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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/ilp.h>
#include <isl/union_set.h>
#include "isl_sample.h"
#include <isl_seq.h>
#include "isl_equalities.h"
#include <isl_aff_private.h>
#include <isl_local_space_private.h>
#include <isl_mat_private.h>
#include <isl_val_private.h>
#include <isl_vec_private.h>
#include <isl_lp_private.h>
#include <isl_ilp_private.h>
/* Given a basic set "bset", construct a basic set U such that for
* each element x in U, the whole unit box positioned at x is inside
* the given basic set.
* Note that U may not contain all points that satisfy this property.
*
* We simply add the sum of all negative coefficients to the constant
* term. This ensures that if x satisfies the resulting constraints,
* then x plus any sum of unit vectors satisfies the original constraints.
*/
static __isl_give isl_basic_set *unit_box_base_points(
__isl_take isl_basic_set *bset)
{
int i, j, k;
struct isl_basic_set *unit_box = NULL;
isl_size total;
if (!bset)
goto error;
if (bset->n_eq != 0) {
isl_space *space = isl_basic_set_get_space(bset);
isl_basic_set_free(bset);
return isl_basic_set_empty(space);
}
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0)
goto error;
unit_box = isl_basic_set_alloc_space(isl_basic_set_get_space(bset),
0, 0, bset->n_ineq);
for (i = 0; i < bset->n_ineq; ++i) {
k = isl_basic_set_alloc_inequality(unit_box);
if (k < 0)
goto error;
isl_seq_cpy(unit_box->ineq[k], bset->ineq[i], 1 + total);
for (j = 0; j < total; ++j) {
if (isl_int_is_nonneg(unit_box->ineq[k][1 + j]))
continue;
isl_int_add(unit_box->ineq[k][0],
unit_box->ineq[k][0], unit_box->ineq[k][1 + j]);
}
}
isl_basic_set_free(bset);
return unit_box;
error:
isl_basic_set_free(bset);
isl_basic_set_free(unit_box);
return NULL;
}
/* Find an integer point in "bset", preferably one that is
* close to minimizing "f".
*
* We first check if we can easily put unit boxes inside bset.
* If so, we take the best base point of any of the unit boxes we can find
* and round it up to the nearest integer.
* If not, we simply pick any integer point in "bset".
*/
static __isl_give isl_vec *initial_solution(__isl_keep isl_basic_set *bset,
isl_int *f)
{
enum isl_lp_result res;
struct isl_basic_set *unit_box;
struct isl_vec *sol;
unit_box = unit_box_base_points(isl_basic_set_copy(bset));
res = isl_basic_set_solve_lp(unit_box, 0, f, bset->ctx->one,
NULL, NULL, &sol);
if (res == isl_lp_ok) {
isl_basic_set_free(unit_box);
return isl_vec_ceil(sol);
}
isl_basic_set_free(unit_box);
return isl_basic_set_sample_vec(isl_basic_set_copy(bset));
}
/* Restrict "bset" to those points with values for f in the interval [l, u].
*/
static __isl_give isl_basic_set *add_bounds(__isl_take isl_basic_set *bset,
isl_int *f, isl_int l, isl_int u)
{
int k;
isl_size total;
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0)
return isl_basic_set_free(bset);
bset = isl_basic_set_extend_constraints(bset, 0, 2);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_cpy(bset->ineq[k], f, 1 + total);
isl_int_sub(bset->ineq[k][0], bset->ineq[k][0], l);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_neg(bset->ineq[k], f, 1 + total);
isl_int_add(bset->ineq[k][0], bset->ineq[k][0], u);
return bset;
error:
isl_basic_set_free(bset);
return NULL;
}
/* Find an integer point in "bset" that minimizes f (in any) such that
* the value of f lies inside the interval [l, u].
* Return this integer point if it can be found.
* Otherwise, return sol.
*
* We perform a number of steps until l > u.
* In each step, we look for an integer point with value in either
* the whole interval [l, u] or half of the interval [l, l+floor(u-l-1/2)].
* The choice depends on whether we have found an integer point in the
* previous step. If so, we look for the next point in half of the remaining
* interval.
* If we find a point, the current solution is updated and u is set
* to its value minus 1.
* If no point can be found, we update l to the upper bound of the interval
* we checked (u or l+floor(u-l-1/2)) plus 1.
