/*

 * Copyright 2005-2007 Universiteit Leiden

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 * Copyright 2010      INRIA Saclay

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,

 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,

 * B-3001 Leuven, Belgium

 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,

 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 

 */

#include <isl_map_private.h>

#include <isl_factorization.h>

#include <isl_space_private.h>

#include <isl_mat_private.h>

static __isl_give isl_factorizer *isl_factorizer_alloc(

	__isl_take isl_morph *morph, int n_group)

{

	isl_factorizer *f = NULL;

	int *len = NULL;

	if (!morph)

		return NULL;

	if (n_group > 0) {

		len = isl_alloc_array(morph->dom->ctx, int, n_group);

		if (!len)

			goto error;

	}

	f = isl_alloc_type(morph->dom->ctx, struct isl_factorizer);

	if (!f)

		goto error;

	f->morph = morph;

	f->n_group = n_group;

	f->len = len;

	return f;

error:

	free(len);

	isl_morph_free(morph);

	return NULL;

}

void isl_factorizer_free(__isl_take isl_factorizer *f)

{

	if (!f)

		return;

	isl_morph_free(f->morph);

	free(f->len);

	free(f);

}

void isl_factorizer_dump(__isl_take isl_factorizer *f)

{

	int i;

	if (!f)

		return;

	isl_morph_print_internal(f->morph, stderr);

	fprintf(stderr, "[");

	for (i = 0; i < f->n_group; ++i) {

		if (i)

			fprintf(stderr, ", ");

		fprintf(stderr, "%d", f->len[i]);

	}

	fprintf(stderr, "]\n");

}

__isl_give isl_factorizer *isl_factorizer_identity(__isl_keep isl_basic_set *bset)

{

	return isl_factorizer_alloc(isl_morph_identity(bset), 0);

}

__isl_give isl_factorizer *isl_factorizer_groups(__isl_keep isl_basic_set *bset,

	__isl_take isl_mat *Q, __isl_take isl_mat *U, int n, int *len)

{

	int i;

	unsigned nvar;

	unsigned ovar;

	isl_space *dim;

	isl_basic_set *dom;

	isl_basic_set *ran;

	isl_morph *morph;

	isl_factorizer *f;

	isl_mat *id;

	if (!bset || !Q || !U)

		goto error;

	ovar = 1 + isl_space_offset(bset->dim, isl_dim_set);

	id = isl_mat_identity(bset->ctx, ovar);

	Q = isl_mat_diagonal(isl_mat_copy(id), Q);

	U = isl_mat_diagonal(id, U);

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	dim = isl_basic_set_get_space(bset);

	dom = isl_basic_set_universe(isl_space_copy(dim));

	dim = isl_space_drop_dims(dim, isl_dim_set, 0, nvar);

	dim = isl_space_add_dims(dim, isl_dim_set, nvar);

	ran = isl_basic_set_universe(dim);

	morph = isl_morph_alloc(dom, ran, Q, U);

	f = isl_factorizer_alloc(morph, n);

	if (!f)

		return NULL;

	for (i = 0; i < n; ++i)

		f->len[i] = len[i];

	return f;

error:

	isl_mat_free(Q);

	isl_mat_free(U);

	return NULL;

}

struct isl_factor_groups {

	int *pos;		/* for each column: row position of pivot */

	int *group;		/* group to which a column belongs */

	int *cnt;		/* number of columns in the group */

	int *rowgroup;		/* group to which a constraint belongs */

};

/* Initialize isl_factor_groups structure: find pivot row positions,

 * each column initially belongs to its own group and the groups

 * of the constraints are still unknown.

 */

static int init_groups(struct isl_factor_groups *g, __isl_keep isl_mat *H)

{

	int i, j;

	if (!H)

		return -1;

	g->pos = isl_alloc_array(H->ctx, int, H->n_col);

	g->group = isl_alloc_array(H->ctx, int, H->n_col);

	g->cnt = isl_alloc_array(H->ctx, int, H->n_col);

	g->rowgroup = isl_alloc_array(H->ctx, int, H->n_row);

	if (!g->pos || !g->group || !g->cnt || !g->rowgroup)

		return -1;

	for (i = 0; i < H->n_row; ++i)

		g->rowgroup[i] = -1;

	for (i = 0, j = 0; i < H->n_col; ++i) {

		for ( ; j < H->n_row; ++j)

			if (!isl_int_is_zero(H->row[j][i]))

				break;

		g->pos[i] = j;

	}

	for (i = 0; i < H->n_col; ++i) {

		g->group[i] = i;

		g->cnt[i] = 1;

	}

	return 0;

}

/* Update group[k] to the group column k belongs to.

 * When merging two groups, only the group of the current

 * group leader is changed.  Here we change the group of

 * the other members to also point to the group that the

 * old group leader now points to.

 */

static void update_group(struct isl_factor_groups *g, int k)

{

	int p = g->group[k];

	while (g->cnt[p] == 0)

		p = g->group[p];

	g->group[k] = p;

}

/* Merge group i with all groups of the subsequent columns

 * with non-zero coefficients in row j of H.

