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 struct reducer
: public polar_decomposer
{
1570 int lower
; // call base when only this many variables is left
1572 reducer(Polyhedron
*P
) {
1575 //den.SetLength(dim);
1582 void start(unsigned MaxRays
);
1590 virtual void handle_polar(Polyhedron
*P
, int sign
);
1591 void reduce(ZZ c
, ZZ cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1592 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
) = 0;
1593 virtual void split(vec_ZZ
& num
, ZZ
& num_s
, vec_ZZ
& num_p
,
1594 mat_ZZ
& den_f
, vec_ZZ
& den_s
, mat_ZZ
& den_r
) = 0;
1597 void reducer::reduce(ZZ c
, ZZ cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1599 unsigned len
= den_f
.NumRows(); // number of factors in den
1601 if (num
.length() == lower
) {
1602 base(c
, cd
, num
, den_f
);
1605 assert(num
.length() > 1);
1612 split(num
, num_s
, num_p
, den_f
, den_s
, den_r
);
1615 den_p
.SetLength(len
);
1617 normalize(c
, num_s
, num_p
, den_s
, den_p
, den_r
);
1619 int only_param
= 0; // k-r-s from text
1620 int no_param
= 0; // r from text
1621 for (int k
= 0; k
< len
; ++k
) {
1624 else if (den_s
[k
] == 0)
1627 if (no_param
== 0) {
1628 reduce(c
, cd
, num_p
, den_r
);
1632 pden
.SetDims(only_param
, den_r
.NumCols());
1634 for (k
= 0, l
= 0; k
< len
; ++k
)
1636 pden
[l
++] = den_r
[k
];
1638 for (k
= 0; k
< len
; ++k
)
1642 dpoly
n(no_param
, num_s
);
1643 dpoly
D(no_param
, den_s
[k
], 1);
1644 for ( ; ++k
< len
; )
1645 if (den_p
[k
] == 0) {
1646 dpoly
fact(no_param
, den_s
[k
], 1);
1650 if (no_param
+ only_param
== len
) {
1651 mpq_set_si(tcount
, 0, 1);
1652 n
.div(D
, tcount
, one
);
1655 value2zz(mpq_numref(tcount
), qn
);
1656 value2zz(mpq_denref(tcount
), qd
);
1662 reduce(qn
, qd
, num_p
, pden
);
1666 for (k
= 0; k
< len
; ++k
) {
1667 if (den_s
[k
] == 0 || den_p
[k
] == 0)
1670 dpoly
pd(no_param
-1, den_s
[k
], 1);
1673 for (l
= 0; l
< k
; ++l
)
1674 if (den_r
[l
] == den_r
[k
])
1678 r
= new dpoly_r(n
, pd
, l
, len
);
1680 dpoly_r
*nr
= new dpoly_r(r
, pd
, l
, len
);
1686 dpoly_r
*rc
= r
->div(D
);
1690 int common
= pden
.NumRows();
1691 vector
< dpoly_r_term
* >& final
= rc
->c
[rc
->len
-1];
1693 for (int j
= 0; j
< final
.size(); ++j
) {
1694 if (final
[j
]->coeff
== 0)
1697 pden
.SetDims(rows
, pden
.NumCols());
1698 for (int k
= 0; k
< rc
->dim
; ++k
) {
1699 int n
= final
[j
]->powers
[k
];
1702 pden
.SetDims(rows
+n
, pden
.NumCols());
1703 for (int l
= 0; l
< n
; ++l
)
1704 pden
[rows
+l
] = den_r
[k
];
1707 final
[j
]->coeff
*= c
;
1708 reduce(final
[j
]->coeff
, rc
->denom
, num_p
, pden
);
1717 void reducer::handle_polar(Polyhedron
*C
, int s
)
1719 assert(C
->NbRays
-1 == dim
);
1723 lattice_point(P
->Ray
[j
]+1, C
, vertex
);
1726 den
.SetDims(dim
, dim
);
1729 for (r
= 0; r
< dim
; ++r
)
1730 values2zz(C
->Ray
[r
]+1, den
[r
], dim
);
1732 reduce(sgn
, one
, vertex
, den
);
1735 void reducer::start(unsigned MaxRays
)
1737 for (j
= 0; j
< P
->NbRays
; ++j
) {
1738 Polyhedron
*C
= supporting_cone(P
, j
);
1739 decompose(C
, MaxRays
);
1743 struct ireducer
: public reducer
{
1744 ireducer(Polyhedron
*P
) : reducer(P
) {}
1746 virtual void split(vec_ZZ
& num
, ZZ
& num_s
, vec_ZZ
& num_p
,
1747 mat_ZZ
& den_f
, vec_ZZ
& den_s
, mat_ZZ
& den_r
) {
1748 unsigned len
= den_f
.NumRows(); // number of factors in den
1749 unsigned d
= num
.length() - 1;
1751 den_s
.SetLength(len
);
1752 den_r
.SetDims(len
, d
);
1754 for (int r
= 0; r
< len
; ++r
) {
1755 den_s
[r
] = den_f
[r
][0];
1756 for (int k
= 1; k
<= d
; ++k
)
1757 den_r
[r
][k
-1] = den_f
[r
][k
];
1762 for (int k
= 1 ; k
<= d
; ++k
)
1763 num_p
[k
-1] = num
[k
];
1767 // incremental counter
1768 struct icounter
: public ireducer
{
1771 icounter(Polyhedron
*P
) : ireducer(P
) {
1778 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1781 void icounter::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1784 unsigned len
= den_f
.NumRows(); // number of factors in den
1786 den_s
.SetLength(len
);
1788 for (r
= 0; r
< len
; ++r
)
1789 den_s
[r
] = den_f
[r
][0];
1790 normalize(c
, num_s
, den_s
);
1792 dpoly
n(len
, num_s
);
1793 dpoly
D(len
, den_s
[0], 1);
1794 for (int k
= 1; k
< len
; ++k
) {
1795 dpoly
fact(len
, den_s
[k
], 1);
1798 mpq_set_si(tcount
, 0, 1);
1799 n
.div(D
, tcount
, one
);
1802 mpz_mul(mpq_numref(tcount
), mpq_numref(tcount
), tn
);
1803 mpz_mul(mpq_denref(tcount
), mpq_denref(tcount
), td
);
1804 mpq_canonicalize(tcount
);
1805 mpq_add(count
, count
, tcount
);
1808 struct partial_ireducer
: public ireducer
{
1811 partial_ireducer(Polyhedron
*P
, unsigned nparam
) : ireducer(P
) {
1812 gf
= new gen_fun(Polyhedron_Project(P
, nparam
));
1815 ~partial_ireducer() {
1817 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1818 void start(unsigned MaxRays
);
1821 void partial_ireducer::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1823 gf
->add(c
, cd
, num
, den_f
);
1826 void partial_ireducer::start(unsigned MaxRays
)
1828 for (j
= 0; j
< P
->NbRays
; ++j
) {
1829 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
1832 Polyhedron
*C
= supporting_cone(P
, j
);
1833 decompose(C
, MaxRays
);
1837 struct partial_reducer
: public reducer
{
1842 partial_reducer(Polyhedron
*P
, unsigned nparam
) : reducer(P
) {
1843 gf
= new gen_fun(Polyhedron_Project(P
, nparam
));
1846 tmp
.SetLength(dim
- nparam
);
1847 randomvector(P
, lambda
, dim
- nparam
);
1849 ~partial_reducer() {
1851 virtual void base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
);
1852 void start(unsigned MaxRays
);
1854 virtual void split(vec_ZZ
& num
, ZZ
& num_s
, vec_ZZ
& num_p
,
1855 mat_ZZ
& den_f
, vec_ZZ
& den_s
, mat_ZZ
& den_r
) {
1856 unsigned len
= den_f
.NumRows(); // number of factors in den
1857 unsigned nvar
= tmp
.length();
1859 den_s
.SetLength(len
);
1860 den_r
.SetDims(len
, lower
);
1862 for (int r
= 0; r
< len
; ++r
) {
1863 for (int k
= 0; k
< nvar
; ++k
)
1864 tmp
[k
] = den_f
[r
][k
];
1865 den_s
[r
] = tmp
* lambda
;
1867 for (int k
= nvar
; k
< dim
; ++k
)
1868 den_r
[r
][k
-nvar
] = den_f
[r
][k
];
1871 for (int k
= 0; k
< nvar
; ++k
)
1873 num_s
= tmp
*lambda
;
1874 num_p
.SetLength(lower
);
1875 for (int k
= nvar
; k
< dim
; ++k
)
1876 num_p
[k
-nvar
] = num
[k
];
1880 void partial_reducer::base(ZZ
& c
, ZZ
& cd
, vec_ZZ
& num
, mat_ZZ
& den_f
)
1882 gf
->add(c
, cd
, num
, den_f
);
1885 void partial_reducer::start(unsigned MaxRays
)
1887 for (j
= 0; j
< P
->NbRays
; ++j
) {
1888 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
1891 Polyhedron
*C
= supporting_cone(P
, j
);
1892 decompose(C
, MaxRays
);
1896 struct bfc_term_base
{
1897 // the number of times a given factor appears in the denominator
1901 bfc_term_base(int len
) {
1902 powers
= new int[len
];
1905 virtual ~bfc_term_base() {
1910 struct bfc_term
: public bfc_term_base
{
1914 bfc_term(int len
) : bfc_term_base(len
) {}
1917 struct bfe_term
: public bfc_term_base
{
1918 vector
<evalue
*> factors
;
1920 bfe_term(int len
) : bfc_term_base(len
) {
1924 for (int i
= 0; i
< factors
.size(); ++i
) {
1927 free_evalue_refs(factors
[i
]);
1933 typedef vector
< bfc_term_base
* > bfc_vec
;
1937 struct bf_base
: public virtual polar_decomposer
{
1945 int lower
; // call base when only this many variables is left
1947 bf_base(Polyhedron
*P
, unsigned dim
) {
1962 void start(unsigned MaxRays
);
1963 virtual void handle_polar(Polyhedron
*P
, int sign
);
1964 int setup_factors(Polyhedron
*P
, mat_ZZ
& factors
, bfc_term_base
* t
, int s
);
1966 bfc_term_base
* find_bfc_term(bfc_vec
& v
, int *powers
, int len
);
1967 void add_term(bfc_term_base
*t
, vec_ZZ
& num1
, vec_ZZ
& num
);
1968 void add_term(bfc_term_base
*t
, vec_ZZ
& num
);
1970 void reduce(mat_ZZ
& factors
, bfc_vec
& v
);
1971 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
) = 0;
1973 virtual bfc_term_base
* new_bf_term(int len
) = 0;
1974 virtual void set_factor(bfc_term_base
*t
, int k
, int change
) = 0;
1975 virtual void set_factor(bfc_term_base
*t
, int k
, mpq_t
&f
, int change
) = 0;
1976 virtual void set_factor(bfc_term_base
*t
, int k
, ZZ
& n
, ZZ
& d
, int change
) = 0;
1977 virtual void update_term(bfc_term_base
*t
, int i
) = 0;
1978 virtual void insert_term(bfc_term_base
*t
, int i
) = 0;
1979 virtual bool constant_vertex(int dim
) = 0;
1980 virtual void cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
,
1984 static int lex_cmp(vec_ZZ
& a
, vec_ZZ
& b
)
1986 assert(a
.length() == b
.length());
1988 for (int j
= 0; j
< a
.length(); ++j
)
1990 return a
[j
] < b
[j
] ? -1 : 1;
1994 void bf_base::add_term(bfc_term_base
*t
, vec_ZZ
& num_orig
, vec_ZZ
& extra_num
)
1997 int d
= num_orig
.length();
1999 for (int l
= 0; l
< d
-1; ++l
)
2000 num
[l
] = num_orig
[l
+1] + extra_num
[l
];
2005 void bf_base::add_term(bfc_term_base
*t
, vec_ZZ
& num
)
2007 int len
= t
->terms
.NumRows();
2009 for (i
= 0; i
< len
; ++i
) {
2010 r
= lex_cmp(t
->terms
[i
], num
);
2014 if (i
== len
|| r
> 0) {
2015 t
->terms
.SetDims(len
+1, num
.length());
2019 // i < len && r == 0
2024 static void print_int_vector(int *v
, int len
, char *name
)
2026 cerr
<< name
<< endl
;
2027 for (int j
= 0; j
< len
; ++j
) {
2028 cerr
<< v
[j
] << " ";
2033 static void print_bfc_terms(mat_ZZ
& factors
, bfc_vec
& v
)
2036 cerr
<< "factors" << endl
;
2037 cerr
<< factors
<< endl
;
2038 for (int i
= 0; i
< v
.size(); ++i
) {
2039 cerr
<< "term: " << i
<< endl
;
2040 print_int_vector(v
[i
]->powers
, factors
.NumRows(), "powers");
2041 cerr
<< "terms" << endl
;
2042 cerr
<< v
[i
]->terms
<< endl
;
2043 bfc_term
