8 #include <NTL/mat_ZZ.h>
12 #include <polylib/polylibgmp.h>
13 #include "ev_operations.h"
26 using std::ostringstream
;
28 #define ALLOC(p) (((long *) (p))[0])
29 #define SIZE(p) (((long *) (p))[1])
30 #define DATA(p) ((mp_limb_t *) (((long *) (p)) + 2))
32 static void value2zz(Value v
, ZZ
& z
)
34 int sa
= v
[0]._mp_size
;
35 int abs_sa
= sa
< 0 ? -sa
: sa
;
37 _ntl_gsetlength(&z
.rep
, abs_sa
);
38 mp_limb_t
* adata
= DATA(z
.rep
);
39 for (int i
= 0; i
< abs_sa
; ++i
)
40 adata
[i
] = v
[0]._mp_d
[i
];
44 static void zz2value(ZZ
& z
, Value
& v
)
52 int abs_sa
= sa
< 0 ? -sa
: sa
;
54 mp_limb_t
* adata
= DATA(z
.rep
);
55 mpz_realloc2(v
, __GMP_BITS_PER_MP_LIMB
* abs_sa
);
56 for (int i
= 0; i
< abs_sa
; ++i
)
57 v
[0]._mp_d
[i
] = adata
[i
];
62 #define ALLOC(p) p = (typeof(p))malloc(sizeof(*p))
65 * We just ignore the last column and row
66 * If the final element is not equal to one
67 * then the result will actually be a multiple of the input
69 static void matrix2zz(Matrix
*M
, mat_ZZ
& m
, unsigned nr
, unsigned nc
)
73 for (int i
= 0; i
< nr
; ++i
) {
74 // assert(value_one_p(M->p[i][M->NbColumns - 1]));
75 for (int j
= 0; j
< nc
; ++j
) {
76 value2zz(M
->p
[i
][j
], m
[i
][j
]);
81 static void values2zz(Value
*p
, vec_ZZ
& v
, int len
)
85 for (int i
= 0; i
< len
; ++i
) {
92 static void zz2values(vec_ZZ
& v
, Value
*p
)
94 for (int i
= 0; i
< v
.length(); ++i
)
98 static void rays(mat_ZZ
& r
, Polyhedron
*C
)
100 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
101 assert(C
->NbRays
- 1 == C
->Dimension
);
106 for (i
= 0, c
= 0; i
< dim
; ++i
)
107 if (value_zero_p(C
->Ray
[i
][dim
+1])) {
108 for (int j
= 0; j
< dim
; ++j
) {
109 value2zz(C
->Ray
[i
][j
+1], tmp
);
116 static Matrix
* rays(Polyhedron
*C
)
118 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
119 assert(C
->NbRays
- 1 == C
->Dimension
);
121 Matrix
*M
= Matrix_Alloc(dim
+1, dim
+1);
125 for (i
= 0, c
= 0; i
<= dim
&& c
< dim
; ++i
)
126 if (value_zero_p(C
->Ray
[i
][dim
+1])) {
127 Vector_Copy(C
->Ray
[i
] + 1, M
->p
[c
], dim
);
128 value_set_si(M
->p
[c
++][dim
], 0);
131 value_set_si(M
->p
[dim
][dim
], 1);
136 static Matrix
* rays2(Polyhedron
*C
)
138 unsigned dim
= C
->NbRays
- 1; /* don't count zero vertex */
139 assert(C
->NbRays
- 1 == C
->Dimension
);
141 Matrix
*M
= Matrix_Alloc(dim
, dim
);
145 for (i
= 0, c
= 0; i
<= dim
&& c
< dim
; ++i
)
146 if (value_zero_p(C
->Ray
[i
][dim
+1]))
147 Vector_Copy(C
->Ray
[i
] + 1, M
->p
[c
++], dim
);
154 * Returns the largest absolute value in the vector
156 static ZZ
max(vec_ZZ
& v
)
159 for (int i
= 1; i
< v
.length(); ++i
)
169 Rays
= Matrix_Copy(M
);
172 cone(Polyhedron
*C
) {
173 Cone
= Polyhedron_Copy(C
);
179 matrix2zz(Rays
, A
, Rays
->NbRows
- 1, Rays
->NbColumns
- 1);
180 det
= determinant(A
);
187 Vector
* short_vector(vec_ZZ
& lambda
) {
188 Matrix
*M
= Matrix_Copy(Rays
);
189 Matrix
*inv
= Matrix_Alloc(M
->NbRows
, M
->NbColumns
);
190 int ok
= Matrix_Inverse(M
, inv
);
197 matrix2zz(inv
, B
, inv
->NbRows
- 1, inv
->NbColumns
- 1);
198 long r
= LLL(det2
, B
, U
);
202 for (int i
= 1; i
< B
.NumRows(); ++i
) {
214 Vector
*z
= Vector_Alloc(U
[index
].length()+1);
216 zz2values(U
[index
], z
->p
);
217 value_set_si(z
->p
[U
[index
].length()], 0);
221 Polyhedron
*C
= poly();
223 for (i
= 0; i
< C
->NbConstraints
; ++i
) {
224 Inner_Product(z
->p
, C
->Constraint
[i
]+1, z
->Size
-1, &tmp
);
225 if (value_pos_p(tmp
))
228 if (i
== C
->NbConstraints
) {
229 value_set_si(tmp
, -1);
230 Vector_Scale(z
->p
, z
->p
, tmp
, z
->Size
-1);
237 Polyhedron_Free(Cone
);
243 Matrix
*M
= Matrix_Alloc(Rays
->NbRows
+1, Rays
->NbColumns
+1);
244 for (int i
= 0; i
< Rays
->NbRows
; ++i
) {
245 Vector_Copy(Rays
->p
[i
], M
->p
[i
]+1, Rays
->NbColumns
);
246 value_set_si(M
->p
[i
][0], 1);
248 Vector_Set(M
->p
[Rays
->NbRows
]+1, 0, Rays
->NbColumns
-1);
249 value_set_si(M
->p
[Rays
->NbRows
][0], 1);
250 value_set_si(M
->p
[Rays
->NbRows
][Rays
->NbColumns
], 1);
251 Cone
= Rays2Polyhedron(M
, M
->NbRows
+1);
252 assert(Cone
->NbConstraints
== Cone
->NbRays
);
266 dpoly(int d
, ZZ
& degree
, int offset
= 0) {
267 coeff
.SetLength(d
+1);
269 int min
= d
+ offset
;
