex
.SetDims(V
->Vertex
->NbRows
, nparam
+1);
1362 value_set_si(lcm
, 1);
1363 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
1364 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
1366 if (value_notone_p(lcm
)) {
1367 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
1368 for (int j
= 0 ; j
< dim
; ++j
) {
1369 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
1370 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
1373 term
->E
= lattice_point(i
, lambda
, mv
, lcm
, PD
);
1381 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
1382 assert(value_one_p(V
->Vertex
->p
[i
][nparam
+1])); // for now
1383 values2zz(V
->Vertex
->p
[i
], vertex
[i
], nparam
+1);
1387 num
= lambda
* vertex
;
1391 for (int j
= 0; j
< nparam
; ++j
)
1397 term
->E
= multi_monom(num
);
1401 term
->constant
= num
[nparam
];
1404 term
->coeff
= num
[p
];
1411 static void normalize(ZZ
& sign
, ZZ
& num
, vec_ZZ
& den
)
1413 unsigned dim
= den
.length();
1417 for (int j
= 0; j
< den
.length(); ++j
) {
1421 den
[j
] = abs(den
[j
]);
1430 * f: the powers in the denominator for the remaining vars
1431 * each row refers to a factor
1432 * den_s: for each factor, the power of (s+1)
1434 * num_s: powers in the numerator corresponding to the summed vars
1435 * num_p: powers in the numerator corresponding to the remaining vars
1436 * number of rays in cone: "dim" = "k"
1437 * length of each ray: "dim" = "d"
1438 * for now, it is assumed: k == d
1440 * den_p: for each factor
1441 * 0: independent of remaining vars
1442 * 1: power corresponds to corresponding row in f
1444 * all inputs are subject to change
1446 static void normalize(ZZ
& sign
,
1447 ZZ
& num_s
, vec_ZZ
& num_p
, vec_ZZ
& den_s
, vec_ZZ
& den_p
,
1450 unsigned dim
= f
.NumRows();
1451 unsigned nparam
= num_p
.length();
1452 unsigned nvar
= dim
- nparam
;
1456 for (int j
= 0; j
< den_s
.length(); ++j
) {
1457 if (den_s
[j
] == 0) {
1462 for (k
= 0; k
< nparam
; ++k
)
1476 den_s
[j
] = abs(den_s
[j
]);
1485 struct counter
: public polar_decomposer
{
1497 counter(Polyhedron
*P
) {
1500 rays
.SetDims(dim
, dim
);
1505 void start(unsigned MaxRays
);
1511 virtual void handle_polar(Polyhedron
*P
, int sign
);
1514 struct OrthogonalException
{} Orthogonal
;
1516 void counter::handle_polar(Polyhedron
*C
, int s
)
1519 assert(C
->NbRays
-1 == dim
);
1520 add_rays(rays
, C
, &r
);
1521 for (int k
= 0; k
< dim
; ++k
) {
1522 if (lambda
* rays
[k
] == 0)
1528 lattice_point(P
->Ray
[j
]+1, C
, vertex
);
1529 num
= vertex
* lambda
;
1530 den
= rays
* lambda
;
1531 normalize(sign
, num
, den
);
1534 dpoly
n(dim
, den
[0], 1);
1535 for (int k
= 1; k
< dim
; ++k
) {
1536 dpoly
fact(dim
, den
[k
], 1);
1539 d
.div(n
, count
, sign
);
1542 void counter::start(unsigned MaxRays
)
1546 randomvector(P
, lambda
, dim
);
1547 for (j
= 0; j
< P
->NbRays
; ++j
) {
1548 Polyhedron
*C
= supporting_cone(P
, j
);
1549 decompose(C
, MaxRays
);
1552 } catch (OrthogonalException
&e
) {
1553 mpq_set_si(count
, 0, 0);
1558 /* base for non-parametric counting */
1559 struct np_base
: public polar_decomposer
{
1564 np_base(Polyhedron
*P
, unsigned dim
) {
1570 struct reducer
: public np_base
{
1579 int lower
; // call base when only this many variables is left
1581 reducer(Polyhedron
*P
) : np_base(P
, P
->Dimension
) {
1582 //den.SetLength(dim);
1589 void start(unsigned MaxRays
);
1597 virtual void handle_polar(Polyhedron
*P
, int sign
);
1598 void reduce(ZZ c
, ZZ cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1599 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
) = 0;
1600 virtual void split(vec_ZZ
& num
, ZZ
& num_s
, vec_ZZ
& num_p
,
1601 mat_ZZ
& den_f
, vec_ZZ
& den_s
, mat_ZZ
& den_r
) = 0;
1604 void reducer::reduce(ZZ c
, ZZ cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1606 unsigned len
= den_f
.NumRows(); // number of factors in den
1608 if (num
.length() == lower
) {
1609 base(c
, cd
, num
, den_f
);
1612 assert(num
.length() > 1);
1619 split(num
, num_s
, num_p
, den_f
, den_s
, den_r
);
1622 den_p
.SetLength(len
);
1624 normalize(c
, num_s
, num_p
, den_s
, den_p
, den_r
);
1626 int only_param
= 0; // k-r-s from text
1627 int no_param
= 0; // r from text
1628 for (int k
= 0; k
< len
; ++k
) {
1631 else if (den_s
[k
] == 0)
1634 if (no_param
== 0) {
1635 reduce(c
, cd
, num_p
, den_r
);
1639 pden
.SetDims(only_param
, den_r
.NumCols());
1641 for (k
= 0, l
= 0; k
< len
; ++k
)
1643 pden
[l
++] = den_r
[k
];
1645 for (k
= 0; k
< len
; ++k
)
1649 dpoly
n(no_param
, num_s
);
1650 dpoly
D(no_param
, den_s
[k
], 1);
1651 for ( ; ++k
< len
; )
1652 if (den_p
[k
] == 0) {
1653 dpoly
fact(no_param
, den_s
[k
], 1);
1657 if (no_param
+ only_param
== len
) {
1658 mpq_set_si(tcount
, 0, 1);
1659 n
.div(D
, tcount
, one
);
1662 value2zz(mpq_numref(tcount
), qn
);
1663 value2zz(mpq_denref(tcount
), qd
);
1669 reduce(qn
, qd
, num_p
, pden
);
1673 for (k
= 0; k
< len
; ++k
) {
1674 if (den_s
[k
] == 0 || den_p
[k
] == 0)
1677 dpoly
pd(no_param
-1, den_s
[k
], 1);
1680 for (l
= 0; l
< k
; ++l
)
1681 if (den_r
[l
] == den_r
[k
])
1685 r
= new dpoly_r(n
, pd
, l
, len
);
1687 dpoly_r
*nr
= new dpoly_r(r
, pd
, l
, len
);
1693 dpoly_r
*rc
= r
->div(D
);
1697 int common
= pden
.NumRows();
1698 vector
< dpoly_r_term
* >& final
= rc
->c
[rc
->len
-1];
1700 for (int j
= 0; j
< final
.size(); ++j
) {
1701 if (final
[j
]->coeff
== 0)
1704 pden
.SetDims(rows
, pden
.NumCols());
1705 for (int k
= 0; k
< rc
->dim
; ++k
) {
1706 int n
= final
[j
]->powers
[k
];
1709 pden
.SetDims(rows
+n
, pden
.NumCols());
1710 for (int l
= 0; l
< n
; ++l
)
1711 pden
[rows
+l
] = den_r
[k
];
1714 final
[j
]->coeff
*= c
;
1715 reduce(final
[j
]->coeff
, rc
->denom
, num_p
, pden
);
1724 void reducer::handle_polar(Polyhedron
*C
, int s
)
1726 assert(C
->NbRays
-1 == dim
);
1730 lattice_point(P
->Ray
[current_vertex
]+1, C
, vertex
);
1733 den
.SetDims(dim
, dim
);
1736 for (r
= 0; r
< dim
; ++r
)
1737 values2zz(C
->Ray
[r
]+1, den
[r
], dim
);
1739 reduce(sgn
, one
, vertex
, den
);
1742 void reducer::start(unsigned MaxRays
)
1744 for (current_vertex
= 0; current_vertex
< P
->NbRays
; ++current_vertex
) {
1745 Polyhedron
*C
= supporting_cone(P
, current_vertex
);
1746 decompose(C
, MaxRays
);
1750 struct ireducer
: public reducer
{
1751 ireducer(Polyhedron
*P
) : reducer(P
) {}
1753 virtual void split(vec_ZZ
& num
, ZZ
& num_s
, vec_ZZ
& num_p
,
1754 mat_ZZ
& den_f
, vec_ZZ
& den_s
, mat_ZZ
& den_r
) {
1755 unsigned len
= den_f
.NumRows(); // number of factors in den
1756 unsigned d
= num
.length() - 1;
1758 den_s
.SetLength(len
);
1759 den_r
.SetDims(len
, d
);
1761 for (int r
= 0; r
< len
; ++r
) {
1762 den_s
[r
] = den_f
[r
][0];
1763 for (int k
= 1; k
<= d
; ++k
)
1764 den_r
[r
][k
-1] = den_f
[r
][k
];
1769 for (int k
= 1 ; k
<= d
; ++k
)
1770 num_p
[k
-1] = num
[k
];
1774 // incremental counter
1775 struct icounter
: public ireducer
{
1778 icounter(Polyhedron
*P
) : ireducer(P
) {
1785 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1788 void icounter::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1791 unsigned len
= den_f
.NumRows(); // number of factors in den
1793 den_s
.SetLength(len
);
1795 for (r
= 0; r
< len
; ++r
)
1796 den_s
[r
] = den_f
[r
][0];
1797 normalize(c
, num_s
, den_s
);
1799 dpoly
n(len
, num_s
);
1800 dpoly
D(len
, den_s
[0], 1);
1801 for (int k
= 1; k
< len
; ++k
) {
1802 dpoly
fact(len
, den_s
[k
], 1);
1805 mpq_set_si(tcount
, 0, 1);
1806 n
.div(D
, tcount
, one
);
1809 mpz_mul(mpq_numref(tcount
), mpq_numref(tcount
), tn
);
1810 mpz_mul(mpq_denref(tcount
), mpq_denref(tcount
), td
);
1811 mpq_canonicalize(tcount
);
1812 mpq_add(count
, count
, tcount
);
1815 /* base for generating function counting */
1820 gf_base(np_base
*npb
, unsigned nparam
) : base(npb
) {
1821 gf
= new gen_fun(Polyhedron_Project(base
->P
, nparam
));
1823 void start(unsigned MaxRays
);
1826 void gf_base::start(unsigned MaxRays
)
1828 for (int i
= 0; i
< base
->P
->NbRays
; ++i
) {
1829 if (!value_pos_p(base
->P
->Ray
[i
][base
->dim
+1]))
1832 Polyhedron
*C
= supporting_cone(base
->P
, i
);
1833 base
->current_vertex
= i
;
1834 base
->decompose(C
, MaxRays
);
1838 struct partial_ireducer
: public ireducer
, public gf_base
{
1839 partial_ireducer(Polyhedron
*P
, unsigned nparam
) :
1840 ireducer(P
), gf_base(this, nparam
) {
1843 ~partial_ireducer() {
1845 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1846 /* we want to override the start method from reducer with the one from gf_base */
1847 void start(unsigned MaxRays
) {
1848 gf_base::start(MaxRays
);
1852 void partial_ireducer::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1854 gf
->add(c
, cd
, num
, den_f
);
1857 struct partial_reducer
: public reducer
, public gf_base
{
1861 partial_reducer(Polyhedron
*P
, unsigned nparam
) :
1862 reducer(P
), gf_base(this, nparam
) {
1865 tmp
.SetLength(dim
- nparam
);
1866 randomvector(P
, lambda
, dim
- nparam
);
1868 ~partial_reducer() {
1870 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1871 /* we want to override the start method from reducer with the one from gf_base */
1872 void start(unsigned MaxRays
) {
1873 gf_base::start(MaxRays
);
1876 virtual void split(vec_ZZ
& num
, ZZ
& num_s
, vec_ZZ
& num_p
,
1877 mat_ZZ
& den_f
, vec_ZZ
& den_s
, mat_ZZ
& den_r
) {
1878 unsigned len
= den_f
.NumRows(); // number of factors in den
1879 unsigned nvar
= tmp
.length();
1881 den_s
.SetLength(len
);
1882 den_r
.SetDims(len
, lower
);
1884 for (int r
= 0; r
< len
; ++r
) {
1885 for (int k
= 0; k
< nvar
; ++k
)
1886 tmp
[k
] = den_f
[r
][k
];
1887 den_s
[r
] = tmp
* lambda
;
1889 for (int k
= nvar
; k
< dim
; ++k
)
1890 den_r
[r
][k
-nvar
] = den_f
[r
][k
];
1893 for (int k
= 0; k
< nvar
; ++k
)
1895 num_s
= tmp
*lambda
;
1896 num_p
.SetLength(lower
);
1897 for (int k
= nvar
; k
< dim
; ++k
)
1898 num_p
[k
-nvar
] = num
[k
];
1902 void partial_reducer::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1904 gf
->add(c
, cd
, num
, den_f
);
1907 struct bfc_term_base
{
1908 // the number of times a given factor appears in the denominator
1912 bfc_term_base(int len
) {
1913 powers
= new int[len
];
1916 virtual ~bfc_term_base() {
1921 struct bfc_term
: public bfc_term_base
{
1925 bfc_term(int len
) : bfc_term_base(len
) {}
1928 struct bfe_term
: public bfc_term_base
{
1929 vector
<evalue
*> factors
;
1931 bfe_term(int len
) : bfc_term_base(len
) {
1935 for (int i
= 0; i
< factors
.size(); ++i
) {
1938 free_evalue_refs(factors
[i
]);
1944 typedef vector
< bfc_term_base
* > bfc_vec
;
1948 struct bf_base
: public np_base
{
1953 int lower
; // call base when only this many variables is left
1955 bf_base(Polyhedron
*P
