File: isl_lp.c

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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;
	unsigned dim = isl_basic_map_total_dim(bmap);

	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(struct isl_basic_set *bset, int max,
				      isl_int *f, isl_int d, isl_int *opt,
				      isl_int *opt_denom,
				      struct 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,
				      struct 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) {
		unsigned total = isl_space_dim(map->dim, isl_dim_all);
		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,
				      struct 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;
	int 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 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);
}