270 if (degree
< ZZ(INIT_VAL
, min
))
271 min
= to_int(degree
);
273 ZZ c
= ZZ(INIT_VAL
, 1);
276 for (int i
= 1; i
<= min
; ++i
) {
277 c
*= (degree
-i
+ 1);
282 void operator *= (dpoly
& f
) {
283 assert(coeff
.length() == f
.coeff
.length());
285 coeff
= f
.coeff
[0] * coeff
;
286 for (int i
= 1; i
< coeff
.length(); ++i
)
287 for (int j
= 0; i
+j
< coeff
.length(); ++j
)
288 coeff
[i
+j
] += f
.coeff
[i
] * old
[j
];
290 void div(dpoly
& d
, mpq_t count
, ZZ
& sign
) {
291 int len
= coeff
.length();
294 mpq_t
* c
= new mpq_t
[coeff
.length()];
297 for (int i
= 0; i
< len
; ++i
) {
299 zz2value(coeff
[i
], tmp
);
300 mpq_set_z(c
[i
], tmp
);
302 for (int j
= 1; j
<= i
; ++j
) {
303 zz2value(d
.coeff
[j
], tmp
);
304 mpq_set_z(qtmp
, tmp
);
305 mpq_mul(qtmp
, qtmp
, c
[i
-j
]);
306 mpq_sub(c
[i
], c
[i
], qtmp
);
309 zz2value(d
.coeff
[0], tmp
);
310 mpq_set_z(qtmp
, tmp
);
311 mpq_div(c
[i
], c
[i
], qtmp
);
314 mpq_sub(count
, count
, c
[len
-1]);
316 mpq_add(count
, count
, c
[len
-1]);
320 for (int i
= 0; i
< len
; ++i
)
332 dpoly_n(int d
, ZZ
& degree_0
, ZZ
& degree_1
, int offset
= 0) {
336 zz2value(degree_0
, d0
);
337 zz2value(degree_1
, d1
);
338 coeff
= Matrix_Alloc(d
+1, d
+1+1);
339 value_set_si(coeff
->p
[0][0], 1);
340 value_set_si(coeff
->p
[0][d
+1], 1);
341 for (int i
= 1; i
<= d
; ++i
) {
342 value_multiply(coeff
->p
[i
][0], coeff
->p
[i
-1][0], d0
);
343 Vector_Combine(coeff
->p
[i
-1], coeff
->p
[i
-1]+1, coeff
->p
[i
]+1,
345 value_set_si(coeff
->p
[i
][d
+1], i
);
346 value_multiply(coeff
->p
[i
][d
+1], coeff
->p
[i
][d
+1], coeff
->p
[i
-1][d
+1]);
347 value_decrement(d0
, d0
);
352 void div(dpoly
& d
, Vector
*count
, ZZ
& sign
) {
353 int len
= coeff
->NbRows
;
354 Matrix
* c
= Matrix_Alloc(coeff
->NbRows
, coeff
->NbColumns
);
357 for (int i
= 0; i
< len
; ++i
) {
358 Vector_Copy(coeff
->p
[i
], c
->p
[i
], len
+1);
359 for (int j
= 1; j
<= i
; ++j
) {
360 zz2value(d
.coeff
[j
], tmp
);
361 value_multiply(tmp
, tmp
, c
->p
[i
][len
]);
362 value_oppose(tmp
, tmp
);
363 Vector_Combine(c
->p
[i
], c
->p
[i
-j
], c
->p
[i
],
364 c
->p
[i
-j
][len
], tmp
, len
);
365 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], c
->p
[i
-j
][len
]);
367 zz2value(d
.coeff
[0], tmp
);
368 value_multiply(c
->p
[i
][len
], c
->p
[i
][len
], tmp
);
371 value_set_si(tmp
, -1);
372 Vector_Scale(c
->p
[len
-1], count
->p
, tmp
, len
);
373 value_assign(count
->p
[len
], c
->p
[len
-1][len
]);
375 Vector_Copy(c
->p
[len
-1], count
->p
, len
+1);
376 Vector_Normalize(count
->p
, len
+1);
383 * Barvinok's Decomposition of a simplicial cone
385 * Returns two lists of polyhedra
387 void barvinok_decompose(Polyhedron
*C
, Polyhedron
**ppos
, Polyhedron
**pneg
)
389 Polyhedron
*pos
= *ppos
, *neg
= *pneg
;
390 vector
<cone
*> nonuni
;
391 cone
* c
= new cone(C
);
398 Polyhedron
*p
= Polyhedron_Copy(c
->Cone
);
404 while (!nonuni
.empty()) {
407 Vector
* v
= c
->short_vector(lambda
);
408 for (int i
= 0; i
< c
->Rays
->NbRows
- 1; ++i
) {
411 Matrix
* M
= Matrix_Copy(c
->Rays
);
412 Vector_Copy(v
->p
, M
->p
[i
], v
->Size
);
413 cone
* pc
= new cone(M
);
414 assert (pc
->det
!= 0);
415 if (abs(pc
->det
) > 1) {
416 assert(abs(pc
->det
) < abs(c
->det
));
417 nonuni
.push_back(pc
);
419 Polyhedron
*p
= pc
->poly();
421 if (sign(pc
->det
) == s
) {
440 * Returns a single list of npos "positive" cones followed by nneg
442 * The input cone is freed
444 void decompose(Polyhedron
*cone
, Polyhedron
**parts
, int *npos
, int *nneg
, unsigned MaxRays
)
446 Polyhedron_Polarize(cone
);
447 if (cone
->NbRays
- 1 != cone
->Dimension
) {
448 Polyhedron
*tmp
= cone
;
449 cone
= triangularize_cone(cone
, MaxRays
);
450 Polyhedron_Free(tmp
);
452 Polyhedron
*polpos
= NULL
, *polneg
= NULL
;
453 *npos
= 0; *nneg
= 0;
454 for (Polyhedron
*Polar
= cone
; Polar
; Polar
= Polar
->next
)
455 barvinok_decompose(Polar
, &polpos
, &polneg
);
458 for (Polyhedron
*i
= polpos
; i
; i
= i
->next
) {
459 Polyhedron_Polarize(i
);
463 for (Polyhedron
*i
= polneg
; i
; i
= i
->next
) {
464 Polyhedron_Polarize(i
);
475 const int MAX_TRY
=10;
477 * Searches for a vector that is not othogonal to any
478 * of the rays in rays.
