/*

 * 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_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>

#include <isl/deprecated/ilp_int.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 struct isl_basic_set *unit_box_base_points(struct isl_basic_set *bset)

{

	int i, j, k;

	struct isl_basic_set *unit_box = NULL;

	unsigned total;

	if (!bset)

		goto error;

	if (bset->n_eq != 0) {

		unit_box = isl_basic_set_empty_like(bset);

		isl_basic_set_free(bset);

		return unit_box;

	}

	total = isl_basic_set_total_dim(bset);

	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 struct isl_vec *initial_solution(struct 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 struct isl_basic_set *add_bounds(struct isl_basic_set *bset,

	isl_int *f, isl_int l, isl_int u)

{

	int k;

	unsigned total;

	total = isl_basic_set_total_dim(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 struct isl_vec *solve_ilp_search(struct isl_basic_set *bset,

	isl_int *f, isl_int *opt, struct 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(struct isl_basic_set *bset,

				      isl_int *f, isl_int *opt,

				      struct 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(struct isl_basic_set *bset, int max,

				      isl_int *f, isl_int *opt,

				      struct isl_vec **sol_p)

{

	unsigned 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_total_dim(bset);

	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(struct isl_basic_set *bset, int max,

				      isl_int *f, isl_int *opt,

				      struct isl_vec **sol_p)

{

	unsigned dim;

	enum isl_lp_result res;

	if (!bset)

		return isl_lp_error;

	if (sol_p)

		*sol_p = NULL;

	isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto 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_total_dim(bset);

	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;

error:

	isl_basic_set_free(bset);

	return isl_lp_error;

}

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;

}

static __isl_give isl_mat *extract_divs(__isl_keep isl_basic_set *bset)

{

	int i;

	isl_ctx *ctx = isl_basic_set_get_ctx(bset);

	isl_mat *div;

	div = isl_mat_alloc(ctx, bset->n_div,

			    1 + 1 + isl_basic_set_total_dim(bset));

	if (!div)

		return NULL;

	for (i = 0; i < bset->n_div; ++i)

		isl_seq_cpy(div->row[i], bset->div[i], div->n_col);

	return div;

}

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;

	int 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 basic_set_opt(bset, max, obj, opt);

	bset = isl_basic_set_copy(bset);

	obj = isl_aff_copy(obj);

	bset_div = extract_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_ok)

			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;

	if (!set || !obj)

		return isl_lp_error;

	if (isl_space_match(set->dim, isl_dim_param,

			    obj->ls->dim, isl_dim_param))

		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;

}

enum isl_lp_result isl_basic_set_max(__isl_keep isl_basic_set *bset,

	__isl_keep isl_aff *obj, isl_int *opt)

{

	return isl_basic_set_opt(bset, 1, obj, opt);

}

enum isl_lp_result isl_set_max(__isl_keep isl_set *set,

	__isl_keep isl_aff *obj, isl_int *opt)

{

	return isl_set_opt(set, 1, obj, opt);

}

enum isl_lp_result isl_set_min(__isl_keep isl_set *set,

	__isl_keep isl_aff *obj, isl_int *opt)

{

	return isl_set_opt(set, 0, obj, opt);

}

/* 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 "bset" 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 "bset" 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 "bset" 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);

}