* bfct
= static_cast<bfc_term
*>(v
[i
]);
2044 cerr
<< bfct
->cn
<< endl
;
2045 cerr
<< bfct
->cd
<< endl
;
2049 static void print_bfe_terms(mat_ZZ
& factors
, bfc_vec
& v
)
2052 cerr
<< "factors" << endl
;
2053 cerr
<< factors
<< endl
;
2054 for (int i
= 0; i
< v
.size(); ++i
) {
2055 cerr
<< "term: " << i
<< endl
;
2056 print_int_vector(v
[i
]->powers
, factors
.NumRows(), "powers");
2057 cerr
<< "terms" << endl
;
2058 cerr
<< v
[i
]->terms
<< endl
;
2059 bfe_term
* bfet
= static_cast<bfe_term
*>(v
[i
]);
2060 for (int j
= 0; j
< v
[i
]->terms
.NumRows(); ++j
) {
2061 char * test
[] = {"a", "b"};
2062 print_evalue(stderr
, bfet
->factors
[j
], test
);
2063 fprintf(stderr
, "\n");
2068 bfc_term_base
* bf_base::find_bfc_term(bfc_vec
& v
, int *powers
, int len
)
2070 bfc_vec::iterator i
;
2071 for (i
= v
.begin(); i
!= v
.end(); ++i
) {
2073 for (j
= 0; j
< len
; ++j
)
2074 if ((*i
)->powers
[j
] != powers
[j
])
2078 if ((*i
)->powers
[j
] > powers
[j
])
2082 bfc_term_base
* t
= new_bf_term(len
);
2084 memcpy(t
->powers
, powers
, len
* sizeof(int));
2105 int no_param
; // r from text
2106 int only_param
; // k-r-s from text
2107 int total_power
; // k from text
2109 // created in compute_reduced_factors
2111 // set in update_powers
2116 bf_reducer(mat_ZZ
& factors
, bfc_vec
& v
, bf_base
*bf
)
2117 : factors(factors
), v(v
), bf(bf
) {
2118 nf
= factors
.NumRows();
2119 d
= factors
.NumCols();
2120 old2new
= new int[nf
];
2123 extra_num
.SetLength(d
-1);
2132 void compute_reduced_factors();
2133 void compute_extra_num(int i
);
2137 void update_powers(int *powers
, int len
);
2140 void bf_reducer::compute_extra_num(int i
)
2144 no_param
= 0; // r from text
2145 only_param
= 0; // k-r-s from text
2146 total_power
= 0; // k from text
2148 for (int j
= 0; j
< nf
; ++j
) {
2149 if (v
[i
]->powers
[j
] == 0)
2152 total_power
+= v
[i
]->powers
[j
];
2153 if (factors
[j
][0] == 0) {
2154 only_param
+= v
[i
]->powers
[j
];
2158 if (old2new
[j
] == -1)
2159 no_param
+= v
[i
]->powers
[j
];
2161 extra_num
+= -sign
[j
] * v
[i
]->powers
[j
] * nfactors
[old2new
[j
]];
2162 changes
+= v
[i
]->powers
[j
];
2166 void bf_reducer::update_powers(int *powers
, int len
)
2168 for (int l
= 0; l
< nnf
; ++l
)
2169 npowers
[l
] = bpowers
[l
];
2171 l_extra_num
= extra_num
;
2172 l_changes
= changes
;
2174 for (int l
= 0; l
< len
; ++l
) {
2178 assert(old2new
[l
] != -1);
2180 npowers
[old2new
[l
]] += n
;
2181 // interpretation of sign has been inverted
2182 // since we inverted the power for specialization
2184 l_extra_num
+= n
* nfactors
[old2new
[l
]];
2191 void bf_reducer::compute_reduced_factors()
2193 unsigned nf
= factors
.NumRows();
2194 unsigned d
= factors
.NumCols();
2196 nfactors
.SetDims(nnf
, d
-1);
2198 for (int i
= 0; i
< nf
; ++i
) {
2201 for (j
= 0; j
< nnf
; ++j
) {
2203 for (k
= 1; k
< d
; ++k
)
2204 if (factors
[i
][k
] != 0 || nfactors
[j
][k
-1] != 0)
2206 if (k
< d
&& factors
[i
][k
] == -nfactors
[j
][k
-1])
2209 if (factors
[i
][k
] != s
* nfactors
[j
][k
-1])
2217 for (k
= 1; k
< d
; ++k
)
2218 if (factors
[i
][k
] != 0)
2221 if (factors
[i
][k
] < 0)
2223 nfactors
.SetDims(++nnf
, d
-1);
2224 for (int k
= 1; k
< d
; ++k
)
2225 nfactors
[j
][k
-1] = s
* factors
[i
][k
];
2231 npowers
= new int[nnf
];
2232 bpowers
= new int[nnf
];
2235 void bf_reducer::reduce()
2237 compute_reduced_factors();
2239 for (int i
= 0; i
< v
.size(); ++i
) {
2240 compute_extra_num(i
);
2242 if (no_param
== 0) {
2244 extra_num
.SetLength(d
-1);
2247 for (int k
= 0; k
< nnf
; ++k
)
2249 for (int k
= 0; k
< nf
; ++k
) {
2250 assert(old2new
[k
] != -1);
2251 npowers
[old2new
[k
]] += v
[i
]->powers
[k
];
2252 if (sign
[k
] == -1) {
2253 extra_num
+= v
[i
]->powers
[k
] * nfactors
[old2new
[k
]];
2254 changes
+= v
[i
]->powers
[k
];
2258 bfc_term_base
* t
= bf
->find_bfc_term(vn
, npowers
, nnf
);
2259 for (int k
= 0; k
< v
[i
]->terms
.NumRows(); ++k
) {
2260 bf
->set_factor(v
[i
], k
, changes
% 2);
2261 bf
->add_term(t
, v
[i
]->terms
[k
], extra_num
);
2264 // powers of "constant" part
2265 for (int k
= 0; k
< nnf
; ++k
)
2267 for (int k
= 0; k
< nf
; ++k
) {
2268 if (factors
[k
][0] != 0)
2270 assert(old2new
[k
] != -1);
2271 bpowers
[old2new
[k
]] += v
[i
]->powers
[k
];
2272 if (sign
[k
] == -1) {
2273 extra_num
+= v
[i
]->powers
[k
] * nfactors
[old2new
[k
]];
2274 changes
+= v
[i
]->powers
[k
];
2279 for (j
= 0; j
< nf
; ++j
)
2280 if (old2new
[j
] == -1 && v
[i
]->powers
[j
] > 0)
2283 dpoly
D(no_param
, factors
[j
][0], 1);
2284 for (int k
= 1; k
< v
[i
]->powers
[j
]; ++k
) {
2285 dpoly
fact(no_param
, factors
[j
][0], 1);
2289 if (old2new
[j
] == -1)
2290 for (int k
= 0; k
< v
[i
]->powers
[j
]; ++k
) {
2291 dpoly
fact(no_param
, factors
[j
][0], 1);
2295 if (no_param
+ only_param
== total_power
&&
2296 bf
->constant_vertex(d
)) {
2297 bfc_term_base
* t
= NULL
;
2302 for (int k
= 0; k
< v
[i
]->terms
.NumRows(); ++k
) {
2303 dpoly
n(no_param
, v
[i
]->terms
[k
][0]);
2304 mpq_set_si(bf
->tcount
, 0, 1);
2305 n
.div(D
, bf
->tcount
, bf
->one
);
2307 if (value_zero_p(mpq_numref(bf
->tcount
)))
2311 t
= bf
->find_bfc_term(vn
, bpowers
, nnf
);
2312 bf
->set_factor(v
[i
], k
, bf
->tcount
, changes
% 2);
2313 bf
->add_term(t
, v
[i
]->terms
[k
], extra_num
);
2316 for (int j
= 0; j
< v
[i
]->terms
.NumRows(); ++j
) {
2317 dpoly
n(no_param
, v
[i
]->terms
[j
][0]);
2320 if (no_param
+ only_param
== total_power
)
2321 r
= new dpoly_r(n
, nf
);
2323 for (int k
= 0; k
< nf
; ++k
) {
2324 if (v
[i
]->powers
[k
] == 0)
2326 if (factors
[k
][0] == 0 || old2new
[k
] == -1)
2329 dpoly
pd(no_param
-1, factors
[k
][0], 1);
2331 for (int l
= 0; l
< v
[i
]->powers
[k
]; ++l
) {
2333 for (q
= 0; q
< k
; ++q
)
2334 if (old2new
[q
] == old2new
[k
] &&
2339 r
= new dpoly_r(n
, pd
, q
, nf
);
2341 dpoly_r
*nr
= new dpoly_r(r
, pd
, q
, nf
);
2348 dpoly_r
*rc
= r
->div(D
);
2351 if (bf
->constant_vertex(d
)) {
2352 vector
< dpoly_r_term
* >& final
= rc
->c
[rc
->len
-1];
2354 for (int k
= 0; k
< final
.size(); ++k
) {
2355 if (final
[k
]->coeff
== 0)
2358 update_powers(final
[k
]->powers
, rc
->dim
);
2360 bfc_term_base
* t
= bf
->find_bfc_term(vn
, npowers
, nnf
);
2361 bf
->set_factor(v
[i
], j
, final
[k
]->coeff
, rc
->denom
, l_changes
% 2);
2362 bf
->add_term(t
, v
[i
]->terms
[j
], l_extra_num
);
2365 bf
->cum(this, v
[i
], j
, rc
);
2376 void bf_base::reduce(mat_ZZ
& factors
, bfc_vec
& v
)
2378 assert(v
.size() > 0);
2379 unsigned nf
= factors
.NumRows();
2380 unsigned d
= factors
.NumCols();
2383 return base(factors
, v
);
2385 bf_reducer
bfr(factors
, v
, this);
2389 if (bfr
.vn
.size() > 0)
2390 reduce(bfr
.nfactors
, bfr
.vn
);
2393 int bf_base::setup_factors(Polyhedron
*C
, mat_ZZ
& factors
,
2394 bfc_term_base
* t
, int s
)
2396 factors
.SetDims(dim
, dim
);
2400 for (r
= 0; r
< dim
; ++r
)
2403 for (r
= 0; r
< dim
; ++r
) {
2404 values2zz(C
->Ray
[r
]+1, factors
[r
], dim
);
2406 for (k
= 0; k
< dim
; ++k
)
2407 if (factors
[r
][k
] != 0)
2409 if (factors
[r
][k
] < 0) {
2410 factors
[r
] = -factors
[r
];
2411 t
->terms
[0] += factors
[r
];
2419 void bf_base::handle_polar(Polyhedron
*C
, int s
)
2421 bfc_term
* t
= new bfc_term(dim
);
2422 vector
< bfc_term_base
* > v
;
2425 assert(C
->NbRays
-1 == dim
);
2430 t
->terms
.SetDims(1, dim
);
2431 lattice_point(P
->Ray
[j
]+1, C
, t
->terms
[0]);
2433 // the elements of factors are always lexpositive
2435 s
= setup_factors(C
, factors
, t
, s
);
2443 void bf_base::start(unsigned MaxRays
)
2445 for (j
= 0; j
< P
->NbRays
; ++j
) {
2446 Polyhedron
*C
= supporting_cone(P
, j
);
2447 decompose(C
, MaxRays
);
2451 struct bfcounter_base
: public bf_base
{
2455 bfcounter_base(Polyhedron
*P
) : bf_base(P
, P
->Dimension
) {
2458 bfc_term_base
* new_bf_term(int len
) {
2459 bfc_term
* t
= new bfc_term(len
);
2465 virtual void set_factor(bfc_term_base
*t
, int k
, int change
) {
2466 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2473 virtual void set_factor(bfc_term_base
*t
, int k
, mpq_t
&f
, int change
) {
2474 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2475 value2zz(mpq_numref(f
), cn
);
2476 value2zz(mpq_denref(f
), cd
);
2483 virtual void set_factor(bfc_term_base
*t
, int k
, ZZ
& n
, ZZ
& d
, int change
) {
2484 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2485 cn
= bfct
->cn
[k
] * n
;
2488 cd
= bfct
->cd
[k
] * d
;
2491 virtual void insert_term(bfc_term_base
*t
, int i
) {
2492 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2493 int len
= t
->terms
.NumRows()-1; // already increased by one
2495 bfct
->cn
.SetLength(len
+1);
2496 bfct
->cd
.SetLength(len
+1);
2497 for (int j
= len
; j
> i
; --j
) {
2498 bfct
->cn
[j
] = bfct
->cn
[j
-1];
2499 bfct
->cd
[j
] = bfct
->cd
[j
-1];
2500 t
->terms
[j
] = t
->terms
[j
-1];
2506 virtual void update_term(bfc_term_base
*t
, int i
) {
2507 bfc_term
* bfct
= static_cast<bfc_term
*>(t
);
2509 ZZ g
= GCD(bfct
->cd
[i
], cd
);
2510 ZZ n
= cn
* bfct
->cd
[i
]/g
+ bfct
->cn
[i
] * cd
/g
;
2511 ZZ d
= bfct
->cd
[i
] * cd
/ g
;
2516 virtual bool constant_vertex(int dim
) { return true; }
2517 virtual void cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
, dpoly_r
*r
) {
2522 struct bfcounter
: public bfcounter_base
{
2525 bfcounter(Polyhedron
*P
) : bfcounter_base(P
) {
2532 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
);
2535 void bfcounter::base(mat_ZZ
& factors
, bfc_vec
& v
)
2537 unsigned nf
= factors
.NumRows();
2539 for (int i
= 0; i
< v
.size(); ++i
) {
2540 bfc_term
* bfct
= static_cast<bfc_term
*>(v
[i
]);
2541 int total_power
