1 /*
2  * Copyright 2008-2009 Katholieke Universiteit Leuven
3  *
4  * Use of this software is governed by the MIT license
5  *
6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8  */
9 
10 #ifndef ISL_TAB_H
11 #define ISL_TAB_H
12 
13 #include <isl/lp.h>
14 #include <isl/map.h>
15 #include <isl/mat.h>
16 #include <isl/set.h>
17 #include <isl_config.h>
18 
19 struct isl_tab_var {
20 	int index;
21 	unsigned is_row : 1;
22 	unsigned is_nonneg : 1;
23 	unsigned is_zero : 1;
24 	unsigned is_redundant : 1;
25 	unsigned marked : 1;
26 	unsigned frozen : 1;
27 	unsigned negated : 1;
28 };
29 
30 enum isl_tab_undo_type {
31 	isl_tab_undo_bottom,
32 	isl_tab_undo_rational,
33 	isl_tab_undo_empty,
34 	isl_tab_undo_nonneg,
35 	isl_tab_undo_redundant,
36 	isl_tab_undo_freeze,
37 	isl_tab_undo_zero,
38 	isl_tab_undo_allocate,
39 	isl_tab_undo_relax,
40 	isl_tab_undo_unrestrict,
41 	isl_tab_undo_bmap_ineq,
42 	isl_tab_undo_bmap_eq,
43 	isl_tab_undo_bmap_div,
44 	isl_tab_undo_saved_basis,
45 	isl_tab_undo_drop_sample,
46 	isl_tab_undo_saved_samples,
47 	isl_tab_undo_callback,
48 };
49 
50 struct isl_tab_callback {
51 	isl_stat (*run)(struct isl_tab_callback *cb);
52 };
53 
54 union isl_tab_undo_val {
55 	int		var_index;
56 	int		*col_var;
57 	int		n;
58 	struct isl_tab_callback	*callback;
59 };
60 
61 struct isl_tab_undo {
62 	enum isl_tab_undo_type	type;
63 	union isl_tab_undo_val	u;
64 	struct isl_tab_undo	*next;
65 };
66 
67 /* The tableau maintains equality relations.
68  * Each column and each row is associated to a variable or a constraint.
69  * The "value" of an inequality constraint is the value of the corresponding
70  * slack variable.
71  * The "row_var" and "col_var" arrays map column and row indices
72  * to indices in the "var" and "con" arrays.  The elements of these
73  * arrays maintain extra information about the variables and the constraints.
74  * Each row expresses the corresponding row variable as an affine expression
75  * of the column variables.
76  * The first two columns in the matrix contain the common denominator of
77  * the row and the numerator of the constant term.
78  * If "M" is set, then the third column represents the "big parameter".
79  * The third (M = 0) or fourth (M = 1) column
80  * in the matrix is called column 0 with respect to the col_var array.
81  * The sample value of the tableau is the value that assigns zero
82  * to all the column variables and the constant term of each affine
83  * expression to the corresponding row variable.
84  * The operations on the tableau maintain the property that the sample
85  * value satisfies the non-negativity constraints (usually on the slack
86  * variables).
87  *
88  * The big parameter represents an arbitrarily big (and divisible)
89  * positive number.  If present, then the sign of a row is determined
90  * lexicographically, with the sign of the big parameter coefficient
91  * considered first.  The big parameter is only used while
92  * solving PILP problems.
93  *
94  * The first n_dead column variables have their values fixed to zero.
95  * The corresponding tab_vars are flagged "is_zero".
96  * Some of the rows that have have zero coefficients in all but
97  * the dead columns are also flagged "is_zero".
98  *
99  * The first n_redundant rows correspond to inequality constraints
100  * that are always satisfied for any value satisfying the non-redundant
101  * rows.  The corresponding tab_vars are flagged "is_redundant".
102  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
103  * since the constraint has been reduced to 0 = 0 and is therefore always
104  * satisfied.
105  *
106  * There are "n_var" variables in total.  The first "n_param" of these
107  * are called parameters and the last "n_div" of these are called divs.
108  * The basic tableau operations makes no distinction between different
109  * kinds of variables.  These special variables are only used while
110  * solving PILP problems.
111  *
112  * Dead columns and redundant rows are detected on the fly.
