nexmon – Rev 1
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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
*/
#include <isl_map_private.h>
#include <isl/seq.h>
#include <isl/set.h>
#include <isl/map.h>
#include "isl_tab.h"
#include <isl_point_private.h>
static void expand_constraint(isl_vec *v, unsigned dim,
isl_int *c, int *div_map, unsigned n_div)
{
int i;
isl_seq_cpy(v->el, c, 1 + dim);
isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
for (i = 0; i < n_div; ++i)
isl_int_set(v->el[1 + dim + div_map[i]], c[1 + dim + i]);
}
/* Add all constraints of bmap to tab. The equalities of bmap
* are added as a pair of inequalities.
*/
static int tab_add_constraints(struct isl_tab *tab,
__isl_keep isl_basic_map *bmap, int *div_map)
{
int i;
unsigned dim;
unsigned tab_total;
unsigned bmap_total;
isl_vec *v;
if (!tab || !bmap)
return -1;
tab_total = isl_basic_map_total_dim(tab->bmap);
bmap_total = isl_basic_map_total_dim(bmap);
dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
return -1;
v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
if (!v)
return -1;
for (i = 0; i < bmap->n_eq; ++i) {
expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
if (isl_tab_add_ineq(tab, v->el) < 0)
goto error;
isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
if (isl_tab_add_ineq(tab, v->el) < 0)
goto error;
isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
if (tab->empty)
break;
}
for (i = 0; i < bmap->n_ineq; ++i) {
expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
if (isl_tab_add_ineq(tab, v->el) < 0)
goto error;
if (tab->empty)
break;
}
isl_vec_free(v);
return 0;
error:
isl_vec_free(v);
return -1;
}
/* Add a specific constraint of bmap (or its opposite) to tab.
* The position of the constraint is specified by "c", where
* the equalities of bmap are counted twice, once for the inequality
* that is equal to the equality, and once for its negation.
*/
static int tab_add_constraint(struct isl_tab *tab,
__isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
{
unsigned dim;
unsigned tab_total;
unsigned bmap_total;
isl_vec *v;
int r;
if (!tab || !bmap)
return -1;
tab_total = isl_basic_map_total_dim(tab->bmap);
bmap_total = isl_basic_map_total_dim(bmap);
dim = isl_space_dim(tab->bmap->dim, isl_dim_all);
v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
if (!v)
return -1;
if (c < 2 * bmap->n_eq) {
if ((c % 2) != oppose)
isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
1 + bmap_total);
if (oppose)
isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
r = isl_tab_add_ineq(tab, v->el);
if (oppose)
isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
if ((c % 2) != oppose)
isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
1 + bmap_total);
} else {
c -= 2 * bmap->n_eq;
if (oppose) {
isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
1 + bmap_total);
isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
}
expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
r = isl_tab_add_ineq(tab, v->el);
if (oppose) {
isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
1 + bmap_total);
}
}
isl_vec_free(v);
return r;
}
static int tab_add_divs(struct isl_tab *tab, __isl_keep isl_basic_map *bmap,
int **div_map)
{
int i, j;
struct isl_vec *vec;
unsigned total;
unsigned dim;
if (!bmap)
return -1;
if (!bmap->n_div)
return 0;
if (!*div_map)
*div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
if (!*div_map)
return -1;
total = isl_basic_map_total_dim(tab->bmap);
dim = total - tab->bmap->n_div;
vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
if (!vec)
return -1;
for (i = 0; i < bmap->n_div; ++i) {
isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
for (j = 0; j < i; ++j)
isl_int_set(vec->el[2 + dim + (*div_map)[j]],
bmap->div[i][2 + dim + j]);
for (j = 0; j < tab->bmap->n_div; ++j)
if (isl_seq_eq(tab->bmap->div[j],
vec->el, 2 + dim + tab->bmap->n_div))
break;
(*div_map)[i] = j;
if (j == tab->bmap->n_div) {
vec->size = 2 + dim + tab->bmap->n_div;
if (isl_tab_add_div(tab, vec, NULL, NULL) < 0)
goto error;
}
}
isl_vec_free(vec);
return 0;
error:
isl_vec_free(vec);
return -1;
}
/* Freeze all constraints of tableau tab.