= 0;
2542 // factor is always positive, so we always
2544 for (int k
= 0; k
< nf
; ++k
)
2545 total_power
+= v
[i
]->powers
[k
];
2548 for (j
= 0; j
< nf
; ++j
)
2549 if (v
[i
]->powers
[j
] > 0)
2552 dpoly
D(total_power
, factors
[j
][0], 1);
2553 for (int k
= 1; k
< v
[i
]->powers
[j
]; ++k
) {
2554 dpoly
fact(total_power
, factors
[j
][0], 1);
2558 for (int k
= 0; k
< v
[i
]->powers
[j
]; ++k
) {
2559 dpoly
fact(total_power
, factors
[j
][0], 1);
2563 for (int k
= 0; k
< v
[i
]->terms
.NumRows(); ++k
) {
2564 dpoly
n(total_power
, v
[i
]->terms
[k
][0]);
2565 mpq_set_si(tcount
, 0, 1);
2566 n
.div(D
, tcount
, one
);
2567 if (total_power
% 2)
2568 bfct
->cn
[k
] = -bfct
->cn
[k
];
2569 zz2value(bfct
->cn
[k
], tn
);
2570 zz2value(bfct
->cd
[k
], td
);
2572 mpz_mul(mpq_numref(tcount
), mpq_numref(tcount
), tn
);
2573 mpz_mul(mpq_denref(tcount
), mpq_denref(tcount
), td
);
2574 mpq_canonicalize(tcount
);
2575 mpq_add(count
, count
, tcount
);
2581 struct partial_bfcounter
: public bfcounter_base
{
2584 partial_bfcounter(Polyhedron
*P
, unsigned nparam
) : bfcounter_base(P
) {
2585 gf
= new gen_fun(Polyhedron_Project(P
, nparam
));
2588 ~partial_bfcounter() {
2590 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
);
2591 void start(unsigned MaxRays
);
2594 void partial_bfcounter::base(mat_ZZ
& factors
, bfc_vec
& v
)
2597 unsigned nf
= factors
.NumRows();
2599 for (int i
= 0; i
< v
.size(); ++i
) {
2600 bfc_term
* bfct
= static_cast<bfc_term
*>(v
[i
]);
2601 den
.SetDims(0, lower
);
2602 int total_power
= 0;
2604 for (int j
= 0; j
< nf
; ++j
) {
2605 total_power
+= v
[i
]->powers
[j
];
2606 den
.SetDims(total_power
, lower
);
2607 for (int k
= 0; k
< v
[i
]->powers
[j
]; ++k
)
2608 den
[p
++] = factors
[j
];
2610 for (int j
= 0; j
< v
[i
]->terms
.NumRows(); ++j
)
2611 gf
->add(bfct
->cn
[j
], bfct
->cd
[j
], v
[i
]->terms
[j
], den
);
2616 void partial_bfcounter::start(unsigned MaxRays
)
2618 for (j
= 0; j
< P
->NbRays
; ++j
) {
2619 if (!value_pos_p(P
->Ray
[j
][dim
+1]))
2622 Polyhedron
*C
= supporting_cone(P
, j
);
2623 decompose(C
, MaxRays
);
2628 typedef Polyhedron
* Polyhedron_p
;
2630 static void barvinok_count_f(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
);
2632 void barvinok_count(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
2640 value_set_si(*result
, 0);
2644 for (; r
< P
->NbRays
; ++r
)
2645 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
2647 if (P
->NbBid
!=0 || r
< P
->NbRays
) {
2648 value_set_si(*result
, -1);
2652 P
= remove_equalities(P
);
2655 value_set_si(*result
, 0);
2660 if (P
->Dimension
== 0) {
2661 /* Test whether the constraints are satisfied */
2662 POL_ENSURE_VERTICES(P
);
2663 value_set_si(*result
, !emptyQ(P
));
2668 Q
= Polyhedron_Factor(P
, 0, NbMaxCons
);
2676 barvinok_count_f(P
, result
, NbMaxCons
);
2681 for (Q
= P
->next
; Q
; Q
= Q
->next
) {
2682 barvinok_count_f(Q
, &factor
, NbMaxCons
);
2683 value_multiply(*result
, *result
, factor
);
2686 value_clear(factor
);
2693 static void barvinok_count_f(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
2695 if (P
->Dimension
== 1)
2696 return Line_Length(P
, result
);
2698 int c
= P
->NbConstraints
;
2699 POL_ENSURE_FACETS(P
);
2700 if (c
!= P
->NbConstraints
|| P
->NbEq
!= 0)
2701 return barvinok_count(P
, result
, NbMaxCons
);
2703 POL_ENSURE_VERTICES(P
);
2705 #ifdef USE_INCREMENTAL_BF
2707 #elif defined USE_INCREMENTAL_DF
2712 cnt
.start(NbMaxCons
);
2714 assert(value_one_p(&cnt
.count
[0]._mp_den
));
2715 value_assign(*result
, &cnt
.count
[0]._mp_num
);
2718 static void uni_polynom(int param
, Vector
*c
, evalue
*EP
)
2720 unsigned dim
= c
->Size
-2;
2722 value_set_si(EP
->d
,0);
2723 EP
->x
.p
= new_enode(polynomial
, dim
+1, param
+1);
2724 for (int j
= 0; j
<= dim
; ++j
)
2725 evalue_set(&EP
->x
.p
->arr
[j
], c
->p
[j
], c
->p
[dim
+1]);
2728 static void multi_polynom(Vector
*c
, evalue
* X
, evalue
*EP
)
2730 unsigned dim
= c
->Size
-2;
2734 evalue_set(&EC
, c
->p
[dim
], c
->p
[dim
+1]);
2737 evalue_set(EP
, c
->p
[dim
], c
->p
[dim
+1]);
2739 for (int i
= dim
-1; i
>= 0; --i
) {
2741 value_assign(EC
.x
.n
, c
->p
[i
]);
2744 free_evalue_refs(&EC
);
2747 Polyhedron
*unfringe (Polyhedron
*P
, unsigned MaxRays
)
2749 int len
= P
->Dimension
+2;
2750 Polyhedron
*T
, *R
= P
;
2753 Vector
*row
= Vector_Alloc(len
);
2754 value_set_si(row
->p
[0], 1);
2756 R
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
2758 Matrix
*M
= Matrix_Alloc(2, len
-1);
2759 value_set_si(M
->p
[1][len
-2], 1);
2760 for (int v
= 0; v
< P
->Dimension
; ++v
) {
2761 value_set_si(M
->p
[0][v
], 1);
2762 Polyhedron
*I
= Polyhedron_Image(P
, M
, 2+1);
2763 value_set_si(M
->p
[0][v
], 0);
2764 for (int r
= 0; r
< I
->NbConstraints
; ++r
) {
2765 if (value_zero_p(I
->Constraint
[r
][0]))
2767 if (value_zero_p(I
->Constraint
[r
][1]))
2769 if (value_one_p(I
->Constraint
[r
][1]))
2771 if (value_mone_p(I
->Constraint
[r
][1]))
2773 value_absolute(g
, I
->Constraint
[r
][1]);
2774 Vector_Set(row
->p
+1, 0, len
-2);
2775 value_division(row
->p
[1+v
], I
->Constraint
[r
][1], g
);
2776 mpz_fdiv_q(row
->p
[len
-1], I
->Constraint
[r
][2], g
);
2778 R
= AddConstraints(row
->p
, 1, R
, MaxRays
);
2790 static Polyhedron
*reduce_domain(Polyhedron
*D
, Matrix
*CT
, Polyhedron
*CEq
,
2791 Polyhedron
**fVD
, int nd
, unsigned MaxRays
)
2796 Dt
= CT
? DomainPreimage(D
, CT
, MaxRays
) : D
;
2797 Polyhedron
*rVD
= DomainIntersection(Dt
, CEq
, MaxRays
);
2799 /* if rVD is empty or too small in geometric dimension */
2800 if(!rVD
|| emptyQ(rVD
) ||
2801 (rVD
->Dimension
-rVD
->NbEq
< Dt
->Dimension
-Dt
->NbEq
-CEq
->NbEq
)) {
2806 return 0; /* empty validity domain */
2812 fVD
[nd
] = Domain_Copy(rVD
);
2813 for (int i
= 0 ; i
< nd
; ++i
) {
2814 Polyhedron
*I
= DomainIntersection(fVD
[nd
], fVD
[i
], MaxRays
);
2819 Polyhedron
*F
= DomainSimplify(I
, fVD
[nd
], MaxRays
);
2821 Polyhedron
*T
= rVD
;
2822 rVD
= DomainDifference(rVD
, F
, MaxRays
);
2829 rVD
= DomainConstraintSimplify(rVD
, MaxRays
);
2831 Domain_Free(fVD
[nd
]);
2838 barvinok_count(rVD
, &c
, MaxRays
);
2839 if (value_zero_p(c
)) {
2848 static bool Polyhedron_is_infinite(Polyhedron
*P
, unsigned nparam
)
2851 for (r
= 0; r
< P
->NbRays
; ++r
)
2852 if (value_zero_p(P
->Ray
[r
][0]) ||
2853 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
2855 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
2856 if (value_notzero_p(P
->Ray
[r
][i
+1]))
2858 if (i
>= P
->Dimension
)
2861 return r
< P
->NbRays
;
2864 /* Check whether all rays point in the positive directions
2865 * for the parameters
2867 static bool Polyhedron_has_positive_rays(Polyhedron
*P
, unsigned nparam
)
2870 for (r
= 0; r
< P
->NbRays
; ++r
)
2871 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
2873 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
2874 if (value_neg_p(P
->Ray
[r
][i
+1]))
2880 typedef evalue
* evalue_p
;
2882 struct enumerator
: public polar_decomposer
{
2896 enumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) {
2900 randomvector(P
, lambda
, dim
);
2901 rays
.SetDims(dim
, dim
);
2903 c
= Vector_Alloc(dim
+2);
2905 vE
= new evalue_p
[nbV
];
2906 for (int j
= 0; j
< nbV
; ++j
)
2912 void decompose_at(Param_Vertices
*V
, int _i
, unsigned MaxRays
) {
2913 Polyhedron
*C
= supporting_cone_p(P
, V
);
2917 vE
[_i
] = new evalue
;
2918 value_init(vE
[_i
]->d
);
2919 evalue_set_si(vE
[_i
], 0, 1);
2921 decompose(C
, MaxRays
);
2928 for (int j
= 0; j
< nbV
; ++j
)
2930 free_evalue_refs(vE
[j
]);
2936 virtual void handle_polar(Polyhedron
*P
, int sign
);
2939 void enumerator::handle_polar(Polyhedron
*C
, int s
)
2942 assert(C
->NbRays
-1 == dim
);
2943 add_rays(rays
, C
, &r
);
2944 for (int k
= 0; k
< dim
; ++k
) {
2945 if (lambda
* rays
[k
] == 0)
2951 lattice_point(V
, C
, lambda
, &num
, 0);
2952 den
= rays
* lambda
;
2953 normalize(sign
, num
.constant
, den
);
2955 dpoly
n(dim
, den
[0], 1);
2956 for (int k
= 1; k
< dim
; ++k
) {
2957 dpoly
fact(dim
, den
[k
], 1);
2960 if (num
.E
!= NULL
) {
2961 ZZ
one(INIT_VAL
, 1);
2962 dpoly_n
d(dim
, num
.constant
, one
);
2965 multi_polynom(c
, num
.E
, &EV
);
2967 free_evalue_refs(&EV
);
2968 free_evalue_refs(num
.E
);
2970 } else if (num
.pos
!= -1) {
2971 dpoly_n
d(dim
, num
.constant
, num
.coeff
);
2974 uni_polynom(num
.pos
, c
, &EV
);
2976 free_evalue_refs(&EV
);
2978 mpq_set_si(count
, 0, 1);
2979 dpoly
d(dim
, num
.constant
);
2980 d
.div(n
, count
, sign
);
2983 evalue_set(&EV
, &count
[0]._mp_num
, &count
[0]._mp_den
);
2985 free_evalue_refs(&EV
);
2989 struct enumerator_base
: public virtual polar_decomposer
{
2998 enumerator_base(Polyhedron
*P
, unsigned dim
, unsigned nbV
) {
3003 vE
= new evalue_p
[nbV
];
3004 for (int j
= 0; j
< nbV
; ++j
)
3007 E_vertex
= new evalue_p
[dim
];
3010 evalue_set_si(&mone
, -1, 1);
3013 void decompose_at(Param_Vertices
*V
, int _i
, unsigned MaxRays
/*, Polyhedron *pVD*/) {
3014 Polyhedron
*C
= supporting_cone_p(P
, V
);
3019 vE
[_i
] = new evalue
;
3020 value_init(vE
[_i
]->d
);
3021 evalue_set_si(vE
[_i
], 0, 1);
3023 decompose(C
, MaxRays
);
3026 ~enumerator_base() {
3027 for (int j
= 0; j
< nbV
; ++j
)
3029 free_evalue_refs(vE
[j
]);
3036 free_evalue_refs(&mone
);
3039 evalue
*E_num(int i
, int d
) {
3040 return E_vertex
[i
+ (dim
-d
)];
3049 cumulator(evalue
*factor
, evalue
*v
, dpoly_r
*r
) :
3050 factor(factor
), v(v
), r(r
) {}
3054 virtual void add_term(int *powers
, int len
, evalue
*f2
) = 0;
3057 void cumulator::cumulate()
3059 evalue cum
; // factor * 1 * E_num[0]/1 * (E_num[0]-1)/2 *...
