| 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 | #include <isl_ctx_private.h> |
| 11 | #include <isl_map_private.h> |
| 12 | #include <isl/ilp.h> |
| 13 | #include <isl/union_set.h> |
| 14 | #include "isl_sample.h" |
| 15 | #include <isl_seq.h> |
| 16 | #include "isl_equalities.h" |
| 17 | #include <isl_aff_private.h> |
| 18 | #include <isl_local_space_private.h> |
| 19 | #include <isl_mat_private.h> |
| 20 | #include <isl_val_private.h> |
| 21 | #include <isl_vec_private.h> |
| 22 | #include <isl_lp_private.h> |
| 23 | #include <isl_ilp_private.h> |
| 24 | |
| 25 | /* Given a basic set "bset", construct a basic set U such that for |
| 26 | * each element x in U, the whole unit box positioned at x is inside |
| 27 | * the given basic set. |
| 28 | * Note that U may not contain all points that satisfy this property. |
| 29 | * |
| 30 | * We simply add the sum of all negative coefficients to the constant |
| 31 | * term. This ensures that if x satisfies the resulting constraints, |
| 32 | * then x plus any sum of unit vectors satisfies the original constraints. |
| 33 | */ |
| 34 | static __isl_give isl_basic_set *unit_box_base_points( |
| 35 | __isl_take isl_basic_set *bset) |
| 36 | { |
| 37 | int i, j, k; |
| 38 | struct isl_basic_set *unit_box = NULL; |
| 39 | isl_size total; |
| 40 | |
| 41 | if (!bset) |
| 42 | goto error; |
| 43 | |
| 44 | if (bset->n_eq != 0) { |
| 45 | isl_space *space = isl_basic_set_get_space(bset); |
| 46 | isl_basic_set_free(bset); |
| 47 | return isl_basic_set_empty(space); |
| 48 | } |
| 49 | |
| 50 | total = isl_basic_set_dim(bset, type: isl_dim_all); |
| 51 | if (total < 0) |
| 52 | goto error; |
| 53 | unit_box = isl_basic_set_alloc_space(space: isl_basic_set_get_space(bset), |
| 54 | extra: 0, n_eq: 0, n_ineq: bset->n_ineq); |
| 55 | |
| 56 | for (i = 0; i < bset->n_ineq; ++i) { |
| 57 | k = isl_basic_set_alloc_inequality(bset: unit_box); |
| 58 | if (k < 0) |
| 59 | goto error; |
| 60 | isl_seq_cpy(dst: unit_box->ineq[k], src: bset->ineq[i], len: 1 + total); |
| 61 | for (j = 0; j < total; ++j) { |
| 62 | if (isl_int_is_nonneg(unit_box->ineq[k][1 + j])) |
| 63 | continue; |
| 64 | isl_int_add(unit_box->ineq[k][0], |
| 65 | unit_box->ineq[k][0], unit_box->ineq[k][1 + j]); |
| 66 | } |
| 67 | } |
| 68 | |
| 69 | isl_basic_set_free(bset); |
| 70 | return unit_box; |
| 71 | error: |
| 72 | isl_basic_set_free(bset); |
| 73 | isl_basic_set_free(bset: unit_box); |
| 74 | return NULL; |
| 75 | } |
| 76 | |
| 77 | /* Find an integer point in "bset", preferably one that is |
| 78 | * close to minimizing "f". |
| 79 | * |
| 80 | * We first check if we can easily put unit boxes inside bset. |
| 81 | * If so, we take the best base point of any of the unit boxes we can find |
| 82 | * and round it up to the nearest integer. |
| 83 | * If not, we simply pick any integer point in "bset". |
| 84 | */ |
| 85 | static __isl_give isl_vec *initial_solution(__isl_keep isl_basic_set *bset, |
| 86 | isl_int *f) |
| 87 | { |
| 88 | enum isl_lp_result res; |
| 89 | struct isl_basic_set *unit_box; |
| 90 | struct isl_vec *sol; |
| 91 | |
| 92 | unit_box = unit_box_base_points(bset: isl_basic_set_copy(bset)); |
| 93 | |
| 94 | res = isl_basic_set_solve_lp(bset: unit_box, max: 0, f, denom: bset->ctx->one, |
| 95 | NULL, NULL, sol: &sol); |
| 96 | if (res == isl_lp_ok) { |
| 97 | isl_basic_set_free(bset: unit_box); |
| 98 | return isl_vec_ceil(vec: sol); |
| 99 | } |
| 100 | |
| 101 | isl_basic_set_free(bset: unit_box); |
| 102 | |
| 103 | return isl_basic_set_sample_vec(bset: isl_basic_set_copy(bset)); |
| 104 | } |
| 105 | |
| 106 | /* Restrict "bset" to those points with values for f in the interval [l, u]. |
| 107 | */ |
| 108 | static __isl_give isl_basic_set *add_bounds(__isl_take isl_basic_set *bset, |
| 109 | isl_int *f, isl_int l, isl_int u) |
| 110 | { |
| 111 | int k; |
| 112 | isl_size total; |
| 113 | |
| 114 | total = isl_basic_set_dim(bset, type: isl_dim_all); |
| 115 | if (total < 0) |
| 116 | return isl_basic_set_free(bset); |
