/*

 * Copyright 2010-2011 INRIA Saclay

 * Copyright 2014      Ecole Normale Superieure

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,

 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,

 * 91893 Orsay, France 

 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France

 */

#include <isl_map_private.h>

#include <isl_aff_private.h>

#include <isl_morph.h>

#include <isl_seq.h>

#include <isl_mat_private.h>

#include <isl_space_private.h>

#include <isl_equalities.h>

isl_ctx *isl_morph_get_ctx(__isl_keep isl_morph *morph)

{

	if (!morph)

		return NULL;

	return isl_basic_set_get_ctx(morph->dom);

}

__isl_give isl_morph *isl_morph_alloc(

	__isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,

	__isl_take isl_mat *map, __isl_take isl_mat *inv)

{

	isl_morph *morph;

	if (!dom || !ran || !map || !inv)

		goto error;

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

	if (!morph)

		goto error;

	morph->ref = 1;

	morph->dom = dom;

	morph->ran = ran;

	morph->map = map;

	morph->inv = inv;

	return morph;

error:

	isl_basic_set_free(dom);

	isl_basic_set_free(ran);

	isl_mat_free(map);

	isl_mat_free(inv);

	return NULL;

}

__isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)

{

	if (!morph)

		return NULL;

	morph->ref++;

	return morph;

}

__isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)

{

	if (!morph)

		return NULL;

	return isl_morph_alloc(isl_basic_set_copy(morph->dom),

		isl_basic_set_copy(morph->ran),

		isl_mat_copy(morph->map), isl_mat_copy(morph->inv));

}

__isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)

{

	if (!morph)

		return NULL;

	if (morph->ref == 1)

		return morph;

	morph->ref--;

	return isl_morph_dup(morph);

}

void isl_morph_free(__isl_take isl_morph *morph)

{

	if (!morph)

		return;

	if (--morph->ref > 0)

		return;

	isl_basic_set_free(morph->dom);

	isl_basic_set_free(morph->ran);

	isl_mat_free(morph->map);

	isl_mat_free(morph->inv);

	free(morph);

}

/* Is "morph" an identity on the parameters?

 */

static int identity_on_parameters(__isl_keep isl_morph *morph)

{

	int is_identity;

	unsigned nparam;

	isl_mat *sub;

	nparam = isl_morph_dom_dim(morph, isl_dim_param);

	if (nparam != isl_morph_ran_dim(morph, isl_dim_param))

		return 0;

	if (nparam == 0)

		return 1;

	sub = isl_mat_sub_alloc(morph->map, 0, 1 + nparam, 0, 1 + nparam);

	is_identity = isl_mat_is_scaled_identity(sub);

	isl_mat_free(sub);

	return is_identity;

}

/* Return an affine expression of the variables of the range of "morph"

 * in terms of the parameters and the variables of the domain on "morph".

 *

 * In order for the space manipulations to make sense, we require

 * that the parameters are not modified by "morph".

 */

__isl_give isl_multi_aff *isl_morph_get_var_multi_aff(

	__isl_keep isl_morph *morph)

{

	isl_space *dom, *ran, *space;

	isl_local_space *ls;

	isl_multi_aff *ma;

	unsigned nparam, nvar;

	int i;

	int is_identity;

	if (!morph)

		return NULL;

	is_identity = identity_on_parameters(morph);

	if (is_identity < 0)

		return NULL;

	if (!is_identity)

		isl_die(isl_morph_get_ctx(morph), isl_error_invalid,

			"cannot handle parameter compression", return NULL);

	dom = isl_morph_get_dom_space(morph);

	ls = isl_local_space_from_space(isl_space_copy(dom));

	ran = isl_morph_get_ran_space(morph);

	space = isl_space_map_from_domain_and_range(dom, ran);

	ma = isl_multi_aff_zero(space);

	nparam = isl_multi_aff_dim(ma, isl_dim_param);

	nvar = isl_multi_aff_dim(ma, isl_dim_out);

	for (i = 0; i < nvar; ++i) {

		isl_val *val;

		isl_vec *v;

		isl_aff *aff;

		v = isl_mat_get_row(morph->map, 1 + nparam + i);

		v = isl_vec_insert_els(v, 0, 1);

		val = isl_mat_get_element_val(morph->map, 0, 0);

		v = isl_vec_set_element_val(v, 0, val);

		aff = isl_aff_alloc_vec(isl_local_space_copy(ls), v);

		ma = isl_multi_aff_set_aff(ma, i, aff);

	}

	isl_local_space_free(ls);

	return ma;

}

/* Return the domain space of "morph".