480 static void nonorthog(mat_ZZ
& rays
, vec_ZZ
& lambda
)
482 int dim
= rays
.NumCols();
484 lambda
.SetLength(dim
);
485 for (int i
= 2; !found
&& i
<= 50*dim
; i
+=4) {
486 for (int j
= 0; j
< MAX_TRY
; ++j
) {
487 for (int k
= 0; k
< dim
; ++k
) {
488 int r
= random_int(i
)+2;
489 int v
= (2*(r
%2)-1) * (r
>> 1);
493 for (; k
< rays
.NumRows(); ++k
)
494 if (lambda
* rays
[k
] == 0)
496 if (k
== rays
.NumRows()) {
505 static void add_rays(mat_ZZ
& rays
, Polyhedron
*i
, int *r
)
507 unsigned dim
= i
->Dimension
;
508 for (int k
= 0; k
< i
->NbRays
; ++k
) {
509 if (!value_zero_p(i
->Ray
[k
][dim
+1]))
511 values2zz(i
->Ray
[k
]+1, rays
[(*r
)++], dim
);
515 void lattice_point(Value
* values
, Polyhedron
*i
, vec_ZZ
& lambda
, ZZ
& num
)
518 unsigned dim
= i
->Dimension
;
519 if(!value_one_p(values
[dim
])) {
520 Matrix
* Rays
= rays(i
);
521 Matrix
*inv
= Matrix_Alloc(Rays
->NbRows
, Rays
->NbColumns
);
522 int ok
= Matrix_Inverse(Rays
, inv
);
526 Vector
*lambda
= Vector_Alloc(dim
+1);
527 Vector_Matrix_Product(values
, inv
, lambda
->p
);
529 for (int j
= 0; j
< dim
; ++j
)
530 mpz_cdiv_q(lambda
->p
[j
], lambda
->p
[j
], lambda
->p
[dim
]);
531 value_set_si(lambda
->p
[dim
], 1);
532 Vector
*A
= Vector_Alloc(dim
+1);
533 Vector_Matrix_Product(lambda
->p
, Rays
, A
->p
);
536 values2zz(A
->p
, vertex
, dim
);
539 values2zz(values
, vertex
, dim
);
541 num
= vertex
* lambda
;
544 static evalue
*term(int param
, ZZ
& c
, Value
*den
= NULL
)
546 evalue
*EP
= new evalue();
548 value_set_si(EP
->d
,0);
549 EP
->x
.p
= new_enode(polynomial
, 2, param
+ 1);
550 evalue_set_si(&EP
->x
.p
->arr
[0], 0, 1);
551 value_init(EP
->x
.p
->arr
[1].x
.n
);
553 value_set_si(EP
->x
.p
->arr
[1].d
, 1);
555 value_assign(EP
->x
.p
->arr
[1].d
, *den
);
556 zz2value(c
, EP
->x
.p
->arr
[1].x
.n
);
560 static void vertex_period(
561 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*T
,
562 Value lcm
, int p
, Vector
*val
,
563 evalue
*E
, evalue
* ev
,
566 unsigned nparam
= T
->NbRows
- 1;
567 unsigned dim
= i
->Dimension
;
573 Vector
* values
= Vector_Alloc(dim
+ 1);
574 Vector_Matrix_Product(val
->p
, T
, values
->p
);
575 value_assign(values
->p
[dim
], lcm
);
576 lattice_point(values
->p
, i
, lambda
, num
);
581 zz2value(num
, ev
->x
.n
);
582 value_assign(ev
->d
, lcm
);
589 values2zz(T
->p
[p
], vertex
, dim
);
590 nump
= vertex
* lambda
;
591 if (First_Non_Zero(val
->p
, p
) == -1) {
592 value_assign(tmp
, lcm
);
593 evalue
*ET
= term(p
, nump
, &tmp
);
595 free_evalue_refs(ET
);
599 value_assign(tmp
, lcm
);
600 if (First_Non_Zero(T
->p
[p
], dim
) != -1)
601 Vector_Gcd(T
->p
[p
], dim
, &tmp
);
603 if (value_lt(tmp
, lcm
)) {
606 value_division(tmp
, lcm
, tmp
);
607 value_set_si(ev
->d
, 0);
608 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
609 value2zz(tmp
, count
);
611 value_decrement(tmp
, tmp
);
613 ZZ new_offset
= offset
- count
* nump
;
614 value_assign(val
->p
[p
], tmp
);
615 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
,
616 &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)], new_offset
);
617 } while (value_pos_p(tmp
));
619 vertex_period(i
, lambda
, T
, lcm
, p
+1, val
, E
, ev
, offset
);
623 static void mask_r(Matrix
*f
, int nr
, Vector
*lcm
, int p
, Vector
*val
, evalue
*ev
)
625 unsigned nparam
= lcm
->Size
;
628 Vector
* prod
= Vector_Alloc(f
->NbRows
);
629 Matrix_Vector_Product(f
, val
->p
, prod
->p
);
631 for (int i
= 0; i
< nr
; ++i
) {
632 value_modulus(prod
->p
[i
], prod
->p
[i
], f
->p
[i
][nparam
+1]);
633 isint
&= value_zero_p(prod
->p
[i
]);
635 value_set_si(ev
->d
, 1);
637 value_set_si(ev
->x
.n
, isint
);
644 if (value_one_p(lcm
->p
[p
]))
645 mask_r(f
, nr
, lcm
, p
+1, val
, ev
);
647 value_assign(tmp
, lcm
->p
[p
]);
648 value_set_si(ev
->d
, 0);
649 ev
->x
.p
= new_enode(periodic
, VALUE_TO_INT(tmp
), p
+1);
651 value_decrement(tmp
, tmp
);
652 value_assign(val
->p
[p
], tmp
);
653 mask_r(f
, nr
, lcm
, p
+1, val
, &ev
->x
.p
->arr
[VALUE_TO_INT(tmp
)]);
654 } while (value_pos_p(tmp
));
659 static evalue
*multi_monom(vec_ZZ
& p
)
661 evalue
*X
= new evalue();
664 unsigned nparam
= p
.length()-1;
665 zz2value(p
[nparam
], X
->x
.n
);
666 value_set_si(X
->d
, 1);
667 for (int i
= 0; i
< nparam
; ++i
) {
670 evalue
*T
= term(i
, p
[i
]);
679 * Check whether mapping polyhedron P on the affine combination
680 * num yields a range that has a fixed quotient on integer
682 * If zero is true, then we are only interested in the quotient
683 * for the cases where the remainder is zero.
684 * Returns NULL if false and a newly allocated value if true.
686 static Value
*fixed_quotient(Polyhedron
*P
, vec_ZZ
& num
, Value d
, bool zero
)
689 int len
= num
.length();
690 Matrix
*T
= Matrix_Alloc(2, len
);
691 zz2values(num
, T
->p
[0]);
692 value_set_si(T
->p
[1][len
-1], 1);
693 Polyhedron
*I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
697 for (i
= 0; i
< I
->NbRays
; ++i
)
698 if (value_zero_p(I
->Ray
[i
][2])) {
707 value_oppose(I
->Constraint
[0][2], I
->Constraint
[0][2]);
708 /* There should never be a remainder here */
709 if (value_pos_p(I
->Constraint
[0][1]))
710 mpz_fdiv_q(min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
