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 18struct isl_tab_var { 19 int index; 20 unsigned is_row : 1; 21 unsigned is_nonneg : 1; 22 unsigned is_zero : 1; 23 unsigned is_redundant : 1; 24 unsigned marked : 1; 25 unsigned frozen : 1; 26 unsigned negated : 1; 27}; 28 29enum isl_tab_undo_type { 30 isl_tab_undo_bottom, 31 isl_tab_undo_empty, 32 isl_tab_undo_nonneg, 33 isl_tab_undo_redundant, 34 isl_tab_undo_freeze, 35 isl_tab_undo_zero, 36 isl_tab_undo_allocate, 37 isl_tab_undo_relax, 38 isl_tab_undo_unrestrict, 39 isl_tab_undo_bmap_ineq, 40 isl_tab_undo_bmap_eq, 41 isl_tab_undo_bmap_div, 42 isl_tab_undo_saved_basis, 43 isl_tab_undo_drop_sample, 44 isl_tab_undo_saved_samples, 45 isl_tab_undo_callback, 46}; 47 48struct isl_tab_callback { 49 int (*run)(struct isl_tab_callback *cb); 50}; 51 52union isl_tab_undo_val { 53 int var_index; 54 int *col_var; 55 int n; 56 struct isl_tab_callback *callback; 57}; 58 59struct isl_tab_undo { 60 enum isl_tab_undo_type type; 61 union isl_tab_undo_val u; 62 struct isl_tab_undo *next; 63}; 64 65/* The tableau maintains equality relations. 66 * Each column and each row is associated to a variable or a constraint. 67 * The "value" of an inequality constraint is the value of the corresponding 68 * slack variable. 69 * The "row_var" and "col_var" arrays map column and row indices 70 * to indices in the "var" and "con" arrays. The elements of these 71 * arrays maintain extra information about the variables and the constraints. 72 * Each row expresses the corresponding row variable as an affine expression 73 * of the column variables. 74 * The first two columns in the matrix contain the common denominator of 75 * the row and the numerator of the constant term. 76 * If "M" is set, then the third column represents the "big parameter". 77 * The third (M = 0) or fourth (M = 1) column 78 * in the matrix is called column 0 with respect to the col_var array. 79 * The sample value of the tableau is the value that assigns zero 80 * to all the column variables and the constant term of each affine 81 * expression to the corresponding row variable. 82 * The operations on the tableau maintain the property that the sample 83 * value satisfies the non-negativity constraints (usually on the slack 84 * variables). 85 * 86 * The big parameter represents an arbitrarily big (and divisible) 87 * positive number. If present, then the sign of a row is determined 88 * lexicographically, with the sign of the big parameter coefficient 89 * considered first. The big parameter is only used while 90 * solving PILP problems. 91 * 92 * The first n_dead column variables have their values fixed to zero. 93 * The corresponding tab_vars are flagged "is_zero". 94 * Some of the rows that have have zero coefficients in all but 95 * the dead columns are also flagged "is_zero". 96 * 97 * The first n_redundant rows correspond to inequality constraints 98 * that are always satisfied for any value satisfying the non-redundant 99 * rows. The corresponding tab_vars are flagged "is_redundant". 100 * A row variable that is flagged "is_zero" is also flagged "is_redundant" 101 * since the constraint has been reduced to 0 = 0 and is therefore always 102 * satisfied. 103 * 104 * There are "n_var" variables in total. The first "n_param" of these 105 * are called parameters and the last "n_div" of these are called divs. 106 * The basic tableau operations makes no distinction between different 107 * kinds of variables. These special variables are only used while 108 * solving PILP problems. 109 * 110 * Dead columns and redundant rows are detected on the fly. 111 * However, the basic operations do not ensure that all dead columns 112 * or all redundant rows are detected. 113 * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used 114 * to perform and exhaustive search for dead columns and redundant rows. 115 * 116 * The samples matrix contains "n_sample" integer points that have at some 117 * point been elements satisfying the tableau. The first "n_outside" 118 * of them no longer satisfy the tableau. They are kept because they 119 * can be reinstated during rollback when the constraint that cut them 120 * out is removed. These samples are only maintained for the context 121 * tableau while solving PILP problems. 122 * 123 * If "preserve" is set, then we want to keep all constraints in the 124 * tableau, even if they turn out to be redundant. 125 */ 126enum isl_tab_row_sign { 127 isl_tab_row_unknown = 0, 128 isl_tab_row_pos, 129 isl_tab_row_neg, 130 isl_tab_row_any, 131}; 132struct isl_tab { 133 struct isl_mat *mat; 134 135 unsigned n_row; 136 unsigned n_col; 137 unsigned n_dead; 138 unsigned n_redundant; 139 140 unsigned n_var; 141 unsigned n_param; 142 unsigned n_div; 143 unsigned max_var; 144 unsigned n_con; 145 unsigned n_eq; 146 unsigned max_con; 147 struct isl_tab_var *var; 148 struct isl_tab_var *con; 149 int *row_var; /* v >= 0 -> var v; v < 0 -> con ~v */ 150 int *col_var; /* v >= 0 -> var v; v < 0 -> con ~v */ 151 enum isl_tab_row_sign *row_sign; 152 153 struct isl_tab_undo bottom; 154 struct isl_tab_undo *top; 155 156 struct isl_vec *dual; 157 struct isl_basic_map *bmap; 158 159 unsigned n_sample; 160 unsigned n_outside; 161 int *sample_index; 162 struct isl_mat *samples; 163 164 int n_zero; 165 int n_unbounded; 166 struct isl_mat *basis; 167 168 int (*conflict)(int con, void *user); 169 void *conflict_user; 170 171 unsigned strict_redundant : 1; 172 unsigned need_undo : 1; 173 unsigned preserve : 1; 174 unsigned rational : 1; 175 unsigned empty : 1; 176 unsigned in_undo : 1; 177 unsigned M : 1; 178 unsigned cone : 1; 179}; 180 181struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx, 182 unsigned n_row, unsigned n_var, unsigned M); 183void isl_tab_free(struct isl_tab *tab); 184 185isl_ctx *isl_tab_get_ctx(struct isl_tab *tab); 186 187__isl_give struct isl_tab *isl_tab_from_basic_map( 188 __isl_keep isl_basic_map *bmap, int track); 189__isl_give struct isl_tab *isl_tab_from_basic_set( 190 __isl_keep isl_basic_set *bset, int track); 191struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset, 192 int parametric); 193int isl_tab_cone_is_bounded(struct isl_tab *tab); 194struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap, 195 struct isl_tab *tab); 196struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset, 197 struct isl_tab *tab); 198int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED; 199__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab, 200 __isl_take isl_basic_map *bmap); 201int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED; 202#define ISL_TAB_SAVE_DUAL (1 << 0) 203enum isl_lp_result isl_tab_min(struct isl_tab *tab, 204 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom, 205 unsigned flags) WARN_UNUSED; 206 207struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) WARN_UNUSED; 208int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED; 209int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED; 210int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED; 211 212int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED; 213 214int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap) WARN_UNUSED; 215int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset) WARN_UNUSED; 216__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab); 217 218int isl_tab_is_equality(struct isl_tab *tab, int con); 219int isl_tab_is_redundant(struct isl_tab *tab, int con); 220 221int isl_tab_sample_is_integer(struct isl_tab *tab); 222struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab); 223 224enum isl_ineq_type { 225 isl_ineq_error = -1, 226 isl_ineq_redundant, 227 isl_ineq_separate, 228 isl_ineq_cut, 229 isl_ineq_adj_eq, 230 isl_ineq_adj_ineq, 231}; 232 233enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq); 234 235struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab); 236int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED; 237 238struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED; 239int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED; 240int isl_tab_unrestrict(struct isl_tab *tab, int con) WARN_UNUSED; 241 242void isl_tab_dump(__isl_keep struct isl_tab *tab); 243 244struct isl_map *isl_tab_basic_map_partial_lexopt( 245 struct isl_basic_map *bmap, struct isl_basic_set *dom, 246 struct isl_set **empty, int max); 247__isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff( 248 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, 249 __isl_give isl_set **empty, int max); 250 251/* An isl_region represents a sequence of consecutive variables. 252 * pos is the location (starting at 0) of the first variable in the sequence. 253 */ 254struct isl_region { 255 int pos; 256 int len; 257}; 258 259__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin( 260 __isl_take isl_basic_set *bset, int n_op, int n_region, 261 struct isl_region *region, 262 int (*conflict)(int con, void *user), void *user); 263__isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin( 264 __isl_take isl_basic_set *bset); 265 266/* private */ 267 268struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i); 269int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED; 270int isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED; 271struct isl_tab *isl_tab_dup(struct isl_tab *tab); 272struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2); 273int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED; 274int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED; 275int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED; 276int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED; 277int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED; 278int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED; 279int isl_tab_row_is_redundant(struct isl_tab *tab, int row); 280int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var); 281int isl_tab_sign_of_max(struct isl_tab *tab, int con); 282int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED; 283 284int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type) WARN_UNUSED; 285int isl_tab_push_var(struct isl_tab *tab, 286 enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED; 287int isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED; 288 289struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED; 290struct isl_tab *isl_tab_add_sample(struct isl_tab *tab, 291 __isl_take isl_vec *sample) WARN_UNUSED; 292struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s); 293int isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED; 294 295struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab, 296 struct isl_tab *tab_cone) WARN_UNUSED; 297 298int isl_tab_push_callback(struct isl_tab *tab, 299 struct isl_tab_callback *callback) WARN_UNUSED; 300 301int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div, 302 int (*add_ineq)(void *user, isl_int *), void *user); 303 304#endif 305