113  * However, the basic operations do not ensure that all dead columns
114  * or all redundant rows are detected.
115  * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
116  * to perform an exhaustive search for dead columns and redundant rows.
117  *
118  * The samples matrix contains "n_sample" integer points that have at some
119  * point been elements satisfying the tableau.  The first "n_outside"
120  * of them no longer satisfy the tableau.  They are kept because they
121  * can be reinstated during rollback when the constraint that cut them
122  * out is removed.  These samples are only maintained for the context
123  * tableau while solving PILP problems.
124  *
125  * If "preserve" is set, then we want to keep all constraints in the
126  * tableau, even if they turn out to be redundant.
127  */
128 enum isl_tab_row_sign {
129 	isl_tab_row_unknown = 0,
130 	isl_tab_row_pos,
131 	isl_tab_row_neg,
132 	isl_tab_row_any,
133 };
134 struct isl_tab {
135 	struct isl_mat *mat;
136 
137 	unsigned n_row;
138 	unsigned n_col;
139 	unsigned n_dead;
140 	unsigned n_redundant;
141 
142 	unsigned n_var;
143 	unsigned n_param;
144 	unsigned n_div;
145 	unsigned max_var;
146 	unsigned n_con;
147 	unsigned n_eq;
148 	unsigned max_con;
149 	struct isl_tab_var *var;
150 	struct isl_tab_var *con;
151 	int *row_var;	/* v >= 0 -> var v;	v < 0 -> con ~v */
152 	int *col_var;	/* v >= 0 -> var v;	v < 0 -> con ~v */
153 	enum isl_tab_row_sign *row_sign;
154 
155 	struct isl_tab_undo bottom;
156 	struct isl_tab_undo *top;
157 
158 	struct isl_vec *dual;
159 	struct isl_basic_map *bmap;
160 
161 	unsigned n_sample;
162 	unsigned n_outside;
163 	int *sample_index;
164 	struct isl_mat *samples;
165 
166 	int n_zero;
167 	int n_unbounded;
168 	struct isl_mat *basis;
169 
170 	int (*conflict)(int con, void *user);
171 	void *conflict_user;
172 
173 	unsigned strict_redundant : 1;
174 	unsigned need_undo : 1;
175 	unsigned preserve : 1;
176 	unsigned rational : 1;
177 	unsigned empty : 1;
178 	unsigned in_undo : 1;
179 	unsigned M : 1;
180 	unsigned cone : 1;
181 };
182 
183 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
184 	unsigned n_row, unsigned n_var, unsigned M);
185 void isl_tab_free(struct isl_tab *tab);
186 
187 isl_ctx *isl_tab_get_ctx(struct isl_tab *tab);
188 
189 __isl_give struct isl_tab *isl_tab_from_basic_map(
190 	__isl_keep isl_basic_map *bmap, int track);
191 __isl_give struct isl_tab *isl_tab_from_basic_set(
192 	__isl_keep isl_basic_set *bset, int track);
193 struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
194 	int parametric);
195 isl_bool isl_tab_cone_is_bounded(struct isl_tab *tab);
196 __isl_give isl_basic_map *isl_basic_map_update_from_tab(
197 	__isl_take isl_basic_map *bmap, struct isl_tab *tab);
198 __isl_give isl_basic_set *isl_basic_set_update_from_tab(
199 	__isl_take isl_basic_set *bset, struct isl_tab *tab);
200 int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;
201 __isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
202 	__isl_take isl_basic_map *bmap);
203 int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
204 isl_stat isl_tab_restore_redundant(struct isl_tab *tab);
205 #define ISL_TAB_SAVE_DUAL	(1 << 0)
206 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
207 	isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
208 	unsigned flags) WARN_UNUSED;
209 
210 isl_stat isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
211 isl_stat isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
212 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
213 
214 int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
215 
216 isl_stat isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
217 	WARN_UNUSED;
218 isl_stat isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
219 	WARN_UNUSED;
220 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab);
221 
222 int isl_tab_is_equality(struct isl_tab *tab, int con);
223 int isl_tab_is_redundant(struct isl_tab *tab, int con);
224 
225 int isl_tab_sample_is_integer(struct isl_tab *tab);
226 __isl_give isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
227 
228 enum isl_ineq_type {
229 	isl_ineq_error = -1,
230 	isl_ineq_redundant,
231 	isl_ineq_separate,
232 	isl_ineq_cut,
233 	isl_ineq_adj_eq,
234 	isl_ineq_adj_ineq,
235 };
236 
237 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
238 
239 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
240 isl_stat isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
241 isl_bool isl_tab_need_undo(struct isl_tab *tab);