, unsigned dim
) : np_base(P
, dim
) {
1968 void start(unsigned MaxRays
);
1969 virtual void handle_polar(Polyhedron
*P
, int sign
);
1970 int setup_factors(Polyhedron
*P
, mat_ZZ
& factors
, bfc_term_base
* t
, int s
);
1972 bfc_term_base
* find_bfc_term(bfc_vec
& v
, int *powers
, int len
);
1973 void add_term(bfc_term_base
*t
, vec_ZZ
& num1
, vec_ZZ
& num
);
1974 void add_term(bfc_term_base
*t
, vec_ZZ
& num
);
1976 void reduce(mat_ZZ
& factors
, bfc_vec
& v
);
1977 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
) = 0;
1979 virtual bfc_term_base
* new_bf_term(int len
) = 0;
1980 virtual void set_factor(bfc_term_base
*t
, int k
, int change
) = 0;
1981 virtual void set_factor(bfc_term_base
*t
, int k
, mpq_t
&f
, int change
) = 0;
1982 virtual void set_factor(bfc_term_base
*t
, int k
, ZZ
& n
, ZZ
& d
, int change
) = 0;
1983 virtual void update_term(bfc_term_base
*t
, int i
) = 0;
1984 virtual void insert_term(bfc_term_base
*t
, int i
) = 0;
1985 virtual bool constant_vertex(int dim
) = 0;
1986 virtual void cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
,
1990 static int lex_cmp(vec_ZZ
& a
, vec_ZZ
& b
)
1992 assert(a
.length() == b
.length());
1994 for (int j
= 0; j
< a
.length(); ++j
)
1996 return a
[j
] < b
[j
] ? -1 : 1;
2000 void bf_base::add_term(bfc_term_base
*t
, vec_ZZ
& num_orig
, vec_ZZ
& extra_num
)
2003 int d
= num_orig
.length();
2005 for (int l
= 0; l
< d
-1; ++l
)
2006 num
[l
] = num_orig
[l
+1] + extra_num
[l
];
2011 void bf_base::add_term(bfc_term_base
*t
, vec_ZZ
& num
)
2013 int len
= t
->terms
.NumRows();
2015 for (i
= 0; i
< len
; ++i
) {
2016 r
= lex_cmp(t
->terms
[i
], num
);
2020 if (i
== len
|| r
> 0) {
2021 t
->terms
.SetDims(len
+1, num
.length());
2025 // i < len && r == 0
2030 static void print_int_vector(int *v
, int len
, char *name
)
2032 cerr
<< name
<< endl
;
2033 for (int j
= 0; j
< len
; ++j
) {
2034 cerr
<< v
[j
] << " ";
2039 static void print_bfc_terms(mat_ZZ
& factors
, bfc_vec
& v
)
2042 cerr
<< "factors" << endl
;
2043 cerr
<< factors
<< endl
;
2044 for (int i
= 0; i
< v
.size(); ++i
) {
2045 cerr
<< "term: " << i
<< endl
;
2046 print_int_vector(v
[i
]->powers
, factors
.NumRows(), "powers");
2047 cerr
<< "terms" << endl
;
2048 cerr
<< v
[i
]->terms
<< endl
;
2049 bfc_term
* bfct
= static_cast<bfc_term
*>(v
[i
]);
2050 cerr
<< bfct
->cn
<< endl
;
2051 cerr
<< bfct
->cd
<< endl
;
2055 static void print_bfe_terms(mat_ZZ
& factors
, bfc_vec
& v
)
2058 cerr
<< "factors" << endl
;
2059 cerr
<< factors
<< endl
;
2060 for (int i
= 0; i
< v
.size(); ++i
) {
2061 cerr
<< "term: " << i
<< endl
;
2062 print_int_vector(v
[i
]->powers
, factors
.NumRows(), "powers");
2063 cerr
<< "terms" << endl
;
2064 cerr
<< v
[i
]->terms
<< endl
;
2065 bfe_term
* bfet
= static_cast<bfe_term
*>(v
[i
]);
2066 for (int j
= 0; j
< v
[i
]->terms
.NumRows(); ++j
) {
2067 char * test
[] = {"a", "b"};
2068 print_evalue(stderr
, bfet
->factors
[j
], test
);
2069 fprintf(stderr
, "\n");
2074 bfc_term_base
* bf_base::find_bfc_term(bfc_vec
& v
, int *powers
, int len
)
2076 bfc_vec::iterator i
;
2077 for (i
= v
.begin(); i
!= v
.end(); ++i
) {
2079 for (j
= 0; j
< len
; ++j
)
2080 if ((*i
)->powers
[j
] != powers
[j
])
2084 if ((*i
)->powers
[j
] > powers
[j
])
2088 bfc_term_base
* t
= new_bf_term(len
);
2090 memcpy(t
->powers
, powers
, len
* sizeof(int));
2111 int no_param
; // r from text
2112 int only_param
; // k-r-s from text
2113 int total_power
; // k from text
2115 // created in compute_reduced_factors
2117 // set in update_powers
2122 bf_reducer(mat_ZZ
& factors
, bfc_vec
& v
, bf_base
*bf
)
2123 : factors(factors
), v(v
), bf(bf
) {
2124 nf
= factors
.NumRows();
2125 d
= factors
.NumCols();
2126 old2new
= new int[nf
];
2129 extra_num
.SetLength(d
-1);
2138 void compute_reduced_factors();
2139 void compute_extra_num(int i
);
2143 void update_powers(int *powers
, int len
);
2146 void bf_reducer::compute_extra_num(int i
)
2150 no_param
= 0; // r from text
2151 only_param
= 0; // k-r-s from text
2152 total_power
= 0; // k from text
2154 for (int j
= 0; j
< nf
; ++j
) {
2155 if (v
[i
]->powers
[j
] == 0)
2158 total_power
+= v
[i
]->powers
[j
];
2159 if (factors
[j
][0] == 0) {
2160 only_param
+= v
[i
]->powers
[j
];
2164 if (old2new
[j
] == -1)
2165 no_param
+= v
[i
]->powers
[j
];
2167 extra_num
+= -sign
[j
] * v
[i
]->powers
[j
] * nfactors
[old2new
[j
]];
2168 changes
+= v
[i
]->powers
[j
];
2172 void bf_reducer::update_powers(int *powers
, int len
)
2174 for (int l
= 0; l
< nnf
; ++l
)
2175 npowers
[l
] = bpowers
[l
];
2177 l_extra_num
= extra_num
;
2178 l_changes
= changes
;
2180 for (int l
= 0; l
< len
; ++l
) {
2184 assert(old2new
[l
] != -1);
2186 npowers
[old2new
[l
]] += n
;
2187 // interpretation of sign has been inverted
2188 // since we inverted the power for specialization
2190 l_extra_num
+= n
* nfactors
[old2new
[l
]];
2197 void bf_reducer::compute_reduced_factors()
2199 unsigned nf
= factors
.NumRows();
2200 unsigned d
= factors
.NumCols();
2202 nfactors
.SetDims(nnf
, d
-1);
2204 for (int i
= 0; i
< nf
; ++i
) {
2207 for (j
= 0; j
< nnf
; ++j
) {
2209 for (k
= 1; k
< d
; ++k
)
2210 if (factors
[i
][k
] != 0 || nfactors
[j
][k
-1] != 0)
2212 if (k
< d
&& factors
[i
][k
] == -nfactors
[j
][k
-1])
2215 if (factors
[i
][k
] != s
* nfactors
[j
][k
-1])
2223 for (k
= 1; k
< d
; ++k
)
2224 if (factors
[i
][k
] != 0)
2227 if (factors
[i
][k
] < 0)
2229 nfactors
.SetDims(++nnf
, d
-1);
2230 for (int k
= 1; k
< d
; ++k
)
2231 nfactors
[j
][k
-1] = s
* factors
[i
][k
];
2237 npowers
= new int[nnf
];
2238 bpowers
= new int[nnf
];
2241 void bf_reducer::reduce()
2243 compute_reduced_factors();
2245 for (int i
= 0; i
< v
.size(); ++i
) {
2246 compute_extra_num(i
);
2248 if (no_param
== 0) {
2250 extra_num
.SetLength(d
-1);
2253 for (int k
= 0; k
< nnf
; ++k
)
2255 for (int k
= 0; k
< nf
; ++k
) {
2256 assert(old2new
[k
] != -1);
2257 npowers
[old2new
[k
]] += v
[i
]->powers
[k
];
2258 if (sign
[k
] == -1) {
2259 extra_num
+= v
[i
]->powers
[k
] * nfactors
[old2new
[k
]];
2260 changes
+= v
[i
]->powers
[k
];
2264 bfc_term_base
* t
= bf
->find_bfc_term(vn
, npowers
, nnf
);
2265 for (int k
= 0; k
< v
[i
]->terms
.NumRows(); ++k
) {
2266 bf
->set_factor(v
[i
], k
, changes
% 2);
2267 bf
->add_term(t
, v
[i
]->terms
[k
], extra_num
);
2270 // powers of "constant" part
2271 for (int k
= 0; k
< nnf
; ++k
)
2273 for (int k
= 0; k
< nf
; ++k
) {
2274 if (factors
[k
][0] != 0)
2276 assert(old2new
[k
] != -1);
2277 bpowers
[old2new
[k
]] += v
[i
]->powers
[k
];
2278 if (sign
[k
] == -1) {
2279 extra_num
+= v
[i
]->powers
[k
] * nfactors
[old2new
[k
]];
2280 changes
+= v
[i
]->powers
[k
];
2285 for (j
= 0; j
< nf
; ++j
)
2286 if (old2new
[j
] == -1 && v
[i
]->powers
[j
] > 0)
2289 dpoly
D(no_param
, factors
[j
][0], 1);
2290 for (int k
= 1; k
< v
[i
]->powers
[j
]; ++k
) {
2291 dpoly
fact(no_param
, factors
[j
][0], 1);
2295 if (old2new
[j
] == -1)
2296 for (int k
= 0; k
< v
[i
]->powers
[j
]; ++k
) {
2297 dpoly
fact(no_param
, factors
[j
][0], 1);
2301 if (no_param
+ only_param
== total_power
&&
2302 bf
->constant_vertex(d
)) {
2303 bfc_term_base
* t
= NULL
;
2308 for (int k
= 0; k
< v
[i
]->terms
.NumRows(); ++k
) {
2309 dpoly
n(no_param
, v
[i
]->terms
[k
][0]);
2310 mpq_set_si(bf
->tcount
, 0, 1);
2311 n
.div(D
, bf
->tcount
, bf
->one
);
2313 if (value_zero_p(mpq_numref(bf
->tcount
)))
2317 t
= bf
->find_bfc_term(vn
, bpowers
, nnf
);
2318 bf
->set_factor(v
[i
], k
, bf
->tcount
, changes
% 2);
2319 bf
->add_term(t
, v
[i
]->terms
[k
], extra_num
);
2322 for (int j
= 0; j
< v
[i
]->terms
.NumRows(); ++j
) {
2323 dpoly
n(no_param
, v
[i
]->terms
[j
][0]);
2326 if (no_param
+ only_param
== total_power
)
2327 r
= new dpoly_r(n
, nf
);
2329 for (int k
= 0; k
< nf
; ++k
) {
2330 if (v
[i
]->powers
[k
] == 0)
2332 if (factors
[k
][0] == 0 || old2new
[k
] == -1)
2335 dpoly
pd(no_param
-1, factors
[k
][0], 1);
2337 for (int l
= 0; l
< v
[i
]->powers
[k
]; ++l
) {
2339 for (q
= 0; q
< k
; ++q
)
2340 if (old2new
[q
] == old2new
[k
] &&
2345 r
= new dpoly_r(n
, pd
, q
, nf
);
2347 dpoly_r
*nr
= new dpoly_r(r
, pd
, q
, nf
);
2354 dpoly_r
*rc
= r
->div(D
);
2357 if (bf
->constant_vertex(d
)) {
2358 vector
< dpoly_r_term
* >& final
= rc
->c
[rc
->len
-1];
2360 for (int k
= 0; k
< final
.size(); ++k
) {
2361 if (final
[k
]->coeff
== 0)
2364 update_powers(final
[k
]->powers
, rc
->dim
);
2366 bfc_term_base
* t
= bf
->find_bfc_term(vn
, npowers
, nnf
);
2367 bf
->set_factor(v
[i
], j
, final
[k
]->coeff
, rc
->denom
, l_changes
% 2);
2368 bf
->add_term(t
, v
[i
]->terms
[j
], l_extra_num
);
2371 bf
->cum(this, v
[i
], j
, rc
);
2382 void bf_base::reduce(mat_ZZ
& factors
, bfc_vec
& v
)
2384 assert(v
.size() > 0);
2385 unsigned nf
= factors
.NumRows();
2386 unsigned d
= factors
.NumCols();
2389 return base(factors
, v
);
2391 bf_reducer
bfr(factors
, v
, this);
2395 if (bfr
.vn
.size() > 0)
2396 reduce(bfr
.nfactors
, bfr
.vn
);
2399 int bf_base::setup_factors(Polyhedron
*C
, mat_ZZ
& factors
,
2400 bfc_term_base
* t
, int s
)
2402 factors
.SetDims(dim
, dim
);
2406 for (r
= 0; r
< dim
; ++r
)
2409 for (r
= 0; r
< dim
; ++r
) {
2410 values2zz(C
->Ray
[r
]+1, factors
[r
], dim
);
2412 for (k
= 0; k
< dim
; ++k
)
2413 if (factors
[r
][k
] != 0)
2415 if (factors
[r
][k
] < 0) {
2416 factors
[r
] = -factors
[r
];
2417 t
->terms
[0] += factors
[r
];
2425 void bf_base::handle_polar(Polyhedron
*C
, int s
)
2427 bfc_term
* t
= new bfc_term(dim
);
2428 vector
< bfc_term_base
* > v
;
2431 assert(C
->NbRays
-1 == dim
);
2436 t
->terms
.SetDims(1, dim
);
2437 lattice_point(P
->Ray
[current_vertex
]+1, C
, t
->terms
[0]);
2439 // the elements of factors are always lexpositive
2441 s
= setup_factors(C
, factors
, t
, s
);
2449 void bf_base::start(unsigned MaxRays
)
2451 for (current_vertex
= 0; current_vertex
< P
->NbRays
; ++current_vertex
) {
2452 Polyhedron
*C
= supporting_cone(P
, current_vertex
);
2453 decompose(C
, MaxRays
);
2457 struct bfcounter_base
: public bf_base
{
2461 bfcounter_base(Polyhedron
*P
) : bf_base(P
, P
->Dimension
) {
2464 bfc_term_base
* new_bf_term(int len
) {
2465 bfc_term
* t
= new bfc_term(len
);
2471 virtual void set_factor(bfc_term_base
*t
, int k
, int change
) {
2472 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2479 virtual void set_factor(bfc_term_base
*t
, int k
, mpq_t
&f
, int change
) {
2480 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2481 value2zz(mpq_numref(f
), cn
);
2482 value2zz(mpq_denref(f
), cd
);
2489 virtual void set_factor(bfc_term_base
*t
, int k
, ZZ
& n
, ZZ
& d
, int change
) {
2490 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2491 cn
= bfct
->cn
[k
] * n
;
