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/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_insert_var(struct isl_tab *tab, int pos) WARN_UNUSED;
 303 int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
 304 int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
 305 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
 306 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
 307 int isl_tab_sign_of_max(struct isl_tab *tab, int con);
 308 int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
 309
 310 isl_stat isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
 311         WARN_UNUSED;
 312 isl_stat isl_tab_push_var(struct isl_tab *tab,
 313         enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
 314 isl_stat isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
 315
 316 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
 317 int isl_tab_add_sample(struct isl_tab *tab,
 318         __isl_take isl_vec *sample) WARN_UNUSED;
 319 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
 320 isl_stat isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
 321
 322 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
 323         struct isl_tab *tab_cone) WARN_UNUSED;
 324 isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value);
 325 isl_stat isl_tab_detect_constants(struct isl_tab *tab);
 326
 327 isl_stat isl_tab_push_callback(struct isl_tab *tab,
 328         struct isl_tab_callback *callback) WARN_UNUSED;
 329
 330 int isl_tab_insert_div(struct isl_tab *tab, int pos, __isl_keep isl_vec *div,
 331         isl_stat (*add_ineq)(void *user, isl_int *), void *user);
 332 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div);
 333
 334 int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift) WARN_UNUSED;
 335
 336 isl_stat isl_tab_swap_constraints(struct isl_tab *tab, int con1, int con2);
 337
 338 #endif