712 mpz_fdiv_q(min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
713 value_assign(max
, min
);
714 } else for (i
= 0; i
< I
->NbConstraints
; ++i
) {
715 value_oppose(I
->Constraint
[i
][2], I
->Constraint
[i
][2]);
716 if (value_pos_p(I
->Constraint
[i
][1]))
717 mpz_cdiv_q(min
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
719 mpz_fdiv_q(max
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
724 mpz_cdiv_q(min
, min
, d
);
726 mpz_fdiv_q(min
, min
, d
);
727 mpz_fdiv_q(max
, max
, d
);
728 if (value_eq(min
, max
)) {
731 value_assign(*ret
, min
);
739 * Normalize linear expression coef modulo m
740 * Removes common factor and reduces coefficients
741 * Returns index of first non-zero coefficient or len
743 static int normal_mod(Value
*coef
, int len
, Value
*m
)
748 Vector_Gcd(coef
, len
, &gcd
);
750 Vector_AntiScale(coef
, coef
, gcd
, len
);
752 value_division(*m
, *m
, gcd
);
759 for (j
= 0; j
< len
; ++j
)
760 mpz_fdiv_r(coef
[j
], coef
[j
], *m
);
761 for (j
= 0; j
< len
; ++j
)
762 if (value_notzero_p(coef
[j
]))
769 static void mask(Matrix
*f
, evalue
*factor
)
771 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
774 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
775 if (value_notone_p(f
->p
[n
][nc
-1]) &&
776 value_notmone_p(f
->p
[n
][nc
-1]))
790 value_set_si(EV
.x
.n
, 1);
792 for (n
= 0; n
< nr
; ++n
) {
793 value_assign(m
, f
->p
[n
][nc
-1]);
794 if (value_one_p(m
) || value_mone_p(m
))
797 int j
= normal_mod(f
->p
[n
], nc
-1, &m
);
799 free_evalue_refs(factor
);
800 value_init(factor
->d
);
801 evalue_set_si(factor
, 0, 1);
805 values2zz(f
->p
[n
], row
, nc
-1);
808 if (j
< (nc
-1)-1 && row
[j
] > g
/2) {
809 for (int k
= j
; k
< (nc
-1); ++k
)
815 value_set_si(EP
.d
, 0);
816 EP
.x
.p
= new_enode(relation
, 2, 0);
817 value_clear(EP
.x
.p
->arr
[1].d
);
818 EP
.x
.p
->arr
[1] = *factor
;
819 evalue
*ev
= &EP
.x
.p
->arr
[0];
820 value_set_si(ev
->d
, 0);
821 ev
->x
.p
= new_enode(fractional
, 3, -1);
822 evalue_set_si(&ev
->x
.p
->arr
[1], 0, 1);
823 evalue_set_si(&ev
->x
.p
->arr
[2], 1, 1);
824 evalue
*E
= multi_monom(row
);
825 value_assign(EV
.d
, m
);
827 value_clear(ev
->x
.p
->arr
[0].d
);
828 ev
->x
.p
->arr
[0] = *E
;
834 free_evalue_refs(&EV
);
840 static void mask(Matrix
*f
, evalue
*factor
)
842 int nr
= f
->NbRows
, nc
= f
->NbColumns
;
845 for (n
= 0; n
< nr
&& value_notzero_p(f
->p
[n
][nc
-1]); ++n
)
846 if (value_notone_p(f
->p
[n
][nc
-1]) &&
847 value_notmone_p(f
->p
[n
][nc
-1]))
855 unsigned np
= nc
- 2;
856 Vector
*lcm
= Vector_Alloc(np
);
857 Vector
*val
= Vector_Alloc(nc
);
858 Vector_Set(val
->p
, 0, nc
);
859 value_set_si(val
->p
[np
], 1);
860 Vector_Set(lcm
->p
, 1, np
);
861 for (n
= 0; n
< nr
; ++n
) {
862 if (value_one_p(f
->p
[n
][nc
-1]) ||
863 value_mone_p(f
->p
[n
][nc
-1]))
865 for (int j
= 0; j
< np
; ++j
)
866 if (value_notzero_p(f
->p
[n
][j
])) {
867 Gcd(f
->p
[n
][j
], f
->p
[n
][nc
-1], &tmp
);
868 value_division(tmp
, f
->p
[n
][nc
-1], tmp
);
869 value_lcm(tmp
, lcm
->p
[j
], &lcm
->p
[j
]);
874 mask_r(f
, nr
, lcm
, 0, val
, &EP
);
879 free_evalue_refs(&EP
);
890 static bool mod_needed(Polyhedron
*PD
, vec_ZZ
& num
, Value d
, evalue
*E
)
892 Value
*q
= fixed_quotient(PD
, num
, d
, false);
897 value_oppose(*q
, *q
);
900 value_set_si(EV
.d
, 1);
902 value_multiply(EV
.x
.n
, *q
, d
);
904 free_evalue_refs(&EV
);
910 static void ceil_mod(Value
*coef
, int len
, Value d
, ZZ
& f
, evalue
*EP
, Polyhedron
*PD
)
916 Vector_Scale(coef
, coef
, m
, len
);
919 int j
= normal_mod(coef
, len
, &m
);
927 values2zz(coef
, num
, len
);
934 evalue_set_si(&tmp
, 0, 1);
938 while (j
< len
-1 && (num
[j
] == g
/2 || num
[j
] == 0))
940 if (j
< len
-1 && num
[j
] > g
/2) {
941 for (int k
= j
; k
< len
-1; ++k
)
944 num
[len
-1] = g
- 1 - num
[len
-1];
945 value_assign(tmp
.d
, m
);
947 zz2value(t
, tmp
.x
.n
);
953 ZZ t
= num
[len
-1] * f
;
954 zz2value(t
, tmp
.x
.n
);
955 value_assign(tmp
.d
, m
);
958 evalue
*E
= multi_monom(num
);
962 if (PD
&& !mod_needed(PD
, num
, m
, E
)) {
965 value_assign(EV
.d
, m
);
970 value_set_si(EV
.x
.n
, 1);
971 value_assign(EV
.d
, m
);
974 value_set_si(EV
.d
, 0);
975 EV
.x
.p
= new_enode(fractional
, 3, -1);
976 evalue_copy(&EV
.x
.p
->arr
[0], E
);
977 evalue_set_si(&EV
.x
.p
->arr
[1], 0, 1);
978 value_init(EV
.x
.p
->arr
[2].x
.n
);
979 zz2value(f
, EV
.x
.p
->arr
[2].x
.n
);
980 value_set_si(EV
.x
.p
->arr
[2].d
, 1);
985 free_evalue_refs(&EV
);
990 free_evalue_refs(&tmp
);
996 evalue
* bv_ceil3(Value
*coef
, int len
, Value d
, Polyhedron
*P
)
998 Vector
*val
= Vector_Alloc(len
);
1002 value_set_si(t
, -1);
1003 Vector_Scale(coef
, val
->p
, t
, len
);
1004 value_absolute(t
, d
);
1007 values2zz(val
->p
, num
, len
);
1008 evalue
*EP
= multi_monom(num
);
1012 value_init(tmp
.x
.n
);
1013 value_set_si(tmp
.x
.n
, 1);
1014 value_assign(tmp
.d
, t
);
1020 ceil_mod(val
->p
, len
, t
, one
, EP
, P
);
1023 /* copy EP to malloc'ed evalue */
1029 free_evalue_refs(&tmp
);
1036 evalue
* lattice_point(
1037 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1039 unsigned nparam
= W
->NbColumns
- 1;
1041 Matrix
* Rays
= rays2(i
);
1042 Matrix
*T
= Transpose(Rays
);
1043 Matrix
*T2
= Matrix_Copy(T
);
1044 Matrix
*inv