*/
static int tab_freeze_constraints(struct isl_tab *tab)
{
int i;
for (i = 0; i < tab->n_con; ++i)
if (isl_tab_freeze_constraint(tab, i) < 0)
return -1;
return 0;
}
/* Check for redundant constraints starting at offset.
* Put the indices of the redundant constraints in index
* and return the number of redundant constraints.
*/
static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,
int offset, int **index)
{
int i, n;
int n_test = tab->n_con - offset;
if (isl_tab_detect_redundant(tab) < 0)
return -1;
if (!*index)
*index = isl_alloc_array(ctx, int, n_test);
if (!*index)
return -1;
for (n = 0, i = 0; i < n_test; ++i) {
int r;
r = isl_tab_is_redundant(tab, offset + i);
if (r < 0)
return -1;
if (r)
continue;
(*index)[n++] = i;
}
return n;
}
/* basic_map_collect_diff calls add on each of the pieces of
* the set difference between bmap and map until the add method
* return a negative value.
*/
struct isl_diff_collector {
int (*add)(struct isl_diff_collector *dc,
__isl_take isl_basic_map *bmap);
};
/* Compute the set difference between bmap and map and call
* dc->add on each of the piece until this function returns
* a negative value.
* Return 0 on success and -1 on error. dc->add returning
* a negative value is treated as an error, but the calling
* function can interpret the results based on the state of dc.
*
* Assumes that map has known divs.
*
* The difference is computed by a backtracking algorithm.
* Each level corresponds to a basic map in "map".
* When a node in entered for the first time, we check
* if the corresonding basic map intersects the current piece
* of "bmap". If not, we move to the next level.
* Otherwise, we split the current piece into as many
* pieces as there are non-redundant constraints of the current
* basic map in the intersection. Each of these pieces is
* handled by a child of the current node.
* In particular, if there are n non-redundant constraints,
* then for each 0 <= i < n, a piece is cut off by adding
* constraints 0 <= j < i and adding the opposite of constraint i.
* If there are no non-redundant constraints, meaning that the current
* piece is a subset of the current basic map, then we simply backtrack.
*
* In the leaves, we check if the remaining piece has any integer points
* and if so, pass it along to dc->add. As a special case, if nothing
* has been removed when we end up in a leaf, we simply pass along
* the original basic map.
*/
static int basic_map_collect_diff(__isl_take isl_basic_map *bmap,
__isl_take isl_map *map, struct isl_diff_collector *dc)
{
int i;
int modified;
int level;
int init;
int empty;
isl_ctx *ctx;
struct isl_tab *tab = NULL;
struct isl_tab_undo **snap = NULL;
int *k = NULL;
int *n = NULL;
int **index = NULL;
int **div_map = NULL;
empty = isl_basic_map_is_empty(bmap);
if (empty) {
isl_basic_map_free(bmap);
isl_map_free(map);
return empty < 0 ? -1 : 0;
}
bmap = isl_basic_map_cow(bmap);
map = isl_map_cow(map);
if (!bmap || !map)
goto error;
ctx = map->ctx;
snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
k = isl_alloc_array(map->ctx, int, map->n);
n = isl_alloc_array(map->ctx, int, map->n);
index = isl_calloc_array(map->ctx, int *, map->n);
div_map = isl_calloc_array(map->ctx, int *, map->n);
if (!snap || !k || !n || !index || !div_map)
goto error;