*/
static __isl_give isl_vec *solve_ilp_search(__isl_keep isl_basic_set *bset,
isl_int *f, isl_int *opt, __isl_take isl_vec *sol, isl_int l, isl_int u)
{
isl_int tmp;
int divide = 1;
isl_int_init(tmp);
while (isl_int_le(l, u)) {
struct isl_basic_set *slice;
struct isl_vec *sample;
if (!divide)
isl_int_set(tmp, u);
else {
isl_int_sub(tmp, u, l);
isl_int_fdiv_q_ui(tmp, tmp, 2);
isl_int_add(tmp, tmp, l);
}
slice = add_bounds(isl_basic_set_copy(bset), f, l, tmp);
sample = isl_basic_set_sample_vec(slice);
if (!sample) {
isl_vec_free(sol);
sol = NULL;
break;
}
if (sample->size > 0) {
isl_vec_free(sol);
sol = sample;
isl_seq_inner_product(f, sol->el, sol->size, opt);
isl_int_sub_ui(u, *opt, 1);
divide = 1;
} else {
isl_vec_free(sample);
if (!divide)
break;
isl_int_add_ui(l, tmp, 1);
divide = 0;
}
}
isl_int_clear(tmp);
return sol;
}
/* Find an integer point in "bset" that minimizes f (if any).
* If sol_p is not NULL then the integer point is returned in *sol_p.
* The optimal value of f is returned in *opt.
*
* The algorithm maintains a currently best solution and an interval [l, u]
* of values of f for which integer solutions could potentially still be found.
* The initial value of the best solution so far is any solution.
* The initial value of l is minimal value of f over the rationals
* (rounded up to the nearest integer).
* The initial value of u is the value of f at the initial solution minus 1.
*
* We then call solve_ilp_search to perform a binary search on the interval.
*/
static enum isl_lp_result solve_ilp(__isl_keep isl_basic_set *bset,
isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p)
{
enum isl_lp_result res;
isl_int l, u;
struct isl_vec *sol;
res = isl_basic_set_solve_lp(bset, 0, f, bset->ctx->one,
opt, NULL, &sol);
if (res == isl_lp_ok && isl_int_is_one(sol->el[0])) {
if (sol_p)
*sol_p = sol;
else
isl_vec_free(sol);
return isl_lp_ok;
}
isl_vec_free(sol);
if (res == isl_lp_error || res == isl_lp_empty)
return res;
sol = initial_solution(bset, f);
if (!sol)
return isl_lp_error;
if (sol->size == 0) {
isl_vec_free(sol);
return isl_lp_empty;
}
if (res == isl_lp_unbounded) {
isl_vec_free(sol);
return isl_lp_unbounded;
}
isl_int_init(l);
isl_int_init(u);
isl_int_set(l, *opt);
isl_seq_inner_product(f, sol->el, sol->size, opt);
isl_int_sub_ui(u, *opt, 1);
sol = solve_ilp_search(bset, f, opt, sol, l, u);
if (!sol)
res = isl_lp_error;
isl_int_clear(l);
isl_int_clear(u);
if (sol_p)
*sol_p = sol;
else
isl_vec_free(sol);
return res;
}
static enum isl_lp_result solve_ilp_with_eq(__isl_keep isl_basic_set *bset,
int max, isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p)
{
isl_size dim;
enum isl_lp_result res;
struct isl_mat *T = NULL;
struct isl_vec *v;
bset = isl_basic_set_copy(bset);
dim = isl_basic_set_dim(bset, isl_dim_all);
if (dim < 0)
goto error;
v = isl_vec_alloc(bset->ctx, 1 + dim);
if (!v)
goto error;
isl_seq_cpy(v->el, f, 1 + dim);
bset = isl_basic_set_remove_equalities(bset, &T, NULL);
v = isl_vec_mat_product(v, isl_mat_copy(T));
if (!v)
goto error;
res = isl_basic_set_solve_ilp(bset, max, v->el, opt, sol_p);
isl_vec_free(v);
if (res == isl_lp_ok && sol_p) {
*sol_p = isl_mat_vec_product(T, *sol_p);
if (!*sol_p)
res = isl_lp_error;
} else
isl_mat_free(T);
isl_basic_set_free(bset);
return res;
error:
isl_mat_free(T);
isl_basic_set_free(bset);
return isl_lp_error;
}
/* Find an integer point in "bset" that minimizes (or maximizes if max is set)
* f (if any).
