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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
*/
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl/lp.h>
#include <isl_seq.h>
#include "isl_tab.h"
#include <isl_options_private.h>
#include <isl_local_space_private.h>
#include <isl_aff_private.h>
#include <isl_mat_private.h>
#include <isl_val_private.h>
#include <isl_vec_private.h>
#include <bset_to_bmap.c>
#include <set_to_map.c>
enum isl_lp_result isl_tab_solve_lp(__isl_keep isl_basic_map *bmap,
int maximize, isl_int *f, isl_int denom, isl_int *opt,
isl_int *opt_denom, __isl_give isl_vec **sol)
{
struct isl_tab *tab;
enum isl_lp_result res;
isl_size dim = isl_basic_map_dim(bmap, isl_dim_all);
if (dim < 0)
return isl_lp_error;
if (maximize)
isl_seq_neg(f, f, 1 + dim);
bmap = isl_basic_map_gauss(bmap, NULL);
tab = isl_tab_from_basic_map(bmap, 0);
res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
if (res == isl_lp_ok && sol) {
*sol = isl_tab_get_sample_value(tab);
if (!*sol)
res = isl_lp_error;
}
isl_tab_free(tab);
if (maximize)
isl_seq_neg(f, f, 1 + dim);
if (maximize && opt)
isl_int_neg(*opt, *opt);
return res;
}
/* Given a basic map "bmap" and an affine combination of the variables "f"
* with denominator "denom", set *opt / *opt_denom to the minimal
* (or maximal if "maximize" is true) value attained by f/d over "bmap",
* assuming the basic map is not empty and the expression cannot attain
* arbitrarily small (or large) values.
* If opt_denom is NULL, then *opt is rounded up (or down)
* to the nearest integer.
* The return value reflects the nature of the result (empty, unbounded,
* minimal or maximal value returned in *opt).
*/
enum isl_lp_result isl_basic_map_solve_lp(__isl_keep isl_basic_map *bmap,
int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
__isl_give isl_vec **sol)
{
if (sol)
*sol = NULL;
if (!bmap)
return isl_lp_error;
return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
}
enum isl_lp_result isl_basic_set_solve_lp(__isl_keep isl_basic_set *bset,
int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
__isl_give isl_vec **sol)
{
return isl_basic_map_solve_lp(bset_to_bmap(bset), max,
f, d, opt, opt_denom, sol);
}
enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
isl_int *f, isl_int d, isl_int *opt,
isl_int *opt_denom,
__isl_give isl_vec **sol)
{
int i;
isl_int o;
isl_int t;
isl_int opt_i;
isl_int opt_denom_i;
enum isl_lp_result res;
int max_div;
isl_vec *v = NULL;
if (!map)
return isl_lp_error;
if (map->n == 0)
return isl_lp_empty;
max_div = 0;
for (i = 0; i < map->n; ++i)
if (map->p[i]->n_div > max_div)
max_div = map->p[i]->n_div;
if (max_div > 0) {
isl_size total = isl_map_dim(map, isl_dim_all);
if (total < 0)
return isl_lp_error;
v = isl_vec_alloc(map->ctx, 1 + total + max_div);
if (!v)
return isl_lp_error;
isl_seq_cpy(v->el, f, 1 + total);
isl_seq_clr(v->el + 1 + total, max_div);
f = v->el;
}
if (!opt && map->n > 1 && sol) {
isl_int_init(o);
opt = &o;
}
if (map->n > 0)
isl_int_init(opt_i);
if (map->n > 0 && opt_denom) {
isl_int_init(opt_denom_i);
isl_int_init(t);
}
res = isl_basic_map_solve_lp(map->p[0], max, f, d,
opt, opt_denom, sol);
if (res == isl_lp_error || res == isl_lp_unbounded)
goto done;
if (sol)
*sol = NULL;
for (i = 1; i < map->n; ++i) {
isl_vec *sol_i = NULL;
enum isl_lp_result res_i;
int better;
res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
&opt_i,
opt_denom ? &opt_denom_i : NULL,
sol ? &sol_i : NULL);
if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
res = res_i;
goto done;
}
if (res_i == isl_lp_empty)
continue;
if (res == isl_lp_empty) {
better = 1;
} else if (!opt_denom) {
if (max)
better = isl_int_gt(opt_i, *opt);
else
better = isl_int_lt(opt_i, *opt);
} else {
isl_int_mul(t, opt_i, *opt_denom);
isl_int_submul(t, *opt, opt_denom_i);
if (max)
better = isl_int_is_pos(t);
else
better = isl_int_is_neg(t);
}
if (better) {
res = res_i;
if (opt)
isl_int_set(*opt, opt_i);
if (opt_denom)
isl_int_set(*opt_denom, opt_denom_i);
if (sol) {
isl_vec_free(*sol);
*sol = sol_i;
}
} else
isl_vec_free(sol_i);
}
done:
isl_vec_free(v);
if (map->n > 0 && opt_denom) {
isl_int_clear(opt_denom_i);
isl_int_clear(t);
}
if (map->n > 0)
isl_int_clear(opt_i);
if (opt == &o)
isl_int_clear(o);
return res;
}
enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
isl_int *f, isl_int d, isl_int *opt,
isl_int *opt_denom,
__isl_give isl_vec **sol)
{
return isl_map_solve_lp(set_to_map(set), max,
f, d, opt, opt_denom, sol);
}
/* Return the optimal (rational) value of "obj" over "bset", assuming
* that "obj" and "bset" have aligned parameters and divs.
