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
25static 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 isl_size dim = isl_basic_map_dim(bmap, type: isl_dim_all);
32
33 if (dim < 0)
34 return isl_lp_error;
35 if (maximize)
36 isl_seq_neg(dst: f, src: f, len: 1 + dim);
37
38 bmap = isl_basic_map_gauss(bmap, NULL);
39 tab = isl_tab_from_basic_map(bmap, track: 0);
40 res = isl_tab_min(tab, f, denom, opt, opt_denom, flags: 0);
41 if (res == isl_lp_ok && sol) {
42 *sol = isl_tab_get_sample_value(tab);
43 if (!*sol)
44 res = isl_lp_error;
45 }
46 isl_tab_free(tab);
47
48 if (maximize)
49 isl_seq_neg(dst: f, src: f, len: 1 + dim);
50 if (maximize && opt)
51 isl_int_neg(*opt, *opt);
52
53 return res;
54}
55
56/* Given a basic map "bmap" and an affine combination of the variables "f"
57 * with denominator "denom", set *opt / *opt_denom to the minimal
58 * (or maximal if "maximize" is true) value attained by f/d over "bmap",
59 * assuming the basic map is not empty and the expression cannot attain
60 * arbitrarily small (or large) values.
61 * If opt_denom is NULL, then *opt is rounded up (or down)
62 * to the nearest integer.
63 * The return value reflects the nature of the result (empty, unbounded,
64 * minimal or maximal value returned in *opt).
65 */
66enum isl_lp_result isl_basic_map_solve_lp(__isl_keep isl_basic_map *bmap,
67 int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
68 __isl_give isl_vec **sol)
69{
70 if (sol)
71 *sol = NULL;
72
73 if (!bmap)
74 return isl_lp_error;
75
76 return isl_tab_solve_lp(bmap, maximize: max, f, denom: d, opt, opt_denom, sol);
77}
78
79enum isl_lp_result isl_basic_set_solve_lp(__isl_keep isl_basic_set *bset,
80 int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
81 __isl_give isl_vec **sol)
82{
83 return isl_basic_map_solve_lp(bmap: bset_to_bmap(bset), max,
84 f, d, opt, opt_denom, sol);
85}
86
87enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
88 isl_int *f, isl_int d, isl_int *opt,
89 isl_int *opt_denom,
90 __isl_give isl_vec **sol)
91{
92 int i;
93 isl_int o;
94 isl_int t;
95 isl_int opt_i;
96 isl_int opt_denom_i;
97 enum isl_lp_result res;
98 int max_div;
99 isl_vec *v = NULL;
100
101 if (!map)
102 return isl_lp_error;
103 if (map->n == 0)
104 return isl_lp_empty;
105
106 max_div = 0;
107 for (i = 0; i < map->n; ++i)
108 if (map->p[i]->n_div > max_div)
109 max_div = map->p[i]->n_div;
110 if (max_div > 0) {
111 isl_size total = isl_map_dim(map, type: isl_dim_all);
112 if (total < 0)
113 return isl_lp_error;
114 v = isl_vec_alloc(ctx: map->ctx, size: 1 + total + max_div);
115 if (!v)
116 return isl_lp_error;
117 isl_seq_cpy(dst: v->el, src: f, len: 1 + total);
118 isl_seq_clr(p: v->el + 1 + total, len: max_div);
119 f = v->el;
120 }
121
122 if (!opt && map->n > 1 && sol) {
123 isl_int_init(o);
124 opt = &o;
125 }
126 if (map->n > 0)
127 isl_int_init(opt_i);
128 if (map->n > 0 && opt_denom) {
129 isl_int_init(opt_denom_i);
130 isl_int_init(t);
131 }
132
133 res = isl_basic_map_solve_lp(bmap: map->p[0], max, f, d,
134 opt, opt_denom, sol);
135 if (res == isl_lp_error || res == isl_lp_unbounded)