* If sol_p is not NULL then the integer point is returned in *sol_p.
* The optimal value of f is returned in *opt.
*
* If there is any equality among the points in "bset", then we first
* project it out. Otherwise, we continue with solve_ilp above.
*/
enum isl_lp_result isl_basic_set_solve_ilp(__isl_keep isl_basic_set *bset,
int max, isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p)
{
isl_size dim;
enum isl_lp_result res;
if (sol_p)
*sol_p = NULL;
if (isl_basic_set_check_no_params(bset) < 0)
return isl_lp_error;
if (isl_basic_set_plain_is_empty(bset))
return isl_lp_empty;
if (bset->n_eq)
return solve_ilp_with_eq(bset, max, f, opt, sol_p);
dim = isl_basic_set_dim(bset, isl_dim_all);
if (dim < 0)
return isl_lp_error;
if (max)
isl_seq_neg(f, f, 1 + dim);
res = solve_ilp(bset, f, opt, sol_p);
if (max) {
isl_seq_neg(f, f, 1 + dim);
isl_int_neg(*opt, *opt);
}
return res;
}
static enum isl_lp_result basic_set_opt(__isl_keep isl_basic_set *bset, int max,
__isl_keep isl_aff *obj, isl_int *opt)
{
enum isl_lp_result res;
if (!obj)
return isl_lp_error;
bset = isl_basic_set_copy(bset);
bset = isl_basic_set_underlying_set(bset);
res = isl_basic_set_solve_ilp(bset, max, obj->v->el + 1, opt, NULL);
isl_basic_set_free(bset);
return res;
}
enum isl_lp_result isl_basic_set_opt(__isl_keep isl_basic_set *bset, int max,
__isl_keep isl_aff *obj, isl_int *opt)
{
int *exp1 = NULL;
int *exp2 = NULL;
isl_ctx *ctx;
isl_mat *bset_div = NULL;
isl_mat *div = NULL;
enum isl_lp_result res;
isl_size bset_n_div, obj_n_div;
if (!bset || !obj)
return isl_lp_error;
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 isl_lp_error);
if (!isl_int_is_one(obj->v->el[0]))
isl_die(ctx, isl_error_unsupported,
"expecting integer affine expression",
return isl_lp_error);
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 isl_lp_error;
if (bset_n_div == 0 && obj_n_div == 0)
return basic_set_opt(bset, max, obj, opt);
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(bset, max, obj, opt);
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 isl_lp_error;
}
/* Compute the minimum (maximum if max is set) of the integer affine
* expression obj over the points in set and put the result in *opt.
*
* The parameters are assumed to have been aligned.
*/
static enum isl_lp_result isl_set_opt_aligned(__isl_keep isl_set *set, int max,
__isl_keep isl_aff *obj, isl_int *opt)
{
int i;
enum isl_lp_result res;
int empty = 1;
isl_int opt_i;
if (!set || !obj)
return isl_lp_error;
if (set->n == 0)
return isl_lp_empty;
res = isl_basic_set_opt(set->p[0], max, obj, opt);
if (res == isl_lp_error || res == isl_lp_unbounded)
return res;
if (set->n == 1)
return res;
if (res == isl_lp_ok)
empty = 0;
isl_int_init(opt_i);
for (i = 1; i < set->n; ++i) {
res = isl_basic_set_opt(set->p[i], max, obj, &opt_i);
if (res == isl_lp_error || res == isl_lp_unbounded) {
isl_int_clear(opt_i);
return res;
}
if (res == isl_lp_empty)
continue;
empty = 0;
if (max ? isl_int_gt(opt_i, *opt) : isl_int_lt(opt_i, *opt))
isl_int_set(*opt, opt_i);
}
isl_int_clear(opt_i);
return empty ? isl_lp_empty : isl_lp_ok;
}
/* Compute the minimum (maximum if max is set) of the integer affine
* expression obj over the points in set and put the result in *opt.