= Matrix_Alloc(T2
->NbRows
, T2
->NbColumns
);
1045 int ok
= Matrix_Inverse(T2
, inv
);
1050 matrix2zz(W
, vertex
, W
->NbRows
, W
->NbColumns
);
1053 num
= lambda
* vertex
;
1055 evalue
*EP
= multi_monom(num
);
1059 value_init(tmp
.x
.n
);
1060 value_set_si(tmp
.x
.n
, 1);
1061 value_assign(tmp
.d
, lcm
);
1065 Matrix
*L
= Matrix_Alloc(inv
->NbRows
, W
->NbColumns
);
1066 Matrix_Product(inv
, W
, L
);
1069 matrix2zz(T
, RT
, T
->NbRows
, T
->NbColumns
);
1072 vec_ZZ p
= lambda
* RT
;
1074 for (int i
= 0; i
< L
->NbRows
; ++i
) {
1075 ceil_mod(L
->p
[i
], nparam
+1, lcm
, p
[i
], EP
, PD
);
1081 free_evalue_refs(&tmp
);
1085 evalue
* lattice_point(
1086 Polyhedron
*i
, vec_ZZ
& lambda
, Matrix
*W
, Value lcm
, Polyhedron
*PD
)
1088 Matrix
*T
= Transpose(W
);
1089 unsigned nparam
= T
->NbRows
- 1;
1091 evalue
*EP
= new evalue();
1093 evalue_set_si(EP
, 0, 1);
1096 Vector
*val
= Vector_Alloc(nparam
+1);
1097 value_set_si(val
->p
[nparam
], 1);
1098 ZZ
offset(INIT_VAL
, 0);
1100 vertex_period(i
, lambda
, T
, lcm
, 0, val
, EP
, &ev
, offset
);
1103 free_evalue_refs(&ev
);
1114 Param_Vertices
* V
, Polyhedron
*i
, vec_ZZ
& lambda
, term_info
* term
,
1117 unsigned nparam
= V
->Vertex
->NbColumns
- 2;
1118 unsigned dim
= i
->Dimension
;
1120 vertex
.SetDims(V
->Vertex
->NbRows
, nparam
+1);
1124 value_set_si(lcm
, 1);
1125 for (int j
= 0; j
< V
->Vertex
->NbRows
; ++j
) {
1126 value_lcm(lcm
, V
->Vertex
->p
[j
][nparam
+1], &lcm
);
1128 if (value_notone_p(lcm
)) {
1129 Matrix
* mv
= Matrix_Alloc(dim
, nparam
+1);
1130 for (int j
= 0 ; j
< dim
; ++j
) {
1131 value_division(tmp
, lcm
, V
->Vertex
->p
[j
][nparam
+1]);
1132 Vector_Scale(V
->Vertex
->p
[j
], mv
->p
[j
], tmp
, nparam
+1);
1135 term
->E
= lattice_point(i
, lambda
, mv
, lcm
, PD
);
1143 for (int i
= 0; i
< V
->Vertex
->NbRows
; ++i
) {
1144 assert(value_one_p(V
->Vertex
->p
[i
][nparam
+1])); // for now
1145 values2zz(V
->Vertex
->p
[i
], vertex
[i
], nparam
+1);
1149 num
= lambda
* vertex
;
1153 for (int j
= 0; j
< nparam
; ++j
)
1159 term
->E
= multi_monom(num
);
1163 term
->constant
= num
[nparam
];
1166 term
->coeff
= num
[p
];
1173 void normalize(Polyhedron
*i
, vec_ZZ
& lambda
, ZZ
& sign
, ZZ
& num
, vec_ZZ
& den
)
1175 unsigned dim
= i
->Dimension
;
1179 rays
.SetDims(dim
, dim
);
1180 add_rays(rays
, i
, &r
);
1181 den
= rays
* lambda
;
1184 for (int j
= 0; j
< den
.length(); ++j
) {
1188 den
[j
] = abs(den
[j
]);
1196 void barvinok_count(Polyhedron
*P
, Value
* result
, unsigned NbMaxCons
)
1198 Polyhedron
** vcone
;
1201 sign
.SetLength(ncone
);
1209 value_set_si(*result
, 0);
1213 for (; r
< P
->NbRays
; ++r
)
1214 if (value_zero_p(P
->Ray
[r
][P
->Dimension
+1]))
1216 if (P
->NbBid
!=0 || r
< P
->NbRays
) {
1217 value_set_si(*result
, -1);
1221 P
= remove_equalities(P
);
1224 value_set_si(*result
, 0);
1230 value_set_si(factor
, 1);
1231 Q
= Polyhedron_Reduce(P
, &factor
);
1238 if (P
->Dimension
== 0) {
1239 value_assign(*result
, factor
);
1242 value_clear(factor
);
1247 vcone
= new (Polyhedron
*)[P
->NbRays
];
1249 for (int j
= 0; j
< P
->NbRays
; ++j
) {
1251 Polyhedron
*C
= supporting_cone(P
, j
);
1252 decompose(C
, &vcone
[j
], &npos
, &nneg
, NbMaxCons
);
1253 ncone
+= npos
+ nneg
;
1254 sign
.SetLength(ncone
);
1255 for (int k
= 0; k
< npos
; ++k
)
1256 sign
[ncone
-nneg
-k
-1] = 1;
1257 for (int k
= 0; k
< nneg
; ++k
)
1258 sign
[ncone
-k
-1] = -1;
1262 rays
.SetDims(ncone
* dim
, dim
);
1264 for (int j
= 0; j
< P
->NbRays
; ++j
) {
1265 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
) {
1266 assert(i
->NbRays
-1 == dim
);
1267 add_rays(rays
, i
, &r
);
1271 nonorthog(rays
, lambda
);
1275 num
.SetLength(ncone
);
1276 den
.SetDims(ncone
,dim
);
1279 for (int j
= 0; j
< P
->NbRays
; ++j
) {
1280 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
) {
1281 lattice_point(P
->Ray
[j
]+1, i
, lambda
, num
[f
]);
1282 normalize(i
, lambda
, sign
[f
], num
[f
], den
[f
]);
1287 for (int j
= 1; j
< num
.length(); ++j
)
1290 for (int j
= 0; j
< num
.length(); ++j
)
1296 for (int j
= 0; j
< P
->NbRays
; ++j
) {
1297 for (Polyhedron
*i
= vcone
[j
]; i
; i
= i
->next
) {
1298 dpoly
d(dim
, num
[f
]);
1299 dpoly
n(dim
, den
[f
][0], 1);
1300 for (int k
= 1; k
< dim
; ++k
) {
1301 dpoly
fact(dim
, den
[f
][k
], 1);
1304 d
.div(n
, count
, sign
[f
]);
1308 assert(value_one_p(&count
[0]._mp_den
));
1309 value_multiply(*result
, &count
[0]._mp_num
, factor
);
1312 for (int j
= 0; j
< P
->NbRays
; ++j
)
1313 Domain_Free(vcone
[j
]);
1319 value_clear(factor
);
1322 static void uni_polynom(int param
, Vector
*c
, evalue
*EP
)
1324 unsigned dim
= c
->Size
-2;
1326 value_set_si(EP
->d
,0);
1327 EP
->x
.p
= new_enode(polynomial
, dim
+1, param
+1);
1328 for (int j
= 0; j
<= dim
; ++j
)
1329 evalue_set(&EP
->x
.p
->arr
[j
], c
->p
[j
], c
->p
[dim
+1]);
1332 static void multi_polynom(Vector
*c
, evalue
* X
, evalue
*EP
)
1334 unsigned dim
= c
->Size
-2;
1338 evalue_set(&EC
, c
->p
[dim
], c
->p
[dim
+1]);
1341 evalue_set(EP
, c
->p
[dim
], c
->p
[dim
+1]);
1343 for (int i
= dim
-1; i
>= 0; --i
) {
1345 value_assign(EC
.x
.n
, c
->p
[i
]);
1348 free_evalue_refs(&EC
);
1351 Polyhedron
*unfringe (Polyhedron
*P
, unsigned MaxRays
)
1353 int len
= P