| 117 | bset = isl_basic_set_extend_constraints(base: bset, n_eq: 0, n_ineq: 2); |
| 118 | |
| 119 | k = isl_basic_set_alloc_inequality(bset); |
| 120 | if (k < 0) |
| 121 | goto error; |
| 122 | isl_seq_cpy(dst: bset->ineq[k], src: f, len: 1 + total); |
| 123 | isl_int_sub(bset->ineq[k][0], bset->ineq[k][0], l); |
| 124 | |
| 125 | k = isl_basic_set_alloc_inequality(bset); |
| 126 | if (k < 0) |
| 127 | goto error; |
| 128 | isl_seq_neg(dst: bset->ineq[k], src: f, len: 1 + total); |
| 129 | isl_int_add(bset->ineq[k][0], bset->ineq[k][0], u); |
| 130 | |
| 131 | return bset; |
| 132 | error: |
| 133 | isl_basic_set_free(bset); |
| 134 | return NULL; |
| 135 | } |
| 136 | |
| 137 | /* Find an integer point in "bset" that minimizes f (in any) such that |
| 138 | * the value of f lies inside the interval [l, u]. |
| 139 | * Return this integer point if it can be found. |
| 140 | * Otherwise, return sol. |
| 141 | * |
| 142 | * We perform a number of steps until l > u. |
| 143 | * In each step, we look for an integer point with value in either |
| 144 | * the whole interval [l, u] or half of the interval [l, l+floor(u-l-1/2)]. |
| 145 | * The choice depends on whether we have found an integer point in the |
| 146 | * previous step. If so, we look for the next point in half of the remaining |
| 147 | * interval. |
| 148 | * If we find a point, the current solution is updated and u is set |
| 149 | * to its value minus 1. |
| 150 | * If no point can be found, we update l to the upper bound of the interval |
| 151 | * we checked (u or l+floor(u-l-1/2)) plus 1. |
| 152 | */ |
| 153 | static __isl_give isl_vec *solve_ilp_search(__isl_keep isl_basic_set *bset, |
| 154 | isl_int *f, isl_int *opt, __isl_take isl_vec *sol, isl_int l, isl_int u) |
| 155 | { |
| 156 | isl_int tmp; |
| 157 | int divide = 1; |
| 158 | |
| 159 | isl_int_init(tmp); |
| 160 | |
| 161 | while (isl_int_le(l, u)) { |
| 162 | struct isl_basic_set *slice; |
| 163 | struct isl_vec *sample; |
| 164 | |
| 165 | if (!divide) |
| 166 | isl_int_set(tmp, u); |
| 167 | else { |
| 168 | isl_int_sub(tmp, u, l); |
| 169 | isl_int_fdiv_q_ui(tmp, tmp, 2); |
| 170 | isl_int_add(tmp, tmp, l); |
| 171 | } |
| 172 | slice = add_bounds(bset: isl_basic_set_copy(bset), f, l, u: tmp); |
| 173 | sample = isl_basic_set_sample_vec(bset: slice); |
| 174 | if (!sample) { |
| 175 | isl_vec_free(vec: sol); |
| 176 | sol = NULL; |
| 177 | break; |
| 178 | } |
| 179 | if (sample->size > 0) { |
| 180 | isl_vec_free(vec: sol); |
| 181 | sol = sample; |
| 182 | isl_seq_inner_product(p1: f, p2: sol->el, len: sol->size, prod: opt); |
| 183 | isl_int_sub_ui(u, *opt, 1); |
| 184 | divide = 1; |
| 185 | } else { |
| 186 | isl_vec_free(vec: sample); |
| 187 | if (!divide) |
| 188 | break; |
| 189 | isl_int_add_ui(l, tmp, 1); |
| 190 | divide = 0; |
| 191 | } |
| 192 | } |
| 193 | |
| 194 | isl_int_clear(tmp); |
| 195 | |
| 196 | return sol; |
| 197 | } |
| 198 | |
| 199 | /* Find an integer point in "bset" that minimizes f (if any). |
| 200 | * If sol_p is not NULL then the integer point is returned in *sol_p. |
| 201 | * The optimal value of f is returned in *opt. |
| 202 | * |
| 203 | * The algorithm maintains a currently best solution and an interval [l, u] |
| 204 | * of values of f for which integer solutions could potentially still be found. |
| 205 | * The initial value of the best solution so far is any solution. |
| 206 | * The initial value of l is minimal value of f over the rationals |
| 207 | * (rounded up to the nearest integer). |
| 208 | * The initial value of u is the value of f at the initial solution minus 1. |
| 209 | * |
| 210 | * We then call solve_ilp_search to perform a binary search on the interval. |
| 211 | */ |
| 212 | static enum isl_lp_result solve_ilp(__isl_keep isl_basic_set *bset, |
| 213 | isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p) |
| 214 | { |
| 215 | enum isl_lp_result res; |
| 216 | isl_int l, u; |
| 217 | struct isl_vec *sol; |
| 218 | |
| 219 | res = isl_basic_set_solve_lp(bset, max: 0, f, denom: bset->ctx->one, |
