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/*
* 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>
#include <isl_id_private.h>
#include <isl_aff_private.h>
#include <isl_vec_private.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);
}
__isl_null isl_morph *isl_morph_free(__isl_take isl_morph *morph)
{
if (!morph)
return NULL;
if (--morph->ref > 0)
return NULL;
isl_basic_set_free(morph->dom);
isl_basic_set_free(morph->ran);
isl_mat_free(morph->map);
isl_mat_free(morph->inv);
free(morph);
return NULL;
}
/* Is "morph" an identity on the parameters?
*/
static isl_bool identity_on_parameters(__isl_keep isl_morph *morph)
{
isl_bool is_identity;
isl_size nparam, nparam_ran;
isl_mat *sub;
nparam = isl_morph_dom_dim(morph, isl_dim_param);
nparam_ran = isl_morph_ran_dim(morph, isl_dim_param);
if (nparam < 0 || nparam_ran < 0)
return isl_bool_error;
if (nparam != nparam_ran)
return isl_bool_false;
if (nparam == 0)
return isl_bool_true;
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;
isl_size nparam, nvar;
int i;
isl_bool 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);
if (nparam < 0 || nvar < 0)
ma = isl_multi_aff_free(ma);
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".
*/
static __isl_keep isl_space *isl_morph_peek_dom_space(
__isl_keep isl_morph *morph)
{
if (!morph)
return NULL;
return isl_basic_set_peek_space(morph->dom);
}
/* Return a copy of the domain space of "morph".
*/
__isl_give isl_space *isl_morph_get_dom_space(__isl_keep isl_morph *morph)
{
return isl_space_copy(isl_morph_peek_dom_space(morph));
}
/* Check that the match against "space" with result "match" was successful.
*/
static isl_stat check_space_match(__isl_keep isl_space *space, isl_bool match)
{
if (match < 0)
return isl_stat_error;
if (!match)
isl_die(isl_space_get_ctx(space), isl_error_invalid,
"spaces don't match", return isl_stat_error);
return isl_stat_ok;
}
/* Check that "morph" can be applied to the "space".
*/
isl_stat isl_morph_check_applies(__isl_keep isl_morph *morph,
__isl_keep isl_space *space)
{
isl_space *dom_space;
isl_bool applies;
dom_space = isl_morph_peek_dom_space(morph);
applies = isl_space_is_equal(dom_space, space);
return check_space_match(space, applies);
}
__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);
}
isl_size isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
{
if (!morph)
return isl_size_error;
return isl_basic_set_dim(morph->dom, type);
}
isl_size isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
{
if (!morph)
return isl_size_error;
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)
{
isl_size n;
morph = isl_morph_cow(morph);
if (!morph)
return NULL;
n = isl_basic_set_dim(morph->dom, isl_dim_set);
if (n < 0)
return isl_morph_free(morph);
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)
{
isl_size n;
morph = isl_morph_cow(morph);
if (!morph)
return NULL;
n = isl_basic_set_dim(morph->ran, isl_dim_set);
if (n < 0)
return isl_morph_free(morph);
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;
}
/* Replace the identifier of the tuple of the range of the morph by "id".
*/
static __isl_give isl_morph *isl_morph_set_ran_tuple_id(
__isl_take isl_morph *morph, __isl_keep isl_id *id)
{
morph = isl_morph_cow(morph);
if (!morph)
return NULL;
morph->ran = isl_basic_set_set_tuple_id(morph->ran, isl_id_copy(id));
if (!morph->ran)
return isl_morph_free(morph);
return morph;
}
void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
{
if (!morph)
return;
isl_basic_set_dump(morph->dom);
isl_basic_set_dump(morph->ran);
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;
isl_size total;
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0)
return NULL;
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;
isl_size total;
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0)
return NULL;
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));
}
/* 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;
isl_size total;
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0 || isl_basic_set_check_no_locals(bset) < 0)
return NULL;
eq = isl_basic_set_alloc_space(isl_basic_set_get_space(bset), 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 + i], 1 + total);
}
return eq;
error:
isl_basic_set_free(eq);
return NULL;
}
/* Given a basic set, exploit the equalities in the basic set to construct
* a morphism that maps the basic set to a lower-dimensional space.
* Specifically, the morphism reduces the number of dimensions of type "type".
*
* 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.
*
* Use isl_mat_final_variable_compression to construct a compression
*
* x = T x'
*
* x' = Q x
*
* If T is a zero-column matrix, then the set of equality constraints
* do not admit a solution. In this case, an empty morphism is returned.
