Line data Source code
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/lp.h>
13 : #include <isl_seq.h>
14 : #include "isl_tab.h"
15 : #include <isl_options_private.h>
16 : #include <isl_local_space_private.h>
17 : #include <isl_aff_private.h>
18 : #include <isl_mat_private.h>
19 : #include <isl_val_private.h>
20 : #include <isl_vec_private.h>
21 :
22 : #include <bset_to_bmap.c>
23 : #include <set_to_map.c>
24 :
25 2340004929 : enum isl_lp_result isl_tab_solve_lp(__isl_keep isl_basic_map *bmap,
26 : int maximize, isl_int *f, isl_int denom, isl_int *opt,
27 : isl_int *opt_denom, __isl_give isl_vec **sol)
28 : {
29 : struct isl_tab *tab;
30 : enum isl_lp_result res;
31 2340004929 : unsigned dim = isl_basic_map_total_dim(bmap);
32 :
33 2340004929 : if (maximize)
34 0 : isl_seq_neg(f, f, 1 + dim);
35 :
36 2340004929 : bmap = isl_basic_map_gauss(bmap, NULL);
37 2340004929 : tab = isl_tab_from_basic_map(bmap, 0);
38 2340004929 : res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
39 2340004929 : if (res == isl_lp_ok && sol) {
40 0 : *sol = isl_tab_get_sample_value(tab);
41 0 : if (!*sol)
42 0 : res = isl_lp_error;
43 : }
44 2340004929 : isl_tab_free(tab);
45 :
46 2340004929 : if (maximize)
47 0 : isl_seq_neg(f, f, 1 + dim);
48 2340004929 : if (maximize && opt)
49 0 : isl_int_neg(*opt, *opt);
50 :
51 2340004929 : return res;
52 : }
53 :
54 : /* Given a basic map "bmap" and an affine combination of the variables "f"
55 : * with denominator "denom", set *opt / *opt_denom to the minimal
56 : * (or maximal if "maximize" is true) value attained by f/d over "bmap",
57 : * assuming the basic map is not empty and the expression cannot attain
58 : * arbitrarily small (or large) values.
59 : * If opt_denom is NULL, then *opt is rounded up (or down)
60 : * to the nearest integer.
61 : * The return value reflects the nature of the result (empty, unbounded,
62 : * minimal or maximal value returned in *opt).
63 : */
64 2340004929 : enum isl_lp_result isl_basic_map_solve_lp(__isl_keep isl_basic_map *bmap,
65 : int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
66 : __isl_give isl_vec **sol)
67 : {
68 2340004929 : if (sol)
69 0 : *sol = NULL;
70 :
71 2340004929 : if (!bmap)
72 0 : return isl_lp_error;
73 :
74 2340004929 : return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
75 : }
76 :
77 2340004929 : enum isl_lp_result isl_basic_set_solve_lp(struct isl_basic_set *bset, int max,
78 : isl_int *f, isl_int d, isl_int *opt,
79 : isl_int *opt_denom,
80 : struct isl_vec **sol)
81 : {
82 2340004929 : return isl_basic_map_solve_lp(bset_to_bmap(bset), max,
83 : f, d, opt, opt_denom, sol);
84 : }
85 :
86 0 : enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
87 : isl_int *f, isl_int d, isl_int *opt,
88 : isl_int *opt_denom,
89 : struct isl_vec **sol)
90 : {
91 : int i;
92 : isl_int o;
93 : isl_int t;
94 : isl_int opt_i;
95 : isl_int opt_denom_i;
96 : enum isl_lp_result res;
97 : int max_div;
98 0 : isl_vec *v = NULL;
99 :
100 0 : if (!map)
101 0 : return isl_lp_error;
102 0 : if (map->n == 0)
103 0 : return isl_lp_empty;
104 :
105 0 : max_div = 0;
106 0 : for (i = 0; i < map->n; ++i)
107 0 : if (map->p[i]->n_div > max_div)
108 0 : max_div = map->p[i]->n_div;
109 0 : if (max_div > 0) {
110 0 : unsigned total = isl_space_dim(map->dim, isl_dim_all);
111 0 : v = isl_vec_alloc(map->ctx, 1 + total + max_div);
112 0 : if (!v)
113 0 : return isl_lp_error;
114 0 : isl_seq_cpy(v->el, f, 1 + total);
115 0 : isl_seq_clr(v->el + 1 + total, max_div);
116 0 : f = v->el;
117 : }
118 :
119 0 : if (!opt && map->n > 1 && sol) {
