1 /* 2 * Copyright 2006-2007 Universiteit Leiden 3 * Copyright 2008-2009 Katholieke Universiteit Leuven 4 * 5 * Use of this software is governed by the MIT license 6 * 7 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science, 8 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands 9 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A, 10 * B-3001 Leuven, Belgium 11 */ 12 13 #include <stdlib.h> 14 #include <isl_ctx_private.h> 15 #include <isl_map_private.h> 16 #include <isl_vec_private.h> 17 #include <isl_options_private.h> 18 #include "isl_basis_reduction.h" 19 20 static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha) 21 { 22 int i; 23 24 for (i = 0; i < n; ++i) 25 GBR_lp_get_alpha(lp, first + i, &alpha[i]); 26 } 27 28 /* Compute a reduced basis for the set represented by the tableau "tab". 29 * tab->basis, which must be initialized by the calling function to an affine 30 * unimodular basis, is updated to reflect the reduced basis. 31 * The first tab->n_zero rows of the basis (ignoring the constant row) 32 * are assumed to correspond to equalities and are left untouched. 33 * tab->n_zero is updated to reflect any additional equalities that 34 * have been detected in the first rows of the new basis. 35 * The final tab->n_unbounded rows of the basis are assumed to correspond 36 * to unbounded directions and are also left untouched. 37 * In particular this means that the remaining rows are assumed to 38 * correspond to bounded directions. 39 * 40 * This function implements the algorithm described in 41 * "An Implementation of the Generalized Basis Reduction Algorithm 42 * for Integer Programming" of Cook el al. to compute a reduced basis. 43 * We use \epsilon = 1/4. 44 * 45 * If ctx->opt->gbr_only_first is set, the user is only interested 46 * in the first direction. In this case we stop the basis reduction when 47 * the width in the first direction becomes smaller than 2. 48 */ 49 struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab) 50 { 51 unsigned dim; 52 struct isl_ctx *ctx; 53 struct isl_mat *B; 54 int i; 55 GBR_LP *lp = NULL; 56 GBR_type F_old, alpha, F_new; 57 int row; 58 isl_int tmp; 59 struct isl_vec *b_tmp; 60 GBR_type *F = NULL; 61 GBR_type *alpha_buffer[2] = { NULL, NULL }; 62 GBR_type *alpha_saved; 63 GBR_type F_saved; 64 int use_saved = 0; 65 isl_int mu[2]; 66 GBR_type mu_F[2]; 67 GBR_type two; 68 GBR_type one; 69 int empty = 0; 70 int fixed = 0; 71 int fixed_saved = 0; 72 int mu_fixed[2]; 73 int n_bounded; 74 int gbr_only_first; 75 76 if (!tab) 77 return NULL; 78 79 if (tab->empty) 80 return tab; 81 82 ctx = tab->mat->ctx; 83 gbr_only_first = ctx->opt->gbr_only_first; 84 dim = tab->n_var; 85 B = tab->basis; 86 if (!B) 87 return tab; 88 89 n_bounded = dim - tab->n_unbounded; 90 if (n_bounded <= tab->n_zero + 1) 91 return tab; 92 93 isl_int_init(tmp); 94 isl_int_init(mu[0]); 95 isl_int_init(mu[1]); 96 97 GBR_init(alpha); 98 GBR_init(F_old); 99 GBR_init(F_new); 100 GBR_init(F_saved); 101 GBR_init(mu_F[0]); 102 GBR_init(mu_F[1]); 103 GBR_init(two); 104 GBR_init(one); 