1 /* Source code for an implementation of the Omega test, an integer 2 programming algorithm for dependence analysis, by William Pugh, 3 appeared in Supercomputing '91 and CACM Aug 92. 4 5 This code has no license restrictions, and is considered public 6 domain. 7 8 Changes copyright (C) 2005, 2006, 2007, 2009 Free Software Foundation, Inc. 9 Contributed by Sebastian Pop <sebastian.pop@inria.fr> 10 11 This file is part of GCC. 12 13 GCC is free software; you can redistribute it and/or modify it under 14 the terms of the GNU General Public License as published by the Free 15 Software Foundation; either version 3, or (at your option) any later 16 version. 17 18 GCC is distributed in the hope that it will be useful, but WITHOUT ANY 19 WARRANTY; without even the implied warranty of MERCHANTABILITY or 20 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 21 for more details. 22 23 You should have received a copy of the GNU General Public License 24 along with GCC; see the file COPYING3. If not see 25 <http://www.gnu.org/licenses/>. */ 26 27 #include "config.h" 28 #include "params.h" 29 30 #ifndef GCC_OMEGA_H 31 #define GCC_OMEGA_H 32 33 #define OMEGA_MAX_VARS PARAM_VALUE (PARAM_OMEGA_MAX_VARS) 34 #define OMEGA_MAX_GEQS PARAM_VALUE (PARAM_OMEGA_MAX_GEQS) 35 #define OMEGA_MAX_EQS PARAM_VALUE (PARAM_OMEGA_MAX_EQS) 36 37 #define pos_infinity (0x7ffffff) 38 #define neg_infinity (-0x7ffffff) 39 40 /* Results of the Omega solver. */ 41 enum omega_result { 42 omega_false = 0, 43 omega_true = 1, 44 45 /* Value returned when the solver is unable to determine an 46 answer. */ 47 omega_unknown = 2, 48 49 /* Value used for asking the solver to simplify the system. */ 50 omega_simplify = 3 51 }; 52 53 /* Values used for labeling equations. Private (not used outside the 54 solver). */ 55 enum omega_eqn_color { 56 omega_black = 0, 57 omega_red = 1 58 }; 59 60 /* Structure for equations. */ 61 typedef struct eqn_d 62 { 63 int key; 64 int touched; 65 enum omega_eqn_color color; 66 67 /* Array of coefficients for the equation. The layout of the data 68 is as follows: coef[0] is the constant, coef[i] for 1 <= i <= 69 OMEGA_MAX_VARS, are the coefficients for each dimension. Examples: 70 the equation 0 = 9 + x + 0y + 5z is encoded as [9 1 0 5], the 71 inequality 0 <= -8 + x + 2y + 3z is encoded as [-8 1 2 3]. */ 72 int *coef; 73 } *eqn; 74 75 typedef struct omega_pb_d 76 { 77 /* The number of variables in the system of equations. */ 78 int num_vars; 79 80 /* Safe variables are not eliminated during the Fourier-Motzkin 81 simplification of the system. Safe variables are all those 82 variables that are placed at the beginning of the array of 83 variables: PB->var[1, ..., SAFE_VARS]. PB->var[0] is not used, 84 as PB->eqs[x]->coef[0] represents the constant of the equation. */ 85 int safe_vars; 86 87 /* Number of elements in eqs[]. */ 88 int num_eqs; 89 /* Number of elements in geqs[]. */ 90 int num_geqs; 91 /* Number of elements in subs[]. */ 92 int num_subs; 93 94 int hash_version; 95 bool variables_initialized; 96 bool variables_freed; 97 98 /* Index or name of variables. Negative integers are reserved for 99 wildcard variables. Maps the index of variables in the original 100 problem to the new index of the variable. The index for a 101 variable in the coef array of an equation can change as some 102 variables are eliminated. */ 103 int *var; 