120 0 : isl_int_init(o);
121 0 : opt = &o;
122 : }
123 0 : if (map->n > 0)
124 0 : isl_int_init(opt_i);
125 0 : if (map->n > 0 && opt_denom) {
126 0 : isl_int_init(opt_denom_i);
127 0 : isl_int_init(t);
128 : }
129 :
130 0 : res = isl_basic_map_solve_lp(map->p[0], max, f, d,
131 : opt, opt_denom, sol);
132 0 : if (res == isl_lp_error || res == isl_lp_unbounded)
133 : goto done;
134 :
135 0 : if (sol)
136 0 : *sol = NULL;
137 :
138 0 : for (i = 1; i < map->n; ++i) {
139 0 : isl_vec *sol_i = NULL;
140 : enum isl_lp_result res_i;
141 : int better;
142 :
143 0 : res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
144 : &opt_i,
145 : opt_denom ? &opt_denom_i : NULL,
146 : sol ? &sol_i : NULL);
147 0 : if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
148 0 : res = res_i;
149 0 : goto done;
150 : }
151 0 : if (res_i == isl_lp_empty)
152 0 : continue;
153 0 : if (res == isl_lp_empty) {
154 0 : better = 1;
155 0 : } else if (!opt_denom) {
156 0 : if (max)
157 0 : better = isl_int_gt(opt_i, *opt);
158 : else
159 0 : better = isl_int_lt(opt_i, *opt);
160 : } else {
161 0 : isl_int_mul(t, opt_i, *opt_denom);
162 0 : isl_int_submul(t, *opt, opt_denom_i);
163 0 : if (max)
164 0 : better = isl_int_is_pos(t);
165 : else
166 0 : better = isl_int_is_neg(t);
167 : }
168 0 : if (better) {
169 0 : res = res_i;
170 0 : if (opt)
171 0 : isl_int_set(*opt, opt_i);
172 0 : if (opt_denom)
173 0 : isl_int_set(*opt_denom, opt_denom_i);
174 0 : if (sol) {
175 0 : isl_vec_free(*sol);
176 0 : *sol = sol_i;
177 : }
178 : } else
179 0 : isl_vec_free(sol_i);
180 : }
181 :
182 : done:
183 0 : isl_vec_free(v);
184 0 : if (map->n > 0 && opt_denom) {
185 0 : isl_int_clear(opt_denom_i);
186 0 : isl_int_clear(t);
187 : }
188 0 : if (map->n > 0)
189 0 : isl_int_clear(opt_i);
190 0 : if (opt == &o)
191 0 : isl_int_clear(o);
192 0 : return res;
193 : }
194 :
195 0 : enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
196 : isl_int *f, isl_int d, isl_int *opt,
197 : isl_int *opt_denom,
198 : struct isl_vec **sol)
199 : {
200 0 : return isl_map_solve_lp(set_to_map(set), max,
201 : f, d, opt, opt_denom, sol);
202 : }
203 :
204 : /* Return the optimal (rational) value of "obj" over "bset", assuming
205 : * that "obj" and "bset" have aligned parameters and divs.
206 : * If "max" is set, then the maximal value is computed.
207 : * Otherwise, the minimal value is computed.
208 : *
209 : * Return infinity or negative infinity if the optimal value is unbounded and
210 : * NaN if "bset" is empty.
211 : *
212 : * Call isl_basic_set_solve_lp and translate the results.
213 : */
214 0 : static __isl_give isl_val *basic_set_opt_lp(
215 : __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
216 : {
217 : isl_ctx *ctx;
218 : isl_val *res;
219 : enum isl_lp_result lp_res;
220 :
221 0 : if (!bset || !obj)
222 0 : return NULL;
223 :
224 0 : ctx = isl_aff_get_ctx(obj);
225 0 : res = isl_val_alloc(ctx);
226 0 : if (!res)
227 0 : return NULL;
228 0 : lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
229 0 : obj->v->el[0], &res->n, &res->d, NULL);
230 0 : if (lp_res == isl_lp_ok)
231 0 : return isl_val_normalize(res);
232 0 : isl_val_free(res);
233 0 : if (lp_res == isl_lp_error)
234 0 : return NULL;
235 0 : if (lp_res == isl_lp_empty)
236 0 : return isl_val_nan(ctx);
237 0 : if (max)
238 0 : return isl_val_infty(ctx);
239 : else
240 0 : return isl_val_neginfty(ctx);
241 : }
242 :
243 : /* Return the optimal (rational) value of "obj" over "bset", assuming
244 : * that "obj" and "bset" have aligned parameters.