105 106 b_tmp = isl_vec_alloc(ctx, dim); 107 if (!b_tmp) 108 goto error; 109 110 F = isl_alloc_array(ctx, GBR_type, n_bounded); 111 alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded); 112 alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded); 113 alpha_saved = alpha_buffer[0]; 114 115 if (!F || !alpha_buffer[0] || !alpha_buffer[1]) 116 goto error; 117 118 for (i = 0; i < n_bounded; ++i) { 119 GBR_init(F[i]); 120 GBR_init(alpha_buffer[0][i]); 121 GBR_init(alpha_buffer[1][i]); 122 } 123 124 GBR_set_ui(two, 2); 125 GBR_set_ui(one, 1); 126 127 lp = GBR_lp_init(tab); 128 if (!lp) 129 goto error; 130 131 i = tab->n_zero; 132 133 GBR_lp_set_obj(lp, B->row[1+i]+1, dim); 134 ctx->stats->gbr_solved_lps++; 135 if (GBR_lp_solve(lp) < 0) 136 goto error; 137 GBR_lp_get_obj_val(lp, &F[i]); 138 139 if (GBR_lt(F[i], one)) { 140 if (!GBR_is_zero(F[i])) { 141 empty = GBR_lp_cut(lp, B->row[1+i]+1); 142 if (empty) 143 goto done; 144 GBR_set_ui(F[i], 0); 145 } 146 tab->n_zero++; 147 } 148 149 do { 150 if (i+1 == tab->n_zero) { 151 GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim); 152 ctx->stats->gbr_solved_lps++; 153 if (GBR_lp_solve(lp) < 0) 154 goto error; 155 GBR_lp_get_obj_val(lp, &F_new); 156 fixed = GBR_lp_is_fixed(lp); 157 GBR_set_ui(alpha, 0); 158 } else if (use_saved) { 159 row = GBR_lp_next_row(lp); 160 GBR_set(F_new, F_saved); 161 fixed = fixed_saved; 162 GBR_set(alpha, alpha_saved[i]); 163 } else { 164 row = GBR_lp_add_row(lp, B->row[1+i]+1, dim); 165 GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim); 166 ctx->stats->gbr_solved_lps++; 167 if (GBR_lp_solve(lp) < 0) 168 goto error; 169 GBR_lp_get_obj_val(lp, &F_new); 170 fixed = GBR_lp_is_fixed(lp); 171 172 GBR_lp_get_alpha(lp, row, &alpha); 173 174 if (i > 0) 175 save_alpha(lp, row-i, i, alpha_saved); 176 177 if (GBR_lp_del_row(lp) < 0) 178 goto error; 179 } 180 GBR_set(F[i+1], F_new); 181 182 GBR_floor(mu[0], alpha); 183 GBR_ceil(mu[1], alpha); 184 185 if (isl_int_eq(mu[0], mu[1])) 186 isl_int_set(tmp, mu[0]); 187 else { 188 int j; 189 190 for (j = 0; j <= 1; ++j) { 191 isl_int_set(tmp, mu[j]); 192 isl_seq_combine(b_tmp->el, 193 ctx->one, B->row[1+i+1]+1, 194 tmp, B->row[1+i]+1, dim); 195 GBR_lp_set_obj(lp, b_tmp->el, dim); 196 ctx->stats->gbr_solved_lps++; 197 if (GBR_lp_solve(lp) < 0) 198 goto error; 199 GBR_lp_get_obj_val(lp, &mu_F[j]); 200 mu_fixed[j] = GBR_lp_is_fixed(lp); 201 if (i > 0) 202 save_alpha(lp, row-i, i, alpha_buffer[j]); 203 } 204 205 if (GBR_lt(mu_F[0], mu_F[1])) 206 j = 0; 207 else 208 j = 1; 209 210 isl_int_set(tmp, mu[j]); 211 GBR_set(F_new, mu_F[j]); 212 fixed = mu_fixed[j]; 213 alpha_saved = alpha_buffer[j]; 214 } 215 isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1, 216 tmp, B->row[1+i]+1, dim); 217 218 if (i+1 == tab->n_zero && fixed) { 219 if (!GBR_is_zero(F[i+1])) { 220 empty = GBR_lp_cut(lp, B->row[1+i+1]+1); 221 if (empty) 222 goto done; 223 GBR_set_ui(F[i+1], 0); 224 } 225 tab->n_zero++; 226 } 227 228 GBR_set(F_old, F[i]); 229 230 use_saved = 0; 231 /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */ 232 GBR_set_ui(mu_F[0], 4); 233 GBR_mul(mu_F[0], mu_F[0], F_new); 234 GBR_set_ui(mu_F[1], 3); 235 GBR_mul(mu_F[1], mu_F[1], F_old); 236 if (GBR_lt(mu_F[0], mu_F[1])) { 237 B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1); 238 if (i > tab->n_zero) { 239 use_saved = 1; 240 GBR_set(F_saved, F_new); 241 fixed_saved = fixed; 242 if (GBR_lp_del_row(lp) < 0) 243 goto error; 244 --i; 245 } else { 246 GBR_set(F[tab->n_zero], F_new); 247 if (gbr_only_first && GBR_lt(F[tab->n_zero], two)) 248 break; 249 250 if (fixed) { 251 if (!GBR_is_zero(F[tab->n_zero])) { 252 empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1); 253 if (empty) 254 goto done; 255 GBR_set_ui(F[tab->n_zero], 0); 256 } 257 tab->n_zero++; 258 } 259 } 260 } else { 261 GBR_lp_add_row(lp, B->row[1+i]+1, dim); 262 ++i; 263 } 264 } while (i < n_bounded - 1); 265 266 if (0) { 267 done: 268 if (empty < 0) { 269 error: 270 isl_mat_free(B); 271 B = NULL; 272 } 273 } 274 275 GBR_lp_delete(lp); 276 277 if (alpha_buffer[1]) 278 for (i = 0; i < n_bounded; ++i) { 279 GBR_clear(F[i]); 280 GBR_clear(alpha_buffer[0][i]); 281 GBR_clear(alpha_buffer[1][i]); 282 } 283 free(F); 284 free(alpha_buffer[0]); 285 free(alpha_buffer[1]); 286 287 isl_vec_free(b_tmp); 288 289 GBR_clear(alpha); 290 GBR_clear(F_old); 291 GBR_clear(F_new); 292 GBR_clear(F_saved); 293 GBR_clear(mu_F[0]); 294 GBR_clear(mu_F[1]); 295 GBR_clear(two); 296 GBR_clear(one); 297 298 isl_int_clear(tmp); 299 isl_int_clear(mu[0]); 300 isl_int_clear(mu[1]); 301 302 tab->basis = B; 303 304 return tab; 305 } 306 307 /* Compute an affine form of a reduced basis of the given basic 308 * non-parametric set, which is assumed to be bounded and not 309 * include any integer divisions. 310 * The first column and the first row correspond to the constant term. 311 * 312 * If the input contains any equalities, we first create an initial 313 * basis with the equalities first. Otherwise, we start off with 314 * the identity matrix. 315 */ 316 __isl_give isl_mat *isl_basic_set_reduced_basis(__isl_keep isl_basic_set *bset) 317 { 318 struct isl_mat *basis; 319 struct isl_tab *tab; 320 321 if (isl_basic_set_check_no_locals(bset) < 0 || 322 isl_basic_set_check_no_params(bset) < 0) 323 return NULL; 324 325 tab = isl_tab_from_basic_set(bset, 0); 326 if (!tab) 327 return NULL; 328 329 if (bset->n_eq == 0) 330 tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var); 331 else { 332 isl_mat *eq; 333 isl_size nvar = isl_basic_set_dim(bset, isl_dim_all); 334 if (nvar < 0) 335 goto error; 336 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 337 1, nvar); 338 eq = isl_mat_left_hermite(eq, 0, NULL, &tab->basis); 339 tab->basis = isl_mat_lin_to_aff(tab->basis); 340 tab->n_zero = bset->n_eq; 341 isl_mat_free(eq); 342 } 343 tab = isl_tab_compute_reduced_basis(tab); 344 if (!tab) 345 return NULL; 346 347 basis = isl_mat_copy(tab->basis); 348 349 isl_tab_free(tab); 350 351 return basis; 352 error: 353 isl_tab_free(tab); 354 return NULL; 355 } 356
Indexes created Sun Sep 06 00:23:55 UTC 2026