136 goto done;
137
138 if (sol)
139 *sol = NULL;
140
141 for (i = 1; i < map->n; ++i) {
142 isl_vec *sol_i = NULL;
143 enum isl_lp_result res_i;
144 int better;
145
146 res_i = isl_basic_map_solve_lp(bmap: map->p[i], max, f, d,
147 opt: &opt_i,
148 opt_denom: opt_denom ? &opt_denom_i : NULL,
149 sol: sol ? &sol_i : NULL);
150 if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
151 res = res_i;
152 goto done;
153 }
154 if (res_i == isl_lp_empty)
155 continue;
156 if (res == isl_lp_empty) {
157 better = 1;
158 } else if (!opt_denom) {
159 if (max)
160 better = isl_int_gt(opt_i, *opt);
161 else
162 better = isl_int_lt(opt_i, *opt);
163 } else {
164 isl_int_mul(t, opt_i, *opt_denom);
165 isl_int_submul(t, *opt, opt_denom_i);
166 if (max)
167 better = isl_int_is_pos(t);
168 else
169 better = isl_int_is_neg(t);
170 }
171 if (better) {
172 res = res_i;
173 if (opt)
174 isl_int_set(*opt, opt_i);
175 if (opt_denom)
176 isl_int_set(*opt_denom, opt_denom_i);
177 if (sol) {
178 isl_vec_free(vec: *sol);
179 *sol = sol_i;
180 }
181 } else
182 isl_vec_free(vec: sol_i);
183 }
184
185done:
186 isl_vec_free(vec: v);
187 if (map->n > 0 && opt_denom) {
188 isl_int_clear(opt_denom_i);
189 isl_int_clear(t);
190 }
191 if (map->n > 0)
192 isl_int_clear(opt_i);
193 if (opt == &o)
194 isl_int_clear(o);
195 return res;
196}
197
198enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
199 isl_int *f, isl_int d, isl_int *opt,
200 isl_int *opt_denom,
201 __isl_give isl_vec **sol)
202{
203 return isl_map_solve_lp(map: set_to_map(set), max,
204 f, d, opt, opt_denom, sol);
205}
206
207/* Return the optimal (rational) value of "obj" over "bset", assuming
208 * that "obj" and "bset" have aligned parameters and divs.
209 * If "max" is set, then the maximal value is computed.
210 * Otherwise, the minimal value is computed.
211 *
212 * Return infinity or negative infinity if the optimal value is unbounded and
213 * NaN if "bset" is empty.
214 *
215 * Call isl_basic_set_solve_lp and translate the results.
216 */
217static __isl_give isl_val *basic_set_opt_lp(
218 __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
219{
220 isl_ctx *ctx;
221 isl_val *res;
222 enum isl_lp_result lp_res;
223
224 if (!bset || !obj)
225 return NULL;
226
227 ctx = isl_aff_get_ctx(aff: obj);
228 res = isl_val_alloc(ctx);
229 if (!res)
230 return NULL;
231 lp_res = isl_basic_set_solve_lp(bset, max, f: obj->v->el + 1,
232 d: obj->v->el[0], opt: &res->n, opt_denom: &res->d, NULL);
233 if (lp_res == isl_lp_ok)
234 return isl_val_normalize(v: res);
235 isl_val_free(v: res);
236 if (lp_res == isl_lp_error)
237 return NULL;
238 if (lp_res == isl_lp_empty)
239 return isl_val_nan(ctx);
240 if (max)
241 return isl_val_infty(ctx);
242 else
243 return isl_val_neginfty(ctx);
244}
245
246/* Return the optimal (rational) value of "obj" over "bset", assuming
247 * that "obj" and "bset" have aligned parameters.
248 * If "max" is set, then the maximal value is computed.
249 * Otherwise, the minimal value is computed.
250 *
251 * Return infinity or negative infinity if the optimal value is unbounded and
252 * NaN if "bset" is empty.