2494 cd
= bfct
->cd
[k
] * d
;
2497 virtual void insert_term(bfc_term_base
*t
, int i
) {
2498 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2499 int len
= t
->terms
.NumRows()-1; // already increased by one
2501 bfct
->cn
.SetLength(len
+1);
2502 bfct
->cd
.SetLength(len
+1);
2503 for (int j
= len
; j
> i
; --j
) {
2504 bfct
->cn
[j
] = bfct
->cn
[j
-1];
2505 bfct
->cd
[j
] = bfct
->cd
[j
-1];
2506 t
->terms
[j
] = t
->terms
[j
-1];
2512 virtual void update_term(bfc_term_base
*t
, int i
) {
2513 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2515 ZZ g
= GCD(bfct
->cd
[i
], cd
);
2516 ZZ n
= cn
* bfct
->cd
[i
]/g
+ bfct
->cn
[i
] * cd
/g
;
2517 ZZ d
= bfct
->cd
[i
] * cd
/ g
;
2522 virtual bool constant_vertex(int dim
) { return true; }
2523 virtual void cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
, dpoly_r
*r
) {
2528 struct bfcounter
: public bfcounter_base
{
2531 bfcounter(Polyhedron
*P
) : bfcounter_base(P
) {
2538 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
);
2541 void bfcounter::base(mat_ZZ
& factors
, bfc_vec
& v
)
2543 unsigned nf
= factors
.NumRows();
2545 for (int i
= 0; i
< v
.size(); ++i
) {
2546 bfc_term
* bfct
= static_cast<bfc_term
*>(v
[i
]);
2547 int total_power
= 0;
2548 // factor is always positive, so we always
2550 for (int k
= 0; k
< nf
; ++k
)
2551 total_power
+= v
[i
]->powers
[k
];
2554 for (j
= 0; j
< nf
; ++j
)
2555 if (v
[i
]->powers
[j
] > 0)
2558 dpoly
D(total_power
, factors
[j
][0], 1);
2559 for (int k
= 1; k
< v
[i
]->powers
[j
]; ++k
) {
2560 dpoly
fact(total_power
, factors
[j
][0], 1);
2564 for (int k
= 0; k
< v
[i
]->powers
[j
]; ++k
) {
2565 dpoly
fact(total_power
, factors
[j
][0], 1);
2569 for (int k
= 0; k
< v
[i
]->terms
.NumRows(); ++k
) {
2570 dpoly
n(total_power
, v
[i
]->terms
[k
][0]);
2571 mpq_set_si(tcount
, 0, 1);
2572 n
.div(D
, tcount
, one
);
2573 if (total_power
% 2)
2574 bfct
->cn
[k
] = -bfct
->cn
[k
];
2575 zz2value(bfct
->cn
[k
], tn
);
2576 zz2value(bfct
->cd
[k
], td
);
2578 mpz_mul(mpq_numref(tcount
), mpq_numref(tcount
), tn
);
2579 mpz_mul(mpq_denref(tcount
), mpq_denref(tcount
), td
);
2580 mpq_canonicalize(tcount
);
2581 mpq_add(count
, count
, tcount
);
2587 struct partial_bfcounter
: public bfcounter_base
, public gf_base
{
2588 partial_bfcounter(Polyhedron
*P
, unsigned nparam
) :
2589 bfcounter_base(P
), gf_base(this, nparam
) {
2592 ~partial_bfcounter() {
2594 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
);
2595 /* we want to override the start method from bf_base with the one from gf_base */
2596 void start(unsigned MaxRays
) {
2597 gf_base::start(MaxRays
);
2601 void partial_bfcounter::base(mat_ZZ
& factors
, bfc_vec
& v
)
2604 unsigned nf
= factors
.NumRows();
2606 for (int i
= 0; i
< v
.size(); ++i
) {
2607 bfc_term
* bfct
= static_cast<bfc_term
*>(v
[i
]);
2608 den
.SetDims(0, lower
);
2609 int total_power
= 0;
2611 for (int j
= 0; j
< nf
; ++j
) {
2612 total_power
+= v
[i
]->powers
[j
];
2613 den
.SetDims(total_power
, lower
);
2614 for (int k
= 0; k
< v
[i
]->powers
[j
]; ++k
)
2615 den
[p
++] = factors
[j
];
2617 for (int j
= 0; j
< v
[i
]->terms
.NumRows(); ++j
)
2618 gf
->add(bfct
->cn
[j
], bfct
->cd
[j
], v
[i
]->terms
[j
], den
);
2624 typedef Polyhedron
* Polyhedron_p
;
2626 static void barvinok_count_f(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
);
2628 void barvinok_count(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
2636 value_set_si(*result
, 0);
2640 for (; r
< P
->NbRays
; ++r
)
2641 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2643 if (P
->NbBid
!=0 || r
< P
->NbRays
) {
2644 value_set_si(*result
, -1);
2648 P
= remove_equalities(P
);
2651 value_set_si(*result
, 0);
2656 if (P
->Dimension
== 0) {
2657 /* Test whether the constraints are satisfied */
2658 POL_ENSURE_VERTICES(P
);
2659 value_set_si(*result
, !emptyQ(P
));
2664 Q
= Polyhedron_Factor(P
, 0, NbMaxCons
);
2672 barvinok_count_f(P
, result
, NbMaxCons
);
2677 for (Q
= P
->next
; Q
; Q
= Q
->next
) {
2678 barvinok_count_f(Q
, &factor
, NbMaxCons
);
2679 value_multiply(*result
, *result
, factor
);
2682 value_clear(factor
);
2689 static void barvinok_count_f(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
2691 if (P
->Dimension
== 1)
2692 return Line_Length(P
, result
);
2694 int c
= P
->NbConstraints
;
2695 POL_ENSURE_FACETS(P
);
2696 if (c
!= P
->NbConstraints
|| P
->NbEq
!= 0)
2697 return barvinok_count(P
, result
, NbMaxCons
);
2699 POL_ENSURE_VERTICES(P
);
2701 #ifdef USE_INCREMENTAL_BF
2703 #elif defined USE_INCREMENTAL_DF
2708 cnt
.start(NbMaxCons
);
2710 assert(value_one_p(&cnt
.count
[0]._mp_den
));
2711 value_assign(*result
, &cnt
.count
[0]._mp_num
);
2714 static void uni_polynom(int param
, Vector
*c
, evalue
*EP
)
2716 unsigned dim
= c
->Size
-2;
2718 value_set_si(EP
->d
,0);
2719 EP
->x
.p
= new_enode(polynomial
, dim
+1, param
+1);
2720 for (int j
= 0; j
<= dim
; ++j
)
2721 evalue_set(&EP
->x
.p
->arr
[j
], c
->p
[j
], c
->p
[dim
+1]);
2724 static void multi_polynom(Vector
*c
, evalue
* X
, evalue
*EP
)
2726 unsigned dim
= c
->Size
-2;
2730 evalue_set(&EC
, c
->p
[dim
], c
->p
[dim
+1]);
2733 evalue_set(EP
, c
->p
[dim
], c
->p
[dim
+1]);
2735 for (int i
= dim
-1; i
>= 0; --i
) {
2737 value_assign(EC
.x
.n
, c
->p
[i
]);
2740 free_evalue_refs(&EC
);
2743 Polyhedron
*unfringe (Polyhedron
*P
, unsigned MaxRays
)
2745 int len
= P
->Dimension
+2;
2746 Polyhedron
*T
, *R
= P
;
2749 Vector
*row
= Vector_Alloc(len
);
2750 value_set_si(row
->p
[0], 1);
2752 R
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
2754 Matrix
*M
= Matrix_Alloc(2, len
-1);
2755 value_set_si(M
->p
[1][len
-2], 1);
2756 for (int v
= 0; v
< P
->Dimension
; ++v
) {
2757 value_set_si(M
->p
[0][v
], 1);
2758 Polyhedron
*I
= Polyhedron_Image(P
, M
, 2+1);
2759 value_set_si(M
->p
[0][v
], 0);
2760 for (int r
= 0; r
< I
->NbConstraints
; ++r
) {
2761 if (value_zero_p(I
->Constraint
[r
][0]))
2763 if (value_zero_p(I
->Constraint
[r
][1]))
2765 if (value_one_p(I
->Constraint
[r
][1]))
2767 if (value_mone_p(I
->Constraint
[r
][1]))
2769 value_absolute(g
, I
->Constraint
[r
][1]);
2770 Vector_Set(row
->p
+1, 0, len
-2);
2771 value_division(row
->p
[1+v
], I
->Constraint
[r
][1], g
);
2772 mpz_fdiv_q(row
->p
[len
-1], I
->Constraint
[r
][2], g
);
2774 R
= AddConstraints(row
->p
, 1, R
, MaxRays
);
2786 static Polyhedron
*reduce_domain(Polyhedron
*D
, Matrix
*CT
, Polyhedron
*CEq
,
2787 Polyhedron
**fVD
, int nd
, unsigned MaxRays
)
2792 Dt
= CT
? DomainPreimage(D
, CT
, MaxRays
) : D
;
2793 Polyhedron
*rVD
= DomainIntersection(Dt
, CEq
, MaxRays
);
2795 /* if rVD is empty or too small in geometric dimension */
2796 if(!rVD
|| emptyQ(rVD
) ||
2797 (rVD
->Dimension
-rVD
->NbEq
< Dt
->Dimension
-Dt
->NbEq
-CEq
->NbEq
)) {
2802 return 0; /* empty validity domain */
2808 fVD
[nd
] = Domain_Copy(rVD
);
2809 for (int i
= 0 ; i
< nd
; ++i
) {
2810 Polyhedron
*I
= DomainIntersection(fVD
[nd
], fVD
[i
], MaxRays
);
2815 Polyhedron
*F
= DomainSimplify(I
, fVD
[nd
], MaxRays
);
2817 Polyhedron
*T
= rVD
;
2818 rVD
= DomainDifference(rVD
, F
, MaxRays
);
2825 rVD
= DomainConstraintSimplify(rVD
, MaxRays
);
2827 Domain_Free(fVD
[nd
]);
2834 barvinok_count(rVD
, &c
, MaxRays
);
2835 if (value_zero_p(c
)) {
2844 /* this procedure may have false negatives */
2845 static bool Polyhedron_is_infinite(Polyhedron
*P
, unsigned nparam
)
2848 for (r
= 0; r
< P
->NbRays
; ++r
) {
2849 if (!value_zero_p(P
->Ray
[r
][0]) &&
2850 !value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2852 if (First_Non_Zero(P
->Ray
[r
]+1+P
->Dimension
-nparam
, nparam
) == -1)
2858 /* Check whether all rays point in the positive directions
2859 * for the parameters
2861 static bool Polyhedron_has_positive_rays(Polyhedron
*P
, unsigned nparam
)
2864 for (r
= 0; r
< P
->NbRays
; ++r
)
2865 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
2867 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
2868 if (value_neg_p(P
->Ray
[r
][i
+1]))
2874 typedef evalue
* evalue_p
;
2876 struct enumerator
: public polar_decomposer
{
2890 enumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) {
2894 randomvector(P
, lambda
, dim
);
2895 rays
.SetDims(dim
, dim
);
2897 c
= Vector_Alloc(dim
+2);
2899 vE
= new evalue_p
[nbV
];
2900 for (int j
= 0; j
< nbV
; ++j
)
2906 void decompose_at(Param_Vertices
*V
, int _i
, unsigned MaxRays
) {
2907 Polyhedron
*C
= supporting_cone_p(P
, V
);
2911 vE
[_i
] = new evalue
;
2912 value_init(vE
[_i
]->d
);
2913 evalue_set_si(vE
[_i
], 0, 1);
2915 decompose(C
, MaxRays
);
2922 for (int j
= 0; j
< nbV
; ++j
)
2924 free_evalue_refs(vE
[j
]);
2930 virtual void handle_polar(Polyhedron
*P
, int sign
);
2933 void enumerator::handle_polar(Polyhedron
*C
, int s
)
2936 assert(C
->NbRays
-1 == dim
);
2937 add_rays(rays
, C
, &r
);
2938 for (int k
= 0; k
< dim
; ++k
) {
2939 if (lambda
* rays
[k
] == 0)
2945 lattice_point(V
, C
, lambda
, &num
, 0);
2946 den
= rays
* lambda
;
2947 normalize(sign
, num
.constant
, den
);
2949 dpoly
n(dim
, den
[0], 1);
2950 for (int k
= 1; k
< dim
; ++k
) {
2951 dpoly
fact(dim
, den
[k
], 1);
2954 if (num
.E
!= NULL
) {
2955 ZZ
one(INIT_VAL
, 1);
2956 dpoly_n
d(dim
, num
.constant
, one
);
2959 multi_polynom(c
, num
.E
, &EV
);
2961 free_evalue_refs(&EV
);
2962 free_evalue_refs(num
.E
);
2964 } else if (num
.pos
!= -1) {
2965 dpoly_n
d(dim
, num
.constant
, num
.coeff
);
2968 uni_polynom(num
.pos
, c
, &EV
);
2970 free_evalue_refs(&EV
);
2972 mpq_set_si(count
, 0, 1);
2973 dpoly
d(dim
, num
.constant
);
2974 d
.div(n
, count
, sign
);
2977 evalue_set(&EV
, &count
[0]._mp_num
, &count
[0]._mp_den
);
2979 free_evalue_refs(&EV
);
2983 struct enumerator_base
{
2991 polar_decomposer
*pd
;
2993 enumerator_base(Polyhedron
*P
, unsigned dim
, unsigned nbV
, polar_decomposer
*pd
)
3000 vE
= new evalue_p
[nbV
];
3001 for (int j
= 0; j
< nbV
; ++j
)
3004 E_vertex
= new evalue_p
[dim
];
3007 evalue_set_si(&mone
, -1, 1);
3010 void decompose_at(Param_Vertices
*V
, int _i
, unsigned MaxRays
/*, Polyhedron *pVD*/) {
3011 Polyhedron
*C
= supporting_cone_p(P
, V
);
3016 vE
[_i
] = new evalue
;
3017 value_init(vE
[_i
]->d
);
3018 evalue_set_si(vE
[_i
], 0, 1);
3020 pd
->decompose(C
, MaxRays
);
3023 ~enumerator_base() {
3024 for (int j
= 0; j
< nbV
; ++j
)
3026 free_evalue_refs(vE
[j
]);
3033 free_evalue_refs(&mone
);
3036 evalue
*E_num(int i
, int d
) {
3037 return E_vertex
[i
+ (dim
-d
)];
3046 cumulator(evalue
*factor
, evalue
*v
, dpoly_r
*r
) :
3047 factor(factor
), v(v
), r(r
) {}
3051 virtual void add_term(int *powers
, int len
, evalue
*f2
) = 0;
3054 void cumulator::cumulate()
3056 evalue cum
; // factor * 1 * E_num[0]/1 * (E_num[0]-1)/2 *...