bmap = isl_basic_map_order_divs(bmap);
map = isl_map_order_divs(map);
tab = isl_tab_from_basic_map(bmap, 1);
modified = 0;
level = 0;
init = 1;
while (level >= 0) {
if (level >= map->n) {
int empty;
struct isl_basic_map *bm;
if (!modified) {
if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
goto error;
break;
}
bm = isl_basic_map_copy(tab->bmap);
bm = isl_basic_map_cow(bm);
bm = isl_basic_map_update_from_tab(bm, tab);
bm = isl_basic_map_simplify(bm);
bm = isl_basic_map_finalize(bm);
empty = isl_basic_map_is_empty(bm);
if (empty)
isl_basic_map_free(bm);
else if (dc->add(dc, bm) < 0)
goto error;
if (empty < 0)
goto error;
level--;
init = 0;
continue;
}
if (init) {
int offset;
struct isl_tab_undo *snap2;
snap2 = isl_tab_snap(tab);
if (tab_add_divs(tab, map->p[level],
&div_map[level]) < 0)
goto error;
offset = tab->n_con;
snap[level] = isl_tab_snap(tab);
if (tab_freeze_constraints(tab) < 0)
goto error;
if (tab_add_constraints(tab, map->p[level],
div_map[level]) < 0)
goto error;
k[level] = 0;
n[level] = 0;
if (tab->empty) {
if (isl_tab_rollback(tab, snap2) < 0)
goto error;
level++;
continue;
}
modified = 1;
n[level] = n_non_redundant(ctx, tab, offset,
&index[level]);
if (n[level] < 0)
goto error;
if (n[level] == 0) {
level--;
init = 0;
continue;
}
if (isl_tab_rollback(tab, snap[level]) < 0)
goto error;
if (tab_add_constraint(tab, map->p[level],
div_map[level], index[level][0], 1) < 0)
goto error;
level++;
continue;
} else {
if (k[level] + 1 >= n[level]) {
level--;
continue;
}
if (isl_tab_rollback(tab, snap[level]) < 0)
goto error;
if (tab_add_constraint(tab, map->p[level],
div_map[level],
index[level][k[level]], 0) < 0)
goto error;
snap[level] = isl_tab_snap(tab);
k[level]++;
if (tab_add_constraint(tab, map->p[level],
div_map[level],
index[level][k[level]], 1) < 0)
goto error;
level++;
init = 1;
continue;
}
}
isl_tab_free(tab);
free(snap);
free(n);
free(k);
for (i = 0; index && i < map->n; ++i)
free(index[i]);
free(index);
for (i = 0; div_map && i < map->n; ++i)
free(div_map[i]);
free(div_map);
isl_basic_map_free(bmap);
isl_map_free(map);
return 0;
error:
isl_tab_free(tab);
free(snap);
free(n);
free(k);
for (i = 0; index && i < map->n; ++i)
free(index[i]);
free(index);
for (i = 0; div_map && i < map->n; ++i)
free(div_map[i]);
free(div_map);
isl_basic_map_free(bmap);
isl_map_free(map);
return -1;
}
/* A diff collector that actually collects all parts of the
* set difference in the field diff.
*/
struct isl_subtract_diff_collector {
struct isl_diff_collector dc;
struct isl_map *diff;
};
/* isl_subtract_diff_collector callback.
*/
static int basic_map_subtract_add(struct isl_diff_collector *dc,
__isl_take isl_basic_map *bmap)
{
struct isl_subtract_diff_collector *sdc;
sdc = (struct isl_subtract_diff_collector *)dc;
sdc->diff = isl_map_union_disjoint(sdc->diff,
isl_map_from_basic_map(bmap));
return sdc->diff ? 0 : -1;
}
/* Return the set difference between bmap and map.
*/
static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
__isl_take isl_map *map)
{
struct isl_subtract_diff_collector sdc;
sdc.dc.add = &basic_map_subtract_add;
sdc.diff = isl_map_empty_like_basic_map(bmap);
if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
isl_map_free(sdc.diff);
sdc.diff = NULL;
}
return sdc.diff;
}
/* Return the set difference between map1 and map2.