253 *
254 * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
255 */
256static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
257 __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
258{
259 int *exp1 = NULL;
260 int *exp2 = NULL;
261 isl_ctx *ctx;
262 isl_mat *bset_div = NULL;
263 isl_mat *div = NULL;
264 isl_val *res;
265 isl_size bset_n_div, obj_n_div;
266
267 if (!bset || !obj)
268 return NULL;
269
270 ctx = isl_aff_get_ctx(aff: obj);
271 if (!isl_space_is_equal(space1: bset->dim, space2: obj->ls->dim))
272 isl_die(ctx, isl_error_invalid,
273 "spaces don't match", return NULL);
274
275 bset_n_div = isl_basic_set_dim(bset, type: isl_dim_div);
276 obj_n_div = isl_aff_dim(aff: obj, type: isl_dim_div);
277 if (bset_n_div < 0 || obj_n_div < 0)
278 return NULL;
279 if (bset_n_div == 0 && obj_n_div == 0)
280 return basic_set_opt_lp(bset, max, obj);
281
282 bset = isl_basic_set_copy(bset);
283 obj = isl_aff_copy(aff: obj);
284
285 bset_div = isl_basic_set_get_divs(bset);
286 exp1 = isl_alloc_array(ctx, int, bset_n_div);
287 exp2 = isl_alloc_array(ctx, int, obj_n_div);
288 if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
289 goto error;
290
291 div = isl_merge_divs(div1: bset_div, div2: obj->ls->div, exp1, exp2);
292
293 bset = isl_basic_set_expand_divs(bset, div: isl_mat_copy(mat: div), exp: exp1);
294 obj = isl_aff_expand_divs(aff: obj, div: isl_mat_copy(mat: div), exp: exp2);
295
296 res = basic_set_opt_lp(bset, max, obj);
297
298 isl_mat_free(mat: bset_div);
299 isl_mat_free(mat: div);
300 free(ptr: exp1);
301 free(ptr: exp2);
302 isl_basic_set_free(bset);
303 isl_aff_free(aff: obj);
304
305 return res;
306error:
307 isl_mat_free(mat: div);
308 isl_mat_free(mat: bset_div);
309 free(ptr: exp1);
310 free(ptr: exp2);
311 isl_basic_set_free(bset);
312 isl_aff_free(aff: obj);
313 return NULL;
314}
315
316/* Return the optimal (rational) value of "obj" over "bset".
317 * If "max" is set, then the maximal value is computed.
318 * Otherwise, the minimal value is computed.
319 *
320 * Return infinity or negative infinity if the optimal value is unbounded and
321 * NaN if "bset" is empty.
322 */
323static __isl_give isl_val *isl_basic_set_opt_lp_val(
324 __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
325{
326 isl_bool equal;
327 isl_val *res;
328
329 if (!bset || !obj)
330 return NULL;
331
332 equal = isl_basic_set_space_has_equal_params(bset, space: obj->ls->dim);
333 if (equal < 0)
334 return NULL;
335 if (equal)
336 return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
337
338 bset = isl_basic_set_copy(bset);
339 obj = isl_aff_copy(aff: obj);
340 bset = isl_basic_set_align_params(bset, model: isl_aff_get_domain_space(aff: obj));
341 obj = isl_aff_align_params(aff: obj, model: isl_basic_set_get_space(bset));
342
343 res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
344
345 isl_basic_set_free(bset);
346 isl_aff_free(aff: obj);
347
348 return res;
349}
350
351/* Return the minimal (rational) value of "obj" over "bset".
352 *
353 * Return negative infinity if the minimal value is unbounded and
354 * NaN if "bset" is empty.
355 */
356__isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
357 __isl_keep isl_aff *obj)
358{
359 return isl_basic_set_opt_lp_val(bset, max: 0, obj);
360}
361
362/* Return the maximal (rational) value of "obj" over "bset".
363 *
364 * Return infinity if the maximal value is unbounded and
365 * NaN if "bset" is empty.
366 */
367__isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
368 __isl_keep isl_aff *obj)
369{
370 return isl_basic_set_opt_lp_val(bset, max: 1, obj);
371}
372

source code of polly/lib/External/isl/isl_lp.c