 */

__isl_give isl_space *isl_morph_get_dom_space(__isl_keep isl_morph *morph)

{

	if (!morph)

		return NULL;

	return isl_basic_set_get_space(morph->dom);

}

__isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)

{

	if (!morph)

		return NULL;

	return isl_space_copy(morph->ran->dim);

}

unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)

{

	if (!morph)

		return 0;

	return isl_basic_set_dim(morph->dom, type);

}

unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)

{

	if (!morph)

		return 0;

	return isl_basic_set_dim(morph->ran, type);

}

__isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,

	enum isl_dim_type type, unsigned first, unsigned n)

{

	unsigned dom_offset;

	if (n == 0)

		return morph;

	morph = isl_morph_cow(morph);

	if (!morph)

		return NULL;

	dom_offset = 1 + isl_space_offset(morph->dom->dim, type);

	morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);

	morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);

	morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);

	if (morph->dom && morph->ran && morph->map && morph->inv)

		return morph;

	isl_morph_free(morph);

	return NULL;

}

__isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,

	enum isl_dim_type type, unsigned first, unsigned n)

{

	unsigned ran_offset;

	if (n == 0)

		return morph;

	morph = isl_morph_cow(morph);

	if (!morph)

		return NULL;

	ran_offset = 1 + isl_space_offset(morph->ran->dim, type);

	morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);

	morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);

	morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);

	if (morph->dom && morph->ran && morph->map && morph->inv)

		return morph;

	isl_morph_free(morph);

	return NULL;

}

/* Project domain of morph onto its parameter domain.

 */

__isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)

{

	unsigned n;

	morph = isl_morph_cow(morph);

	if (!morph)

		return NULL;

	n = isl_basic_set_dim(morph->dom, isl_dim_set);

	morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);

	if (!morph)

		return NULL;

	morph->dom = isl_basic_set_params(morph->dom);

	if (morph->dom)

		return morph;

	isl_morph_free(morph);

	return NULL;

}

/* Project range of morph onto its parameter domain.

 */

__isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)

{

	unsigned n;

	morph = isl_morph_cow(morph);

	if (!morph)

		return NULL;

	n = isl_basic_set_dim(morph->ran, isl_dim_set);

	morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);

	if (!morph)

		return NULL;

	morph->ran = isl_basic_set_params(morph->ran);

	if (morph->ran)

		return morph;

	isl_morph_free(morph);

	return NULL;

}

void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)

{

	if (!morph)

		return;

	isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);

	isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);

	isl_mat_print_internal(morph->map, out, 4);

	isl_mat_print_internal(morph->inv, out, 4);

}

void isl_morph_dump(__isl_take isl_morph *morph)

{

	isl_morph_print_internal(morph, stderr);

}

__isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)

{

	isl_mat *id;

	isl_basic_set *universe;

	unsigned total;

	if (!bset)

		return NULL;

	total = isl_basic_set_total_dim(bset);

	id = isl_mat_identity(bset->ctx, 1 + total);

	universe = isl_basic_set_universe(isl_space_copy(bset->dim));

	return isl_morph_alloc(universe, isl_basic_set_copy(universe),

		id, isl_mat_copy(id));

}

/* Create a(n identity) morphism between empty sets of the same dimension

 * a "bset".

 */

__isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)

{

	isl_mat *id;

	isl_basic_set *empty;

	unsigned total;

	if (!bset)

		return NULL;

	total = isl_basic_set_total_dim(bset);

	id = isl_mat_identity(bset->ctx, 1 + total);

	empty = isl_basic_set_empty(isl_space_copy(bset->dim));

	return isl_morph_alloc(empty, isl_basic_set_copy(empty),

		id, isl_mat_copy(id));

}

/* Given a matrix that maps a (possibly) parametric domain to

 * a parametric domain, add in rows that map the "nparam" parameters onto

 * themselves.

 */

static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,

	unsigned nparam)

{

	int i;

	if (nparam == 0)

		return mat;

	if (!mat)

		return NULL;

	mat = isl_mat_insert_rows(mat, 1, nparam);

	if (!mat)

		return NULL;

	for (i = 0; i < nparam; ++i) {

		isl_seq_clr(mat->row[1 + i], mat->n_col);

		isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);

	}

	return mat;

}

/* Construct a basic set described by the "n" equalities of "bset" starting

 * at "first".

