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1 office 1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 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  
18 struct isl_tab_var {
19 int index;
20 unsigned is_row : 1;
21 unsigned is_nonneg : 1;
22 unsigned is_zero : 1;
23 unsigned is_redundant : 1;
24 unsigned marked : 1;
25 unsigned frozen : 1;
26 unsigned negated : 1;
27 };
28  
29 enum isl_tab_undo_type {
30 isl_tab_undo_bottom,
31 isl_tab_undo_empty,
32 isl_tab_undo_nonneg,
33 isl_tab_undo_redundant,
34 isl_tab_undo_freeze,
35 isl_tab_undo_zero,
36 isl_tab_undo_allocate,
37 isl_tab_undo_relax,
38 isl_tab_undo_bmap_ineq,
39 isl_tab_undo_bmap_eq,
40 isl_tab_undo_bmap_div,
41 isl_tab_undo_saved_basis,
42 isl_tab_undo_drop_sample,
43 isl_tab_undo_saved_samples,
44 isl_tab_undo_callback,
45 };
46  
47 struct isl_tab_callback {
48 int (*run)(struct isl_tab_callback *cb);
49 };
50  
51 union isl_tab_undo_val {
52 int var_index;
53 int *col_var;
54 int n;
55 struct isl_tab_callback *callback;
56 };
57  
58 struct isl_tab_undo {
59 enum isl_tab_undo_type type;
60 union isl_tab_undo_val u;
61 struct isl_tab_undo *next;
62 };
63  
64 /* The tableau maintains equality relations.
65 * Each column and each row is associated to a variable or a constraint.
66 * The "value" of an inequality constraint is the value of the corresponding
67 * slack variable.
68 * The "row_var" and "col_var" arrays map column and row indices
69 * to indices in the "var" and "con" arrays. The elements of these
70 * arrays maintain extra information about the variables and the constraints.
71 * Each row expresses the corresponding row variable as an affine expression
72 * of the column variables.
73 * The first two columns in the matrix contain the common denominator of
74 * the row and the numerator of the constant term.
75 * If "M" is set, then the third column represents the "big parameter".
76 * The third (M = 0) or fourth (M = 1) column
77 * in the matrix is called column 0 with respect to the col_var array.
78 * The sample value of the tableau is the value that assigns zero
79 * to all the column variables and the constant term of each affine
80 * expression to the corresponding row variable.
81 * The operations on the tableau maintain the property that the sample
82 * value satisfies the non-negativity constraints (usually on the slack
83 * variables).
84 *
85 * The big parameter represents an arbitrarily big (and divisible)
86 * positive number. If present, then the sign of a row is determined
87 * lexicographically, with the sign of the big parameter coefficient
88 * considered first. The big parameter is only used while
89 * solving PILP problems.
90 *
91 * The first n_dead column variables have their values fixed to zero.
92 * The corresponding tab_vars are flagged "is_zero".
93 * Some of the rows that have have zero coefficients in all but
94 * the dead columns are also flagged "is_zero".
95 *
96 * The first n_redundant rows correspond to inequality constraints
97 * that are always satisfied for any value satisfying the non-redundant
98 * rows. The corresponding tab_vars are flagged "is_redundant".
99 * A row variable that is flagged "is_zero" is also flagged "is_redundant"
100 * since the constraint has been reduced to 0 = 0 and is therefore always
101 * satisfied.
102 *
103 * There are "n_var" variables in total. The first "n_param" of these
104 * are called parameters and the last "n_div" of these are called divs.
105 * The basic tableau operations makes no distinction between different
106 * kinds of variables. These special variables are only used while
107 * solving PILP problems.
108 *
109 * Dead columns and redundant rows are detected on the fly.
110 * However, the basic operations do not ensure that all dead columns
111 * or all redundant rows are detected.
112 * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
113 * to perform and exhaustive search for dead columns and redundant rows.
114 *
115 * The samples matrix contains "n_sample" integer points that have at some
116 * point been elements satisfying the tableau. The first "n_outside"
117 * of them no longer satisfy the tableau. They are kept because they
118 * can be reinstated during rollback when the constraint that cut them
119 * out is removed. These samples are only maintained for the context
120 * tableau while solving PILP problems.
121 *
122 * If "preserve" is set, then we want to keep all constraints in the
123 * tableau, even if they turn out to be redundant.