| 220 | opt, NULL, sol: &sol); |
| 221 | if (res == isl_lp_ok && isl_int_is_one(sol->el[0])) { |
| 222 | if (sol_p) |
| 223 | *sol_p = sol; |
| 224 | else |
| 225 | isl_vec_free(vec: sol); |
| 226 | return isl_lp_ok; |
| 227 | } |
| 228 | isl_vec_free(vec: sol); |
| 229 | if (res == isl_lp_error || res == isl_lp_empty) |
| 230 | return res; |
| 231 | |
| 232 | sol = initial_solution(bset, f); |
| 233 | if (!sol) |
| 234 | return isl_lp_error; |
| 235 | if (sol->size == 0) { |
| 236 | isl_vec_free(vec: sol); |
| 237 | return isl_lp_empty; |
| 238 | } |
| 239 | if (res == isl_lp_unbounded) { |
| 240 | isl_vec_free(vec: sol); |
| 241 | return isl_lp_unbounded; |
| 242 | } |
| 243 | |
| 244 | isl_int_init(l); |
| 245 | isl_int_init(u); |
| 246 | |
| 247 | isl_int_set(l, *opt); |
| 248 | |
| 249 | isl_seq_inner_product(p1: f, p2: sol->el, len: sol->size, prod: opt); |
| 250 | isl_int_sub_ui(u, *opt, 1); |
| 251 | |
| 252 | sol = solve_ilp_search(bset, f, opt, sol, l, u); |
| 253 | if (!sol) |
| 254 | res = isl_lp_error; |
| 255 | |
| 256 | isl_int_clear(l); |
| 257 | isl_int_clear(u); |
| 258 | |
| 259 | if (sol_p) |
| 260 | *sol_p = sol; |
| 261 | else |
| 262 | isl_vec_free(vec: sol); |
| 263 | |
| 264 | return res; |
| 265 | } |
| 266 | |
| 267 | static enum isl_lp_result solve_ilp_with_eq(__isl_keep isl_basic_set *bset, |
| 268 | int max, isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p) |
| 269 | { |
| 270 | isl_size dim; |
| 271 | enum isl_lp_result res; |
| 272 | struct isl_mat *T = NULL; |
| 273 | struct isl_vec *v; |
| 274 | |
| 275 | bset = isl_basic_set_copy(bset); |
| 276 | dim = isl_basic_set_dim(bset, type: isl_dim_all); |
| 277 | if (dim < 0) |
| 278 | goto error; |
| 279 | v = isl_vec_alloc(ctx: bset->ctx, size: 1 + dim); |
| 280 | if (!v) |
| 281 | goto error; |
| 282 | isl_seq_cpy(dst: v->el, src: f, len: 1 + dim); |
| 283 | bset = isl_basic_set_remove_equalities(bset, T: &T, NULL); |
| 284 | v = isl_vec_mat_product(vec: v, mat: isl_mat_copy(mat: T)); |
| 285 | if (!v) |
| 286 | goto error; |
| 287 | res = isl_basic_set_solve_ilp(bset, max, f: v->el, opt, sol_p); |
| 288 | isl_vec_free(vec: v); |
| 289 | if (res == isl_lp_ok && sol_p) { |
| 290 | *sol_p = isl_mat_vec_product(mat: T, vec: *sol_p); |
| 291 | if (!*sol_p) |
| 292 | res = isl_lp_error; |
| 293 | } else |
| 294 | isl_mat_free(mat: T); |
| 295 | isl_basic_set_free(bset); |
| 296 | return res; |
| 297 | error: |
| 298 | isl_mat_free(mat: T); |
| 299 | isl_basic_set_free(bset); |
| 300 | return isl_lp_error; |
| 301 | } |
| 302 | |
| 303 | /* Find an integer point in "bset" that minimizes (or maximizes if max is set) |
| 304 | * f (if any). |
| 305 | * If sol_p is not NULL then the integer point is returned in *sol_p. |
| 306 | * The optimal value of f is returned in *opt. |
| 307 | * |
| 308 | * If there is any equality among the points in "bset", then we first |
| 309 | * project it out. Otherwise, we continue with solve_ilp above. |
| 310 | */ |
| 311 | enum isl_lp_result isl_basic_set_solve_ilp(__isl_keep isl_basic_set *bset, |
| 312 | int max, isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p) |
| 313 | { |
| 314 | isl_size dim; |
| 315 | enum isl_lp_result res; |
| 316 | |
| 317 | if (sol_p) |
| 318 | *sol_p = NULL; |
| 319 | |
| 320 | if (isl_basic_set_check_no_params(bset) < 0) |
| 321 | return isl_lp_error; |
| 322 | |
| 323 | if (isl_basic_set_plain_is_empty(bset)) |
| 324 | return isl_lp_empty; |
| 325 | |
| 326 | if (bset->n_eq) |
| 327 | return solve_ilp_with_eq(bset, max, f, opt, sol_p); |
| 328 | |
| 329 | dim = isl_basic_set_dim(bset, type: isl_dim_all); |
| 330 | if (dim < 0) |
| 331 | return isl_lp_error; |
| 332 | |
| 333 | if (max) |
| 334 | isl_seq_neg(dst: f, src: f, len: 1 + dim); |
| 335 | |
| 336 | res = solve_ilp(bset, f, opt, sol_p); |
| 337 | |
| 338 | if (max) { |
| 339 | isl_seq_neg(dst: f, src: f, len: 1 + dim); |
| 340 | isl_int_neg(*opt, *opt); |
| 341 | } |
| 342 | |
| 343 | return res; |
| 344 | } |
| 345 | |
| 346 | static enum isl_lp_result basic_set_opt(__isl_keep isl_basic_set *bset, int max, |