3061 evalue t
; // E_num[0] - (m-1)
3067 evalue_set_si(&mone
, -1, 1);
3071 evalue_copy(&cum
, factor
);
3074 value_set_si(f
.d
, 1);
3075 value_set_si(f
.x
.n
, 1);
3080 for (cst
= &t
; value_zero_p(cst
->d
); ) {
3081 if (cst
->x
.p
->type
== fractional
)
3082 cst
= &cst
->x
.p
->arr
[1];
3084 cst
= &cst
->x
.p
->arr
[0];
3088 for (int m
= 0; m
< r
->len
; ++m
) {
3091 value_set_si(f
.d
, m
);
3094 value_subtract(cst
->x
.n
, cst
->x
.n
, cst
->d
);
3101 vector
< dpoly_r_term
* >& current
= r
->c
[r
->len
-1-m
];
3102 for (int j
= 0; j
< current
.size(); ++j
) {
3103 if (current
[j
]->coeff
== 0)
3105 evalue
*f2
= new evalue
;
3107 value_init(f2
->x
.n
);
3108 zz2value(current
[j
]->coeff
, f2
->x
.n
);
3109 zz2value(r
->denom
, f2
->d
);
3112 add_term(current
[j
]->powers
, r
->dim
, f2
);
3115 free_evalue_refs(&f
);
3116 free_evalue_refs(&t
);
3117 free_evalue_refs(&cum
);
3119 free_evalue_refs(&mone
);
3123 struct E_poly_term
{
3128 struct ie_cum
: public cumulator
{
3129 vector
<E_poly_term
*> terms
;
3131 ie_cum(evalue
*factor
, evalue
*v
, dpoly_r
*r
) : cumulator(factor
, v
, r
) {}
3133 virtual void add_term(int *powers
, int len
, evalue
*f2
);
3136 void ie_cum::add_term(int *powers
, int len
, evalue
*f2
)
3139 for (k
= 0; k
< terms
.size(); ++k
) {
3140 if (memcmp(terms
[k
]->powers
, powers
, len
* sizeof(int)) == 0) {
3141 eadd(f2
, terms
[k
]->E
);
3142 free_evalue_refs(f2
);
3147 if (k
>= terms
.size()) {
3148 E_poly_term
*ET
= new E_poly_term
;
3149 ET
->powers
= new int[len
];
3150 memcpy(ET
->powers
, powers
, len
* sizeof(int));
3152 terms
.push_back(ET
);
3156 struct ienumerator
: public virtual polar_decomposer
, public enumerator_base
{
3162 ienumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) :
3163 enumerator_base(P
, dim
, nbV
) {
3164 vertex
.SetLength(dim
);
3166 den
.SetDims(dim
, dim
);
3174 virtual void handle_polar(Polyhedron
*P
, int sign
);
3175 void reduce(evalue
*factor
, vec_ZZ
& num
, mat_ZZ
& den_f
);
3178 static evalue
* new_zero_ep()
3183 evalue_set_si(EP
, 0, 1);
3187 void lattice_point(Param_Vertices
*V
, Polyhedron
*C
, vec_ZZ
& num
,
3190 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
3191 unsigned dim
= C
->Dimension
;
3193 vertex
.SetLength(nparam
+1);
3198 value_set_si(lcm
, 1);
3200 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
3201 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
3204 if (value_notone_p(lcm
)) {
3205 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
3206 for (int j
= 0 ; j
< dim
; ++j
) {
3207 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
3208 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
3211 Matrix
* Rays
= rays2(C
);
3212 Matrix
*T
= Transpose(Rays
);
3213 Matrix
*T2
= Matrix_Copy(T
);
3214 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
3215 int ok
= Matrix_Inverse(T2
, inv
);
3219 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, mv
->NbColumns
);
3220 Matrix_Product(inv
, mv
, L
);
3229 evalue
*remainders
[dim
];
3230 for (int i
= 0; i
< dim
; ++i
) {
3231 remainders
[i
] = new_zero_ep();
3233 ceil(L
->p
[i
], nparam
+1, lcm
, one
, remainders
[i
], 0);
3238 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
3239 values2zz(mv
->p
[i
], vertex
, nparam
+1);
3240 E_vertex
[i
] = multi_monom(vertex
);
3243 value_set_si(f
.x
.n
, 1);
3244 value_assign(f
.d
, lcm
);
3246 emul(&f
, E_vertex
[i
]);
3248 for (int j
= 0; j
< dim
; ++j
) {
3249 if (value_zero_p(T
->p
[i
][j
]))
3253 evalue_copy(&cp
, remainders
[j
]);
3254 if (value_notone_p(T
->p
[i
][j
])) {
3255 value_set_si(f
.d
, 1);
3256 value_assign(f
.x
.n
, T
->p
[i
][j
]);
3259 eadd(&cp
, E_vertex
[i
]);
3260 free_evalue_refs(&cp
);
3263 for (int i
= 0; i
< dim
; ++i
) {
3264 free_evalue_refs(remainders
[i
]);
3265 free(remainders
[i
]);
3268 free_evalue_refs(&f
);
3279 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
3281 if (First_Non_Zero(V
->Vertex
->p
[i
], nparam
) == -1) {
3283 value2zz(V
->Vertex
->p
[i
][nparam
], num
[i
]);
3285 values2zz(V
->Vertex
->p
[i
], vertex
, nparam
+1);
3286 E_vertex
[i
] = multi_monom(vertex
);
3292 void ienumerator::reduce(
3293 evalue
*factor
, vec_ZZ
& num
, mat_ZZ
& den_f
)
3295 unsigned len
= den_f
.NumRows(); // number of factors in den
3296 unsigned dim
= num
.length();
3299 eadd(factor
, vE
[_i
]);
3304 den_s
.SetLength(len
);
3306 den_r
.SetDims(len
, dim
-1);
3310 for (r
= 0; r
< len
; ++r
) {
3311 den_s
[r
] = den_f
[r
][0];
3312 for (k
= 0; k
<= dim
-1; ++k
)
3314 den_r
[r
][k
-(k
>0)] = den_f
[r
][k
];
3319 num_p
.SetLength(dim
-1);
3320 for (k
= 0 ; k
<= dim
-1; ++k
)
3322 num_p
[k
-(k
>0)] = num
[k
];
3325 den_p
.SetLength(len
);
3329 normalize(one
, num_s
, num_p
, den_s
, den_p
, den_r
);
3331 emul(&mone
, factor
);
3335 for (int k
= 0; k
< len
; ++k
) {
3338 else if (den_s
[k
] == 0)
3341 if (no_param
== 0) {
3342 reduce(factor
, num_p
, den_r
);
3346 pden
.SetDims(only_param
, dim
-1);
3348 for (k
= 0, l
= 0; k
< len
; ++k
)
3350 pden
[l
++] = den_r
[k
];
3352 for (k
= 0; k
< len
; ++k
)
3356 dpoly
n(no_param
, num_s
);
3357 dpoly
D(no_param
, den_s
[k
], 1);
3358 for ( ; ++k
< len
; )
3359 if (den_p
[k
] == 0) {
3360 dpoly
fact(no_param
, den_s
[k
], 1);
3365 // if no_param + only_param == len then all powers
3366 // below will be all zero
3367 if (no_param
+ only_param
== len
) {
3368 if (E_num(0, dim
) != 0)
3369 r
= new dpoly_r(n
, len
);
3371 mpq_set_si(tcount
, 0, 1);
3373 n
.div(D
, tcount
, one
);
3375 if (value_notzero_p(mpq_numref(tcount
))) {
3379 value_assign(f
.x
.n
, mpq_numref(tcount
));
3380 value_assign(f
.d
, mpq_denref(tcount
));
3382 reduce(factor
, num_p
, pden
);
3383 free_evalue_refs(&f
);
3388 for (k
= 0; k
< len
; ++k
) {
3389 if (den_s
[k
] == 0 || den_p
[k
] == 0)
3392 dpoly
pd(no_param
-1, den_s
[k
], 1);
3395 for (l
= 0; l
< k
; ++l
)
3396 if (den_r
[l
] == den_r
[k
])
3400 r
= new dpoly_r(n
, pd
, l
, len
);
3402 dpoly_r
*nr
= new dpoly_r(r
, pd
, l
, len
);
3408 dpoly_r
*rc
= r
->div(D
);
3411 if (E_num(0, dim
) == 0) {
3412 int common
= pden
.NumRows();
3413 vector
< dpoly_r_term
* >& final
= r
->c
[r
->len
-1];
3419 zz2value(r
->denom
, f
.d
);
3420 for (int j
= 0; j
< final
.size(); ++j
) {
3421 if (final
[j
]->coeff
== 0)
3424 for (int k
= 0; k
< r
->dim
; ++k
) {
3425 int n
= final
[j
]->powers
[k
];
3428 pden
.SetDims(rows
+n
, pden
.NumCols());
3429 for (int l
= 0; l
< n
; ++l
)
3430 pden
[rows
+l
] = den_r
[k
];
3434 evalue_copy(&t
, factor
);
3435 zz2value(final
[j
]->coeff
, f
.x
.n
);
3437 reduce(&t
, num_p
, pden
);
3438 free_evalue_refs(&t
);
3440 free_evalue_refs(&f
);
3442 ie_cum
cum(factor
, E_num(0, dim
), r
);
3445 int common
= pden
.NumRows();
3447 for (int j
= 0; j
< cum
.terms
.size(); ++j
) {
3449 pden
.SetDims(rows
, pden
.NumCols());
3450 for (int k
= 0; k
< r
->dim
; ++k
) {
3451 int n
= cum
.terms
[j
]->powers
[k
];
3454 pden
.SetDims(rows
+n
, pden
.NumCols());
3455 for (int l
= 0; l
< n
; ++l
)
3456 pden
[rows
+l
] = den_r
[k
];
3459 reduce(cum
.terms
[j
]->E
, num_p
, pden
);
3460 free_evalue_refs(cum
.terms
[j
]->E
);
3461 delete cum
.terms
[j
]->E
;
3462 delete [] cum
.terms
[j
]->powers
;
3463 delete cum
.terms
[j
];
3470 static int type_offset(enode
*p
)
3472 return p
->type
== fractional
? 1 :
3473 p
->type
== flooring
? 1 : 0;
3476 static int edegree(evalue
*e
)
3481 if (value_notzero_p(e
->d
))
3485 int i
= type_offset(p
);
3486 if (p
->size
-i
-1 > d
)
3487 d
= p
->size
- i
- 1;
3488 for (; i
< p
->size
; i
++) {
3489 int d2
= edegree(&p
->arr
[i
]);
3496 void ienumerator::handle_polar(Polyhedron
*C
, int s
)
3498 assert(C
->NbRays
-1 == dim
);
3500 lattice_point(V
, C
, vertex
, E_vertex
);
3503 for (r
= 0; r
< dim
; ++r
)
3504 values2zz(C
->Ray
[r
]+1, den
[r
], dim
);
3508 evalue_set_si(&one
, s
, 1);
3509 reduce(&one
, vertex
, den
);
3510 free_evalue_refs(&one
);
3512 for (int i
= 0; i
< dim
; ++i
)
3514 free_evalue_refs(E_vertex
[i
]);
3520 char * test[] = {"a", "b"};
3523 evalue_copy(&E, vE[_i]);
3524 frac2floor_in_domain(&E, pVD);
3525 printf("***** Curr value:");
3526 print_evalue(stdout, &E, test);
3527 fprintf(stdout, "\n");
3533 struct bfenumerator
: public bf_base
, public enumerator_base
{
3536 bfenumerator(Polyhedron
*P
, unsigned dim
, unsigned nbV
) :
3537 bf_base(P
, dim
), enumerator_base(P
, dim
, nbV
) {
3545 virtual void handle_polar(Polyhedron
*P
, int sign
);
3546 virtual void base(mat_ZZ
& factors
, bfc_vec
& v
);
3548 bfc_term_base
* new_bf_term(int len
) {
3549 bfe_term
* t
= new bfe_term(len
);
3553 virtual void set_factor(bfc_term_base
*t
, int k
, int change
) {
3554 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3555 factor
= bfet
->factors
[k
];
3556 assert(factor
!= NULL
);
3557 bfet
->factors
[k
] = NULL
;
3559 emul(&mone
, factor
);
3562 virtual void set_factor(bfc_term_base
*t
, int k
, mpq_t
&q
, int change
) {
3563 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3564 factor
= bfet
->factors
[k
];
3565 assert(factor
!= NULL
);
3566 bfet
->factors
[k
] = NULL
;
3572 value_oppose(f
.x
.n
, mpq_numref(q
));
3574 value_assign(f
.x
.n
, mpq_numref(q
));
3575 value_assign(f
.d
, mpq_denref(q
));
3579 virtual void set_factor(bfc_term_base
*t
, int k
, ZZ
& n
, ZZ
& d
, int change
) {
3580 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3582 factor
= new evalue
;
3589 value_oppose(f
.x
.n
, f
.x
.n
);
3592 value_init(factor
->d
);
3593 evalue_copy(factor
, bfet
->factors
[k
]);
3597 void set_factor(evalue
*f
, int change
) {
3603 virtual void insert_term(bfc_term_base
*t
, int i
) {
3604 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3605 int len
= t
->terms
.NumRows()-1; // already increased by one
3607 bfet
->factors
.resize(len
+1);
3608 for (int j
= len
; j
> i
; --j
) {
3609 bfet
->factors
[j
] = bfet
->factors
[j
-1];
3610 t
->terms
[j
] = t
->terms
[j
-1];
3612 bfet
->factors
[i
] = factor
;
3616 virtual void update_term(bfc_term_base
*t
, int i
) {
3617 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3619 eadd(factor
, bfet
->factors
[i
]);
3620 free_evalue_refs(factor
);
3624 virtual bool constant_vertex(int dim
) { return E_num(0, dim
) == 0; }
3626 virtual void cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
, dpoly_r
*r
);
3629 struct bfe_cum
: public cumulator
{
3631 bfc_term_base
*told
;
3635 bfe_cum(evalue
*factor
, evalue
*v
, dpoly_r
*r
, bf_reducer
*bfr
,
3636 bfc_term_base
*t
, int k
, bfenumerator
*e
) :
3637 cumulator(factor
, v
, r
), told(t
), k(k
),
3641 virtual void add_term(int *powers
, int len
, evalue
*f2
);
3644 void bfe_cum::add_term(int *powers
, int len
, evalue
*f2
)
3646 bfr
->update_powers(powers
, len
);
3648 bfc_term_base
* t
= bfe
->find_bfc_term(bfr
->vn
, bfr
->npowers
, bfr
->nnf
);
3649 bfe
->set_factor(f2
, bfr
->l_changes
% 2);
3650 bfe
->add_term(t
, told
->terms
[k
], bfr
->l_extra_num
);
3653 void bfenumerator::cum(bf_reducer
*bfr
, bfc_term_base
*t
, int k
,
3656 bfe_term
* bfet
= static_cast<bfe_term
*>(t
);
3657 bfe_cum
cum(bfet
->factors
[k
], E_num(0, bfr
->d
), r
, bfr
, t
, k
, this);
3661 void bfenumerator::base(mat_ZZ
& factors
, bfc_vec
& v
)
3663 for (int i
= 0; i
< v
.size(); ++i
) {
3664 assert(v
[i
]->terms
.NumRows() == 1);
3665 evalue
*factor
= static_cast<bfe_term
*>(v
[i
])->factors
[0];
3666 eadd(factor
, vE
[_i
]);
3671 void bfenumerator::handle_polar(Polyhedron
*C
, int s
)
3673 assert(C
->NbRays