124 */
125 enum isl_tab_row_sign {
126 isl_tab_row_unknown = 0,
127 isl_tab_row_pos,
128 isl_tab_row_neg,
129 isl_tab_row_any,
130 };
131 struct isl_tab {
132 struct isl_mat *mat;
133  
134 unsigned n_row;
135 unsigned n_col;
136 unsigned n_dead;
137 unsigned n_redundant;
138  
139 unsigned n_var;
140 unsigned n_param;
141 unsigned n_div;
142 unsigned max_var;
143 unsigned n_con;
144 unsigned n_eq;
145 unsigned max_con;
146 struct isl_tab_var *var;
147 struct isl_tab_var *con;
148 int *row_var; /* v >= 0 -> var v; v < 0 -> con ~v */
149 int *col_var; /* v >= 0 -> var v; v < 0 -> con ~v */
150 enum isl_tab_row_sign *row_sign;
151  
152 struct isl_tab_undo bottom;
153 struct isl_tab_undo *top;
154  
155 struct isl_vec *dual;
156 struct isl_basic_map *bmap;
157  
158 unsigned n_sample;
159 unsigned n_outside;
160 int *sample_index;
161 struct isl_mat *samples;
162  
163 int n_zero;
164 int n_unbounded;
165 struct isl_mat *basis;
166  
167 int (*conflict)(int con, void *user);
168 void *conflict_user;
169  
170 unsigned strict_redundant : 1;
171 unsigned need_undo : 1;
172 unsigned preserve : 1;
173 unsigned rational : 1;
174 unsigned empty : 1;
175 unsigned in_undo : 1;
176 unsigned M : 1;
177 unsigned cone : 1;
178 };
179  
180 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
181 unsigned n_row, unsigned n_var, unsigned M);
182 void isl_tab_free(struct isl_tab *tab);
183  
184 __isl_give struct isl_tab *isl_tab_from_basic_map(
185 __isl_keep isl_basic_map *bmap, int track);
186 __isl_give struct isl_tab *isl_tab_from_basic_set(
187 __isl_keep isl_basic_set *bset, int track);
188 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset,
189 int parametric);
190 int isl_tab_cone_is_bounded(struct isl_tab *tab);
191 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
192 struct isl_tab *tab);
193 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
194 struct isl_tab *tab);
195 int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;
196 int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
197 #define ISL_TAB_SAVE_DUAL (1 << 0)
198 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
199 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
200 unsigned flags) WARN_UNUSED;
201  
202 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
203 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
204 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
205 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
206  
207 int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
208  
209 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap) WARN_UNUSED;
210 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset) WARN_UNUSED;
211 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab);
212  
213 int isl_tab_is_equality(struct isl_tab *tab, int con);
214 int isl_tab_is_redundant(struct isl_tab *tab, int con);
215  
216 int isl_tab_sample_is_integer(struct isl_tab *tab);
217 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
218  
219 enum isl_ineq_type {
220 isl_ineq_error = -1,
221 isl_ineq_redundant,
222 isl_ineq_separate,
223 isl_ineq_cut,
224 isl_ineq_adj_eq,
225 isl_ineq_adj_ineq,
226 };
227  
228 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
229  
230 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
231 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
232  
233 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
234 int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
235  
236 void isl_tab_dump(__isl_keep struct isl_tab *tab);
237  
238 struct isl_map *isl_tab_basic_map_partial_lexopt(
239 struct isl_basic_map *bmap, struct isl_basic_set *dom,
240 struct isl_set **empty, int max);
241 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff(
242 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
243 __isl_give isl_set **empty, int max);
244  
245 /* An isl_region represents a sequence of consecutive variables.
246 * pos is the location (starting at 0) of the first variable in the sequence.
247 */
248 struct isl_region {
249 int pos;
250 int len;
251 };
252  
253 __isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
254 __isl_take isl_basic_set *bset, int n_op, int n_region,
255 struct isl_region *region,
256 int (*conflict)(int con, void *user), void *user);
257 __isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
258 __isl_take isl_basic_set *bset);
259  
260 /* private */
261  
262 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
263 int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
264 int isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
265 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
266 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
267 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
268 int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
269 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
270 int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED;
271 int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
272 int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
273 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
274 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
275 int isl_tab_sign_of_max(struct isl_tab *tab, int con);
276 int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
277  
278 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type) WARN_UNUSED;
279 int isl_tab_push_var(struct isl_tab *tab,
280 enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
281 int isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
282  
283 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
284 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
285 __isl_take isl_vec *sample) WARN_UNUSED;
286 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
287 int isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
288  
289 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
290 struct isl_tab *tab_cone) WARN_UNUSED;
291  
292 int isl_tab_push_callback(struct isl_tab *tab,
293 struct isl_tab_callback *callback) WARN_UNUSED;
294  
295 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
296 int (*add_ineq)(void *user, isl_int *), void *user);
297  
298 #endif