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(struct isl_basic_set *bset, 194 int parametric); 195 isl_bool isl_tab_cone_is_bounded(struct isl_tab *tab); 196 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap, 197 struct isl_tab *tab); 198 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset, 199 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 struct 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_allocate_var(struct isl_tab *tab) 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