Merge branch 'maint'
[isl.git] / isl_lp.c
blob0c2f5ff812b2994ec6b30a41bb806774e9019e8f
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
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>
22 #include <bset_to_bmap.c>
23 #include <set_to_map.c>
25 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)
29 struct isl_tab *tab;
30 enum isl_lp_result res;
31 unsigned dim = isl_basic_map_total_dim(bmap);
33 if (maximize)
34 isl_seq_neg(f, f, 1 + dim);
36 bmap = isl_basic_map_gauss(bmap, NULL);
37 tab = isl_tab_from_basic_map(bmap, 0);
38 res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
39 if (res == isl_lp_ok && sol) {
40 *sol = isl_tab_get_sample_value(tab);
41 if (!*sol)
42 res = isl_lp_error;
44 isl_tab_free(tab);
46 if (maximize)
47 isl_seq_neg(f, f, 1 + dim);
48 if (maximize && opt)
49 isl_int_neg(*opt, *opt);
51 return res;
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).
64 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)
68 if (sol)
69 *sol = NULL;
71 if (!bmap)
72 return isl_lp_error;
74 return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
77 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)
82 return isl_basic_map_solve_lp(bset_to_bmap(bset), max,
83 f, d, opt, opt_denom, sol);
86 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)
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 isl_vec *v = NULL;
100 if (!map)
101 return isl_lp_error;
102 if (map->n == 0)
103 return isl_lp_empty;
105 max_div = 0;
106 for (i = 0; i < map->n; ++i)
107 if (map->p[i]->n_div > max_div)
108 max_div = map->p[i]->n_div;
109 if (max_div > 0) {
110 unsigned total = isl_space_dim(map->dim, isl_dim_all);
111 v = isl_vec_alloc(map->ctx, 1 + total + max_div);
112 if (!v)
113 return isl_lp_error;
114 isl_seq_cpy(v->el, f, 1 + total);
115 isl_seq_clr(v->el + 1 + total, max_div);
116 f = v->el;
119 if (!opt && map->n > 1 && sol) {
120 isl_int_init(o);
121 opt = &o;
123 if (map->n > 0)
124 isl_int_init(opt_i);
125 if (map->n > 0 && opt_denom) {
126 isl_int_init(opt_denom_i);
127 isl_int_init(t);
130 res = isl_basic_map_solve_lp(map->p[0], max, f, d,
131 opt, opt_denom, sol);
132 if (res == isl_lp_error || res == isl_lp_unbounded)
133 goto done;
135 if (sol)
136 *sol = NULL;
138 for (i = 1; i < map->n; ++i) {
139 isl_vec *sol_i = NULL;
140 enum isl_lp_result res_i;
141 int better;
143 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 if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
148 res = res_i;
149 goto done;
151 if (res_i == isl_lp_empty)
152 continue;
153 if (res == isl_lp_empty) {
154 better = 1;
155 } else if (!opt_denom) {
156 if (max)
157 better = isl_int_gt(opt_i, *opt);
158 else
159 better = isl_int_lt(opt_i, *opt);
160 } else {
161 isl_int_mul(t, opt_i, *opt_denom);
162 isl_int_submul(t, *opt, opt_denom_i);
163 if (max)
164 better = isl_int_is_pos(t);
165 else
166 better = isl_int_is_neg(t);
168 if (better) {
169 res = res_i;
170 if (opt)
171 isl_int_set(*opt, opt_i);
172 if (opt_denom)
173 isl_int_set(*opt_denom, opt_denom_i);
174 if (sol) {
175 isl_vec_free(*sol);
176 *sol = sol_i;
178 } else
179 isl_vec_free(sol_i);
182 done:
183 isl_vec_free(v);
184 if (map->n > 0 && opt_denom) {
185 isl_int_clear(opt_denom_i);
186 isl_int_clear(t);
188 if (map->n > 0)
189 isl_int_clear(opt_i);
190 if (opt == &o)
191 isl_int_clear(o);
192 return res;
195 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)
200 return isl_map_solve_lp(set_to_map(set), max,
201 f, d, opt, opt_denom, sol);
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.
