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 };
  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