 * (The previous columns are all zero; otherwise we would have handled

 * the row before.)

 */

static int update_group_i_with_row_j(struct isl_factor_groups *g, int i, int j,

	__isl_keep isl_mat *H)

{

	int k;

	g->rowgroup[j] = g->group[i];

	for (k = i + 1; k < H->n_col && j >= g->pos[k]; ++k) {

		update_group(g, k);

		update_group(g, i);

		if (g->group[k] != g->group[i] &&

		    !isl_int_is_zero(H->row[j][k])) {

			isl_assert(H->ctx, g->cnt[g->group[k]] != 0, return -1);

			isl_assert(H->ctx, g->cnt[g->group[i]] != 0, return -1);

			if (g->group[i] < g->group[k]) {

				g->cnt[g->group[i]] += g->cnt[g->group[k]];

				g->cnt[g->group[k]] = 0;

				g->group[g->group[k]] = g->group[i];

			} else {

				g->cnt[g->group[k]] += g->cnt[g->group[i]];

				g->cnt[g->group[i]] = 0;

				g->group[g->group[i]] = g->group[k];

			}

		}

	}

	return 0;

}

/* Update the group information based on the constraint matrix.

 */

static int update_groups(struct isl_factor_groups *g, __isl_keep isl_mat *H)

{

	int i, j;

	for (i = 0; i < H->n_col && g->cnt[0] < H->n_col; ++i) {

		if (g->pos[i] == H->n_row)

			continue; /* A line direction */

		if (g->rowgroup[g->pos[i]] == -1)

			g->rowgroup[g->pos[i]] = i;

		for (j = g->pos[i] + 1; j < H->n_row; ++j) {

			if (isl_int_is_zero(H->row[j][i]))

				continue;

			if (g->rowgroup[j] != -1)

				continue;

			if (update_group_i_with_row_j(g, i, j, H) < 0)

				return -1;

		}

	}

	for (i = 1; i < H->n_col; ++i)

		update_group(g, i);

	return 0;

}

static void clear_groups(struct isl_factor_groups *g)

{

	if (!g)

		return;

	free(g->pos);

	free(g->group);

	free(g->cnt);

	free(g->rowgroup);

}

/* Determine if the set variables of the basic set can be factorized and

 * return the results in an isl_factorizer.

 *

 * The algorithm works by first computing the Hermite normal form

 * and then grouping columns linked by one or more constraints together,

 * where a constraints "links" two or more columns if the constraint

 * has nonzero coefficients in the columns.

 */

__isl_give isl_factorizer *isl_basic_set_factorizer(

	__isl_keep isl_basic_set *bset)

{

	int i, j, n, done;

	isl_mat *H, *U, *Q;

	unsigned nvar;

	struct isl_factor_groups g = { 0 };

	isl_factorizer *f;

	if (!bset)

		return NULL;

	isl_assert(bset->ctx, isl_basic_set_dim(bset, isl_dim_div) == 0,

		return NULL);

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	if (nvar <= 1)

		return isl_factorizer_identity(bset);

	H = isl_mat_alloc(bset->ctx, bset->n_eq + bset->n_ineq, nvar);

	if (!H)

		return NULL;

	isl_mat_sub_copy(bset->ctx, H->row, bset->eq, bset->n_eq,

		0, 1 + isl_space_offset(bset->dim, isl_dim_set), nvar);

	isl_mat_sub_copy(bset->ctx, H->row + bset->n_eq, bset->ineq, bset->n_ineq,

		0, 1 + isl_space_offset(bset->dim, isl_dim_set), nvar);

	H = isl_mat_left_hermite(H, 0, &U, &Q);

	if (init_groups(&g, H) < 0)

		goto error;

	if (update_groups(&g, H) < 0)

		goto error;

	if (g.cnt[0] == nvar) {

		isl_mat_free(H);

		isl_mat_free(U);

		isl_mat_free(Q);

		clear_groups(&g);

		return isl_factorizer_identity(bset);

	}

	done = 0;

	n = 0;

	while (done != nvar) {

		int group = g.group[done];

		for (i = 1; i < g.cnt[group]; ++i) {

			if (g.group[done + i] == group)

				continue;

			for (j = done + g.cnt[group]; j < nvar; ++j)

				if (g.group[j] == group)

					break;

			if (j == nvar)

				isl_die(bset->ctx, isl_error_internal,

					"internal error", goto error);

			g.group[j] = g.group[done + i];

			Q = isl_mat_swap_rows(Q, done + i, j);

			U = isl_mat_swap_cols(U, done + i, j);

		}

		done += g.cnt[group];

		g.pos[n++] = g.cnt[group];

	}

	f = isl_factorizer_groups(bset, Q, U, n, g.pos);

	isl_mat_free(H);

	clear_groups(&g);

	return f;

error:

	isl_mat_free(H);

	isl_mat_free(U);

	isl_mat_free(Q);

	clear_groups(&g);

	return NULL;

}