/*

 * 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 <assert.h>

#include <isl_map_private.h>

#include <isl_seq.h>

#include "isl_tab.h"

#include <isl_int.h>

#include <isl_config.h>

struct tab_lp {

	struct isl_ctx  *ctx;

	struct isl_vec  *row;

	struct isl_tab  *tab;

	struct isl_tab_undo	**stack;

	isl_int		*obj;

	isl_int		 opt;

	isl_int		 opt_denom;

	isl_int		 tmp;

	isl_int		 tmp2;

	int	         neq;

	unsigned	 dim;

	/* number of constraints in initial product tableau */

	int		 con_offset;

	/* objective function has fixed or no integer value */

	int		 is_fixed;

};

#ifdef USE_GMP_FOR_MP

#define GBR_type		    	    mpq_t

#define GBR_init(v)		    	    mpq_init(v)

#define GBR_clear(v)		    	    mpq_clear(v)

#define GBR_set(a,b)			    mpq_set(a,b)

#define GBR_set_ui(a,b)			    mpq_set_ui(a,b,1)

#define GBR_mul(a,b,c)			    mpq_mul(a,b,c)

#define GBR_lt(a,b)			    (mpq_cmp(a,b) < 0)

#define GBR_is_zero(a)			    (mpq_sgn(a) == 0)

#define GBR_numref(a)			    mpq_numref(a)

#define GBR_denref(a)			    mpq_denref(a)

#define GBR_floor(a,b)			    mpz_fdiv_q(a,GBR_numref(b),GBR_denref(b))

#define GBR_ceil(a,b)			    mpz_cdiv_q(a,GBR_numref(b),GBR_denref(b))

#endif /* USE_GMP_FOR_MP */

#ifdef USE_IMATH_FOR_MP

#include <imrat.h>

#define GBR_type		    	    mp_rat

#define GBR_init(v)		    	    v = mp_rat_alloc()

#define GBR_clear(v)		    	    mp_rat_free(v)

#define GBR_set(a,b)			    mp_rat_copy(b,a)

#define GBR_set_ui(a,b)			    mp_rat_set_uvalue(a,b,1)

#define GBR_mul(a,b,c)			    mp_rat_mul(b,c,a)

#define GBR_lt(a,b)			    (mp_rat_compare(a,b) < 0)

#define GBR_is_zero(a)			    (mp_rat_compare_zero(a) == 0)

#define GBR_numref(a)			    mp_rat_numer_ref(a)

#define GBR_denref(a)			    mp_rat_denom_ref(a)

#define GBR_floor(a,b)			    impz_fdiv_q(a,GBR_numref(b),GBR_denref(b))

#define GBR_ceil(a,b)			    impz_cdiv_q(a,GBR_numref(b),GBR_denref(b))

#endif /* USE_IMATH_FOR_MP */

static struct tab_lp *init_lp(struct isl_tab *tab);

static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim);

static int solve_lp(struct tab_lp *lp);

static void get_obj_val(struct tab_lp* lp, GBR_type *F);

static void delete_lp(struct tab_lp *lp);

static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim);

static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha);

static int del_lp_row(struct tab_lp *lp) WARN_UNUSED;

static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row);

#define GBR_LP			    	    struct tab_lp

#define GBR_lp_init(P)		    	    init_lp(P)

#define GBR_lp_set_obj(lp, obj, dim)	    set_lp_obj(lp, obj, dim)

#define GBR_lp_solve(lp)		    solve_lp(lp)

#define GBR_lp_get_obj_val(lp, F)	    get_obj_val(lp, F)

#define GBR_lp_delete(lp)		    delete_lp(lp)

#define GBR_lp_next_row(lp)		    lp->neq

#define GBR_lp_add_row(lp, row, dim)	    add_lp_row(lp, row, dim)

#define GBR_lp_get_alpha(lp, row, alpha)    get_alpha(lp, row, alpha)

#define GBR_lp_del_row(lp)		    del_lp_row(lp)

#define GBR_lp_is_fixed(lp)		    (lp)->is_fixed

#define GBR_lp_cut(lp, obj)	    	    cut_lp_to_hyperplane(lp, obj)

#include "basis_reduction_templ.c"

/* Set up a tableau for the Cartesian product of bset with itself.

 * This could be optimized by first setting up a tableau for bset

 * and then performing the Cartesian product on the tableau.