* If "max" is set, then the maximal value is computed.
* Otherwise, the minimal value is computed.
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "bset" is empty.
*
* Call isl_basic_set_solve_lp and translate the results.
*/
static __isl_give isl_val *basic_set_opt_lp(
__isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
{
isl_ctx *ctx;
isl_val *res;
enum isl_lp_result lp_res;
if (!bset || !obj)
return NULL;
ctx = isl_aff_get_ctx(obj);
res = isl_val_alloc(ctx);
if (!res)
return NULL;
lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
obj->v->el[0], &res->n, &res->d, NULL);
if (lp_res == isl_lp_ok)
return isl_val_normalize(res);
isl_val_free(res);
if (lp_res == isl_lp_error)
return NULL;
if (lp_res == isl_lp_empty)
return isl_val_nan(ctx);
if (max)
return isl_val_infty(ctx);
else
return isl_val_neginfty(ctx);
}
/* Return the optimal (rational) value of "obj" over "bset", assuming
* that "obj" and "bset" have aligned parameters.
* If "max" is set, then the maximal value is computed.
* Otherwise, the minimal value is computed.
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "bset" is empty.
*
* Align the divs of "bset" and "obj" and call basic_set_opt_lp.
*/
static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
__isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
{
int *exp1 = NULL;
int *exp2 = NULL;
isl_ctx *ctx;
isl_mat *bset_div = NULL;
isl_mat *div = NULL;
isl_val *res;
isl_size bset_n_div, obj_n_div;
if (!bset || !obj)
return NULL;
ctx = isl_aff_get_ctx(obj);
if (!isl_space_is_equal(bset->dim, obj->ls->dim))
isl_die(ctx, isl_error_invalid,
"spaces don't match", return NULL);
bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
obj_n_div = isl_aff_dim(obj, isl_dim_div);
if (bset_n_div < 0 || obj_n_div < 0)
return NULL;
if (bset_n_div == 0 && obj_n_div == 0)
return basic_set_opt_lp(bset, max, obj);
bset = isl_basic_set_copy(bset);
obj = isl_aff_copy(obj);
bset_div = isl_basic_set_get_divs(bset);
exp1 = isl_alloc_array(ctx, int, bset_n_div);
exp2 = isl_alloc_array(ctx, int, obj_n_div);
if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
goto error;
div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
res = basic_set_opt_lp(bset, max, obj);
isl_mat_free(bset_div);
isl_mat_free(div);
free(exp1);
free(exp2);
isl_basic_set_free(bset);
isl_aff_free(obj);
return res;
error:
isl_mat_free(div);
isl_mat_free(bset_div);
free(exp1);
free(exp2);
isl_basic_set_free(bset);
isl_aff_free(obj);
return NULL;
}
/* Return the optimal (rational) value of "obj" over "bset".
* If "max" is set, then the maximal value is computed.
* Otherwise, the minimal value is computed.
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "bset" is empty.
*/
static __isl_give isl_val *isl_basic_set_opt_lp_val(
__isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
{
isl_bool equal;
isl_val *res;
if (!bset || !obj)
return NULL;
equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
if (equal < 0)
return NULL;
if (equal)
return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
bset = isl_basic_set_copy(bset);
obj = isl_aff_copy(obj);
bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
isl_basic_set_free(bset);
isl_aff_free(obj);
return res;
}
/* Return the minimal (rational) value of "obj" over "bset".
*
* Return negative infinity if the minimal value is unbounded and
* NaN if "bset" is empty.
*/
__isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
__isl_keep isl_aff *obj)
{
return isl_basic_set_opt_lp_val(bset, 0, obj);
}
/* Return the maximal (rational) value of "obj" over "bset".
*
* Return infinity if the maximal value is unbounded and
* NaN if "bset" is empty.
*/
__isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
__isl_keep isl_aff *obj)
{
return isl_basic_set_opt_lp_val(bset, 1, obj);
}
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