->Dimension
+2;
1354 Polyhedron
*T
, *R
= P
;
1358 Polyhedron_Print(stdout
, P_VALUE_FMT
, P
);
1359 Vector
*row
= Vector_Alloc(len
);
1360 value_set_si(row
->p
[0], 1);
1362 R
= DomainConstraintSimplify(Polyhedron_Copy(P
), MaxRays
);
1364 Matrix
*M
= Matrix_Alloc(2, len
-1);
1365 value_set_si(M
->p
[1][len
-2], 1);
1366 for (int v
= 0; v
< P
->Dimension
; ++v
) {
1367 value_set_si(M
->p
[0][v
], 1);
1368 Polyhedron
*I
= Polyhedron_Image(P
, M
, 2+1);
1369 Polyhedron_Print(stdout
, P_VALUE_FMT
, I
);
1370 value_set_si(M
->p
[0][v
], 0);
1371 for (int r
= 0; r
< I
->NbConstraints
; ++r
) {
1372 if (value_zero_p(I
->Constraint
[r
][0]))
1374 if (value_zero_p(I
->Constraint
[r
][1]))
1376 if (value_one_p(I
->Constraint
[r
][1]))
1378 if (value_mone_p(I
->Constraint
[r
][1]))
1380 value_absolute(g
, I
->Constraint
[r
][1]);
1381 Vector_Set(row
->p
+1, 0, len
-2);
1382 value_division(row
->p
[1+v
], I
->Constraint
[r
][1], g
);
1383 mpz_fdiv_q(row
->p
[len
-1], I
->Constraint
[r
][2], g
);
1385 Vector_Print(stdout
, P_VALUE_FMT
, row
);
1387 R
= AddConstraints(row
->p
, 1, R
, MaxRays
);
1393 Polyhedron_Print(stdout
, P_VALUE_FMT
, R
);
1398 evalue
* barvinok_enumerate_ev(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
1400 //P = unfringe(P, MaxRays);
1401 Polyhedron
*CEq
= NULL
, *rVD
, *pVD
, *fVD
, *CA
;
1403 Param_Polyhedron
*PP
= NULL
;
1404 Param_Domain
*D
, *next
;
1407 unsigned nparam
= C
->Dimension
;
1410 value_init(eres
->d
);
1411 value_set_si(eres
->d
, 0);
1414 value_init(factor
.d
);
1415 evalue_set_si(&factor
, 1, 1);
1417 CA
= align_context(C
, P
->Dimension
, MaxRays
);
1418 P
= DomainIntersection(P
, CA
, MaxRays
);
1419 Polyhedron_Free(CA
);
1421 if (C
->Dimension
== 0 || emptyQ(P
)) {
1423 eres
->x
.p
= new_enode(partition
, 2, -1);
1424 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[0],
1425 DomainConstraintSimplify(CEq
? CEq
: Polyhedron_Copy(C
), MaxRays
));
1426 value_set_si(eres
->x
.p
->arr
[1].d
, 1);
1427 value_init(eres
->x
.p
->arr
[1].x
.n
);
1429 value_set_si(eres
->x
.p
->arr
[1].x
.n
, 0);
1431 barvinok_count(P
, &eres
->x
.p
->arr
[1].x
.n
, MaxRays
);
1433 emul(&factor
, eres
);
1434 reduce_evalue(eres
);
1435 free_evalue_refs(&factor
);
1440 Param_Polyhedron_Free(PP
);
1444 for (r
= 0; r
< P
->NbRays
; ++r
)
1445 if (value_zero_p(P
->Ray
[r
][0]) ||
1446 value_zero_p(P
->Ray
[r
][P
->Dimension
+1])) {
1448 for (i
= P
->Dimension
- nparam
; i
< P
->Dimension
; ++i
)
1449 if (value_notzero_p(P
->Ray
[r
][i
+1]))
1451 if (i
>= P
->Dimension
)
1459 P
= remove_equalities_p(P
, P
->Dimension
-nparam
, &f
);
1462 if (P
->Dimension
== nparam
) {
1464 P
= Universe_Polyhedron(0);
1469 Polyhedron
*Q
= ParamPolyhedron_Reduce(P
, P
->Dimension
-nparam
, &factor
);
1472 if (Q
->Dimension
== nparam
) {
1474 P
= Universe_Polyhedron(0);
1479 Polyhedron
*oldP
= P
;
1480 PP
= Polyhedron2Param_SimplifiedDomain(&P
,C
,MaxRays
,&CEq
,&CT
);
1482 Polyhedron_Free(oldP
);
1484 if (isIdentity(CT
)) {
1488 assert(CT
->NbRows
!= CT
->NbColumns
);
1489 if (CT
->NbRows
== 1) // no more parameters
1491 nparam
= CT
->NbRows
- 1;
1494 unsigned dim
= P
->Dimension
- nparam
;
1495 Polyhedron
** vcone
= new (Polyhedron
*)[PP
->nbV
];
1496 int * npos
= new int[PP
->nbV
];
1497 int * nneg
= new int[PP
->nbV
];
1501 for (i
= 0, V
= PP
->V
; V
; ++i
, V
= V
->next
) {
1502 Polyhedron
*C
= supporting_cone_p(P
, V
);
1503 decompose(C
, &vcone
[i
], &npos
[i
], &nneg
[i
], MaxRays
);
1506 Vector
*c
= Vector_Alloc(dim
+2);
1509 for (nd
= 0, D
=PP
->D
; D
; ++nd
, D
=D
->next
);
1510 struct section
{ Polyhedron
*D
; Polyhedron
*full
; evalue E
; };
1511 section
*s
= new section
[nd
];
1513 for(nd
= 0, D
=PP
->D
; D
; D
=next
) {
1516 fVD
= Domain_Copy(D
->Domain
);
1517 D
->Domain
= DomainConstraintSimplify(D
->Domain
, MaxRays
);
1518 pVD
= rVD
= D
->Domain
;
1522 Dt
= CT
? DomainPreimage(D
->Domain
,CT
,MaxRays
) : D
->Domain
;
1523 rVD
= DomainIntersection(Dt
,CEq
,MaxRays
);
1525 /* if rVD is empty or too small in geometric dimension */
1526 if(!rVD
|| emptyQ(rVD
) ||
1527 (rVD
->Dimension
-rVD
->NbEq
< Dt
->Dimension
-Dt
->NbEq
-CEq
->NbEq
)) {
1532 continue; /* empty validity domain */
1538 fVD
= Domain_Copy(rVD
);
1539 for (int i
= 0 ; i
< nd
; ++i
) {
1540 Polyhedron
*I
= DomainIntersection(fVD
, s
[i
].full
, MaxRays
);
1545 Polyhedron
*F
= DomainSimplify(I
, fVD
, MaxRays
);
1547 Polyhedron
*T
= rVD
;
1548 rVD
= DomainDifference(rVD
, F
, MaxRays
);
1554 rVD
= DomainConstraintSimplify(rVD
, MaxRays
);
1559 pVD
= CT
? DomainImage(rVD
,CT
,MaxRays
) : rVD
;
1562 sign
.SetLength(ncone
);
1563 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
1564 ncone
+= npos
[_i
] + nneg
[_i
];
1565 sign
.SetLength(ncone
);
1566 for (int k
= 0; k
< npos
[_i
]; ++k
)
1567 sign
[ncone
-nneg
[_i
]-k
-1] = 1;
1568 for (int k
= 0; k
< nneg
[_i
]; ++k
)
1569 sign
[ncone
-k
-1] = -1;
1570 END_FORALL_PVertex_in_ParamPolyhedron
;
1573 rays
.SetDims(ncone
* dim
, dim
);
1575 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
) // _i is internal counter
1576 for (Polyhedron
*i
= vcone
[_i
]; i
; i
= i
->next
) {
1577 assert(i
->NbRays
-1 == dim
);
1578 add_rays(rays
, i
, &r
);
1580 END_FORALL_PVertex_in_ParamPolyhedron