| 347 | __isl_keep isl_aff *obj, isl_int *opt) |
| 348 | { |
| 349 | enum isl_lp_result res; |
| 350 | |
| 351 | if (!obj) |
| 352 | return isl_lp_error; |
| 353 | bset = isl_basic_set_copy(bset); |
| 354 | bset = isl_basic_set_underlying_set(bset); |
| 355 | res = isl_basic_set_solve_ilp(bset, max, f: obj->v->el + 1, opt, NULL); |
| 356 | isl_basic_set_free(bset); |
| 357 | return res; |
| 358 | } |
| 359 | |
| 360 | enum isl_lp_result isl_basic_set_opt(__isl_keep isl_basic_set *bset, int max, |
| 361 | __isl_keep isl_aff *obj, isl_int *opt) |
| 362 | { |
| 363 | int *exp1 = NULL; |
| 364 | int *exp2 = NULL; |
| 365 | isl_ctx *ctx; |
| 366 | isl_mat *bset_div = NULL; |
| 367 | isl_mat *div = NULL; |
| 368 | enum isl_lp_result res; |
| 369 | isl_size bset_n_div, obj_n_div; |
| 370 | |
| 371 | if (!bset || !obj) |
| 372 | return isl_lp_error; |
| 373 | |
| 374 | ctx = isl_aff_get_ctx(aff: obj); |
| 375 | if (!isl_space_is_equal(space1: bset->dim, space2: obj->ls->dim)) |
| 376 | isl_die(ctx, isl_error_invalid, |
| 377 | "spaces don't match" , return isl_lp_error); |
| 378 | if (!isl_int_is_one(obj->v->el[0])) |
| 379 | isl_die(ctx, isl_error_unsupported, |
| 380 | "expecting integer affine expression" , |
| 381 | return isl_lp_error); |
| 382 | |
| 383 | bset_n_div = isl_basic_set_dim(bset, type: isl_dim_div); |
| 384 | obj_n_div = isl_aff_dim(aff: obj, type: isl_dim_div); |
| 385 | if (bset_n_div < 0 || obj_n_div < 0) |
| 386 | return isl_lp_error; |
| 387 | if (bset_n_div == 0 && obj_n_div == 0) |
| 388 | return basic_set_opt(bset, max, obj, opt); |
| 389 | |
| 390 | bset = isl_basic_set_copy(bset); |
| 391 | obj = isl_aff_copy(aff: obj); |
| 392 | |
| 393 | bset_div = isl_basic_set_get_divs(bset); |
| 394 | exp1 = isl_alloc_array(ctx, int, bset_n_div); |
| 395 | exp2 = isl_alloc_array(ctx, int, obj_n_div); |
| 396 | if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2)) |
| 397 | goto error; |
| 398 | |
| 399 | div = isl_merge_divs(div1: bset_div, div2: obj->ls->div, exp1, exp2); |
| 400 | |
| 401 | bset = isl_basic_set_expand_divs(bset, div: isl_mat_copy(mat: div), exp: exp1); |
| 402 | obj = isl_aff_expand_divs(aff: obj, div: isl_mat_copy(mat: div), exp: exp2); |
| 403 | |
| 404 | res = basic_set_opt(bset, max, obj, opt); |
| 405 | |
| 406 | isl_mat_free(mat: bset_div); |
| 407 | isl_mat_free(mat: div); |
| 408 | free(ptr: exp1); |
| 409 | free(ptr: exp2); |
| 410 | isl_basic_set_free(bset); |
| 411 | isl_aff_free(aff: obj); |
| 412 | |
| 413 | return res; |
| 414 | error: |
| 415 | isl_mat_free(mat: div); |
| 416 | isl_mat_free(mat: bset_div); |
| 417 | free(ptr: exp1); |
| 418 | free(ptr: exp2); |
| 419 | isl_basic_set_free(bset); |
| 420 | isl_aff_free(aff: obj); |
| 421 | return isl_lp_error; |
| 422 | } |
| 423 | |
| 424 | /* Compute the minimum (maximum if max is set) of the integer affine |
| 425 | * expression obj over the points in set and put the result in *opt. |
| 426 | * |
| 427 | * The parameters are assumed to have been aligned. |
| 428 | */ |
| 429 | static enum isl_lp_result isl_set_opt_aligned(__isl_keep isl_set *set, int max, |
| 430 | __isl_keep isl_aff *obj, isl_int *opt) |
| 431 | { |
| 432 | int i; |
| 433 | enum isl_lp_result res; |
| 434 | int empty = 1; |
| 435 | isl_int opt_i; |
| 436 | |
| 437 | if (!set || !obj) |
| 438 | return isl_lp_error; |
| 439 | if (set->n == 0) |
| 440 | return isl_lp_empty; |
| 441 | |
| 442 | res = isl_basic_set_opt(bset: set->p[0], max, obj, opt); |
| 443 | if (res == isl_lp_error || res == isl_lp_unbounded) |
| 444 | return res; |
| 445 | if (set->n == 1) |
| 446 | return res; |
| 447 | if (res == isl_lp_ok) |
| 448 | empty = 0; |
| 449 | |
| 450 | isl_int_init(opt_i); |
| 451 | for (i = 1; i < set->n; ++i) { |
| 452 | res = isl_basic_set_opt(bset: set->p[i], max, obj, opt: &opt_i); |
| 453 | if (res == isl_lp_error || res == isl_lp_unbounded) { |
| 454 | isl_int_clear(opt_i); |
| 455 | return res; |
| 456 | } |
| 457 | if (res == isl_lp_empty) |
| 458 | continue; |