*
* 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;
isl_size ntype;
unsigned orest;
unsigned nrest;
isl_size total;
int f_eq, n_eq;
isl_space *space;
isl_mat *E, *Q, *C;
isl_basic_set *dom, *ran;
if (!bset)
return NULL;
if (isl_basic_set_plain_is_empty(bset))
return isl_morph_empty(bset);
if (isl_basic_set_check_no_locals(bset) < 0)
return NULL;
ntype = isl_basic_set_dim(bset, type);
total = isl_basic_set_dim(bset, isl_dim_all);
if (ntype < 0 || total < 0)
return NULL;
otype = isl_basic_set_offset(bset, type);
orest = otype + ntype;
nrest = total - (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);
E = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, 0, orest);
C = isl_mat_final_variable_compression(E, otype - 1, &Q);
if (!Q)
C = isl_mat_free(C);
if (C && C->n_col == 0) {
isl_mat_free(C);
isl_mat_free(Q);
return isl_morph_empty(bset);
}
Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
space = isl_space_copy(bset->dim);
space = isl_space_drop_dims(space, type, 0, ntype);
space = isl_space_add_dims(space, type, ntype - n_eq);
ran = isl_basic_set_universe(space);
dom = copy_equalities(bset, f_eq, n_eq);
return isl_morph_alloc(dom, ran, Q, C);
}
/* Given a basic set, exploit the equalities in the basic set to construct
* a morphism that maps the basic set to a lower-dimensional space
* with identifier "id".
* Specifically, the morphism reduces the number of set dimensions.
*/
__isl_give isl_morph *isl_basic_set_variable_compression_with_id(
__isl_keep isl_basic_set *bset, __isl_keep isl_id *id)
{
isl_morph *morph;
morph = isl_basic_set_variable_compression(bset, isl_dim_set);
morph = isl_morph_set_ran_tuple_id(morph, id);
return morph;
}
/* 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)
{
isl_size nparam;
isl_size nvar;
isl_size 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 (nparam < 0 || nvar < 0 || n_div < 0)
return NULL;
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);
}
/* Construct an isl_multi_aff that corresponds
* to the affine transformation matrix "mat" and
* that lives in an anonymous space.
*/
static __isl_give isl_multi_aff *isl_multi_aff_from_aff_mat_anonymous(
__isl_take isl_mat *mat)
{
isl_size n_row, n_col;
isl_ctx *ctx;
isl_space *space;
ctx = isl_mat_get_ctx(mat);
n_row = isl_mat_rows(mat);
n_col = isl_mat_cols(mat);
if (n_row < 0 || n_col < 0)
space = NULL;
else
space = isl_space_alloc(ctx, 0, n_col - 1, n_row - 1);
return isl_multi_aff_from_aff_mat(space, mat);
}
/* Apply the morphism to the basic set.
* In particular, compute the preimage of "bset" under the inverse mapping
* in morph and intersect with the range of the morphism.
* Note that the mapping in morph applies to both parameters and set dimensions,
* so the parameters need to be treated as set dimensions during the call
* to isl_basic_set_preimage_multi_aff.
*/
__isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
__isl_take isl_basic_set *bset)
{
isl_size n_param;
isl_space *space;
isl_multi_aff *ma;
if (!morph || isl_basic_set_check_equal_space(bset, morph->dom) < 0)
goto error;
n_param = isl_basic_set_dim(morph->dom, isl_dim_param);
if (n_param < 0)
goto error;
ma = isl_multi_aff_from_aff_mat_anonymous(isl_mat_copy(morph->inv));
bset = isl_basic_set_move_dims(bset, isl_dim_set, 0,
isl_dim_param, 0, n_param);
bset = isl_basic_set_preimage_multi_aff(bset, ma);
space = isl_basic_set_get_space(morph->ran);
bset = isl_basic_set_reset_space(bset, space);
bset = isl_basic_set_intersect(bset, isl_basic_set_copy(morph->ran));
isl_morph_free(morph);
return bset;
error:
isl_morph_free(morph);
isl_basic_set_free(bset);
return NULL;
}
/* Apply the morphism to the set.
* In particular, compute the preimage of "set" under the inverse mapping
* in morph and intersect with the range of the morphism.
* Note that the mapping in morph applies to both parameters and set dimensions,
* so the parameters need to be treated as set dimensions during the call
* to isl_set_preimage_multi_aff.
*/
__isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
__isl_take isl_set *set)
{
isl_size n_param;
isl_space *space;
isl_multi_aff *ma;
isl_basic_set *ran;
if (!morph || isl_set_basic_set_check_equal_space(set, morph->dom) < 0)
goto error;
n_param = isl_basic_set_dim(morph->dom, isl_dim_param);
if (n_param < 0)
goto error;
ma = isl_multi_aff_from_aff_mat_anonymous(isl_mat_copy(morph->inv));
set = isl_set_move_dims(set, isl_dim_set, 0, isl_dim_param, 0, n_param);
set = isl_set_preimage_multi_aff(set, ma);
space = isl_basic_set_get_space(morph->ran);
set = isl_set_reset_space(set, space);
ran = isl_basic_set_copy(morph->ran);
set = isl_set_intersect(set, isl_set_from_basic_set(ran));
isl_morph_free(morph);
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 equalities
* 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)
{
isl_morph *morph, *morph2;
bset = isl_basic_set_copy(bset);
bset = isl_basic_set_detect_equalities(bset);
morph = isl_basic_set_variable_compression(bset, isl_dim_param);
bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
morph2 = isl_basic_set_parameter_compression(bset);
bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
morph = isl_morph_compose(morph2, morph);
morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
isl_basic_set_free(bset);
morph = isl_morph_compose(morph2, morph);
return morph;
}
__isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
__isl_take isl_vec *vec)
{
if (!morph)
goto error;
vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
isl_morph_free(morph);
return vec;
error:
isl_morph_free(morph);
isl_vec_free(vec);
return NULL;
}
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