*/
enum isl_lp_result isl_set_opt(__isl_keep isl_set *set, int max,
__isl_keep isl_aff *obj, isl_int *opt)
{
enum isl_lp_result res;
isl_bool aligned;
if (!set || !obj)
return isl_lp_error;
aligned = isl_set_space_has_equal_params(set, obj->ls->dim);
if (aligned < 0)
return isl_lp_error;
if (aligned)
return isl_set_opt_aligned(set, max, obj, opt);
set = isl_set_copy(set);
obj = isl_aff_copy(obj);
set = isl_set_align_params(set, isl_aff_get_domain_space(obj));
obj = isl_aff_align_params(obj, isl_set_get_space(set));
res = isl_set_opt_aligned(set, max, obj, opt);
isl_set_free(set);
isl_aff_free(obj);
return res;
}
/* Convert the result of a function that returns an isl_lp_result
* to an isl_val. The numerator of "v" is set to the optimal value
* if lp_res is isl_lp_ok. "max" is set if a maximum was computed.
*
* Return "v" with denominator set to 1 if lp_res is isl_lp_ok.
* Return NULL on error.
* Return a NaN if lp_res is isl_lp_empty.
* Return infinity or negative infinity if lp_res is isl_lp_unbounded,
* depending on "max".
*/
static __isl_give isl_val *convert_lp_result(enum isl_lp_result lp_res,
__isl_take isl_val *v, int max)
{
isl_ctx *ctx;
if (lp_res == isl_lp_ok) {
isl_int_set_si(v->d, 1);
return isl_val_normalize(v);
}
ctx = isl_val_get_ctx(v);
isl_val_free(v);
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 minimum (maximum if max is set) of the integer affine
* expression "obj" over the points in "bset".
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "bset" is empty.
*
* Call isl_basic_set_opt and translate the results.
*/
__isl_give isl_val *isl_basic_set_opt_val(__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_opt(bset, max, obj, &res->n);
return convert_lp_result(lp_res, res, max);
}
/* Return the maximum of the integer affine
* expression "obj" over the points in "bset".
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "bset" is empty.
*/
__isl_give isl_val *isl_basic_set_max_val(__isl_keep isl_basic_set *bset,
__isl_keep isl_aff *obj)
{
return isl_basic_set_opt_val(bset, 1, obj);
}
/* Return the minimum (maximum if max is set) of the integer affine
* expression "obj" over the points in "set".
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "set" is empty.
*
* Call isl_set_opt and translate the results.
*/
__isl_give isl_val *isl_set_opt_val(__isl_keep isl_set *set, int max,
__isl_keep isl_aff *obj)
{
isl_ctx *ctx;
isl_val *res;
enum isl_lp_result lp_res;
if (!set || !obj)
return NULL;
ctx = isl_aff_get_ctx(obj);
res = isl_val_alloc(ctx);
if (!res)
return NULL;
lp_res = isl_set_opt(set, max, obj, &res->n);
return convert_lp_result(lp_res, res, max);
}
/* Return the minimum of the integer affine
* expression "obj" over the points in "set".
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "set" is empty.
*/
__isl_give isl_val *isl_set_min_val(__isl_keep isl_set *set,
__isl_keep isl_aff *obj)
{
return isl_set_opt_val(set, 0, obj);
}
/* Return the maximum of the integer affine
* expression "obj" over the points in "set".
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if "set" is empty.
*/
__isl_give isl_val *isl_set_max_val(__isl_keep isl_set *set,
__isl_keep isl_aff *obj)
{
return isl_set_opt_val(set, 1, obj);
}
/* Return the optimum (min or max depending on "max") of "v1" and "v2",
* where either may be NaN, signifying an uninitialized value.
* That is, if either is NaN, then return the other one.
*/
static __isl_give isl_val *val_opt(__isl_take isl_val *v1,
__isl_take isl_val *v2, int max)
{
if (!v1 || !v2)
goto error;
if (isl_val_is_nan(v1)) {
isl_val_free(v1);
return v2;
}
if (isl_val_is_nan(v2)) {
isl_val_free(v2);
return v1;
}
if (max)
return isl_val_max(v1, v2);
else
return isl_val_min(v1, v2);
error:
isl_val_free(v1);
isl_val_free(v2);
return NULL;
}
/* Internal data structure for isl_pw_aff_opt_val.
*
* "max" is set if the maximum should be computed.