245 : * If "max" is set, then the maximal value is computed.
246 : * Otherwise, the minimal value is computed.
247 : *
248 : * Return infinity or negative infinity if the optimal value is unbounded and
249 : * NaN if "bset" is empty.
250 : *
251 : * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
252 : */
253 0 : static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
254 : __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
255 : {
256 0 : int *exp1 = NULL;
257 0 : int *exp2 = NULL;
258 : isl_ctx *ctx;
259 0 : isl_mat *bset_div = NULL;
260 0 : isl_mat *div = NULL;
261 : isl_val *res;
262 : int bset_n_div, obj_n_div;
263 :
264 0 : if (!bset || !obj)
265 0 : return NULL;
266 :
267 0 : ctx = isl_aff_get_ctx(obj);
268 0 : if (!isl_space_is_equal(bset->dim, obj->ls->dim))
269 0 : isl_die(ctx, isl_error_invalid,
270 : "spaces don't match", return NULL);
271 :
272 0 : bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
273 0 : obj_n_div = isl_aff_dim(obj, isl_dim_div);
274 0 : if (bset_n_div == 0 && obj_n_div == 0)
275 0 : return basic_set_opt_lp(bset, max, obj);
276 :
277 0 : bset = isl_basic_set_copy(bset);
278 0 : obj = isl_aff_copy(obj);
279 :
280 0 : bset_div = isl_basic_set_get_divs(bset);
281 0 : exp1 = isl_alloc_array(ctx, int, bset_n_div);
282 0 : exp2 = isl_alloc_array(ctx, int, obj_n_div);
283 0 : if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
284 : goto error;
285 :
286 0 : div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
287 :
288 0 : bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
289 0 : obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
290 :
291 0 : res = basic_set_opt_lp(bset, max, obj);
292 :
293 0 : isl_mat_free(bset_div);
294 0 : isl_mat_free(div);
295 0 : free(exp1);
296 0 : free(exp2);
297 0 : isl_basic_set_free(bset);
298 0 : isl_aff_free(obj);
299 :
300 0 : return res;
301 : error:
302 0 : isl_mat_free(div);
303 0 : isl_mat_free(bset_div);
304 0 : free(exp1);
305 0 : free(exp2);
306 0 : isl_basic_set_free(bset);
307 0 : isl_aff_free(obj);
308 0 : return NULL;
309 : }
310 :
311 : /* Return the optimal (rational) value of "obj" over "bset".
312 : * If "max" is set, then the maximal value is computed.
313 : * Otherwise, the minimal value is computed.
314 : *
315 : * Return infinity or negative infinity if the optimal value is unbounded and
316 : * NaN if "bset" is empty.
317 : */
318 0 : static __isl_give isl_val *isl_basic_set_opt_lp_val(
319 : __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
320 : {
321 : isl_bool equal;
322 : isl_val *res;
323 :
324 0 : if (!bset || !obj)
325 0 : return NULL;
326 :
327 0 : equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
328 0 : if (equal < 0)
329 0 : return NULL;
330 0 : if (equal)
331 0 : return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
332 :
333 0 : bset = isl_basic_set_copy(bset);
334 0 : obj = isl_aff_copy(obj);
335 0 : bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
336 0 : obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
337 :
338 0 : res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
339 :
340 0 : isl_basic_set_free(bset);
341 0 : isl_aff_free(obj);
342 :
343 0 : return res;
344 : }
345 :
346 : /* Return the minimal (rational) value of "obj" over "bset".
347 : *
348 : * Return negative infinity if the minimal value is unbounded and
349 : * NaN if "bset" is empty.
350 : */
351 0 : __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
352 : __isl_keep isl_aff *obj)
353 : {
354 0 : return isl_basic_set_opt_lp_val(bset, 0, obj);
355 : }
356 :
357 : /* Return the maximal (rational) value of "obj" over "bset".
358 : *
359 : * Return infinity if the maximal value is unbounded and
360 : * NaN if "bset" is empty.
361 : */
362 0 : __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
363 : __isl_keep isl_aff *obj)
364 : {
365 0 : return isl_basic_set_opt_lp_val(bset, 1, obj);
366 : }
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