3058 evalue t
; // E_num[0] - (m-1)
3064 evalue_set_si(&mone
, -1, 1);
3068 evalue_copy(&cum
, factor
);
3071 value_set_si(f
.d
, 1);
3072 value_set_si(f
.x
.n
, 1);
3077 for (cst
= &t
; value_zero_p(cst
->d
); ) {
3078 if (cst
->x
.p
->type
== fractional
)
3079 cst
= &cst
->x
.p
->arr
[1];
3081 cst
= &cst
->x
.p
->arr
[0];
3085 for (int m
= 0; m
< r
->len
; ++m
) {
3088 value_set_si(f
.d
, m
);
3091 value_subtract(cst
->x
.n
, cst
->x
.n
, cst
->d
);
3098 vector
< dpoly_r_term
* >& current
= r
->c
[r
->len
-1-m
];
3099 for (int j
= 0; j
< current
.size(); ++j
) {
3100 if (current
[j
]->coeff
== 0)
3102 evalue
*f2
= new evalue
;
3104 value_init(f2
->x
.n
);
3105 zz2value(current
[j
]->coeff
, f2
->x
.n
);
3106 zz2value(r
->denom
, f2
->d
);
3109 add_term(current
[j
]->powers
, r
->dim
, f2
);
3112 free_evalue_refs(&f
);
3113 free_evalue_refs(&t
);
3114 free_evalue_refs(&cum
);
3116 free_evalue_refs(&mone
);
3120 struct E_poly_term
{
3125 struct ie_cum
: public cumulator
{
3126 vector
<E_poly_term
*> terms
;
3128 ie_cum(evalue
*factor
, evalue
*v
, dpoly_r
*r
) : cumulator(factor
, v
, r
) {}
3130 virtual void add_term(int *powers
, int len
, evalue
*f2
);
3133 void ie_cum::add_term(int *powers
, int len
, evalue
*f2
)
3136 for (k
= 0; k
< terms
.size(); ++k
) {
3137 if (memcmp(terms
[k
]->powers
, powers
, len
* sizeof(int)) == 0) {
3138 eadd(f2
, terms
[k
]->E
);
3139 free_evalue_refs(f2
);
3144 if (k
>= terms
.size()) {
3145 E_poly_term
*ET
= new E_poly_term
;
3146 ET
->powers
= new int[len
];
3147 memcpy(ET
->powers
, powers
, len
* sizeof(int));
3149 terms
.push_back(ET
);
3153 struct ienumerator
: public polar_decomposer
, public enumerator_base
{
3159 ienumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) :
3160 enumerator_base(P
, dim
, nbV
, this) {
3161 vertex
.SetLength(dim
);
3163 den
.SetDims(dim
, dim
);
3171 virtual void handle_polar(Polyhedron
*P
, int sign
);
3172 void reduce(evalue
*factor
, vec_ZZ
& num
, mat_ZZ
& den_f
);
3175 static evalue
* new_zero_ep()
3180 evalue_set_si(EP
, 0, 1);
3184 void lattice_point(Param_Vertices
*V
, Polyhedron
*C
, vec_ZZ
& num
,
3187 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
3188 unsigned dim
= C
->Dimension
;
3190 vertex
.SetLength(nparam
+1);
3195 value_set_si(lcm
, 1);
3197 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
3198 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
3201 if (value_notone_p(lcm
)) {
3202 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
3203 for (int j
= 0 ; j
< dim
; ++j
) {
3204 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
3205 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
3208 Matrix
* Rays
= rays2(C
);
3209 Matrix
*T
= Transpose(Rays
);
3210 Matrix
*T2
= Matrix_Copy(T
);
3211 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
3212 int ok
= Matrix_Inverse(T2
, inv
);
3216 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, mv
->NbColumns
);
3217 Matrix_Product(inv
, mv
, L
);
3226 evalue
*remainders
[dim
];
3227 for (int i
= 0; i
< dim
; ++i
) {
3228 remainders
[i
] = new_zero_ep();
3230 ceil(L
->p
[i
], nparam
+1, lcm
, one
, remainders
[i
], 0);
3235 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
3236 values2zz(mv
->p
[i
], vertex
, nparam
+1);
3237 E_vertex
[i
] = multi_monom(vertex
);
3240 value_set_si(f
.x
.n
, 1);
3241 value_assign(f
.d
, lcm
);
3243 emul(&f
, E_vertex
[i
]);
3245 for (int j
= 0; j
< dim
; ++j
) {
3246 if (value_zero_p(T
->p
[i
][j
]))
3250 evalue_copy(&cp
, remainders
[j
]);
3251 if (value_notone_p(T
->p
[i
][j
])) {
3252 value_set_si(f
.d
, 1);
3253 value_assign(f
.x
.n
, T
->p
[i
][j
]);
3256 eadd(&cp
, E_vertex
[i
]);
3257 free_evalue_refs(&cp
);
3260 for (int i
= 0; i
< dim
; ++i
) {
3261 free_evalue_refs(remainders
[i
]);
3262 free(remainders
[i
]);
3265 free_evalue_refs(&f
);
3276 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
3278 if (First_Non_Zero(V
->Vertex
->p
[i
], nparam
) == -1) {
3280 value2zz(V
->Vertex
->p
[i
][nparam
], num
[i
]);
3282 values2zz(V
->Vertex
->p
[i
], vertex
, nparam
+1);
3283 E_vertex
[i
] = multi_monom(vertex
);
3289 void ienumerator::reduce(
3290 evalue
*factor
, vec_ZZ
& num
, mat_ZZ
& den_f
)
3292 unsigned len
= den_f
.NumRows(); // number of factors in den
3293 unsigned dim
= num
.length();
3296 eadd(factor
, vE
[_i
]);
3301 den_s
.SetLength(len
);
3303 den_r
.SetDims(len
, dim
-1);
3307 for (r
= 0; r
< len
; ++r
) {
3308 den_s
[r
] = den_f
[r
][0];
3309 for (k
= 0; k
<= dim
-1; ++k
)
3311 den_r
[r
][k
-(k
>0)] = den_f
[r
][k
];
3316 num_p
.SetLength(dim
-1);
3317 for (k
= 0 ; k
<= dim
-1; ++k
)
3319 num_p
[k
-(k
>0)] = num
[k
];
3322 den_p
.SetLength(len
);
3326 normalize(one
, num_s
, num_p
, den_s
, den_p
, den_r
);
3328 emul(&mone
, factor
);
3332 for (int k
= 0; k
< len
; ++k
) {
3335 else if (den_s
[k
] == 0)
3338 if (no_param
== 0) {
3339 reduce(factor
, num_p
, den_r
);
3343 pden
.SetDims(only_param
, dim
-1);
3345 for (k
= 0, l
= 0; k
< len
; ++k
)
3347 pden
[l
++] = den_r
[k
];
3349 for (k
= 0; k
< len
; ++k
)
3353 dpoly
n(no_param
, num_s
);
3354 dpoly
D(no_param
, den_s
[k
], 1);
3355 for ( ; ++k
< len
; )
3356 if (den_p
[k
] == 0) {
3357 dpoly
fact(no_param
, den_s
[k
], 1);
3362 // if no_param + only_param == len then all powers
3363 // below will be all zero
3364 if (no_param
+ only_param
== len
) {
3365 if (E_num(0, dim
) != 0)
3366 r
= new dpoly_r(n
, len
);
3368 mpq_set_si(tcount
, 0, 1);
3370 n
.div(D
, tcount
, one
);
3372 if (value_notzero_p(mpq_numref(tcount
))) {
3376 value_assign(f
.x
.n
, mpq_numref(tcount
));
3377 value_assign(f
.d
, mpq_denref(tcount
));
3379 reduce(factor
, num_p
, pden
);
3380 free_evalue_refs(&f
);
3385 for (k
= 0; k
< len
; ++k
) {
3386 if (den_s
[k
] == 0 || den_p
[k
] == 0)
3389 dpoly
pd(no_param
-1, den_s
[k
], 1);
3392 for (l
= 0; l
< k
; ++l
)
3393 if (den_r
[l
] == den_r
[k
])
3397 r
= new dpoly_r(n
, pd
, l
, len
);
3399 dpoly_r
*nr
= new dpoly_r(r
, pd
, l
, len
);
3405 dpoly_r
*rc
= r
->div(D
);
3408 if (E_num(0, dim
) == 0) {
3409 int common
= pden
.NumRows();
3410 vector
< dpoly_r_term
* >& final
= r
->c
[r
->len
-1];
3416 zz2value(r
->denom
, f
.d
);
3417 for (int j
= 0; j
< final
.size(); ++j
) {
3418 if (final
[j
]->coeff
== 0)
3421 for (int k
= 0; k
< r
->dim
; ++k
) {
3422 int n
= final
[j
]->powers
[k
];
3425 pden
.SetDims(rows
+n
, pden
.NumCols());
3426 for (int l
= 0; l
< n
; ++l
)
3427 pden
[rows
+l
] = den_r
[k
];
3431 evalue_copy(&t
, factor
);
3432 zz2value(final
[j
]->coeff
, f
.x
.n
);
3434 reduce(&t
, num_p
, pden
);
3435 free_evalue_refs(&t
);
3437 free_evalue_refs(&f
);
3439 ie_cum
cum(factor
, E_num(0, dim
), r
);
3442 int common
= pden
.NumRows();
3444 for (int j
= 0; j
< cum
.terms
.size(); ++j
) {
3446 pden
.SetDims(rows
, pden
.NumCols());
3447 for (int k
= 0; k
< r
->dim
; ++k
) {
3448 int n
= cum
.terms
[j
]->powers
[k
];
3451 pden
.SetDims(rows
+n
, pden
.NumCols());
3452 for (int l
= 0; l
< n
; ++l
)
3453 pden
[rows
+l
] = den_r
[k
];
3456 reduce(cum
.terms
[j
]->E
, num_p
, pden
);
3457 free_evalue_refs(cum
.terms
[j
]->E
);
3458 delete cum
.terms
[j
]->E
;
3459 delete [] cum
.terms
[j
]->powers
;
3460 delete cum
.terms
[j
];
3467 static int type_offset(enode
*p
)
3469 return p
->type
== fractional
? 1 :
3470 p
->type
== flooring
? 1 : 0;
3473 static int edegree(evalue
*e
)
3478 if (value_notzero_p(e
->d
))
3482 int i
= type_offset(p
);
3483 if (p
->size
-i
-1 > d
)
3484 d
= p
->size
- i
- 1;
3485 for (; i
< p
->size
; i
++) {
3486 int d2
= edegree(&p
->arr
[i
]);
3493 void ienumerator::handle_polar(Polyhedron
*C
, int s
)
3495 assert(C
->NbRays
-1 == dim
);
3497 lattice_point(V
, C
, vertex
, E_vertex
);
3500 for (r
= 0; r
< dim
; ++r
)
3501 values2zz(C
->Ray
[r
]+1, den
[r
], dim
);
3505 evalue_set_si(&one
, s
, 1);
3506 reduce(&one
, vertex
, den
);
3507 free_evalue_refs(&one
);
3509 for (int i
= 0; i
< dim
; ++i
)
3511 free_evalue_refs(E_vertex
[i
]);
3517 char * test[] = {"a", "b"};
3520 evalue_copy(&E, vE[_i]);
3521 frac2floor_in_domain(&E, pVD);
3522 printf("***** Curr value:");
3523 print_evalue(stdout, &E, test);
3524 fprintf(stdout, "\n");
3530 struct bfenumerator
: public bf_base
, public enumerator_base
{
3533 bfenumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) :
3534 bf_base(P
, dim
), enumerator_base(P
, dim
, nbV
, this) {
3542 virtual void handle_polar(Polyhedron
*P
, int sign
);
3543 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
);
3545 bfc_term_base
* new_bf_term(int len
) {
3546 bfe_term
* t
= new bfe_term(len
);
3550 virtual void set_factor(bfc_term_base
*t
, int k
, int change
) {
3551 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3552 factor
= bfet
->factors
[k
];
3553 assert(factor
!= NULL
);
3554 bfet
->factors
[k
] = NULL
;
3556 emul(&mone
, factor
);
3559 virtual void set_factor(bfc_term_base
*t
, int k
, mpq_t
&q
, int change
) {
3560 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3561 factor
= bfet
->factors
[k
];
3562 assert(factor
!= NULL
);
3563 bfet
->factors
[k
] = NULL
;
3569 value_oppose(f
.x
.n
, mpq_numref(q
));
3571 value_assign(f
.x
.n
, mpq_numref(q
));
3572 value_assign(f
.d
, mpq_denref(q
));
3576 virtual void set_factor(bfc_term_base
*t
, int k
, ZZ
& n
, ZZ
& d
, int change
) {
3577 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3579 factor
= new evalue
;
3586 value_oppose(f
.x
.n
, f
.x
.n
);
3589 value_init(factor
->d
);
3590 evalue_copy(factor
, bfet
->factors
[k
]);
3594 void set_factor(evalue
*f
, int change
) {
3600 virtual void insert_term(bfc_term_base
*t
, int i
) {
3601 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3602 int len
= t
->terms
.NumRows()-1; // already increased by one
3604 bfet
->factors
.resize(len
+1);
3605 for (int j
= len
; j
> i
; --j
) {
3606 bfet
->factors
[j
] = bfet
->factors
[j
-1];
3607 t
->terms
[j
] = t
->terms
[j
-1];
3609 bfet
->factors
[i
] = factor
;
3613 virtual void update_term(bfc_term_base
*t
, int i
) {
3614 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3616 eadd(factor
, bfet
->factors
[i
]);
3617 free_evalue_refs(factor
);
3621 virtual bool constant_vertex(int dim
) { return E_num(0, dim
) == 0; }
3623 virtual void cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
, dpoly_r
*r
);
3626 struct bfe_cum
: public cumulator
{
3628 bfc_term_base
*told
;
3632 bfe_cum(evalue
*factor
, evalue
*v
, dpoly_r
*r
, bf_reducer
*bfr
,
3633 bfc_term_base
*t
, int k
, bfenumerator
*e
) :
3634 cumulator(factor
, v
, r
), told(t
), k(k
),
3638 virtual void add_term(int *powers
, int len
, evalue
*f2
);
3641 void bfe_cum::add_term(int *powers
, int len
, evalue
*f2
)
3643 bfr
->update_powers(powers
, len
);
3645 bfc_term_base
* t
= bfe
->find_bfc_term(bfr
->vn
, bfr
->npowers
, bfr
->nnf
);
3646 bfe
->set_factor(f2
, bfr
->l_changes
% 2);
3647 bfe
->add_term(t
, told
->terms
[k
], bfr
->l_extra_num
);
3650 void bfenumerator::cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
,
3653 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3654 bfe_cum
cum(bfet
->factors
[k
], E_num(0, bfr
->d
), r
, bfr
, t
, k
, this);
3658 void bfenumerator::base(mat_ZZ
& factors
, bfc_vec
& v
)
3660 for (int i
= 0; i
< v
.size(); ++i
) {
3661 assert(v
[i
]->terms
.NumRows() == 1);
3662 evalue
*factor
= static_cast<bfe_term
*>(v
[i
])->factors
[0];
3663 eadd(factor
, vE
[_i
]);
3668 void bfenumerator::handle_polar(Polyhedron
*C
, int s
)
3670 assert(C
->NbRays
-1 == enumerator_base::dim
);
3672 bfe_term
* t
= new bfe_term(enumerator_base::dim
);
3673 vector
< bfc_term_base
* > v
;
3676 t
->factors