* (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
*/
static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,
__isl_take isl_map *map2)
{
int i;
struct isl_map *diff;
if (!map1 || !map2)
goto error;
isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
if (isl_map_is_empty(map2)) {
isl_map_free(map2);
return map1;
}
map1 = isl_map_compute_divs(map1);
map2 = isl_map_compute_divs(map2);
if (!map1 || !map2)
goto error;
map1 = isl_map_remove_empty_parts(map1);
map2 = isl_map_remove_empty_parts(map2);
diff = isl_map_empty_like(map1);
for (i = 0; i < map1->n; ++i) {
struct isl_map *d;
d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
isl_map_copy(map2));
if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
diff = isl_map_union_disjoint(diff, d);
else
diff = isl_map_union(diff, d);
}
isl_map_free(map1);
isl_map_free(map2);
return diff;
error:
isl_map_free(map1);
isl_map_free(map2);
return NULL;
}
__isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
__isl_take isl_map *map2)
{
return isl_map_align_params_map_map_and(map1, map2, &map_subtract);
}
struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
{
return (struct isl_set *)
isl_map_subtract(
(struct isl_map *)set1, (struct isl_map *)set2);
}
/* Remove the elements of "dom" from the domain of "map".
*/
static __isl_give isl_map *map_subtract_domain(__isl_take isl_map *map,
__isl_take isl_set *dom)
{
isl_map *ext_dom;
if (!isl_map_compatible_domain(map, dom))
isl_die(isl_set_get_ctx(dom), isl_error_invalid,
"incompatible spaces", goto error);
ext_dom = isl_map_universe(isl_map_get_space(map));
ext_dom = isl_map_intersect_domain(ext_dom, dom);
return isl_map_subtract(map, ext_dom);
error:
isl_map_free(map);
isl_set_free(dom);
return NULL;
}
__isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,
__isl_take isl_set *dom)
{
return isl_map_align_params_map_map_and(map, dom, &map_subtract_domain);
}
/* Remove the elements of "dom" from the range of "map".
*/
static __isl_give isl_map *map_subtract_range(__isl_take isl_map *map,
__isl_take isl_set *dom)
{
isl_map *ext_dom;
if (!isl_map_compatible_range(map, dom))
isl_die(isl_set_get_ctx(dom), isl_error_invalid,
"incompatible spaces", goto error);
ext_dom = isl_map_universe(isl_map_get_space(map));
ext_dom = isl_map_intersect_range(ext_dom, dom);
return isl_map_subtract(map, ext_dom);
error:
isl_map_free(map);
isl_set_free(dom);
return NULL;
}
__isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,
__isl_take isl_set *dom)
{
return isl_map_align_params_map_map_and(map, dom, &map_subtract_range);
}
/* A diff collector that aborts as soon as its add function is called,
* setting empty to 0.
*/
struct isl_is_empty_diff_collector {
struct isl_diff_collector dc;
int empty;
};
/* isl_is_empty_diff_collector callback.
*/
static int basic_map_is_empty_add(struct isl_diff_collector *dc,
__isl_take isl_basic_map *bmap)
{
struct isl_is_empty_diff_collector *edc;
edc = (struct isl_is_empty_diff_collector *)dc;
edc->empty = 0;
isl_basic_map_free(bmap);
return -1;
}
/* Check if bmap \ map is empty by computing this set difference
* and breaking off as soon as the difference is known to be non-empty.
*/
static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
__isl_keep isl_map *map)
{
int r;
struct isl_is_empty_diff_collector edc;
r = isl_basic_map_plain_is_empty(bmap);
if (r)
return r;
edc.dc.add = &basic_map_is_empty_add;
edc.empty = 1;
r = basic_map_collect_diff(isl_basic_map_copy(bmap),
isl_map_copy(map), &edc.dc);
if (!edc.empty)
return 0;
return r < 0 ? -1 : 1;
}
/* Check if map1 \ map2 is empty by checking if the set difference is empty
* for each of the basic maps in map1.
*/
static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
{
int i;
int is_empty = 1;
if (!map1 || !map2)
return -1;
for (i = 0; i < map1->n; ++i) {
is_empty = basic_map_diff_is_empty(map1->p[i], map2);
if (is_empty < 0 || !is_empty)
break;
}
return is_empty;
}
/* Return 1 if "bmap" contains a single element.
*/
int isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
{
if (!bmap)
return -1;
if (bmap->n_div)
return 0;
if (bmap->n_ineq)
return 0;
return bmap->n_eq == isl_basic_map_total_dim(bmap);
}
/* Return 1 if "map" contains a single element.
