basis_reduction_tab.c

/*
 * 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))
#define GBR_set_num_neg(a, b)		    mpz_neg(GBR_numref(*a), b);
#define GBR_set_den(a, b)		    mpz_set(GBR_denref(*a), 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)
#ifdef USE_SMALL_INT_OPT
#define GBR_numref(a)	isl_sioimath_encode_big(mp_rat_numer_ref(a))
#define GBR_denref(a)	isl_sioimath_encode_big(mp_rat_denom_ref(a))
#define GBR_floor(a, b)	isl_sioimath_fdiv_q(&(a), GBR_numref(b), GBR_denref(b))
#define GBR_ceil(a, b)	isl_sioimath_cdiv_q(&(a), GBR_numref(b), GBR_denref(b))
#define GBR_set_num_neg(a, b)                              \
	do {                                               \
		isl_sioimath_scratchspace_t scratch;       \
		impz_neg(mp_rat_numer_ref(*a),             \
		    isl_sioimath_bigarg_src(b, &scratch)); \
	} while (0)
#define GBR_set_den(a, b)                                  \
	do {                                               \
		isl_sioimath_scratchspace_t scratch;       \
		impz_set(mp_rat_denom_ref(*a),             \
		    isl_sioimath_bigarg_src(b, &scratch)); \
	} while (0)
#else /* USE_SMALL_INT_OPT */
#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))
#define GBR_set_num_neg(a, b)	impz_neg(GBR_numref(*a), b)
#define GBR_set_den(a, b)	impz_set(GBR_denref(*a), b)
#endif /* USE_SMALL_INT_OPT */
#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 < 0)
		return -1;
	if (res != isl_lp_ok)
		isl_die(lp->ctx, isl_error_internal,
			"unexpected missing (bounded) solution", 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)
{
	GBR_set_num_neg(F, lp->opt);
	GBR_set_den(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;
	GBR_set_num_neg(alpha, lp->tab->dual->el[1 + row]);
	GBR_set_den(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]);
}