 */

static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,

	unsigned first, unsigned n)

{

	int i, k;

	isl_basic_set *eq;

	unsigned total;

	isl_assert(bset->ctx, bset->n_div == 0, return NULL);

	total = isl_basic_set_total_dim(bset);

	eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);

	if (!eq)

		return NULL;

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

		k = isl_basic_set_alloc_equality(eq);

		if (k < 0)

			goto error;

		isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);

	}

	return eq;

error:

	isl_basic_set_free(eq);

	return NULL;

}

/* Given a basic set, exploit the equalties in the basic set to construct

 * a morphishm that maps the basic set to a lower-dimensional space.

 * Specifically, the morphism reduces the number of dimensions of type "type".

 *

 * This function is a slight generalization of isl_mat_variable_compression

 * in that it allows the input to be parametric and that it allows for the

 * compression of either parameters or set variables.

 *

 * We first select the equalities of interest, that is those that involve

 * variables of type "type" and no later variables.

 * Denote those equalities as

 *

 *		-C(p) + M x = 0

 *

 * where C(p) depends on the parameters if type == isl_dim_set and

 * is a constant if type == isl_dim_param.

 *

 * First compute the (left) Hermite normal form of M,

 *

 *		M [U1 U2] = M U = H = [H1 0]

 * or

 *		              M = H Q = [H1 0] [Q1]

 *                                             [Q2]

 *

 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).

 * Define the transformed variables as

 *

 *		x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x

 *		            [ x2' ]           [Q2]

 *

 * The equalities then become

 *

 *		-C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)

 *

 * If the denominator of the constant term does not divide the

 * the common denominator of the parametric terms, then every

 * integer point is mapped to a non-integer point and then the original set has no

 * integer solutions (since the x' are a unimodular transformation

 * of the x).  In this case, an empty morphism is returned.

 * Otherwise, the transformation is given by

 *

 *		x = U1 H1^{-1} C(p) + U2 x2'

 *

 * The inverse transformation is simply

 *

 *		x2' = Q2 x

 *

 * Both matrices are extended to map the full original space to the full

 * compressed space.

 */

__isl_give isl_morph *isl_basic_set_variable_compression(

	__isl_keep isl_basic_set *bset, enum isl_dim_type type)

{

	unsigned otype;

	unsigned ntype;

	unsigned orest;

	unsigned nrest;

	int f_eq, n_eq;

	isl_space *dim;

	isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;

	isl_basic_set *dom, *ran;

	if (!bset)

		return NULL;

	if (isl_basic_set_plain_is_empty(bset))

		return isl_morph_empty(bset);

	isl_assert(bset->ctx, bset->n_div == 0, return NULL);

	otype = 1 + isl_space_offset(bset->dim, type);

	ntype = isl_basic_set_dim(bset, type);

	orest = otype + ntype;

	nrest = isl_basic_set_total_dim(bset) - (orest - 1);

	for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)

		if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)

			break;

	for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)

		if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)

			break;

	if (n_eq == 0)

		return isl_morph_identity(bset);

	H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);

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

	if (!H || !U || !Q)

		goto error;

	Q = isl_mat_drop_rows(Q, 0, n_eq);

	Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);

	Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));

	C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);

	if (!C)

		goto error;

	isl_int_set_si(C->row[0][0], 1);

	isl_seq_clr(C->row[0] + 1, otype - 1);

	isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);

	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);

	H1 = isl_mat_lin_to_aff(H1);

	C = isl_mat_inverse_product(H1, C);

	if (!C)

		goto error;

	isl_mat_free(H);

	if (!isl_int_is_one(C->row[0][0])) {

		int i;

		isl_int g;

		isl_int_init(g);

		for (i = 0; i < n_eq; ++i) {

			isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);

			isl_int_gcd(g, g, C->row[0][0]);

			if (!isl_int_is_divisible_by(C->row[1 + i][0], g))

				break;

		}

		isl_int_clear(g);

		if (i < n_eq) {

			isl_mat_free(C);

			isl_mat_free(U);

			isl_mat_free(Q);

			return isl_morph_empty(bset);

		}

		C = isl_mat_normalize(C);

	}

	U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);

	U1 = isl_mat_lin_to_aff(U1);

	U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);

	U2 = isl_mat_lin_to_aff(U2);

	isl_mat_free(U);

	C = isl_mat_product(U1, C);

	C = isl_mat_aff_direct_sum(C, U2);

	C = insert_parameter_rows(C, otype - 1);

	C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));

	dim = isl_space_copy(bset->dim);

	dim = isl_space_drop_dims(dim, type, 0, ntype);

	dim = isl_space_add_dims(dim, type, ntype - n_eq);

	ran = isl_basic_set_universe(dim);

	dom = copy_equalities(bset, f_eq, n_eq);

	return isl_morph_alloc(dom, ran, Q, C);

error:

	isl_mat_free(C);

	isl_mat_free(H);

	isl_mat_free(U);

	isl_mat_free(Q);

	return NULL;

}

/* Construct a parameter compression for "bset".

