isl_tab.h

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