| 459 | empty = 0; |
| 460 | if (max ? isl_int_gt(opt_i, *opt) : isl_int_lt(opt_i, *opt)) |
| 461 | isl_int_set(*opt, opt_i); |
| 462 | } |
| 463 | isl_int_clear(opt_i); |
| 464 | |
| 465 | return empty ? isl_lp_empty : isl_lp_ok; |
| 466 | } |
| 467 | |
| 468 | /* Compute the minimum (maximum if max is set) of the integer affine |
| 469 | * expression obj over the points in set and put the result in *opt. |
| 470 | */ |
| 471 | enum isl_lp_result isl_set_opt(__isl_keep isl_set *set, int max, |
| 472 | __isl_keep isl_aff *obj, isl_int *opt) |
| 473 | { |
| 474 | enum isl_lp_result res; |
| 475 | isl_bool aligned; |
| 476 | |
| 477 | if (!set || !obj) |
| 478 | return isl_lp_error; |
| 479 | |
| 480 | aligned = isl_set_space_has_equal_params(set, space: obj->ls->dim); |
| 481 | if (aligned < 0) |
| 482 | return isl_lp_error; |
| 483 | if (aligned) |
| 484 | return isl_set_opt_aligned(set, max, obj, opt); |
| 485 | |
| 486 | set = isl_set_copy(set); |
| 487 | obj = isl_aff_copy(aff: obj); |
| 488 | set = isl_set_align_params(set, model: isl_aff_get_domain_space(aff: obj)); |
| 489 | obj = isl_aff_align_params(aff: obj, model: isl_set_get_space(set)); |
| 490 | |
| 491 | res = isl_set_opt_aligned(set, max, obj, opt); |
| 492 | |
| 493 | isl_set_free(set); |
| 494 | isl_aff_free(aff: obj); |
| 495 | |
| 496 | return res; |
| 497 | } |
| 498 | |
| 499 | /* Convert the result of a function that returns an isl_lp_result |
| 500 | * to an isl_val. The numerator of "v" is set to the optimal value |
| 501 | * if lp_res is isl_lp_ok. "max" is set if a maximum was computed. |
| 502 | * |
| 503 | * Return "v" with denominator set to 1 if lp_res is isl_lp_ok. |
| 504 | * Return NULL on error. |
| 505 | * Return a NaN if lp_res is isl_lp_empty. |
| 506 | * Return infinity or negative infinity if lp_res is isl_lp_unbounded, |
| 507 | * depending on "max". |
| 508 | */ |
| 509 | static __isl_give isl_val *convert_lp_result(enum isl_lp_result lp_res, |
| 510 | __isl_take isl_val *v, int max) |
| 511 | { |
| 512 | isl_ctx *ctx; |
| 513 | |
| 514 | if (lp_res == isl_lp_ok) { |
| 515 | isl_int_set_si(v->d, 1); |
| 516 | return isl_val_normalize(v); |
| 517 | } |
| 518 | ctx = isl_val_get_ctx(val: v); |
| 519 | isl_val_free(v); |
| 520 | if (lp_res == isl_lp_error) |
| 521 | return NULL; |
| 522 | if (lp_res == isl_lp_empty) |
| 523 | return isl_val_nan(ctx); |
| 524 | if (max) |
| 525 | return isl_val_infty(ctx); |
| 526 | else |
| 527 | return isl_val_neginfty(ctx); |
| 528 | } |
| 529 | |
| 530 | /* Return the minimum (maximum if max is set) of the integer affine |
| 531 | * expression "obj" over the points in "bset". |
| 532 | * |
| 533 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 534 | * NaN if "bset" is empty. |
| 535 | * |
| 536 | * Call isl_basic_set_opt and translate the results. |
| 537 | */ |
| 538 | __isl_give isl_val *isl_basic_set_opt_val(__isl_keep isl_basic_set *bset, |
| 539 | int max, __isl_keep isl_aff *obj) |
| 540 | { |
| 541 | isl_ctx *ctx; |
| 542 | isl_val *res; |
| 543 | enum isl_lp_result lp_res; |
| 544 | |
| 545 | if (!bset || !obj) |
| 546 | return NULL; |
| 547 | |
| 548 | ctx = isl_aff_get_ctx(aff: obj); |
| 549 | res = isl_val_alloc(ctx); |
| 550 | if (!res) |
| 551 | return NULL; |
| 552 | lp_res = isl_basic_set_opt(bset, max, obj, opt: &res->n); |
| 553 | return convert_lp_result(lp_res, v: res, max); |
| 554 | } |
| 555 | |
| 556 | /* Return the maximum of the integer affine |
| 557 | * expression "obj" over the points in "bset". |
| 558 | * |
| 559 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 560 | * NaN if "bset" is empty. |
| 561 | */ |
| 562 | __isl_give isl_val *isl_basic_set_max_val(__isl_keep isl_basic_set *bset, |
| 563 | __isl_keep isl_aff *obj) |
| 564 | { |
| 565 | return isl_basic_set_opt_val(bset, max: 1, obj); |
| 566 | } |
| 567 | |
| 568 | /* Return the minimum (maximum if max is set) of the integer affine |
| 569 | * expression "obj" over the points in "set". |
| 570 | * |
| 571 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 572 | * NaN if "set" is empty. |