 * We basically just call isl_mat_parameter_compression with the right input

 * and then extend the resulting matrix to include the variables.

 *

 * The implementation assumes that "bset" does not have any equalities

 * that only involve the parameters and that isl_basic_set_gauss has

 * been applied to "bset".

 *

 * Let the equalities be given as

 *

 *	B(p) + A x = 0.

 *

 * We use isl_mat_parameter_compression_ext to compute the compression

 *

 *	p = T p'.

 */

__isl_give isl_morph *isl_basic_set_parameter_compression(

	__isl_keep isl_basic_set *bset)

{

	unsigned nparam;

	unsigned nvar;

	unsigned n_div;

	int n_eq;

	isl_mat *H, *B;

	isl_mat *map, *inv;

	isl_basic_set *dom, *ran;

	if (!bset)

		return NULL;

	if (isl_basic_set_plain_is_empty(bset))

		return isl_morph_empty(bset);

	if (bset->n_eq == 0)

		return isl_morph_identity(bset);

	n_eq = bset->n_eq;

	nparam = isl_basic_set_dim(bset, isl_dim_param);

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	n_div = isl_basic_set_dim(bset, isl_dim_div);

	if (isl_seq_first_non_zero(bset->eq[bset->n_eq - 1] + 1 + nparam,

				    nvar + n_div) == -1)

		isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,

			"input not allowed to have parameter equalities",

			return NULL);

	if (n_eq > nvar + n_div)

		isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,

			"input not gaussed", return NULL);

	B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);

	H = isl_mat_sub_alloc6(bset->ctx, bset->eq,

				0, n_eq, 1 + nparam, nvar + n_div);

	inv = isl_mat_parameter_compression_ext(B, H);

	inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));

	map = isl_mat_right_inverse(isl_mat_copy(inv));

	dom = isl_basic_set_universe(isl_space_copy(bset->dim));

	ran = isl_basic_set_universe(isl_space_copy(bset->dim));

	return isl_morph_alloc(dom, ran, map, inv);

}

/* Add stride constraints to "bset" based on the inverse mapping

 * that was plugged in.  In particular, if morph maps x' to x,

 * the the constraints of the original input

 *

 *	A x' + b >= 0

 *

 * have been rewritten to

 *

 *	A inv x + b >= 0

 *

 * However, this substitution may loose information on the integrality of x',

 * so we need to impose that

 *

 *	inv x

 *

 * is integral.  If inv = B/d, this means that we need to impose that

 *

 *	B x = 0		mod d

 *

 * or

 *

 *	exists alpha in Z^m: B x = d alpha

 *

 * This function is similar to add_strides in isl_affine_hull.c

 */

static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,

	__isl_keep isl_morph *morph)

{

	int i, div, k;

	isl_int gcd;

	if (isl_int_is_one(morph->inv->row[0][0]))

		return bset;

	isl_int_init(gcd);

	for (i = 0; 1 + i < morph->inv->n_row; ++i) {

		isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd;;

		if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))

			continue;

		div = isl_basic_set_alloc_div(bset);

		if (div < 0)

			goto error;

		isl_int_set_si(bset->div[div][0], 0);

		k = isl_basic_set_alloc_equality(bset);

		if (k < 0)

			goto error;

		isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],

			    morph->inv->n_col);

		isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);

		isl_int_set(bset->eq[k][morph->inv->n_col + div],

			    morph->inv->row[0][0]);

	}

	isl_int_clear(gcd);

	return bset;

error:

	isl_int_clear(gcd);

	isl_basic_set_free(bset);

	return NULL;

}

/* Apply the morphism to the basic set.

 * We basically just compute the preimage of "bset" under the inverse mapping

 * in morph, add in stride constraints and intersect with the range

 * of the morphism.