;
1582 nonorthog(rays
, lambda
);
1585 den
.SetDims(ncone
,dim
);
1586 term_info
*num
= new term_info
[ncone
];
1589 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
)
1590 for (Polyhedron
*i
= vcone
[_i
]; i
; i
= i
->next
) {
1591 lattice_point(V
, i
, lambda
, &num
[f
], pVD
);
1592 normalize(i
, lambda
, sign
[f
], num
[f
].constant
, den
[f
]);
1595 END_FORALL_PVertex_in_ParamPolyhedron
;
1596 ZZ min
= num
[0].constant
;
1597 for (int j
= 1; j
< ncone
; ++j
)
1598 if (num
[j
].constant
< min
)
1599 min
= num
[j
].constant
;
1600 for (int j
= 0; j
< ncone
; ++j
)
1601 num
[j
].constant
-= min
;
1603 value_init(s
[nd
].E
.d
);
1604 evalue_set_si(&s
[nd
].E
, 0, 1);
1607 FORALL_PVertex_in_ParamPolyhedron(V
,D
,PP
)
1608 for (Polyhedron
*i
= vcone
[_i
]; i
; i
= i
->next
) {
1609 dpoly
n(dim
, den
[f
][0], 1);
1610 for (int k
= 1; k
< dim
; ++k
) {
1611 dpoly
fact(dim
, den
[f
][k
], 1);
1614 if (num
[f
].E
!= NULL
) {
1615 ZZ
one(INIT_VAL
, 1);
1616 dpoly_n
d(dim
, num
[f
].constant
, one
);
1617 d
.div(n
, c
, sign
[f
]);
1619 multi_polynom(c
, num
[f
].E
, &EV
);
1620 eadd(&EV
, &s
[nd
].E
);
1621 free_evalue_refs(&EV
);
1622 free_evalue_refs(num
[f
].E
);
1624 } else if (num
[f
].pos
!= -1) {
1625 dpoly_n
d(dim
, num
[f
].constant
, num
[f
].coeff
);
1626 d
.div(n
, c
, sign
[f
]);
1628 uni_polynom(num
[f
].pos
, c
, &EV
);
1629 eadd(&EV
, &s
[nd
].E
);
1630 free_evalue_refs(&EV
);
1632 mpq_set_si(count
, 0, 1);
1633 dpoly
d(dim
, num
[f
].constant
);
1634 d
.div(n
, count
, sign
[f
]);
1637 evalue_set(&EV
, &count
[0]._mp_num
, &count
[0]._mp_den
);
1638 eadd(&EV
, &s
[nd
].E
);
1639 free_evalue_refs(&EV
);
1643 END_FORALL_PVertex_in_ParamPolyhedron
;
1649 addeliminatedparams_evalue(&s
[nd
].E
, CT
);
1657 eres
->x
.p
= new_enode(partition
, 2*nd
, -1);
1658 for (int j
= 0; j
< nd
; ++j
) {
1659 EVALUE_SET_DOMAIN(eres
->x
.p
->arr
[2*j
], s
[j
].D
);
1660 value_clear(eres
->x
.p
->arr
[2*j
+1].d
);
1661 eres
->x
.p
->arr
[2*j
+1] = s
[j
].E
;
1662 Domain_Free(s
[j
].full
);
1668 for (int j
= 0; j
< PP
->nbV
; ++j
)
1669 Domain_Free(vcone
[j
]);
1675 Polyhedron_Free(CEq
);
1680 Enumeration
* barvinok_enumerate(Polyhedron
*P
, Polyhedron
* C
, unsigned MaxRays
)
1682 Enumeration
*en
, *res
= NULL
;
1683 evalue
*EP
= barvinok_enumerate_ev(P
, C
, MaxRays
);
1684 for (int i
= 0; i
< EP
->x
.p
->size
/2; ++i
) {
1685 en
= (Enumeration
*)malloc(sizeof(Enumeration
));
1688 res
->ValidityDomain
= EVALUE_DOMAIN(EP
->x
.p
->arr
[2*i
]);
1689 value_clear(EP
->x
.p
->arr
[2*i
].d
);
1690 res
->EP
= EP
->x
.p
->arr
[2*i
+1];
1698 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
1700 for (int r
= 0; r
< n
; ++r
)
1701 value_swap(V
[r
][i
], V
[r
][j
]);
1704 static void SwapColumns(Polyhedron
*P
, int i
, int j
)
1706 SwapColumns(P
->Constraint
, P
->NbConstraints
, i
, j
);
1707 SwapColumns(P
->Ray
, P
->NbRays
, i
, j
);
1713 INDEPENDENT
= 1 << 2,
1716 evalue
* barvinok_enumerate_e(Polyhedron
*P
,
1717 unsigned exist
, unsigned nparam
, unsigned MaxRays
)
1719 //Polyhedron_Print(stderr, P_VALUE_FMT, P);
1721 Polyhedron
*U
= Universe_Polyhedron(nparam
);
1722 evalue
*EP
= barvinok_enumerate_ev(P
, U
, MaxRays
);
1723 //char *param_name[] = {"P", "Q", "R", "S", "T" };
1724 //print_evalue(stdout, EP, param_name);
1729 int nvar
= P
->Dimension
- exist
- nparam
;
1730 int len
= P
->Dimension
+ 2;
1732 //printf("%d %d %d\n", nvar, exist, nparam);
1736 for (r
= 0; r
< P
->NbEq
; ++r
)
1737 if ((first
= First_Non_Zero(P
->Constraint
[r
]+1+nvar
, exist
)) != -1)
1740 if (First_Non_Zero(P
->Constraint
[r
]+1+nvar
+first
+1,
1741 exist
-first
-1) != -1) {
1745 Vector
*row
= Vector_Alloc(exist
);
1746 Vector_Copy(P
->Constraint
[r
]+1+nvar
, row
->p
, exist
);
1747 Vector_Gcd(row
->p
, exist
, &g
);
1748 if (value_notone_p(g
))
1749 Vector_AntiScale(row
->p
, row
->p
, g
, exist
);
1752 Matrix
*M
= unimodular_complete(row
);
1753 Matrix
*M2
= Matrix_Alloc(P
->Dimension
+1, P
->Dimension
+1);
1754 for (r
= 0; r
< nvar
; ++r
)
1755 value_set_si(M2
->p
[r
][r
], 1);
1756 for ( ; r
< nvar
+exist
; ++r
)
1757 Vector_Copy(M
->p
[r
-nvar
], M2
->p
[r
]+nvar
, exist
);
1758 for ( ; r
< P
->Dimension
+1; ++r
)
1759 value_set_si(M2
->p
[r
][r
], 1);
1760 Polyhedron
*T
= Polyhedron_Image(P
, M2
, MaxRays
);
1761 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
1769 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
1771 Polyhedron
*T
= Polyhedron_Copy(P
);
1772 SwapColumns(T
, nvar
+1, nvar
+1+first
);
1773 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
1780 Vector
*row
= Vector_Alloc(len
);
1781 value_set_si(row
->p
[0], 1);
1786 enum constraint info
[exist
];
1787 for (int i
= 0; i
< exist
; ++i
) {
1789 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
1790 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
1792 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
1793 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
1795 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
1796 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1, row
->p
+1,
1797 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
1798 if (!(info
[i
] & INDEPENDENT
)) {
1800 for (j
= 0; j
< exist
; ++j
)