| 573 | * |
| 574 | * Call isl_set_opt and translate the results. |
| 575 | */ |
| 576 | __isl_give isl_val *isl_set_opt_val(__isl_keep isl_set *set, int max, |
| 577 | __isl_keep isl_aff *obj) |
| 578 | { |
| 579 | isl_ctx *ctx; |
| 580 | isl_val *res; |
| 581 | enum isl_lp_result lp_res; |
| 582 | |
| 583 | if (!set || !obj) |
| 584 | return NULL; |
| 585 | |
| 586 | ctx = isl_aff_get_ctx(aff: obj); |
| 587 | res = isl_val_alloc(ctx); |
| 588 | if (!res) |
| 589 | return NULL; |
| 590 | lp_res = isl_set_opt(set, max, obj, opt: &res->n); |
| 591 | return convert_lp_result(lp_res, v: res, max); |
| 592 | } |
| 593 | |
| 594 | /* Return the minimum of the integer affine |
| 595 | * expression "obj" over the points in "set". |
| 596 | * |
| 597 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 598 | * NaN if "set" is empty. |
| 599 | */ |
| 600 | __isl_give isl_val *isl_set_min_val(__isl_keep isl_set *set, |
| 601 | __isl_keep isl_aff *obj) |
| 602 | { |
| 603 | return isl_set_opt_val(set, max: 0, obj); |
| 604 | } |
| 605 | |
| 606 | /* Return the maximum of the integer affine |
| 607 | * expression "obj" over the points in "set". |
| 608 | * |
| 609 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 610 | * NaN if "set" is empty. |
| 611 | */ |
| 612 | __isl_give isl_val *isl_set_max_val(__isl_keep isl_set *set, |
| 613 | __isl_keep isl_aff *obj) |
| 614 | { |
| 615 | return isl_set_opt_val(set, max: 1, obj); |
| 616 | } |
| 617 | |
| 618 | /* Return the optimum (min or max depending on "max") of "v1" and "v2", |
| 619 | * where either may be NaN, signifying an uninitialized value. |
| 620 | * That is, if either is NaN, then return the other one. |
| 621 | */ |
| 622 | static __isl_give isl_val *val_opt(__isl_take isl_val *v1, |
| 623 | __isl_take isl_val *v2, int max) |
| 624 | { |
| 625 | if (!v1 || !v2) |
| 626 | goto error; |
| 627 | if (isl_val_is_nan(v: v1)) { |
| 628 | isl_val_free(v: v1); |
| 629 | return v2; |
| 630 | } |
| 631 | if (isl_val_is_nan(v: v2)) { |
| 632 | isl_val_free(v: v2); |
| 633 | return v1; |
| 634 | } |
| 635 | if (max) |
| 636 | return isl_val_max(v1, v2); |
| 637 | else |
| 638 | return isl_val_min(v1, v2); |
| 639 | error: |
| 640 | isl_val_free(v: v1); |
| 641 | isl_val_free(v: v2); |
| 642 | return NULL; |
| 643 | } |
| 644 | |
| 645 | /* Internal data structure for isl_pw_aff_opt_val. |
| 646 | * |
| 647 | * "max" is set if the maximum should be computed. |
| 648 | * "res" contains the current optimum and is initialized to NaN. |
| 649 | */ |
| 650 | struct isl_pw_aff_opt_data { |
| 651 | int max; |
| 652 | |
| 653 | isl_val *res; |
| 654 | }; |
| 655 | |
| 656 | /* Update the optimum in data->res with respect to the affine function |
| 657 | * "aff" defined over "set". |
| 658 | */ |
| 659 | static isl_stat piece_opt(__isl_take isl_set *set, __isl_take isl_aff *aff, |
| 660 | void *user) |
| 661 | { |
| 662 | struct isl_pw_aff_opt_data *data = user; |
| 663 | isl_val *opt; |
| 664 | |
| 665 | opt = isl_set_opt_val(set, max: data->max, obj: aff); |
| 666 | isl_set_free(set); |
| 667 | isl_aff_free(aff); |
| 668 | |
| 669 | data->res = val_opt(v1: data->res, v2: opt, max: data->max); |
| 670 | if (!data->res) |
| 671 | return isl_stat_error; |
| 672 | |
| 673 | return isl_stat_ok; |
| 674 | } |
| 675 | |
| 676 | /* Return the minimum (maximum if "max" is set) of the integer piecewise affine |
| 677 | * expression "pa" over its definition domain. |
| 678 | * |
| 679 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 680 | * NaN if the domain of "pa" is empty. |
| 681 | * |
| 682 | * Initialize the result to NaN and then update it for each of the pieces |
| 683 | * in "pa". |
| 684 | */ |
| 685 | static __isl_give isl_val *isl_pw_aff_opt_val(__isl_take isl_pw_aff *pa, |
| 686 | int max) |
| 687 | { |
| 688 | struct isl_pw_aff_opt_data data = { max }; |
| 689 | |
| 690 | data.res = isl_val_nan(ctx: isl_pw_aff_get_ctx(pwaff: pa)); |
| 691 | if (isl_pw_aff_foreach_piece(pwaff: pa, fn: &piece_opt, user: &data) < 0) |