* "res" contains the current optimum and is initialized to NaN.
*/
struct isl_pw_aff_opt_data {
int max;
isl_val *res;
};
/* Update the optimum in data->res with respect to the affine function
* "aff" defined over "set".
*/
static isl_stat piece_opt(__isl_take isl_set *set, __isl_take isl_aff *aff,
void *user)
{
struct isl_pw_aff_opt_data *data = user;
isl_val *opt;
opt = isl_set_opt_val(set, data->max, aff);
isl_set_free(set);
isl_aff_free(aff);
data->res = val_opt(data->res, opt, data->max);
if (!data->res)
return isl_stat_error;
return isl_stat_ok;
}
/* Return the minimum (maximum if "max" is set) of the integer piecewise affine
* expression "pa" over its definition domain.
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if the domain of "pa" is empty.
*
* Initialize the result to NaN and then update it for each of the pieces
* in "pa".
*/
static __isl_give isl_val *isl_pw_aff_opt_val(__isl_take isl_pw_aff *pa,
int max)
{
struct isl_pw_aff_opt_data data = { max };
data.res = isl_val_nan(isl_pw_aff_get_ctx(pa));
if (isl_pw_aff_foreach_piece(pa, &piece_opt, &data) < 0)
data.res = isl_val_free(data.res);
isl_pw_aff_free(pa);
return data.res;
}
#undef TYPE
#define TYPE isl_pw_multi_aff
#include "isl_ilp_opt_multi_val_templ.c"
#undef TYPE
#define TYPE isl_multi_pw_aff
#include "isl_ilp_opt_multi_val_templ.c"
/* Internal data structure for isl_union_pw_aff_opt_val.
*
* "max" is set if the maximum should be computed.
* "res" contains the current optimum and is initialized to NaN.
*/
struct isl_union_pw_aff_opt_data {
int max;
isl_val *res;
};
/* Update the optimum in data->res with the optimum of "pa".
*/
static isl_stat pw_aff_opt(__isl_take isl_pw_aff *pa, void *user)
{
struct isl_union_pw_aff_opt_data *data = user;
isl_val *opt;
opt = isl_pw_aff_opt_val(pa, data->max);
data->res = val_opt(data->res, opt, data->max);
if (!data->res)
return isl_stat_error;
return isl_stat_ok;
}
/* Return the minimum (maximum if "max" is set) of the integer piecewise affine
* expression "upa" over its definition domain.
*
* Return infinity or negative infinity if the optimal value is unbounded and
* NaN if the domain of the expression is empty.
*
* Initialize the result to NaN and then update it
* for each of the piecewise affine expressions in "upa".
*/
static __isl_give isl_val *isl_union_pw_aff_opt_val(
__isl_take isl_union_pw_aff *upa, int max)
{
struct isl_union_pw_aff_opt_data data = { max };
data.res = isl_val_nan(isl_union_pw_aff_get_ctx(upa));
if (isl_union_pw_aff_foreach_pw_aff(upa, &pw_aff_opt, &data) < 0)
data.res = isl_val_free(data.res);
isl_union_pw_aff_free(upa);
return data.res;
}
/* Return the minimum of the integer piecewise affine
* expression "upa" over its definition domain.
*
* Return negative infinity if the optimal value is unbounded and
* NaN if the domain of the expression is empty.
*/
__isl_give isl_val *isl_union_pw_aff_min_val(__isl_take isl_union_pw_aff *upa)
{
return isl_union_pw_aff_opt_val(upa, 0);
}
/* Return the maximum of the integer piecewise affine
* expression "upa" over its definition domain.
*
* Return infinity if the optimal value is unbounded and
* NaN if the domain of the expression is empty.
*/
__isl_give isl_val *isl_union_pw_aff_max_val(__isl_take isl_union_pw_aff *upa)
{
return isl_union_pw_aff_opt_val(upa, 1);
}
/* Return a list of minima (maxima if "max" is set)
* for each of the expressions in "mupa" over their domains.
*
* An element in the list is infinity or negative infinity if the optimal
* value of the corresponding expression is unbounded and
* NaN if the domain of the expression is empty.
*
* Iterate over all the expressions in "mupa" and collect the results.