 */

static struct isl_tab *gbr_tab(struct isl_tab *tab, struct isl_vec *row)

{

	unsigned dim;

	struct isl_tab *prod;

	if (!tab || !row)

		return NULL;

	dim = tab->n_var;

	prod = isl_tab_product(tab, tab);

	if (isl_tab_extend_cons(prod, 3 * dim + 1) < 0) {

		isl_tab_free(prod);

		return NULL;

	}

	return prod;

}

static struct tab_lp *init_lp(struct isl_tab *tab)

{

	struct tab_lp *lp = NULL;

	if (!tab)

		return NULL;

	lp = isl_calloc_type(tab->mat->ctx, struct tab_lp);

	if (!lp)

		return NULL;

	isl_int_init(lp->opt);

	isl_int_init(lp->opt_denom);

	isl_int_init(lp->tmp);

	isl_int_init(lp->tmp2);

	lp->dim = tab->n_var;

	lp->ctx = tab->mat->ctx;

	isl_ctx_ref(lp->ctx);

	lp->stack = isl_alloc_array(lp->ctx, struct isl_tab_undo *, lp->dim);

	lp->row = isl_vec_alloc(lp->ctx, 1 + 2 * lp->dim);

	if (!lp->row)

		goto error;

	lp->tab = gbr_tab(tab, lp->row);

	if (!lp->tab)

		goto error;

	lp->con_offset = lp->tab->n_con;

	lp->obj = NULL;

	lp->neq = 0;

	return lp;

error:

	delete_lp(lp);

	return NULL;

}

static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim)

{

	lp->obj = row;

}

static int solve_lp(struct tab_lp *lp)

{

	enum isl_lp_result res;

	unsigned flags = 0;

	lp->is_fixed = 0;

	isl_int_set_si(lp->row->el[0], 0);

	isl_seq_cpy(lp->row->el + 1, lp->obj, lp->dim);

	isl_seq_neg(lp->row->el + 1 + lp->dim, lp->obj, lp->dim);

	if (lp->neq)

		flags = ISL_TAB_SAVE_DUAL;

	res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,

			  &lp->opt, &lp->opt_denom, flags);

	isl_int_mul_ui(lp->opt_denom, lp->opt_denom, 2);

	if (isl_int_abs_lt(lp->opt, lp->opt_denom)) {

		struct isl_vec *sample = isl_tab_get_sample_value(lp->tab);

		if (!sample)

			return -1;

		isl_seq_inner_product(lp->obj, sample->el + 1, lp->dim, &lp->tmp);

		isl_seq_inner_product(lp->obj, sample->el + 1 + lp->dim, lp->dim, &lp->tmp2);

		isl_int_cdiv_q(lp->tmp, lp->tmp, sample->el[0]);

		isl_int_fdiv_q(lp->tmp2, lp->tmp2, sample->el[0]);

		if (isl_int_ge(lp->tmp, lp->tmp2))

			lp->is_fixed = 1;

		isl_vec_free(sample);

	}

	isl_int_divexact_ui(lp->opt_denom, lp->opt_denom, 2);

	if (res != isl_lp_ok)

		return -1;

	return 0;

}

/* The current objective function has a fixed (or no) integer value.

 * Cut the tableau to the hyperplane that fixes this value in

 * both halves of the tableau.

 * Return 1 if the resulting tableau is empty.

 */

static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row)

{

	enum isl_lp_result res;

	isl_int_set_si(lp->row->el[0], 0);

	isl_seq_cpy(lp->row->el + 1, row, lp->dim);

	isl_seq_clr(lp->row->el + 1 + lp->dim, lp->dim);

	res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,

			  &lp->tmp, NULL, 0);

	if (res != isl_lp_ok)

		return -1;

	isl_int_neg(lp->row->el[0], lp->tmp);

	if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)

		return -1;

	isl_seq_cpy(lp->row->el + 1 + lp->dim, row, lp->dim);

	isl_seq_clr(lp->row->el + 1, lp->dim);

	if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)

		return -1;

	lp->con_offset += 2;

	return lp->tab->empty;

}

static void get_obj_val(struct tab_lp* lp, GBR_type *F)

{

	isl_int_neg(GBR_numref(*F), lp->opt);

	isl_int_set(GBR_denref(*F), lp->opt_denom);

}

static void delete_lp(struct tab_lp *lp)

{

	if (!lp)

		return;

	isl_int_clear(lp->opt);

	isl_int_clear(lp->opt_denom);

	isl_int_clear(lp->tmp);

	isl_int_clear(lp->tmp2);

	isl_vec_free(lp->row);

	free(lp->stack);

	isl_tab_free(lp->tab);

	isl_ctx_deref(lp->ctx);

	free(lp);

}

static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim)

{

	lp->stack[lp->neq] = isl_tab_snap(lp->tab);

	isl_int_set_si(lp->row->el[0], 0);

	isl_seq_cpy(lp->row->el + 1, row, lp->dim);

	isl_seq_neg(lp->row->el + 1 + lp->dim, row, lp->dim);

	if (isl_tab_add_valid_eq(lp->tab, lp->row->el) < 0)

		return -1;

	return lp->neq++;

}

static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha)

{

	row += lp->con_offset;

	isl_int_neg(GBR_numref(*alpha), lp->tab->dual->el[1 + row]);

	isl_int_set(GBR_denref(*alpha), lp->tab->dual->el[0]);

}

static int del_lp_row(struct tab_lp *lp)

{

	lp->neq--;

	return isl_tab_rollback(lp->tab, lp->stack[lp->neq]);

}