.resize(1);
3678 t
->terms
.SetDims(1, enumerator_base::dim
);
3679 lattice_point(V
, C
, t
->terms
[0], E_vertex
);
3681 // the elements of factors are always lexpositive
3683 s
= setup_factors(C
, factors
, t
, s
);
3685 t
->factors
[0] = new evalue
;
3686 value_init(t
->factors
[0]->d
);
3687 evalue_set_si(t
->factors
[0], s
, 1);
3690 for (int i
= 0; i
< enumerator_base::dim
; ++i
)
3692 free_evalue_refs(E_vertex
[i
]);
3697 #ifdef HAVE_CORRECT_VERTICES
3698 static inline Param_Polyhedron
*Polyhedron2Param_SD(Polyhedron
**Din
,
3699 Polyhedron
*Cin
,int WS
,Polyhedron
**CEq
,Matrix
**CT
)
3701 if (WS
& POL_NO_DUAL
)
3703 return Polyhedron2Param_SimplifiedDomain(Din
, Cin
, WS
, CEq
, CT
);
3706 static Param_Polyhedron
*Polyhedron2Param_SD(Polyhedron
**Din
,
3707 Polyhedron
*Cin
,int WS
,Polyhedron
**CEq
,Matrix
**CT
)
3709 static char data
[] = " 1 0 0 0 0 1 -18 "
3710 " 1 0 0 -20 0 19 1 "
3711 " 1 0 1 20 0 -20 16 "
3714 " 1 4 -20 0 0 -1 23 "
3715 " 1 -4 20 0 0 1 -22 "
3716 " 1 0 1 0 20 -20 16 "
3717 " 1 0 0 0 -20 19 1 ";
3718 static int checked
= 0;
3723 Matrix
*M
= Matrix_Alloc(9, 7);
3724 for (i
= 0; i
< 9; ++i
)
3725 for (int j
= 0; j
< 7; ++j
) {
3726 sscanf(p
, "%d%n", &v
, &n
);
3728 value_set_si(M
->p
[i
][j
], v
);
3730 Polyhedron
*P
= Constraints2Polyhedron(M
, 1024);
3733 Polyhedron
*U
= Universe_Polyhedron(1);
3735 Param_Polyhedron
*PP
=
3736 Polyhedron2Param_SimplifiedDomain(&P
, U
, 1024, NULL
, NULL
);
3739 Polyhedron_Free(P2
);
3742 for (i
= 0, V
= PP
->V
; V
; ++i
, V
= V
->next
)
3745 Param_Polyhedron_Free(PP
);
3747 fprintf(stderr
, "WARNING: results may be incorrect\n");
3749 "WARNING: use latest version of PolyLib to remove this warning\n");
3753 return Polyhedron2Param_SimplifiedDomain(Din
, Cin
, WS
, CEq
, CT
);
3757 static evalue
* barvinok_enumerate_ev_f(Polyhedron
*P
, Polyhedron
* C
,
3761 static evalue
* barvinok_enumerate_cst(Polyhedron
*P
, Polyhedron
* C
,
3766 ALLOC(evalue
, eres
);
3767 value_init(eres
->d
);
3768 value_set_si(eres
->d
, 0);
3769 eres
->x
.p
= new_enode(partition
, 2, C
->Dimension
);
3770 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[0], DomainConstraintSimplify(C
, MaxRays
));
3771 value_set_si(eres
->x
.p
->arr
[1].d
, 1);
3772 value_init(eres
->x
.p
->arr
[1].x
.n
);
3774 value_set_si(eres
->x
.p
->arr
[1].x
.n
, 0);
3776 barvinok_count(P
, &eres
->x
.p
->arr
[1].x
.n
, MaxRays
);
3781 evalue
* barvinok_enumerate_ev(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
3783 //P = unfringe(P, MaxRays);
3784 Polyhedron
*Corig
= C
;
3785 Polyhedron
*CEq
= NULL
, *rVD
, *CA
;
3787 unsigned nparam
= C
->Dimension
;
3791 value_init(factor
.d
);
3792 evalue_set_si(&factor
, 1, 1);
3794 CA
= align_context(C
, P
->Dimension
, MaxRays
);
3795 P
= DomainIntersection(P
, CA
, MaxRays
);
3796 Polyhedron_Free(CA
);
3799 POL_ENSURE_FACETS(P
);
3800 POL_ENSURE_VERTICES(P
);
3801 POL_ENSURE_FACETS(C
);
3802 POL_ENSURE_VERTICES(C
);
3804 if (C
->Dimension
== 0 || emptyQ(P
)) {
3806 eres
= barvinok_enumerate_cst(P
, CEq
? CEq
: Polyhedron_Copy(C
),
3809 emul(&factor
, eres
);
3810 reduce_evalue(eres
);
3811 free_evalue_refs(&factor
);
3818 if (Polyhedron_is_infinite(P
, nparam
))
3823 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, &f
);
3827 if (P
->Dimension
== nparam
) {
3829 P
= Universe_Polyhedron(0);
3833 Polyhedron
*T
= Polyhedron_Factor(P
, nparam
, MaxRays
);
3834 if (T
|| (P
->Dimension
== nparam
+1)) {
3837 for (Q
= T
? T
: P
; Q
; Q
= Q
->next
) {
3838 Polyhedron
*next
= Q
->next
;
3842 if (Q
->Dimension
!= C
->Dimension
)
3843 QC
= Polyhedron_Project(Q
, nparam
);
3846 C
= DomainIntersection(C
, QC
, MaxRays
);
3848 Polyhedron_Free(C2
);
3850 Polyhedron_Free(QC
);
3858 if (T
->Dimension
== C
->Dimension
) {
3865 Polyhedron
*next
= P
->next
;
3867 eres
= barvinok_enumerate_ev_f(P
, C
, MaxRays
);
3874 for (Q
= P
->next
; Q
; Q
= Q
->next
) {
3875 Polyhedron
*next
= Q
->next
;
3878 f
= barvinok_enumerate_ev_f(Q
, C
, MaxRays
);
3880 free_evalue_refs(f
);
3890 static evalue
* barvinok_enumerate_ev_f(Polyhedron
*P
, Polyhedron
* C
,
3893 unsigned nparam
= C
->Dimension
;
3895 if (P
->Dimension
- nparam
== 1)
3896 return ParamLine_Length(P
, C
, MaxRays
);
3898 Param_Polyhedron
*PP
= NULL
;
3899 Polyhedron
*CEq
= NULL
, *pVD
;
3901 Param_Domain
*D
, *next
;
3904 Polyhedron
*Porig
= P
;
3906 PP
= Polyhedron2Param_SD(&P
,C
,MaxRays
,&CEq
,&CT
);
3908 if (isIdentity(CT
)) {
3912 assert(CT
->NbRows
!= CT
->NbColumns
);
3913 if (CT
->NbRows
== 1) { // no more parameters
3914 eres
= barvinok_enumerate_cst(P
, CEq
, MaxRays
);
3919 Param_Polyhedron_Free(PP
);
3925 nparam
= CT
->NbRows
- 1;
3928 unsigned dim
= P
->Dimension
- nparam
;
3930 ALLOC(evalue
, eres
);
3931 value_init(eres
->d
);
3932 value_set_si(eres
->d
, 0);
3935 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
3936 struct section
{ Polyhedron
*D
; evalue E
; };
3937 section
*s
= new section
[nd
];
3938 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
3941 #ifdef USE_INCREMENTAL_BF
3942 bfenumerator
et(P
, dim
, PP
->nbV
);
3943 #elif defined USE_INCREMENTAL_DF
3944 ienumerator
et(P
, dim
, PP
->nbV
);
3946 enumerator
et(P
, dim
, PP
->nbV
);
3949 for(nd
= 0, D
=PP
->D
; D
; D
=next
) {
3952 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
3957 pVD
= CT
? DomainImage(rVD
,CT
,MaxRays
) : rVD
;
3959 value_init(s
[nd
].E
.d
);
3960 evalue_set_si(&s
[nd
].E
, 0, 1);
3963 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
3966 et
.decompose_at(V
, _i
, MaxRays
);
3967 } catch (OrthogonalException
&e
) {
3970 for (; nd
>= 0; --nd
) {
3971 free_evalue_refs(&s
[nd
].E
);
3972 Domain_Free(s
[nd
].D
);
3973 Domain_Free(fVD
[nd
]);
3977 eadd(et
.vE
[_i
] , &s
[nd
].E
);
3978 END_FORALL_PVertex_in_ParamPolyhedron
;
3979 reduce_in_domain(&s
[nd
].E
, pVD
);
3982 addeliminatedparams_evalue(&s
[nd
].E
, CT
);
3989 evalue_set_si(eres
, 0, 1);
3991 eres
->x
.p
= new_enode(partition
, 2*nd
, C
->Dimension
);
3992 for (int j
= 0; j
< nd
; ++j
) {
3993 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[2*j
], s
[j
].D
);
3994 value_clear(eres
->x
.p
->arr
[2*j
+1].d
);
3995 eres
->x
.p
->arr
[2*j
+1] = s
[j
].E
;
3996 Domain_Free(fVD
[j
]);
4003 Polyhedron_Free(CEq
);
4007 Enumeration
* barvinok_enumerate(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
4009 evalue
*EP
= barvinok_enumerate_ev(P
, C
, MaxRays
);
4011 return partition2enumeration(EP
);
4014 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
4016 for (int r
= 0; r
< n
; ++r
)
4017 value_swap(V
[r
][i
], V
[r
][j
]);
4020 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
4022 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
4023 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
4026 static void negative_test_constraint(Value
*l
, Value
*u
, Value
*c
, int pos
,
4029 value_oppose(*v
, u
[pos
+1]);
4030 Vector_Combine(l
+1, u
+1, c
+1, *v
, l
[pos
+1], len
-1);
4031 value_multiply(*v
, *v
, l
[pos
+1]);
4032 value_subtract(c
[len
-1], c
[len
-1], *v
);
4033 value_set_si(*v
, -1);
4034 Vector_Scale(c
+1, c
+1, *v
, len
-1);
4035 value_decrement(c
[len
-1], c
[len
-1]);
4036 ConstraintSimplify(c
, c
, len
, v
);
4039 static bool parallel_constraints(Value
*l
, Value
*u
, Value
*c
, int pos
,
4048 Vector_Gcd(&l
[1+pos
], len
, &g1
);
4049 Vector_Gcd(&u
[1+pos
], len
, &g2
);
4050 Vector_Combine(l
+1+pos
, u
+1+pos
, c
+1, g2
, g1
, len
);
4051 parallel
= First_Non_Zero(c
+1, len
) == -1;
4059 static void negative_test_constraint7(Value
*l
, Value
*u
, Value
*c
, int pos
,
4060 int exist
, int len
, Value
*v
)
4065 Vector_Gcd(&u
[1+pos
], exist
, v
);
4066 Vector_Gcd(&l
[1+pos
], exist
, &g
);
4067 Vector_Combine(l
+1, u
+1, c
+1, *v
, g
, len
-1);
4068 value_multiply(*v
, *v
, g
);
4069 value_subtract(c
[len
-1], c
[len
-1], *v
);
4070 value_set_si(*v
, -1);
4071 Vector_Scale(c
+1, c
+1, *v
, len
-1);
4072 value_decrement(c
[len
-1], c
[len
-1]);
4073 ConstraintSimplify(c
, c
, len
, v
);
4078 static void oppose_constraint(Value
*c
, int len
, Value
*v
)
4080 value_set_si(*v
, -1);
4081 Vector_Scale(c
+1, c
+1, *v
, len
-1);
4082 value_decrement(c
[len
-1], c
[len
-1]);
4085 static bool SplitOnConstraint(Polyhedron
*P
, int i
, int l
, int u
,
4086 int nvar
, int len
, int exist
, int MaxRays
,
4087 Vector
*row
, Value
& f
, bool independent
,
4088 Polyhedron
**pos
, Polyhedron
**neg
)
4090 negative_test_constraint(P
->Constraint
[l
], P
->Constraint
[u
],
4091 row
->p
, nvar
+i
, len
, &f
);
4092 *neg
= AddConstraints(row
->p
, 1, P
, MaxRays
);
4094 /* We found an independent, but useless constraint
4095 * Maybe we should detect this earlier and not
4096 * mark the variable as INDEPENDENT
4098 if (emptyQ((*neg
))) {
4099 Polyhedron_Free(*neg
);
4103 oppose_constraint(row
->p
, len
, &f
);
4104 *pos
= AddConstraints(row
->p
, 1, P
, MaxRays
);
4106 if (emptyQ((*pos
))) {
4107 Polyhedron_Free(*neg
);
4108 Polyhedron_Free(*pos
);
4116 * unimodularly transform P such that constraint r is transformed
4117 * into a constraint that involves only a single (the first)
4118 * existential variable
4121 static Polyhedron
*rotate_along(Polyhedron
*P
, int r
, int nvar
, int exist
,
4127 Vector
*row
= Vector_Alloc(exist
);
4128 Vector_Copy(P
->Constraint
[r
]+1+nvar
, row
->p
, exist
);
4129 Vector_Gcd(row
->p
, exist
, &g
);
4130 if (value_notone_p(g
))
4131 Vector_AntiScale(row
->p
, row
->p
, g
, exist
);
4134 Matrix
*M
= unimodular_complete(row
);
4135 Matrix
*M2
= Matrix_Alloc(P
->Dimension
+1, P
->Dimension
+1);
4136 for (r
= 0; r
< nvar
; ++r
)
4137 value_set_si(M2
->p
[r
][r
], 1);
4138 for ( ; r
< nvar
+exist
; ++r
)
4139 Vector_Copy(M
->p
[r
-nvar
], M2
->p
[r
]+nvar
, exist
);
4140 for ( ; r
< P
->Dimension
+1; ++r
)
4141 value_set_si(M2
->p
[r
][r
], 1);
4142 Polyhedron
*T
= Polyhedron_Image(P
, M2
, MaxRays
);
4151 static bool SplitOnVar(Polyhedron
*P
, int i
,
4152 int nvar
, int len
, int exist
, int MaxRays
,
4153 Vector
*row
, Value
& f
, bool independent
,
4154 Polyhedron
**pos
, Polyhedron
**neg
)
4158 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
4159 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
4163 for (j
= 0; j
< exist
; ++j
)
4164 if (j
!= i
&& value_notzero_p(P
->Constraint
[l
][nvar
+j
+1]))
4170 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
4171 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
4175 for (j
= 0; j
< exist
; ++j
)
4176 if (j
!= i
&& value_notzero_p(P
->Constraint
[u
][nvar
+j
+1]))
4182 if (SplitOnConstraint(P
, i
, l
, u
,
4183 nvar
, len
, exist
, MaxRays
,
4184 row
, f
, independent
,
4188 SwapColumns(*neg
, nvar
+1, nvar
+1+i
);
4198 static bool double_bound_pair(Polyhedron
*P
, int nvar
, int exist
,
4199 int i
, int l1
, int l2
,
4200 Polyhedron
**pos
, Polyhedron
**neg
)
4204 Vector
*row
= Vector_Alloc(P
->Dimension
+2);
4205 value_set_si(row
->p
[0], 1);
4206 value_oppose(f
, P
->Constraint
[l1
][nvar
+i
+1]);
4207 Vector_Combine(P
->Constraint
[l1
]+1, P
->Constraint
[l2
]+1,
4209 P
->Constraint
[l2
][nvar
+i
+1], f
,
4211 ConstraintSimplify(row
->p
, row
->p
, P
->Dimension
+2, &f
);
4212 *pos
= AddConstraints(row
->p
, 1, P
, 0);
4213 value_set_si(f
, -1);
4214 Vector_Scale(row
->p
+1, row
->p
+1, f
, P
->Dimension
+1);
4215 value_decrement(row
->p
[P
->Dimension
+1], row
->p
[P
->Dimension
+1]);
4216 *neg
= AddConstraints(row
->p
, 1, P
, 0);
4220 return !emptyQ((*pos
)) && !emptyQ((*neg
));
4223 static bool double_bound(Polyhedron
*P
, int nvar
, int exist
,
4224 Polyhedron
**pos
, Polyhedron
**neg
)
4226 for (int i
= 0; i
< exist