104 105 int *forwarding_address; 106 107 /* Inequalities in the system of constraints. */ 108 eqn geqs; 109 110 /* Equations in the system of constraints. */ 111 eqn eqs; 112 113 /* A map of substituted variables. */ 114 eqn subs; 115 } *omega_pb; 116 117 extern void omega_initialize (void); 118 extern omega_pb omega_alloc_problem (int, int); 119 extern enum omega_result omega_solve_problem (omega_pb, enum omega_result); 120 extern enum omega_result omega_simplify_problem (omega_pb); 121 extern enum omega_result omega_simplify_approximate (omega_pb); 122 extern enum omega_result omega_constrain_variable_sign (omega_pb, 123 enum omega_eqn_color, 124 int, int); 125 extern void debug_omega_problem (omega_pb); 126 extern void omega_print_problem (FILE *, omega_pb); 127 extern void omega_print_red_equations (FILE *, omega_pb); 128 extern int omega_count_red_equations (omega_pb); 129 extern void omega_pretty_print_problem (FILE *, omega_pb); 130 extern void omega_unprotect_variable (omega_pb, int var); 131 extern void omega_negate_geq (omega_pb, int); 132 extern void omega_convert_eq_to_geqs (omega_pb, int eq); 133 extern void omega_print_eqn (FILE *, omega_pb, eqn, bool, int); 134 extern bool omega_problem_has_red_equations (omega_pb); 135 extern enum omega_result omega_eliminate_redundant (omega_pb, bool); 136 extern void omega_eliminate_red (omega_pb, bool); 137 extern void omega_constrain_variable_value (omega_pb, enum omega_eqn_color, 138 int, int); 139 extern bool omega_query_variable (omega_pb, int, int *, int *); 140 extern int omega_query_variable_signs (omega_pb, int, int, int, int, 141 int, int, bool *, int *); 142 extern bool omega_query_variable_bounds (omega_pb, int, int *, int *); 143 extern void (*omega_when_reduced) (omega_pb); 144 extern void omega_no_procedure (omega_pb); 145 146 /* Return true when variable I in problem PB is a wildcard. */ 147 148 static inline bool 149 omega_wildcard_p (omega_pb pb, int i) 150 { 151 return (pb->var[i] < 0); 152 } 153 154 /* Return true when variable I in problem PB is a safe variable. */ 155 156 static inline bool 157 omega_safe_var_p (omega_pb pb, int i) 158 { 159 /* The constant of an equation is not a variable. */ 160 gcc_assert (0 < i); 161 return (i <= pb->safe_vars); 162 } 163 164 /* Print to FILE equality E from PB. */ 165 166 static inline void 167 omega_print_eq (FILE *file, omega_pb pb, eqn e) 168 { 169 omega_print_eqn (file, pb, e, false, 0); 170 } 171 172 /* Print to FILE inequality E from PB. */ 173 174 static inline void 175 omega_print_geq (FILE *file, omega_pb pb, eqn e) 176 { 177 omega_print_eqn (file, pb, e, true, 0); 178 } 179 180 /* Print to FILE inequality E from PB. */ 181 182 static inline void 183 omega_print_geq_extra (FILE *file, omega_pb pb, eqn e) 184 { 185 omega_print_eqn (file, pb, e, true, 1); 186 } 187 188 /* E1 = E2, make a copy of E2 into E1. Equations contain S variables. */ 189 190 static inline void 191 omega_copy_eqn (eqn e1, eqn e2, int s) 192 { 193 e1->key = e2->key; 194 e1->touched = e2->touched; 195 e1->color = e2->color; 196 197 memcpy (e1->coef, e2->coef, (s + 1) * sizeof (int)); 198 } 199 200 /* Initialize E = 0. Equation E contains S variables. */ 201 202 static inline void 203 omega_init_eqn_zero (eqn e, int s) 204 { 205 e->key = 0; 206 e->touched = 0; 207 e->color = omega_black; 208 209 memset (e->coef, 0, (s + 1) * sizeof (int)); 210 } 211 212 /* Allocate N equations with S variables. */ 213 214 static inline eqn 215 omega_alloc_eqns (int s, int n) 216 { 217 int i; 218 eqn res = (eqn) (xcalloc (n, sizeof (struct eqn_d))); 219 220 for (i = n - 1; i >= 0; i--) 221 { 222 res[i].coef = (int *) (xcalloc (OMEGA_MAX_VARS + 1, sizeof (int))); 223 omega_init_eqn_zero (&res[i], s); 224 } 225 226 return res; 227 } 228 229 /* Free N equations from array EQ. */ 230 231 static inline void 232 omega_free_eqns (eqn eq, int n) 233 { 234 int i; 235 236 for (i = n - 1; i >= 0; i--) 237 free (eq[i].coef); 238 239 free (eq); 240 } 241 242 /* Returns true when E is an inequality with a single variable. */ 243 244 static inline bool 245 single_var_geq (eqn e, int nv ATTRIBUTE_UNUSED) 246 { 247 return (e->key != 0 248 && -OMEGA_MAX_VARS <= e->key && e->key <= OMEGA_MAX_VARS); 249 } 250 251 /* Allocate a new equality with all coefficients 0, and tagged with 252 COLOR. Return the index of this equality in problem PB. */ 253 254 static inline int 255 omega_add_zero_eq (omega_pb pb, enum omega_eqn_color color) 256 { 257 int idx = pb->num_eqs++; 258 259 gcc_assert (pb->num_eqs <= OMEGA_MAX_EQS); 260 omega_init_eqn_zero (&pb->eqs[idx], pb->num_vars); 261 pb->eqs[idx].color = color; 262 return idx; 263 } 264 265 /* Allocate a new inequality with all coefficients 0, and tagged with 266 COLOR. Return the index of this inequality in problem PB. */ 267 268 static inline int 269 omega_add_zero_geq (omega_pb pb, enum omega_eqn_color color) 270 { 271 int idx = pb->num_geqs; 272 273 pb->num_geqs++; 274 gcc_assert (pb->num_geqs <= OMEGA_MAX_GEQS); 275 omega_init_eqn_zero (&pb->geqs[idx], pb->num_vars); 276 pb->geqs[idx].touched = 1; 277 pb->geqs[idx].color = color; 278 return idx; 279 } 280 281 /* Initialize variables for problem PB. */ 282 283 static inline void 284 omega_initialize_variables (omega_pb pb) 285 { 286 int i; 287 288 for (i = pb->num_vars; i >= 0; i--) 289 pb->forwarding_address[i] = pb->var[i] = i; 290 291 pb->variables_initialized = true; 292 } 293 294 /* Free problem PB. */ 295 296 static inline void 297 omega_free_problem (omega_pb pb) 298 { 299 free (pb->var); 300 free (pb->forwarding_address); 301 omega_free_eqns (pb->geqs, OMEGA_MAX_GEQS); 302 omega_free_eqns (pb->eqs, OMEGA_MAX_EQS); 303 omega_free_eqns (pb->subs, OMEGA_MAX_VARS + 1); 304 free (pb); 305 } 306 307 /* Copy omega problems: P1 = P2. */ 308 309 static inline void 310 omega_copy_problem (omega_pb p1, omega_pb p2) 311 { 312 int e, i; 313 314 p1->num_vars = p2->num_vars; 315 p1->hash_version = p2->hash_version; 316 p1->variables_initialized = p2->variables_initialized; 317 p1->variables_freed = p2->variables_freed; 318 p1->safe_vars = p2->safe_vars; 319 p1->num_eqs = p2->num_eqs; 320 p1->num_subs = p2->num_subs; 321 p1->num_geqs = p2->num_geqs; 322 323 for (e = p2->num_eqs - 1; e >= 0; e--) 324 omega_copy_eqn (&(p1->eqs[e]), &(p2->eqs[e]), p2->num_vars); 325 326 for (e = p2->num_geqs - 1; e >= 0; e--) 327 omega_copy_eqn (&(p1->geqs[e]), &(p2->geqs[e]), p2->num_vars); 328 329 for (e = p2->num_subs - 1; e >= 0; e--) 330 omega_copy_eqn (&(p1->subs[e]), &(p2->subs[e]), p2->num_vars); 331 332 for (i = p2->num_vars; i >= 0; i--) 333 p1->var[i] = p2->var[i]; 334 335 for (i = OMEGA_MAX_VARS; i >= 0; i--) 336 p1->forwarding_address[i] = p2->forwarding_address[i]; 337 } 338 339 #endif /* GCC_OMEGA_H */ 340