-1 == enumerator_base::dim
);
3675 bfe_term
* t
= new bfe_term(enumerator_base::dim
);
3676 vector
< bfc_term_base
* > v
;
3679 t
->factors
.resize(1);
3681 t
->terms
.SetDims(1, enumerator_base::dim
);
3682 lattice_point(V
, C
, t
->terms
[0], E_vertex
);
3684 // the elements of factors are always lexpositive
3686 s
= setup_factors(C
, factors
, t
, s
);
3688 t
->factors
[0] = new evalue
;
3689 value_init(t
->factors
[0]->d
);
3690 evalue_set_si(t
->factors
[0], s
, 1);
3693 for (int i
= 0; i
< enumerator_base::dim
; ++i
)
3695 free_evalue_refs(E_vertex
[i
]);
3700 #ifdef HAVE_CORRECT_VERTICES
3701 static inline Param_Polyhedron
*Polyhedron2Param_SD(Polyhedron
**Din
,
3702 Polyhedron
*Cin
,int WS
,Polyhedron
**CEq
,Matrix
**CT
)
3704 return Polyhedron2Param_SimplifiedDomain(Din
, Cin
, WS
, CEq
, CT
);
3707 static Param_Polyhedron
*Polyhedron2Param_SD(Polyhedron
**Din
,
3708 Polyhedron
*Cin
,int WS
,Polyhedron
**CEq
,Matrix
**CT
)
3710 static char data
[] = " 1 0 0 0 0 1 -18 "
3711 " 1 0 0 -20 0 19 1 "
3712 " 1 0 1 20 0 -20 16 "
3715 " 1 4 -20 0 0 -1 23 "
3716 " 1 -4 20 0 0 1 -22 "
3717 " 1 0 1 0 20 -20 16 "
3718 " 1 0 0 0 -20 19 1 ";
3719 static int checked
= 0;
3724 Matrix
*M
= Matrix_Alloc(9, 7);
3725 for (i
= 0; i
< 9; ++i
)
3726 for (int j
= 0; j
< 7; ++j
) {
3727 sscanf(p
, "%d%n", &v
, &n
);
3729 value_set_si(M
->p
[i
][j
], v
);
3731 Polyhedron
*P
= Constraints2Polyhedron(M
, 1024);
3734 Polyhedron
*U
= Universe_Polyhedron(1);
3736 Param_Polyhedron
*PP
=
3737 Polyhedron2Param_SimplifiedDomain(&P
, U
, 1024, NULL
, NULL
);
3740 Polyhedron_Free(P2
);
3743 for (i
= 0, V
= PP
->V
; V
; ++i
, V
= V
->next
)
3746 Param_Polyhedron_Free(PP
);
3748 fprintf(stderr
, "WARNING: results may be incorrect\n");
3750 "WARNING: use latest version of PolyLib to remove this warning\n");
3754 return Polyhedron2Param_SimplifiedDomain(Din
, Cin
, WS
, CEq
, CT
);
3758 static evalue
* barvinok_enumerate_ev_f(Polyhedron
*P
, Polyhedron
* C
,
3762 static evalue
* barvinok_enumerate_cst(Polyhedron
*P
, Polyhedron
* C
,
3767 ALLOC(evalue
, eres
);
3768 value_init(eres
->d
);
3769 value_set_si(eres
->d
, 0);
3770 eres
->x
.p
= new_enode(partition
, 2, C
->Dimension
);
3771 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[0], DomainConstraintSimplify(C
, MaxRays
));
3772 value_set_si(eres
->x
.p
->arr
[1].d
, 1);
3773 value_init(eres
->x
.p
->arr
[1].x
.n
);
3775 value_set_si(eres
->x
.p
->arr
[1].x
.n
, 0);
3777 barvinok_count(P
, &eres
->x
.p
->arr
[1].x
.n
, MaxRays
);
3782 evalue
* barvinok_enumerate_ev(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
3784 //P = unfringe(P, MaxRays);
3785 Polyhedron
*Corig
= C
;
3786 Polyhedron
*CEq
= NULL
, *rVD
, *CA
;
3788 unsigned nparam
= C
->Dimension
;
3792 value_init(factor
.d
);
3793 evalue_set_si(&factor
, 1, 1);
3796 POL_ENSURE_FACETS(P
);
3797 POL_ENSURE_VERTICES(P
);
3798 POL_ENSURE_FACETS(C
);
3799 POL_ENSURE_VERTICES(C
);
3801 CA
= align_context(C
, P
->Dimension
, MaxRays
);
3802 P
= DomainIntersection(P
, CA
, MaxRays
);
3803 Polyhedron_Free(CA
);
3805 if (C
->Dimension
== 0 || emptyQ(P
)) {
3807 eres
= barvinok_enumerate_cst(P
, CEq
? CEq
: Polyhedron_Copy(C
),
3810 emul(&factor
, eres
);
3811 reduce_evalue(eres
);
3812 free_evalue_refs(&factor
);
3819 if (Polyhedron_is_infinite(P
, nparam
))
3824 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, &f
);
3828 if (P
->Dimension
== nparam
) {
3830 P
= Universe_Polyhedron(0);
3834 Polyhedron
*T
= Polyhedron_Factor(P
, nparam
, MaxRays
);
3835 if (T
|| (P
->Dimension
== nparam
+1)) {
3838 for (Q
= T
? T
: P
; Q
; Q
= Q
->next
) {
3839 Polyhedron
*next
= Q
->next
;
3843 if (Q
->Dimension
!= C
->Dimension
)
3844 QC
= Polyhedron_Project(Q
, nparam
);
3847 C
= DomainIntersection(C
, QC
, MaxRays
);
3849 Polyhedron_Free(C2
);
3851 Polyhedron_Free(QC
);
3859 if (T
->Dimension
== C
->Dimension
) {
3866 Polyhedron
*next
= P
->next
;
3868 eres
= barvinok_enumerate_ev_f(P
, C
, MaxRays
);
3875 for (Q
= P
->next
; Q
; Q
= Q
->next
) {
3876 Polyhedron
*next
= Q
->next
;
3879 f
= barvinok_enumerate_ev_f(Q
, C
, MaxRays
);
3881 free_evalue_refs(f
);
3891 static evalue
* barvinok_enumerate_ev_f(Polyhedron
*P
, Polyhedron
* C
,
3894 unsigned nparam
= C
->Dimension
;
3896 if (P
->Dimension
- nparam
== 1)
3897 return ParamLine_Length(P
, C
, MaxRays
);
3899 Param_Polyhedron
*PP
= NULL
;
3900 Polyhedron
*CEq
= NULL
, *pVD
;
3902 Param_Domain
*D
, *next
;
3905 Polyhedron
*Porig
= P
;
3907 PP
= Polyhedron2Param_SD(&P
,C
,MaxRays
,&CEq
,&CT
);
3909 if (isIdentity(CT
)) {
3913 assert(CT
->NbRows
!= CT
->NbColumns
);
3914 if (CT
->NbRows
== 1) { // no more parameters
3915 eres
= barvinok_enumerate_cst(P
, CEq
, MaxRays
);
3920 Param_Polyhedron_Free(PP
);
3926 nparam
= CT
->NbRows
- 1;
3929 unsigned dim
= P
->Dimension
- nparam
;
3931 ALLOC(evalue
, eres
);
3932 value_init(eres
->d
);
3933 value_set_si(eres
->d
, 0);
3936 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
3937 struct section
{ Polyhedron
*D
; evalue E
; };
3938 section
*s
= new section
[nd
];
3939 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
3942 #ifdef USE_INCREMENTAL_BF
3943 bfenumerator
et(P
, dim
, PP
->nbV
);
3944 #elif defined USE_INCREMENTAL_DF
3945 ienumerator
et(P
, dim
, PP
->nbV
);
3947 enumerator
et(P
, dim
, PP
->nbV
);
3950 for(nd
= 0, D
=PP
->D
; D
; D
=next
) {
3953 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
3958 pVD
= CT
? DomainImage(rVD
,CT
,MaxRays
) : rVD
;
3960 value_init(s
[nd
].E
.d
);
3961 evalue_set_si(&s
[nd
].E
, 0, 1);
3964 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
3967 et
.decompose_at(V
, _i
, MaxRays
);
3968 } catch (OrthogonalException
&e
) {
3971 for (; nd
>= 0; --nd
) {
3972 free_evalue_refs(&s
[nd
].E
);
3973 Domain_Free(s
[nd
].D
);
3974 Domain_Free(fVD
[nd
]);
3978 eadd(et
.vE
[_i
] , &s
[nd
].E
);
3979 END_FORALL_PVertex_in_ParamPolyhedron
;
3980 reduce_in_domain(&s
[nd
].E
, pVD
);
3983 addeliminatedparams_evalue(&s
[nd
].E
, CT
);
3990 evalue_set_si(eres
, 0, 1);
3992 eres
->x
.p
= new_enode(partition
, 2*nd
, C
->Dimension
);
3993 for (int j
= 0; j
< nd
; ++j
) {
3994 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[2*j
], s
[j
].D
);
3995 value_clear(eres
->x
.p
->arr
[2*j
+1].d
);
3996 eres
->x
.p
->arr
[2*j
+1] = s
[j
].E
;
3997 Domain_Free(fVD
[j
]);
4004 Polyhedron_Free(CEq
);
4008 Enumeration
* barvinok_enumerate(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
4010 evalue
*EP
= barvinok_enumerate_ev(P
, C
, MaxRays
);
4012 return partition2enumeration(EP
);
4015 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
4017 for (int r
= 0; r
< n
; ++r
)
4018 value_swap(V
[r
][i
], V
[r
][j
]);
4021 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
4023 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
4024 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
4027 static void negative_test_constraint(Value
*l
, Value
*u
, Value
*c
, int pos
,
4030 value_oppose(*v
, u
[pos
+1]);
4031 Vector_Combine(l
+1, u
+1, c
+1, *v
, l
[pos
+1], len
-1);
4032 value_multiply(*v
, *v
, l
[pos
+1]);
4033 value_subtract(c
[len
-1], c
[len
-1], *v
);
4034 value_set_si(*v
, -1);
4035 Vector_Scale(c
+1, c
+1, *v
, len
-1);
4036 value_decrement(c
[len
-1], c
[len
-1]);
4037 ConstraintSimplify(c
, c
, len
, v
);
4040 static bool parallel_constraints(Value
*l
, Value
*u
, Value
*c
, int pos
,
4049 Vector_Gcd(&l
[1+pos
], len
, &g1
);
4050 Vector_Gcd(&u
[1+pos
], len
, &g2
);
4051 Vector_Combine(l
+1+pos
, u
+1+pos
, c
+1, g2
, g1
, len
);
4052 parallel
= First_Non_Zero(c
+1, len
) == -1;
4060 static void negative_test_constraint7(Value
*l
, Value
*u
, Value
*c
, int pos
,
4061 int exist
, int len
, Value
*v
)
4066 Vector_Gcd(&u
[1+pos
], exist
, v
);
4067 Vector_Gcd(&l
[1+pos
], exist
, &g
);
4068 Vector_Combine(l
+1, u
+1, c
+1, *v
, g
, len
-1);
4069 value_multiply(*v
, *v
, g
);
4070 value_subtract(c
[len
-1], c
[len
-1], *v
);
4071 value_set_si(*v
, -1);
4072 Vector_Scale(c
+1, c
+1, *v
, len
-1);
4073 value_decrement(c
[len
-1], c
[len
-1]);
4074 ConstraintSimplify(c
, c
, len
, v
);
4079 static void oppose_constraint(Value
*c
, int len
, Value
*v
)
4081 value_set_si(*v
, -1);
4082 Vector_Scale(c
+1, c
+1, *v
, len
-1);
4083 value_decrement(c
[len
-1], c
[len
-1]);
4086 static bool SplitOnConstraint(Polyhedron
*P
, int i
, int l
, int u
,
4087 int nvar
, int len
, int exist
, int MaxRays
,
4088 Vector
*row
, Value
& f
, bool independent
,
4089 Polyhedron
**pos
, Polyhedron
**neg
)
4091 negative_test_constraint(P
->Constraint
[l
], P
->Constraint
[u
],
4092 row
->p
, nvar
+i
, len
, &f
);
4093 *neg
= AddConstraints(row
->p
, 1, P
, MaxRays
);
4095 /* We found an independent, but useless constraint
4096 * Maybe we should detect this earlier and not
4097 * mark the variable as INDEPENDENT
4099 if (emptyQ((*neg
))) {
4100 Polyhedron_Free(*neg
);
4104 oppose_constraint(row
->p
, len
, &f
);
4105 *pos
= AddConstraints(row
->p
, 1, P
, MaxRays
);
4107 if (emptyQ((*pos
))) {
4108 Polyhedron_Free(*neg
);
4109 Polyhedron_Free(*pos
);
4117 * unimodularly transform P such that constraint r is transformed
4118 * into a constraint that involves only a single (the first)
4119 * existential variable
4122 static Polyhedron
*rotate_along(Polyhedron
*P
, int r
, int nvar
, int exist
,
4128 Vector
*row
= Vector_Alloc(exist
);
4129 Vector_Copy(P
->Constraint
[r
]+1+nvar
, row
->p
, exist
);
4130 Vector_Gcd(row
->p
, exist
, &g
);
4131 if (value_notone_p(g
))
4132 Vector_AntiScale(row
->p
, row
->p
, g
, exist
);
4135 Matrix
*M
= unimodular_complete(row
);
4136 Matrix
*M2
= Matrix_Alloc(P
->Dimension
+1, P
->Dimension
+1);
4137 for (r
= 0; r
< nvar
; ++r
)
4138 value_set_si(M2
->p
[r
][r
], 1);
4139 for ( ; r
< nvar
+exist
; ++r
)
4140 Vector_Copy(M
->p
[r
-nvar
], M2
->p
[r
]+nvar
, exist
);
4141 for ( ; r
< P
->Dimension
+1; ++r
)
4142 value_set_si(M2
->p
[r
][r
], 1);
4143 Polyhedron
*T
= Polyhedron_Image(P
, M2
, MaxRays
);
4152 static bool SplitOnVar(Polyhedron
*P
, int i
,
4153 int nvar
, int len
, int exist
, int MaxRays
,
4154 Vector
*row
, Value
& f
, bool independent
,
4155 Polyhedron
**pos
, Polyhedron
**neg
)
4159 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
4160 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
4164 for (j
= 0; j
< exist
; ++j
)
4165 if (j
!= i
&& value_notzero_p(P
->Constraint
[l
][nvar
+j
+1]))
4171 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
4172 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
4176 for (j
= 0; j
< exist
; ++j
)
4177 if (j
!= i
&& value_notzero_p(P
->Constraint
[u
][nvar
+j
+1]))
4183 if (SplitOnConstraint(P
, i
, l
, u
,
4184 nvar
, len
, exist
, MaxRays
,
4185 row
, f
, independent
,
4189 SwapColumns(*neg
, nvar
+1, nvar
+1+i
);
4199 static bool double_bound_pair(Polyhedron
*P
, int nvar
, int exist
,
4200 int i
, int l1
, int l2
,
4201 Polyhedron
**pos
, Polyhedron
**neg
)
4205 Vector
*row
= Vector_Alloc(P
->Dimension
+2);
4206 value_set_si(row
->p
[0], 1);
4207 value_oppose(f
, P
->Constraint
[l1
][nvar
+i
+1]);
4208 Vector_Combine(P
->Constraint
[l1
]+1, P
->Constraint
[l2
]+1,
4210 P
->Constraint
[l2
][nvar
+i
+1], f
,
4212 ConstraintSimplify(row
->p
, row
->p
, P
->Dimension
+2, &f
);
4213 *pos
= AddConstraints(row
->p
, 1, P
, 0);
4214 value_set_si(f
, -1);
4215 Vector_Scale(row
->p
+1, row
->p
+1, f
, P
->Dimension
+1);
4216 value_decrement(row
->p
[P
->Dimension