1801 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
1804 //printf("independent: i: %d, l: %d, u: %d\n", i, l, u);
1805 info
[i
] = (constraint
)(info
[i
] | INDEPENDENT
);
1808 if (info
[i
] & ALL_POS
) {
1809 value_addto(row
->p
[len
-1], row
->p
[len
-1],
1810 P
->Constraint
[l
][nvar
+i
+1]);
1811 value_addto(row
->p
[len
-1], row
->p
[len
-1], f
);
1812 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
1813 value_substract(row
->p
[len
-1], row
->p
[len
-1], f
);
1814 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
1815 Vector_Gcd(row
->p
+1, len
- 2, &f
);
1816 if (value_notone_p(f
)) {
1817 Vector_AntiScale(row
->p
+1, row
->p
+1, f
, len
-2);
1818 mpz_fdiv_q(row
->p
[len
-1], row
->p
[len
-1], f
);
1820 value_set_si(f
, -1);
1821 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
1822 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
1823 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1825 //printf("not all_pos: i: %d, l: %d, u: %d\n", i, l, u);
1826 info
[i
] = (constraint
)(info
[i
] ^ ALL_POS
);
1828 //puts("pos remainder");
1829 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
1832 if (!(info
[i
] & ONE_NEG
)) {
1834 for (j
= 0; j
< exist
; ++j
)
1836 (value_notzero_p(P
->Constraint
[l
][nvar
+j
+1]) ||
1837 value_notzero_p(P
->Constraint
[u
][nvar
+j
+1])))
1840 /* recalculate constant */
1841 /* We actually recalculate the whole row for
1842 * now, because it may have already been scaled
1844 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
1845 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1,
1847 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
1849 Vector_Combine(P->Constraint[l]+len-1,
1850 P->Constraint[u]+len-1, row->p+len-1,
1851 f, P->Constraint[l][nvar+i+1], 1);
1853 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
1854 value_substract(row
->p
[len
-1], row
->p
[len
-1], f
);
1855 value_set_si(f
, -1);
1856 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
1857 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
1858 Vector_Gcd(row
->p
+1, len
- 2, &f
);
1859 if (value_notone_p(f
)) {
1860 Vector_AntiScale(row
->p
+1, row
->p
+1, f
, len
-2);
1861 mpz_fdiv_q(row
->p
[len
-1], row
->p
[len
-1], f
);
1863 value_set_si(f
, -1);
1864 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
1865 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
1867 //Vector_Print(stdout, P_VALUE_FMT, row);
1868 Polyhedron
*T
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1870 //printf("one_neg i: %d, l: %d, u: %d\n", i, l, u);
1871 info
[i
] = (constraint
)(info
[i
] | ONE_NEG
);
1873 //puts("neg remainder");
1874 //Polyhedron_Print(stdout, P_VALUE_FMT, T);
1878 if (!(info
[i
] & ALL_POS
) && (info
[i
] & ONE_NEG
))
1882 if (info
[i
] & ALL_POS
)
1889 for (int i = 0; i < exist; ++i)
1890 printf("%i: %i\n", i, info[i]);
1892 for (int i
= 0; i
< exist
; ++i
)
1893 if (info
[i
] & ALL_POS
) {
1895 // Maybe we should chew off some of the fat here
1896 Matrix
*M
= Matrix_Alloc(P
->Dimension
, P
->Dimension
+1);
1897 for (int j
= 0; j
< P
->Dimension
; ++j
)
1898 value_set_si(M
->p
[j
][j
+ (j
>= i
+nvar
)], 1);
1899 Polyhedron
*T
= Polyhedron_Image(P
, M
, MaxRays
);
1901 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
1907 for (int i
= 0; i
< exist
; ++i
)
1908 if (info
[i
] & ONE_NEG
) {
1912 return barvinok_enumerate_e(P
, exist
-1, nparam
, MaxRays
);
1914 Polyhedron
*T
= Polyhedron_Copy(P
);
1915 SwapColumns(T
, nvar
+1, nvar
+1+i
);
1916 evalue
*EP
= barvinok_enumerate_e(T
, exist
-1, nparam
, MaxRays
);
1921 for (int i
= 0; i
< exist
; ++i
)
1922 if (info
[i
] & INDEPENDENT
) {
1923 /* Find constraint again and split off negative part */
1925 for (int l
= P
->NbEq
; l
< P
->NbConstraints
; ++l
) {
1926 if (value_negz_p(P
->Constraint
[l
][nvar
+i
+1]))
1928 for (int u
= P
->NbEq
; u
< P
->NbConstraints
; ++u
) {
1929 if (value_posz_p(P
->Constraint
[u
][nvar
+i
+1]))
1931 value_oppose(f
, P
->Constraint
[u
][nvar
+i
+1]);
1932 Vector_Combine(P
->Constraint
[l
]+1, P
->Constraint
[u
]+1,
1934 f
, P
->Constraint
[l
][nvar
+i
+1], len
-1);
1937 for (j
= 0; j
< exist
; ++j
)
1938 if (j
!= i
&& value_notzero_p(row
->p
[nvar
+j
+1]))
1943 //printf("l: %d, u: %d\n", l, u);
1944 value_multiply(f
, f
, P
->Constraint
[l
][nvar
+i
+1]);
1945 value_substract(row
->p
[len
-1], row
->p
[len
-1], f
);
1946 value_set_si(f
, -1);
1947 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
1948 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
1949 Vector_Gcd(row
->p
+1, len
- 2, &f
);
1950 if (value_notone_p(f
)) {
1951 Vector_AntiScale(row
->p
+1, row
->p
+1, f
, len
-2);
1952 mpz_fdiv_q(row
->p
[len
-1], row
->p
[len
-1], f
);
1954 Polyhedron
*neg
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1955 value_set_si(f
, -1);
1956 Vector_Scale(row
->p
+1, row
->p
+1, f
, len
-1);
1957 value_decrement(row
->p
[len
-1], row
->p
[len
-1]);
1958 Polyhedron
*pos
= AddConstraints(row
->p
, 1, P
, MaxRays
);
1960 assert(i
== 0); // for now
1962 barvinok_enumerate_e(neg
, exist
-1, nparam
, MaxRays
);
1964 barvinok_enumerate_e(pos
, exist
, nparam
, MaxRays
);
1966 free_evalue_refs(E
);
1968 Polyhedron_Free(neg
);
1969 Polyhedron_Free(pos
);
1975 assert(0); // can't happen