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