 */

__isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,

	__isl_take isl_basic_set *bset)

{

	isl_basic_set *res = NULL;

	isl_mat *mat = NULL;

	int i, k;

	int max_stride;

	if (!morph || !bset)

		goto error;

	isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),

		    goto error);

	max_stride = morph->inv->n_row - 1;

	if (isl_int_is_one(morph->inv->row[0][0]))

		max_stride = 0;

	res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),

		bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);

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

		if (isl_basic_set_alloc_div(res) < 0)

			goto error;

	mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,

					0, morph->inv->n_row);

	mat = isl_mat_product(mat, isl_mat_copy(morph->inv));

	if (!mat)

		goto error;

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

		k = isl_basic_set_alloc_equality(res);

		if (k < 0)

			goto error;

		isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);

		isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,

				morph->inv->row[0][0], bset->n_div);

	}

	isl_mat_free(mat);

	mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,

					0, morph->inv->n_row);

	mat = isl_mat_product(mat, isl_mat_copy(morph->inv));

	if (!mat)

		goto error;

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

		k = isl_basic_set_alloc_inequality(res);

		if (k < 0)

			goto error;

		isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);

		isl_seq_scale(res->ineq[k] + mat->n_col,

				bset->ineq[i] + mat->n_col,

				morph->inv->row[0][0], bset->n_div);

	}

	isl_mat_free(mat);

	mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,

					1, morph->inv->n_row);

	mat = isl_mat_product(mat, isl_mat_copy(morph->inv));

	if (!mat)

		goto error;

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

		isl_int_mul(res->div[i][0],

				morph->inv->row[0][0], bset->div[i][0]);

		isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);

		isl_seq_scale(res->div[i] + 1 + mat->n_col,

				bset->div[i] + 1 + mat->n_col,

				morph->inv->row[0][0], bset->n_div);

	}

	isl_mat_free(mat);

	res = add_strides(res, morph);

	if (isl_basic_set_is_rational(bset))

		res = isl_basic_set_set_rational(res);

	res = isl_basic_set_simplify(res);

	res = isl_basic_set_finalize(res);

	res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));

	isl_morph_free(morph);

	isl_basic_set_free(bset);

	return res;

error:

	isl_mat_free(mat);

	isl_morph_free(morph);

	isl_basic_set_free(bset);

	isl_basic_set_free(res);

	return NULL;

}

/* Apply the morphism to the set.

 */

__isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,

	__isl_take isl_set *set)

{

	int i;

	if (!morph || !set)

		goto error;

	isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);

	set = isl_set_cow(set);

	if (!set)

		goto error;

	isl_space_free(set->dim);

	set->dim = isl_space_copy(morph->ran->dim);

	if (!set->dim)

		goto error;

	for (i = 0; i < set->n; ++i) {

		set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);

		if (!set->p[i])

			goto error;

	}

	isl_morph_free(morph);

	ISL_F_CLR(set, ISL_SET_NORMALIZED);

	return set;

error:

	isl_set_free(set);

	isl_morph_free(morph);

	return NULL;

}

/* Construct a morphism that first does morph2 and then morph1.

 */

__isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,

	__isl_take isl_morph *morph2)

{

	isl_mat *map, *inv;

	isl_basic_set *dom, *ran;

	if (!morph1 || !morph2)

		goto error;

	map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));

	inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));

	dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),

				  isl_basic_set_copy(morph1->dom));

	dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));

	ran = isl_morph_basic_set(isl_morph_copy(morph1),

				  isl_basic_set_copy(morph2->ran));

	ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));

	isl_morph_free(morph1);

	isl_morph_free(morph2);

	return isl_morph_alloc(dom, ran, map, inv);

error:

	isl_morph_free(morph1);

	isl_morph_free(morph2);

	return NULL;

}

__isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)

{

	isl_basic_set *bset;

	isl_mat *mat;

	morph = isl_morph_cow(morph);

	if (!morph)

		return NULL;

	bset = morph->dom;

	morph->dom = morph->ran;

	morph->ran = bset;

	mat = morph->map;

	morph->map = morph->inv;

	morph->inv = mat;

	return morph;

}

/* We detect all the equalities first to avoid implicit equalties

 * being discovered during the computations.  In particular,

 * the compression on the variables could expose additional stride

 * constraints on the parameters.  This would result in existentially

 * quantified variables after applying the resulting morph, which

 * in turn could break invariants of the calling functions.

 */

__isl_give isl_morph *isl_basic_set_full_compression(

	__isl_keep isl_basic_set *bset)