209 * Return infinity or negative infinity if the optimal value is unbounded and
210 * NaN if "bset" is empty.
212 * Call isl_basic_set_solve_lp and translate the results.
214 static __isl_give isl_val *basic_set_opt_lp(
215 __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
217 isl_ctx *ctx;
218 isl_val *res;
219 enum isl_lp_result lp_res;
221 if (!bset || !obj)
222 return NULL;
224 ctx = isl_aff_get_ctx(obj);
225 res = isl_val_alloc(ctx);
226 if (!res)
227 return NULL;
228 lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
229 obj->v->el[0], &res->n, &res->d, NULL);
230 if (lp_res == isl_lp_ok)
231 return isl_val_normalize(res);
232 isl_val_free(res);
233 if (lp_res == isl_lp_error)
234 return NULL;
235 if (lp_res == isl_lp_empty)
236 return isl_val_nan(ctx);
237 if (max)
238 return isl_val_infty(ctx);
239 else
240 return isl_val_neginfty(ctx);
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.
248 * Return infinity or negative infinity if the optimal value is unbounded and
249 * NaN if "bset" is empty.
251 * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
253 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)
256 int *exp1 = NULL;
257 int *exp2 = NULL;
258 isl_ctx *ctx;
259 isl_mat *bset_div = NULL;
260 isl_mat *div = NULL;
261 isl_val *res;
262 int bset_n_div, obj_n_div;
264 if (!bset || !obj)
265 return NULL;
267 ctx = isl_aff_get_ctx(obj);
268 if (!isl_space_is_equal(bset->dim, obj->ls->dim))
269 isl_die(ctx, isl_error_invalid,
270 "spaces don't match", return NULL);
272 bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
273 obj_n_div = isl_aff_dim(obj, isl_dim_div);
274 if (bset_n_div == 0 && obj_n_div == 0)
275 return basic_set_opt_lp(bset, max, obj);
277 bset = isl_basic_set_copy(bset);
278 obj = isl_aff_copy(obj);
280 bset_div = isl_basic_set_get_divs(bset);
281 exp1 = isl_alloc_array(ctx, int, bset_n_div);
282 exp2 = isl_alloc_array(ctx, int, obj_n_div);
283 if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
284 goto error;
286 div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
288 bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
289 obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
291 res = basic_set_opt_lp(bset, max, obj);
293 isl_mat_free(bset_div);
294 isl_mat_free(div);
295 free(exp1);
296 free(exp2);
297 isl_basic_set_free(bset);
298 isl_aff_free(obj);
300 return res;
301 error:
302 isl_mat_free(div);
303 isl_mat_free(bset_div);
304 free(exp1);
305 free(exp2);
306 isl_basic_set_free(bset);
307 isl_aff_free(obj);
308 return NULL;
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.
315 * Return infinity or negative infinity if the optimal value is unbounded and
316 * NaN if "bset" is empty.
318 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)
321 isl_bool equal;
322 isl_val *res;
324 if (!bset || !obj)
325 return NULL;
327 equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
328 if (equal < 0)
329 return NULL;
330 if (equal)
331 return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
333 bset = isl_basic_set_copy(bset);
334 obj = isl_aff_copy(obj);
335 bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
336 obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
338 res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
340 isl_basic_set_free(bset);
341 isl_aff_free(obj);
343 return res;
346 /* Return the minimal (rational) value of "obj" over "bset".
348 * Return negative infinity if the minimal value is unbounded and
349 * NaN if "bset" is empty.
351 __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
352 __isl_keep isl_aff *obj)
354 return isl_basic_set_opt_lp_val(bset, 0, obj);
357 /* Return the maximal (rational) value of "obj" over "bset".
359 * Return infinity if the maximal value is unbounded and
360 * NaN if "bset" is empty.
362 __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
363 __isl_keep isl_aff *obj)
365 return isl_basic_set_opt_lp_val(bset, 1, obj);