; ++i
) {
4228 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
4229 if (value_negz_p(P
->Constraint
[l1
][nvar
+i
+1]))
4231 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
4232 if (value_negz_p(P
->Constraint
[l2
][nvar
+i
+1]))
4234 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
4238 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
4239 if (value_posz_p(P
->Constraint
[l1
][nvar
+i
+1]))
4241 if (l1
< P
->NbConstraints
)
4242 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
4243 if (value_posz_p(P
->Constraint
[l2
][nvar
+i
+1]))
4245 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
4257 INDEPENDENT
= 1 << 2,
4261 static evalue
* enumerate_or(Polyhedron
*D
,
4262 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4265 fprintf(stderr
, "\nER: Or\n");
4266 #endif /* DEBUG_ER */
4268 Polyhedron
*N
= D
->next
;
4271 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
4274 for (D
= N
; D
; D
= N
) {
4279 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
4282 free_evalue_refs(EN
);
4292 static evalue
* enumerate_sum(Polyhedron
*P
,
4293 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4295 int nvar
= P
->Dimension
- exist
- nparam
;
4296 int toswap
= nvar
< exist
? nvar
: exist
;
4297 for (int i
= 0; i
< toswap
; ++i
)
4298 SwapColumns(P
, 1 + i
, nvar
+exist
- i
);
4302 fprintf(stderr
, "\nER: Sum\n");
4303 #endif /* DEBUG_ER */
4305 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
4307 for (int i
= 0; i
< /* nvar */ nparam
; ++i
) {
4308 Matrix
*C
= Matrix_Alloc(1, 1 + nparam
+ 1);
4309 value_set_si(C
->p
[0][0], 1);
4311 value_init(split
.d
);
4312 value_set_si(split
.d
, 0);
4313 split
.x
.p
= new_enode(partition
, 4, nparam
);
4314 value_set_si(C
->p
[0][1+i
], 1);
4315 Matrix
*C2
= Matrix_Copy(C
);
4316 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[0],
4317 Constraints2Polyhedron(C2
, MaxRays
));
4319 evalue_set_si(&split
.x
.p
->arr
[1], 1, 1);
4320 value_set_si(C
->p
[0][1+i
], -1);
4321 value_set_si(C
->p
[0][1+nparam
], -1);
4322 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[2],
4323 Constraints2Polyhedron(C
, MaxRays
));
4324 evalue_set_si(&split
.x
.p
->arr
[3], 1, 1);
4326 free_evalue_refs(&split
);
4330 evalue_range_reduction(EP
);
4332 evalue_frac2floor(EP
);
4334 evalue
*sum
= esum(EP
, nvar
);
4336 free_evalue_refs(EP
);
4340 evalue_range_reduction(EP
);
4345 static evalue
* split_sure(Polyhedron
*P
, Polyhedron
*S
,
4346 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4348 int nvar
= P
->Dimension
- exist
- nparam
;
4350 Matrix
*M
= Matrix_Alloc(exist
, S
->Dimension
+2);
4351 for (int i
= 0; i
< exist
; ++i
)
4352 value_set_si(M
->p
[i
][nvar
+i
+1], 1);
4354 S
= DomainAddRays(S
, M
, MaxRays
);
4356 Polyhedron
*F
= DomainAddRays(P
, M
, MaxRays
);
4357 Polyhedron
*D
= DomainDifference(F
, S
, MaxRays
);
4359 D
= Disjoint_Domain(D
, 0, MaxRays
);
4364 M
= Matrix_Alloc(P
->Dimension
+1-exist
, P
->Dimension
+1);
4365 for (int j
= 0; j
< nvar
; ++j
)
4366 value_set_si(M
->p
[j
][j
], 1);
4367 for (int j
= 0; j
< nparam
+1; ++j
)
4368 value_set_si(M
->p
[nvar
+j
][nvar
+exist
+j
], 1);
4369 Polyhedron
*T
= Polyhedron_Image(S
, M
, MaxRays
);
4370 evalue
*EP
= barvinok_enumerate_e(T
, 0, nparam
, MaxRays
);
4375 for (Polyhedron
*Q
= D
; Q
; Q
= Q
->next
) {
4376 Polyhedron
*N
= Q
->next
;
4378 T
= DomainIntersection(P
, Q
, MaxRays
);
4379 evalue
*E
= barvinok_enumerate_e(T
, exist
, nparam
, MaxRays
);
4381 free_evalue_refs(E
);
4390 static evalue
* enumerate_sure(Polyhedron
*P
,
4391 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4395 int nvar
= P
->Dimension
- exist
- nparam
;
4401 for (i
= 0; i
< exist
; ++i
) {
4402 Matrix
*M
= Matrix_Alloc(S
->NbConstraints
, S
->Dimension
+2);
4404 value_set_si(lcm
, 1);
4405 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
4406 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
4408 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
4410 value_lcm(lcm
, S
->Constraint
[j
][1+nvar
+i
], &lcm
);
4413 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
4414 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
4416 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
4418 value_division(f
, lcm
, S
->Constraint
[j
][1+nvar
+i
]);
4419 Vector_Scale(S
->Constraint
[j
], M
->p
[c
], f
, S
->Dimension
+2);
4420 value_subtract(M
->p
[c
][S
->Dimension
+1],
4421 M
->p
[c
][S
->Dimension
+1],
4423 value_increment(M
->p
[c
][S
->Dimension
+1],
4424 M
->p
[c
][S
->Dimension
+1]);
4428 S
= AddConstraints(M
->p
[0], c
, S
, MaxRays
);
4443 fprintf(stderr
, "\nER: Sure\n");
4444 #endif /* DEBUG_ER */
4446 return split_sure(P
, S
, exist
, nparam
, MaxRays
);
4449 static evalue
* enumerate_sure2(Polyhedron
*P
,
4450 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4452 int nvar
= P
->Dimension
- exist
- nparam
;
4454 for (r
= 0; r
< P
->NbRays
; ++r
)
4455 if (value_one_p(P
->Ray
[r
][0]) &&
4456 value_one_p(P
->Ray
[r
][P
->Dimension
+1]))
4462 Matrix
*M
= Matrix_Alloc(nvar
+ 1 + nparam
, P
->Dimension
+2);
4463 for (int i
= 0; i
< nvar
; ++i
)
4464 value_set_si(M
->p
[i
][1+i
], 1);
4465 for (int i
= 0; i
< nparam
; ++i
)
4466 value_set_si(M
->p
[i
+nvar
][1+nvar
+exist
+i
], 1);
4467 Vector_Copy(P
->Ray
[r
]+1+nvar
, M
->p
[nvar
+nparam
]+1+nvar
, exist
);
4468 value_set_si(M
->p
[nvar
+nparam
][0], 1);
4469 value_set_si(M
->p
[nvar
+nparam
][P
->Dimension
+1], 1);
4470 Polyhedron
* F
= Rays2Polyhedron(M
, MaxRays
);
4473 Polyhedron
*I
= DomainIntersection(F
, P
, MaxRays
);
4477 fprintf(stderr
, "\nER: Sure2\n");
4478 #endif /* DEBUG_ER */
4480 return split_sure(P
, I
, exist
, nparam
, MaxRays
);
4483 static evalue
* enumerate_cyclic(Polyhedron
*P
,
4484 unsigned exist
, unsigned nparam
,
4485 evalue
* EP
, int r
, int p
, unsigned MaxRays
)
4487 int nvar
= P
->Dimension
- exist
- nparam
;
4489 /* If EP in its fractional maps only contains references
4490 * to the remainder parameter with appropriate coefficients
4491 * then we could in principle avoid adding existentially
4492 * quantified variables to the validity domains.
4493 * We'd have to replace the remainder by m { p/m }
4494 * and multiply with an appropriate factor that is one
4495 * only in the appropriate range.
4496 * This last multiplication can be avoided if EP
4497 * has a single validity domain with no (further)
4498 * constraints on the remainder parameter
4501 Matrix
*CT
= Matrix_Alloc(nparam
+1, nparam
+3);
4502 Matrix
*M
= Matrix_Alloc(1, 1+nparam
+3);
4503 for (int j
= 0; j
< nparam
; ++j
)
4505 value_set_si(CT
->p
[j
][j
], 1);
4506 value_set_si(CT
->p
[p
][nparam
+1], 1);
4507 value_set_si(CT
->p
[nparam
][nparam
+2], 1);
4508 value_set_si(M
->p
[0][1+p
], -1);
4509 value_absolute(M
->p
[0][1+nparam
], P
->Ray
[0][1+nvar
+exist
+p
]);
4510 value_set_si(M
->p
[0][1+nparam
+1], 1);
4511 Polyhedron
*CEq
= Constraints2Polyhedron(M
, 1);
4513 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
4514 Polyhedron_Free(CEq
);
4520 static void enumerate_vd_add_ray(evalue
*EP
, Matrix
*Rays
, unsigned MaxRays
)
4522 if (value_notzero_p(EP
->d
))
4525 assert(EP
->x
.p
->type
== partition
);
4526 assert(EP
->x
.p
->pos
== EVALUE_DOMAIN(EP
->x
.p
->arr
[0])->Dimension
);
4527 for (int i
= 0; i
< EP
->x
.p
->size
/2; ++i
) {
4528 Polyhedron
*D
= EVALUE_DOMAIN(EP
->x
.p
->arr
[2*i
]);
4529 Polyhedron
*N
= DomainAddRays(D
, Rays
, MaxRays
);
4530 EVALUE_SET_DOMAIN(EP
->x
.p
->arr
[2*i
], N
);
4535 static evalue
* enumerate_line(Polyhedron
*P
,
4536 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4542 fprintf(stderr
, "\nER: Line\n");
4543 #endif /* DEBUG_ER */
4545 int nvar
= P
->Dimension
- exist
- nparam
;
4547 for (i
= 0; i
< nparam
; ++i
)
4548 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
4551 for (j
= i
+1; j
< nparam
; ++j
)
4552 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
4554 assert(j
>= nparam
); // for now
4556 Matrix
*M
= Matrix_Alloc(2, P
->Dimension
+2);
4557 value_set_si(M
->p
[0][0], 1);
4558 value_set_si(M
->p
[0][1+nvar
+exist
+i
], 1);
4559 value_set_si(M
->p
[1][0], 1);
4560 value_set_si(M
->p
[1][1+nvar
+exist
+i
], -1);
4561 value_absolute(M
->p
[1][1+P
->Dimension
], P
->Ray
[0][1+nvar
+exist
+i
]);
4562 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
4563 Polyhedron
*S
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
4564 evalue
*EP
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
4568 return enumerate_cyclic(P
, exist
, nparam
, EP
, 0, i
, MaxRays
);
4571 static int single_param_pos(Polyhedron
*P
, unsigned exist
, unsigned nparam
,
4574 int nvar
= P
->Dimension
- exist
- nparam
;
4575 if (First_Non_Zero(P
->Ray
[r
]+1, nvar
) != -1)
4577 int i
= First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
, nparam
);
4580 if (First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
+1, nparam
-i
-1) != -1)
4585 static evalue
* enumerate_remove_ray(Polyhedron
*P
, int r
,
4586 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4589 fprintf(stderr
, "\nER: RedundantRay\n");
4590 #endif /* DEBUG_ER */
4594 value_set_si(one
, 1);
4595 int len
= P
->NbRays
-1;
4596 Matrix
*M
= Matrix_Alloc(2 * len
, P
->Dimension
+2);
4597 Vector_Copy(P
->Ray
[0], M
->p
[0], r
* (P
->Dimension
+2));
4598 Vector_Copy(P
->Ray
[r
+1], M
->p
[r
], (len
-r
) * (P
->Dimension
+2));
4599 for (int j
= 0; j
< P
->NbRays
; ++j
) {
4602 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[len
+j
-(j
>r
)],
4603 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
4606 P
= Rays2Polyhedron(M
, MaxRays
);
4608 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
4615 static evalue
* enumerate_redundant_ray(Polyhedron
*P
,
4616 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4618 assert(P
->NbBid
== 0);
4619 int nvar
= P
->Dimension
- exist
- nparam
;
4623 for (int r
= 0; r
< P
->NbRays
; ++r
) {
4624 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
4626 int i1
= single_param_pos(P
, exist
, nparam
, r
);
4629 for (int r2
= r
+1; r2
< P
->NbRays
; ++r2
) {
4630 if (value_notzero_p(P
->Ray
[r2
][P
->Dimension
+1]))
4632 int i2
= single_param_pos(P
, exist
, nparam
, r2
);
4638 value_division(m
, P
->Ray
[r
][1+nvar
+exist
+i1
],
4639 P
->Ray
[r2
][1+nvar
+exist
+i1
]);
4640 value_multiply(m
, m
, P
->Ray
[r2
][1+nvar
+exist
+i1
]);
4641 /* r2 divides r => r redundant */
4642 if (value_eq(m
, P
->Ray
[r
][1+nvar
+exist
+i1
])) {
4644 return enumerate_remove_ray(P
, r
, exist
, nparam
, MaxRays
);
4647 value_division(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
],
4648 P
->Ray
[r
][1+nvar
+exist
+i1
]);
4649 value_multiply(m
, m
, P
->Ray
[r
][1+nvar
+exist
+i1
]);
4650 /* r divides r2 => r2 redundant */
4651 if (value_eq(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
])) {
4653 return enumerate_remove_ray(P
, r2
, exist
, nparam
, MaxRays
);
4661 static Polyhedron
*upper_bound(Polyhedron
*P
,
4662 int pos
, Value
*max
, Polyhedron
**R
)
4671 for (Polyhedron
*Q
= P
; Q
; Q
= N
) {
4673 for (r
= 0; r
< P
->NbRays
; ++r
) {
4674 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]) &&
4675 value_pos_p(P
->Ray
[r
][1+pos
]))
4678 if (r
< P
->NbRays
) {
4686 for (r
= 0; r
< P
->NbRays
; ++r
) {
4687 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
4689 mpz_fdiv_q(v
, P
->Ray
[r
][1+pos
], P
->Ray
[r
][1+P
->Dimension
]);
4690 if ((!Q
->next
&& r
== 0) || value_gt(v
, *max
))
4691 value_assign(*max
, v
);
4698 static evalue
* enumerate_ray(Polyhedron
*P
,
4699 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4701 assert(P
->NbBid
== 0);