+1], row
->p
[P
->Dimension
+1]);
4217 *neg
= AddConstraints(row
->p
, 1, P
, 0);
4221 return !emptyQ((*pos
)) && !emptyQ((*neg
));
4224 static bool double_bound(Polyhedron
*P
, int nvar
, int exist
,
4225 Polyhedron
**pos
, Polyhedron
**neg
)
4227 for (int i
= 0; i
< exist
; ++i
) {
4229 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
4230 if (value_negz_p(P
->Constraint
[l1
][nvar
+i
+1]))
4232 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
4233 if (value_negz_p(P
->Constraint
[l2
][nvar
+i
+1]))
4235 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
4239 for (l1
= P
->NbEq
; l1
< P
->NbConstraints
; ++l1
) {
4240 if (value_posz_p(P
->Constraint
[l1
][nvar
+i
+1]))
4242 if (l1
< P
->NbConstraints
)
4243 for (l2
= l1
+ 1; l2
< P
->NbConstraints
; ++l2
) {
4244 if (value_posz_p(P
->Constraint
[l2
][nvar
+i
+1]))
4246 if (double_bound_pair(P
, nvar
, exist
, i
, l1
, l2
, pos
, neg
))
4258 INDEPENDENT
= 1 << 2,
4262 static evalue
* enumerate_or(Polyhedron
*D
,
4263 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4266 fprintf(stderr
, "\nER: Or\n");
4267 #endif /* DEBUG_ER */
4269 Polyhedron
*N
= D
->next
;
4272 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
4275 for (D
= N
; D
; D
= N
) {
4280 barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
4283 free_evalue_refs(EN
);
4293 static evalue
* enumerate_sum(Polyhedron
*P
,
4294 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4296 int nvar
= P
->Dimension
- exist
- nparam
;
4297 int toswap
= nvar
< exist
? nvar
: exist
;
4298 for (int i
= 0; i
< toswap
; ++i
)
4299 SwapColumns(P
, 1 + i
, nvar
+exist
- i
);
4303 fprintf(stderr
, "\nER: Sum\n");
4304 #endif /* DEBUG_ER */
4306 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
4308 for (int i
= 0; i
< /* nvar */ nparam
; ++i
) {
4309 Matrix
*C
= Matrix_Alloc(1, 1 + nparam
+ 1);
4310 value_set_si(C
->p
[0][0], 1);
4312 value_init(split
.d
);
4313 value_set_si(split
.d
, 0);
4314 split
.x
.p
= new_enode(partition
, 4, nparam
);
4315 value_set_si(C
->p
[0][1+i
], 1);
4316 Matrix
*C2
= Matrix_Copy(C
);
4317 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[0],
4318 Constraints2Polyhedron(C2
, MaxRays
));
4320 evalue_set_si(&split
.x
.p
->arr
[1], 1, 1);
4321 value_set_si(C
->p
[0][1+i
], -1);
4322 value_set_si(C
->p
[0][1+nparam
], -1);
4323 EVALUE_SET_DOMAIN(split
.x
.p
->arr
[2],
4324 Constraints2Polyhedron(C
, MaxRays
));
4325 evalue_set_si(&split
.x
.p
->arr
[3], 1, 1);
4327 free_evalue_refs(&split
);
4331 evalue_range_reduction(EP
);
4333 evalue_frac2floor(EP
);
4335 evalue
*sum
= esum(EP
, nvar
);
4337 free_evalue_refs(EP
);
4341 evalue_range_reduction(EP
);
4346 static evalue
* split_sure(Polyhedron
*P
, Polyhedron
*S
,
4347 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4349 int nvar
= P
->Dimension
- exist
- nparam
;
4351 Matrix
*M
= Matrix_Alloc(exist
, S
->Dimension
+2);
4352 for (int i
= 0; i
< exist
; ++i
)
4353 value_set_si(M
->p
[i
][nvar
+i
+1], 1);
4355 S
= DomainAddRays(S
, M
, MaxRays
);
4357 Polyhedron
*F
= DomainAddRays(P
, M
, MaxRays
);
4358 Polyhedron
*D
= DomainDifference(F
, S
, MaxRays
);
4360 D
= Disjoint_Domain(D
, 0, MaxRays
);
4365 M
= Matrix_Alloc(P
->Dimension
+1-exist
, P
->Dimension
+1);
4366 for (int j
= 0; j
< nvar
; ++j
)
4367 value_set_si(M
->p
[j
][j
], 1);
4368 for (int j
= 0; j
< nparam
+1; ++j
)
4369 value_set_si(M
->p
[nvar
+j
][nvar
+exist
+j
], 1);
4370 Polyhedron
*T
= Polyhedron_Image(S
, M
, MaxRays
);
4371 evalue
*EP
= barvinok_enumerate_e(T
, 0, nparam
, MaxRays
);
4376 for (Polyhedron
*Q
= D
; Q
; Q
= Q
->next
) {
4377 Polyhedron
*N
= Q
->next
;
4379 T
= DomainIntersection(P
, Q
, MaxRays
);
4380 evalue
*E
= barvinok_enumerate_e(T
, exist
, nparam
, MaxRays
);
4382 free_evalue_refs(E
);
4391 static evalue
* enumerate_sure(Polyhedron
*P
,
4392 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4396 int nvar
= P
->Dimension
- exist
- nparam
;
4402 for (i
= 0; i
< exist
; ++i
) {
4403 Matrix
*M
= Matrix_Alloc(S
->NbConstraints
, S
->Dimension
+2);
4405 value_set_si(lcm
, 1);
4406 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
4407 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
4409 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
4411 value_lcm(lcm
, S
->Constraint
[j
][1+nvar
+i
], &lcm
);
4414 for (int j
= 0; j
< S
->NbConstraints
; ++j
) {
4415 if (value_negz_p(S
->Constraint
[j
][1+nvar
+i
]))
4417 if (value_one_p(S
->Constraint
[j
][1+nvar
+i
]))
4419 value_division(f
, lcm
, S
->Constraint
[j
][1+nvar
+i
]);
4420 Vector_Scale(S
->Constraint
[j
], M
->p
[c
], f
, S
->Dimension
+2);
4421 value_subtract(M
->p
[c
][S
->Dimension
+1],
4422 M
->p
[c
][S
->Dimension
+1],
4424 value_increment(M
->p
[c
][S
->Dimension
+1],
4425 M
->p
[c
][S
->Dimension
+1]);
4429 S
= AddConstraints(M
->p
[0], c
, S
, MaxRays
);
4444 fprintf(stderr
, "\nER: Sure\n");
4445 #endif /* DEBUG_ER */
4447 return split_sure(P
, S
, exist
, nparam
, MaxRays
);
4450 static evalue
* enumerate_sure2(Polyhedron
*P
,
4451 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4453 int nvar
= P
->Dimension
- exist
- nparam
;
4455 for (r
= 0; r
< P
->NbRays
; ++r
)
4456 if (value_one_p(P
->Ray
[r
][0]) &&
4457 value_one_p(P
->Ray
[r
][P
->Dimension
+1]))
4463 Matrix
*M
= Matrix_Alloc(nvar
+ 1 + nparam
, P
->Dimension
+2);
4464 for (int i
= 0; i
< nvar
; ++i
)
4465 value_set_si(M
->p
[i
][1+i
], 1);
4466 for (int i
= 0; i
< nparam
; ++i
)
4467 value_set_si(M
->p
[i
+nvar
][1+nvar
+exist
+i
], 1);
4468 Vector_Copy(P
->Ray
[r
]+1+nvar
, M
->p
[nvar
+nparam
]+1+nvar
, exist
);
4469 value_set_si(M
->p
[nvar
+nparam
][0], 1);
4470 value_set_si(M
->p
[nvar
+nparam
][P
->Dimension
+1], 1);
4471 Polyhedron
* F
= Rays2Polyhedron(M
, MaxRays
);
4474 Polyhedron
*I
= DomainIntersection(F
, P
, MaxRays
);
4478 fprintf(stderr
, "\nER: Sure2\n");
4479 #endif /* DEBUG_ER */
4481 return split_sure(P
, I
, exist
, nparam
, MaxRays
);
4484 static evalue
* enumerate_cyclic(Polyhedron
*P
,
4485 unsigned exist
, unsigned nparam
,
4486 evalue
* EP
, int r
, int p
, unsigned MaxRays
)
4488 int nvar
= P
->Dimension
- exist
- nparam
;
4490 /* If EP in its fractional maps only contains references
4491 * to the remainder parameter with appropriate coefficients
4492 * then we could in principle avoid adding existentially
4493 * quantified variables to the validity domains.
4494 * We'd have to replace the remainder by m { p/m }
4495 * and multiply with an appropriate factor that is one
4496 * only in the appropriate range.
4497 * This last multiplication can be avoided if EP
4498 * has a single validity domain with no (further)
4499 * constraints on the remainder parameter
4502 Matrix
*CT
= Matrix_Alloc(nparam
+1, nparam
+3);
4503 Matrix
*M
= Matrix_Alloc(1, 1+nparam
+3);
4504 for (int j
= 0; j
< nparam
; ++j
)
4506 value_set_si(CT
->p
[j
][j
], 1);
4507 value_set_si(CT
->p
[p
][nparam
+1], 1);
4508 value_set_si(CT
->p
[nparam
][nparam
+2], 1);
4509 value_set_si(M
->p
[0][1+p
], -1);
4510 value_absolute(M
->p
[0][1+nparam
], P
->Ray
[0][1+nvar
+exist
+p
]);
4511 value_set_si(M
->p
[0][1+nparam
+1], 1);
4512 Polyhedron
*CEq
= Constraints2Polyhedron(M
, 1);
4514 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
4515 Polyhedron_Free(CEq
);
4521 static void enumerate_vd_add_ray(evalue
*EP
, Matrix
*Rays
, unsigned MaxRays
)
4523 if (value_notzero_p(EP
->d
))
4526 assert(EP
->x
.p
->type
== partition
);
4527 assert(EP
->x
.p
->pos
== EVALUE_DOMAIN(EP
->x
.p
->arr
[0])->Dimension
);
4528 for (int i
= 0; i
< EP
->x
.p
->size
/2; ++i
) {
4529 Polyhedron
*D
= EVALUE_DOMAIN(EP
->x
.p
->arr
[2*i
]);
4530 Polyhedron
*N
= DomainAddRays(D
, Rays
, MaxRays
);
4531 EVALUE_SET_DOMAIN(EP
->x
.p
->arr
[2*i
], N
);
4536 static evalue
* enumerate_line(Polyhedron
*P
,
4537 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4543 fprintf(stderr
, "\nER: Line\n");
4544 #endif /* DEBUG_ER */
4546 int nvar
= P
->Dimension
- exist
- nparam
;
4548 for (i
= 0; i
< nparam
; ++i
)
4549 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
4552 for (j
= i
+1; j
< nparam
; ++j
)
4553 if (value_notzero_p(P
->Ray
[0][1+nvar
+exist
+i
]))
4555 assert(j
>= nparam
); // for now
4557 Matrix
*M
= Matrix_Alloc(2, P
->Dimension
+2);
4558 value_set_si(M
->p
[0][0], 1);
4559 value_set_si(M
->p
[0][1+nvar
+exist
+i
], 1);
4560 value_set_si(M
->p
[1][0], 1);
4561 value_set_si(M
->p
[1][1+nvar
+exist
+i
], -1);
4562 value_absolute(M
->p
[1][1+P
->Dimension
], P
->Ray
[0][1+nvar
+exist
+i
]);
4563 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
4564 Polyhedron
*S
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
4565 evalue
*EP
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
4569 return enumerate_cyclic(P
, exist
, nparam
, EP
, 0, i
, MaxRays
);
4572 static int single_param_pos(Polyhedron
*P
, unsigned exist
, unsigned nparam
,
4575 int nvar
= P
->Dimension
- exist
- nparam
;
4576 if (First_Non_Zero(P
->Ray
[r
]+1, nvar
) != -1)
4578 int i
= First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
, nparam
);
4581 if (First_Non_Zero(P
->Ray
[r
]+1+nvar
+exist
+1, nparam
-i
-1) != -1)
4586 static evalue
* enumerate_remove_ray(Polyhedron
*P
, int r
,
4587 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4590 fprintf(stderr
, "\nER: RedundantRay\n");
4591 #endif /* DEBUG_ER */
4595 value_set_si(one
, 1);
4596 int len
= P
->NbRays
-1;
4597 Matrix
*M
= Matrix_Alloc(2 * len
, P
->Dimension
+2);
4598 Vector_Copy(P
->Ray
[0], M
->p
[0], r
* (P
->Dimension
+2));
4599 Vector_Copy(P
->Ray
[r
+1], M
->p
[r
], (len
-r
) * (P
->Dimension
+2));
4600 for (int j
= 0; j
< P
->NbRays
; ++j
) {
4603 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[len
+j
-(j
>r
)],
4604 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
4607 P
= Rays2Polyhedron(M
, MaxRays
);
4609 evalue
*EP
= barvinok_enumerate_e(P
, exist
, nparam
, MaxRays
);
4616 static evalue
* enumerate_redundant_ray(Polyhedron
*P
,
4617 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4619 assert(P
->NbBid
== 0);
4620 int nvar
= P
->Dimension
- exist
- nparam
;
4624 for (int r
= 0; r
< P
->NbRays
; ++r
) {
4625 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
4627 int i1
= single_param_pos(P
, exist
, nparam
, r
);
4630 for (int r2
= r
+1; r2
< P
->NbRays
; ++r2
) {
4631 if (value_notzero_p(P
->Ray
[r2
][P
->Dimension
+1]))
4633 int i2
= single_param_pos(P
, exist
, nparam
, r2
);
4639 value_division(m
, P
->Ray
[r
][1+nvar
+exist
+i1
],
4640 P
->Ray
[r2
][1+nvar
+exist
+i1
]);
4641 value_multiply(m
, m
, P
->Ray
[r2
][1+nvar
+exist
+i1
]);
4642 /* r2 divides r => r redundant */
4643 if (value_eq(m
, P
->Ray
[r
][1+nvar
+exist
+i1
])) {
4645 return enumerate_remove_ray(P
, r
, exist
, nparam
, MaxRays
);
4648 value_division(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
],
4649 P
->Ray
[r
][1+nvar
+exist
+i1
]);
4650 value_multiply(m
, m
, P
->Ray
[r
][1+nvar
+exist
+i1
]);
4651 /* r divides r2 => r2 redundant */
4652 if (value_eq(m
, P
->Ray
[r2
][1+nvar
+exist
+i1
])) {
4654 return enumerate_remove_ray(P
, r2
, exist
, nparam
, MaxRays
);
4662 static Polyhedron
*upper_bound(Polyhedron
*P
,
4663 int pos
, Value
*max
, Polyhedron
**R
)
4672 for (Polyhedron
*Q
= P
; Q
; Q
= N
) {
4674 for (r
= 0; r
< P
->NbRays
; ++r
) {
4675 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]) &&
4676 value_pos_p(P
->Ray
[r
][1+pos
]))
4679 if (r
< P
->NbRays
) {