| 692 | data.res = isl_val_free(v: data.res); |
| 693 | |
| 694 | isl_pw_aff_free(pwaff: pa); |
| 695 | return data.res; |
| 696 | } |
| 697 | |
| 698 | #undef TYPE |
| 699 | #define TYPE isl_pw_aff |
| 700 | #include "isl_ilp_opt_fn_val_templ.c" |
| 701 | |
| 702 | #undef TYPE |
| 703 | #define TYPE isl_pw_multi_aff |
| 704 | #include "isl_ilp_opt_multi_val_templ.c" |
| 705 | |
| 706 | #undef TYPE |
| 707 | #define TYPE isl_multi_pw_aff |
| 708 | #include "isl_ilp_opt_multi_val_templ.c" |
| 709 | |
| 710 | /* Internal data structure for isl_union_pw_aff_opt_val. |
| 711 | * |
| 712 | * "max" is set if the maximum should be computed. |
| 713 | * "res" contains the current optimum and is initialized to NaN. |
| 714 | */ |
| 715 | struct isl_union_pw_aff_opt_data { |
| 716 | int max; |
| 717 | |
| 718 | isl_val *res; |
| 719 | }; |
| 720 | |
| 721 | /* Update the optimum in data->res with the optimum of "pa". |
| 722 | */ |
| 723 | static isl_stat pw_aff_opt(__isl_take isl_pw_aff *pa, void *user) |
| 724 | { |
| 725 | struct isl_union_pw_aff_opt_data *data = user; |
| 726 | isl_val *opt; |
| 727 | |
| 728 | opt = isl_pw_aff_opt_val(pa, max: data->max); |
| 729 | |
| 730 | data->res = val_opt(v1: data->res, v2: opt, max: data->max); |
| 731 | if (!data->res) |
| 732 | return isl_stat_error; |
| 733 | |
| 734 | return isl_stat_ok; |
| 735 | } |
| 736 | |
| 737 | /* Return the minimum (maximum if "max" is set) of the integer piecewise affine |
| 738 | * expression "upa" over its definition domain. |
| 739 | * |
| 740 | * Return infinity or negative infinity if the optimal value is unbounded and |
| 741 | * NaN if the domain of the expression is empty. |
| 742 | * |
| 743 | * Initialize the result to NaN and then update it |
| 744 | * for each of the piecewise affine expressions in "upa". |
| 745 | */ |
| 746 | static __isl_give isl_val *isl_union_pw_aff_opt_val( |
| 747 | __isl_take isl_union_pw_aff *upa, int max) |
| 748 | { |
| 749 | struct isl_union_pw_aff_opt_data data = { max }; |
| 750 | |
| 751 | data.res = isl_val_nan(ctx: isl_union_pw_aff_get_ctx(upa)); |
| 752 | if (isl_union_pw_aff_foreach_pw_aff(upa, fn: &pw_aff_opt, user: &data) < 0) |
| 753 | data.res = isl_val_free(v: data.res); |
| 754 | isl_union_pw_aff_free(upa); |
| 755 | |
| 756 | return data.res; |
| 757 | } |
| 758 | |
| 759 | #undef TYPE |
| 760 | #define TYPE isl_union_pw_aff |
| 761 | #include "isl_ilp_opt_fn_val_templ.c" |
| 762 | |
| 763 | /* Return a list of minima (maxima if "max" is set) |
| 764 | * for each of the expressions in "mupa" over their domains. |
| 765 | * |
| 766 | * An element in the list is infinity or negative infinity if the optimal |
| 767 | * value of the corresponding expression is unbounded and |
| 768 | * NaN if the domain of the expression is empty. |
| 769 | * |
| 770 | * Iterate over all the expressions in "mupa" and collect the results. |
| 771 | */ |
| 772 | static __isl_give isl_multi_val *isl_multi_union_pw_aff_opt_multi_val( |
| 773 | __isl_take isl_multi_union_pw_aff *mupa, int max) |
| 774 | { |
| 775 | int i; |
| 776 | isl_size n; |
| 777 | isl_multi_val *mv; |
| 778 | |
| 779 | n = isl_multi_union_pw_aff_size(multi: mupa); |
| 780 | if (n < 0) |
| 781 | mupa = isl_multi_union_pw_aff_free(multi: mupa); |
| 782 | if (!mupa) |
| 783 | return NULL; |
| 784 | |
| 785 | mv = isl_multi_val_zero(space: isl_multi_union_pw_aff_get_space(multi: mupa)); |
| 786 | |
| 787 | for (i = 0; i < n; ++i) { |
| 788 | isl_val *v; |
| 789 | isl_union_pw_aff *upa; |
| 790 | |
| 791 | upa = isl_multi_union_pw_aff_get_union_pw_aff(multi: mupa, pos: i); |
| 792 | v = isl_union_pw_aff_opt_val(upa, max); |
| 793 | mv = isl_multi_val_set_val(multi: mv, pos: i, el: v); |
| 794 | } |
| 795 | |
| 796 | isl_multi_union_pw_aff_free(multi: mupa); |
| 797 | return mv; |
| 798 | } |
| 799 | |
| 800 | /* Return a list of minima (maxima if "max" is set) over the points in "uset" |
| 801 | * for each of the expressions in "obj". |
| 802 | * |
| 803 | * An element in the list is infinity or negative infinity if the optimal |
