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
20struct 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
31enum 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
51struct isl_tab_callback {
52 isl_stat (*run)(struct isl_tab_callback *cb);
53};
54
55union isl_tab_undo_val {
56 int var_index;
57 int *col_var;
58 int n;
59 struct isl_tab_callback *callback;
60};
61
62struct 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 */
129enum 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};
135struct 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
184struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
185 unsigned n_row, unsigned n_var, unsigned M);
186void isl_tab_free(struct isl_tab *tab);
187
188isl_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);
194struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
195 int parametric);
196isl_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);
201int 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);
204int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
205isl_stat isl_tab_restore_redundant(struct isl_tab *tab);
206#define ISL_TAB_SAVE_DUAL (1 << 0)
207enum 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
211isl_stat isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
212isl_stat isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
213int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
214
215int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
216
217isl_stat isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
218 WARN_UNUSED;
219isl_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
223int isl_tab_is_equality(struct isl_tab *tab, int con);
224int isl_tab_is_redundant(struct isl_tab *tab, int con);
225
226int isl_tab_sample_is_integer(struct isl_tab *tab);
227__isl_give isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
228
229enum 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
238enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
239
240struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
241isl_stat isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
242isl_bool isl_tab_need_undo(struct isl_tab *tab);
243void isl_tab_clear_undo(struct isl_tab *tab);
244
245int isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
246int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
247int isl_tab_unrestrict(struct isl_tab *tab, int con) WARN_UNUSED;
248
249void 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 */
269struct 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
279struct isl_tab_lexmin;
280typedef 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);
284int 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
294struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
295int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
296int isl_tab_mark_rational(struct isl_tab *tab) WARN_UNUSED;
297isl_stat isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
298struct isl_tab *isl_tab_dup(struct isl_tab *tab);
299struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
300int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
301int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
302int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
303int isl_tab_insert_var(struct isl_tab *tab, int pos) WARN_UNUSED;
304int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
305int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
306int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
307int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
308int isl_tab_sign_of_max(struct isl_tab *tab, int con);
309int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
310
311isl_stat isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
312 WARN_UNUSED;
313isl_stat isl_tab_push_var(struct isl_tab *tab,
314 enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
315isl_stat isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
316
317struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
318int isl_tab_add_sample(struct isl_tab *tab,
319 __isl_take isl_vec *sample) WARN_UNUSED;
320struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
321isl_stat isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
322
323struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
324 struct isl_tab *tab_cone) WARN_UNUSED;
325isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value);
326isl_stat isl_tab_detect_constants(struct isl_tab *tab);
327
328isl_stat isl_tab_push_callback(struct isl_tab *tab,
329 struct isl_tab_callback *callback) WARN_UNUSED;
330
331int 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);
333int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div);
334
335int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift) WARN_UNUSED;
336
337isl_stat isl_tab_swap_constraints(struct isl_tab *tab, int con1, int con2);
338
339#endif
340

source code of polly/lib/External/isl/isl_tab.h