4687 for (r
= 0; r
< P
->NbRays
; ++r
) {
4688 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
4690 mpz_fdiv_q(v
, P
->Ray
[r
][1+pos
], P
->Ray
[r
][1+P
->Dimension
]);
4691 if ((!Q
->next
&& r
== 0) || value_gt(v
, *max
))
4692 value_assign(*max
, v
);
4699 static evalue
* enumerate_ray(Polyhedron
*P
,
4700 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4702 assert(P
->NbBid
== 0);
4703 int nvar
= P
->Dimension
- exist
- nparam
;
4706 for (r
= 0; r
< P
->NbRays
; ++r
)
4707 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
4713 for (r2
= r
+1; r2
< P
->NbRays
; ++r2
)
4714 if (value_zero_p(P
->Ray
[r2
][P
->Dimension
+1]))
4716 if (r2
< P
->NbRays
) {
4718 return enumerate_sum(P
, exist
, nparam
, MaxRays
);
4722 fprintf(stderr
, "\nER: Ray\n");
4723 #endif /* DEBUG_ER */
4729 value_set_si(one
, 1);
4730 int i
= single_param_pos(P
, exist
, nparam
, r
);
4731 assert(i
!= -1); // for now;
4733 Matrix
*M
= Matrix_Alloc(P
->NbRays
, P
->Dimension
+2);
4734 for (int j
= 0; j
< P
->NbRays
; ++j
) {
4735 Vector_Combine(P
->Ray
[j
], P
->Ray
[r
], M
->p
[j
],
4736 one
, P
->Ray
[j
][P
->Dimension
+1], P
->Dimension
+2);
4738 Polyhedron
*S
= Rays2Polyhedron(M
, MaxRays
);
4740 Polyhedron
*D
= DomainDifference(P
, S
, MaxRays
);
4742 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
4743 assert(value_pos_p(P
->Ray
[r
][1+nvar
+exist
+i
])); // for now
4745 D
= upper_bound(D
, nvar
+exist
+i
, &m
, &R
);
4749 M
= Matrix_Alloc(2, P
->Dimension
+2);
4750 value_set_si(M
->p
[0][0], 1);
4751 value_set_si(M
->p
[1][0], 1);
4752 value_set_si(M
->p
[0][1+nvar
+exist
+i
], -1);
4753 value_set_si(M
->p
[1][1+nvar
+exist
+i
], 1);
4754 value_assign(M
->p
[0][1+P
->Dimension
], m
);
4755 value_oppose(M
->p
[1][1+P
->Dimension
], m
);
4756 value_addto(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
],
4757 P
->Ray
[r
][1+nvar
+exist
+i
]);
4758 value_decrement(M
->p
[1][1+P
->Dimension
], M
->p
[1][1+P
->Dimension
]);
4759 // Matrix_Print(stderr, P_VALUE_FMT, M);
4760 D
= AddConstraints(M
->p
[0], 2, P
, MaxRays
);
4761 // Polyhedron_Print(stderr, P_VALUE_FMT, D);
4762 value_subtract(M
->p
[0][1+P
->Dimension
], M
->p
[0][1+P
->Dimension
],
4763 P
->Ray
[r
][1+nvar
+exist
+i
]);
4764 // Matrix_Print(stderr, P_VALUE_FMT, M);
4765 S
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
4766 // Polyhedron_Print(stderr, P_VALUE_FMT, S);
4769 evalue
*EP
= barvinok_enumerate_e(D
, exist
, nparam
, MaxRays
);
4774 if (value_notone_p(P
->Ray
[r
][1+nvar
+exist
+i
]))
4775 EP
= enumerate_cyclic(P
, exist
, nparam
, EP
, r
, i
, MaxRays
);
4777 M
= Matrix_Alloc(1, nparam
+2);
4778 value_set_si(M
->p
[0][0], 1);
4779 value_set_si(M
->p
[0][1+i
], 1);
4780 enumerate_vd_add_ray(EP
, M
, MaxRays
);
4785 evalue
*E
= barvinok_enumerate_e(S
, exist
, nparam
, MaxRays
);
4787 free_evalue_refs(E
);
4794 evalue
*ER
= enumerate_or(R
, exist
, nparam
, MaxRays
);
4796 free_evalue_refs(ER
);
4803 static evalue
* enumerate_vd(Polyhedron
**PA
,
4804 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
4806 Polyhedron
*P
= *PA
;
4807 int nvar
= P
->Dimension
- exist
- nparam
;
4808 Param_Polyhedron
*PP
= NULL
;
4809 Polyhedron
*C
= Universe_Polyhedron(nparam
);
4813 PP
= Polyhedron2Param_SimplifiedDomain(&PR
,C
,MaxRays
,&CEq
,&CT
);
4817 Param_Domain
*D
, *last
;
4820 for (nd
= 0, D
=PP
->D
; D
; D
=D
->next
, ++nd
)
4823 Polyhedron
**VD
= new Polyhedron_p
[nd
];
4824 Polyhedron
**fVD
= new Polyhedron_p
[nd
];
4825 for(nd
= 0, D
=PP
->D
; D
; D
=D
->next
) {
4826 Polyhedron
*rVD
= reduce_domain(D
->Domain
, CT
, CEq
,
4840 /* This doesn't seem to have any effect */
4842 Polyhedron
*CA
= align_context(VD
[0], P
->Dimension
, MaxRays
);
4844 P
= DomainIntersection(P
, CA
, MaxRays
);
4847 Polyhedron_Free(CA
);
4852 if (!EP
&& CT
->NbColumns
!= CT
->NbRows
) {
4853 Polyhedron
*CEqr
= DomainImage(CEq
, CT
, MaxRays
);
4854 Polyhedron
*CA
= align_context(CEqr
, PR
->Dimension
, MaxRays
);
4855 Polyhedron
*I
= DomainIntersection(PR
, CA
, MaxRays
);
4856 Polyhedron_Free(CEqr
);
4857 Polyhedron_Free(CA
);
4859 fprintf(stderr
, "\nER: Eliminate\n");
4860 #endif /* DEBUG_ER */
4861 nparam
-= CT
->NbColumns
- CT
->NbRows
;
4862 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
4863 nparam
+= CT
->NbColumns
- CT
->NbRows
;
4864 addeliminatedparams_enum(EP
, CT
, CEq
, MaxRays
, nparam
);
4868 Polyhedron_Free(PR
);
4871 if (!EP
&& nd
> 1) {
4873 fprintf(stderr
, "\nER: VD\n");
4874 #endif /* DEBUG_ER */
4875 for (int i
= 0; i
< nd
; ++i
) {
4876 Polyhedron
*CA
= align_context(VD
[i
], P
->Dimension
, MaxRays
);
4877 Polyhedron
*I
= DomainIntersection(P
, CA
, MaxRays
);
4880 EP
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
4882 evalue
*E
= barvinok_enumerate_e(I
, exist
, nparam
, MaxRays
);
4884 free_evalue_refs(E
);
4888 Polyhedron_Free(CA
);
4892 for (int i
= 0; i
< nd
; ++i
) {
4893 Polyhedron_Free(VD
[i
]);
4894 Polyhedron_Free(fVD
[i
]);
4900 if (!EP
&& nvar
== 0) {
4903 Param_Vertices
*V
, *V2
;
4904 Matrix
* M
= Matrix_Alloc(1, P
->Dimension
+2);
4906 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
4908 FORALL_PVertex_in_ParamPolyhedron(V2
, last
, PP
) {
4915 for (int i
= 0; i
< exist
; ++i
) {
4916 value_oppose(f
, V
->Vertex
->p
[i
][nparam
+1]);
4917 Vector_Combine(V
->Vertex
->p
[i
],
4919 M
->p
[0] + 1 + nvar
+ exist
,
4920 V2
->Vertex
->p
[i
][nparam
+1],
4924 for (j
= 0; j
< nparam
; ++j
)
4925 if (value_notzero_p(M
->p
[0][1+nvar
+exist
+j
]))
4929 ConstraintSimplify(M
->p
[0], M
->p
[0],
4930 P
->Dimension
+2, &f
);
4931 value_set_si(M
->p
[0][0], 0);
4932 Polyhedron
*para
= AddConstraints(M
->p
[0], 1, P
,
4935 Polyhedron_Free(para
);
4938 Polyhedron
*pos
, *neg
;
4939 value_set_si(M
->p
[0][0], 1);
4940 value_decrement(M
->p
[0][P
->Dimension
+1],
4941 M
->p
[0][P
->Dimension
+1]);
4942 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
4943 value_set_si(f
, -1);
4944 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
4946 value_decrement(M
->p
[0][P
->Dimension
+1],
4947 M
->p
[0][P
->Dimension
+1]);
4948 value_decrement(M
->p
[0][P
->Dimension
+1],
4949 M
->p
[0][P
->Dimension
+1]);
4950 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
4951 if (emptyQ(neg
) && emptyQ(pos
)) {
4952 Polyhedron_Free(para
);
4953 Polyhedron_Free(pos
);
4954 Polyhedron_Free(neg
);
4958 fprintf(stderr
, "\nER: Order\n");
4959 #endif /* DEBUG_ER */
4960 EP
= barvinok_enumerate_e(para
, exist
, nparam
, MaxRays
);
4963 E
= barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
4965 free_evalue_refs(E
);
4969 E
= barvinok_enumerate_e(neg
, exist
, nparam
, MaxRays
);
4971 free_evalue_refs(E
);
4974 Polyhedron_Free(para
);
4975 Polyhedron_Free(pos
);
4976 Polyhedron_Free(neg
);
4981 } END_FORALL_PVertex_in_ParamPolyhedron
;
4984 } END_FORALL_PVertex_in_ParamPolyhedron
;
4987 /* Search for vertex coordinate to split on */
4988 /* First look for one independent of the parameters */
4989 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
4990 for (int i
= 0; i
< exist
; ++i
) {
4992 for (j
= 0; j
< nparam
; ++j
)
4993 if (value_notzero_p(V
->Vertex
->p
[i
][j
]))
4997 value_set_si(M
->p
[0][0], 1);
4998 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
4999 Vector_Copy(V
->Vertex
->p
[i
],
5000 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
5001 value_oppose(M
->p
[0][1+nvar
+i
],
5002 V
->Vertex
->p
[i
][nparam
+1]);
5004 Polyhedron
*pos
, *neg
;
5005 value_set_si(M
->p
[0][0], 1);
5006 value_decrement(M
->p
[0][P
->Dimension
+1],
5007 M
->p
[0][P
->Dimension
+1]);
5008 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5009 value_set_si(f
, -1);
5010 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
5012 value_decrement(M
->p
[0][P
->Dimension
+1],
5013 M
->p
[0][P
->Dimension
+1]);
5014 value_decrement(M
->p
[0][P
->Dimension
+1],
5015 M
->p
[0][P
->Dimension
+1]);
5016 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5017 if (emptyQ(neg
) || emptyQ(pos
)) {
5018 Polyhedron_Free(pos
);
5019 Polyhedron_Free(neg
);
5022 Polyhedron_Free(pos
);
5023 value_increment(M
->p
[0][P
->Dimension
+1],
5024 M
->p
[0][P
->Dimension
+1]);
5025 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5027 fprintf(stderr
, "\nER: Vertex\n");
5028 #endif /* DEBUG_ER */
5030 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
5035 } END_FORALL_PVertex_in_ParamPolyhedron
;
5039 /* Search for vertex coordinate to split on */
5040 /* Now look for one that depends on the parameters */
5041 FORALL_PVertex_in_ParamPolyhedron(V
, last
, PP
) {
5042 for (int i
= 0; i
< exist
; ++i
) {
5043 value_set_si(M
->p
[0][0], 1);
5044 Vector_Set(M
->p
[0]+1, 0, nvar
+exist
);
5045 Vector_Copy(V
->Vertex
->p
[i
],
5046 M
->p
[0] + 1 + nvar
+ exist
, nparam
+1);
5047 value_oppose(M
->p
[0][1+nvar
+i
],
5048 V
->Vertex
->p
[i
][nparam
+1]);
5050 Polyhedron
*pos
, *neg
;
5051 value_set_si(M
->p
[0][0], 1);
5052 value_decrement(M
->p
[0][P
->Dimension
+1],
5053 M
->p
[0][P
->Dimension
+1]);
5054 neg
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5055 value_set_si(f
, -1);
5056 Vector_Scale(M
->p
[0]+1, M
->p
[0]+1, f
,
5058 value_decrement(M
->p
[0][P
->Dimension
+1],
5059 M
->p
[0][P
->Dimension
+1]);
5060 value_decrement(M
->p
[0][P
->Dimension
+1],
5061 M
->p
[0][P
->Dimension
+1]);
5062 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5063 if (emptyQ(neg
) || emptyQ(pos
)) {
5064 Polyhedron_Free(pos
);
5065 Polyhedron_Free(neg
);
5068 Polyhedron_Free(pos
);
5069 value_increment(M
->p
[0][P
->Dimension
+1],
5070 M
->p
[0][P
->Dimension
+1]);
5071 pos
= AddConstraints(M
->p
[0], 1, P
, MaxRays
);
5073 fprintf(stderr
, "\nER: ParamVertex\n");
5074 #endif /* DEBUG_ER */
5076 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
5081 } END_FORALL_PVertex_in_ParamPolyhedron
;
5089 Polyhedron_Free(CEq
);
5093 Param_Polyhedron_Free(PP
);
5100 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
5101 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5106 evalue
*barvinok_enumerate_pip(Polyhedron
*P
,
5107 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5109 int nvar
= P
->Dimension
- exist
- nparam
;
5110 evalue
*EP
= new_zero_ep();
5111 Polyhedron
*Q
, *N
, *T
= 0;
5117 fprintf(stderr
, "\nER: PIP\n");
5118 #endif /* DEBUG_ER */
5120 for (int i
= 0; i
< P
->Dimension
; ++i
) {
5123 bool posray
= false;
5124 bool negray
= false;
5125 value_set_si(min
, 0);
5126 for (int j
= 0; j
< P
->NbRays
; ++j
) {
5127 if (value_pos_p(P
->Ray
[j
][1+i
])) {
5129 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
5131 } else if (value_neg_p(P
->Ray
[j
][1+i
])) {
5133 if (value_zero_p(P
->Ray
[j
][1+P
->Dimension
]))
5137 P
->Ray
[j
][1+i
], P
->Ray
[j
][1+P
->Dimension
]);
5138 if (value_lt(tmp
, min
))
5139 value_assign(min
, tmp
);
5144 assert(!(posray
&& negray
));
5145 assert(!negray
); // for now
5146 Polyhedron
*O
= T
? T
: P
;
5147 /* shift by a safe amount */
5148 Matrix
*M
= Matrix_Alloc(O
->NbRays
, O
->Dimension
+2);
5149 Vector_Copy(O
->Ray
[0], M
->p
[0], O
->NbRays
* (O
->Dimension
+2));
5150 for (int j
= 0; j
< P
->NbRays
; ++j
) {
5151 if (value_notzero_p(M
->p
[j
][1+P
->Dimension
])) {
5152 value_multiply(tmp
, min
, M
->p
[j
][1+P
->Dimension
]);
5153 value_subtract(M
->p
[j
][1+i
], M
->p
[j
][1+i
], tmp
);
5158 T
= Rays2Polyhedron(M
, MaxRays
);
5161 /* negating a parameter requires that we substitute in the
5162 * sign again afterwards.