*/
int isl_map_plain_is_singleton(__isl_keep isl_map *map)
{
if (!map)
return -1;
if (map->n != 1)
return 0;
return isl_basic_map_plain_is_singleton(map->p[0]);
}
/* Given a singleton basic map, extract the single element
* as an isl_point.
*/
static __isl_give isl_point *singleton_extract_point(
__isl_keep isl_basic_map *bmap)
{
int j;
unsigned dim;
struct isl_vec *point;
isl_int m;
if (!bmap)
return NULL;
dim = isl_basic_map_total_dim(bmap);
isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
point = isl_vec_alloc(bmap->ctx, 1 + dim);
if (!point)
return NULL;
isl_int_init(m);
isl_int_set_si(point->el[0], 1);
for (j = 0; j < bmap->n_eq; ++j) {
int i = dim - 1 - j;
isl_assert(bmap->ctx,
isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
goto error);
isl_assert(bmap->ctx,
isl_int_is_one(bmap->eq[j][1 + i]) ||
isl_int_is_negone(bmap->eq[j][1 + i]),
goto error);
isl_assert(bmap->ctx,
isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
goto error);
isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
isl_int_divexact(m, bmap->eq[j][1 + i], m);
isl_int_abs(m, m);
isl_seq_scale(point->el, point->el, m, 1 + i);
isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
isl_int_neg(m, m);
isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
}
isl_int_clear(m);
return isl_point_alloc(isl_basic_map_get_space(bmap), point);
error:
isl_int_clear(m);
isl_vec_free(point);
return NULL;
}
/* Return 1 is the singleton map "map1" is a subset of "map2",
* i.e., if the single element of "map1" is also an element of "map2".
* Assumes "map2" has known divs.
*/
static int map_is_singleton_subset(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
{
int i;
int is_subset = 0;
struct isl_point *point;
if (!map1 || !map2)
return -1;
if (map1->n != 1)
return -1;
point = singleton_extract_point(map1->p[0]);
if (!point)
return -1;
for (i = 0; i < map2->n; ++i) {
is_subset = isl_basic_map_contains_point(map2->p[i], point);
if (is_subset)
break;
}
isl_point_free(point);
return is_subset;
}
static int map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
{
int is_subset = 0;
if (!map1 || !map2)
return -1;
if (!isl_map_has_equal_space(map1, map2))
return 0;
if (isl_map_is_empty(map1))
return 1;
if (isl_map_is_empty(map2))
return 0;
if (isl_map_plain_is_universe(map2))
return 1;
map2 = isl_map_compute_divs(isl_map_copy(map2));
if (isl_map_plain_is_singleton(map1)) {
is_subset = map_is_singleton_subset(map1, map2);
isl_map_free(map2);
return is_subset;
}
is_subset = map_diff_is_empty(map1, map2);
isl_map_free(map2);
return is_subset;
}
int isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
{
return isl_map_align_params_map_map_and_test(map1, map2,
&map_is_subset);
}
int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
{
return isl_map_is_subset(
(struct isl_map *)set1, (struct isl_map *)set2);
}
__isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
{
int i;
struct isl_subtract_diff_collector sdc;
sdc.dc.add = &basic_map_subtract_add;
if (!map)
return NULL;
if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
return map;
if (map->n <= 1)
return map;
map = isl_map_compute_divs(map);
map = isl_map_remove_empty_parts(map);
if (!map || map->n <= 1)
return map;
sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
for (i = 1; i < map->n; ++i) {
struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
struct isl_map *copy = isl_map_copy(sdc.diff);
if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
isl_map_free(sdc.diff);
sdc.diff = NULL;
break;
}
}
isl_map_free(map);
return sdc.diff;
}
__isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
{
return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
}
__isl_give isl_map *isl_map_complement(__isl_take isl_map *map)
{
isl_map *universe;
if (!map)
return NULL;
universe = isl_map_universe(isl_map_get_space(map));
return isl_map_subtract(universe, map);
}
__isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
{
return isl_map_complement(set);
}