4702 int nvar
= P
->Dimension
- exist
- nparam
;
4705 for (r
= 0; r
< P
->NbRays
; ++r
)
4706 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
4712 for (r2
= r
+1; r2
< P
->NbRays
; ++r2
)
4713 if (value_zero_p(P
->Ray
[r2
][P
->Dimension
+1]))
4715 if (r2
< P
->NbRays
) {
4717 return enumerate_sum(P
, exist
, nparam
, MaxRays
);
4721 fprintf(stderr
, "\nER: Ray\n");
4722 #endif /* DEBUG_ER */
4728 value_set_si(one
, 1);
4729 int i
= single_param_pos(P
, exist
, nparam
, r
);
4730 assert(i
!= -1); // for now;
4732 Matrix
*M
= Matrix_Alloc(P
->NbRays
, P
->Dimension
+2);
4733 for (int j
= 0; j
< P
->NbRays
; ++j
) {
4734 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[j
],
4735 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
4737 Polyhedron
*S
= Rays2Polyhedron(M
, MaxRays
);
4739 Polyhedron
*D
= DomainDifference(P
, S
, MaxRays
);
4741 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
4742 assert(value_pos_p(P
->Ray
[r
][1+nvar
+exist
+i
])); // for now
4744 D
= upper_bound(D
, nvar
+exist
+i
, &m
, &R
);
4748 M
= Matrix_Alloc(2, P
->Dimension
+2);
4749 value_set_si(M
->p
[0][0], 1);
4750 value_set_si(M
->p
[1][0], 1);
4751 value_set_si(M
->p
[0][1+nvar
+exist
+i
], -1);
4752 value_set_si(M
->p
[1][1+nvar
+exist
+i
], 1);
4753 value_assign(M
->p
[0][1+P
->Dimension
], m
);
4754 value_oppose(M
->p
[1][1+P
->Dimension
], m
);
4755 value_addto(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
],
4756 P
->Ray
[r
][1+nvar
+exist
+i
]);
4757 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
4758 // Matrix_Print(stderr, P_VALUE_FMT, M);
4759 D
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
4760 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
4761 value_subtract(M
->p
[0][1+P
->Dimension
], M
->p
[0][1+P
->Dimension
],
4762 P
->Ray
[r
][1+nvar
+exist
+i
]);
4763 // Matrix_Print(stderr, P_VALUE_FMT, M);
4764 S
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
4765 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
4768 evalue
*EP
= barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
4773 if (value_notone_p(P
->Ray
[r
][1+nvar
+exist
+i
]))
4774 EP
= enumerate_cyclic(P
, exist
, nparam
, EP
, r
, i
, MaxRays
);
4776 M
= Matrix_Alloc(1, nparam
+2);
4777 value_set_si(M
->p
[0][0], 1);
4778 value_set_si(M
->p
[0][1+i
], 1);
4779 enumerate_vd_add_ray(EP
, M
, MaxRays
);
4784 evalue
*E
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
4786 free_evalue_refs(E
);
4793 evalue
*ER
= enumerate_or(R
, exist
, nparam
, MaxRays
);
4795 free_evalue_refs(ER
);
4802 static evalue
* enumerate_vd(Polyhedron
**PA
,
4803 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4805 Polyhedron
*P
= *PA
;
4806 int nvar
= P
->Dimension
- exist
- nparam
;
4807 Param_Polyhedron
*PP
= NULL
;
4808 Polyhedron
*C
= Universe_Polyhedron(nparam
);
4812 PP
= Polyhedron2Param_SimplifiedDomain(&PR
,C
,MaxRays
,&CEq
,&CT
);
4816 Param_Domain
*D
, *last
;
4819 for (nd
= 0, D
=PP
->D
; D
; D
=D
->next
, ++nd
)
4822 Polyhedron
**VD
= new Polyhedron_p
[nd
];
4823 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
4824 for(nd
= 0, D
=PP
->D
; D
; D
=D
->next
) {
4825 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
4839 /* This doesn't seem to have any effect */
4841 Polyhedron
*CA
= align_context(VD
[0], P
->Dimension
, MaxRays
);
4843 P
= DomainIntersection(P
, CA
, MaxRays
);
4846 Polyhedron_Free(CA
);
4851 if (!EP
&& CT
->NbColumns
!= CT
->NbRows
) {
4852 Polyhedron
*CEqr
= DomainImage(CEq
, CT
, MaxRays
);
4853 Polyhedron
*CA
= align_context(CEqr
, PR
->Dimension
, MaxRays
);
4854 Polyhedron
*I
= DomainIntersection(PR
, CA
, MaxRays
);
4855 Polyhedron_Free(CEqr
);
4856 Polyhedron_Free(CA
);
4858 fprintf(stderr
, "\nER: Eliminate\n");
4859 #endif /* DEBUG_ER */
4860 nparam
-= CT
->NbColumns
- CT
->NbRows
;
4861 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
4862 nparam
+= CT
->NbColumns
- CT
->NbRows
;
4863 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
4867 Polyhedron_Free(PR
);
4870 if (!EP
&& nd
> 1) {
4872 fprintf(stderr
, "\nER: VD\n");
4873 #endif /* DEBUG_ER */
4874 for (int i
= 0; i
< nd
; ++i
) {
4875 Polyhedron
*CA
= align_context(VD
[i
], P
->Dimension
, MaxRays
);
4876 Polyhedron
*I
= DomainIntersection(P
, CA
, MaxRays
);
4879 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
4881 evalue
*E
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
4883 free_evalue_refs(E
);
4887 Polyhedron_Free(CA
);
4891 for (int i
= 0; i
< nd
; ++i
) {
4892 Polyhedron_Free(VD
[i
]);
4893 Polyhedron_Free(fVD
[i
]);
4899 if (!EP
&& nvar
== 0) {
4902 Param_Vertices
*V
, *V2
;
4903 Matrix
* M
= Matrix_Alloc(1, P
->Dimension
+2);
4905 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
4907 FORALL_PVertex_in_ParamPolyhedron(V2
, last
, PP
) {
4914 for (int i
= 0; i
< exist
; ++i
) {
4915 value_oppose(f
, V
->Vertex
->p
[i
][nparam
+1]);
4916 Vector_Combine(V
->Vertex
->p
[i
],
4918 M
->p
[0] + 1 + nvar
+ exist
,
4919 V2
->Vertex
->p
[i
][nparam
+1],
4923 for (j
= 0; j
< nparam
; ++j
)
4924 if (value_notzero_p(M
->p
[0][1+nvar
+exist
+j
]))
4928 ConstraintSimplify(M
->p
[0], M
->p
[0],
4929 P
->Dimension
+2, &f
);
4930 value_set_si(M
->p
[0][0], 0);
4931 Polyhedron
*para
= AddConstraints(M
->p
[0], 1, P
,
4934 Polyhedron_Free(para
);
4937 Polyhedron
*pos
, *neg
;
4938 value_set_si(M
->p
[0][0], 1);
4939 value_decrement(M
->p
[0][P
->Dimension
+1],
4940 M
->p
[0][P
->Dimension
+1]);
4941 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
4942 value_set_si(f
, -1);
4943 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
4945 value_decrement(M
->p
[0][P
->Dimension
+1],
4946 M
->p
[0][P
->Dimension
+1]);
4947 value_decrement(M
->p
[0][P
->Dimension
+1],
4948 M
->p
[0][P
->Dimension
+1]);
4949 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
4950 if (emptyQ(neg
) && emptyQ(pos
)) {
4951 Polyhedron_Free(para
);
4952 Polyhedron_Free(pos
);
4953 Polyhedron_Free(neg
);
4957 fprintf(stderr
, "\nER: Order\n");
4958 #endif /* DEBUG_ER */
4959 EP
= barvinok_enumerate_e(para
, exist
, nparam
, MaxRays
);
4962 E
= barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
4964 free_evalue_refs(E
);
4968 E
= barvinok_enumerate_e(neg
, exist
, nparam
, MaxRays
);
4970 free_evalue_refs(E
);
4973 Polyhedron_Free(para
);
4974 Polyhedron_Free(pos
);
4975 Polyhedron_Free(neg
);
4980 } END_FORALL_PVertex_in_ParamPolyhedron
;
4983 } END_FORALL_PVertex_in_ParamPolyhedron
;
4986 /* Search for vertex coordinate to split on */
4987 /* First look for one independent of the parameters */
4988 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
4989 for (int i
= 0; i
< exist
; ++i
) {
4991 for (j
= 0; j
< nparam
; ++j
)
4992 if (value_notzero_p(V
->Vertex
->p
[i
][j
]))
4996 value_set_si(M
->p
[0][0], 1);
4997 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
4998 Vector_Copy(V
->Vertex
->p
[i
],
4999 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
5000 value_oppose(M
->p
[0][1+nvar
+i
],
5001 V
->Vertex
->p
[i
][nparam
+1]);
5003 Polyhedron
*pos
, *neg
;
5004 value_set_si(M
->p
[0][0], 1);
5005 value_decrement(M
->p
[0][P
->Dimension
+1],
5006 M
->p
[0][P
->Dimension
+1]);
5007 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5008 value_set_si(f
, -1);
5009 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
5011 value_decrement(M
->p
[0][P
->Dimension
+1],
5012 M
->p
[0][P
->Dimension
+1]);
5013 value_decrement(M
->p
[0][P
->Dimension
+1],
5014 M
->p
[0][P
->Dimension
+1]);
5015 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5016 if (emptyQ(neg
) || emptyQ(pos
)) {
5017 Polyhedron_Free(pos
);
5018 Polyhedron_Free(neg
);
5021 Polyhedron_Free(pos
);
5022 value_increment(M
->p
[0][P
->Dimension
+1],
5023 M
->p
[0][P
->Dimension
+1]);
5024 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5026 fprintf(stderr
, "\nER: Vertex\n");
5027 #endif /* DEBUG_ER */
5029 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
5034 } END_FORALL_PVertex_in_ParamPolyhedron
;
5038 /* Search for vertex coordinate to split on */
5039 /* Now look for one that depends on the parameters */
5040 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
5041 for (int i
= 0; i
< exist
; ++i
) {
5042 value_set_si(M
->p
[0][0], 1);
5043 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
5044 Vector_Copy(V
->Vertex
->p
[i
],
5045 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
5046 value_oppose(M
->p
[0][1+nvar
+i
],
5047 V
->Vertex
->p
[i
][nparam
+1]);
5049 Polyhedron
*pos
, *neg
;
5050 value_set_si(M
->p
[0][0], 1);
5051 value_decrement(M
->p
[0][P
->Dimension
+1],
5052 M
->p
[0][P
->Dimension
+1]);
5053 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5054 value_set_si(f
, -1);
5055 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
5057 value_decrement(M
->p
[0][P
->Dimension
+1],
5058 M
->p
[0][P
->Dimension
+1]);
5059 value_decrement(M
->p
[0][P
->Dimension
+1],
5060 M
->p
[0][P
->Dimension
+1]);
5061 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5062 if (emptyQ(neg
) || emptyQ(pos
)) {
5063 Polyhedron_Free(pos
);
5064 Polyhedron_Free(neg
);
5067 Polyhedron_Free(pos
);
5068 value_increment(M
->p
[0][P
->Dimension
+1],
5069 M
->p
[0][P
->Dimension
+1]);
5070 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5072 fprintf(stderr
, "\nER: ParamVertex\n");
5073 #endif /* DEBUG_ER */
5075 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
5080 } END_FORALL_PVertex_in_ParamPolyhedron
;
5088 Polyhedron_Free(CEq
);
5092 Param_Polyhedron_Free(PP
);
5099 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
5100 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5105 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
5106 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5108 int nvar
= P
->Dimension
- exist
- nparam
;
5109 evalue
*EP
= new_zero_ep();
5113 fprintf(stderr
, "\nER: PIP\n");
5114 #endif /* DEBUG_ER */
5116 Polyhedron
*D
= pip_projectout(P
, nvar
, exist
, nparam
);
5117 for (Q
= D
; Q
; Q
= N
) {
5121 exist
= Q
->Dimension
- nvar
- nparam
;
5122 E
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
5125 free_evalue_refs(E
);
5134 static bool is_single(Value
*row
, int pos
, int len
)
5136 return First_Non_Zero(row
, pos
) == -1 &&
5137 First_Non_Zero(row
+pos
+1, len
-pos
-1) == -1;
5140 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
5141 unsigned exist
, unsigned nparam
, unsigned MaxRays
);
5144 static int er_level
= 0;
5146 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
5147 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5149 fprintf(stderr
, "\nER: level %i\n", er_level
);
5151 Polyhedron_PrintConstraints(stderr
, P_VALUE_FMT
, P
);
5152 fprintf(stderr
, "\nE %d\nP %d\n", exist
, nparam
);
5154 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
5155 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
5161 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
5162 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5164 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
5165 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
5171 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
5172 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5175 Polyhedron
*U
= Universe_Polyhedron(nparam
);
5176 evalue
*EP
= barvinok_enumerate_ev(P
, U
, MaxRays
);
5177 //char *param_name[] = {"P", "Q", "R", "S", "T" };
5178 //print_evalue(stdout, EP, param_name);
5183 int nvar
= P
->Dimension
- exist
- nparam
;
5184 int len
= P
->Dimension
+ 2;
5187 POL_ENSURE_FACETS(P
);
5188 POL_ENSURE_VERTICES(P
);
5191 return new_zero_ep();
5193 if (nvar