| 804 | * value of the corresponding expression is unbounded and |
| 805 | * NaN if the intersection of "uset" with the domain of the expression |
| 806 | * is empty. |
| 807 | */ |
| 808 | static __isl_give isl_multi_val *isl_union_set_opt_multi_union_pw_aff( |
| 809 | __isl_keep isl_union_set *uset, int max, |
| 810 | __isl_keep isl_multi_union_pw_aff *obj) |
| 811 | { |
| 812 | uset = isl_union_set_copy(uset); |
| 813 | obj = isl_multi_union_pw_aff_copy(multi: obj); |
| 814 | obj = isl_multi_union_pw_aff_intersect_domain(mupa: obj, uset); |
| 815 | return isl_multi_union_pw_aff_opt_multi_val(mupa: obj, max); |
| 816 | } |
| 817 | |
| 818 | /* Return a list of minima over the points in "uset" |
| 819 | * for each of the expressions in "obj". |
| 820 | * |
| 821 | * An element in the list is infinity or negative infinity if the optimal |
| 822 | * value of the corresponding expression is unbounded and |
| 823 | * NaN if the intersection of "uset" with the domain of the expression |
| 824 | * is empty. |
| 825 | */ |
| 826 | __isl_give isl_multi_val *isl_union_set_min_multi_union_pw_aff( |
| 827 | __isl_keep isl_union_set *uset, __isl_keep isl_multi_union_pw_aff *obj) |
| 828 | { |
| 829 | return isl_union_set_opt_multi_union_pw_aff(uset, max: 0, obj); |
| 830 | } |
| 831 | |
| 832 | /* Return a list of minima |
| 833 | * for each of the expressions in "mupa" over their domains. |
| 834 | * |
| 835 | * An element in the list is negative infinity if the optimal |
| 836 | * value of the corresponding expression is unbounded and |
| 837 | * NaN if the domain of the expression is empty. |
| 838 | */ |
| 839 | __isl_give isl_multi_val *isl_multi_union_pw_aff_min_multi_val( |
| 840 | __isl_take isl_multi_union_pw_aff *mupa) |
| 841 | { |
| 842 | return isl_multi_union_pw_aff_opt_multi_val(mupa, max: 0); |
| 843 | } |
| 844 | |
| 845 | /* Return a list of maxima |
| 846 | * for each of the expressions in "mupa" over their domains. |
| 847 | * |
| 848 | * An element in the list is infinity if the optimal |
| 849 | * value of the corresponding expression is unbounded and |
| 850 | * NaN if the domain of the expression is empty. |
| 851 | */ |
| 852 | __isl_give isl_multi_val *isl_multi_union_pw_aff_max_multi_val( |
| 853 | __isl_take isl_multi_union_pw_aff *mupa) |
| 854 | { |
| 855 | return isl_multi_union_pw_aff_opt_multi_val(mupa, max: 1); |
| 856 | } |
| 857 | |
| 858 | #undef BASE |
| 859 | #define BASE basic_set |
| 860 | #include "isl_ilp_opt_val_templ.c" |
| 861 | |
| 862 | /* Return the maximal value attained by the given set dimension, |
| 863 | * independently of the parameter values and of any other dimensions. |
| 864 | * |
| 865 | * Return infinity if the optimal value is unbounded and |
| 866 | * NaN if "bset" is empty. |
| 867 | */ |
| 868 | __isl_give isl_val *isl_basic_set_dim_max_val(__isl_take isl_basic_set *bset, |
| 869 | int pos) |
| 870 | { |
| 871 | return isl_basic_set_dim_opt_val(set: bset, max: 1, pos); |
| 872 | } |
| 873 | |
| 874 | #undef BASE |
| 875 | #define BASE set |
| 876 | #include "isl_ilp_opt_val_templ.c" |
| 877 | |
| 878 | /* Return the minimal value attained by the given set dimension, |
| 879 | * independently of the parameter values and of any other dimensions. |
| 880 | * |
| 881 | * Return negative infinity if the optimal value is unbounded and |
| 882 | * NaN if "set" is empty. |
| 883 | */ |
| 884 | __isl_give isl_val *isl_set_dim_min_val(__isl_take isl_set *set, int pos) |
| 885 | { |
| 886 | return isl_set_dim_opt_val(set, max: 0, pos); |
| 887 | } |
| 888 | |
| 889 | /* Return the maximal value attained by the given set dimension, |
| 890 | * independently of the parameter values and of any other dimensions. |
| 891 | * |
| 892 | * Return infinity if the optimal value is unbounded and |
| 893 | * NaN if "set" is empty. |
| 894 | */ |
| 895 | __isl_give isl_val *isl_set_dim_max_val(__isl_take isl_set *set, int pos) |
| 896 | { |
| 897 | return isl_set_dim_opt_val(set, max: 1, pos); |
| 898 | } |
| 899 | |