*/
static __isl_give isl_multi_val *isl_multi_union_pw_aff_opt_multi_val(
__isl_take isl_multi_union_pw_aff *mupa, int max)
{
int i;
isl_size n;
isl_multi_val *mv;
n = isl_multi_union_pw_aff_size(mupa);
if (n < 0)
mupa = isl_multi_union_pw_aff_free(mupa);
if (!mupa)
return NULL;
mv = isl_multi_val_zero(isl_multi_union_pw_aff_get_space(mupa));
for (i = 0; i < n; ++i) {
isl_val *v;
isl_union_pw_aff *upa;
upa = isl_multi_union_pw_aff_get_union_pw_aff(mupa, i);
v = isl_union_pw_aff_opt_val(upa, max);
mv = isl_multi_val_set_val(mv, i, v);
}
isl_multi_union_pw_aff_free(mupa);
return mv;
}
/* Return a list of minima (maxima if "max" is set) over the points in "uset"
* for each of the expressions in "obj".
*
* An element in the list is infinity or negative infinity if the optimal
* value of the corresponding expression is unbounded and
* NaN if the intersection of "uset" with the domain of the expression
* is empty.
*/
static __isl_give isl_multi_val *isl_union_set_opt_multi_union_pw_aff(
__isl_keep isl_union_set *uset, int max,
__isl_keep isl_multi_union_pw_aff *obj)
{
uset = isl_union_set_copy(uset);
obj = isl_multi_union_pw_aff_copy(obj);
obj = isl_multi_union_pw_aff_intersect_domain(obj, uset);
return isl_multi_union_pw_aff_opt_multi_val(obj, max);
}
/* Return a list of minima over the points in "uset"
* for each of the expressions in "obj".
*
* An element in the list is infinity or negative infinity if the optimal
* value of the corresponding expression is unbounded and
* NaN if the intersection of "uset" with the domain of the expression
* is empty.
*/
__isl_give isl_multi_val *isl_union_set_min_multi_union_pw_aff(
__isl_keep isl_union_set *uset, __isl_keep isl_multi_union_pw_aff *obj)
{
return isl_union_set_opt_multi_union_pw_aff(uset, 0, obj);
}
/* Return a list of minima
* for each of the expressions in "mupa" over their domains.
*
* An element in the list is negative infinity if the optimal
* value of the corresponding expression is unbounded and
* NaN if the domain of the expression is empty.
*/
__isl_give isl_multi_val *isl_multi_union_pw_aff_min_multi_val(
__isl_take isl_multi_union_pw_aff *mupa)
{
return isl_multi_union_pw_aff_opt_multi_val(mupa, 0);
}
/* Return a list of maxima
* for each of the expressions in "mupa" over their domains.
*
* An element in the list is infinity if the optimal
* value of the corresponding expression is unbounded and
* NaN if the domain of the expression is empty.
*/
__isl_give isl_multi_val *isl_multi_union_pw_aff_max_multi_val(
__isl_take isl_multi_union_pw_aff *mupa)
{
return isl_multi_union_pw_aff_opt_multi_val(mupa, 1);
}
#undef BASE
#define BASE basic_set
#include "isl_ilp_opt_val_templ.c"
/* Return the maximal value attained by the given set dimension,
* independently of the parameter values and of any other dimensions.
*
* Return infinity if the optimal value is unbounded and
* NaN if "bset" is empty.
*/
__isl_give isl_val *isl_basic_set_dim_max_val(__isl_take isl_basic_set *bset,
int pos)
{
return isl_basic_set_dim_opt_val(bset, 1, pos);
}
#undef BASE
#define BASE set
#include "isl_ilp_opt_val_templ.c"
/* Return the minimal value attained by the given set dimension,
* independently of the parameter values and of any other dimensions.
*
* Return negative infinity if the optimal value is unbounded and
* NaN if "set" is empty.
*/
__isl_give isl_val *isl_set_dim_min_val(__isl_take isl_set *set, int pos)
{
return isl_set_dim_opt_val(set, 0, pos);
}
/* Return the maximal value attained by the given set dimension,
* independently of the parameter values and of any other dimensions.
*
* Return infinity if the optimal value is unbounded and
* NaN if "set" is empty.
*/
__isl_give isl_val *isl_set_dim_max_val(__isl_take isl_set *set, int pos)
{
return isl_set_dim_opt_val(set, 1, pos);
}
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