242 void isl_tab_clear_undo(struct isl_tab *tab);
243 
244 int isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
245 int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
246 int isl_tab_unrestrict(struct isl_tab *tab, int con) WARN_UNUSED;
247 
248 void isl_tab_dump(__isl_keep struct isl_tab *tab);
249 
250 /* Compute maximum instead of minimum. */
251 #define ISL_OPT_MAX		(1 << 0)
252 /* Compute full instead of partial optimum; also, domain argument is NULL. */
253 #define ISL_OPT_FULL		(1 << 1)
254 /* Result should be free of (unknown) quantified variables. */
255 #define ISL_OPT_QE		(1 << 2)
256 __isl_give isl_map *isl_tab_basic_map_partial_lexopt(
257 	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
258 	__isl_give isl_set **empty, unsigned flags);
259 __isl_give isl_pw_multi_aff *isl_tab_basic_map_partial_lexopt_pw_multi_aff(
260 	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
261 	__isl_give isl_set **empty, unsigned flags);
262 
263 /* An isl_trivial_region represents a non-triviality region.
264  * The region is trivial if applying "trivial" to a given sequence
265  * of variables results in a zero vector.
266  * pos is the location (starting at 0) of the first variable in the sequence.
267  */
268 struct isl_trivial_region {
269 	int pos;
270 	isl_mat *trivial;
271 };
272 
273 __isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
274 	__isl_take isl_basic_set *bset, int n_op, int n_region,
275 	struct isl_trivial_region *region,
276 	int (*conflict)(int con, void *user), void *user);
277 
278 struct isl_tab_lexmin;
279 typedef struct isl_tab_lexmin isl_tab_lexmin;
280 
281 __isl_give isl_tab_lexmin *isl_tab_lexmin_from_basic_set(
282 	__isl_take isl_basic_set *bset);
283 int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin *tl);
284 __isl_give isl_tab_lexmin *isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin *tl,
285 	isl_int *eq);
286 __isl_give isl_tab_lexmin *isl_tab_lexmin_cut_to_integer(
287 	__isl_take isl_tab_lexmin *tl);
288 __isl_give isl_vec *isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin *tl);
289 __isl_null isl_tab_lexmin *isl_tab_lexmin_free(__isl_take isl_tab_lexmin *tl);
290 
291 /* private */
292 
293 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
294 int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
295 int isl_tab_mark_rational(struct isl_tab *tab) WARN_UNUSED;
296 isl_stat isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
297 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
298 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
299 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
300 int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
301 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
302 int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED;
303 int isl_tab_insert_var(struct isl_tab *tab, int pos) WARN_UNUSED;
304 int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
305 int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
306 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
307 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
308 int isl_tab_sign_of_max(struct isl_tab *tab, int con);
309 int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
310 
311 isl_stat isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
312 	WARN_UNUSED;
313 isl_stat isl_tab_push_var(struct isl_tab *tab,
314 	enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
315 isl_stat isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
316 
317 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
318 int isl_tab_add_sample(struct isl_tab *tab,
319 	__isl_take isl_vec *sample) WARN_UNUSED;
320 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
321 isl_stat isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
322 
323 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
324 	struct isl_tab *tab_cone) WARN_UNUSED;
325 isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value);
326 isl_stat isl_tab_detect_constants(struct isl_tab *tab);
327 
328 isl_stat isl_tab_push_callback(struct isl_tab *tab,
329 	struct isl_tab_callback *callback) WARN_UNUSED;
330 
331 int isl_tab_insert_div(struct isl_tab *tab, int pos, __isl_keep isl_vec *div,
332 	isl_stat (*add_ineq)(void *user, isl_int *), void *user);
333 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div);
334 
335 int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift) WARN_UNUSED;
336 
337 isl_stat isl_tab_swap_constraints(struct isl_tab *tab, int con1, int con2);
338 
339 #endif
340