From: Sven Verdoolaege <skimo@kotnet.org>
Date: Wed, 12 May 2010 09:36:58 +0000 (+0200)
Subject: add rudimentary isl_morph
X-Git-Tag: isl-0.03~170
X-Git-Url: http://review.tizen.org/git/?a=commitdiff_plain;h=2a410ae0874aee465eb49c8d1723a3dec6187ee9;p=platform%2Fupstream%2Fisl.git

add rudimentary isl_morph
---

diff --git a/Makefile.am b/Makefile.am
index 4c932d3..ee14250 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -60,6 +60,8 @@ libisl_la_SOURCES = \
 	isl_map_private.h \
 	isl_map_piplib.h \
 	isl_mat.c \
+	isl_morph.c \
+	isl_morph.h \
 	isl_name.c \
 	isl_name.h \
 	isl_obj.c \
diff --git a/isl_morph.c b/isl_morph.c
new file mode 100644
index 0000000..30f1154
--- /dev/null
+++ b/isl_morph.c
@@ -0,0 +1,697 @@
+/*
+ * Copyright 2010      INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
+ * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
+ * 91893 Orsay, France 
+ */
+
+#include <isl_morph.h>
+#include <isl_seq.h>
+#include <isl_map_private.h>
+#include <isl_dim_private.h>
+#include <isl_equalities.h>
+
+static __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(in_dim->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);
+}
+
+__isl_give isl_dim *isl_morph_get_ran_dim(__isl_keep isl_morph *morph)
+{
+	if (!morph)
+		return NULL;
+	
+	return isl_dim_copy(morph->ran->dim);
+}
+
+__isl_give isl_morph *isl_morph_drop_dims(__isl_take isl_morph *morph,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	unsigned dom_offset;
+	unsigned ran_offset;
+
+	if (n == 0)
+		return morph;
+
+	morph = isl_morph_cow(morph);
+	if (!morph)
+		return NULL;
+
+	dom_offset = 1 + isl_dim_offset(morph->dom->dim, type);
+	ran_offset = 1 + isl_dim_offset(morph->ran->dim, type);
+
+	morph->dom = isl_basic_set_drop(morph->dom, type, first, n);
+	morph->ran = isl_basic_set_drop(morph->ran, type, first, n);
+
+	morph->map = isl_mat_drop_cols(morph->map, dom_offset + 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);
+	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;
+}
+
+void isl_morph_dump(__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_dump(morph->map, out, 4);
+	isl_mat_dump(morph->inv, out, 4);
+}
+
+__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_dim_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_dim_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_dim(isl_dim_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 a 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;
+	unsigned total;
+	int f_eq, n_eq;
+	isl_dim *dim;
+	isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
+	isl_basic_set *dom, *ran;
+
+	if (!bset)
+		return NULL;
+
+	if (isl_basic_set_fast_is_empty(bset))
+		return isl_morph_empty(bset);
+
+	isl_assert(bset->ctx, bset->n_div == 0, return NULL);
+
+	otype = 1 + isl_dim_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_alloc(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->ctx, H->row, 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->ctx, U->row, 0, U->n_row, 0, n_eq);
+	U1 = isl_mat_lin_to_aff(U1);
+	U2 = isl_mat_sub_alloc(U->ctx, U->row, 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_dim_copy(bset->dim);
+	dim = isl_dim_drop(dim, type, 0, ntype);
+	dim = isl_dim_add(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.
+ *
+ * Let the equalities be given as
+ *
+ *	B(p) + A x = 0
+ *
+ * and let [H 0] be the Hermite Normal Form of A, then
+ *
+ *	H^-1 B(p)
+ *
+ * needs to be integer, so we impose that each row is divisible by
+ * the denominator.