== 0 && nparam
== 0) {
5194 evalue
*EP
= new_zero_ep();
5195 barvinok_count(P
, &EP
->x
.n
, MaxRays
);
5196 if (value_pos_p(EP
->x
.n
))
5197 value_set_si(EP
->x
.n
, 1);
5202 for (r
= 0; r
< P
->NbRays
; ++r
)
5203 if (value_zero_p(P
->Ray
[r
][0]) ||
5204 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
5206 for (i
= 0; i
< nvar
; ++i
)
5207 if (value_notzero_p(P
->Ray
[r
][i
+1]))
5211 for (i
= nvar
+ exist
; i
< nvar
+ exist
+ nparam
; ++i
)
5212 if (value_notzero_p(P
->Ray
[r
][i
+1]))
5214 if (i
>= nvar
+ exist
+ nparam
)
5217 if (r
< P
->NbRays
) {
5218 evalue
*EP
= new_zero_ep();
5219 value_set_si(EP
->x
.n
, -1);
5224 for (r
= 0; r
< P
->NbEq
; ++r
)
5225 if ((first
= First_Non_Zero(P
->Constraint
[r
]+1+nvar
, exist
)) != -1)
5228 if (First_Non_Zero(P
->Constraint
[r
]+1+nvar
+first
+1,
5229 exist
-first
-1) != -1) {
5230 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
5232 fprintf(stderr
, "\nER: Equality\n");
5233 #endif /* DEBUG_ER */
5234 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5239 fprintf(stderr
, "\nER: Fixed\n");
5240 #endif /* DEBUG_ER */
5242 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
5244 Polyhedron
*T
= Polyhedron_Copy(P
);
5245 SwapColumns(T
, nvar
+1, nvar
+1+first
);
5246 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5253 Vector
*row
= Vector_Alloc(len
);
5254 value_set_si(row
->p
[0], 1);
5259 enum constraint
* info
= new constraint
[exist
];
5260 for (int i
= 0; i
< exist
; ++i
) {
5262 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
5263 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
5265 bool l_parallel
= is_single(P
->Constraint
[l
]+nvar
+1, i
, exist
);
5266 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
5267 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
5269 bool lu_parallel
= l_parallel
||
5270 is_single(P
->Constraint
[u
]+nvar
+1, i
, exist
);
5271 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
5272 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1, row
->p
+1,
5273 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
5274 if (!(info
[i
] & INDEPENDENT
)) {
5276 for (j
= 0; j
< exist
; ++j
)
5277 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
5280 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
5281 info
[i
] = (constraint
)(info
[i
] | INDEPENDENT
);
5284 if (info
[i
] & ALL_POS
) {
5285 value_addto(row
->p
[len
-1], row
->p
[len
-1],
5286 P
->Constraint
[l
][nvar
+i
+1]);
5287 value_addto(row
->p
[len
-1], row
->p
[len
-1], f
);
5288 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
5289 value_subtract(row
->p
[len
-1], row
->p
[len
-1], f
);
5290 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
5291 ConstraintSimplify(row
->p
, row
->p
, len
, &f
);
5292 value_set_si(f
, -1);
5293 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
5294 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
5295 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
5297 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
5298 info
[i
] = (constraint
)(info
[i
] ^ ALL_POS
);
5300 //puts("pos remainder");
5301 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
5304 if (!(info
[i
] & ONE_NEG
)) {
5306 negative_test_constraint(P
->Constraint
[l
],
5308 row
->p
, nvar
+i
, len
, &f
);
5309 oppose_constraint(row
->p
, len
, &f
);
5310 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
5312 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
5313 info
[i
] = (constraint
)(info
[i
] | ONE_NEG
);
5315 //puts("neg remainder");
5316 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
5318 } else if (!(info
[i
] & ROT_NEG
)) {
5319 if (parallel_constraints(P
->Constraint
[l
],
5321 row
->p
, nvar
, exist
)) {
5322 negative_test_constraint7(P
->Constraint
[l
],
5324 row
->p
, nvar
, exist
,
5326 oppose_constraint(row
->p
, len
, &f
);
5327 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
5329 // printf("rot_neg i: %d, l: %d, u: %d\n", i, l, u);
5330 info
[i
] = (constraint
)(info
[i
] | ROT_NEG
);
5333 //puts("neg remainder");
5334 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
5339 if (!(info
[i
] & ALL_POS
) && (info
[i
] & (ONE_NEG
| ROT_NEG
)))
5343 if (info
[i
] & ALL_POS
)
5350 for (int i = 0; i < exist; ++i)
5351 printf("%i: %i\n", i, info[i]);
5353 for (int i
= 0; i
< exist
; ++i
)
5354 if (info
[i
] & ALL_POS
) {
5356 fprintf(stderr
, "\nER: Positive\n");
5357 #endif /* DEBUG_ER */
5359 // Maybe we should chew off some of the fat here
5360 Matrix
*M
= Matrix_Alloc(P
->Dimension
, P
->Dimension
+1);
5361 for (int j
= 0; j
< P
->Dimension
; ++j
)
5362 value_set_si(M
->p
[j
][j
+ (j
>= i
+nvar
)], 1);
5363 Polyhedron
*T
= Polyhedron_Image(P
, M
, MaxRays
);
5365 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5372 for (int i
= 0; i
< exist
; ++i
)
5373 if (info
[i
] & ONE_NEG
) {
5375 fprintf(stderr
, "\nER: Negative\n");
5376 #endif /* DEBUG_ER */
5381 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
5383 Polyhedron
*T
= Polyhedron_Copy(P
);
5384 SwapColumns(T
, nvar
+1, nvar
+1+i
);
5385 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5390 for (int i
= 0; i
< exist
; ++i
)
5391 if (info
[i
] & ROT_NEG
) {
5393 fprintf(stderr
, "\nER: Rotate\n");
5394 #endif /* DEBUG_ER */
5398 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
5399 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5403 for (int i
= 0; i
< exist
; ++i
)
5404 if (info
[i
] & INDEPENDENT
) {
5405 Polyhedron
*pos
, *neg
;
5407 /* Find constraint again and split off negative part */
5409 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
5410 row
, f
, true, &pos
, &neg
)) {
5412 fprintf(stderr
, "\nER: Split\n");
5413 #endif /* DEBUG_ER */
5416 barvinok_enumerate_e(neg
, exist
-1, nparam
, MaxRays
);
5418 barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
5420 free_evalue_refs(E
);
5422 Polyhedron_Free(neg
);
5423 Polyhedron_Free(pos
);
5437 EP
= enumerate_line(P
, exist
, nparam
, MaxRays
);
5441 EP
= barvinok_enumerate_pip(P
, exist
, nparam
, MaxRays
);
5445 EP
= enumerate_redundant_ray(P
, exist
, nparam
, MaxRays
);
5449 EP
= enumerate_sure(P
, exist
, nparam
, MaxRays
);
5453 EP
= enumerate_ray(P
, exist
, nparam
, MaxRays
);
5457 EP
= enumerate_sure2(P
, exist
, nparam
, MaxRays
);
5461 F
= unfringe(P
, MaxRays
);
5462 if (!PolyhedronIncludes(F
, P
)) {
5464 fprintf(stderr
, "\nER: Fringed\n");
5465 #endif /* DEBUG_ER */
5466 EP
= barvinok_enumerate_e(F
, exist
, nparam
, MaxRays
);
5473 EP
= enumerate_vd(&P
, exist
, nparam
, MaxRays
);
5478 EP
= enumerate_sum(P
, exist
, nparam
, MaxRays
);
5485 Polyhedron
*pos
, *neg
;
5486 for (i
= 0; i
< exist
; ++i
)
5487 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
5488 row
, f
, false, &pos
, &neg
))
5494 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
5506 /* "align" matrix to have nrows by inserting
5507 * the necessary number of rows and an equal number of columns in front
5509 static Matrix
*align_matrix(Matrix
*M
, int nrows
)
5511 int newrows
= nrows
- M
->NbRows
;
5512 Matrix
*M2
= Matrix_Alloc(nrows
, newrows
+ M
->NbColumns
);
5513 for (int i
= 0; i
< newrows
; ++i
)
5514 value_set_si(M2
->p
[i
][i
], 1);
5515 for (int i
= 0; i
< M
->NbRows
; ++i
)
5516 Vector_Copy(M
->p
[i
], M2
->p
[newrows
+i
]+newrows
, M
->NbColumns
);
5520 static void split_param_compression(Matrix
*CP
, mat_ZZ
& map
, vec_ZZ
& offset
)
5522 Matrix
*T
= Transpose(CP
);
5523 matrix2zz(T
, map
, T
->NbRows
-1, T
->NbColumns
-1);
5524 values2zz(T
->p
[T
->NbRows
-1], offset
, T
->NbColumns
-1);
5529 * remove equalities that require a "compression" of the parameters
5531 #ifndef HAVE_COMPRESS_PARMS
5532 static Polyhedron
*remove_more_equalities(Polyhedron
*P
, unsigned nparam
,
5533 Matrix
**CP
, unsigned MaxRays
)
5538 static Polyhedron
*remove_more_equalities(Polyhedron
*P
, unsigned nparam
,
5539 Matrix
**CP
, unsigned MaxRays
)
5544 /* compress_parms doesn't like equalities that only involve parameters */
5545 for (int i
= 0; i
< P
->NbEq
; ++i
)
5546 assert(First_Non_Zero(P
->Constraint
[i
]+1, P
->Dimension
-nparam
) != -1);
5548 M
= Matrix_Alloc(P
->NbEq
, P
->Dimension
+2);
5549 Vector_Copy(P
->Constraint
[0], M
->p
[0], P
->NbEq
* (P
->Dimension
+2));
5550 *CP
= compress_parms(M
, nparam
);
5551 T
= align_matrix(*CP
, P
->Dimension
+1);
5552 Q
= Polyhedron_Preimage(P
, T
, MaxRays
);
5555 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, NULL
);
5562 gen_fun
* barvinok_series(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
5566 unsigned nparam
= C
->Dimension
;
5568 CA
= align_context(C
, P
->Dimension
, MaxRays
);
5569 P
= DomainIntersection(P
, CA
, MaxRays
);
5570 Polyhedron_Free(CA
);
5577 assert(!Polyhedron_is_infinite(P
, nparam
));
5578 assert(P
->NbBid
== 0);
5579 assert(Polyhedron_has_positive_rays(P
, nparam
));
5581 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, NULL
);
5583 P
= remove_more_equalities(P
, nparam
, &CP
, MaxRays
);
5584 assert(P
->NbEq
== 0);
5586 #ifdef USE_INCREMENTAL_BF
5587 partial_bfcounter
red(P
, nparam
);
5588 #elif defined USE_INCREMENTAL_DF
5589 partial_ireducer
red(P
, nparam
);
5591 partial_reducer
red(P
, nparam
);
5598 split_param_compression(CP
, map
, offset
);
5599 red
.gf
->substitute(CP
, map
, offset
);
5605 static Polyhedron
*skew_into_positive_orthant(Polyhedron
*D
, unsigned nparam
,
5611 for (Polyhedron
*P
= D
; P
; P
= P
->next
) {
5612 POL_ENSURE_VERTICES(P
);
5613 assert(!Polyhedron_is_infinite(P
, nparam
));
5614 assert(P
->NbBid
== 0);
5615 assert(Polyhedron_has_positive_rays(P
, nparam
));
5617 for (int r
= 0; r
< P
->NbRays
; ++r
) {
5618 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
5620 for (int i
= 0; i
< nparam
; ++i
) {
5622 if (value_posz_p(P
->Ray
[r
][i
+1]))
5625 M
= Matrix_Alloc(D
->Dimension
+1, D
->Dimension
+1);
5626 for (int i
= 0; i
< D
->Dimension
+1; ++i
)
5627 value_set_si(M
->p
[i
][i
], 1);
5629 Inner_Product(P
->Ray
[r
]+1, M
->p
[i
], D
->Dimension
+1, &tmp
);
5630 if (value_posz_p(tmp
))
5633 for (j
= P
->Dimension
- nparam
; j
< P
->Dimension
; ++j
)
5634 if (value_pos_p(P
->Ray
[r
][j
+1]))
5636 assert(j
< P
->Dimension
);
5637 value_pdivision(tmp
, P
->Ray
[r
][j
+1], P
->Ray
[r
][i
+1]);
5638 value_subtract(M
->p
[i
][j
], M
->p
[i
][j
], tmp
);
5644 D
= DomainImage(D
, M
, MaxRays
);
5650 evalue
* barvinok_enumerate_union(Polyhedron
*D
, Polyhedron
* C
, unsigned MaxRays
)
5653 Polyhedron
*conv
, *D2
;
5655 unsigned nparam
= C
->Dimension
;
5659 D2
= skew_into_positive_orthant(D
, nparam
, MaxRays
);
5660 for (Polyhedron
*P
= D2
; P
; P
= P
->next
) {
5661 assert(P
->Dimension
== D2
->Dimension
);
5662 POL_ENSURE_VERTICES(P
);
5663 /* it doesn't matter which reducer we use, since we don't actually
5664 * reduce anything here
5666 partial_reducer
red(P
, P
->Dimension
);
5671 gen_fun
*hp
= gf
->Hadamard_product(red
.gf
, MaxRays
);
5672 gf
->add(one
, one
, red
.gf
);
5673 gf
->add(mone
, one
, hp
);
5678 /* we actually only need the convex union of the parameter space
5679 * but the reducer classes currently expect a polyhedron in
5680 * the combined space
5682 conv
= DomainConvex(D2
, MaxRays
);
5683 #ifdef USE_INCREMENTAL_DF
5684 partial_ireducer
red(conv
, nparam
);
5686 partial_reducer
red(conv
, nparam
);
5688 for (int i
= 0; i
< gf
->term
.size(); ++i
) {
5689 for (int j
= 0; j
< gf
->term
[i
]->n
.power
.NumRows(); ++j
) {
5690 red
.reduce(gf
->term
[i
]->n
.coeff
[j
][0], gf
->term
[i
]->n
.coeff
[j
][1],
5691 gf
->term
[i
]->n
.power
[j
], gf
->term
[i
]->d
.power
);
5697 Polyhedron_Free(conv
);