5165 assert(i
< nvar
+exist
);
5167 T
= Polyhedron_Copy(P
);
5168 for (int j
= 0; j
< T
->NbRays
; ++j
)
5169 value_oppose(T
->Ray
[j
][1+i
], T
->Ray
[j
][1+i
]);
5170 for (int j
= 0; j
< T
->NbConstraints
; ++j
)
5171 value_oppose(T
->Constraint
[j
][1+i
], T
->Constraint
[j
][1+i
]);
5177 Polyhedron
*D
= pip_lexminmax(T
? T
: P
, nvar
, exist
, nparam
, 0);
5178 for (Q
= D
; Q
; Q
= N
) {
5182 exist
= Q
->Dimension
- nvar
- nparam
;
5183 E
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
5186 free_evalue_refs(E
);
5198 static bool is_single(Value
*row
, int pos
, int len
)
5200 return First_Non_Zero(row
, pos
) == -1 &&
5201 First_Non_Zero(row
+pos
+1, len
-pos
-1) == -1;
5204 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
5205 unsigned exist
, unsigned nparam
, unsigned MaxRays
);
5208 static int er_level
= 0;
5210 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
5211 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5213 fprintf(stderr
, "\nER: level %i\n", er_level
);
5214 int nvar
= P
->Dimension
- exist
- nparam
;
5215 fprintf(stderr
, "%d %d %d\n", nvar
, exist
, nparam
);
5217 Polyhedron_Print(stderr
, P_VALUE_FMT
, P
);
5219 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
5220 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
5226 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
5227 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5229 P
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
5230 evalue
*EP
= barvinok_enumerate_e_r(P
, exist
, nparam
, MaxRays
);
5236 static evalue
* barvinok_enumerate_e_r(Polyhedron
*P
,
5237 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
5240 Polyhedron
*U
= Universe_Polyhedron(nparam
);
5241 evalue
*EP
= barvinok_enumerate_ev(P
, U
, MaxRays
);
5242 //char *param_name[] = {"P", "Q", "R", "S", "T" };
5243 //print_evalue(stdout, EP, param_name);
5248 int nvar
= P
->Dimension
- exist
- nparam
;
5249 int len
= P
->Dimension
+ 2;
5252 POL_ENSURE_FACETS(P
);
5253 POL_ENSURE_VERTICES(P
);
5256 return new_zero_ep();
5258 if (nvar
== 0 && nparam
== 0) {
5259 evalue
*EP
= new_zero_ep();
5260 barvinok_count(P
, &EP
->x
.n
, MaxRays
);
5261 if (value_pos_p(EP
->x
.n
))
5262 value_set_si(EP
->x
.n
, 1);
5267 for (r
= 0; r
< P
->NbRays
; ++r
)
5268 if (value_zero_p(P
->Ray
[r
][0]) ||
5269 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
5271 for (i
= 0; i
< nvar
; ++i
)
5272 if (value_notzero_p(P
->Ray
[r
][i
+1]))
5276 for (i
= nvar
+ exist
; i
< nvar
+ exist
+ nparam
; ++i
)
5277 if (value_notzero_p(P
->Ray
[r
][i
+1]))
5279 if (i
>= nvar
+ exist
+ nparam
)
5282 if (r
< P
->NbRays
) {
5283 evalue
*EP
= new_zero_ep();
5284 value_set_si(EP
->x
.n
, -1);
5289 for (r
= 0; r
< P
->NbEq
; ++r
)
5290 if ((first
= First_Non_Zero(P
->Constraint
[r
]+1+nvar
, exist
)) != -1)
5293 if (First_Non_Zero(P
->Constraint
[r
]+1+nvar
+first
+1,
5294 exist
-first
-1) != -1) {
5295 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
5297 fprintf(stderr
, "\nER: Equality\n");
5298 #endif /* DEBUG_ER */
5299 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5304 fprintf(stderr
, "\nER: Fixed\n");
5305 #endif /* DEBUG_ER */
5307 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
5309 Polyhedron
*T
= Polyhedron_Copy(P
);
5310 SwapColumns(T
, nvar
+1, nvar
+1+first
);
5311 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5318 Vector
*row
= Vector_Alloc(len
);
5319 value_set_si(row
->p
[0], 1);
5324 enum constraint
* info
= new constraint
[exist
];
5325 for (int i
= 0; i
< exist
; ++i
) {
5327 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
5328 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
5330 bool l_parallel
= is_single(P
->Constraint
[l
]+nvar
+1, i
, exist
);
5331 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
5332 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
5334 bool lu_parallel
= l_parallel
||
5335 is_single(P
->Constraint
[u
]+nvar
+1, i
, exist
);
5336 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
5337 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1, row
->p
+1,
5338 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
5339 if (!(info
[i
] & INDEPENDENT
)) {
5341 for (j
= 0; j
< exist
; ++j
)
5342 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
5345 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
5346 info
[i
] = (constraint
)(info
[i
] | INDEPENDENT
);
5349 if (info
[i
] & ALL_POS
) {
5350 value_addto(row
->p
[len
-1], row
->p
[len
-1],
5351 P
->Constraint
[l
][nvar
+i
+1]);
5352 value_addto(row
->p
[len
-1], row
->p
[len
-1], f
);
5353 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
5354 value_subtract(row
->p
[len
-1], row
->p
[len
-1], f
);
5355 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
5356 ConstraintSimplify(row
->p
, row
->p
, len
, &f
);
5357 value_set_si(f
, -1);
5358 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
5359 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
5360 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
5362 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
5363 info
[i
] = (constraint
)(info
[i
] ^ ALL_POS
);
5365 //puts("pos remainder");
5366 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
5369 if (!(info
[i
] & ONE_NEG
)) {
5371 negative_test_constraint(P
->Constraint
[l
],
5373 row
->p
, nvar
+i
, len
, &f
);
5374 oppose_constraint(row
->p
, len
, &f
);
5375 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
5377 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
5378 info
[i
] = (constraint
)(info
[i
] | ONE_NEG
);
5380 //puts("neg remainder");
5381 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
5383 } else if (!(info
[i
] & ROT_NEG
)) {
5384 if (parallel_constraints(P
->Constraint
[l
],
5386 row
->p
, nvar
, exist
)) {
5387 negative_test_constraint7(P
->Constraint
[l
],
5389 row
->p
, nvar
, exist
,
5391 oppose_constraint(row
->p
, len
, &f
);
5392 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
5394 // printf("rot_neg i: %d, l: %d, u: %d\n", i, l, u);
5395 info
[i
] = (constraint
)(info
[i
] | ROT_NEG
);
5398 //puts("neg remainder");
5399 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
5404 if (!(info
[i
] & ALL_POS
) && (info
[i
] & (ONE_NEG
| ROT_NEG
)))
5408 if (info
[i
] & ALL_POS
)
5415 for (int i = 0; i < exist; ++i)
5416 printf("%i: %i\n", i, info[i]);
5418 for (int i
= 0; i
< exist
; ++i
)
5419 if (info
[i
] & ALL_POS
) {
5421 fprintf(stderr
, "\nER: Positive\n");
5422 #endif /* DEBUG_ER */
5424 // Maybe we should chew off some of the fat here
5425 Matrix
*M
= Matrix_Alloc(P
->Dimension
, P
->Dimension
+1);
5426 for (int j
= 0; j
< P
->Dimension
; ++j
)
5427 value_set_si(M
->p
[j
][j
+ (j
>= i
+nvar
)], 1);
5428 Polyhedron
*T
= Polyhedron_Image(P
, M
, MaxRays
);
5430 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5437 for (int i
= 0; i
< exist
; ++i
)
5438 if (info
[i
] & ONE_NEG
) {
5440 fprintf(stderr
, "\nER: Negative\n");
5441 #endif /* DEBUG_ER */
5446 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
5448 Polyhedron
*T
= Polyhedron_Copy(P
);
5449 SwapColumns(T
, nvar
+1, nvar
+1+i
);
5450 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5455 for (int i
= 0; i
< exist
; ++i
)
5456 if (info
[i
] & ROT_NEG
) {
5458 fprintf(stderr
, "\nER: Rotate\n");
5459 #endif /* DEBUG_ER */
5463 Polyhedron
*T
= rotate_along(P
, r
, nvar
, exist
, MaxRays
);
5464 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
5468 for (int i
= 0; i
< exist
; ++i
)
5469 if (info
[i
] & INDEPENDENT
) {
5470 Polyhedron
*pos
, *neg
;
5472 /* Find constraint again and split off negative part */
5474 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
5475 row
, f
, true, &pos
, &neg
)) {
5477 fprintf(stderr
, "\nER: Split\n");
5478 #endif /* DEBUG_ER */
5481 barvinok_enumerate_e(neg
, exist
-1, nparam
, MaxRays
);
5483 barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
5485 free_evalue_refs(E
);
5487 Polyhedron_Free(neg
);
5488 Polyhedron_Free(pos
);
5502 EP
= enumerate_line(P
, exist
, nparam
, MaxRays
);
5506 EP
= barvinok_enumerate_pip(P
, exist
, nparam
, MaxRays
);
5510 EP
= enumerate_redundant_ray(P
, exist
, nparam
, MaxRays
);
5514 EP
= enumerate_sure(P
, exist
, nparam
, MaxRays
);
5518 EP
= enumerate_ray(P
, exist
, nparam
, MaxRays
);
5522 EP
= enumerate_sure2(P
, exist
, nparam
, MaxRays
);
5526 F
= unfringe(P
, MaxRays
);
5527 if (!PolyhedronIncludes(F
, P
)) {
5529 fprintf(stderr
, "\nER: Fringed\n");
5530 #endif /* DEBUG_ER */
5531 EP
= barvinok_enumerate_e(F
, exist
, nparam
, MaxRays
);
5538 EP
= enumerate_vd(&P
, exist
, nparam
, MaxRays
);
5543 EP
= enumerate_sum(P
, exist
, nparam
, MaxRays
);
5550 Polyhedron
*pos
, *neg
;
5551 for (i
= 0; i
< exist
; ++i
)
5552 if (SplitOnVar(P
, i
, nvar
, len
, exist
, MaxRays
,
5553 row
, f
, false, &pos
, &neg
))
5559 EP
= enumerate_or(pos
, exist
, nparam
, MaxRays
);
5571 gen_fun
* barvinok_series(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
5574 unsigned nparam
= C
->Dimension
;
5578 sign
.SetLength(ncone
);
5580 CA
= align_context(C
, P
->Dimension
, MaxRays
);
5581 P
= DomainIntersection(P
, CA
, MaxRays
);
5582 Polyhedron_Free(CA
);
5584 assert(!Polyhedron_is_infinite(P
, nparam
));
5585 assert(P
->NbBid
== 0);
5586 assert(Polyhedron_has_positive_rays(P
, nparam
));
5588 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, NULL
);
5589 assert(P
->NbEq
== 0);
5591 #ifdef USE_INCREMENTAL_BF
5592 partial_bfcounter
red(P
, nparam
);
5593 #elif defined USE_INCREMENTAL_DF
5594 partial_ireducer
red(P
, nparam
);
5596 partial_reducer
red(P
, nparam
);