+ */
+__isl_give isl_morph *isl_basic_set_parameter_compression(
+	__isl_keep isl_basic_set *bset)
+{
+	unsigned nparam;
+	unsigned nvar;
+	int n_eq;
+	isl_mat *H, *B;
+	isl_vec *d;
+	isl_mat *map, *inv;
+	isl_basic_set *dom, *ran;
+
+	if (!bset)
+		return NULL;
+
+	if (isl_basic_set_fast_is_empty(bset))
+		return isl_morph_empty(bset);
+	if (bset->n_eq == 0)
+		return isl_morph_identity(bset);
+
+	isl_assert(bset->ctx, bset->n_div == 0, return NULL);
+
+	n_eq = bset->n_eq;
+	nparam = isl_basic_set_dim(bset, isl_dim_param);
+	nvar = isl_basic_set_dim(bset, isl_dim_set);
+
+	isl_assert(bset->ctx, n_eq <= nvar, return NULL);
+
+	d = isl_vec_alloc(bset->ctx, n_eq);
+	B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
+	H = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
+	H = isl_mat_left_hermite(H, 0, NULL, NULL);
+	H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
+	H = isl_mat_lin_to_aff(H);
+	H = isl_mat_right_inverse(H);
+	if (!H || !d)
+		goto error;
+	isl_seq_set(d->el, H->row[0][0], d->size);
+	H = isl_mat_drop_rows(H, 0, 1);
+	H = isl_mat_drop_cols(H, 0, 1);
+	B = isl_mat_product(H, B);
+	inv = isl_mat_parameter_compression(B, d);
+	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_dim_copy(bset->dim));
+	ran = isl_basic_set_universe(isl_dim_copy(bset->dim));
+
+	return isl_morph_alloc(dom, ran, map, inv);
+error:
+	isl_mat_free(H);
+	isl_mat_free(B);
+	isl_vec_free(d);
+	return NULL;
+}
+
+/* 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
+ *
+ */
+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;
+		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_dim_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_dim(isl_dim_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_alloc(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_alloc(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_alloc(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);
+
+	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_dim_equal(set->dim, morph->dom->dim), goto error);
+
+	set = isl_set_cow(set);
+	if (!set)
+		goto error;
+
+	isl_dim_free(set->dim);
+	set->dim = isl_dim_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;
+}
diff --git a/isl_morph.h b/isl_morph.h
new file mode 100644
index 0000000..37348ca
--- /dev/null
+++ b/isl_morph.h
@@ -0,0 +1,66 @@
+/*
+ * Copyright 2010      INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
+ * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
+ * 91893 Orsay, France 
+ */
+
+#ifndef ISL_MORHP_H
+#define ISL_MORHP_H
+
+#include <stdio.h>
+#include <isl_dim.h>
+#include <isl_mat.h>
+#include <isl_set.h>
+
+#if defined(__cplusplus)
+extern "C" {
+#endif
+
+/* An isl_morph is a "morphism" on (basic) sets.
+ * "map" is an affine mapping from "dom" to "ran"
+ * and "inv" is the inverse mapping.
+ */
+struct isl_morph {
+	int ref;
+
+	isl_basic_set *dom;
+	isl_basic_set *ran;
+
+	isl_mat *map;
+	isl_mat *inv;
+};
+typedef struct isl_morph isl_morph;
+
+__isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph);
+void isl_morph_free(__isl_take isl_morph *morph);
+
+__isl_give isl_dim *isl_morph_get_ran_dim(__isl_keep isl_morph *morph);
+
+__isl_give isl_morph *isl_morph_drop_dims(__isl_take isl_morph *morph,
+	enum isl_dim_type type, unsigned first, unsigned n);
+
+__isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
+	__isl_take isl_morph *morph2);
+__isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph);
+
+void isl_morph_dump(__isl_take isl_morph *morph, FILE *out);
+
+__isl_give isl_morph *isl_basic_set_variable_compression(
+	__isl_keep isl_basic_set *bset, enum isl_dim_type type);
+__isl_give isl_morph *isl_basic_set_parameter_compression(
+	__isl_keep isl_basic_set *bset);
+
+__isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
+	__isl_take isl_basic_set *bset);
+__isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
+	__isl_take isl_set *set);
+
+#if defined(__cplusplus)
+}
+#endif
+
+#endif